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1.100862.pdf | Use of superlattices to realize inverted GaAs/AlGaAs heterojunctions with low
temperature mobility of 2×106 cm2/Vs
T. Sajoto, M. Santos, J. J. Heremans, M. Shayegan, M. Heiblum, M. V. Weckwerth, and U. Meirav
Citation: Applied Physics Letters 54, 840 (1989); doi: 10.1063/1.100862
View online: http://dx.doi.org/10.1063/1.100862
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68.58.13.105 On: Sat, 26 Apr 2014 23:05:02Use of superlattices to realize inverted GaAs/ AIGaAs heterojunctlons with
low~tempera.ture mobility of 2X 106 cm2/V s
T. Sajoto, M. Santos, J. J. Heremans, and M. Shayegar.
Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544
M. Heiblum, M. V. Weckwerth, and U. Meirav
IB11.f T. J. Watson Research Centef~ Yorktown Heights, New York 10598
(Received 7 October 1988; accepted for publication 10 December 1(88)
Reproducible realization of high quality inverted interfaces (GaAs on AIGaAs) grown by
molecular beam epitaxy is reported. Effective use of thin-layer GaAs/ AlAs superlattices in
place of an AIGaAs barrier was made to reduce the number of impurities and the roughness at
these interfaces. The low-temperature ("'" 4 K) mobility for electrons at these interfaces is as
high as 2 X 10° cmz /V s for an electron density of "'" 5 X lOiI cm-z-a factor offour
improvement over the highest mobility reported for inverted interfaces.
Recent improvements in growth systems and tech
niques have led to the realization of two-dimensional elec
tron systems (20ES) at selectively doped GaAs/ AIGaAs
interfaces with low-temperature mobilities well above
1 X 106 cm2/V S.l These high mobilities have been achieved
in normal (AIGaAs on GaAs) interfaces; the inverted inter
faces (GaAs on AIGaAs) in general have been oflower qual
ity. This inferior quality has been attributed to the interface
roughness as well as impurity segregation (towards the in
terface) during the growth of AIGaAs. The inverted inter
faces, however, are quite important since they are integral
parts of GaAs/ AIGaAs quantum wells and superlattices,
and have device applications.
Recently, the realization of high-mobility 2DES at in
verted GaAsl AIGaAs interfaces was reported.l-4 This was
achieved by studying the kinetics of the growth via reflection
high-energy electron diffraction measurements, and by opti
mizing the growth techniques. The highest low-temperature
mobility reported,) however, was ll=4.6X 105 cm2/V s,
about an order of magnitude lower than the highest mobili
ties reported for normal interfaces.
We report here the realization of high quality inverted
GaAsl AIGaAs interfaces imbedded in an inverted semicon
ductor-insulator-semiconductor (ISIS) structure (Fig. 1).2
In this structure, the density of the 2DES at the AIGaAs/
GaAs interface can be continuously varied by applying a
positive voltage to the gate (the nl-doped substrate). The
low-temperature (T =4 K) mobility in our interfaces is as
high as 2 X 10° cm2/V s-a factor of 4 larger than the highest
mobility value reported for inverted interfaces.' We at
tribute this significant improvement to our use of thin-layer
GaAsl AlAs supcrlattices in place of AIGaAs barriers [Fig.
1 (a) J to trap impurities and to improve the interface
smoothness.
The structures were grown in a modular Varian Gen II
molecular beam epitaxy (MBE) system consisting of a
growth, a buffer, and a load-lock chamber with base pres
sures of 3 X 10-11, 7 X 10-11, and 2 Xl o-g Torr, respective
ly. We have been able to grow high quality normal interfaces
with extremely low disorder in the same MBE system.5-7
Details of the system and wafer preparation were given pre
viously.5 The structure of a typical high-mobility ISIS struc-ture (M9 5) is schematically shown in Fig. 1 (a). First, we
carefully outgassed the substrate [n I Si:GaAs (100) 1 in the
buffer and growth chambers.s After the removal of the sur
face oxide, a 200 A.. undoped GaAs was grown. We then
determined the substrate temperature (Ts) by measuring
the congruent sublimation temperature (from the changes
in the reflection electron diffraction pattern) and also with
the use of an infrared pyrometer. After a 10 min wait at
T.., = 640°C, we lowered 1'." to 590 °C and started the
growth. A 65-period superlattice ofGaAs (23 A)I AIAs( 8.5
A..) was first grown. This thin-layer superlattice has an aver
age AlAs mole fraction of27%. The first 25 periods of this
superlattice had 3 s interruptions after each GaAs layer. For
the first 15 periods, Ts was 590°C; 1'.., was then raised to
620 °C (in lOa/period increments). Finally, a 2700 A GaAs
layer which included a planar sheet (8 layer) of Si was
M9S
I 200 ftc GaAs I
Si ~ ... ••••••• .. '·.,'1
1.8 x 1()12 em·2
2500 A Ga"-s 2DEG
8.5 A AlAs
23.f.. GaAs
3.5 A ALh 40x { f-------j
{ 3 S
25x interrupt -+-1-------1
23 A (;"A,
11 + Su hstrate
Si : GaAs I
I I E
(a) (II)
FrG. 1. Schematic description of an ISIS structure. Shown on the right is
the potential diagmm corresponding to the accumul~.tiol! mooe, achieved
by applying a positive gate voltage Vg to the n+ substmte. On the left, the
design stmcture for sample M95 is schematically shown. Note the use of a
thin-layer GaAsl AlAs superlattice in place of AIGaAs barrieI'.
840 Appl. Phys. Lett. 54 (9), 27 February 1989 0003-6951/89/090840-03$01.00 @ 1989 American Institute of Physics 840
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68.58.13.105 On: Sat, 26 Apr 2014 23:05:02grown, Just prior to the doping with Si, Ts was lowered to
580 "C.
Mesas =O.3llm deep were etched, and four (or six)
lithographically defined AuGe/Nbl Au shallow ohmic con
tacts were alloyed (to a depth of =0,25 pm, avoiding short
ing to the gate) to form Van der Pauw (or a Hall bar) pat~
tern. The transport coefficients were measured at low
temperatures (TS 4.2 K) and in magnetic fields up to 0.5 T.
The measured HaH mobilities for several structures (M95,
M98, and M99) are shown in Fig. 2 as a function of the
electron areal density ens) which was varied by applying a
positive gate voltage to the n+ substrate, The dependence of
ns on the gate voltage for the structure M98 is also shown in
Fig. 2. The mobilities plotted in Fig. 2 are the highest ever
reported for any inverted GaAsl AIGaAs interface.
We attribute the significant improvement in the mobil~
ity to the use of the GaAsl AlAs superlattice instead of an
AIGaAs barrier. The effectiveness of the GaAsl AlAs inter
faces and superlattices in impurity trapping, surface smooth
ing, and defect reduction has been already established.8-w
Other aspects of our structure design and growth procedure
that may be partly contributing to the realization of high
mobility are the following. To reduce the possibility of any 5i
atoms reaching the 2DES, we did not grow any n + -GaAs
buffer layer (note that no Si was deposited except for the l)
layer near the surface). In fact, after outgassing the Si fur
nace (prior to growth), it was kept at 150"C below its oper
ating temperature during the growth of the AIAs/GaAs su
perlattice and the first 850 A of GaAs layer (to reduce
possible outgassing from this furnace at the 2DES inter
face). The lower Ts at the beginning of the growth of the
'" ~
'" S
(,I
v.
Q
""" ><
::L
~
f...
::l .....
~
0
~ 25
20
15
!.o
s
0
D . .
o
D OU!,ClDi:lO [J
onuoo
" o D " " " o o M99
M98 5
>
4
I'<l
~
3 ,...
C
>-
~
2 :;-.
2§
FIG. 2. Dependence of mobility on2DES density in several ISIS structures
is shown. The variation of the 2DES density with the gate voltage is also
shown for structure M98.
841 Appl. Phys. Lett, Vol, 54, No.9, 27 February 1989 15 1500
M99 /-/ T '" 4.2 K
to n s = 2.3 x 10 Hcm'2
Cl 3(\ ~ I '" I t::
""". 5 I 1000 Z c.'"
" ' 1 / I ~
I '" t:<i ..:
0 I t:<i
"11 l~ f... ;
c.: ..:
500
,~vv " a:'
Il
() 2 3 4
B ( T j
FIG. 3. Transport coefficients P,x and Pxy for sample M99 are shown as a
function of magnetic field at a fixed gate voltage. The vertical arrows indi
cate some of the Landau-level filling factors at which the integral quantum
Hall effect is observed.
superlattice was used to reduce the migration ofSi and other
impurities with the growth fronL
The average composition ofthe barrier (determined by
the thickness of the AlAs and GaAs thin layers in the super
lattice) and its total thickness for M98 and M99 were differ
ent than those for M95 (shown in Fig. 1). We do not have an
explanation for the differences in the mobilities for these
structures at this point but the data in Fig. 2 show that these
structures all have very high mobilities. Similar structures
grown in a different MBE system (a Riber 1000-1) also had
mobilities well in excess of the values achieved for inverted
interfaces that were grown in the same machine but which
had net employed superlattices.2•3
I { j
~ 1
> 1 ~ < t
" a." CARRIER DENSITY ( x lOll cm'2)
1.92 4.31
\! '\
\ 3
\~ \ 4
~
5
~
.--~-
~~ M99
B=3T 6.67
T = 1.5 K
6
I 7 , 8
~ + 10
:;
-
0 +-~-r-~-'--¥---'--~-'"'"r-~---"rL-~.- (I
2 3 4
GATE VOLTAGE ( V ) M
~
>.
c..~
FIG. 4. Transport coefficients Pxx and Pxy for sample M99 are shown at a
fixed magnetic field and as a function of the gate voltage. The vertical ar
rows indicate the filling factors at which the integral quantum Hall effect is
observed.
Sajoto eta!. 841
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68.58.13.105 On: Sat, 26 Apr 2014 23:05:02We have also performed transport measurements at
higher magnetic fields (B S; 6 T) and low temperatures
(1.5< T<4.2 K). Representative data for structure M99 are
shown in Figs. 3 and 4. In Fig. 3, the diagonal resistivity
(Pxx) and the Hall resistivity (Pxy) are plotted as a function
of magnetic field at a fixed gate voltage (n, = 2.3 X 1011
em -2). In Fig. 4, the magnetic field is kept constant and P.u
and Pxy are shown as a function of the applied gate voltage.
In both figures, well-resolved Shubnikov-de Haas oscilla
tions in Pu and quantum Hall plateaus in Pxy are observed.
The data in Fig. 4 are especially noteworthy-the realization
of such a high quality 2DES with variable density has seldom
been achieved before.
In summary, effective use of thin layer GaAsl AlAs su
perlattiees to grow very high-mobility inverted GaAsl
AIGaAs interfaces is reported.
We thank v. J. Goldman, S. A. Lyon, andD. C. Tsuifor
advice. Support of this work by National Science Founda
tion grants No, ECS-8553110 and DMR-8705002, Depart
ment of Defense University Research Instrumentation Pro-
842 Appl. Phys. Lett., Vol. 54, No.9, 27 February i 989 gram grant No. DAAL03-87-G-0105, and a grant by the
New Jersey Commission on Science and Technology is ac
knowledged.
'See, c.g., J. H. English, A. C. Gossard, H. L. Stormer, and K. W. Baldwin,
Appl. Phys. Lett. 50, 1825 (1987).
2U. Meirav, M. Heiblurn, and F. Stem, App!. Phys. Lett. 52, 1268 (1988).
3H. Shtrikman, M. Heiblum, K. Sea, D. E. Galbi, and L. Osterling, J. Vac.
Sci. Technol. B 6, 670 (1988).
4N. M. Cho, D. J. Kim, A. Madhukar, P. G. Newman, D. D. Smith, T.
Aucoin, and G. J. Iafrate, App1. Phys. Lett. 52, 2037 (1988).
'M. Shayegan, V. J. Goldman, C. Jiang, T. Sajoto, and M. Santos, App!.
Phys. Lett. 52,1086 (1988).
OM. Shayegan, V. J. Goldman, T. Sajoto, M. Santos, C. Jiang, and H. Ito, J.
Cryst. Growth (in press).
7M. Shayegan, V. J. Goldman, M. Santos, T. Sajoto, L. Engel, and D. C.
Tsui, AppL Phys. Lett. 53, 2080 (1988).
"I'. M. Petroff, R. C. Miller, A. C. Gossard, and W. Wiegmann, AppL
Phys. Lett. 44, 216 (l984).
9T. J. Drummond, J. Klem, D. Arnold, R. Fischer, R. E. Thome, W. G.
Lyons, and H. MorkO<!, Appl. Phys, Lett. 42, 615 (1983).
10M. Shinohara, T. Ito, and Y. Imamura, J. Appl. Phys. 58, 3449 (1985).
Sajoto et at. 842
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1.343042.pdf | Properties of hydrogenated amorphous germanium nitrogen alloys prepared by
reactive sputtering
I. Honma, H. Kawai, H. Komiyama, and K. Tanaka
Citation: Journal of Applied Physics 65, 1074 (1989); doi: 10.1063/1.343042
View online: http://dx.doi.org/10.1063/1.343042
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/3?ver=pdfcov
Published by the AIP Publishing
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J. Appl. Phys. 51, 2167 (1980); 10.1063/1.327891
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43Properties of hydrogenated amorphous germanium .. nitrogen alloys
prepared by reactive sputtering
I. Honma, H. Kawai, H. Komiyama, and K. Tanakaa)
Department of Chemical Engineering, The Faculty 0/ Engineering, University of Tokyo,
Bunkyo-ku, Tokyo 1 J 3, Japan
(Received 19 February 1988; accepted for publication 12 August 1988)
Hydrogenated amorphous germanium-nitrogen alloys (a-GeNx :H) were synthesized as a new
group of amorphous semiconductors by rf( 13.56 MHz) reactive sputtering of a Ge target in a
gas mixture of Ar + Nz + H2 under a variety of deposition conditions such as gas ratio, rf
discharge power, and substrate temperature. Structural, optical, and electrical properties of
those a-GeNx:H alloys were systematically measured and are discussed in relation to their
preparation conditions. The optical band gap E()4 of a-GeNx :H aHoys could be continuously
controlled in the range from 1.1 eV to 3.3 eV primarily depending on the atomic N/Ge ratio in
the film. The role of hydrogen and nitrogen in the optical and electrical properties of the
material is also crucially demonstrated.
I. INTRODUCTION
In recent trends of research on amorphous semiconduc
tors, Si-based amorphous alloys such as a-SiGe:H,
a-SiNx :H, and a-SiCx:H have attracted increasing attention
as promising materials for various photoelectronic de
vices. \-5 In the field of solar cells especially, it is urgently
needed to control the optical band gap of the materials for
optically matching solar radiation. One of the key issues for
achieving high-efficiency tandem-type solar cells is to devel
op highly photosensitive bottom layer materials with optical
band gaps lower than 1.5 eV, and several works have been
done on a-SiGe:H. 6. 7 The basic idea for designing those nar
row gap materials is to reduce the optical gap ( "'" 1.75 e V) of
a-Si:H by introducing other elements such as Ge or Sn;
namely, the band gap of a-Si:H can be reduced by introduc
ing weaker chemical bonds such as Si-Ge or Si-Sn into the Si
Si network.
Another approach to find out new materials is to start
with a-Ge (Eo=O.75 eV). Chambouleyron made initial ef
forts to control the Tauc optical gap Eo using a-GeN x alloys
in the range of 0.9 e V < Eo < 2.7 e V although their electronic
properties were rather poor due to the absence of defect
killers in the network. 8.9 The first data on hydrogenated
amorphous germanium nitride (a-GeN x :H) were reported
in our earHer work, and the role of hydrogen was tentatively
discussed. 10 The present motivation to study the a-GeNx:H
system is based on the following three items:
( 1) According to Matt's 8-N rule, nitrogen is consid
ered to be incorporated at a threefold coordinated atom into
the amorphous Ge:H networ-k, thereby reducing the average
coordination number of a-GeNx:H with increasing N con
tent; a decrease of the average coordination number may
produce structural flexibility of the amorphous network,
probably resulting in the reduction of defect states.
(2) The introduction of nitrogen into the a-Ge network
will provide an ionic nature to the chemical bonds, which not
aJ Permanent address: Electrotechnical Laboratory, Tsukuba, Ibaraki 305,
Japan. only causes a continuous change of optical band gap with
varying N content, but also gives rise to the network flexibil
ity through the relaxation of the bending force of chemical
bonds.
(3) Hydrogen will playa role as defect killer of Ge or N
dangling bonds in the a-GeNx:H network and sweep the
midgap states as is the case in a-Si:H.
In this paper, we report the syntheses of hydrogenated
amorphous germanium-nitrogen compounds (a-GeNx :H)
using a reactive-sputtering technique while systematicaBy
varying the deposition conditions. Structural, optical, and
electrical properties of a-GeNx :H are presented, and are dis
cussed in connection with the preparation conditions. The
roles of nitrogen as well as hydrogen in the network are clari
fied through detailed experimental results. Photoconducti
vi.ties of some a-GeN.~ :H alloys are also presented.
II. EXPERIMENT
Film samples of a-GeNx :H were prepared by IT reactive
sputtering of a Ge target 8 em in diameter in a mixture of
Ar + Nz + Hz gases. The target-to-substrate distance was
maintained at 12 em. A schematic diagram of the sputtering
system is shown in Fig. 1. The vacuum chamber was preeva
cuated down to 1 X 10-6 Torr by a combination of rotary
and oil diffusion pumps, and then high-purity research
grade gases were introduced through a variable leak valve.
The desired gas composition was set by controlling the flow
rate ratio of Ar + Hz (or Ar only), Nz, and Hz through a
thermal mass controller (TMC) in each gas line. The total
pressure of the sputtering gas was varied from 5 X 10-3 Torr
to 5x 10-2 Torr and the rfpowcr varied from 0.07 to 0.3
kW. Coming 7059 glasses and high-resistivity silicon wafers
were used as substrates for optical-absorption measurements
in the visible and infrared range. The substrate temperature
was changed from room temperature to 400 "C, being detect
ed by a thermocouple fixed on the substrate holder.
Figure 2 shows the volume fraction of each gas in the
starting sputtering gas mixture scanned in the present work
and rough features of resultant films, which are described in
1074 J. Appi. Phys. 65 (3), 1 February 1989 0021 -8979/89/031 074-09$02.40 ® 1969 American Institute of Physics 1074
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43Sputtering System
Substrate
Shutter
FIG" 1. A schematic diagram of the reactive-sputtering system in the pres
ent experiment.
the triangle diagram. As shown in the figure, mirrorlike con
tinuous and/or optically transparent a-GcNx:H films were
obtained in a wide range of the parameter space, while films
became milky when they were deposited using a sputtering
gas involving Hz higher than 50%. X-ray diffraction
(XRD), x-ray photoelectron spectroscopy (XPS), Auger
electron spectroscopy (AES), differential thermal analyses
(DTA), differential thermal gravimetry (DTG), and in
frared absorption measurements were carried out for as-pre
pared and annealed samples. In parallel with the above
structural characterization, the optical band gap, dark and
photoconductivity of the samples were measured as func
tions of their deposition conditions.
1110 RESULTS AND DISCUSSIONS
A. film structure and deposition mechanism
The structure of as-deposited a-GeN x:H films was
checked by x-ray diffraction and no discernible crystalline
Ar H2
FIG. 2. Triangle diagram showing apparent features of the a-GeN x:il sys
tem Wllich are deposited using Ar-N 2-H2 sputtering gas. Rf power of 0.1 k W
and the substrate temperature of 80°C were used. Open circles (0) indicate
the mirrorlike or transparent films and solid circles (e) indicate the milky
films.
1075 J. Appl. Phys., Vol. 65, No.3, 1 February 1989 peaks were observed in any diffraction pattern, indicating
that the structure is amorphous. The Auger analyses indicat
ed no sign of impurity peaks except for surface oxygen and
hydrocarbons which were easily etched out by I-min Ar
sputtering. As is shown in Fig. 2, by adding hydrogen to
more than 50% in the sputtering gas, the surface of deposit
ed films turned milky and many pinholes appeared. Phe
nomenologically, it seems that the formation of the milky
surface is dependent only on the amount of hydrogen in the
plasma gas and is independent of the rf power and the sub
strate temperature. It is plausible that a large amount of hy
drogen radicals and/or ions attack and etch the surface, pre
venting the continuous growth of the film. This discussion is
consistent with the result of Veprek et al. on H etching of a-
S· II 1-
Figure 3 shows the relationship between the atomic N/
Ge ratio of a-GeN x :H films measured by XPS and the pres
sure ratio of nitrogen to total gas (P N, / P tot) during the de
position. AU of the sampies were deposited on the water
cooled substrates at O.l-kW IT power and total pressure of
5 X 10-3 Torr. Each atomic N/Ge ratio was determined
from the integrated intensities of the spectra of N Is and
Ge 3p inner orbitais, using a sensitivity factor of 1.80 and
3.63 for N Is and Ge 3p, respectively. It is dear that the
atomic N/Ge ratio increases almost in proportion to P 1><, /
Plot at least up to 40%. This simple relationship is strongly
related to the reaction mechanism in the reactive sputtering.
An increase of the nitrogen composition in the sputtering gas
means an increase ofthe amount of reactive nitrogen species
in the plasma, and their mass flux impinging onto the film
surface also increases. Ifwe assume that the nitridation reac
tion mainly proceeds on the film-growing surface, which is
most likely because ofa large mean free path (=2 em), it is
quite conceivable that the film composition (N/Ge ratio) is
determined by the relative ratio of the germanium and nitro
gen fluxes at the surface, being consistent with the relation
shown in the figure.
B. Chemical bonding
The bonding states of the a-GeN.x:H series deposited
under the PNJPtot ratio ranging from 10% to 50% were
studied by IR absorption measurements. The results are
shown in Fig. 4. Four main absorption bands are clearly
observed in every curve, which are assigned to the Ge-N
stretching (700 em -I), N-H bending (l150 em-oj), N-H2
bending (1500 em-1 ), and N-H stretching (3300 cm-1),
40
(j> §2 20 z
10
o o
10 20 30 40 50
PN2/PtOt ("10) FIG. 3. The relationship
between the atomic N/Ge ra
tio of a-GeN,:H films mea
sured by XPS and the nitro
gen content in the gas phase.
Honma etal. 1075
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43PN
YFtot o .J.
Ge-H
wagging
V:'O%
20 Of. ::i
d
~_30'"
N-H:> ~40% bending N H N-H -
",."hing beodlog fSO%
Ge-N
stretching
4000 2000 1500 1000 500
WAVE NUMBER (em-I)
FIG. 4. Infrared transmittance measurem<!nts for a-GeN,:Ii series. PN,I
PM ratio in the gas phase wa.~ varied from 10% to 50%.
respectively.2,9 However, absorption peaks of Ge-H wagging
near 580 cm.-J and Ge-H stretching around 1900 to 2000
cm-1 are scarcely observed. The lack of Ge-H bonds in a
GeNx:H film suggests that the so-called "preferential at
tachment" ofH to N takes place when hydrogen radicals are
adsorbed on the growing surface of the Ge-N-H
network. 12,13 This argument is based on the assumption that
the difference between the bonding energy ofN-H (4,5 eV)
and that of Ge-H (3,g eV) determined for their isolated
molecules still holds qualitatively even in a tetrahedral
network as listed in Table 1. In other words, some kind of
chemical equilibrium seems to hold on the growing surface,
and the system tends to approach the free-energy minimum
through the formation of N--H bonds.
It is also observed that the peak position of the Ge-N
stretching mode (700 em-I) as wen as the N-H bending
mode (1150 em-I) in a-GeN,,:H alloys is shifting toward
higher wave numbers with increasing nitrogen content. Fig
ure 5 shows the chemical shift of the peak position of Ge-N
band stretching and N-H band bending in a-GeNx:H alloys
as functions of P N" / P lot ratio for two different substrate tem
peratures. This peak shift probably originates from an in
crease in the bond ionicity in the network, since the differ-
TABLE 1. Chemical bonding energy,
Ge-Ge
(eV)
2,6 Ge--H
(eV) N--H
(eV)
4.5
1076 J. Appl. Phys., Vol. 65, No.3, 1 February 1989 ~
N-H bending band u
..... ';)
e RT. 1150
1140
1130
1120
Ie 750 1110
u
740 R.T . 1100
. ~ 730
~ 720 200°C Q..
.x 710 0
ct stretching band
700
0 10 20 30 40 50 60
PN2' Ptot ( Gio )
FIG. 5, The chemical shift of the peak position of Ge-N band stretching and
N -H band bending. The substrate temperatures used in the experiment were
room temperature and 200 'c,
ence in the electronegativity between Ge and N should make
some fraction of the valence electrons transfer from germa
nium to nitrogen atoms. Namely, when the material con
tains nitrogen in atomic percentage higher than a certain
value, the stretching force of Ge-Nand! or N-H bond in
off-stoichiometric a-GeNx:H films is enlarged by the back
bonding nitrogen, 14 The small difference in the peak position
between the room temperature and 200 °C substrate might
be associated with the difference in structural relaxation of
the network, although the details are unclear. Hydrogen
content was estimated to be about 15% in atomic percentage
from the absorption intensity of N-H stretching band near
3300 em -1 in the figure using a known proportionality fae
tor.2,15
Figure 6 shows N Is and Ge 3p XPS spectra of
a-Gel _xNx:H samples for x = 0.1 and 0.3. Surface oxygen
and hydrogen on as-deposited samples were etched out by
lO-min AI' sputtering before XPS measurements. As is clear
in the figure, the energy difference AE between the N Is orbi
tal and the Ge 3p orbital became smaller as the nitrogen con
tent in the film increases. More detailed data are summar
ized in Table II. The energy difference AE between the two
core levels in the a-Gel ._ x Nx:H network decreases from
276.3 to 274.3 eV when x increases from 0.1 toO.3, indicating
that some fraction of electron charge is transferred from ger
manium to nitrogen due to a difference in the electronegati
vity between the two elements. This provides direct evidence
supporting the above discussion that the total bonding ioni
city of the disordered network increases with the N content
and could be varied continuously in off-stoichiometric com
pounds.
Honma eta!. 1076
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43Nls L1 E = 276.30 eV
L1 E :: 274.30 eV
~tOI=30'l. Ge3p
FIG. 6. N Is and Ge 3p spectra of a
GeN x:H alloys obtained by ESCA measure
ments.
450 400 350 134 122 110
Binding Energy (eV)
C. Structural stability
We investigated the structural stability of the
a-GeNx:H films by studying crystallization processes by
DT A (differential thermal analysis), DTG (differential
thermal gravimetry), and/or XRD (x-ray diffraction).
From thermal analyses, a-GeN x :H films were deposited on
aluminum foils (melting point 660 ·C) or polyimide sheets
(stable up to 1000 ·C). When a polyimide film is heated,
water and solvents are evolved gradually in a wide tempera
ture range from 80 to around 300·C and no sharp peaks
appear in the DT A curve up to 1000 0c. Therefore, as far as
crystallization temperature is concerned, it is possible to de
termine it precisely by using a polyimide film as a substrate.
Furthermore, it is well known that thermal shrinkage is very
sman in the polyimide films. The specimens were cut into
tiny chips with an area of 30 mm2, being piled up inside the
sample holder. Each sample was heated up to 1000·C in He
atmosphere using an IR-image furnace at a constant heating
rate of 20 ·C/min.
Figure 7 shows typical results of DT A and DTG mea
surements made on the a-GeN x :H sample prepared under
TABLE U. The results of ESCA measurements for the four a-GeNx:H
films.
Sample PM,IP,o, N/Ge Eb (Ge 3p3/2 ) Eb(N Is) dE"
(%) (%) (eV) (eV) (eV)
1I6sp2 10 10.29 122.20 398.50 276.30
l/7sp2 20 22.48 120.70 395.81 275.10
1l8sp2 30 30.45 121.52 395.82 274.30
120sp 50 122.16 396.46 274.30
a AE = Eb (N is) -Eb (Ge 3p3I2)'
1077 J. Appl. Phys., Vol. 55, No.3, 1 February 1989 PN,IPtOI = lO%andrfpowerofO.l kW. Thesharpexother
mic peak due to the crystallization and the corresponding
decrease ofthe film weight are dearly seen at around 440 ·C
both in the DT A and DTG curves. No sign of a glass transi
tion was observed in the DT A curves of any of the
a-GeN.~ :H samples onow N content (P NIP tOt < 30% ). On
the other hand, the origin of the weight d~crease in the DTG
is thought to be a kind of gas evolution, Nitrogen in the film
is strongly connected with germanium and stays stable in the
network even at 440°C, which has been confirmed by the
infrared measurements to be mentioned later. Hydrogen
probably starts evolving from the film before the tempera
ture reaches 440 °C but could not be detected because of its
small mass. Therefore, the most probable explanation for the
DTG is that argon atoms are evolved out simultaneously
with the crystallization of the film, since it is wen known as a
shock crystallization that several atomic percent of argon
are unintentionally incorporated into reactively sputtered
amorphous films during deposition and released from the
network instantaneously with the crystallization. 16
Figure 8 shows the crystallization temperature Tc of a-
t
.!.! .~ I: _ II
~'"
Ul
t .. a-GeNX:H (PN2'Ptotol0%)
20 OClmin
OTA ~
~~--~--~~--~-~
~ DTG
J'. -----------1
L---2~OO--~~---~~-~~-J
Tennperature (Oe) FIG. 7. The crystallization tempera
ture and the decrease of the film
weight were measured by DT A and
DTG, respectively.
Honma et sf. 1077
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43800 Evaporation
700 Crystalline
&-' 600 FIGo 80 The relationship
between the crystallization
<II
temp~rature T,_ of a-GeN,:H "-500 :::; e alloys and P N / P tot ratioo
QJ 400 Amorphous 00
E
01!1
3OO} l-
0 10 20 30 40 50
PN2' Ptot (Of. )
GeN x :H films determined by DT A as a function of P N, / P tot
during the film deposition. As shown in the figure, the crys
tallization temperature increases with the nitrogen content.
In each specimen, a small amount of weight decrease was
also detected by DTG at around the same temperature as Tc.
It is reasonable to suggest that the increase in Tc is caused by
the increase in the average bonding energy in the amorphous
network.
Figure 9 shows the x-ray diffraction patterns of
a-GeNx:H films before (dashed line) and after (solid line)
the heat treatment at 660 ·C for 20 min, Samples deposited
under P N, / P tot> 30% show no change in their diffraction
patterns, indicating that the amorphous germanium-nitride
phase is stable up to 6oo"C. The samples prepared at PN,/
P tot = 10 and 20% show a crystallization peak in their XRD
scans, while the intensity of the Ge( Ill) peak is rather
small. However, in the XRD of a-Ge:H, the ( 111) peak of
Ge crystal is dearly observed after the heat treatment These
results are consistent with the data shown in Fig. 8.
Figure 10 shows the infrared transmittance spectra of
anneal
600't 20min
-------40 "I.
:i ---------------- ----- 30 ·f.
~20·1.
~
'~~10.1.
C
o 0'.
15 20 25 30 35 40
2 9 ( deg )
FIGo 9. X-ray diffraction patterns of a-GeNx:H films before (dashed line)
and after (solid line), the heat treatment was at 600 'C for 20 mino
1078 J, AppL Physo, VoL 65, Noo 3, 1 February 1989 ::I
d
<II u c g
°E
Ul e:
0 ... I-
stretching
1000 500
WAVE NUMBER (em-i)
BGo to, Infrared transmittance spectra of a-GeNx :H (x = 003) film before
and after the sequential thermal annealing at 300, 450, and 600 'C for 20
min at each temperatureo
a-GeN x:H ex = 0.3) film before and after the sequential
thermal annealings at 300, 450, and 600 ·C for 20 min at each
temperature, The absorption intensity of Ge-N band
stretching at around 700 cm --I remains unchanged up to
600 ·C, while that of N--H band bending at around 1150
cm-I disappears after the annealing at 600 "c. It means that
N-H bonds were broken at least below 600 ·C and hydro
gen atoms were evolved out of the film. From the viewpoint
of chemical bonding theory, the bonding energy of N---H is
larger than that of Ge-N. However, because of a difference
in the coordination number between Ge, N, and H, threefold
coordinated N becomes more stable in the network, while
monovalent H is easily evolved out at lower temperatures.
D. Optical band gap
The optical band gap of deposited films was determined
from the transmittance spectrum traced in a range from ul
traviolet to near-infrared light, We use E04' the photon ener
gy at which the optical absorption coefficient becomes 104
cm --I, to define the optical band gap, The B value, defined by
the relation ahv 0:: B (hv -Eo) 2, was experimentally deter
mined from the slope of the Tauc plot of each optical absorp
tion spectrum,
Figure 11 shows E04 and B values of a-GeNx and
a-GeNx:H series as functions of PNJP10t ratios. All of the
samples were prepared at 0, 1-k W rf power and a substrate
temperature of 80°C. As seen in the figure, E04 increases
while B decreases with increasing P N,I P tot ratio for both
series. These are interpreted simply as the effect of the nitro
gen incorporation. The monotonic increase of E04 can be
ascribed to the increase of the N/Ge ratio in the network in
proportion to the P N, / P tot ratio, as shown in Fig. 3, because
a wider optical gap originates from stronger Ge·-N bonds,
However, at the same time, the inclusion of nitrogen seems
Honmaetal. 1078
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:432.0
1.5 • a-GeNx:H
o u-GeNx
o 10 20 30 40 50
PN
2 I Ptot (%) o
FIG. 11. E,j4 and B values of a-GeN, and a-GeN x:H series for different
PN,IP"" ratios.
to enhance the structural randomness of the network prob
ably because Ge--N bonds with a shorter covalent bond
length and/or threefold coordinated N atoms are mixed into
Ge--Ge bonds with fourfold coordination in the network.
This argument is consistent with the rapid decrease of the B
value with N/Ge ratio in the figure, since the magnitude of B
is partially associated with the structural randomness of the
network.
Figure 12 shows E04 and the deposition rate of
a-GeNx :H films as functions of the nitrogen content in the
FIG. 12. The relationship between the E()4 and P N.! P tot for different rfpow
ers, Deposition rates were also described in the figure.
1079 J. Appl. Phys., Vol. 65, No.3, 1 February 1989 gas phase (P N,I P tot) for different rf powers. As discussed
above, a qualitative relation between E04 and P Nzl P tot holds
in the system of a a-GeN x independent of rf powers. As for
the rf-power dependence, the optical band gap becomes
smaller with increasing rf power for PN,IP tot > 25%. As
shown in the figure, the deposition rate increases in propor
tion to the magnitude of rf power. Therefore, if we assume
that the concentration of the nitrogen reactive species is
nearly kept constant in the plasma independent of rf power,
the increasing power should make the N/Ge ratio in
a-GeN x :H smaller, because the germanium flux to the grow
ing surface of the film increases.
Figure 13 shows the optical band gap E04 as wen as the
deposition rate of a-GeNx:H films plotted against the total
pressure of the sputtering gas at constant P N, I P tot = 50%
and rfpower of 0.1 kW. As shown in the figure, E04 increases
rapidly when the total pressure exceeds 1 X 10-2 Torr, while
the deposition rate decreases. Available data is not sufficient
for discussing a detailed process associated with the above
results, but two possible explanations can be suggested. The
first possibility is that the Ge flux reaching the substrate
decreases much faster than that orN species as the pressure
rises, increasing the N/Ge ratio in the film, The second is
based on a change of the mean free path of the species in the
plasma, resulting in a higher N/Ge ratio through. the gas
phase reaction between Ge and N species.
Figure 14 shows E04 and the film deposition rate as func
tions of the substrate temperature. Both are not so strongly
dependent on the substrate temperature, which is conceiv
able because the optical band gap is mainly determined by
the nitrogen content in the network and the bonded nitrogen
is stabler than H in a-GeNx network, at least up to 600 °C, as
clear from the data in Fig. 10. Namely, once nitrogen makes
the chemical bond with germanium on the growing surface,
it is never reemitted below 350°C and keeps the optical band
gap nearly constant. The role of hydrogen in the amorphous
3.5
> 3.0 (\)
.... ... .c
0 w E
2.5 ::!,
to
0 ~
0 0.9 {j
0::
2.0 c 0 0.8
r~s 0 :;:;
0.7 'iii
&
0.6 (\)
0
T
510 25 50
f10t ( )(10-3 Torr)
FIG, 13, The relationship between E"., deposition rate, and the total pres
sure of the sputtering gas (P to! ). The sample wa.~ prepared under the con
stant P N / P (ot = 50% and the rf power was 0.1 k W.
Honmaetal. 1079
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:432.0 .-
L.. .c -.
0 E
1.5 :l.
/}. 0.2 kW, '1;2' '101 = 50 'I.
a 0.1 kW, PN2i Pta! = 30 'I. 2
> 0
<l> 1.0 a::
c:
~ 2.0 g
~ .~ w
1.0 G;
Cl
100 200 300 400
Substrate Temperature
( °c )
FIG. 14. Ell. as weilas the deposition rate were described as fUlIctions of the
substrate temperature.
Ge~N-H network slightly differs from that in the Si~H
network as far as the optical band gap is concerned. In
a-Si:H, as has been reported by several groups, 17 the optical
band gap increases with an increase of the bonded hydrogen
content, since the band gap of a-Si:H film is mainly deter
mined by the fraction of Si-H bonds and also, to a lesser
degree, by thermal structural relaxation of the network.
Therefore, the optical band gap of a-Si:H becomes narrower
as the substrate temperature rises, because the hydrogen
content in the film decreases. In contrast, in case of
a-GeNx :H, most of the hydrogen is not attached to germani
um but to nitrogen, and these N-H bonds, as wen as the
Ge-N bonds, are themla11y stable at least up to 450 ·C. The
band gap is affected by both Ge-N and N-H bonds. This
is the reason why the optical band gap of a-GeN x :H stays
almost constant up to high temperatures.
Figure 15 shows the relationship between the peak posi
tion of the infrared absorption band due to the Ge-N stretch
ing mode and the optical band gap E04' As is clearly seen in
the figure, E04 increases monotonically with increasing
Ge-N band-stretching peak energy. Both quantities are pd-
;; 3.0
<lI
~
w 2.0
1.0 FIG. 15. The relation
between Eo. and the peak
position of Ge-N stretch
ing band.
T I I ! !
1080 700 750 800
Ge-N stretching band
( em-I)
J. Appl. Phys., Vol. 65, No.3, 1 February 1989 madly determined by the bonding energy of the major frac
tion of chemical bonds, which is associated with the average
bond energy gap of the disordered network. We define the
bond energy gap as the energy splitting between the bonding
and anti bonding states of the chemical bonds, as suggested
by Phillips.1H In other words, the introduction of nitrogen
into the network causes the increase of the bonding ionicity
of the relevant chemical bonds, resulting in an increase of the
average bond energy gap of the network if we assume a con
stant average bond length. It is weB known that the optical
band gap is mainly determined by the bond energy gap.
E. Electric conductivity
The temperature dependence of the conductivity of the
alloys were measnred in a wide temperature range from
-130 to 150 DC. Figure 16 shows the results for a a-GeN :x
and a-GeN x :H alloys. 10 The results for a-Ge and a-Ge:H are
also plotted in the figure for comparison. From the data in
the figure, electric conduction of a-GeN;x:H as well as
a~Ge:H can be characterized as a thermally activated pro
cess, while that of a-GeNx and a-Ge cannot. The curves for
the latter nonhydrogenated samples become a straight line
when plotted by T-1/4, indicating that variable range hop
ping prevails in their electronic conduction. Thus, :it is clear
that hydrogen atoms play an important role in reducing the
density of mid gap states, and thereby the electronic conduc
tion of those alloys is converted from the "hopping" regime
to the "band-conduction" one, which is the same case as in a
Si:H. From the IR absorption data shown in Fig. 4, however,
H does not so effectively terminate Ge dangling bonds but is
rather preferentially attached to N atoms. Nevertheless, the
incorporation ofH atoms in amorphous GeNx results in the
reduction oflocalized states. Considering the fine linearity of
the (7 vs 1/ T curve of the a-GeN x :H film, it is unlikely that
Ge dangling bonds exceeding 1018 ern ,-3 are involved in the
a-GeNx:H network. Two speculations may be possible: one
is that even ifonly 1 % of the total amount of hydrogen in the
film is attached to Ge atoms, Ge dangling bonds amounting
to 1020 cm .' 3 can be adequately eliminated, The other is that
not only Ge dangling bonds but also N dangling bonds con-
FIG. 16. The dark conductivity cris plotted against the reciprocal tempera
ture (lin for (l) a-Ge, (2) a-Ge:H, (3) a-GeN" and (4) a-GeN x:H
(x = 0.1) alloys.
Honmaetal. 1060
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43tribute to the formation of midgap states and the latter are
efficiently terminated with hydrogen. On the other hand, it
has turned out that nitrogen atoms are less important be
cause they fail to reduce the midgap states, although nitro
gen can reduce the average coordination number of a-GeN~
and relax structural constraints stored in the amorphous
network.
Figure 17 shows the optical band gap E04 and the activa
tion energy Il.E of the dark conductivity of a-GeNx:H films
plotted against P N, I P tot. Since the conduction type of those
samples was found to be n type from the sign of their thermo
electric power, the activation energy Il.E corresponds to the
energy difference between the mobility edge Ee of the con
duction band and the Fermi energy Ep, i.e., Il.E = Ee -EF•
As shown in the figure, flE as wen as E'J4 increases as an
increase ofN content, namely, nitrogen seems to be incorpo
rated as a threefold coordinated alloying element. No sign of
fourfold coordinated N atoms (Le., donors) was observed in
the present scanned range of P N, I P tot.
The photoconductivity of the samples was measured un
der exposure to AMl1ight. The best data of the photocon
ductivity-to-dark conductivity ratio (Le., photosensitivity)
was 40, which was obtained from the sample prepared under
relatively higher pressure and higher hydrogen content in
the sputtering gas. It is likely that, under this preparation
condition, a much higher concentration of reactive hydro
gen is generated in the sputtering plasma and thereby Ge
dangling bonds are terminated effectively in comparison to
other deposition conditions. However, the photosensitivity
of these materials does not seem to be as high as a-SiGe:H
alloys, although the preparation conditions are not opti.
mized as yet.6
IV. CONCLUSIONS
Properties of hydrogenated amorphous germanium-ni
trogen alloys prepared by reactive sputtering were presented
for the first time. Structural, optical, and electrical proper
ties of a-GeNx:H alloys are summarized as follows.
( 1) As the nitrogen content increases, the crystalliza
tion temperature of the alloys continuously rises from 360
(N IGe = 0) up to 650·C (N/Ge = 0.4) and the optical
band gapE04 increases from 1.23 (N/Ge = 0) to 3.3 eV (NI
2.0
:> 1.5 01>
~ 0 w 1.0 . w
"" 0.5
o
1081 ~-~
10 20 30 40 50
PN2 / Ptot ( Qt. ) FIG. 17. E.~l4 and the acti
vation energy AE are de
scribed as functions of the
PNjP"" ratio.
J. Appl. Phys., Vol. 65, No.3, 1 February 1989 Ge = 1). One of the key factors determining the fundamen
tal properties of the a-GeNx:H alloys was shown to be the
atomic ratio of N/Ge in the amorphous network, which can
be controlled mainly by the Nz partial pressure in the sput
tering gas.
(2) The inclusion of nitrogen increases the ionicity of
the network Therefore, the bonding forces of the interato
mic chemical bond becomes larger as more nitrogen atoms
are contained in the amorphous network. Crystallization
temperature, optical band gap, and the IR absorption fre
quency increase with increasing nitrogen content in these
alloy materials.
(3) Preferential attachment ofH to N takes place in this
system. According to the difference in bonding energy
between Ge-H and N--H bonds, hydrogen preferentially
bonds to nitrogen rather than germanium. The optical band
gap, which is mainly determined by the N/Ge ratio in the
aHoy, is not affected by the amount of hydrogen involved in
the aHoy network.
( 4 ) On the other hand, the electron transport properties
are greatly affected by the inclusion of hydrogen. The ther
mally activated bandlike conduction predominates in hydro
genated alloys (a-GeNx :H) because of the reduction of the
midgap states. Namely, a large number of defects might be
passivated by hydrogen atoms although the overall preferen
tial attachment of H occurs. In contrast, the carrier trans
port ofH-free a-GeNx is dominated by variable range hop
ping.
(5) Photoconductivity larger than the dark conductiv
ity by a factor of up to 40 times was obtained at an optical
band gap of around !. 5 e V. In the above a-GeN x :H sample,
almost all of the hydrogen is probably combined with nitro
gen and remaining Ge-dangling bonds and N-dangling
bonds might be insufficiently terminated. Moreover, addi
tion of hydrogen to more than 50% in the sputtering gas
degrades the film. As the deposition conditions have not yet
been optimized, many problems remain to be solved for im
proving the photoelectric properties of the materials.
ACKNOWLEDGMENT
We thank Dr. Matsuda for the measurements of photo
conductivity and for fruitful discussions.
IA. Matsuda, M. Koyama, N. Ikuehi, Y. Imanishi, and K. Tanaka,lpn. J.
AppL Phys. 25, L54 ( 1986).
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and K. Tanaka, App!. Phys. Lett. 47, 106! (1985).
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I'S. Veprek, Z. Iqbal, H. R. Oswald, F. A. SaraH, and J. J. Wagner, in Pro-
Honmaetal. 1081
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130.70.241.163 On: Mon, 22 Dec 2014 19:14:43ceedings of the 9th International Conference on Amorphous and Liquid
Semiconductors, Grenoble, 1981 [1. Phys. (Paris) Colloq. C 4, 251
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Honmaetal. 1082
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1.344508.pdf | Hydrogen passivation of acceptors in pInP
W. C. DautremontSmith, J. Lopata, S. J. Pearton, L. A. Koszi, M. Stavola, and V. Swaminathan
Citation: Journal of Applied Physics 66, 1993 (1989); doi: 10.1063/1.344508
View online: http://dx.doi.org/10.1063/1.344508
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and V. Swami nathan
AT& T Bell Laboratories, Murray Hill, New Jersey 07974
(Received 20 March 1989; accepted for publication 31 May 1989)
The problem of hydrogenation ofInP without surface degradation has been surmounted by
exposure of the InP surface to a hydrogen plasma through a thin SiN); (H) cap layer. This
layer is H permeable at the hydrogenation temperature of 250 °e, but P or PHJ impermeable
thus minimizing PH310ss and the attendant In droplet formation. In contrast to our results for
this type of plasma exposure of GaAs, we find that shallow acceptors in InP are heavily
passivated, whereas shallow donors are only very weakly affected. For exampie,p r--InP(Zn)
of 3 X 1018 cm-3 has its residual hole concentration reduced to <;3 X 1014 cm-3 over a depth of
1.3 pm by a 250 ·C, 0.5 h deuteration. The presence of acceptors impedes H (or D)
indiffusion, as indicated by D diffusion under the same conditions occurring to depths of 18
and 35 pm inp-InP (Zn, 2x 1016 cm--3) and n-InP (5 or Sn), respectively. Annealing for 1
min at 350°C causes the acceptor passivation to be lost and the hole concentration to be
returned to its prehydrogenation level, indicating that the passivation has similar thermal
stability to that of acceptors in GaAs, but lower than that of donors.
INTRODUCTION
There has been increasing interest in recent years in the
effects of hydrogenation on the properties of single-crystal
semiconductors. This topic in general has been reviewed by
Pearton et al., ! and more recently for III -V compound semi
conductors, particularly for GaAs, by Dautremont-Smith.2
Previously, we have demonstrated3-S very strong shallow
donor passivation for both group IV and group VI donors in
GaAs and GaAIAs. However, under the same direct expo
sure to a low-frequency hydrogen plasma, we obtained only
relatively small (up to a factor three) reduction in the hole
concentration.6 By contrast, when an indirect microwave
(2.45 GHz) plasma is used as the hydrogen source, some
what stronger passivation of shallow acceptor dopants is ob
served, with a good correlation between the depth of hydro
gen incorporation and the distance over which acceptor
passivation occurs.7 Although under appropriate conditions
a hydrogen plasma can etch III -V semiconductors at a fairly
slow rate,8 the type of hydrogenation treatments generaily
employ~d cause little significant damage to GaAs beyond
-400 A from the surface.
Apart from shallow level passivation in GaAs, hydro
gen has also been shown to deactivate a variety of deep levels
including the predominant center EL2,9 and the common
defects in molecular beam epitaxial GaAs.1O It might be ex
pected that P-based HI-V semiconductors would be less sta
ble under hydrogen plasma exposure because of the tenden
cy to leach out P as phosphine. However, Weber and Singh 11
have recently reported strong hydrogen passivation ofS do
nors and Cd, Zn, and C (but not Mg) acceptors in GaP, as
wen as the deep isoelectronic trap N. There was an increase
in the photoluminescence intensity from the GaP of approxi
mately an order of magnitude after hydrogenation. 11 We
have also observed similar or even larger luminescence in
creases in InP hydrogenated by the method described in this
letter, and this will be discussed in a separate report. 12 In as
grown lnP, Clerjaud et al. have identified a series of sharp optical absorption bands around 2300 em --I due to incorpo
rated H. B Similar absorption Hnes were observed in bulk
GaAs and GaP samples, and it was suggested that the source
of these bands was hydrogen contamination from both the
B203 encapsulant used during growth, and the starting
charge material.
Previous attempts to hydrogenate InP by plasma expo
sure have been unsuccessful because direct exposure to the
plasma causes preferential loss of P as PH3. In droplets are
observed on the InP surface even for low-power density plas
mas, and low ( < 150°C) temperatures.2.11 This surface deg
radation causes a reduction in the overall photolumines
cence intensity from the InP. In this letter we describe a
method for controllably introducing hydrogen into InP by
diffusion through a H-permeable SiNx protective cap. This
is achieved without any visible surface degradation. We
demonstrate strong passivation of acceptors in InP while
there is little effect on donors. The depth of acceptor passiva
tion is found to correlate with the observed depth ofH indif
fusion. Unintentional passivation by hydrogenation of Zn
acceptors in InP has been reported very recently to occur
during post-growth cooldown under an AsH} containing
ambient, due to surface pyrolysis of the AsH). 14,15 Intention
al hydrogen passivation of Zn acceptors in lnP also has been
reported very recently, by Omeljanovsky et al.16 and by Che
vallier et al.,17 in the former case where H was diffused
through a Au cap layer and in the latter case where a thin
InGaAs cap was employed.
EXPERIMENTAL PROCEDURE
Various types oHnP were hydrogenated. In general, for
electrical and atomic profiling measurements, bulk InP was
used. These samples were doped with Zn to give net acceptor
concentrations of 3x Wig cm-3 or 2X 1016 cm--3 or with S
or Sn to give a net donor concentration -5X 1017 cm,-3.
Other samples doped with Zn during vapor phase epitaxy
(VPE) were also utilized. These consisted of 1. 8 !-tm of Zn-
1993 J. Appl. Phys. 66 (5),1 September 1989 0021-8979/89/171993-04$02.40 © i 989 American Institute of Physics 1993
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142.157.212.140 On: Fri, 28 Nov 2014 14:34:34doped InP (p = 1 X 10[8 cm-J) grown on n-type InP sub
strates. This epitaxial material was used predominantly for
sheet resistance measurements.
After native oxide removal in dilute HF, thin SiN~ lay
ers were deposited on InP from an NH3:SiH4:Ar plasma, in a
parallel plate reactor operating at 13.56 MHz. An NH31
SiH4 flow ratio of 9, a chamber pressure of 1 Torr, and a
substrate temperature of 300 ·C were employed. NH3 as the
source of Nand 13.56 MHz plasma frequency were chosen
to enhance the H content and H conduction. Thicknesses of
80 and 200 A for the 0.5 and 2.0 h H2 plasma exposures,
respectively, were employed. The encapsulated samples
were then exposed to a 30 kHz, 0.08 W cm -2 H2 or D2 plas
ma at a pressure of 0.75 Torr. The sample temperature was
maintained at a constant value of 250°C during the plasma
exposures.
After plasma exposure, the SiNx was removed by etch
ing in a HF solution, and the carrier depth profile in the
sample was measured by Polaron electrochemical capaci
tance-voltage (C-V) profiling. Atomic depth profiles of in
diffused deuterium were obtained by Cs -+-negative second
ary-ion mass spectrometry (SIMS) in a Cameca 1MS 3/
system from the D2 plasma exposed samples. O2 was em
ployed in place of H2 on these samples specifically to facili
tate SIMS depth profiling to adequately low detection limits
( " 1 X lOiS em -3). The concentration of D measured in
plasma-treated samples was calibrated by comparison with a
D-implanted InP standard, and is considered to be accurate
to a factor of2. The depth scale of the depth profile of 0 was
obtained by measuring the crater depth after SIMS profiling
at a constant sputter rate. Depths are expected to be accurate
to ± 7%. The sheet resistance of the epitaxial lnP layers
after hydrogenation was obtained from the low-voltage cur
rent-voltage (1-II') characteristics measured between Au:Be
ohmic contacts onp+ -InGaAsP islands on top of the epitax
ialp-InPln-InP structures.
RESULTS AND DISCUSSION
The use of a thin SiN x encapsulating layer on the InP
proved to be effective in preventing surface degradation dur
ing hydrogen plasma exposure. Figure 1 shows an optical
micrograph from an In? sample in which an 80-A-thick
SiN¥ layer was selectively deposited prior to exposure of the
sample to the 30 kHz H2 plasma for O. 5 h at 250°C. The SiN x
was subsequently removed in a HF solution. It is clearly seen
that where the In? was not encapsulated there has been pref
erentialloss ofF, leaving behind In droplets on the surface.
By contrast, the region where the SiNx was present during
the plasma exposure shows no apparent degradation. Long
er exposures to the H2 plasma did result in InP surface deg
radation, however; hence the use of 200 A of SiN x for the 2 h
exposure. That the 80 A SiN x layer is H permeable was dem
onstrated by its use on n-GaAs (Si, 1 X 1017 cm-3) in which
donor passivation was produced to the same depth as in the
uncapped n-GaAs control sample.
Use of this cap layer has permitted the identification of
acceptor passivation in InP. Figure 2 shows the carrier pro
file in a bulk, Zn-doped (p = 3 X lOIS cm-3) sample that
was encapsulated with 80 A SiNx, and exposed to a D2 plas-
1994 J. Appl. Phys., Vol. 66, No.5, 1 September 1989 NOT
PROTECTED
PROTECTED
FIG. 1. Optical micrograph of an InP surface after hydrogen plasma expo
sure at 250 ·C for 0.5 h. Where the surface was directly exposed to the plas
ma there is a high density of In droplets, indicative of a severely degraded
surface quality. Where the surface was protected by an80-A.-thick SiN, cap
during the plasma treatment, there is no apparent degradation,
rna for 0.5 h at 250 ·C. There is at least a four orders of
magnitude decrease in the hole density in the sample within
the first 1.1 pm from the surface. This type of profile is typi
cal of hydrogen passivation, in which the hydrogen diffuses
in from the surface, neutralizing the acceptors to the depth of
its incorporation. We emphasize at this time that neither the
SiNx deposition by itself nor simply heating SiNx encapsu
lated p-InP at 250 °C for 0.5 h produced any detectable car
rier concentration reduction in the p-InP. This indicates that
there is no significant inditfusion of hydrogen from the SiN..;:
film itself, in the absence of an applied H activity gradient.
To further demonstrate the effectiveness of this proce
dure, a wafer composed of a 1. 8-pm-thick layer of p-type lnP
(1 X 1018 cm~3, Zn) (with a contact layer ofp+ -InGaAsP)
on an n-InP substrate, was employed. Metallic ohmic con
tacts were patterned onto the InGaAsP layer with 250 pm
separations and the InGaAsP layer subsequently etched
away to expose the p-InP between the contacts. Using a pro
tective layer of 200 A of SiN x' the wafer was plasma hydro-
p-in"(Zn,3x10t8cm-3)
D2 PLASMA, 0.5h, 250'C
I
3
FIG. 2. Carrier density profile in p+ -InP, which initially had a uniform
doping density of p = 3 X 10'" cm-3, after D plasma exposure at 250 'C for
0.5 h. The InP surface was protected by an 80 A SiNx capping layer.
Dautremont-Smith at al. 1994
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142.157.212.140 On: Fri, 28 Nov 2014 14:34:34~
~ 1017
~
'" u p-InP(Zn,3.IOfB cm-3)
02 PLASMA, 0.5 h, 250·C
! iOiS
~
".~
I! ! ! ! I ! ! I I I I I I ! I I I I I I I I' ! I
o 2:3 4 5
DEPTH (microns)
FIG. 3. SIMS profileoftheatomicdistributionofDinp+ -IuP (Zn, 3 X 1O!8
cm-» after plasma treatment at 250'C for O.S h. The D incorporation
depth matches the distance over which Zn acceptors were passivated.
genated for 2 h at 250 °C as previously described. Measure
ment of the sheet resistance between contacts after
hydrogenation indicated an increase in the p-InP resistance
by a factor of between 103 and 1<t, indicating a reduction in
hole concentration through the full 1.8 ;tm thickness of
about four orders of magnitude. This is consistent with the
1.1 J.lm passivation depth produced by the 0,5 h diffusion
described above.
Figure 3 shows the SIMS elemental D depth profile in
the sample of Fig. 2, giving direct evidence of deuterium
diffusion through the 80 A SiN x cap and into the InP during
plasma exposure. The SIMS measurement of the depth pro
file of deuterium shows an excellent correlation between the
depth of its incorporation and the distance over which the
p-lnP(Zn,2.10 Iocm-3)
Dz PLASMA, 0.5h, 250·C
DEPTH (mie,eos) 50
FIG. 4. SIMS profile of the atomic distribution ofD inp·lnP (Zn, 2X 1016
cm -J) after deuteratioll at 250·C for 0.5 h. Note the increased incorpora
tion depth and lower D concentration compared to that in higher doped
material (Fig. 3).
1995 J. Appl. Phys., Vo!. 66, No.5, i September 1989 Zn acceptors were observed to be passivated. The D concen
tration exceeds by about a factor of 2 the original hole con
centration over this region, but is similar to the total Zn
concentration. The sharp fall-off of the D concentration near
1. 3 J.lm indicates the depth to which D diffusion has been
limited by trapping at or adjacent to Zn acceptors.
TheSIMSresultforbulkp-type (Zn-doped) InPoflow
er doping density (p = 2 X 1016 cm-3) after exposure to the
same D2 plasma for 0.5 h at 250·C through the same 80 A
SiN.< cap layer is shown in Fig. 4. Once again the deuterium
concentration is in excess of the doping density, with the
incorporation depth now being far larger at 18 J.lffi compared
to ~ 1.3 f.J.m in the more highy doped InP. This indicates
rapid D diffusion within the InP lattice, with effective trap
ping of D at the reduced concentration of Zn acceptor sites,
with perhaps additional trapping of D at other defect sites.
We observed very little effect of hydrogen or deuterium
on the carrier profiles in n-type InP, even for plasma expo
sure temperatures as low as 125 ·C. Figure 5 shows the deu
terium depth profile in n-type S-doped (n = 5 X 1017 cm-3)
InP, also given the same D2 plasma exposure for 0.5 h at
250·C with the same SO-A.-thick SiNx cap layer. The D has
penetrated extremely deep ( -40 pm), and the D concentra
tion is below the S doping level by an order of magnitude,
indicating that at least at 250 ·C there is no significant for
mation of donor-D complexes. Identical results were ob
tained with the Sn-doped material. This assertion of little
trapping of D by donors is also consistent with the much
greater permeation depth of the D in n-type material com
pared to p-type InF, Indeed the extensive incorporation
depth ofD in n-type InP under these conditions implies that
the D is predominantly in atomic form during its diffusion.
In other words, D2 formation does not appear to be signifi
cant at 250·C in n-type InP. This depth of diffusion ofD in
the n-InP indicates the diffusion coefficient ofD in the InP
lattice (-5 X 10-9 cm2 s -I at 250·C) in the absence of
trapping, and may also be taken as the upper limit to the
depth of passivation occurring lnp-InP (under these deuter-
10~9
Cl
o n-lnP(S, 5, 1017c",-3)
D2 PLASMA, O,5h, 250·C
20 30 40
DEPTH (m'c,ons) 50
FIG. 5. SIMS profile of the atomic distribution of Din n-InP (S, 5 X 1017
cm -') after deuteratioll at 250·C for 0.5 h.
Dautremont-Smith et al. 1995
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142.157.212.140 On: Fri, 28 Nov 2014 14:34:34ation conditions) as the acceptor concentration is reduced
below the 2X 1016 cm -3 level in the sample of Fig. 3, in
which it is trapping at acceptor sites that is limiting the depth
of diffusion.
The trend in the D diffusion profiles presented here
(Figs. 3-5) is the inverse of that in GaAs, in which the D
diffusion depth in p + -GaAs exceeds that in p --GaAs, which
in turn exceeds that in fI-GaAs.2 In GaAs we proposed an
explanation for this trend based on H (D) being a deep do
nor in GaAs,6.18 and therefore diffusing as H+ inp-GaAs.
The variation in the degree of electric field enhancement of
the H+ diffusion at the progressing hydrogenation front ex
plained the variation in the effective rate of diffusion. Our
results presented here, therefore, are inconsistent with H ex
isting as H+ inp-InP.
We have made some preliminary measurements of the
thermal stability of the hydrogenated compiexes in lnP
(Zn) by monitoring the increase in conductivity of Van der
Pauw geometry Hall samples as a function of annealing tem
perature. Essentially 100% reactivation of these acceptors
occurred for a 350 ac, 1 min anneal. Thus the passivation
stability is less than that of donors, but similar to that of Zn
acceptors, in GaAs.2
The observation that acceptors in InP can be effectively
passivated by hydrogen raises the question of whether unin
tentional hydrogenation might be responsible for any near
surface doping modification effects ascribed to other causes.
One can certainly imagine acceptor passivation occurring
during plasma etching of InP, or dielectrics on its surface,
using hydrogen containing gas chemistries. A prime exam
ple of an etch gas mixture expected to produce passivation is
CH4/H2,19 and we have recently observed such effects in
lnP (Zn), 20 Dautremont-Smith2 has also pointed out the use
of photoresist masks during plasma etching, or the presence
of water vapor or leaks into the plasma reactor, provides a
ready source of hydrogen during the dry etch. In addition, it
is possible that wet processing steps such as etching and boil
ing in solvents may introduce hydrogen, as is the case with
Si. 1 As discussed earlier it is apparent that hydrogen is al
ready present in some bulk InP, 13 and consideration must be
given to its possible redistribution during subsequent high
temperature processing. Finally, partial passivation of Zn
acceptors in InP by unintentional hydrogenation has already
been observed to occur during post-growth cooldown under
AsH3·14.15
SUMMARY
We have described a surface encapsulation method
which allows controllable introduction of hydrogen into InP
from a plasma source. A thin (80 A) layer of SiN x deposited
1996 J. AppL Phys., Vol. 66, No.5, 1 September 1989 onto the InP sample protects the surface from plasma-in
duced degradation, and yet is hydrogen permeable. For an
0.5 h, 250·C D plasma exposure at 0.08 W cm -2, 30 kHz,
there is a four order of magnitude reduction in carrier den
sity within U f..lm of the surface ofp+ -InP. This distance is
identical to the D incorporation depth from SIMS depth
profiles. We ascribe this reduction in carrier concentration
to the formation of acceptor-hydrogen (deuterium) com
plexes. By contrast, n-type InP shows little change in carrier
density upon hydrogenation, but is extremely permeable to
hydrogen diffusion. The original acceptor concentration in
p-type material is restored by short annealing at 350 ·C.
ACKNOWLEDGMENTS
The authors acknowledge the expert techni.cal assis
tance of J. W, Lee for the electrochemical C-V profiling, and
V. Riggs for provision of the VPE grown layer structures.
IS. J. Pearton, J. W. Corbett, and T. S. Shi, Appt Phys. A 43, 153 (1987)0
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1.101403.pdf | Response of YBaCuO thinfilm microbridges to microwave irradiation
B. Häuser, B. B. G. Klopman, G. J. Gerritsma, J. Gao, and H. Rogalla
Citation: Applied Physics Letters 54, 1368 (1989); doi: 10.1063/1.101403
View online: http://dx.doi.org/10.1063/1.101403
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/54/14?ver=pdfcov
Published by the AIP Publishing
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130.18.123.11 On: Thu, 18 Dec 2014 16:03:37Response of YBaCuO thin-fUm microbridges to microwave irradiation
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(Received 17 January 1989; accepted for publication 10 February 1989)
Microbridges with widths of about 10 pm were lift-off structured from rf-sputtered YBaCuO
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dependence of the critical current 10 and the step heights 21" is observed, clearly revealing
Josephson-like behavior. From the grain structure, the critical current, and the microwave
response, it is very likely that grain boundaries as superconductor-normal conductor
superconductor (SNS) contacts dominate the behavior of the bridges.
Since the discovery 1,2 of high Tc superconductivity, a
number of different ceramic materials supcrconducting
above the temperature of liquid nitrogen were discovered.
Although in the meantime some oxidic systems are found to
be even superconducting above 100 K, (Y,RE)BaCuO with
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material due to its less-poisoning compound and its easy fab
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A number of more or less successful attempts were start
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sults in major difficulties in the tunnel junction fabrication
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stead, we chose constant thickness bridges (CTB) as J oseph
son junctions. They were structured from rf-magnetron
sputtered YBaCuO thin films using a lift-off technique. This
technique and the film deposition process are described in
detail elsewhere.3 Briefly, the films were deposited at am
bient temperature on (100) oriented MgO substrates, with
the negative photoresist structure of the desired geometry
being prepared before. After the deposition of the amor
phous films, the photoresist (Shipley AZ 1450) is dissolved
in acetone and thus the negative structure is removed. The
remaining positive structure (see Fig. 1) was treated in flow-
FIG. 1. Microscopic picture of an YBaCuO microbridge. ing oxygen at 920°C, giving rise to 8. rough granularity with
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devices (e.g., single microbridges, quantum interference de
vices) from films with a superconducting transition above 77
K were fabricated.
All measurements were performed in a helium cryostat
with integrated heater. The temperature is controlled by a
chromel-alumel thermocouple with an accuracy of 0.5 K
and can be varied in the range between 4.2 K and ambient
temperature. The J-V characteristics were taken with a four
terminal measuring technique and a precision low-noise am
plifier and current source. The substrates were clamped to
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Microwaves with frequencies of9.3 GHz (Xband) and
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to the sample in the cryostat. The frequency was measured
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meter was used. The use of the X-band waveguide gave rise
to severe microwave amplitude drift during the 55 GHz
measurements due to resonances and multiple modes.
Before applying the microwaves, the critical current of
the microbridges was investigated as a function of the tem
perature (see Fig. 2). As an evidence for the superconduc-
1,,(mAl
1·5
1.0 r
0.5 ~
o # 146
L/l;n=3
o 10 20 30 40 50 60 70 TiKl
FIG. 2. Temperature dependence ofthe critical current of an YBaCuO thin
film microbridge with a width of 10 I,m. (0) experimental e1ata.
(-)theoretical data."
1368 Appl. Phys. Lett. 54 (14), 3 April 1985 0003-6951/89/141368-03$01.00 @ 1989 American Institute of PhYSics 1368
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130.18.123.11 On: Thu, 18 Dec 2014 16:03:37400
200
o -endB T~S6K
)/~9.37GHz
-46 dB
-13dB
FIG. 3. 1-V characteristics of an YBaCuO thin-film microbridge at a tem
perature of 56 K and a microwave frequency ofY.3 GHz.
tor-normal conductor-superconductor (SNS) -Eke behavior
oftne microbridges, the experimental values were fitted with
a theoretical curve4 for SNS junctions as obtained by solving
Usadel's equation with the boundary conditions of Lik
harev. As a fitting parameter the reduced length 1= L /5 n
(L = thickness of the normal conducting layer in the SNS
junction, Sf! = coherence length in the normal conducting
material) was used, yielding a value of 3. Nevertheless, it
should be mentioned that a very low energy gap (less than 3
meV) was needed for this fit, which can be assigned either to
a contribution of flux motion in the contacts or to a low
ohmic shunt resistance, due to normal conducting paths in
the micro bridge.
In order to investigate the behavior of the bridges in
1369 Appl. Phys. Lett., Vol. 54, No. 14,3 April 1989
. ·.· .•. •.• .•. • . .-.·~ •.••• :.:.:.:.:.;O:.:.:.:.:.7.:.:-:.·.· •.•••••••• ,.-•.••••• 0; •••• ' •••••• ;> ••••••••.••.•.• -•• " ••••.• BOO
400
o -rodB
~ -6·81dB
)~ -4.26d8
-1.25dB
OdS
20,() 300 V(~V)
T~56K
\I~55Ghz
FIG, 4. 1-V characteristics of an YBaCuO thin-film microbriuge at a tem
perature of 56 K and a microwave frequency of 55 OH;:.
different temperature regimes, the measurements were car
ried out between 4.2 and 71 K and plotted for 4.2, 56, and 71
K, respectively. Between 4.2 and 71 K clear constant voltage
steps can be observed at mUltiples of the voltage correspond
ing 10 the Josephson frequency (see Fig. 3). At 4.2 K addi
tionally subharmonic steps are visible, revealing a nonsinu
soidal current-phase relation of the bridges. At higher
temperatures,. e.g., 56 and 71 K, this effect disappears and
the microbridges show only harmonic constant voltage steps
when irradiated with X-band or U-band microwaves.
The resulting J-V characteristics for different input
power levels are plotted in Fig. 3 (11 = 9.3 GHz) and Fig. 4
(v = 55 GHz). The experimental data can be interpreted in
terms of a SNS-like behavior of the microbridges, regarding
FIG. 5. Dependence of the critical current Ie
and thc height of the constant voltage steps 2In,
n = 1,2,3, on the microwave current 1'1" at dif
ferent temperatures and microwave frequen
cies. (II) experimental data, (-) theoretical
data; scales normalized to I,. = In (I,I" = 0): (a)
1'= 4.2K,v= 9.3GHz; (b) T= 56K,v= 9.3
GHz; (e) T= 71 K, V= 9.3 GHz; (d) T-~ 56
K,v= 55GHz.
Hauser et al. 1369
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.18.123.11 On: Thu, 18 Dec 2014 16:03:37the remarks as mentioned above. In this case the applicabili
ty of the resistively shunted junction (RSJ) model can be
assumed and a characteristic frequency Vc = 2eR,,/o /h can
be calculated. R" represents the normal state resistance of
the microbridge. The resulting current relaxation times
7(" = lIv, lie in the range 10-10_10-12 s for R,,1o
= 6 X 10 4_2 X 10-5 V. For these times one would expect
between 1 (at 71 K) and 30 (at 4.2 K) constant voltage steps
in the 1-V characteristic. Keeping in mind the low resistance
of the microbridges and the restricted output of the current
source (5 rnA), this is in good agreement with our observa
tions for the lower temperatures. At 71 K significantly more
steps were seen than predicted by this modeL However, with
increasing microwave power their height decreases more
strongly than predicted by theory.s In this case v is of the
order of V,.
Plotting the critical current 10 and the step height 2/" as
a function of the microwave power, reentrant behavior can
be observed, revealing Josephson-like behavioL In order to
examine the applicability of the RSJ model, we simulated the
1-V characteristics for different microwave amplitudes by
solving the appropriate differential equation using a stan
dard fourth-order Runge-Kutta method. The parameter
v/vc was determined by R"Io and v (see above). The result
ing theoretical dependences of 1", n = 0, ... ,3 were compared
with the experimental ones. For the lower temperatures,
1370 Appl. Phys. Lett., Vol. 54, No. 14,3 April 1989 good agreement with the predicted values is achieved [see
Figs.5(a)-5(d)].
In conclusion, it was found that over a wide temperature
range the granular microbridges reveal Josephson-like be
havioL From the experimental data it can be presumed that
the properties of these junctions are dominated by SNS-like
intergrain effects, although vortex motion seems to playa
minor role also. For low temperatures the coupling between
the grains becomes very strong and a dear SNS-like behav
ior is no longer observed. Instead, subharmonic steps appear
in the characteristics indicating a nonsinusoidal current
phase relation. Otherwise, clear steps with reentrant behav
ior are observed when increasing the microwave power at all
investigated temperatures and frequencies. The measured
values for 10 and In are in good agreement with the ones
predicted by the RSJ model.
We gratefully acknowledge the help ofD. H. A. Blank.
'J. G. Bednorzand K. A. Muller, Z. Phys. 64,189 (1986),
2M. K. Wu. J. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L Gao, Z. 1.
Huang, y, Q, Wang, and C. W_ Chu, Phys. Rev. Lett, 58, 908 (1987).
'B. Hauser, M. Diegel, and H. Rogalla, App!. Phys. Lett. 52, 846 (1988).
4A. L. de l,ozanne, Ph.D. thesis, Stanford University, Stanford, CA, 1982.
'Po Russer,], App!. Phys. 43, 2008 (1972).
Hauser at at. 1370
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.18.123.11 On: Thu, 18 Dec 2014 16:03:37 |
1.584443.pdf | Reactive ion etching of GaAs and AlGaAs in a BCl3–Ar discharge
S. S. Cooperman, H. K. Choi, H. H. Sawin, and D. F. Kolesar
Citation: Journal of Vacuum Science & Technology B 7, 41 (1989); doi: 10.1116/1.584443
View online: http://dx.doi.org/10.1116/1.584443
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/7/1?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Sat, 22 Nov 2014 07:07:59Reactive ion etching of GaAs and AIGaAs in a BCI3-Ar discharge
s. s. Cooperman, a) H. K. Choi, H. H. Sawin,b) and D. F. Kolesar
Lincoln Laboratory, Massachusetts Institute of Tech nology. Lexington, Massachusetts 02 173-0073
(Received 2 May 1988; accepted 22 September 1988)
Reactive ion etching of GaAs and AIGaAs has been performed in a BCI} -Ar discharge. Etching
properties have been studied as functions of BC13 percentage (0%-100%), total pressure (2.S-
30.0 mTorr), and power density (0.06-0.22 W/cm2). At low pressures (2.5-12.S mTorr) and
intermediate BCl3 percentages (25%-75%), profiles exhibiting a high degree of anisotropy are
achieved. Under anisotropic conditions, etch rates are about 0.05-0. I Itm/min (at power density
of 0.22 W / cm2), somewhat lower than for other chlorine-containing gases. Conditions for
etching GaAs and AIGaAs at equal rates have been determined. There is a small lag time between
ignition of the glow discharge and the start of etching. The relative concentration of C1 atoms in
the plasma, as measured by optical emission actinometry, correlates well with the etch rate for
various operating parameters.
I. INTRODUCTION
Reactive ion etching (RIE) of GaAs and AIGaAs has be
come of major interest in the fabrication of optoelectronic
integrated circuits because of its potential ability to etch mir
ror facets for semiconductor diode lasers. Chlorine-contain
ing gases, in particular, have been extensively studied in RIE
processes because the Gael", and AIClx products are vola
tile. These gases include chlorine,I,2 chlorine-containing
compounds such as CC12F2 (Ref. 3) and SiCt,,4 and mix
tures such as C12-CC14 (Ref. 5) and C12-Ar.6 While
smooth, vertical sidewalls could be etched in GaAs with
these gases, fluctuating lag times were generally observed
between ignition of the glow discharge and the start of etch
ing, resulting in poor etch rate reproducibility. In addition,
except in a recent study2 employing a load-locked system,
GaAs was etched at a much faster rate than AIGaAs (up to
three times as fast6), making it quite difficult to achieve the
specularly reflecting, vertical facets required for GaAsl Al
GaAs lasers.
The lag time and unequal etching rates of GaAs and
AIGaAs can be attributed to the presence of surface oxides
that are formed on the two materials,7 both beforc and dur
ing etching,8 in the presence of oxygen and water vapor. A
lag time results because the native oxide layer does not react
with the etchant gas, and so must be removed by sputtering
before the gas can etch the semiconductor surface.: The dif
ference between the etching rates of GaAs and AIGaAs
arises because the higher reactivity of Al makes AIGaAs
more susceptible than GaAs to oxide formation.
By using a mixture of BCIl and C12, lag time has been
eliminated and a GaAs etch rate less than twice that of
AIGaAs has been obtained.9 The BCIl reduces native gal
lium and aluminum oxides present on the sample surface10
and scavenges residual oxygen and water vapor in the etch
ing chamber. ,I In this paper we report the etching character
istics of GaAs and AIGaAs using a BCI, -Ar gas mixture in a
RIE system. The addition of Ar produces a more anisotropic
etch than can be expected with BCl3 alone. The concentra
tion of Cl atoms in the BCI, -Ar discharge under various
operating conditions was measured by optical emission ac
tinometry and correlated with the GaAs etch rate. II. APPARATUS AND EXPERIMENTAL PROCEDURE
A. Etching
The etching apparatus used in this study is an MRC Mod
el RIE-51 system, which incorporates a 17-1 stainless-steel
vacuum chamber and anodized aluminum (99.9% pure)
electrodes. The system schematic is shown in Fig. 1. The
19.1-cm-diameter anode and lS.2-cm-diameter cathode are
5,1 em apart. The system uses an rfpower supply operated at
13.S6 MHz. A Pyrex cylinder surrounds the electrodes to
confine the gas flow to the region near the cathode. In order
to keep moisture out of the system, the chamber is enclosed
in a nitrogen glove box, and the samples are exchanged
through a nitrogen load-lock.
The pumping system uses an l1.81/s roughing pump and
a Cryo-Torr cryopump rated at 12001/s for Ar. After the
roughing pump reduces the chamber pressure to 10 2 Torr,
the chamber is opened to the cryopump to achieve a back
ground pressure in the low 10 7 Torr range. During the etch
runs, the BCl, and Ar gas flow rates are adjusted by MKS
260 mass flow controllers, and a constant chamber pressure
is maintained by feedback control oftlle cryopump throttle
CHAMBER WAl..l __ _
PYREX CYUNDER._
GLOW
N,
PURGE GAS PORTS_ ......
FIG. I. Schematic diagram of the RIE system. COLO CATHODE
DISCHARGE GAUGE
CAVO
GATE THROTTLe PUMP
VALVE VALVE
41 J. Vac. Sci. Technol. B 7 (1), Jan/Feb 1959 0734-211X!89/010041-06$01.00 @ 1989 American Vacuum Society 41
. -" --_. -"" -_.". -'.. . ..•. ,.~ ._ .• ~-.......... ' .•.•••. ';'.-; •. ? •...•...•.....•...................•.....•.•• ,... ; ... ;.;.;.; ... ; ... :.;.;-;.;.;-:.;.:.;.;.;.;." ... " ..... '.---. "-.".-.'.' --.. ~ ...•. ; ..•. -.. ; .... "' •.........•.......•.•. ~ ..... -;'.'.';' .•.•.•.•••.• , ..•..•. _<0 c •• ~ •• ,
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Sat, 22 Nov 2014 07:07:5942 Cooperman eta!.: Reactive lon-etching of GaAsand AIGaAs
valve. At the end of each run the BC13 lines are purged with
nitrogen through the roughing pump to avoid the formation
of boric acid.
Both (100) semi-insulating GaAs wafers and AIGaAs
epitaxial layers grown by organometallic vapor phase epi
taxy (OMVPE) on (lOO) GaAs substrates were used in the
etching experiments. In almost all cases, pyrolytic Si02
films were used as masks. After the masks were patterned by
wet etching in buffered HF, the samples were placed in a
nitrogen glove box in order to minimize native oxide growth
on the semiconductor surface prior to etching. The BCl3 gas
was Matheson boron trichloride, c.P. (99.9% purity).
The base line operating conditions used in the study were:
BCl3 percentage, 62.5%; total pressure, 5.0 mTorr; power,
25 W (0.14 W Icm2); and total gas flow rate, 20.0 sccm. One
operating parameter was changed in each series of etching
experiments. The parameters varied were BCI) percentage
(0%-100%), pressure (2.5-30.0 mTorr) , and power (10-
40 W, corresponding to 0.06-0.22 W/cm2). Etch depths
were measured with a DEKT AK IIA depth profiler, and the
cross-section profiles were studied by scanning electron mi
croscopy (SEM).
B. Optical emission actinometry
Conventional emission spectroscopy does not provide a
reliable measure of the atomic CI concentration [Cll in a
glow discharge because this concentration is not the only
variable affecting the C! emission intensity ICCl). This in
tensity is proportional to the product of [Cl], the rate coeffi
cient kCl for the excitation of Cl atoms from the ground state
into the optically emitting state, and the electron density
[e-],
I ( Cl) <X kCl [ Cl) [e -] . (1)
The value of kCI depends on the excitation cross section and
the electron energy distribution.
In the present study, the relative changes in [Cl] pro
duced by varying the RIE operating parameters were deter
mined by optical emission actinometry. This technique,
which was developed by Coburn and Chen, 12 compares the
intensity of an emission line for an active species in a plasma
with the intensity of an emission line for an inert gas, whose
concentration is known from the ratio of its flow rate to the
total flow rate. Lines with similar excitation cross sections
are selected, so that the ratio of their excitation rate coeffi
cients will be approximately constant. The inert gas chosen
in the present experiments was Ar. Taking the ratio of Eq.
(1) to the corresponding expression for leAr) then gives
I(Cl) ex [Cll , (2)
leAr) [ArJ
making (CI] proportional to the product of I(Cl)II(Ar)
and LAr].
The emission intensities compared were those of the
837.6-nm Clline and the 8I1.5-nm Ar line. These lines were
chosen because they have similar excitation cross sections
and are known to provide accurate measurements of the Cl
concentration in a CF) CI discharge. 13 The intensities were
measured with a PAR Model 1451 optical multichannel
J. Vac. Sci. Technol. e, Vol. 7, No.1, Jan/Feb 1989 42
analyzer using a Modcl1453 detector. The intensity at 837.6
nm measured with this system was not due entirely to the CI
emission, but also included a significant contribution from
the Ar line centered at 840.8 nm. To correct for this contri
bution, the various intensities measured for the 8II.5-nm Ar
line in the experiments using a BCl3 -Ar discharge were re
produced in a pure Ar discharge whose pressure was adjust
ed by varying the Ar flow rate with the cryopump opened
fully to the chamber. The Ar intensity at 837.6 nm corre
sponding to each of the 811.5-nm Ar intensities was then
measured and subtracted from the intensity at 837.6 nm
measured in the appropriate BCI) -Ar experiment. Under
base line operating conditions (62.5% BCl3 ) the corrected
value for I(Cl) was about 85% of the total intensity mea
sured at 837.6 nm, while at low BCl3 concentrations the
corrected value was as low as 5% of the measured value.
This method of correction assumes that the ratio of the Ar
emission intensities at 837.6 and 811.5 nm is independent of
the operating conditions, including the BCl3 I Ar ratio.
III. RESULTS
A. Etching properties of GaAs and AIGaAs
In one series of experiments the etching characteristics of
GaAs were studied by varying the BCl3 I Ar ratio while keep
ing the other operating parameters at their base line values.
Figure 2 shows the GaAs etch depth obtained in 20 min as a
function ofBCl3 percentage. For 0% BCl, (i.e., an Ar sput
ter etch) the etch depth is only 0.20 ,urn. Increasing the BCl3
percentage to 25% increases the etch depth to 1.2 pm; a
slower, approximately linear increase is observed for per
centages between 25% and 75%. Above 75% BCI3, the etch
depth levels off at 1.8 ,urn, then decreases to 1.6 {tm as the
percentage rises to 100%. The etch rate for Si02 increases
upon addition ofBC13 up to about 25%, then remains steady
at a rate of about 0.2 {tm in 20 min.
The etch profiles sloped away from the mask at low BCI)
percentages (presumably due to mask erosion) and were
slightly reentrant at BCl3 percentages approaching 100%
(due to the increasingly chemical nature of the etching pro
cess). Between about 25% and 75% BCI3, vertical walls
were formed at the bottom of the channel, as shown in Figs.
2.0
E
2-1.5 c
'e
<:> 1.0 '" J: I-a.
LU c 0.5
:r:
0 I-
U.I
0.0
a 25 50 75 100
BCI 3 ("10)
F](i. 2. Dependence of GaAs etch depth on DCI, percentage for base line
operating conditions: 62.5% BCI" 5.0 mTorr, 25 W, 20.0 seem total gas
flow.
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Sat, 22 Nov 2014 07:07:5943 Cooperman £It al.: Reactive ion etching of GaAs and AiGaAs
FIG. 3. SEM micrographs of GaAs sample etched under base line operating
conditions: (a) cross section and (b) top view. The oxide mask has not been
removed.
3(a) and 3(b). The slanted sidewalls at the top of the chan
nel, which are similar to those obtained by Asakawa and
Sugata 14 in Clz RIE etching using a soft-baked resist mask,
can be attributed to mask erosion. Sidewall striations are
formed perpendicular to the wafer surface. Such striations,
which are generally observed in GaAs RIE, 1,4,6,15 may be due
in part to mask erosion and roughness of the mask edge. 15
The optimum Bel3 percentage for the base line operating
conditions appears to be 62.5%, which yields a higher GaAs
etch rate (L 7 pm in 20 min) and higher selectivity with
respect to the SiOz mask (about 8: 1) than other percentages
E 24F ___ m ........ ~ .. ili.iE .. ~~ 500 I/)
m ~ . r-
2.0 if" ill ."
C 400 W 'E -:;
0 Vi
N 300 <: "- 0 :.t: I- !:i Q" 200 l> w 0.8
Q G')
m
X 0.4 100
~ U I-
W 0 0
0 10 20 30
PRESSURE (mTon)
FIG. 4. GaAs dch depth and self-bias voltage vs total pressure for base line
operating conditions.
J. V<lC. Sci. Techno!. e, Vol. 7, No.1, Jan/Feb 1989 43
FIG. 5. SEM micrograph of GaAs sample etched at high pressure under
base line operating conditions. The oxide mask has been removed.
in the anisotropic regime. Because of the tendency of Bel 1 to
etch oxides, the selectivity is lower than in other chlorine
bearing discharges.6
The GaAs etch depth obtained after 20 min is shown in
Fig. 4 as a function of total pressure for 62.5% BCl3 and the
other base line operating conditions. The depth increases
steadily up to 10 mTorr, At higher pressures the depth ap
pears to level off at about 2.2 pm, but the data are not repro
ducible. Depths as high as 4-5 11m are occasionally observed
for samples etched in the high pressure regime. These sam
ples exhibit a roughened surface, The sidewalls are vertical
at pressures below 12.5 mTorr but become slightly reentrant
at higher pressures because of an increase in the rate of
chemical etching and a decrease in bombardment energy,
which is indicated by a reduction in self-bias voltage.
Sidewall erosion is reduced at high pressures (see Fig. 5),
presumably because the lower energy bombardment results
in less degradation of the mask.
In the low-pressure regime ( < 10 mTarr), etching experi
ments performed under the same operating conditions were
fairly reproducible, yielding very similar profiles and etch
depths that varied by only 5%-10%. The etched surfaces
were quite smooth, although some spikes were formed (see
FIG. 6. SEM micrograph showing characteristic surface morphology of an
etched GaAs sample.
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3.0 600
E 2.5 €
-=-c 500 LII
'E 2.0 C3
oct I-
0 ..I
'" 1.5 400 0 X >
l-e.. 1.0 VI
w oct
Q iii 300
:t: 0.5 ....
U ..I
I-W
W (I)
0.0 200
a 10 20 30 40 50
POWER(W)
FIG. 7. Dependence of GaAs etch depth and self-bias voltage on power for
base line operating conditions.
Fig. 6), possibly because of contamination remaining on the
GaAs surface after sample preparation.
Figure 7 shows the GaAs etch depth after 20 min as a
function of power. The etch depth initially increases sublin
early with increasing power, but the rate ofincrease is almost
constant between 25 and 40 W. Higher powers were not in
vestigated because the Si02 mask was completely etched
above 40 W. The ratio of slanted sidewall to vertical sidewall
increases with increasing power because higher energy bom
bardment results in faster erosion of the mask (see Fig. 8).
The AIGaAs etching characteristics were similar to those
of GaAs for BCI] percentages greater than about 10%. In
this percentage range the GaAs and AIGaAs etch depths
were within 5% of one another, whereas GaAs/ AIGaAs
etch rate ratios> 1.5:1 and 3:1, respectively, have been re
ported for reactive ion etching in BCl3 -e12 plasmas" and
Cl2 -Ar plasmas.6 The similarity in etching rates suggests
that at high enough concentrations the BCl} scavenges re
sidual oxygen and water vapor in the etching chamber suffi
ciently to suppress oxide formation. (For BCll percentages
:;; 10%, the AIGaAs etch rate was only about 80% of that
for GaAs.) The AJGaAs etch depth showed 110 dependence
on the Al mole fraction over the range of mole fractions
studied (0.1-0.4).
Plots of GaAs and AIGaAs etch depths versus time,
shown in Figs. 9 (a) and 9 (b), indicate lag times of about 30 s
FIG. 8. SEM photograph of GaAs sample etched at 40 W for 20 min under
base line operating conditions. The oxide mask has not been removed.
J. Vac. Sci. Teclmol. B, Vol. 7, No.1, Jan/Feb 1989 44
3.0
2.5
E .:. 2.0
:t: l-lL 1.5 w
Q
:t: 1.0 u I-iii
0.5
0.0
0 5 10 15 20 25 30
la} ETCHING TIME (min)
3.0
2.5
E
2-2.0
:t: 1.5 l-ll.
W
C
:x: 1.0
u I-
UJ 0.5
C.O
0 5 10 15 20 25 30
(b) ETCHING TIME (min)
FIG. 9. Dependence of etch dcpth on time for base line operating conditions.
(a) GaAs and (b) AIGaAs.
for GaAs and about 45 s for AIGaAs under the base line
operating conditions. These times are similar to those re
ported for other chlorine-bearing discharges, such as a
Clz -Ar mixture.6 Since the etch rates in this study are
smaller ( < 0.1 ,urn/min), the same fluctuation in lag time
will result in a smaller change in the total etch depth. Zero
lag times have been obtained by using a BCI} -C12 mixture. <)
The large area of sidewall erosion that occurred under
base line operating conditions is understandable, since the
Si02 masks were patterned by wet etching in buffered HF,
which produces an isotropic profile. The thin edges of the
masks were therefore etched away quickly, resulting in
FIG. 10. SEM micrograph ofGaA~ sample etched under base line operating
conditions nsing a trilevel resist mask. Little sidewall erosion has occurred.
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Sat, 22 Nov 2014 07:07:5945 Cooperman et at: Reactive Ion etching of GaAs and AIGaAs
sidewall erosion. Two new masks with vertical features were
tested in an attempt to eliminate such erosion: an SiOz mask
patterned by RIB using CF4, and a trilevel resist mask pat
terned by RIE using O2•16 Some sidewall erosion was still
observed with the dry-etched SiOz mask, presumably be
cause a completely vertical mask profile was not achieved.
Little mask degradation occurred for the trilevel resist mask,
however, so that there was little or no erosion of the etched
sidewall (see Fig. 10). The GaAs surface morphologies were
rougher with the two new masks than with the wet-etched
SiOz mask, perhaps because of ion bombardment of the
semiconductor surface during RIB patterning of the masks.
Another possible explanation is the formation of a carbon
residue on the Si02 mask during the CF4 etch and oxide
formation on the trilevel resist mask during the O2 etch.
B. Cl concentration
The relative dependence of the Cl concentration [Cl J, as
determined by actinometric measurements, on BCI, percen-
£1
0
0 100
lal
30
~
'" ::;
~
l!!
.1::
'" :!
£
(b) PRESSURE /mTorr)
5
'" .t: " :::I
~ 4
~ :c
~ 3
Q.
2
0 10 20 30 40 50
Ie) POWER (W)
FIG. 11. CI concentration dependence on (a) Bel] percentage, (0) total
pressure, and (c) power, for base line operating conditions. The data have
an estimated accuracy of ± 10%.
J. 'lac. Sci. Technol. a, Vol. 7, No.1, Jan/Feb 1989 45
tage, total pressure, and power is shown in Figs. 11 (a),
11 (b), and 11 (c), respectively. Each figure gives the results
of experiments in which one operating parameter was varied
while the others were kept at their base line values. It is seen
that [Cll increases sublinearly with increasing BCI, percen
tage, linearly with increasing total pressure, and sublinearly
with power. These relationships, as well as the correlation
between [CI] and the GaAs etch rate, are discussed in the
following section.
IV. DISCUSSION
The observed dependence of [CIl on the operating param
eters of the RIE system can be understood qualitatively in
terms of the balance between the generation of CI atoms by
dissociation of BCl, and their recombination to form Cl2
molecules, which is expected to be the dominant mechanism
for removal of Cl atoms from the plasma. The generation
rate is proportional to the product of the BCI] concentration
[BCI1] and the electron density, while Richards et al. 13 have
suggested that in a C12 plasma the recombination rate is pro
portional to the square of the Cl concentration. Thus,
BCl3 dissociation: R" = k" [BCI b [e-] ,
Cl recombination: R r = k r [ CI J l Cl] . (3)
(4)
Therefore the steady-state value of [Cl] is predicted to in
crease sub linearly with increasing BCI] percentage, as
shown by the data of Fig. 11 (a) .
Comparison of Figs. 2 and 11 (a) shows that the GaAs
etch depth and [Cll exhibit a similar dependence 011 BCl3
percentage over the range from 12.5% to 87.5%, indicating
that the CI concentration is a major determinant ofthe etch
depth in this range. The drop in the etch depth at BCI] per
centages approaching 100% may be due to changes in the
plasma properties (e.g., electron energy distribution and
sheath voltages) caused by the removal of Ar from the dis
charge.
Figure 11 (b) shows that the value of [Cll increases lin
early with total pressure. If the rate of CI recombination
depends quadratically on [Cl]. in accordance with Eq. (4),
for [Cll to have a linear pressure dependence the rate of Cl
production, i.e., Rei in Eq. (3), would have to have a qua
dratic pressure dependence. Since [BC131 should increase
linearly with pressure, such a quadratic pressure dependence
of Rd would imply that the product kd [e -] increases linear
ly with pressure. The electron concentration is determined
by the diffusive and field-driven losses to the electrodes. At
low pressures, the value of [e --] is expected to be roughly
proportional to pressure, since the electron loss rate is deter
mined by ambipolar ditfusivity and mobility, which are in
versely proportional to pressure. Although the electron en
ergy distribution changes with pressure, k" should not be
very sensitive to pressure, because the dissociation of BCI}
can take place by low-energy processes such as dissociative
attachment, so that the fraction of electrons with sufficient
energy to cause dissociation change..<; little with average elec
tron energy. Therefore the product k" [e ] [BC131 should
exhibit the quadratic pressure dependence required to obtain
the linear pressure dependence observed for [Cll.
The increase in residence time of gas species in the
~ ~ .". -, •• _. -•••••• , ........ 'Y~".' •. ', ••• ' ••••••••••••••••••••••••••••• "; •••••••••••••••••••• "; •.•.••••• ~
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Sat, 22 Nov 2014 07:07:5946 Cooperman et aI.: Reactive ion etching of GaAs and AIGaAs
chamber with increasing pressure should have little effect on
[Cll. At 5 mTorr, for example, the residence time is 1.5 ms,
while the diffusion time from the glow to an electrode is
about 0.2 ms (as given by L2 /4D, where L is the interelec
trode spacing and D is the diffusivity.) At 30 mTorr, the
residence time is again nearly an order of magnitude larger
than the diffusion time. Therefore most Cl atoms have suffi
cient time to experience many collisions with the electrodes
and/or samples, and thus to be lost by recombination or
reaction, before being pumped from the chamber.
Comparison of Figs. 4 and 11 (b) shows that the GaAs
etch depth and [CI] do not have the same depen~ence on
pressure, especially at high pressures, where the etch rate
becomes approximately constant. The difference may be due
to the decrease in ion bombardment energy with increasing
pressure, which tends to reduce the etch rate. It has also been
suggested that the sublimation rate of the etch products may
limit the etch rate at higher pressures. 6
The power dependence of [ CI], as shown in Fig. 11 (c), is
similar to that of the GaAs etch depth (Fig. 7). The increase
in [CIl with increasing power is presumably due to the in
crease in electron density, which in accordance with Eq. (3)
results in a higher BCl3 dissociation rate. The sublinear de
pendence on power may be due to BCl3 depletion or to in
creased Cl recombination rates at higher power levels.
The GaAs etch rates observed in this work are somewhat
lower than those obtained for other chlorine-bearing dis
charges.3-7 This is partly because BCl3 is not believed to be as
efficient a generator of Cl as other gases. For example, opti
cal emission spectroscopy has shown the BCl3 discharges
display lower Cl emission intensities than CC14 discharges. [7
Another reason for the smaller etch depths is the use of very
low power densities (0.06-0.22 W /cm2) in order to avoid
excessive degradation of the Si02 mask, which was com
pletely removed by a 20-min etch above 40 W (0.22
W fcm2). With the trilevel resist mask, however, little
sidewall erosion was observed at 25 W. With this mask, by
increasing the power it should be possible to obtain much
higher etching rates with acceptable sidewall erosion. The
etch rate might also be increased by adding Cl2 to the Bell -
Ar mixture in order to increase the Cl concentration in the
discharge, provided that the BCl3 concentration remains
high enough for efficient scavenging of oxygen and water
vapor.
V. CONCLUSION
Reactive ion etching of GaAs and AIGaAs has been stud
ied using BCl, -Ar gas mixtures. Equirate etching is ob-
J. Vac. Sci. Technol. S, Vol. 7, No.1, Jan/Feb 1989 46
tained for BCl3 percentages greater than a few percent. The
optimum conditions for etching anisotropic profiles are as
follows: (1) BCl3 percentageof62.5%, (2) total pressure of
5.0 mTorr, and (3) power density of 0.14 W/cm2 (25 W).
Data on relative changes in the CI concentration, which were
obtained by optical emission actinometry, show that this
concentration is a major factor in determining the etch rate.
In view of the equirate etching and high degree of anisot
ropy achieved in this study, reactive ion etching in a
BCI) -Ar mixture appears to be a promising technique for
fabricating semiconductor diode lasers and optoelectronic
integrated circuits.
ACKNOWLEDGMENTS
The authors would like to thank P. D. Nader for technical
assistance, M. K. Connors for providing the AIGaAs sam
ples, and P. M. Nitishin for making the SEM studies. This
work was sponsored by the Defense Advanced Re..<;earch
Projects Agency.
a) Present address: Digital Equipment Corporation, Hudson, Massachu
setts 01749.
b) Department of Chemical Engineering, Massachusetts Institute of Tech-
nology, Cambridge, Massachusetts 02139.
'E. L. Hu and R. E. Howard, J. Vac. Sci. Techno!. B 2,85 (1984).
2G. A. Vawter, L. A. Coldren, J. L. Merz, and E. 1. Hu, App!. Phys. Lett.
51,719 (1987).
'J. Chaplart, B. Fay, and N. T. Linh, J. Vac. Sci. Techno!. B I, 1050 (1983).
4M. B. Stern and P. F. Liao, J. Vac. Sci. Techno!. B 1, 1053 (1983).
5H. Nagasaka, H. Okano, and N. Motcgi, in Proceedings o/the Symposium
on Dry Process (Institute of Electrical Engineers of Japan, Tokyo, 1982),
p.79.
0y. Yamada, H. Ito, and H. Inaba, J. Vac. Sci. Techno!. B 3,884 (1985).
7G. Gliiersen, J. Vac. Sci. Techno!. 12, 28 (1975).
"K. Asakawa and S. Sugata, Jpn. J. AppJ. Phys. 22, L653 (1983).
"H. Tamura and H. Kurihara, Jpn. J. App!. Phys. 23, L731 (1984).
I()R. G. Poulson, H. Nentwich, and S. Ingrey, in Proceedings o/the Interna
tional Electron De1lices Meeting, Washington, D. C., 1976 (Electron De
vice Society ofIEEE, New York, 1976), p. 205.
"K. Tokunaga, F. C. Redeker, D. A. Danner, and D. W. Hess, J. Electro
chern. Soc. 128, 851 (1981).
12J. W. Coburn and M. Chen, J. Appl. Phys. 51, 3134 (1980).
13A. D. Richards, B. E. Thompson, K. D. Allen, and H. H. Sawin, J. App!.
Phys. 62,792 (1987); A. D. Richard!'. and H. H. Sawin, ibid., 62, 799
(1987).
14K. Asakawa and S. Sugata, J. Vac. Sci. TechnoL B 3, 402 (1985).
15G. J. Sonek and J. M. Ballantyne, J. Vac. Sci. TechnoL B 2, 653 (1984).
"'H. Gokan, M. Itoh, and S. Esho, J. Vac. Sci. Techno!. B 2,34 (1984).
17D. W. Hess, Solid State Technol21, 189 (1981).
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1.343773.pdf | Etch rates and surface chemistry of GaAs and AlGaAs reactively ion etched in C2H6/H2
S. J. Pearton, W. S. Hobson, and K. S. Jones
Citation: Journal of Applied Physics 66, 5009 (1989); doi: 10.1063/1.343773
View online: http://dx.doi.org/10.1063/1.343773
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35Etch rates and surface chemistry of GaAs and AIGaAs reactively ion
etched in C2HS/H2
s. J. Pearton and W. S. Hobson
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
K. S. Jones
University of Florida, Gainesville, Florida 32611
(Received:; June 1989; accepted for publication 25 July 1989)
The etch rates of GaAs and Al,Ga] _xAs (x = 0.09-1) in C2H6/H2 were investigated as a
function oftime 0-12 min), gas flow rate (5-25 seem), total pressure (4-30 mTorr), plasma
power density (0.56-1.32 W em-2), and percentage ofC2H6 in the discharge (1O%-50%).
The etch rates are constant with time, and decrease with increasing Al content in the AIGaAs.
The maximum etch rates occur at 25% by volume C2H., in H2 and increase linearly with
increasing power density. Increasing the total pressure at constant gas composition reduces the
etch rates by approximately a factor of 2 between 4 and 30 mToH. The etched surfaces have
smooth morphologies for C2H6 concentrations less than -40% of the total gas volume. A
layer of subsurface dislocations approximately 40 A deep were observed in GaAs by
transmission electron microscopy for the highest-power density discharges, while the surfaces
for all samples are As-deficient to a depth of ~ 30 A after reactive ion etching. Polymer
deposition is not significant for CZH6 volumes less than 40% of the total gas volume.
I. INTRODUCTiON
Chlorine-based gas chemistries have been the mainstay
of dry etching techniques for III -V semiconductors since
their demonstration in the early 1980's.,,2 In many device
applications, gases such as Clz, CC14, and SiC14 provide per
fectly adequate anisotropic etching with reasonably smooth
and dean surfaces. 1-5 The problems with the corrosive na
ture of chlorine can be minimized by using chlorofluorocar
bons such as CC12F2 (freon-12) which are noncorrosive and
nontoxic, and therefore less difficult to handle. I However,
there are still several undesirable features of freoll-12 based
dry etching of III -V materials including the often significant
polymer deposition (even for O2 additions to the discharge),
and sensitivity of the etch rates to the condition of the
chamber walls and electrode surface material. The etching of
In-based semiconductors in freon-12 usually leads to very
rough surface morphologies due to the low volatility of indi
um chlorides 0 6-8 The etch rates for GaAs are often very high
( -1 /-lm min -]) and therefore are not controllable for ap
plications requiring the removal of relatively small amounts
of material «500 A) 0 Lastly, environmental concerns with
chlorofluorocarbons affecting the ozone layer in the atmo
sphere have led to moves to ban their use.
There has been extensive interest in the last few years in
the use of methane- or ethane-hydrogen mixtures for reac
tive ion etching of compound semiconductors.9-i2 Smooth
controlled etching has been demonstrated for InP, InGaAs,
InGaAsP, and GaAs using these gas mixtures, although
there has been no detailed study of the surface composition,
etch rates, and residual damage in these materials as a func
tion of the discharge parameters. Although the use ofCH41
H2 or CzH(/H2 has more advantages for the dry etching of
In-based materials, it is worth examining more dosely their
use for GaAs and AIGaAs mesa structures. In particular, InGaAs or InAs capping layers are being increasingly used
on top of GaAs-AlGaAs structures to achieve low contact
resistances, and one would prefer a dry etching chemistry
that is capable of smooth removal of both In-and Ga-based
semiconductors. Moreover the ethane or methane mixtures
leave polymeric deposits around the reactor chamber walls
which are important sources of active species for the etching,
but which are potential sources of contamination if there is
switching between gas mixtures depending on whether a Ga
or In-based layer is to be removed.
In this paper we report an investigation of the etch rates
of GaAs and AlxGal~xAs as a function of etching time,
total pressure, plasma power density, gas flow rate, and gas
composition for reactive ion etching (RIE) in C2H6/H2o
The etched surface morphology was examined by scanning
electron microscopy (SEM) and near-surface damage inves
tigated by transmission electron microscopy (TEM). The
elemental composition in the top 100 A of the etched sam
ples was obtained from Auger electron spectroscopy (AES)
and x-ray photoelectron spectroscopy (XPS) measure
ments. We have previously reported near-surface hydrogen
passivation effects in GaAs and AlGaAs reactively ion
etched in C2H(/Hz as a function of the substrate tempera
ture during the RIE treatment. 13
iI. EXPERIMENT
The GaAs samples used in this work were semi-insulat
ing, undoped, (100) substrates cut from crystals grown by
the liquid-encapsulated Czochralski (LEC) technique. Pri
or to patterning with photoresist they were etched in
5H2S04:1H202:1H20 for 5 min at 70·C to remove residual
polish-induced damage that might affect the etch rate. The
AIGaAs layers were grown by organometallic vapor phase
epitaxy (OMVPE) on GaAs substrates within a barrel~ge-
5009 J. AppL Phys. 66 (10), 15 November 1989 0021-8979/89 /225009-09$02.40 @ 1989 American Institute of Physics 5009
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35ometry reactor operating at atmospheric pressure. The
source chemicals used were trimethylgallium (TMG), tri
methylaluminum (TMA), and arsine (AsH3) at a V-III ra
tio of 30. The layers were grown at 700 °C at a rate of2.2 pm!
h -I, and exhibited featureless surface morphologies. The
AlAs mole fraction was varied from 0.09 to 1, and the com
positions were determined from room-temperature photolu
minescence and electron beam electroreftectance measure
ments. Typically the undoped AIGaAs was n-type with a
carrier concentration around 1O!5 cm-3.
For etch rate measurements the samples were selective
ly patterned with AZU50J photoresist to give a mask with
openings of size 1-50 pm in width. Immediately prior to
loading into the RIE chamber the samples were exposed for
3 min to a 50-W O2 plasma in a barrel reactor and then rinsed
in a mixture of ammonium hydroxide and water to descum
the mask openings and to strip away the native oxide on both
the GaAs and AIGaAs.
All of the samples were etched in a stainless steel, paral
lel plat.e reactor (Materials Research Corporation Model
51) operating in the RIE mode. The lower, powered elec
trode was 15 em in diameter and was covered with a quartz
cover plate which we found was necessary in order to obtain
reproducible etch rates. If the samples were simply laid on
the steel electrode we tended to get rough surface morpholo
gies and Fe was found on these surfaces. In all cases, the
samples were thermally heat sunk to the cathode with high
vacuum grease, and flu oro-optic probe measurements indi
cated that temperature rises during our longest etch times
(12 min) did not exceed 30°C from the ambient tempera
ture. The discharge frequency was 13.56 MHz and the elec
trode spacing was 7 cm. The system was pumped by mechan
ical and diffusion pumps to z.:;3x 10-6 Torr before
introduction of research grade C2H6 and H2 through elec
tronic mass flow controllers. The GaAs and AIGaAs etch
rates were examined for their dependence on total pressure
(discharges could be controllably maintained between 4-30
mTorr in our system), plasma power density (0.56-1.32
W cm-2), CzH6ratio by volume to H2 in the discharge (0.1-
0.5), and gas flow rate (5-25 seem).
After etching, the photoresist on patterned samples was
removed by rinsing in acetone and the etched depth was
measured by Dektak stylus profilometry. The surface mor
phology on these samples was examined by SEM, with all
micrographs taken at an 80° tilt angle. Unpatterned sections
were also prepared for cross-sectional TEM by chemical
thinning and ion milling. A JEOL 200CX microscope was
used, and all micrographs were taken using multibeam
bright-field imaging with seven beams included within the
objective aperture. The sample was tilted such that the beam
direction was parallel to the [110] zone axis. This reduces
any contrast effects at the surface and best allows one to see
the surface topography. Weak beam, dark-field images were
also taken at the same magnification using g220 (S = g) con
ditions. Samples for AES were all analyzed under identical
conditions, and elemental depth profiling was accomplished
by sputtering with 3.5-keV Ar~ ions with a sputtering rate of
4 A min -I. XPS with angle-resolved capabilities was used to
measure both the atomic composition of the near-surface
5010 J. Appl. Phys., Vol. 66, No.1 0, 15 November 1989 region and the chemical bonding of the Ga, As, and Al
atoms. All chemical analysis were performed after removal
from the RIE chamber. Prior to examination with AES or
XPS, the samples were kept in hermetically sealed con
tainers in a dry N2 ambient to avoid oxidation as much as
possible. However, we take the view that exposure to the
ambient is exactly what will happen during practical device
processing steps and analysis of such surfaces is therefore
relevant.
III. RESULTS AND DISCUSSION
A. Etch rate dependencies
Based on the original report by Niggebrugge et al.9 that
reproducible, polymer-free RIE of In-based materials is ob
tained only for relatively small fractions of ethane or meth
ane relative to hydrogen in the discharge, we chose as our
standard etching conditions a 2CzH6: 18H2 ratio, total pres
sure of 4 mTorr, flow rate of20 seem, and a power density of
0.85 W cm-2 (self-bias on the cathode of 430 V). Figure 1
shows the time dependence of etch depth in GaAs and
AIGaAs for RIE times up to 12 min. For the AIGaAs there
appears to be a delay in the commencement of etching upon
ignition oftlle plasma. Since this delay increases for increa.'>
ing Al content in the AIGaAs, this may be related to the need
to etch (or sputter) away aluminum oxide on the sample
surface before true RIE of the AIGaAs begins. The etched
depths for both GaAs and AIGaAs are linear with time, and
we observed no significant difference for the depths mea
sured in small features (2-,um-wide lines) relative to more
open areas (50 pm on a side triangle) in the mask. The aver
age etch rate of GaAs and Alx Gal _ x As as a function of etch
5000.--------------------------,
4500
4000
~ 3500 Q«
~ 3000
a.. w
Cl 2500 a w ::r: ;= 2000
w
1500
1000
500 -CzHs-H2 -Ar
0.85 W' em-2
20 seem
4 mtorr
e GaAs
o A.10.0sGaO.S1 As
.. Aio.2SGaO.72As
" AJ0,41 GaO.5SAs
" A.lO.64 GaO.36As
o Ai.As
ETCH TIME (min)
FlG. 1. Etched depth in GaAs and AIGaAs as a function of time in a
2C2H,,:18H2, 4 mTorr, 0.85 W cm-2 discharge.
Pearton, Hobson, and Jones 5010
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35time are shown in Fig. 2. Our experience with plasma hydro
genation has shown that etching of GaAs and AlGaAs is
minimal under the kind of conditions used in these experi
ments. This implies that the primary reactants responsible
for removal of Ga and Al are organic radicals. There has
been no direct identification of the etch product, although
organometalIics such as trimethylgaHium have been sug
gested. I t. t2 Whatever the exact etch products, the results in
Fig. 2 suggest that the organogamum complex is more easily
desorbed than the corresponding organoaluminum species.
I t has previously been pointed out that the etch rate of HI -V
materials in CH4/H2 decreases with increasing Ga content,9
and our results show that the presence of Al in the material is
even more of an impediment to the etch raie.
The relative fraction of ethane and hydrogen in the dis
charge is a critical parameter in determining the etch rate of
GaAs and AIGaAs, as shown in Fig. 3. The etch-rate peaks
around 25% of C2H6 by volume in the plasma. This is some
what different from the result obtained by Matsui et al.12
who reported maximum etch rates for GaAs around 12%
CzHo by volume. Cheung et al. 10 found their maximum etch
rates to be at a ratio of 1:5 CH4/H2 for GaAs. We might
expect slightly different rates when using C;>Ho/H2 com
pared to CH4/HZ simply because of the different C-to-H ra
tios and the different populations of reactive species to be
found in the respective discharges. The differences between
our results and those of Matsui et al., 12 who had fairly simi
lar etching conditions, might well be due to subtle effects
such as the condition of the reactor walls and the masking
material used on the samples. It has been previously noted
that the reactor walls must be properly conditioned with a
polymer coating to ensure reproducible etching because this
polymer is a source of active species for the plasma. 14 More-
400r--------------------------.
CzHs-H2-Ar
0.85 W·cm-2
20 seem
4 mtorr
• GaAs
c AfO.09GoO.91As
... AfO.2sGoo.nAs '" Ai0,41GoO.5SAs
II AiO.S4GoO.:56As
o AlAs
o::!,
~ !! f ~
~ 200L r--t----""-----------1
u i-
~ .. t T t
~ +---t-----'f-----------"--
~ 100 --I!1!I1-----rt-----.........li!!iIL r----r------___ D
I
Olb-__ ~ __ ~ __ _L __ ~ __ ~ ____ ~~
o :2 4 12 14
ETCH TIME (min)
FIG. 2. Average etch rate of GaAs and AIGaAs as a function of time under
the discharge conditions of Fig. 1.
5011 J. Appl. Phys., Vol. 66, No. 10,15 November 1989 400~·--·-' ---------------,
CZH6-HZ-Ar
....
'e 300,-
E 0.85 W· cm-2
20 seem
4 mtorr o GaAs
o Aio.OgGoO.!H As
.& Aio.2SGoo.nAs
'" A10.41Go O.59As
.. Al0.64GoO.3SAs
u AiAs
FIG. 3. Average etch rateofGaAs and AIGaAs as afullction of gas compo
sition in a C,H6:H" 4 mTorr, 0.85 W cm-2 discharge.
over the type of masking material (photoresist in our case,
Si02 in the case of Matsui et at.) 12 might also effect the rela
tive populations of plasma species at the sample surface. Fin
ally Niggebrugge et al.9 have reported a dependence of etch
rate of InP in CR/H2 on the ratio of masked-to-exposed
areas on the sample and on the relative spacing of samples
from each other. This sensitivity to experimental conditions
is an unfortunate fact weB recognized by most people in the
dry etching arena, being common to almost an dry etch pro
cesses. The increase in etch rate we observe for C2H6 frac
tions up to 25% is presumably due to an increase in the
active species concentration. Above 25% ezHo by volume
there appears to be a competition between polymer depo
sition and etching, and the etch rate decreases with increas
ing ethane concentration. At high C2H6 concentrations
( > 45%) a brown film could be observed on the photoresist
mask, and there was a very heavy polymeric coating around
the reactor walls and on the electrodes.
Under our conditions the etch rates of GaAs and
AIGaAs are independent of the gas flow rates, as shown in
Fig. 4. We estimate the nominal residence times in our reac
torto vary from 1.25 to 0.25 s for flow rates between 5 and 25
seem, but even these relatively small values appear to be
longer than the surface reaction time for removal of Ga, AI,
and As.
The dependence of the average etch rate on the total
pressure in the reactor at constant flow rate (20 secm) is
shown in Fig. 5. This appears to be predominantly related to
the decrease in the cathode self-bias at higher pressures
-430 Vat 4 mTorr and 255 Vat 30 mTorr. It has previous-
ly been established that at higher pressures III-V materials
will etch faster for increasing pressures up to a maximum
Pearton, Hobson, and Jones 5011
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35400~--------------------------,
";"c: 300 -
'E
w I« a::
:z:: 200
u l-
I.&.!
W
~ « a:: w > « 100 C2Hs-HZ-Ar
0.85 W ·em-2
4 mtorr
¥ f,
r---f-------i----!
~---r-------t !
~ , :r----11--------y-
~
OL-__ ~ __ ~ __ ~ __ .-LI __ ~I __ ~I~_~
o 4 8 12 16 20 24 28
GAS FLOW RATE (seem)
FIG. 4. Average etch rate of GaAs and A1GaAs in a 2C2H,,: ISH2, 4 mTon,
0.85 W em -2 discharge as a function of gas flow rate.
value determined by the exact plasma parameters, and then
decrease.9•15 This decrease has been ascribed to increasing
polymer deposition. It is logical that at higher self-biases the
more energetic ion bombardment win be more effective at
removing the polymer by sputtering, and under our condi-
400:-CzHs-H2 -Ar
0.85 W' em-2
20 seem
r~ 300f
@«
w I«
a:: 200
:t:
U I
W
W
~
0::
~ 100 « .. GoAs
o Aio.OgGoO.91 As
.. A.2.0.2sGao.nAs
" .11.10.41 GaO.59As
" A!O.64 G(JO.36As
o AJ.As
TOTAL PRESSURE (mtorr)
FIG. 5. Average etch rate of GaAs and AIGaAs in a 2C2H6:18H2, O.RS
W cm-2 discharge as a function of the total prcssw'e in the re.actor.
5012 J. Appi. Phys., Vol. 66, No. 10, 15 November 1989 500...--------------·---
400 -... ,
c:
E
0<
w 300
I-« a::
:r u I-
W 200-
w (!l « a: w >
~ 100 C2HS-H2-Ar
20 seem
4 mlorr
.. GaAs
o AiO.OgGcO.91 As
.. Aio.2SGoo.nAs
c, Al0.41 GoO.59As
IS AiO.64GcO:ssAs
oAP-As
o '--_1-.._.l..-_~.-1....- I o 0.2 0.4 0.6 0.8 1.0 1.2 1.4
PLASMA POWER DENSITY (W' cm-2)
FIG. 6. Average etch rate of GaAs and AIGaAs in a 2C2H,,: 18H2• 4 mTorr
discharge as a function of the plasma power density.
Hens this appears to be the most significant factor in deter
mining the etch rate as a function of total pressure.
Figure 6 shows the dependence on plasma power den
sity of the etch rates of GaAs and AIGaAs. There is an essen
tially linear increase with increasing power density. This is
consistent with previous observations for a variety of both
Ga-and In-based semiconductors.9-13 The rate of increase in
etch rate is greater for GaAs than for AIGaAs as shown by
the slope of the lines in Fig. 6 and with an increasing AlAs
mole fraction these slopes are further reduced. The self-bias
on the cathode increased from 220 V at a power density of
0.56 W em -2 to 610 Vat 1.3 W cm-' 2. Measurable etch rates
were obtained only for power densities above 0.56 W cm-2,
indicating that the purely chemical component of the etch
ing is very small and some degree of ion sputtering is neces
sary either to increase the desorption rate of the etch prod
ucts or to provide the energy necessary to promote the
surface reactions to completion.
B. Surface morphology
Smooth surface morphologies on GaAs were obtained
for C2H6 concentrations in the discharge ofless than 40% by
volume. Figure 7 shows SEM micrographs from GaAs sam
ples reactively ion etched under similar conditions (4
mTorr, 4 min, 20 seem, 0.85 W cm 2) except that the ratio
of C2H/}:H2 was 2: 18 in one case, and 8: 12 in the other. Under
the former conditions the etched surface is featureless and
there is no evidence of polymer deposition either on the
sidewalls or on the exposed surface. For the high ethane
concentration condition the surface morphology in the field
of view of the SEM is relatively rough. Once again there is
disagreement 1n the literature about the plasma conditions
Pearton, Hobson, and Jones 5012
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35under which the best morphologies are obtained for etching
GaAs.IO•12 In general we observed smooth surfaces for total
pressures less than approximately 20 mTorr and for CzH",
concentrations less than 40%, as described above. The most
anisotropic etching was also obtained under these condi
tions, with vertical sidewalls. For higher pressures and larg
er ethane fractions the sidewalls showed increasing under
cutting. Increasing the plasma power density also improved
both the anisotropy and surface morphology when holding
the other parameters constant, which again emphasizes the
role ion bombardment plays in this etching chemistry.
In general we observed somewhat rougher surface mor
phologies on AIGaAs reiative to GaAs, with poorer mor
phologies for increasing AlAs mole fraction in the AIGaAs<
The range of plasma conditions under which we observed
smooth etching was more restricted with AIGaAs-power
densities had to be at least 0.85 W em -2, total pressures less
than approximately 15 mTorr, and C2H6 concentrations less
than 30% by volume in the discharge. Figure 8 shows SEM
micrographs from A 1009 G3.o.91 As and Alo.04G3.o.36A8 sam
ples after a 4-min RIB treatment in 2C2H6: 18Hz plasma at 4
mTorr and a power density of 0.85 W cm-2
< Under these
conditions the surface morphologies are quite smooth.
We also examined the microscopic smoothness of
C2H6/H2 etched surfaces by cross-sectional TEM. Figure 9
shows TEM micrographs taken in either bright-field or
5013 J. Appl. Phys., Vol. 66, No. 10, 15 November 1989 FIG. 7. SEM micrographs from GaAs
reactively iOIl etched in a 4 mTorr, 0.85
W cm-2, C2H6/H2 discharge. At the
left-hand side the discharge was 2C2H,/
I8H" while at the right-hand side the
discharge had the composition 8C2H,/
12H~.
weak-beam dark-field imagin.g conditions from a GaAs sam
ple etched in a 2CzH6: 18H2, 4 mTon, 1.3 W em -2 discharge
for 4 min. The sample has a smooth surface topography with
a peak-to-valley hei.ght less than 20 A. Under these very
high-power conditions a band of subsurface dislocations ap
proximately 40 A deep is observed. These are more clearly
observed in the weak-beam dark-field image. We can con
trast these results to those obtained for CCl2F2:02 RIE of
GaAs, where under high-power density etching very rough
surface topographies are observed (peak-to-valley heights
-300 A).16 Subsurface bands of dislocations were also ob
served in these CClzFz:02 etched samples. These were re
duced in density, but are not totally eliminated even for an
nealing at 800 °C for 10 s,
c. Surface composition
The composition and chemical bonding in the near-sur
face region of the RIE treated samples were examined by
AES and sman-area XPS. Figure 10 shows AES surface
scans of a GaAs control sample, and samples etched for 4
min in C2H6/H2 under various conditions. Carbon, oxygen,
and the lattice constituents are the only elements detected,
and the main difference between the samples appears to be a
depletion of As in those etched in the C2H(/Hz discharge.
FIG. 8. SEM micrographs from
AIGaAs reactively ion etched in a 4
mTorr, 0.85 W em-', 2C2H,,:18H, dis
charge. At the left-hand side the materi
al was Aio.!)9 Gao." As while at the right
hand side the composition was
Alo.64 Guo J. As.
Pearton, Hobson, and Jones 5013
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35FIG. 9. TEM cross sections from a GaAs sample etched for 4 min in a 1.3
W em -2,4 mTorr, 2C2Iio:18Hz discharge. At top the contrast conditions
are weak beam, dark lleld, showing a shallow band of dislocations. At bOi
tom the image conditions are bright field.
This would be expected because of the high hydrogen con
centration in the plasma which will remove both arsenic and
AS203• Figure 11 shows AES depth profiles of C, 0, Ga, and
As in these same samples. The As deficiency persists to a
depth of -30 A in the etched GaAs, and there appears to be
more oxide present on the surface.
XPS survey spectra from the GaAs control sample, and
a section of GaAs etched for 4 min in a 1.3 W em -2, 4
mTorr, 2C2H&:18H2 discharge are shown in Fig. 12. Based
on this type of data the average elemental composition in the
top 100 A. of each sample was estimated and is reported in
Table I. The surface C concentration varied from 29 to 37
at. % which is within the range expected for atmospheric
contamination. The oxygen concentration in the near-sur
face region is clearly higher on the etched samples, and this
may be related to a higher chemical reactivity of these sur
faces because ofthe ion bombardment occurring during the
RIE treatment. While there may be a slight Ga deficiency in
the etched samples due to more oxidation there is a clear
reduction in the As content near the surface after RIE.
High-resolution XPS data were also obtained for C( Is)
O(1s), Ga(3d), and As(3d) transitions. These data were
curve-fitted to resolve the presence of multiple components.
The resulting binding energies, probable assignments and
atom percent compositions are presented in Table n. The
high-resolution C( ls) data show that a variety of carbon
5014 J. Appl. Phys., Vol. 66, No. 10, i5 November 1989 w
zw
""0 "0 . w 2000
1000
0
-1000
C
-2000
2000
1000
0 ( rA
I
-1000
C
-2000 II
2000
1000
0
-1000
-2000
2000
1000
o
-1000 CONTROL
GoAs
o Go
C2 Hs/H2 2716
O.85W. cm-2
F~ fT., -
Go
0
I I I
-2000~~--~--~--~--~
400 600 1200 1600 2000
KINETIC ENERGY (eV)
FIG. 10. AES survey spectra from GaAs samples etched for 4 min in C,H,/
H2 discharges of various compositions and power densities.
species were present on the samples. These include C~C.
C~~H, C-O---C, C---O-H, o=C--·O-C, and
O==C-O··-H which are detected on an samples, while on
low-power density etched GaAs we also find small traces of
the ketones C3=O and H2C=O. Most of the carbon on all
samples is present as hydrocarbons (C-R where R = C or
H), but ether/alcohol (C-R), and organic acid/ester
(O=C = OR) species are also present. The oxygen is pre
dominantly present as metal oxides although C=O species
are also detected. The Ga and As are present in the form of
GaAs and various oxides GaOx• AsZ03• and AszOs).
AES survey spectra from both etched and unetched
Alo.z8 Gao 72 As and Alo.41 Gao.59As samples are shown in
Fig. 13. There does not appear to be any more C and 0
present on the etched surfaces than on the controls, but the
As is depleted in the former. The near-surface « 100 A)
elemental compositions from all of the samples are given in
Pearton, Hobson, and Jones 50i4
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35100
eo
60
100
80
60
I-z w
(.)
It:
W 0.
::I: 100
0 I-80 «
60
4
3
OJ As
As
As
GoAs
CONTROL
o CONTROL.
GoAl!!
C2HS/Hz
2116
0.85 W. cm-2
FIG. 11. AES depth profiles of
elemental composition in the
near-surface region of GaAs
samples relatively ion etched CzHs/Hz for 4 min in C2Hh/H2 dis-10/10
O.BoW 'cm-2 charges of various composi-
tions and power densities.
'" 0.':-:-__________________ _
~ 1100 0 o t 4
"' -' w
'" w ~
OJ -" :::> z GaAs
C2HS/Hz
"1.3 IN G cm-2
~1L-OO~----o
BINDING ENERGY (.V)
FIG. 12. XPS survey spectra from, top, GaAs control sample, and at bot
tom, a GaAs sample etched for 4 min in a 2C2H,,:18H2, 4 mTorr, 1.3
W cm-2 discharge.
S015 J. Appl. Phys., Vol. 66, No.1 0, 15 November 1989 2000
tUO.2SGaO.72As
1000 CONTROL
-1000
-2000
2000
1000
-1000
w
ZW -2000
"0'" 2000
w
1000
FIG. 13. AES survey spectra from AI".l" GaonAs or AI" •• Gllo,.As sam
ples before and after etching in a 2C2H,,:18H2, 4 mTorr, 0.85 W cm-2 dis
charge.
TABLE I. XPS elemental composition data measured from the top 100 A of
each sample and expressed i.n atomic percent units for the elements detect
ed.
Sample C 0 Al Ga As
GaAs control 29 30 18 23
GaAsRIE-l 29 38 17 16
GaAs RIE-2 37 36 14 14
GaAs RIE-3 33 38 15 14
Ale.l8 Gau.n As control 28 38 9 10 15
Ale.28GaonAs RIE-I 27 41 l! 10 11
AlAs control 27 35 20 18
AIAsRIE-l 29 42 20 9
RIB-! 2C2Ho:18H
" 0.85 W cm--', 4 mTorr
RIE-2 lOC2H6:lOHz, 0.85 W em-2, 4 mTorr
RIE-3 2C2H6:18H2, 1.3 W em-2, 4 mTorr
Pearton, Hobson, and Jones 5015
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35Table I and the XPS peak assignments are listed in Table n.
All of these results point to a degree of As depletion after
RIB in C2H~H2' This is confined to the uppermost 30-40 A
from the surface, as shown in the AES depth profiles of Fig.
14. It is important to note that there is no apparent Al en
richment in the etched AIGaAs. There is a somewhat thicker
oxide on the AIGaAs after RIE relative to the un etched con
trol. All of the samples were cleaned in NH40H:H20 imme
diately prior to their insertion in the reactor, and this re
moves the native oxide. The control samples were cleaned at
this time also, and all of the samples were stored in a dry N2
ambient to minimize subsequent oxidation prior to surface
analysis.
This trend of a thicker oxide on the etched material
holds also for pure AlAs, as evidenced by the XPS data in
Tables I and II. The surface of the AlAs is very clean after
the C2H6/H2 RIE treatment, as shown by the AES survey
spectra in Fig. 15. The As deficiency in this material occurs
to a depth of -40 A as shown by the elemental AES depth
proftIes in the same figure. The oxygen is present predomi-nantly as A1203 while the arsenic is oxidized as both AS203
and As20s' The high-resolution O( Is) data from the AlAs
control sample and its reactively ion etched companion are
shown in Fig. 16. The peak positions of the two components
are the same in both etched and unetched AlAs, and the
spectra differ only slightly in the relative intensities.
IV. SUMMARY AND CONCLUSIONS
The main conclusions of this work may be summarized
as follows:
( 1) The etch rates of GaAs and AIGaAs are constant
with time in CZH6/H2' and are reduced for increasing Al
content in the material. The maximum etch rates for both
types of material occur at a concentration of25% by volume
of CZH6 in the discharge. Some degree of ion bombardment
appears to be necessary for efficient desorption of the etch
products.
TABLE II. High-resolution ESCA data: Binding energies, atom percentages, and peak assignments. [Binding energies were corrected to the binding energy
of the C ( Is) signa! at 284.6 e V. Atom percentages were calculated from the high-resolution data. Peak assignments were based on the binding energies of the
reference compounds.]
Sample
Description C, C2 C, C4 0, O2 03 AI, Ga, Ga2 As, AS2 As,
GaAs control
Binding energies 284.6 285,8 530.8 532.1 19.0 20.3 41.0 44.2
Atom percents 26.0 5.5 21.0 9.2 13.0 5.4 16.0 7.1
GaAs RIE-l
Binding energies 284.6 286.0 287.2 288.7 530.9 532.2 533,5 19.4 20.6 41.3 44.2 45.6
Atom percents 19.0 5.7 2.4 2.1 25.0 11.0 1.9 10.0 6.7 9.8 4.0 2.2
GaAsRIE-2
Binding energies 284.6 286.0 287.5 289,0 531.0 532.4 19.2 20.5 41.3 43.9 45.1
Atom percents 23.0 7.7 3.4 3.0 22.0 14.0 6.8 7.2 9.2 3.1 1.7
GaAs RIE-3
Binding energies 284.6 286.3 288.6 531.2 532.6 19.4 20.7 41.4 44.5 46.0
Atom percentages 20.0 8.4 3.1 27.0 10.0 20.0 17.0 5.4 3.6 1.9
Alo.,. Gao.72 As control
Binding energies 284.6 286.1 288.2 531.1 532.1 74.4 19.3 20.6 41.3 44.2 45.7
Atom percents 20.0 6.6 1.6 23.0 15.0 9.0 6.5 3.5 10.0 2.0 3.0
Ala.2s Gao.72 As RIE-l
Binding energies 284.6 286.0 288.5 530.8 532.2 74.0 19.2 20.3 41.2 43.8 45.3
Atom percents 17.0 6.3 3.3 24.0 17.0 11.0 6.1 3.9 6.6 1.4 1.1
AlAs control
Binding energies 284.6 286.4 530.9 532.2 74.4 41.1 44.2 45.4
Atom percents 25.0 1.8 26.0 8.8 20.0 14.0 13.8 4.0
AlAs RIE-I
Binding energies 284.6 286.4 288.6 531.1 532.5 74.4 41.3 44.3 45.6
Atom percents 23.0 3.8 2.3 30.0 12.0 20.0 S.1 4.0 1.0
Peak assignments C,=C-R(R=C,H) 0, = metal oxides Ga, = GaAs As, '"" GaAs
C=C-O-R O2,03 = C=O, C··O-R Ga, = GaOx AS2 = As203
C,=R 2C=O AI,=AlP, AS3 = As2O,
C4=O=C-O··R
RIE-l 2C2H6:18H2, 0.85 W cm-'z, 4 mTorr
RIE-2 lOC2H6:lOH2, 0.85 W cm-·2, 4 mTorr
RlE-3 2C2H6:18H2, 1.31 W cm-2• 4 mTorr
5016 J. Appl. Phys., Vol. 66, No. 10, 15 November 1989 Pearton, Hobson, and Jones 5016
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136.165.238.131 On: Tue, 23 Dec 2014 11:13:35100.---------------,
1140.28GoO 72A•
60 CONTROL
60
.......... A.
Go
.......... A. _--Go
.. , A.
V:_---60
........... ·As
40 120 200
DEPTH (A)
2000
A!A.
1000 CONTROL FIG. 14. AES depth profiles of ele
mental composition in the near-sur
face region of Al"2.Ga".nAs and
Alo.", Gao.,. As samples etched for 4
min in a 2C2H6:18H2, 4 mTorr. 0.85
W cm-2 discharge.
/ ~, -o
-1000
~I"" -2000 '.'.., 2000
w
1000
o
iDDO
-2000
5017 iOO
eo
60 A~l [AI.
Ie \0
AA.A. ,
CZH6/H2
I .J._
A. f,u
c (}
400 4200
KINEilC ENERGY <oV)
ALA.
CONTROL
___ A!
-~ ,./ ...... " A~
A~A.
C2HS/H2
,~ __ ----Al.
.. ....... A.
o 2000
200 FIG. IS. AES survey and
depth profiles from AlAs sam
ples both before and after etch
ing for 4 min in a 2C2H6: 18H2,
4 mTorr, 0.85 Wem·2 dis
charge.
J. Appl. Phys., Vol. 66, No. 10, i5 November 1989 ft) g
0
I>J l-
e..> w I-
W
0
(f) z e
6
4
2
~540 t; 12
w
...J
W
Il':
~ 8
:::e
:::J z
4 OIS
520 Al.As
CONTROL
BINDiNG ENERGY (eV! 500
500
FIG. 16. High-resolution XPS O( ls) data from AlAs both before and after
etching for 4 min in a 2C,H6, ISH" 4 mTorr, 0.85 W em'-2 discharge.
(2) The etched surface morphology is smooth for CZH6
compositions of <40% for GuAs and 30% for AIGaAs. Sub
surface dislocation loops at a depth of -40 A are observed
for high power density etching of GaAs.
(3) Both GaAs and AIGaAs show As deficiencies to a
depth of 3D-AD A after C2H6/H2 RIB and there is little de
pendence of this depth on plasma power density. The prefer
entiulleaching-out of As from GaAs and AIGaAs in hydro
gen-based plasmas is well documented.
'E. L. Hu and Ro Eo Howard, Appl. Phys. Lett. 31, J022 (1980).
2M. B. Stern and P. F. Liao, J. "lac. Sci. Technol. B 1,1053 (1983).
3 A. Scherer, H. G. Craighead, and E. D. Beebe, J. Yac. Sci. Techno!. B 3,
402 (1985).
43. W. Pang, J. Electmchem. Soc. 133,784 (1986) .
'L, A. Coldren, Mater. Res. Soc. Symp. Froc. 126, 237 (1988).
6y. M. Donnelly, D. L. Flamm, C. W. Tu. and D. E. Ibbotson. J. Electro
chern. Soc. 129, 2533 (1982).
7L. A. Coldren and J. A. Rentschler, J. Vac. Sd. TechnoL 19, 225 (1981).
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(1985).
lOR. Cheung, S. Thorns, S. P. Beamont, G. Doughty, V. Law, and C. D. W.
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2061 (l989).
I"T. R. Hayes, presented at the 15th Annual Plasma Technology Seminar,
San Jose, CA (Tegal), May 1989 (to be published) .
\5N. Vodjdani and P. Farrens, J. Vac. Sci. Technol. B 5, 1591 (1987).
16S. J. Pearton, M. J. Vasile, K. S. Jones, K. T. Short, E. Lane, T. R.
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Pearton, Hobson, and Jones 5017
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1.343789.pdf | Characterization of the TiWGaAs interface after rapid thermal annealing
M. de Potter, W. De Raedt, M. Van Hove, G. Zou, H. Bender, M. Meuris, and M. Van Rossum
Citation: Journal of Applied Physics 66, 4775 (1989); doi: 10.1063/1.343789
View online: http://dx.doi.org/10.1063/1.343789
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/66/10?ver=pdfcov
Published by the AIP Publishing
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132.248.9.8 On: Tue, 23 Dec 2014 03:09:46Characterization of the TiW .. GaAs interface after rapid thermal annealing
M. de Potter, W. De Raedt, M. Van Hove, G. Zou, H. Bender, M. Meuris,
and M. Van Rossum
Interuniversity Microelectronics Center (IMEC), KapeldreeJ 75, B-3030 Leuven, Belgium
(Received 30 January 1989; accepted for publication 12 July 1989)
We report an extensive study of the TiW IGaAs interface after rapid thermal annealing
between 750 and 1050"c' Characterization of the interface was performed by secondary ion
mass-spectroscopy (SIMS), Auger, Rutherford backscattering spectroscopy (RBS), x-ray
diffraction, transmission electron microscopy, and electrical measurements. Schottky barrier
heights extracted from 1-Vand C-V data show a continuous increase with annealing
temperatures up to 950 ·C. The reverse J-V measurements exhibit a transition from tunneling
to avalanche breakdown. SIMS, Auger, and RES show significant motion of the Ti, resulting
in surface accumulation, as well as Ti diffusion into the GaAs substrate. Interface doping by Ti
produces an artificial enhancement of the Schottky barrier height.
I. INTRODUCTiON
The thermal stability of W -based films on GaAs is of
primary importance for the development of refractory gate
processes for self-aligned (MESFET) fabrication. This pro
cess requires the Schottky contact between the gate metal
and GaAs to remain stable at annealing temperatures ex
ceeding 800 ·C (900 ·C for rapid thermal annealing). One of
the first materials under investigation for this purpose has
been sputtered TiW. This compound is well known in silicon
technology for its use as a diffusion barrier, and it has suc
cessfully been used in a self-aligned process for the fabrica
tion of small-scale digital GaAs circuits.1,2 Nevertheless,
subsequent reports on refractory gate processes with TiW
gates have been rather mixed, as severe reproducibility prob
lems seem to occur at high annealing temperatures3 (typical
ly above 700 "C). Attempts have been made to improve the
stability of the metal-semiconductor interface by adding Si
or N as a third component to the TiW metallization.4,5 The
observed improvements were found to depend very strongly
on the composition of the ternary phase, but the barrier deg
radation mechanisms are not yet fully clarified,
In this work, we report on an extensive study of the
TiW IGaAs interface subjected to rapid thermal annealing
(R T A) from 750·C up to 1050 ·C. The interface has been
characterized by physical analysis [secondary ion mass
spectrometry (SIMS), Rutherford backscattering spectros
copy (RBS), transmission electron microscopy (TEM), x
ray diffraction (XRD), Auger spectroscopy J and by elec
trical measurements [current-voltage (1-V) and capaci
tance-voltage (C-Y) measurements on TiW diodes).
II. EXPERIMENT
The substrates were (100) LEe-grown GaAs wafers,
uniformly doped with silicon to a dose of 1017 at./cm3
(p_1O-2 n em). The wafers were degreased with organic
solvents and 90 X 90 pm2 square diode areas were patterned
using standard lithographic techniques, Prior to metaHiza
tion, the wafers were subjected to an in situ Ar plasma clean
ing (50 W, 5 min, 7.5 mTore). The base pressure of the
metallization system was 10-7 Torr. TiW films with a com-position of25 at.% Ti (estimated from RBS data) were dc
sputtered from a compound target at an Ar pressure of 15
mTort. Stress measurements indicated a conversion from
compressive to tensile stress with increasing Ar pressure
(Fig. 1). The thickness of the metallization varied between
50 and 300 nm. The electrical resistivity of as-deposited films
was about 60 p.O cm. Annealing was carried out in a high
purity forming gas atmosphere at temperatures ranging
between 750 and 1050·C for lOs, using a commercial R T A
system (HEATPULSE). During the annealing, the metal
lized surface was protected with a GaAs cap wafer, After the
annealing, AuGe/Ni was alloyed to the backside of the wa
fer in order to form the ohmic contacts.
III. RESULTS
A. Physical measurements
Auger spectra of the TiW films before and after anneal
ing are shown in Fig, 2. It is seen that RTA at 8S0·C results
in Ti and Ga accumulation at the TiW surface, This accumu
lation causes severe Ti depletion in the bulk of the film,
comvessive
~
-5t
-lot
FIG. 1. Stress in 300-nm-thick TiW films 011 GaAs liS Ii function of Ar pres
sure durillg sputtering.
4775 J. Appl. Phys. 66 (10), 15 November 1989 0021-8979/89/224775-05$02.40 © 1989 American Institute of Physics 4775
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132.248.9.8 On: Tue, 23 Dec 2014 03:09:468800e,10" ••••••• Ga
sputter time (min)
FIG. 2. Auger depth profiles of as-deposited and RTA annealed TiW films
on GaAs.
Moreover, there is no indication of a massive build-up of Ti
at the interface, as was observed after furnace annealing at
810 °C.4 On the other hand, there is no significant change in
the W signal profile at the interface. The oxygen concentra-
lOS' -
-2 I (J ·0
~ '10; ~ W TI \'~TiJ
10 as depositea . 700°C: 10--\W
1 j \
10- t=Jn~A
\ Ti
i \W
1900oc. 10" \
l'li'illj'i.:r~rr-Fi o 200 400
depth (nm)
FIG. 3. SIMS depth proliles ofTiW IGaAs films annealed at different tem
peratures.
4776 J. Appl. Phys" Vol. 66, No. 10, 15 November 1989 :30 40 50 60 70 80 90
28
925 ce:. 10"
28 o
N
N
90
FIG. 4. X-ray diffraction spectra of as-deposited and annealed TiW IGaAs
samples.
tion at the surface is high (and correlated with the Ti con
centration), but the bulk oxygen level remains low.
The Auger spectra give a clear overall picture of the film
composition, but the technique is not sensitive to atomic
concentrations below 0.5-1 at. %. Therefore we recorded
SIMS depth profiles of the same samples after various an
nealing temperatures in order to check for in-diffusion of Ti
and W in the GaAs substrate. The SIMS data (Fig. 3) con
firm the motion of Ti and Ga towards the surface and the
stability of W at the interface. However, the most striking
observation is the gradual in-diffusion of Ti into the GaAs.
This diffusion process gives rise to a smooth tail in the Ti
profile extending a few hundred nm deep into the substrate.
Interfacial diffusion could possibly lead to the forma
tion of new phases. However, the Ti SIMS profile does not
contain any step that would indicate the presence of a stoi
chiometric compound. A search for interfacial phases was
performed with grazing angle XRD and high-resolution
cross-sectional TEM. No evidence of the existence of a ho
mogeneous interfacial layer could be found in these data.
The XRD spectra (recorded with CuKa radiation) show
essentially the out-crystallization of pure a-W (Fig. 4) after
RTA. TEM pictures of annealed samples (Fig. 5) do not
bring any evidence for the presence oflayers of Ti-Ga or Ti-
FIG. 5. High-resolution
cross-sectional TEM image
ofthe TiW IGaAs interface
after annealing at 900 'C
for 10 s. No clear morpho
logic structure is detectable
in the TiW film due to the
very strong absorption of
the electron beam by the
metal.
de Potter et a/. 4776
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132.248.9.8 On: Tue, 23 Dec 2014 03:09:4601 ~'~~~~r-~~--
250 300 350
!:)
c: 15
15 u
a 10
~
)(
~ 5
FIG. 6. RES spectra ofTiW IGaAs samples annealed at diiferent tempera
tures.
As phases. The pictures show a fairly uniform TiW IGaAs
interface, with the occasional inclusion of small unidentified
crystallites.
Finally, samples were investigated before and after an
nealing by RBS. Apart from a shift in the W signal, which is
due to the formation ofthe Ti and Ga-rich surface layer, no
substantial changes occur in the overall composition profile
up to 950·C [Figs. 6(a) and 6(b)}. It must, however, be
remembered that the GaAs substrate signal overlaps with
the Ti signal, thereby lowering the sensitivity of the RES
spectra to changes in the Ti concentration. After 1050·C
annealing, a clear shift in the lower edge of the W signal
indicates motion of the W towards the substrate, which
could result either in a diffusion tail ofW into the GaAs or in
the formation of new phases at the W IGaAs interface [Fig.
6 (c) J. This may be compared with earlier observations of
the breakdown ofW-based diodes on GaAs, which showed
the onset of a reaction at the W IGaAs interface between 8S0
and 1000 ·C, depending upon annealing conditions.6
80 Electrical measurements
Current-voltage and capacitance-voltage measure
ments were carried out using, respectively, a HP4145A pa
rameter analyzer and a HP4275A LCR meter. Schottky bar
rier heights (tPb) and ideality factors (n) were estimated
from the forward J-V characteristics using the modified
thermionic emission model:
4777 J. Appl. Pl;ys., Vol. 66, No. 10, 15 November i989 -- as deposited
.......... sao ·e, 10"
----- 900 ·e, 10"
10-8
-1.0 -0.5 0.0 0.5
vOltage (V) 1.0
FIG. 7. Current-voltage characteristics ofTiW IOaAs Schottky diodes an
nealed at diiferent temperatures.
J=A**T2exp( -tPb1kn[exp(qVlnkT) -1],
where J is the current density through the diode and A ** is
the Richardson constant for GaAs (8.6 A cm-2 K-2).7
The measured forward J-V curves of the TiW IGaAs diodes
exhibit linear characteristics over at least five current dec
ades (Fig. 7). The Schottky barrier height tPb was deter
mined from the extrapolated current density at zero bias,
whereas the ideality factor was derived from the slope of the
linear portion. Changes in barrier height and ideality factor
after various annealing temperatures are shown in Fig. 8.
The as-deposited parameters are tPb = 0.71 eVand n = 1.06.
These numbers are representative of good-quality diodes
and show that the surface damage due to sputter cleaning or
sputter deposition is not important. II At up to 950°C anneal
ing, there is a steady increase in both tPb and 1'1, and a decrease
of the reverse leakage current (Fig. 7). Catastrophic break-
-.c:
.~ 1.4
<ll .c. 1.2
'-
<II
'-1.0 '-
0
.Q
0.8
0.6 e * & iflV : -.--~~-;-.--,--.--.-~,,\ I f.2
\ ~JM
\ / '1.8
~os d.posit.d /
I J-I .. . . . 0 n
FlO. 8. Ideality factor (n) and barrier height (,p.) extracted from /-Vand
C-V measurements on TiW IGaAs Schottky diodes as a function of anneal
ing temperature.
de Potter et al. 4777
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132.248.9.8 On: Tue, 23 Dec 2014 03:09:46--.-r-~10 ,/ -I
I r 10
.8
I I. 10-2 -- as deposited
-·-·_·-950 °0. 10"
~ 10-4
:
'-:J
W i! 0.6
OJ _-.~' 01> • __ .-10-6
__ ·--·IL-·~· '11 J:
~ _- I M
]! 10-6 ./" !-
i 0.2
I 10-10 i
L---_S'----''-=_S"'----L- _·...J10_--L--Li ~1~--14
reverse vol tage (V)
FIG. 9. Reverse leakage current vs reverse applied voltage of as-deposited
and annealed TiW IGaAs diodes.
down occurs at 1050·C and results in a drastic decrease of
A. and an increase in both n and the leakage current. The rb .
maximal wafer averaged ¢b value observed in this series of
measurements was 0.95 eV. Measurements of reverse cur
rent characteristics (Fig. 9) reveal a change from a gradual
to an abrupt breakdown curve, which corresponds to a tran
sition from a tunneling to an avalanche breakdown mecha
nism. This interpretation is further supported by tempera
ture-dependent measurements of the breakdown voltage.
The C-V measurements exhibit the same trend as the 1-V
results, but in a more pronounced way (Fig. 8). Barri.er
heights were derived from C-V measurements by plotting 1/
C2 versus the reverse bias voltage applied. These numbers
tum out to be systematically higher than the 1-V results for
annealed diodes, as is usually observed.8 The scatter of the
data was also stronger than in the J-V results, indicating that
local trap concentrations may play an important role in the
barrier enhancement measured by C-V profiling.
IV. DISCUSSION
The major factor affecting the stability of the TiW I
GaAs interface between 750 and 950"e in our experiments
has been identified as the gradual in-diffusion of Ti in the
GaAs substrate. This can be compared with earlier observa
tions. The high reactivity ofTi with GaAs is well known and
metal n
GaAs
----------------~
N d
FIG. 10. Band diagram for a metal/p+ -GaAsln-GaAs contact without
bias. The barrier height is enhanced from the unmodified value ,pho by fi¢h'
4778 J. Appl. Phys., Vol. 66, No. i 0, 15 November 1989 can be inferred from thermodynamic arguments. By using,
e.g., Miedema's thermochemical parameters as a first esti
mate,9.!O a heat release of -280 kJ/mo} can be calculated
for the reaction
2Ti + GaAs-> TiAs + TiGa.
Detailed studies of the TilGaAs interfacial reaction have
been reported by Kim et alY and by Wada. 12 They showed
that titanium starts to react with GaAs at about 400 "C, pro
ducing a layered TiiTix Gal x ITiAs/GaAs microstruc
ture. The observed phases are in agreement with a tentative
ternary phase diagram proposed by Beyers, Kim, and Sin
clair.13 In contrast, similar arguments show that the WI
GaAs interface is thermodynamically stable up to at least
1000 °e.14 The incorporation of Ti into a W matrix, as in
sputtered TiW, seems to result in a somewhat intermediate
situation. Earlier reports have shown unchanged TiW I
GaAs diode characteristics up to at least 700 °e, and metal
lurgical studies have confirmed the stability of the interface
below this temperature.2
Several authors have reported bulk decomposition of
the TiW at temperatures above 750 0c.4•15 Both the surface
and the interface of the film can act as a sink for diffusing Ti
atoms. Accumulation of Ti at the interface has been ob
served after capped furnace annealing.4 U oder the annealing
conditions used in our experiments (i.e., rapid thermal an
nealing with unpassivated surface), the surface is clearly the
preferred Ti sink, and the Ti supply to the interface is not
sufficient to allow formation of stoichiometric Ti-As com
pounds. Instead, the Ti atoms diffusing into the GaAs create
a nonuniform doping profile extending between 50 and 100
nrn into the substrate. Assuming this doping to be predomi
nantly p type, 16.17 we obtain a situation that is most appropri
ately described as a Shannon contact. 18 This mechanism has
already been invoked to explain the increase in barrier height
of refractory metal-nitride contacts with annealing tempera
ture. 19 The occurrence of a thin highly doped p + layer at the
metal-semiconductor interface results in an artificial en
hancement of the barrier height for thermionic emission.
This situation is schematically depicted in Fig. 10. The bar
rier enhancement !J..¢;b and the positionXm of the maximum
barrier are given by19
ACPb = qNaX~.,/2EEo
Xm = (1 + NalNa)d -(NdINa) W.
In these equations, Nd and Na are the donor and acceptor
concentrations, d is the thickness of the p-doped layer, and
Wis the depletion width at a particular applied voltage. The
barrier enhancement should show up in 1-Vas well as in C-V
measurements.
Based on the previous arguments, we attribute the mea
sured rise ofthe TiW barrier height during RT A to the grad
ual build-up of a p+ layer at the contact interface. Similar
changes in refractory metal diode parameters have some
times been attributed to a reduction of the sputtering-in
duced damage with increasing annealing temperature.20
However, this mechanism is unlikely to contribute much to
¢b changes above 800 "C. Another alternative barrier-en
hancement mechanism relies on the formation of an interfa-
de Potter et a/. 4778
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132.248.9.8 On: Tue, 23 Dec 2014 03:09:46cial TiAs layer during annealing. However, there is no evi
dence for the presence of this layer in our samples.
Moreover, the creation of a TiAs phase has been shown to
result in a sharp increase of the barrier height, 11 which is a .
different behavior from the gradual change observed in our
experiments.
The amount of p-doping cannot be deduced from the
SIMS data, which only give the acceptor atom's concentra
tion. However, it can be calculated21,22 that a barrier en
hancement of 0.25 eV, similar to what we experimentally
observe, only requires a 50-nrn-thick layer with a net uni
form doping of 4.5 X 1017 acceptor states/cm3• For these as
sumptions an increase in the ideality factor from 1.0 to 1.2 is
expected, in good agreement with our experimental results.
The same doping phenomenon can explain the transi
tion from a smooth to an abrupt breakdown in the J-V curve
after R T A. Indeed, a soft tunneling breakdown will be sup
pressed by the broadening of the potential barrier and will be
replaced by avalanche multiplication, which is the typical
breakdown mechanism for a p-n junction. This interpreta
tion was confirmed by measurements of the reverse break
down curve above room temperature, which showed a low
ering of the breakdown voltage before annealing with
increasing measurement temperatures, but an increase of the
breakdown point after annealing,
V. CONCLUSIONS
We have investigated the interface behavior of TiW on
GaAs under rapid thermal annealing up to 1050"C. Two
distinct interfacial diffusion phenomena have been found to
occur. Starting at temperatures as low as 750 "C, Ti gradual
ly diffuses into GaAs, whereas Ga moves towards the film
surface. This is accompanied by an increase in the measured
barrier height and breakdown voltage of the Schottky di
odes. The change in electrical characteristics can be ex
plained by the formation of a thin p + doped layer (Shannon
contact) at the interface, due to the in-diffusing Ti atoms. In
a second stage (at 1050°C), W starts moving massively
across the interface, causing the catastrophic failure of the
diodes.
The uncontrolled p doping of the substrates will un
doubtedly cause irreproducible results in a MESFET fabri
cation process. On the other hand, a controlled p doping
4779 J. Appl. Phys., Vol. 66, No. 10,15 November 1989 could be beneficial since it increases the logic swing of the
FET's, and therefore the allowed threshold variation over a
circuit.
ACKNOWLEDGMENTS
The authors would like to thank A. Demesmaeker for
XRD, J. Vanhellemont for TEM, and K Wuyts for RES
analysis. Financial support was received from the Instituut
voor Fundamenteel Onderzoek in Nijverhei.d en Landbouw
(IWONL) and from Bell Telephone Mfg. Co.-Alcatel.
'R. A. Sadler and L. F. Eastman, IEEE Electron. Dev. Lett, BDL.4, 215
(1983).
2E. Kohn, Proceedings of the International Electron Devices Meeting,
Washington, D.C., 1979, p. 469.
'N. Yokoyama, T. Ohnishi, K. Odani, H. Onodera, and M, Abe, IEEE
Trans. Electron Devices ED-29, 1541 (1982).
'A. E. Geissberger, R. A. Sadler, M. L Balzan, andJ. W. Crites,J. Vac. Sci.
Techno!. B 5,1701 (1987).
55. S, Gil!, O. J, Pryce, and J. Woodward, Physica B 129,430 (1985).
"K. M. Yu, S. K. Cheung, T. Sands, J. M. laklevic, N. W. Cheung. and E. E.
Haller, J. App!. Phys. 60, 3235 (1986).
"Y. A. Gol'dberg, E. A. Posse, and B. V. Tsarenkov, SOy. Phys. Semicond.
9,337 (1975).
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Phys. 61, 2054 (1987).
9A. R. Miedema. J. Less-Common Met. 46,67 (1976).
lOA. R. Miedema, P. F. de ChateL and F. R. de Boer, Physica B 100, 1
(1980).
"K. B. Kim, M. Kniffin, R. Sinclair, and C. R. Helms, J, Vac. ScL Techno!.
A 6, 1473 (1988).
"0. Wada, S. Yanagisawa, and H. Takanashi, App!. Phys. Lett, 29, 236
( 1976).
I3R. Beyers, K. B. Kim, and R. Sinclair, J. App!. Phys. 61, 2195 (1987).
14J. Y. Josefowicz and D. B. Rensch. J. Vac. Sci. Techno!. B 5, 1707 (1987).
"R. S. Nowicki and B. Schiefelbein, in Tungsten and Other Refractory Met-
als jilt' VLSI Applications, edited by R. S. Blewer (Materials Research
Society. Pittsburgh, 1985), p. 341.
"'B. V. Kornilov, L. V. Marchukov, and V. K. Ergakov, SOy. Phys. Semi-
cond.8, 14-1 (1974).
'"V. V. Ushakov andA. A. Gippius, SOy. Phys. Semicond.16, 1042 (1982).
'"1. M. Shannon, Solid-State Electron. 19. 537 (1976).
;9L. C. Zhang, C. L. Liang, S. K. Cheung, and N. W. Cheung, J. Vac. Sci.
TechnoL B 5, 1716 (1987).
"'N. Uchitomi, M. Nagaoka, K. Shimada, T. Mizoguchi, and N. Toyoda, J.
Vac. Sci. TechnoL B 4, 1392 (1986).
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Ponce, and D. M, Collins, J. App!. Phys. 61, 5159 (1987).
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(1986).
de Potter et a/. 4779
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1.100951.pdf | Transport properties of twodimensional electron gas systems in deltadoped
Si:In0.53Ga0.47As grown by organometallic chemical vapor deposition
WP. Hong, F. DeRosa, R. Bhat, S. J. Allen, and J. R. Hayes
Citation: Applied Physics Letters 54, 457 (1989); doi: 10.1063/1.100951
View online: http://dx.doi.org/10.1063/1.100951
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/54/5?ver=pdfcov
Published by the AIP Publishing
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136.165.238.131 On: Sat, 20 Dec 2014 12:44:28Transport properties of two",dimensiona! electron gas systems in delta~
doped Si:~nO.53 (1aO.47 As grown by organometaUic chemical vapor deposition
W-P. Hong, F. DeRosa, R Bhat, S. J. Alien, and J. R. Hayes
Bellcore, 331 Newman Springs Road, Red Bank, New Jersey 07701
(Received 28 September 1988; accepted for publication 18 November 1988)
We have investigated the transport properties of a two-dimensional electron gas formed in
delta-doped lno.53 Gao.47As grown by the organometallic chemical vapor deposition technique.
Very high free-electron concentrations of I.4X 1013 and 9.6X 1012 cm-2 have been obtained at
300 and 77 K, respectively. Hall mobilities of 9300 and 14600 cm2/V s were measured with
carrier concentrations of 3.7 X 1012 and 3.0X 1012 cm-2 at 300 and 77 K, respectively. This is a
factor of 3 higher than is expected for homogeneously doped materials having a similar doping.
Schubnikov-de Haas oscillations confirmed the two-dimensional nature of the electronic
structure in these delta-doped materials, and electron effective masses were determined from
cyclotron resonance measurements.
Recently, atomic plane or delta doping of compound
semiconductors has received considerable attention as a
means of obtaining high-density and high-mobility quasi
two-dimensional electron gas (2DEG) systems. This doping
technique has been developed in molecular beam epitaxy
(MBE) I and in the flow rate modulation epitaxy (FME).
The samples were grown by FME in a modified conventional
organometallic chemica! vapor deposition (OMCVD) reac
tor.2 The electron mobility of delta-doped layers may be en
hanced due to reduced impurity scattering in the presence of
screening effects, and the electron concentration may be en
hanced due to a reduced Si autocompensation when the do
pant is incorporated in one plane during the growth inter
ruption. The quasi-two-dimensional nature of the electron
gas in the potential well created by the doped layer was first
demonstrated by Schubnikov-de Haas measurements by
Zrenner et al.3 Previous research in this area, however, has
concentrated on GaAs and Alx Gal _ "As. In this letter, we
report experimental results from a study of electron trans
port properties in OMCVD-grown delta-doped
Ino.53 Ga047As by using Han, Schubnikov-de Haas, and cy
clotron resonance measurements.
Planar delta-doped Inns3 Ga0.47 As layers were grown by
the OMCVD technique at a temperature of 625°C with the
reagents transported to the reactor by palladium-diffused
hydrogen. The growth started with a 1.0 Itm undoped
1no.53 Gan.4-7 As buffer layer, then the atomic planar doping
occurred by dosing the trimethyHndium and trimethylgal
Hum gas valves and opening the silane (SiH4 ) gas valve. The
arsine (AsH;) flow was maintained so that the Si atoms
could be preferentially incorporated on the Ga sites. The
growth was completed after the deposition of a further 1.0
pm of undoped Ino.53 GaOA7 As.
T ABLE I. Growth conditions and transport data from Hall measurements
at 300 and 77 K.
SiB. Ii!! (cm'/V s)
Sample upening time (s) 300 K 77 K
A
B 5
lS 9300
3600 14600
(, 2C<) flu (>< lOll cm ')
3()() K 77 K
3.7
14.0 3.0
9.6 Cloverleaf and Hall bar geometry samples were made
for Hall measurements (Van der Pauw technique) and
Sehubnikov-de Haas measurements, respectively. Ohmic
contacts were made to the samples by annealing indium baBs
under hydrogen flowing for 2 min at 400°C. Samples from
different parts of grown wafers were wedged for cyclotron
resonance measurements. Unlike previous cyclotron reso
nance experiments, which were performed at fixed frequen
cy, swept-frequency cyclotron resonance was obtained.
The electron transport properties were determined for
two different doping concentrations, 3.7X lOl2 em 2 (sam
ple A) and 1.4 X 10 L\ cm 2 (sample B) at 300 K. These
correspond, respectively, to 7.1 X 1018 and 5.2 X lOlCJ cm -3
for equivalently homogeneously doped layers with the iden
tical mean impurity separation.4 Han transport parameters
with growth conditions of these two samples are summar
ized in Table I. Hall mobilities as high as 9300 and 14600
cm2/V s were measured for a doping of 3.7X 1012 and
3.0X 1012 em·· 2 at 300 and 77 K, respectively. If the Hall
mobility were limited mainly by impurity scattering equiva
lent to 3D density, we would expect values as low as 3500
cm2 IV s with the assumption that the compensation ratio is
one. Therefore, at a concentration of 3.7 X 1012 em -2 at 300
75 B= 10 TESLA
T= 6°1{
125 175
FREQUENCY (cm-1) 225
FIG. L Cyclotron resunancc spectra taken at the fixed fidd on samples A
andB.
457 Appl. Phys. Lett. 54 (5), 30 January 1989 0003-6951/89/050457-03$01.00 @ 1969 American Ir.stitute of Physics 457
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136.165.238.131 On: Sat, 20 Dec 2014 12:44:28SAMPLE A
4.5
MAGNETIC FIELD (TESLA)
FIG. 2. Schubnikov-<le Haas oscillations on samples A and B for the mag
netic field perpendicular ttl the doping plane.
K, the mobility enhancement is more than 2.5. The possible
origin of the mobility enhancement is discussed in Refs. 4
and 5. Another interesting aspect of the delta-doping tech
nique is the capability of extremely high free-electron con
centrations. Concentrations of l.4XlOl.l cm2 (5.2Xl019
cm -3) in delta-doped Ino53 Ga0.47 As are a factor of 5 higher
than the highest free-electron concentrations (1.0 X 1019
cm -1) in the conventionally doped layers. These suggest
that delta-doped Ino.53 Gao..!? As could be an excellent candi
date for high performance FETs requiring high driving cur
rent capability.
[n Fig. 1 we show swept-frequency cyclotron resonance
at B = 10 T for two samples which were wedged by 4' to
eliminate Fabry-Perot interference effects. The resonance
spectra are broader in sample B than sample A as would be
expected for a lower mobility sample. From the frequencies
where the resonance reaches peak, we calculated electron
effective masses to be O.OSmo and O.064mo for sample A and
sample B, respectively. The electron effective masses are
larger than that (O.042mo) in pure bulk materials. It is be
lieved to be mainly due to nonparabolicity resulting from the
high degeneracy of the electronic systems.
We expect the electrons to be quantum mechanically
bound to the parent donor plane. To deduce electron sub
band energies describing the binding of the electrons to the
doped region, we have performed low-temperature Schubni
kov-de Haas measurements on the samples. Figure 2 shows
magnetoresistance oscillations up to B = 9 T. The oscilla
tion is stronger in sample A than in sample B, as expected.
But both show a complex osciHatory behavior. The two-di
mensional nature of the electronic structure was confirmed
by tilting the samples with respect to the magnetic field. The
amplitude and position of maxima (or minima) were ob
served to shift to higher magnetic field with the increased tilt
angle.
458 App\. Phys. Lett., Vol. 54, No.5. 30 January 19139 ~
E ->-100
~ w z w
c
~ ..... >-" a..
w
(.,)
Z
~ if)
en
iLl
0::
..J
...!
oct :t: 5 10
MAGNETIC FIELD (TESLA)
5r---------------------------~
2.5~
°O~------~5~------~10~------~15
(0) MAGNETIC FIELD (TESLA)
FIG. 3. (a) Magnetmesistallcc ami occupied Landau levels of two sub
bands vs magnetic field. (b) Hall resistance vs magnetic field.
In the case of sample A, the longitudinal magnetoresis
tance (Pxx) displays a complex oscillatory behavior charac
teristics of more than one electron subband occupation,
while the HaH resistance (Px}') displays a tendency to form
plateaus at the highest magnetic fields [shown in Fig. 3(b) l.
To analyze these data, we note that the weak plateau in Pxy
and the minimum inpxx at B = 11 T must correspond to 10
spin/Landau levels occupied. To reproduce the structure in
Pxx as the magnetic field is lowered, it is necessary to super
impose two sets of Landau levels from two occupied sub
bands. Although we still expect Pxx minimum to occur at
Hong eta!. 458
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136.165.238.131 On: Sat, 20 Dec 2014 12:44:28integral values of 1/ B, the interference of the two sets of
Landau levels modulates the amplitude of the minimum. By
reproducing this modulation of the Pxx minimum we deter
mined the relative separation ofthe subbands to be as shown
in the lower part of Fig. 3 (a). The energy scale was set by the
magnetic field and electron mass, and we estimated the ener
gy splitting to be about 65 meV. We also determined carrier
concentrations in the two subbands to be no = 1.85 X 1012
and nl = 0.55 X 1012 em -2. The total carrier concentration
(no + n1 = 2AX lOE2 em 2) is in good agreement with the
value (2.5 X 1012 cm-2) obtained from Hall measurements.
It is assumed that the Si atoms remain in a single atomic
plane. It has been reported recently,6.7 however, that a PGst
growth diffusion and/or preferential migration depending
on the growth temperature, can occur.
In conclusi.on, we have studied transport properties of
2DEG systems formed in delta-doped Inos] Ga0.47 As grown
by OMCVD, using Hall, Schubnikov-de Haas, and cyclo
tron resonance measurements. Hall mobilities as high as
9300 and 3600 cm2/V s with carrier concentrations of
459 Appl. Phys. Lett., Vol. 54, No.5, 30 January 1989
·.·.·.·.~.·.~.':'".:-.:.-:;:.:.:.x.:.~.:;:-.:-.:.::;:.;.:.:.:.:.;.;o:.;.:.;.:0;.;0;-.;.:0;.;.:.;.; •.•.•••.• ;.;.; •.•.• ; •••••••••••• "? •••• -.; •• ' •••• -; ••••• ;" ••••• '7' •••••••••••••••• 3.7X 1012 and lAX IOU em --2 at 300 K, respectively, have
been obtained. We have analyzed Schubnikov-de Haas mea
surements data and confirmed the two-dimensional nature
of the electronic structure in these materials.
Discussions with R. F. Leheny are gratefully acknowl
edged.
lK. Ploog, J. CrysL Growth 81,304 (1987).
2M. Kobayashi, T. Makimoto, and Y. Horikoshi, Jpn. J. App!. Phys. 25,
L746 (1986).
lA. Zrclmer, H. Reisinger. F. Koch, and K. Ploog, in Proceedings of the
17th Jllternationai Conference un Physics of Semiconductors, San Francis
co, 1984, edited by J. D. Chadi and W. A. Harrison (Springer, Berlin,
1985), p. 325.
4E. Schubert, J. E. Cunningham, and W. T. Tsang, Solid State Commun. 63,
591 (1987).
'G. Gillman, B. Vinter, R Barbier, and A. Tardella, Appl. l'hys. Lett. 52,
972 (1988).
"E. Schubert, J. B. Stark, T. Chiu, and B. Tell, App!. I'hys. Lett. 53, 293
( 1988).
7R. B. Beall, J. B. Clegg, and J. J. Harris, Scmicond. Sci. Techno!. 3, 612
(1988).
Hong etal. 459
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1.100299.pdf | Plasma immersion ion implantation using plasmas generated by radio frequency
techniques
J. Tendys, I. J. Donnelly, M. J. Kenny, and J. T. A. Pollock
Citation: Applied Physics Letters 53, 2143 (1988); doi: 10.1063/1.100299
View online: http://dx.doi.org/10.1063/1.100299
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139.80.14.107 On: Thu, 04 Sep 2014 08:49:22Plasma immersion ion implantation using plasmas generated
by radio frequency techniques
J, Tendys and i. J, Donnelly
Australian Nuclear Science and Technology Organization, Lucas Heights Research Laboratories, PMB ],
Menai NSW 2234, Australia
M. J. Kenny and J, T, A. Pollock
Commonwealth Scientific and Industrial Research Organization, Division of Applied Physics, Lucas
Heights Research Laboratories, PMB 7, Menoi NSW 2234, Australia
(Received 29 July 1988; accepted for publication 20 September 1988)
Medium density (3 X 109 em 3) and high density (3 X 1012 cm-3) pla;;mas, generated by low
and medium power rf techniques, have been used for the implantation of 10-20 keY nitrogen
ions into mild steel targets which were immersed in the plasma and biased to -20 kV. Use of
the high density plasma resulted in significant damage to the surface by arcing. At medium
densities the nitrogen was implanted to a depth and dose consistent with expectations, there
was no arcing damage, and tests showed improved wear and hardness compatible with the
level of impiantation.
A new technique for the ion implantation of materials
has recently been reported by Conrad et al. I In this method
the target is placed in a plasma and biased to high negative
voltages. An ion sheath forms around the target and the plas
ma ions are accelerated through the sheath, implanting the
target surface. This technique has been named plasma im
mersion (or plasma source) ion implantation (PHI). Its ad
vantages over conventional ion implantation using acceler
ated particle beams have been discussed by Conrad et aI, !
Although PIn is only in its infancy the technique has al
ready been demonstrated for nitrogen implantation into
steei, with a consequent improvement in wear properties. 1
The plasma densities used in the pioneering experiments
of Conrad et al.1 were about 2:::< 108 cm -3. In this letter we
describe preliminary results of PIn experiments in which
low and medium power rftechniques have been used to gen
erate nitrogen plasmas of medium (3 X 109 em .. 3) and high
densities (3 X 1012 ern 3). The aim ofthese experiments was
to discover whether rf plasmas are suitable for PIII, and to
make a preliminary investigation of PIn in high density
plasmas. This is of importance because the time for implan
tation to a specified dose reduces as the plasma density is
increased, and because the decrease in sheath width at larger
densities meam; that targets of complex shape should be im
planted more uniformly.
The vacuum vessel is a glass sphere of radius 14 cm with
access through four cylindrical ports. In thc medium density
operation mode 200 W rfpower at 13.5 MHz was inductive~
ly coupled to the plasma through two 20~cm-diam conduct
ing loops on opposite sides of the vessel. This created a visu
any uniform glow discharge plasma in which the ion species
was N2' • The pfasma density, measured using a Langmuir
probe, lay within the range 2:-4 X 109 cm -3, and the electron
"temperature" Te was estimated to be 5 eV, There was no
steady applied magnetic field in this case. To obtain the high
density plasma the device was operated in the rotamak
mode,2 in which a rotating magnetic field was used to inject
-40 k Wand create a magnetically confIned plasma of ion
species N' ,density -3 X 10 l2cm 3, and Te -10 e V. Steady
magnetic fields of about 5 m T are present in this case. In both cases the filling pressure was about 1 mTorT.
The bias voltage power supply can generate voltages up
to 20 kV and currents up to 4 A with pulse widths in the
range 8 fls < Tp < 200 I1s and repetition times 1" r > 50l1s. The
pulses were applied in batches of 1 s duration, separated by
6-9 s intervals. In aU implantation experiments reported
here the fuH 20 kV was used. A new system capable of 50 kV
and 10 A is being developed. The target samples are com~
mercia!, low carbon (0.25%), mild steel (AS1443-1973)
disks of 2,5 cm diameter and 0.5 em thickness, which we
modified only by highly polishing one side at room tempera
ture. They were connected to the power supply via a 3-mm
diam brass rod that was screwed into the convex side of the
disk. The rod was shielded from the plasma by a glass tube.
The sample formed the cathode ofthe bias circuitry, and the
anode was a carbon electrode of area 15 cm2 located in the
plasma, 12 em from the target. The anode clamped the plas
ma potential to a value 20 k V above that of the cathode. In
these experiments the samples were not cooled.
The amount of implantation has been measured, with an
accuracy of 15%, using the 14N(d,a)12C reaction3 with 1.1
MeV deuterons and both backward angle (163°) and glanc
ing angle ( IHn detection of the ex partides. This technique
also allows depth profiling of the 14N, with a resolution of 40
urn.
In the first series of experiments a grass tube covered all
but a 1 cmz circular area on one face of the disk which was
implanted using approximately 400 pulses of 80l1s duration
in the rotamak plasma. The current pulses in the bias circuit
ry were about 300 rnA, although some showed 500 rnA
spikes which are thought to be due to arcing. The nitrogen
dose deduced from the (d,a) reaction was 4 X 1016 em' 2, in
reasonable agreement with expectation based on the mea
sured current and on the formation ofa steady ChHd-Lang
muir sheath4 of width -5 mm. The exposed area exhibited
an erosion or arc spot at its center, and there were arc tracks
under the edges of the glass. Because of the arc damage no
depth profiling, hardness, or wear mearmrements were made
on this sample.
In all further experiments the glass cover was not used,
2143 AppL Phys. lett. 53 (22), 28 November 1988 0003-6951/88/482143-03$01,00 Cc) 1988 American Institute of Physics 2143
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139.80.14.107 On: Thu, 04 Sep 2014 08:49:22and the whole of the sample surface (13 cm2) was exposed.
With this large surface area the rotamak plasmas gave an ion
current to thc target of about 4 A, which was near the limits
of the bias circuitry and made it difficult to control the vol
tage pulse. Therefore, these results must be regarded as pre
liminary. Following the application of 8000 8 f..ls pulses the
sample was found to be covered by a large number of arc
tracks, but examination of the remainder of the surface un
der a microscope showed no apparent damage. The dose to
an undamaged part of the surface was measured by the (d,a)
reaction to be 2 X 1016cm \ a factor 5 below that expected.
It is thought that a significant part of the current to the
sample occurred as low voltage arcs, which did not result in
implantation. No wear measurements were made on this
sample because of the low dose and the extensive arc dam
age.
Table r lists the pulse length and repetition time, the
total number of pulses .IV p' and the dose measured at the
center of the polished face of four samples implanted using
medium density plasmas (Nt at 20 keY), In these cases
there was no evidence of arcing. Based on an observed ion
saturation current of2 rnA at low voltages ( -100 V) which
indicated n I = 2 X 109 em -", the predicted dose of nitrogen
atoms per second of implantation is 2 X ro15 em -2 S 1. As
suming this value, the experiments were designed to give a
dose of 2 X IOl7 em -2 to samples BM51 and EMS3. Al
though the presence of capacitance and secondary electron
currents prevented a straightforward measurement of the
ion current to the samples at 20 keY, this has been estimated
from the rate of sample temperature increase to be about 12
rnA. This increase in ion curren t over the low voltage value is
consistent with a larger Child-Langmuir sheath width at
higher voltages, although, with an expected radius of 10 em,
the sheath would occupy much of the vessel which would
affect the sheath structure and possibly the plasma density,
The ion current estimated for each sample was used to obtain
the total dose values listed in Table 1. Note that these expo
sures are well above the saturation value of the retained
2144 AppL Phys, Lett., Vol. 53, No. 22, 28 November 1988 FIG. L Micrographs of wear tracks for (a) the
unimplanted sample and (b) sample 131\151, fol
lowing 60 min wear under 50 g loading. The indi
cated lengths correspond to I mm.
dose,S which is about 1 X 1017 cm-2 for 10 keY nitrogen into
steel at 30°C. The maximum temperatures reached by each
sample are given in Table I. These were estimated from ther
mistor measurements of the heating and cooling rates at
temperatures up to 200 dc. After implantation the surfaces
of samples BMSl, EMS3, and BM90 had a milky appearance
because of surface etching to depths of several hundred nm,
which is evident in Fig. 1(b). The surface of sample BM59
appeared slightly cloudy, but much less affected than the
other three. These observations are compatible with the
amount of sputtering expected for the total doses and tem
peratures listed in Table I. The retained doses in samples
EM5!, BMS3, and BM90 are aU above the expected satura
tion level, and we believe that this is due to the diffusion
effects discussed below.
Profiles of the nitrogen density versus depth have been
determined for all samples using the 14N (d,a) 12C reaction.
They show a strong peak at the material surface with a fuB
width at half maximum of 40 urn, which is approximately
the resolution of the technique. As the penetration of 10 keY
nitrogen is about 10 nm, we can only say that the measured
distribution near the surface is consistent with that expected,
The glancing angle measurements on BM51 and EM53 indi
cate that there is appreciable nitrogen (15% of detector
broadened peak value) at a depth of 100 nm, with even
greater penetration seen in BM90. This is not observed to the
same extent in the backward angle measurements, nor in
TABLE L Implantation parameters with the medium density plasma.
Total Retained Sample
7p 7,. Np dose dose temperature
Sample (itS) (ILS) (10") (1017cm -2) ( \O'7em .}) eel
BMS! 80 600 1.3 11 2.2 200
EMS3 80 600 1,3 \1 4.5 250
BM90 80 600 0.3 6 5.0 350
BM59 15 200 0,9 3 1.4 300
Tendys eta!. 2144
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139.80.14.107 On: Thu, 04 Sep 2014 08:49:22TABLE n. Wear characteristics measured using a carbide ball-on-disk sys-
tem under 50 g load and O.R ms -, contact velocity. .
Wear time (min)
SampJe
Unimplanted
BMSI
BM59 30 60 120 240
track cross-sectional area (10 -" m 2)
0.9 1.9
<0.1 3.1
<O.!
0.5 5.2
0.1
1.8
sample BMS9. It appears that there is enhanced penetration
due to diffusion, especially in samples EMS1 and BM53
which are at their maximum temperatures for the longest
times, and in BM90 which reaches the highest temperature.
The increased penetration indicated by the glancing angle
compared to the backward angle measurements is probably
an artifact arising from the surface roughness.
Surface micro hardness was measured across the diame
ters of the PIn samples and an unimplanted standard using a
Vickers indenter under 15 g load. These conditions will not
measure the hardness of the implanted layer « 100 urn
thick), but will include a substantial fraction of the unmodi
fied underlayer. However, the measurements provide a
qualitative assessment of the effectiveness of PHI with re
gard to changes in surface hardness. The mean hardness
(VDR) was 120 (standard deviation 20) for the standard,
and in the range 160-180 (s.d. 30) for the implanted sam~
pIes. These measurements demonstrate an increase in hard
ness of up to 50% following PIII.
Wear measurements were made with a machine based
on the pin-an-disk principle, but using a carbide steel baH
(10 mm diameter) as abrader. Contact velocity was 0.8
ms-J with paraffin oil continuously dropped onto the sam
ple surface to provide light lubrication. Wear tracks cut us
ing a 50 g l.oad for various contact times allowed a suitable
comparison between the wear properties of implanted and
unimplanted samples. The wear tracks and the as-implanted
surfaces were examined using interference microscopy (Fig,
1); the wear depth profile was determined by interferometry
using both white and monochromatic light.
A series of wear tracks was cut in samples BMS!, B]\'159,
2145 Appl. Phys. Lett., Vol. 53, No. 22, 28 November 1988 and the standard for contact times i.n the range 30-240 min.
These data are summarized in Table n. Compared with the
unimplanted standard, sample EM51 had its wear resistance
significantly improved by PHI. Only a scuffing track was
observed for wear times less than 240 min [see Fig. 1 (b) J,
Even after 240 min wear, when some breakthrough of the
implanted layer was evident, BMSl was still about 50 times
more wear resistant than the standard. Sample BM59 re
ceived a lower implant dose, was less hard, and was less wear
resistant than EM5!. After 120 min wear, substantial break
through of the modified layer had taken place. at which
point BM59 was about six times more resistant than the
standard. Another indication of the increased hardness
which accompanies PIn of these steel samples was the ob
servation of a small flat worn on the hard carbide abrader
baH. This flat was not observed with the standard sample.
The improved wear characteristics of BMSl compared with
BM59 are possibly due to the 50% extra nitrogen in BM51,
but they may also be connected with the much greater sur
face etching seen on BMSl.
The results presented here show that rf-generated plas
mas of medium density are su.itable for nitrogen implanta
tion in steel to increase its hardness and wear properties. The
high density plasmas appear unsuitable because of arcing
problems, but this may be overcome with improved bias vol
tage circuitry and/or with shorter pulse lengths. A program
aimed at finding the plasma density and preparation method
that optimizes the implantation process is being undertaken.
We acknowledge the assistance ofL. Wielunski with the
dose measurements, D, D. Cohen and G. A. Collins with the
depth profile analysis, and R. A, Clissold with the hardness
and wear testing.
'I. R. Conrad, J. 1.. Radtke, R. A. Dodd, F. J. Worzala, and N. C. Tran. J.
App!. Phys. 62, 4591 (19H7). .
20. Durance, G. R. Hogg, J. Tendys, and P. A. Watterson, Plasma Phys.
ContL Fus. 29, 227 (1987).
'G. K.Hub!eJ'. Nne!. lustrum. Methods I'll, !OJ (1981).
4C. n. Child, Phys. Rev. 32, 492 ( 1911 ).
'1'. Barnavon, J. TOllsset, S. Fayeul1e, 1'. Glliraldellq, D. Treheux, and M.
Robelet, Radiat. Elf. 77. 249 (1983).
Tendys eta!. 2145
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1.576076.pdf | Comparative study of dielectric formation by furnace and rapid isothermal processing
R. Singh, F. Radpour, and P. Chou
Citation: Journal of Vacuum Science & Technology A 7, 1456 (1989); doi: 10.1116/1.576076
View online: http://dx.doi.org/10.1116/1.576076
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/7/3?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 155.33.16.124 On: Wed, 26 Nov 2014 11:58:00Comparative study of dielectric formation by furnace and rapid
isothermal processing
R. Singh, F. Radpour, and P. Chou
School a/Electrical Engineering and Computer Science, University a/Oklahoma, Norman, Oklahoma 73019
(Received 10 October 1988; accepted 9 January 1989)
An examination of our own and results available in the literature indicate that the dielectric
properties of silicon dioxide and tin oxide on Si formed by rapid isothermal processing are
superior compared to furnace processing. A possible explanation based on the primary difference
in the radiation spectrum of the two sources of energy is presented in this paper. Certain physical
and chemical processes can be prompted and/or initiated due to the presence oflight in the rapid
isothermal processing.
I. INTRODUCTION
The inadequacy of conventional furnace annealing for the
fabrication of micron and submicron integrated circuits has
led researchers to investigate alternate methods to furnace
annealing such as lasers, electron beams, lamps, resistance
heaters, and ion beam annealing technologies. Out of the
various alternate techniques mentioned above, rapid isother
mal annealing, based on incoherent sources oflight, is a very
promising technique. I In this process, the sample is thermal
ly isolated and the heating and cooling processes are domi
nated by thermal radiation. In 1980, Nishiyama et al.2 were
the first to use tungsten halogen lamps as a continuous
source of radiation for annealing boron implanted Si wafers.
Since then, in addition to annealing of ion-implanted wafers,
this technique has been extended for many other process
steps such as silicide formation, gettering, formation and an
nealihg of gate dielectrics, oxide reflow, metal alloying, etc.
For this reason, the term rapid isothermal processing3
(RIP) is used to cover a wide range of processing steps
achieved by this technique. Thin films of dielectric materials
are an integral part of various semiconductor devices. As
compared to furnace processing, improved quality of dielec
tric films are formed by RIP.4 In this paper, we report the
oxidation study of silicon dioxide and tin oxide on silicon
formed by RIP. For comparison purpose some results of tin
oxide and silicon dioxide formed by conventional thermal
processing are also presented.
In the following section the experimental results are pre
sented. Section III deals with the discussion of the experi
mental results. Finally, the paper is concluded in the last
section.
II. EXPERfMENTAl
An examination of the results available in literature indi
cate that the dielectric properites of the thin silicon dioxide
films formed by RIP are superior compared to the furnace
processing. 3,4 Figure 1 shows the silicon dioxide thickness as
a function of oxidation time at 900 °C for RIP and furnace
processing in dry oxygen. The RIP data, A and B shown in
Fig. 1; are taken from Refs. 5 and 6, respectively. The fur
nace data are taken from Ref. 7. Similar data have been ob
served at different oxidation temperatures. Thus, the growth
kinetics of thin silicon dioxide formed by furnace and rapid isothermal processing are different.
Thin films of Sn02 grown at low temperature are of cur
rent interest due to their established applications such as
conducting oxide semiconductors as well as potential appli
cation in gas sensors. Silicon substrates used in this work
were n-type phosphorus doped, (100) oriented epiwafers
with resistivity of 4.1 n cm. The silicon wafers were chemi
cally cleaned in TCE, acetone, and methonal each for 10 min
in an ultrasonic cleaner followed by rinsing in deionized wa
ter. After chemical cleaning the silicon samples were imme
diately loaded in the vacuum system and thin films of Sn of
thickness about 575 A. were deposited at 10-6 Torr vacuum.
The Sn/Si samples were transferred to commercial rapid iso
thermal processor, Heatpulse model No. 410 equipped with
gas handling system GHS-Ol. A summary of the processing
history of five typical samples is shown in Table I.
X-ray studies were performed in an x-ray diffractometer
(Rigakud/MAS-llA) using CuKa radiation and a curved
graphite crystal monochrometer, with a step width of 0.05°
and a count time (for each step) of2 s. A smaller step width
and/or larger count time was used to give better precision of
BO,----------------------------------~
~ao~
o~ I
(/)
W
Z40
x::
Q
::c I-
waD o
>< o
0i---------r--------r--------~------~
o a 3 ...
OXIDATION TIME (min)
FIG. 1. The thickness of thermal oxide as a function of growth time.
1456 J. Vac. Sci. Technol. A 7 (3), May/Jun 1989 0734-2101/89/031456-05$01.00 @ 1989 American Vacuum Society 1456
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 155.33.16.124 On: Wed, 26 Nov 2014 11:58:001457 Singh, Radpour, and Chou: Comparative study of dielectric formation 1457
TABLE I. Processing history of oxidation of typical Sn/Si samples.
Rapid isothermal In situ Oxidation In situ
processing (RIP) cleaning temp. ee) annealing in
Sample or thermal temp. eel and N2 temp. eel
no. (TJ and time time and tim~
RIP 6OO/lOs 400/160 s 500/10 s
2 RIP 600/lOs 4OO/300s
3 T 400/10 min 4OOC175 min
4 T 400/10 min 400/75 min 600/10 min
5 T/RIP 400/10 min 400/75 min 500/10 s
2() and intensity measurements. All of the spectra were
scanned from 10° to 120· (valuedof28). The summary of x
ray diffraction results is shown in Table II. It is obvious from
Table II that furnace processing provides mixed phases of
Sn02 and SnO or only SnO phase. On the other hand, RIP
can provide only the single phase of sua:!.
High-frequency (1 MHz) capacitance-voltage was used
to measure the fixed surface state density of Hat band (NFIJ).
The fiat band voltage VFB was determined graphically from
fiat band capacitance and corresponding high-frequency C
V characteristics. The electrical breakdown field EBR of thin
dielectric film was measured using linear voltage ramp tech
nique.
The electrical characteristics of Sn02 samples are shown
in Table III. Clearly, in terms of the dielectric constant E,
Nl'B' and EBR, RIP provides, better results compared to fur
nace processing. A more detailed information of Sn02 re
sults is given in Ref. 4. TABLE III. Electrical charactcriHics of Sn/Si oxides.
Thickness NcB, NFB2 EUR
Processing (A) E (no./cm2) (no'/cm') (MV/em)
RIP
oxidation 534 24.98 1.65 X lO" 3.23 X 1000 1.1
f-annealing
RIP
oxidation 551 8.41 3.01 X 10" 3.25 X 10" 0.8
Furnace
oxidation 568 9.57 3.35X 10" 3.61 X 10" 0.7
m. THEORETICAL MODEL AND DISCUSSION
It is obvious from the results presented above that in order
to explain the difference in the oxidation kinetics, we have to
examine the basic energy transfer mechanism in the two
cases of furnace processing and RIP. First, we will examine
8n02 results followed by Si02 results,
A.5n02
Assuming radiation as the dominant energy-transfer
mechanism, furnace processing at 400 ·C can be represented
by a blackbody radiation at -800 K. As shown in Fig. 2, in
case offurnace processing, only photons with wavelengths of
-1.2 pm and longer have appreciable intensity and could be
available for possible chemical reactions. On the other hand,
in the case of RIP, although the substrate temperature is
400·C (as in the case of furnace processing), the filament
temperature is much higher. A typical intensity versus wave
length curve for tungsten halogen lamps8 is also shown in
TABLE II. X-ray diffraction summary (28 range: 10"-120", Scan time = 85.80 min).
Sample
no.
2
3
4
5 {J-Sn
Orientations
slightly
less
random.
Orientations
relatively
random.
Same orientations
as sample 1 and
(101) being more
prominent.
Small amount.
Mainly of
(200) arId (l0l)
orientations.
J. Vat::. Sci. Techno!. A, Vol. 7, No.3, May/Jun 1989 SnO
(romarchite)
Very small
amount.
None
Essentially
(00l) or
(002)
orientation.
Major
orientation
as sample 3 with
reduced intensity,
The major
phase here;
orientation as
sample 3. Various phases
Su3O. SnO,
(triclinic) (cassitevite)
Most
None prominent
orientations
(110), (Wi).
Increased
None intensity of
(101) phase.
None None
Essentially Orientation
(00l) or (101) much
(002) or (003) stronger
orientation. than others.
Similar to
sample 4 Small amount,
but intensity only (101)
much weaker. is appreciable.
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Fig. 2. Thus, the primary difference in the two oxidation
processes originates from the difference in the radiation
spectrum of the two sources of energy. The potential energy
curves for the O2 molecule are shown in Fig. 3.9 A summary
of the three lowest electronic states of O2 molecules is given
in Table IV. 10 Based on Fig. 3 and Table IV, possible chemi~
cal processes associated with gaseous O2 dissociation are
shown in Fig. 4. In case of furnace processing, photons with
wavelengths of about -1.2 /-Lm and longer are not able to
dissociate gaseous O2 into atomic oxygen, which are usually
more reactive than the O2 molecule.l1 In addition, it has
been known for a long time that atomic oxygen is of primary
importance to the oxidation of condensed~state material
such as metals because of its reactivity and diffustivity
through the oxide layer. 12,13 Also, in the present case furnace
processing at a filament temperature of 800 K does not pro
vide sufficient photonic energy to excite the lone pairs (un
bonded, spin paired electron pairs) associated with each tin
atom in SnO, to higher energy states preferred for Sn02 for
mation. (There is no lone pair in SnOz and tin atoms in Sn02
have their highest known valence state of IV. 14.15) As a re
sult, in the case of furnace oxidation at 400 °C, only SnO can
be formed.
In the case of RIP, lone pair excitation is possible, since
the photons near the UV region are available. On the other
hand, at the same sample temperature, the Sn02 phase can
be readily formed from tin samples oxidized in a rapid iso
thermal processor with incoherent light source such as the
tungsten-halogen lamps. In the later case, there is relatively
only a very small amount of SnO phase both present in the
RIP oxidized samples, This SnO phase can also be readily
removed by in situ rapid isothermal annealing at 500 °C in
Nz following RIP oxidation, whereas furnace oxidation fol
lowed by annealing at 600°C in N2 provides instead a mixed
phase ofSnO, Sn304 and Sn02• Details of this study will be
published elsewhere. 16
1-
~ so
~ 150
W
• 40 > 'ii • 30 Ii
II:
120
~o
0
1200 4CIO aoa 1&!C10 1600 1aaa 12200
Wavalengcn (nm)
FIG. 2. Relativeintensity (not to the same scale) of tungsten-halogen lamps
and blackbody radiation of 800 K as a function of wavelength.
J. Vac. Sci. Technol. A, VOl, 7, No.3, May/Jun 1989 TABLE [V. Three lowest electronic states of 0,.
Mean
lifetime
Molecular Total Antibonding ofthe
electronic spin Multiplicity rrorbitals t:.E A excited
state 0[0, (S) =2S+ 1 ( rr*) (eV) (,urn) state
Ground state Triplet 1 ) 0
.il.
g
First
lowest
excited 0 Singlet 1( '0' 0.977 1.27 64.6 min
state
1~.
Second
lowest
excited 0 Singlet t I 1.628 0.7619 6.9s
l:l/
B.Si0 2
The growth kinetics of thin silicon dioxide in dry oxygen is
one of the most controversial subjects in silicon integrated
circuit processing. Even the growth rate-limiting process is
the subject of much debate. No attempt is being made to
establish the dominance of one mechanism over the other.
However, we will show that the incoherent sources of light
affect the growth kinetics for more than one possible mecha
nism.
In case of rapid isothermal processing, the use of tung
setn-halogen lamps as the source of energy can enhance Si
oxidation through the fonowing possible mechanisms:
Ci) The gas phase oxygen dissociation 02~20 can be pro
moted by RIP. Considering Figs. 3 and 4, it is clear that
oxygen atoms can diffuse more easily through the oxide lay~
er; however, the energy needed for O2 dissociation is high
B
e
a 1 ; 37T,
\ U , ,
FIG. 3. Potential energy curves of 02'
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(5.115 eV). The thermodynamic and kinetic considerations
indicate that the gas phase oxygen molecule thermal disso
ciation is fundamentally limited by Boltzmann distribution.
As shown in Fig. 4, light illumination in the UV, visible, as
well as IR region can supply the necessary thermal energy to
a sample under processing (as specified by the sample tem
perature). Additionally, it can also provide a convenient,
nondestructive, and relatively high (photonic) energy
source (i.e., in the UV-visible region) to circumvent the
above limitation by direct and/or indirect photonic absorp
tions. On the other hand, at typical furnace oxidation tem
peratures, the blackbody radiation is confined to the IR re
gion, which may not be sufficient for certain high activation
energy processes. Certain diffusion processes requiring rela
tively high activation energies cannot be activated in the fur
nace processing.
(ii) Consideration of Figs 4 and 5 shows that O2 dissocia
tion through adsorption on solid surfaces can be promoted.
eV O2 dissociation can also be promoted through chemisorption
on solid surface.
Atomic oxygen is more reactive than its molecular coun
terpart (02) and plays an important role in thin Si02
growth. 17 It may also be noted that O2 dissociation is needed
for solid-state oxidization of silicon into silicon dioxide in
dry oxygen. Silicon dioxide, either crystalline or amorphous,
is structured from networks of chains of tetrahedral 8i04
groups and no peroxide bonding has ever been found. There
fore, in the overall process of Si02 formation, the oxygen
molecules involved in the oxidation process have to be disso
ciated in certain ways. As discussed in the earlier paragraph,
gas phase oxygen dissociation by the thermal process is high
ly ineffective. Experimentally, thermal oxidation of silicon
wafers in dry oxygen has been in practice for more than sev
eral decades. This possible dilemma could be resolved from
the illustration demonstrated in Fig. 5, where a Lennard
Jones chemisorptive dissociation model of a diatomic mole-
----r 620.V(~A) - - [ .... cutoff wavelength of tungsten-halogen lamp]
Far
UV
I
5.
- - - - - 4.14 eV(3000A) r 4.
Near
UV
j
I
Visible Ground State
Oxygen
Molecule
L Ground Sta.te
Oxygen
Atoms
L t
/4.25 eV(2920A) -+ lSi V.B. -+ 5i02 C.B. Transition]
-_:!2(1,;111) -+O(3P)+O(3i2]
[Sn02 Band Gap]
3,53 eV(S51OA)
~3.49 eV(3550A) -@,2(1!:t) ...... 0(3 P) + 0(311:
--3.15 eV(3940A} -+ lSi C.B ..... Si02 C.B. Transition]
j 2. 1.964 eV(6300A) __ [!(3P) .... GenU
__ 1.628 eV(6719A) .... I02(3!:;) -> 02(lEt)
---::------ 1.61 eV(7700A) f=---Ntar
IR
1 -r-
Middle
ill
! ---1.
0.83 eV(1.5/-1)-
0.21 eV(S.Dp) -------0 (Si Band Ga.p]
1.12 eV(l.l1~)
~~V(1.271J) -I02e'!Ei) -> O2(1.6.11) I
r:------771 .E:651 eV(l.90/-I) -+ ~(l.6.gL --02(1EtlJ
..... 0.34 eV(3.6#-,) -+ [1", .. ",0/8000 K black-body rad.]
0,0576 eV(21,5~) [kT at 400CC]
J. Vac. Sci. Technol, A, Vol. 7, No.3, May/Jun 1989 FIG. 4. A schematic representation of
possible chemical processes associated
with gaseous O2 dissociation. Certain
band transition energy values ofSi, Si02,
and Su02 are also indicated.
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1
~
c:J 0 &r: II Z II +
t
SOLID SUBSTRATE
SURFACE X+X
De
FIG. 5. A Lennard-Jones chemisorptive dissociation model of a diatomic
molecule (X2). Showing the energy of the system vs distance of the adsor
bate from the solid substrate surface.
cule (X2) is described.I8 Figure 5 indicates that the heat of
chemisorption for two dissociated X atoms (with energy
close to regular chemical bonding, e.g., ~9 eV 12 per ad
sorbed atoms) is much larger than that of the corresponding
heat of adsorption ofaX2 molecule (usually ,;;;;0.2 eV lad
sorbed molecule19). The resultant activated energy for che
misorptive dissociation ofthe X2 molecule Ea is then consid
erably less than the gas phase X2 dissociation energy De·
Again, at comparable sample temperatures, a RIP incoher
ent light source can provide appropriate photonic energies to
enhance this chemisorptive assisted dissociation of diatomic
molecules more effectively than the radiation from a conven
tional furnace.
(iii) As shown in Fig. 4, the Si-Si bond breaking mecha
nism can be enhanced (8i self-bond energy ~2.1-2.6 eV).zo
(iv) Also as shown in Fig. 4, the hot (band) electron
generation can be promoted.
A thorough understanding of the role of RIP in Si02 for
mation can result in control of the defect chemistry of the
bulk Si02 and Si-Si02 interface. Such a study can provide
useful information about the hot carriers reliability issues of
J. Yac. Sci. Technol. A, Yol. 7, No.3, MaylJun 1989 thin Si02 films used as gate dielectrics in metal-oxide semi
conductor field effect transistors.21
IV. CONCLUSION
In this paper, we have presented an oxidation study of
8n02 and Si02 on silicon substrate formed by rapid isother
mal processing. As compared to furnace processing, im
proved quality of dielectrics are obtained by RIP. A possible
explanation for the improved quality of rapid isothermal
processed samples is due to the primary difference in the
radiation spectrum of the two sources of energy. These pre
liminary results indicate that photochemistry plays a signifi
cant role in the oxide growth by rapid isothermal processing.
More work is needed to understand the definite role of pho
tochemistry in the rapid isothermal oxidation process.
IR. Singh and J. Nulman, Mater. Res. Soc. Symp. Proc. 71, 44 (1986).
2K. Nishiyama, M. Arai, and N. Watanabe, Jpn. J. App!. Phys. 20, 124
(1981).
JR. Singh, J. Appl. Phys< 63, R59 (1988).
4R. Singh and F. Radpour, SPIE Proc. 945, 72 (1988)<
'So E. Lassig, T. J. Debolske, and J. L. Crowley, Mater. Res. Soc. Symp.
Proc.92, !O3 (1987).
oN. E. McGruer, K Singh, J. It Weiss, and K. Rajkanan, J. App\. Phys. 62,
3405 (1987).
7H. Z. Massoud and J. D< Plummer, J< Electrochem. Soc. 132, 2685 ( 1985).
8J. F. Rabek, Experimental ll.fethods in Photochemistry and Photo physics,
Part 1 (Wiley, New York 1982), p. 50.
9 A. G< Gaydon, Dissociation Energies and the Spectra of Diatomic Mole
cules, 3rd ed. (Chapman and Hall, London, 1968), p. 74.
IOH. Okabe, Photochemistry a/Small Molecules, (Wiley, New York 1978),
p. 177.
"E. A. V. Ebasworth, J. A. Connor, and J. J. Turner, The Chemistry of
Oxygen (Pergamon, Oxford, 1973).
12N. Birk and G. M. Meier. Introduction to High Temperature Oxidation of
Metals (Arnold, London, 1983).
Dp. Kofstad. High-Temperature Oxidation of Metals (Wiley, New York,
1966).
14R. W. G. Wyckoff, Crystal Structures, 2nd ed. (Wiley, New York, 1963),
Vol 1, pp. 28-29, 134-136, and 250-252<
"M. Gielen, in Topics in Inorganic and organmetalfic Stereochemistry, edit
ed by G. Geoffroy (Wiley, New York, 1981), Vol. 24, p. 217.
lOp. Chou, R. Singh, F. Radpour, M. Rahmati, H. S. Ullal, and A. J. Nelson
J. App!. Phys. (submitted).
DR. Rajsuman and R. Singh, J. Electrochem. Soc. 135, 237 (1988).
'"R. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cam
bridge University, Cambridge, 1952). P< 437.
19S. R. Morrison, The Chemical Physics of Surfaces (Plenum, New York,
1977), pp. 223-262.
20F. A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry: A Com
prehensive Text (Wiley, New York 1980). p. 375.
21R. Singh, in Proceedings a/the Symposium on Silicon Nitride and Silicon
Dioxide Thin Insulating Films, Electrochemical Society, Fall Meeting,
San Diego, CA, 1986, edited by V. K. Kapoor (Electrochemical Society.
New York, 1987), Vol. 87-10, p. 448.
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1.100468.pdf | Thinfilm high T c superconductors prepared by a simple flash evaporation technique
M. S. Osofsky, P. Lubitz, M. Z. Harford, A. K. Singh, S. B. Qadri, E. F. Skelton, W. T. Elam, R. J. Soulen Jr., W.
L. Lechter, and S. A. Wolf
Citation: Applied Physics Letters 53, 1663 (1988); doi: 10.1063/1.100468
View online: http://dx.doi.org/10.1063/1.100468
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Published by the AIP Publishing
Articles you may be interested in
Oriented thin films of YBaCu(F)O with high T c and J c prepared by electron beam multilayer evaporation
Appl. Phys. Lett. 54, 1573 (1989); 10.1063/1.101317
A flash evaporation technique for oxide superconductors
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High T c superconducting thin films by rapid thermal annealing of Cu/BaO/Y2O3 layered structures
Appl. Phys. Lett. 53, 2229 (1988); 10.1063/1.100510
Plasma oxidation of Ba2YCu3O7 − y thin films
Appl. Phys. Lett. 53, 618 (1988); 10.1063/1.100636
Asdeposited superconducting YBaCuO thin films on Si, Al2O3, and SrTiO3 substrates
Appl. Phys. Lett. 52, 2174 (1988); 10.1063/1.99760
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129.120.242.61 On: Sat, 22 Nov 2014 18:18:14ThinmfUm high Tc superconductors prepared by a simpie flash evaporation
technique
M. s. Osofsky, P. Lubitz, M. Z. Harford, A K. Singh, S. B. Qadri, E. F. Skelton,
W. T. Elam, Fl.. J. Soulen, Jr., W. L. Lechter, and S. A Wolf
Naval Research Laboratory, Washington, DC 20375-5000
(Received 20 June 1988; accepted for publication 1 September 1988)
Thin films of Bi-Sr-Ca-Cu-O and TI-Ba-Ca-Cu-O have been deposited on single-crystal MgO
substrates by a simple flash evaporation technique. Small pellets of the superconducting
compound were fonned by standard techniques, then evaporated to completion on the MgO
substrates using an electron beam. The best films show an onset of superconductivity at
approximately 110 K and zero resistance by 78 K. X-ray diffraction measurements show the
films 10 be tetragonal with nominal lattice parameters of a = 3.85 A and c = 30.66 A. The x
ray data also show the mms to be highly textured with the metal-oxide planes parallel to the
substrate surface.
Superconductivity has been reported recently in the Hi
Sr-Ca-Cu-O system by Maeda et al. I and by Chu et al.2 with
indications of a transition starting at temperatures up to 120
K. Similarly, evidence of superconductivity above 100 K
was found in the Tl-Sa-Ca-Cu-O systems by Sheng and Her
man3 and in T12Ba2Ca2Cu301O by Torardi et al.4 Several
groups have reported data on thin films of this material pre
pared hy sputtering,5 evaporation from mUltiple sources, (, or
laser ablation.7 This letter presents an alternative and yet
simple method to prepare films of this oxide where the stoi
chiometry of the starting material is maintained. There are
at least two crystallographic phases of this material but as of
yet no one has prepared single-phase material of the higher
Tc compound. The technique described below allows the
rapid variation of stoichiometry needed to ultimately deter
mine the composition and structure ofthis higher transition
temperature materiaL
The films were prepared by a flash evaporation tech
nique utilizing a conventional electron beam source and
glass bell jar vacuum system. Superconducting pellets of the
appropriate compoSltlOI1, e.g., Bi4Sr]Ca3Cu40x or
TIzBazCaICu20x, prepared by the conventional solid-state
reaction techniques, I were cut into pieces weighing approxi
mately 0.25 g cach and placed in the electron gun hearth.
The base pressure in the system was about 10 H Torr, but
was about 10 5 Torr during the depositien. Each pellet was
evaporated to completion thereby providing the same ratio
of dements arriving at the substrate that was present in the
starting compound. The substrate, a polished ( 100) face of a
single crystal of MgO was kept at 300 "C. Each area of the
hearth covered by the electron beam spot contained enough
material for depositing approximately 1000 A thickness of
the Bi-Sr-Ca-Cu-O material on the substrate. This limitation
arises from the need to outgas the pellets before starting the
deposition; larger pellets tend to release gas and material
explosively. Evaporating a larger number of pellets could
easily provide films approaching 1 Il,m in thickness. If an
automatic feed system were used, or the material were vacu
um melted externally, much greater thicknesses would be
possible with this technique.
The films were annealed in air at 840°C for times vary-
1663 Appl. Phys. Lett 53 (17). 24 October 1988 lug from 10 min to 16 h in a simple box furnace and then were
quenched to room temperature. The films cculd be crystal
lized and made §uperconducting with anneal times of only a
few minutes, although properties improved with longer an
neals. For example, following a 10 min anneal a sample of
the Bi4Sr 3Ca,CU40" composition showed a transition to
R = 0 at about 75 K; whereas a 4 h anneal raised the R = 0
temperature to 78 K, improved the resistance ratio (the ratio
of the value of the resistance at room temperature to the
value just above the transition), and produced a fraction of
the higher transition temperature phase as evidenced by a
small drop in the resistance between 115 and 110 K.
The resistance versus temperature was measured using a
standard low frequency, ae four-terminal technique with
pressure contacts forming the electrodes and with a current
of approximately 5 pA. The resistance versus temperature
for a 3(,'00-A-thick sample (obtained by evaporating three
pellets) annealed for 4 h at 840 °C and a lOOO-A-thick sam
ple ( obtained by evaporating one pellet) annealed for 10 min
at 840 °C is shown in Fig. ! (a). Nate that there is a small but
detectable drop at about 110 K and a zero resistance at 78 K.
Similar data are shown in Fig. 1 (b) for 11 2000-A-thick
T12Ba2CaCu20x film.
X-ray diffraction data, obtained with radiation from a
Cu x-ray tube, are similar for all of the superconducting sam
ples. The diffraction spectrum for the 2000-A.-thick
T12BazCaCuzOx film annealed for 30 s at 850°C and
quenched in air followed by an anneal for 30 min at 800 °C
(and air quenched} is typical (Fig. 2). The cross-hatched
peaks in the figure are from the MgO substrate; all the other
peaks can be indexed to (OOl) reflections (2<:1<;30) of the
structure reported by Tarascon et al. S for the nominal com
position Bi4(Sr,Ca)f,CU4016I "~ or, equivalently, to that of
Zandbergen et al." for the Bi2Sr2CalCu20x composition.
The c-axis lattice parameter associated with these :is
30.662 ± 0.021 A. A Read photograph, taken with the film
normal oriented at an angle of 1000 with respect to the x-ray
beam, is shown in Fig. 3. The bright, low-angle ring sections
on the right side are representative of the textured nature of
the material. The sample was mounted on a four-circle dif
fractometer and the (001) peaks identified in Fig. 2 were
1663
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129.120.242.61 On: Sat, 22 Nov 2014 18:18:14Bi-S,-Ca-Cu-O
6
S; 1000 A
E-
O) 4
<> I: ..
0;
<II
't <II a::
0 50 70 sa 11 0 130 150
(a)
T(K)
20C
TI-Ba-Ca-Cu-O
2000A
:§' (~ !!,
.,
'OO[ '" ;:: ..
0;
'iii
~. '" a:
0 40 50 SO 70 SO 90 ~oo 110
(b) T(K)
FIG. 1. (a) Upper: Temperature dependence ofthc resistance for two thin
film samples of Bi.,Sr ,C",Cu40X' The lOOO-A.-thick film was annealed for
10 min at 840 'C and 'thc3000-A-thick film was annealed for 4 h at 840 'Co
Both films were quenched to room temperature. (b) Lower: Temperaturc
dependence of the resistance of a 20UD-A-thick TI2J1a2CaCu 20, thin film
annealed for 30 s at 850 'C and quenched followed hy a second anneal f(Jr 30
min at 800 'Co
automatically aligned. The diffractometer (j) coordinates for
(008), (0010), and (0012) peaks of the superconductor
were aU within 0.06° of the value obtained in centering the
(002) reflection of the MgO substrate. This implies that the
~
"
0
r ,
r--
~ t-r
oX
~ ~ '~ \
\ -\ ,
= I c,
""
r i ,-
f-u.
'" e-
7
ANGLE (DEG)
FIG. 2. X-ray diffraction pattern for a 2000-A-thick film of
TleBa2CaC1l20x' All oithe sample peaks have been indexed to the metal
oxide (00l) reflections (2<1,;;30) in the tetragonal lattice identified in Ref.~.
8 and 9; the cross-hatched peaks are from the MgO substrate, (The pm-tion
of the spectrum above 45' was replotted with the ordinate scale factor de
creased by 10.)
1664 Appl. Phys. Lett., Vol. 53, No. 17,24 October 1988 FIG. 3. Read photograph of the film described in Fig. 2. Note the small,
low-angle, circular arcs on tile right side indicating strong texturing. The
elongated spots are from the single-crystal MgO substrate. Diffractometer
measurements show the metal-oxide planes to be aligned parallel to the sub
strate surface to withill 0.06°.
orientation of the metal-oxide planes of the superconductor,
which are normal to the c axis, are aligned with the substrate
surface, i.eo, the MgO (DOl) planes, to within 0.06°, which is
the precision of the instrumenL Oscillation photographs
were taken about the MgO (100) and (010) axes; unit cell
parameters of 3.85 A are inferred from the layer lines on
these photographs. This establishes the tetragonality of the
lattice to within the accuracy of these measurements. These
lattice dimensions, a = 3.85 A. and c = 30.66 ± 0.02 A., are
in good agreement with those reported in Refs. 8 and 9.
In summary, we have demonstrated that a very simple
evaporation technique can provide superconducting films of
Bi-Sr-Ca-Cu-O or TI-Ba-Ca-Cu-O. We have successfully
prepared highly textured films of the 80 K superconductor
with the previously indexed crystallographic structure and
are quite confident that this technique will yield the higher
temperature material.
The authors wish to acknowledge the sponsorship ofthe
Office of Naval Research (ONR), the Office of Naval Tech
nology (ONT), the Strategic Defense Initiative, Office of
Innovative Science and Technology (SDIO/IST), the De
fense Advanced Research Project Agency (DARPA), and
Nuclear Defense Agency (NDA),
IH. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano, Jpn. J. Appl. Phys. 27,
2 (1988).
2C. W. Chu, i.Bechtold, L Gao, P. H. Hor, Z. J. Huang, R. L. Meng, Y. Y.
Sun, Y. Q. Wang, and Y. Y. Xue, l'hys. Rev. Lett. 60, 941 (1988).
3Z. Z. Sheng and A. M. Herma:n, Nature 332, 138 (1988).
"c. C. Torardi, M. A. Subramanian, J. C. Calabrese, J. Gopalakrislman, K.
J. Morrissey, T. R. Askew, R. B. Flippen, U. Chowdhry, and A. W. Sleight,
Science 240,631 (1988).
SR. Adachi, Y. Ichikawa, K. Setsune, S. Hatta, K. Hirochi, and K. Wasa
(unpublished) .
'CO E. Rice, A. F. J. Levi, R. M. Fleming, P. Marsh, K. W. Baldwin, M.
Anzlowar, A. E. White, K. To Short, S. Nakahara, and H. L. Stormer,
App!. l'hys. Lett. 52,1828 (1988).
7C. R. Guarnieri, R. A. Roy, K. L. Saenger, S. A. Shivashankar, D. S. Vee,
1.1. Cuomo (unpublished).
"J. M. Tarascofl, Y. LePage, P. Burlouz, B. G. Bagley, L. H, Green, W. R.
McKinnon, G. W. Hull, M. Giroud, and D. M. Hwang (unpublished).
"n. W. Za:ndbcrgen, P. Groen, G. Van Tcndeloo,l. Van Landuyt, and S.
Amelinckx, Solid State Commun. 66, 397 (1988).
Osofsky et at. 1664
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1.576332.pdf | Plasma enhanced chemical vapor deposition of HgTe–CdTe superlattices
L. M. Williams, P.Y. Lu, S. N. G. Chu, and M. H. Ross
Citation: Journal of Vacuum Science & Technology A 7, 3183 (1989); doi: 10.1116/1.576332
View online: http://dx.doi.org/10.1116/1.576332
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/7/6?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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HgTe–CdTe superlattices and Hg1−x Cd x Te grown by lowtemperature metalorganic chemical vapor
deposition
J. Vac. Sci. Technol. A 5, 3153 (1987); 10.1116/1.574858
CdTe photoluminescence in HgTeCdTe superlattices
J. Appl. Phys. 62, 1516 (1987); 10.1063/1.339614
Multilayers of HgTeCdTe grown by lowtemperature metalorganic chemical vapor deposition
J. Appl. Phys. 62, 295 (1987); 10.1063/1.339144
Interdiffusion in HgTe–CdTe superlattices
J. Vac. Sci. Technol. A 4, 2101 (1986); 10.1116/1.574035
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 155.33.120.209 On: Sat, 22 Nov 2014 05:41:34Plasma enhanced chemical vapor deposition of HgTe-CdTe superlattices
L. M. Williams, P. -Yo Lu, S. N. G. Chu, and M. H. Ross
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
(Received 28 November 1988; accepted 13 June 1989)
Plasma enhanced chemical vapor deposition was used to grow epitaxial layers of cadmium
telluride and mercury telluride from metalorganic compounds. High deposition rates were
obtainable for both of the materials, and the plasma allowed epitaxial growth to occur at
temperatures that were markedly lower than those required for the standard metalorganic
deposition processes. Properties of the mercury telluride and cadmium telluride will be presented.
Superlattices were grown at 150·C that had 70 A. thick mercury telluride layers.
I. INTRODUCTION
HgTe-CdTe superlattices, at present, are of interest for a
variety of infrared device applications. In terms of cost and
simplicity metalorganic chemical vapor deposition
(MOCVD) is preferred over molecular-beam epitaxy
(MBE). Two MOCVD methods have been reported to al
low the growth of HgTe-CdTe superlattices: a precracking
technique1,2 and a photochemical process.3 Although both
methods appear promising, they are relatively new and it is
unclear, at this time, whether either process will yield device
quality material; consequently, further research to find new
processes is warranted.
Plasma enhanced chemical vapor deposition (PECVD)
has a number of features that make it attractive for the
growth HgTe-CdTe superlattices. PECVD allows growth of
epitaxial layers of semiconductors such as gallium arsen
ide,4,5 gallium arsenide phosphide,6 and zinc selenide7 from
hydrides and metalorganic compounds. In addition to high
er growth rates, some materials can be deposited epitaxially
using PECVD at lower temperatures than are required for
non-plasma processes,4,7 and the electronic properties of
some of the plasma deposited layers are superior to those for
the non-plasma deposited layers.5 Similarly, epitaxial mer
cury telluride, having good electronic properties, has been
grown at 85·C using PECVD.8
This paper presents an overview of preliminary results ob
tained using PECVD to grow epitaxial layers of mercury
telluride and cadmium telluride for superlattices. Data on
growth rate, morphology, electronic properties, and compo
sition will be given. Cross-section transmission electron mi
crographs of the superlattices will also be presented.
II. EXPERIMENTAL
A diagram of the reactor is shown in Fig. 1. The reactor is
a parallel-plate system with stainless-steel electrodes (40
mmindiameter). To generate the plasma, 2 W ofrfpower at
15 MHz was applied to the top electrode. Substrates were
placed on the grounded electrode and heated with a resis
tance heater. Dimethylmercury, dimethylcadmium, and di
methyltelluride were delivered to the reactor from bubblers
using hydrogen as a carrier gas. The flow rates of hydrogen
through the bubblers were regulated with mass flow control
lers. For multilayer deposits, the switching and resetting of
the gas flows were computer controlled. System pressures of
0.1 to 0.5 Torr were examined. The substrates were semi-insulating (100) cadmium tel
luride and cadmium zinc telluride from Fermionics, Inc. Be
fore deposition, the substrates were cleaned in acetone and
rinsed in methanol. They were then etched in a dilute bro
mine-methanol solution. The etched substrates were further
rinsed with methanol and then blown dry with nitrogen.
After loading the substrates into the reactor, the reactor was
evacuated. Under flowing hydrogen, the substrates were
heated to the deposition temperature, and the plasma was
started after the flows for the metalorganics had stabilized.
Surface morphology of the films was examined using No
marski differential interference contrast microscopy. Car
bon concentrations were measured using secondary ion mass
spectroscopy. The standard van der Pauw technique was
used to measure carrier concentrations and mobilities.
Cross-section transmission electron micrographs were made
to determine the periods for superlattices with different layer
growth time intervals. Sample thinning for the electron mi
croscopy was done chemically using a technique described
earlier.9 The electron micrographs were obtained with a
Philips 420 electron microscope operating at 120 keY.
III. RESULTS AND DISCUSSION
A. Thick HgTe layers
The growth of thick films of HgTe by PECVD has been
described in more detail in an earlier paper.8 Typical depo-
t
GAS
INLET BELL JAR
C~::::J----l~- TOP ELECTRODE
r-'==~--t-- SUBSTRATE
BOnOM ELECTRODE
" HEATER
REACTOR BASE
-TO PUMP
FIG. 1. PECVD reactor diagram.
3183 J. Vac. Sci. Technol. A 7 (6), Nov/Dec 1989 0734-2101/89/063183-05$01.00 © 1989 American Vacuum Society 3183
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sition rates were 3 to 4.umlh for the growth of good quality
mercury telluride, and the rate varied inversely with tem
perature. In earlier experiments, the PECVD mercury tellu
ride grown at 85 ·C had the best surface morphology and
electronic properties; going to higher or lower temperatures
degraded the properties. However, at present, the morpholo
gy and electronic properties of the mercury telluride grown
at 150 ·C match or surpass that for the layers grown at 85 ·C
during the earlier studies.8 The material grown at 150 ·C is n
type with a carrier concentration of 1.5X 1017 cm-3 and a
mobility of22 000 cm2IV s at 300 K; the mobility increases
to 64 000 cm2 IV s and the carrier concentration decreases to
8 X 1016 at 77 K. The surface morphology of a mercury tellu
ride layer (2.um thick) grown on a cadmium telluride sub
strate at 150 ·C is shown in the Nomarski photograph in Fig.
2. The only significant features are some hillocks that are
induced by the substrate.
The mercury telluride layers are grown under the same
conditions (i.e., pressure, metalorganic flows, rfpower, and
frequency) as those grown in the earlier studies. The im
provement in the electronic properties for the layers deposit
ed at 150·C occurred after changing to a higher purity di
methylmercury source from Alfa Products. All of the
depositions using the high-purity dimethylmercury have
been done at 150 ·C. However, it is possible that layers
grown at other temperatures may also have improved elec
tronic properties. The optimum conditions for PECVD of
mercury telluride are still unknown and further studies are
needed.
B. Thick CdTe layers
For the flow rates and pressures used in this study, cad
mium telluride layers could not be deposited, even at 350 ·C,
unless the plasma was used. The growth rate of the cadmium
telluride was higher than that for the mercury telluride; to
accommodate the higher growth rate, the top electrode had
to be converted to a shower-head arrangement instead of the
single-hole design. Figure 3 shows the deposition rate of
PECVD cadmium telluride as a function of substrate tem
perature. The rate decreases with increasing temperature,
following a behavior similar to that observed for PECVD
FIG. 2. Nomarski micrograph of the surface of a PECVD HgTe layer grown
at 150'C on a CdTe substrate.
J. Vac. Sci. Technol. A, Vol. 7, No.6, Nov/Dec 1989 3184
TEMPERATURE ("C)
8 150 200 250 300 350
-6 -... ......
E
~
III
~ 4 c a:
:z: • 0 a: 2 CII
0
40 60 60 100 120 140
TEMPERATURE ("C)
FIG. 3. Deposition rate data for mercury telIuride and cadmium telIuride
grown by PECVD.
mercury telluride growth. For comparison, deposition rate
data for PECVD mercury telluride are also reproduced in
Fig. 3. Initially, the decrease in growth rate for the mercury
telluride was attributed to the increasing requirement for
mercury, in the gas phase, as temperature increased. How
ever, the results for the cadmium telluride growth suggest
that the rate decrease must be controlled by some other fac
tors; for example, back reactions or etching processes could
become more significant at the higher temperatures.
Epitaxial cadmium telluride layers with good surface
morphology could be grown at -150 ·C. A Nomarski pho
tograph of a 2.5.um thick layer grown on a cadmium zinc
telluride substrate is given in Fig. 4. There is some texture in
the surface, however, the epilayer looks similar to the bare
substrate. The surface is specular to the eye.
Hall measurements done on the deposited cadmium tellu
ride showed the layers to be n type. The layers grown at the
higher temperatures had higher carrier mobilities. The layer
grown at 350 ·C had a room temperature electron mobility
of 600 cm2 IV s and a carrier concentration of 1 X 1016 cm -3,
while the layer shown in Fig. 4, grown at 150 ·C, had a mo
bility of 400 cm2 IV s and the same carrier concentration as
the 350 ·C layer.
C. Multilayers
The first multilayers attempted were intended to be simple
multiples (two, four, six) of thick alternating layers of mer
cury telluride and cadmium telluride. However, two major
difficulties were encountered: the surface morphology was
always rough, and the multilayer structure, usually, would
become polycrystalline at the start or during the growth of
the first cadmium telluride layer (i.e., the second layer).
There was an exception to this behavior for a four-layer
structure grown at 16O·C. A Nomarski photograph of the
cleaved edge of a section of that film is presented in Fig. S; all
four layers are visible and the cleaved edge is smooth for each
layer. The individual layer thicknesses are -2 .urn. The
problem with this layer is that the cleaved edge shown in Fig.
5 is for the material that deposited on the side of the sub
strate; the material on the top surface of the substrate be-
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FIG. 4. Nomarski micrograph of the surface of a PECVD cadmium telluride
layer on a cadmium zinc telluride substrate.
came polycrystalline after the first mercury telluride layer.
At this time, it is unclear why the layers on the side of the
substrate were better than those on the top surface. An ex
planation may be related to the fact that the side surface has
the (110) orientation instead of the (100) orientation of the
top surface.
Both of the difficulties for growing the multilayers were
eliminated by allowing the dimethylmercury flow to stay on
during the growth of the cadmium telluride layers: specular
epitaxial multilayers could be deposited reproducibly at
150 ·C, with this modification. At the temperature and par
tial pressures for deposition, the mercury incorporation effi
ciency is small compared to the cadmium incorporation effi
ciency, resulting in cadmium rich (i.e., x close to 1)
Hgi _ x Cdx Te. For some of the HgTe-CdTe superlattices
grown by molecular-beam epitaxy, the cadmium telluride
layers are deposited with the mercury flux on 10; this also
yields cadmium telluride containing small amounts of mer
cury. Having mercury present during MBE of cadmium tel
luride is believed to prevent the formation of tellurium pre
cipitates and to allow good quality material growth at lower
temperatures than are required for superlattices with pure
cadmium telluride. 10 A mechanism similar to that for the
MBE process may have an influence on the PECVD grown
layers. The higher concentration of methyl radicals that oc
curs when the dimethylmercury is present during PECVD
cadmium telluride growth could also be beneficial. Irvine et
al. II reported getting improved results, attributed to the
higher methyl radical concentration, after adding dimethyl
mercury during photochemical vapor deposition of
Hgi _ x Cdx Te. The PECVD process is sufficiently complex
that both of the above-mentioned phenomena may be occur
ring.
FIG. 5. Nomarski micrograph of cleaved edge for a four-layer structure of
mercury telluride and pure cadmium telluride.
J. Vac. Sci. Technol. A, Vol. 7, No.6, Nov/Dec 1989 3185
Carbon concentration profiles were measured for one of
the simple multilayer structures using secondary ion mass
spectroscopy (SIMS). The structure contained six alternat
ing layers of mercury telluride and cadmium telluride grown
at 150·C on a cadmium telluride substrate. Mercury tellu
ride was the first layer; the total thickness for the six layers
was -3 f.lm (0.6 f.lm for each CdTe layer, 0.4 f.lm for each
HgTe layer). Figure 6 shows the concentration depth pro
files. It is interesting that the concentrations of carbon are
about 25 times higher in the cadmium telluride layers than in
the mercury telluride. The carbon concentrations in the mer
cury telluride layers, for those sputtering conditions, are be
lieved to be at the background level. There are several possi
ble explanations for the large difference in carbon
concentrations for the mercury telluride and the cadmium
telluride. Perhaps the simplest explanation is that when di
methylcadmium is exposed to the plasma, at least under cer
tain conditions, one of the reaction products is a molecule
containing a strong cadmium--carbon bond that results in
the higher carbon content of the cadmium telluride layers.
However, additional experiments will be necessary before
the true mechanism of the carbon incorporation is known.
Whatever the mechanism, the most important aspect of
the carbon concentration measurements is that the low
amounts of carbon present in the mercury telluride is evi
dence that carbon incorporation is not an inherent problem
for PECVD processes wherein the metalorganic compounds
flow directly into the plasma.
D. Superlattices
To determine the smallest period possible, layers were
grown for times ranging from 10 min to 30 s. The layers were
all grown with the substrate at 150·C and a reactor pressure
1022~----------------------------.
CARBON
TIME
FIG. 6. Carbon SIMS concentration depth profiles for a six-layer structure.
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of 0.5 Torr. For the mercury telluride growth, the carrier gas
flows through the dimethylmercury and dimethyltelluride
were 20 and 18 std. cm3/min (sccm), respectively. The cad
mium telluride layers were grown using carrier flows of 20,
6, and 2.4 sccm for dimethylmercury, dimethyltelluride, and
dimethylcadmium, respectively. The metalorganics were
kept at O·C.
A cross-section transmission electron micrograph of a
multiple period superlattice is given in Fig. 7. The first layer
grown was mercury telluride. Each of the first four layers
had a growth time of 10 min. As can be seen in the figure, the
first mercury telluride layer is about three times thicker than
the second mercury telluride layer although the first and
second cadmium telluride layers are about equal in thick
ness. We suspect that the larger thickness of the first mer
cury telluride may be associated with the initiation of the
plasma and subsequent matching of the rf power during the
growth of the first layer. This type of behavior for the growth
of the first layer can be avoided. Following the first four
layers, eight layers were grown using 5 min time intervals,
followed by 20 layers with 1 min growth times, and last, 20
layers were grown using the 30 s time period. The last 20
FIG. 7. Transmission electron micrograph showing cross section of a
PECVD epitaxial HgTe-CdTe multiple period superlattice grown at 150 'c
on a cadmium telluride substrate.
J. Vac. Sci. Technol. A, Vol. 7, No.6, Nov/Dec 1989 3186
layers were not distinct; together they appeared as one ho
mogeneous layer, suggesting that the gases intermixed on
the way from the bubblers to the reactor. However, each of
the layers for the longer growth times are visible in the mi
crograph; the thinnest layers, grown for 1 min each, are
-160 A for cadmium telluride and -180 A for mercury
telluride.
Further reductions in individual layer thickness were ob
tained using a growth interrupt process to hinder intermix
ing of the metalorganics in the feed line. After each layer of
the superlattice was grown, hydrogen and dimethylmercury
were used to purge the gas line and reactor for 30 s before the
next layer was started. This allowed deposition of70 A mer
cury telluride layers and 140 A cadmium telluride layers for
30 s growth times. Figure 8 shows a cross-section transmis
sion electron micrograph of a superlattice grown using the
growth interrupt procedure for the conditions given above.
Of course, the interface sharpness cannot be quantitatively
determined from the cross-section microscopy, however, the
results that have been obtained look promising. Further op
timization of this deposition process should yield smaller
period superlattices with interfaces that are as good as those
obtained by MBE.
The superlattices that were grown for this study and ex
amined by transmission electron microscopy (TEM) are of
good quality, at least within the detection limits of TEM.
There was never any evidence of crystallites, grain boundar
ies, dislocations, or defects of any kind in the transmission
electron micrographs. Additional work is in progress to
further optimize the deposition process and characterize the
layers.
IV. SUMMARY AND CONCLUSIONS
PECVD can be used to grow thick epitaxial layers of mer
cury telluride that have good surface morphology and elec
tronic properties. Pure layers of epitaxial cadmium telluride
can be grown using PECVD, but the quality is only fair and
further work is needed for improvement. However, when
dimethylmercury is present during the cadmium telluride
deposition, the layer quality increases, and the process be
comes more reproducible. Superlattices with mercury tellu
ride layers as thin as 70 A have been produced. PECVD
appears to be a promising method for the growth of HgTe
CdTe superlattices and deserves further research.
FIG. 8. Cross-section transmis
sion electron micrograph of a su
perlattice grown using interrupt
procedure (30 s layer growth and
30 s interruption).
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ACKNOWLEDGMENT
We are grateful to C.-H. Wang for his help and contribu
tions to this project.
'L. M. Williams, P.-Y. Lu, S. N. G. Chu, and C.-H. Wang, J. App!. Phys.
62,295 (1987).
2p._y. Lu, L. M. Williams, C.-H. Wang, and S. N. G. Chu, J. Vac. Sci.
Techno!. A 5,3153 (1987).
3W. L. A1hgren, J. B. James, R. P. Ruth, E. A. Patten, and J.-L. Stauden
mann, in Materials for Infrared Detectors and Sources, edited by R. F. C.
Farrow, J. F. Schetzina, and J. T. Cheung (Materials Research Society,
Pittsburgh, 1987), p. 405.
4K. P. Pande and O. Aina, J. Vac. Sci. Techno!. A 4,673 (1986).
J. Vac. Sci. Technol. A, Vol. 7, No.6, Nov/Dec 1989 3187
5 A. D. Huelsman, R. Reif, and C. G. Fonstad, App!. Phys. Lett. 50, 206
(1987).
6A. D. Huelsman, L. Zien, and R. Reif, App!. Phys. Lett. 52, 726 (1988).
7N. Mino, M. Kobayashi, M. Konagai, and K. Takahashi, J. App!. Phys.
59,2216 (1986).
8L.M. Williams,P.-Y. LU,C.·H. Wang,J.M.Parsey,Jr.,andS. N.G.Chu,
App!. Phys. Lett. 51,1738 (1987).
9S. N. G. Chu and T. T. Sheng, J. Electrochem. Soc. 131,2663 (1983).
IOD. J. Leopold, M. L. Wroge, and J. G. Broerman, App!. Phys. Lett. SO,
924 (1987).
"s. J. C. Irvine, J. B. MuIIin, G. W. Blackmore, O. D. Dosser, and H. Hill
in, Materials for Infrared Detectors and Sources, edited by R. F. C. Far
row, J. F. Schetzina, and J. T. Cheung (Materials Research Society, Pitts·
burgh, 1987), p. 153.
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1.583654.pdf | Nitrogen, oxygen, and argon incorporation during reactive sputter deposition of
titanium nitride
D. S. Williams, F. A. Baiocchi, R. C. Beairsto, J. M. Brown, R. V. Knoell, and S. P. Murarka
Citation: Journal of Vacuum Science & Technology B 5, 1723 (1987); doi: 10.1116/1.583654
View online: http://dx.doi.org/10.1116/1.583654
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/5/6?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.237.29.138 On: Thu, 13 Aug 2015 12:31:12Nitrogen, oxygen, and argon incorporation during reactive sputter
deposition of titanium nitride
D. S. Williams, F. A. Baiocchi, R. C. Beairsto, J. M. Brown, and R. V. Knoel!
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
S. P. Murarka
Rensselaer Polytechnic Institute, Department of Materials Engineering, Troy, New York 12180
(Received 2 June 1987; accepted 3 August 1987)
For the reactive sputter deposition of titanium nitride, stress and resistivity of the films has been
measured as a function of the processing variables target power, substrate bias, pressure, and N2!
Ar ratio. These studies were limited to the conditions that produce titanium nitride of
stoichiometry near 1. Through Rutherford backscattering spectroscopy, the changes in stress and
the conductivity of the films as a function of the processing variables were interpreted in terms of
nitrogen, argon, and oxygen concentration in the films. The increase in resistivity of the films
correlates with increased oxygen incorporation and the increase in compressive stress ofthe films
correlates with increased argon incorporation. The amount of oxygen in the films appears to
produce a unique value of resistivity but the argon concentration that produces a given
compressive stress is a function of the processing parameters that control argon incorporati.on.
t INTRODUCTION
The alloying of transition metals with the elements H, B, C,
0, N, and Si creates a family of structures known as intersti
tial compounds. I These alloys are known as such because the
smaller metalloid atoms are located in the octahedral or te
trahedral sites of the transition metal lattice. These com
pounds can be categorized by the relative sizes of the metal
and the metalloid atoms. For a radius ratio of metalloid- to
metal < -0.59, the lattice of the interstitial compound is
frequently found to be either cubic-or hexagonal-close
packed. For radius ratios> 0.59, the crystal structure of the
interstitia! compounds is usually more complex. For com
pounds of the stoichiometry MX, where X is either carbon,
nitrogen, or oxygen, the structure is frequently the NaG
structure which is composed of a fcc metal lattice with the
octahedral sites filled by the smaller interstitial atom. Exam
ples of these compounds are TiC, ScN, ZrN, VN, and ZrH.
The stoichiometry ofthese structures can vary widely by the
creation of vacancies on either the metal lattice sites or on
the interstitial sites. The result of these variations in stoichi
ometry can lead to a wide range of properties for materials of
nominally the same composition and structure.
Interstitial compounds are finding increased industrial
application because they can be materials of high conductiv
ity (including superconductivity), extreme hardness, and
good thermal stability. The use of titanium nitride is of par
ticular interest in electronic applications because of its low
resistivity and because it performs effectively as a diffusion
barrier to the dissolution of silicon into metals used in var
ious interconnection schemes, The history of successful utili
zation of this material in the electronics industry spans a
decade where TiN has acted as a barrier to the interdiffusion
of platinum into titanium in the gold beam lead metalliza
tion schemes.2•3
For electronics applications, the preferred processes for the deposition of titanium nitride films are: (i) reactively
sputtering or Oi) reactively evaporating titanium in a nitro
gen containing atmosphere. Research has been published on
the deposition technology and on the properties of the titan
ium nitride for sputter deposition processes4--10 and for evap
oration processes./u-12 A summary of the literature includes
the observations that the deposition rate of sputtered titan
ium nitride varies as nitrogen is added to the environment.
This is explained by a process of nit riding the target in order
to decrease the sputter yield at the cathode surface.7~~W The
evaporation of titanium has a strong gettering effect on the
nitrogen partial pressure which results in strong depen
dences of stoichiometry on processing variables. For exam
ple, the resistivity of the deposited films changes as nitrogen
is added to the reactor and as the resultant film stoichiome
try changes from the hexagonal.dose-packed titanium
structure to the tetragonal Ti2N phase and finally to the cu
bic TiN. Through this sequence of phase changes, the resis
tivity and hardness go through maxima and minima" 10 Even
for a single phase, experimental work has shown that the
hardness of TiN is dependent upon the N/Ti ratio in the
filmS and that the conductivity depends upon the nitrogen
partial pressure in the deposition environment. 10 Little work
has been done, however, to correlate the influence of gases
other than nitrogen to film properties. Oxygen is recognized
to cause increases in the resistivityt3 but quantitative data
are sparse. Argon is recognized to cause increases in com
pressive stressJ4 for reactive sputter processes but correla
tion with processing parameters is qualitative.
The purpose of this work is to characterize the depen
dence of stress and resistivity on the incorporated gas con
centration in reactively sputtered TiN films and to correlate
the film stoichiometry and the concentration of oxygen and
argon to the process variables. We will attempt to identify
the extent to which film properties are altered by residual gas
incorporation and to correlate these changes with processing
parameters.
1723 oJ" Vac. Sci. Techno!. 1'35 (6), Nov/Dec 1987 0734-211X/S7!061723-07$01.00 @ 1987 American Vacuum Society 1123
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II. EXPERIMENT
The titanium nitride films were deposited in a planar dc
magnetron sputter station shown schematically in Fig. L
The system is a commercial apparatus (Perkin Elmer 4450)
designed for manufacture. The depositions were made onto
silicon substrates of < 100) orientation by sputtering a high
purity titanium target in an ambient of argon and nitrogen.
Samples were loaded onto a pallet in the turbomolecular
pumped load-lock chamber, baked for 5 min at ~ 100 ·C,
and simultaneously pumped to _10-5 Torr. The pallet was
then loaded into the cryogenic-pumped reaction chamber
and pumped to a base pressure < 10-6 Torr. The target was
precleaned and the vacuum system gettered by striking the
dc plasma in a flowing argon ambient and by sputtering ti
tanium for 1 min with the shutters closed which prevented
deposition onto the wafers. The dc plasma was then extin
guished and the radio frequency (rf) discharge initiated to
backsputter clean the substrates. This 5 min cleaning proce
dure was estimated to remove < 10 A of thermally grown
Si02• The nitrogen flow was then initiated, the dc plasma
restored, and the shutter opened to expose the wafers. The
deposition was continued for times from 1 to 20 min. No
effort was made to control the substrate temperature but the
preheat of the pallet maintained the substrates in the tem
perature range of 80 ·C. The gas flow into the reactor
chamber was controlled by mass flow controllers and the
total pressure was controlled by baffling the cryogenic
pump. The process sequence, including the preheat, the
load-lock evacuation, the substrate rf power, the target dc
power, and the time for each processing step was controlled
by a microprocessor to allow fully automatic operation of
the deposition reactor. The substrates on which the deposi
tions take place were biased relative to ground by the imposi
tion of an rf field. The substrate bias was controlled as a
percentage of the total available power and was recorded as
the resultant bias voltage.
The resistivity, stress, and composition of the deposited
TiN films were characterized. The resistivity was measured
by four-point probe and converted into specific resistivity by
thickness measurements made from Rutherford back
scattering spectroscopy (RBS) and from surface profilo-
FIG. 1. Schematic of sputter deposition apparatus. (A) Sample transfer
pallet; (B) Sample loading door; (Cl Turbomolecular pump; (D) Load
lock door; (E) Rotating shutters; (F) Planar magnetron cathodes; (G)
Gas flow system; (H) Cryogenic pump; (I) dc power supply; (1) rf power
supply.
J. Vac. Sci. Techno!. S, Vol. 5, No.6, Nov/Dec 1987 1724
metry. Steps were etched into the TiN by pH adjusted ethy
lenedinitrite tetracetic acid (EDTA) solutions at room
temperature. The stress calculations were made by measur
ing the radius of curvature of the substrate before and after
deposition of the TiN film and ascribing the change in curva
ture to a uniform biaxial stress in the deposited film. The
radius of curvature measurements were made using an opti
cally leveraged laser apparatus. 15
The composition of the deposited films were analyzed by 2
meV He+ ion backscattering spectroscopy. The elements
analyzed were titanium, nitrogen, argon, and oxygen. The
analysis beam was aligned with the (100) axis of the Si sub
strate to ~ecrease the substrate signal and improve the sig
nal-to-nOIse for measurement of N and O. A typical spec
trum is shown in Fig. 2. The error in the N/Ti ratio is 5%
that in the OITi and Ar/Ti ratios is 10%-15%. The thick~
ness is calculated from the energy width of the titanium peak
at half-height using the bulk density of TiN (5.22 g cm--3).
In general the atom ratios are obtained for the top 300-400 A
of the film. No nonuniformities of composition with depth
were observed, so that the values are valid for the entire
thickness of the film. However, the depth profile for the ar
gon component is not resolved completely because the titan
ium peak covers that portion of the Ar peak corresponding
to the upper one-half of the film. The spectra show that the
argon content increases (sometimes sharply) at the Si/TiN
interface (see insert, Fig. 2). AU samples seem to have a
hig~-Ar c?ntent at this interface regardless of processing
~anables, mcluding the elimination of Ar-ion backsputter
mg ofthe surface prior to TiN deposition. However, the Ar/
Ti ratio given in the figures is a measure of the uniform con
centration within the film, and does not include the contri
bution from argon at the interface. Note that the elements
Ar, N,. and ° are ~orma1ized to the titanium signal through
out thiS work. ThIS technique was used for internal consis
tency in data reduction. Because the stoichiometry of all
films. is N/T~ -1, the residual gas concentration can be ap
proxImated m atom fraction by dividing the respective ratio
by two. Iron was detected in all TiN films at a level of 0.1
at. %.
20.000
16,000
12,000 N
0 ,..!""';\.,* ..J
W ;:
8000
4000 0
+
1.26
ENERGY (MeV I 1.49 L73
FIG. 2. RBS spectra for TiN films deposited at high-and low-substrate bias.
The insert shows 20X expansion of scale with the calculated Ar/Ti ratios,
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III. RESULTS
Several researchers have shown that the N2/ Ar ratio dur
ing reactive sputter deposition determines which of several
phases is deposited. 5,7 ,Il,10 In this work, we have confined our
interest to those deposition conditions that produce TiN of
the NaCl structure. We therefore have varied the processing
parameters over the ranges that produce TiN of stoichiome
try near one. In this sense, our work is a subset of previous
work in that we have investigated a narrow range of param
eter space that produces only the phase that is of interest.
The independent processing variables in our deposition pro
cess that influence the film stoichiometry are the following:
( 1) nitrogen to argon ratio in the gas (N 21 Ar) as measured
in relative flow rates; (2) the total pressure in the sputter
chamber; (3) the rf power applied to the substrate, and (4)
the dc power applied to the cathode. In this section we will
present the influences of these variables on film stoichiome
try, film properties, impurity gas content, and microstruc
ture.
Experiments with varied Nz/ Ar ratios were run at a fixed
argon flow rate of 40 seem with the nitrogen flow varying
from 1 to 10 seem. Depositions were made as a function of
total reactor pressure from values of
~ 5 X 10--3 to -4 X 10-2 Torr. Variations in the N21 Ar ra-
.j._ 1.11
1.07
-105
-:0.99
0.25
FIG. 3. Composite plot of physical properties, gas concentrations, stoichi
ometry, and deposition rate of sputtered TiN as a function of total pressure
during sputter deposition.
J. Vac. Sci. Technol. S, Vol. 5, No.6, Nov/Dec 1987 1725
did not produce measurable variations in the stress or resis
tivity of the deposited films at any of the total pressures in
vestigated. The values ofN/Ti, O/Ti, and Ar/Ti determined
by RBS were also independent of N 21 Ar ratio over the con
ditions investigated.
Figure 3 is a plot of changes in the physical properties and
changes in the residual gas concentration oftitanit'm nitride
as a function of the total pressure of the sputtering process.
These films were deposited with constant substrate bias of 60
W ( -150 V). The changes in the compressive stress of the
films covers nearly a factor of 10 as it decreases from
~4 X 1010 dynes/cm2 at low pressure to -5 X 109 dynesl
cm2 at high-sputtering pressures. The resistivity undergoes a
similar dramatic change as the pressure is increased, but the
resistivity increases as the pressure increases, from values of
-75 pn em at low pressure to -350,un em at high-sputter
ing pressures. From the RBS analysis, the residual oxygen
content in the films increases dramatically as the deposition
pressure increases from values ofO/Ti::.:;O.05 to O/Ti:=.:;O.25
at high pressure. Figure 3 shows that the Ar/Ti ratio de
creases and the deposition rate decreases as the total pres
sure increases. The dependence of Ar/Ti on pressure ap
pears to be a simple linear relationship but the deposition
rate appears to be more strongly dependent upon pressure at
0!5r
~ I z 0.:01 g
;-
~ 005~
~ l ~ 0.00 .
E 200 . u
2:
~ 150-
>-1-
:> iOO-
t;;
iii
l5=' 50l ::.
:::> Z
] 103 ~ i= .....
-"-~--1r-----"=--_-"-'_-J:L -1.00 z
JO.97 ~
z
~ FIG.7b ~
--~7d
_..l. __ -,-_.l._-,-_ .l_--, __ L_L _L-_-L.J
-150 -170 -190 -210 -230 -250
SUBSTRATE BIAS (VOLT)
I I I i I I o 100 200 300 400 500 600
RF SUBSTRATE POWER (WATT)
FIG. 4. Composite plot of stress, resistivity, gas concentrations, deposition
rate, and film stoichiometry of TiN as a function of the rf substrate power.
••••• ,. •••••••• ;.--.-••••••••••••••••••••••• -......... <; ••••••••••••• ,.-• ., •••• • •• ·.·.'.-.·.-••••••• ·.'.v.·.·,.·.-....•. ·· .... -.-.-.... ~ ....••• ; •..• :.~.:.:.;.:.:.; •.....•.•.•. ' •..•. "'7 ••• -••• Y> •••••• -.
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lower pressures. Figure 3 shows also a dependence of the N/
Ti ratio on the total pressure, with values of N/Ti;:::: 0.99 at
low pressure increasing to -1.11 at high-sputteriug pres
sures.
Figure 4 is a composite of the dependence of the physical
properties and the compositional parameters of TiN as a
function of the rf substrate power. The substrate power, as
explained, is selected as a percent of available power and is
given in units of watts. The resultant bias voltage is also
shown. The resistivity decreases linearly with substrate pow
er from values of 150 pH cm at low-substrate power to -75
fl!l cm at 600 W power ( -245 V). The compressive stress
increases as the substrate power increases over the same
range. The O/Ti ratio is measured at values of ~O.l at low
power but decreases to below the detectability limit of RBS
(~O.03) as the power is increased. The Ar/Ti ratio in
creases linearly and the deposition rate decreases with sub
strate power. The N/Ti ratio is weakly dependent upon the
substrate power, but is more strongly influenced by the total
pressure of the sputtering process (Fig. 3).
Figure 5 shows the dependence of film properties and
composition on the cathode power. The de power was varied
from 1.5 to 3.0 kW of the available 10 kW power supply.
Within this range the N/Ti ratio changes from 0.95 at high
cathode power to 1.14 at low-cathode power. Above and
'" __ --' __ -.l_~ __ L __ -1 __ -'-__ --!
1.5 2D 2.5 3D
CATHODE POWER (kilowatt)
FIG. 5. Composite plot of the stress, resistivity, gas concentrations, depo
sition rate, and stoichiometry of TiN as a fUlIction of de cathode power.
J. Vac. Sci. Technol. e, Vol. 5, No.6, Nov/Dec 1987 1726
below this range, phases other than TiN were detected and
therefore those data were excluded from this presentation.
The stress decreases as the de power is increased and reaches
minimum values (-9X 109 dynes/cm2) at the highest tar
get power. The Ar/Ti ratio decreases as the power is in
creased and the deposition rate strongly increases with in
creased cathode power. The increase in cathode power leads
to slight increases of the O/Ti ratio and of the film resistivity.
Microstructural examination of the TiN was conducted
using x-ray diffraction and transmission-electron micros
copy (TEM). The films were all found to be crystalline with
grain sizes of the order of250 A. Lattice parameter measure
ments from TEM diffraction patterns and from x-ray dif
fraction were equivalent within experimental uncertainty for
aU the as-deposited samples, and some sharpening of peak
intensity was the only change observed upon 900 °C vacuum
anneal. The high-temperature anneal did not aIter the argon
concentration in the highly stressed samples, and the textur
ing observed in some samples remained with only slight
grain growth. More detail of the microstructural differences
appears below.
IV. DISCUSSION
The stress and resistivity of TiN films can be influenced by
the incorporation of the two "impurity" gases, argon and
oxygen, as wen as by the incorporation of the reactive sputter
gas nitrogen. Studies have been published on the influence of
processing variables on inert gas entrapmene4•1
f) and also on
the factors that promote residual impurity incorpora
tion. [4,16 .. 18 Similarly, studies of reactive sputtering have
routinely investigated the influence of processing variables
on the stoichiometry of the deposited film. 14,18,19 However,
no studies have attempted to understand the influence of
three gas incorporation processes occurring simultaneously.
The amount of nitrogen detected in the deposited films
follows qualitatively the dependences predicted by an impu
rity incorporation model, which states that the fraction of a
gaseous impurity trapped during film deposition is given by
Ii = [a;NJ(a;N i +R)],
where!i is the fraction of impurity itrapped in the film, at is
the sticking coefficient of i on the deposited film, N; the im
pingement rate of impurity i per unit area, and R is the depo
sition rate of the film. From the figures, the amount of nitro
gen in the films increases as the partial pressure of nitrogen
increases (Fig. 3) and decreases with increased deposition
rate (Fig. 5). The nitrogen also decreases as the substrate
power increases (Fig. 4) as if the films were backsputter
cleaned of nitrogen during the deposition process; this is an
other characteristic of impurity gas incorporation during
film deposition processes with substrate bias, 14
Comparison of these observations to the findings of Poite
vin and Lemperiere7-9 and Sundgren et alp-29 is useful;
their conclusions suggest that although the cathode becomes
nitrided, the transfer of titanium nitride to the substrate oc
curs by the process of dissociation of the TiN into ions and
neutrals, which then react at the substrate surface to form
TiN. The total pressure dependence of the N/Ti ratio in this
work suggests that the molecular nitrogen pressure is more
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important than the flux of nitrogen ions generated by the
decomposition of TiN at the cathode. Increasing the total
pressure is shown in Fig. 3 to increase the N/Ti ratio. The
probability that nitrogen from the cathode (ions or neu
trals) can reach the substrate should decrease as the pressure
is increased. Therefore, finding that nitrogen incorporation
into TiN fonows an impurity gas incorporation behavior
suggests that the TiN deposition process occurs by the reac
tion oftitanium with nitrogen that originates in the gas, not
at the cathode.
Our data shows a strong correlation between the physical
properties of the films (i.e., film resistivity and film stress)
and the type and the amount of impurity gas incorporated
into the films. Furthermore, a strong correlation between
the amount ofthese residual gases and the sputter deposition
processing parameters is indicated. Figures 3, 4, and 5 show
that for each deposition parameter the film stress becomes
more compressive as the amount of argon in the films in
creases. Similarly, the resistivity of TiN is shown in Figs, 3,
4, and 5 to increase as the amount of oxygen in the films
increases. Figure 6 is a plot of the compressive stress as a
function of the Ar/Ti ratio. The increase in argon concentra
tion in the films causes a linear increase in the compressive
stress of the films. However, the film stress created by a gi ven
argon content is a function of how the argon was incorporat
ed. Note that in Fig. 6 the data are a linear function of the gas
composition, but fall into two groups. The first are shown in
Fig. 6 by solid circles (e) which spans a stress range from
5 X 109 to 4 X 1010 dynes/cm2 and incorporates an Ar/Ti ra
tio up to -0.011. The second group, shown by open circles
(0), includes samples oflow stress up to stresses > 5 X 10 10
dynes/cmz which incorporate argon to a ratio> 0.05, The
least squares fit to the two sets of data indicates a monotonic
dependence of stress upon argon incorporation, but Fig. 6
OOr-------------------------------7'
50
_SPrOT CONSTANT
·~·-t VBIAS INCREASE
0.03
~/TITANIUM 0.04 0.05
FIG. 6. The stress of TiN film plotted as a function of the Ar!Ti ratio. The
solid circles (e) were deposited at 600 W rfsubstrate power ( --240 V) at
different N 21 Ar ratios and different pressures. The open circles (0) were
deposited at fixed pressure and N2! Ar ratio at varied rf substrate power.
J. Vac. Sci. Technol. e, Vol. 5, No.6, Nov/Dec 1987 1727
shows that a stress of 4X 1010 dynes/cm2 can be generated
either by Ar/Ti ratios of -0.01 or -0.03 depending on the
deposition parameters. The data plotted as solid circles Ce)
were deposited at different pressures and different N2/ Ar
ratios but at a single, low valueofrfsubstrate power (60 W).
The data represented by open circles (0) were deposited at a
fixed pressure but at consecutively increasing substrate pow
er settings.
The incorporation of argon into sputter deposited films is
a common observation.14 The amount of argon has been
shown by others to be strongly a function of the reactor pres
sure and the substrate bias in agreement with Figs. 2 and 3.
Explanations suggest that argon is incorporated as a result of
the impact of argon ions accelerated toward the substrate
during deposition and by argon incorporation as the result of
the arrival of energetic (> 100 eV) neutral argon atoms
which are reflected from the cathode surface. 16 The role of
total pressure on argon incorporation has been shown 16 to be
similar to that of Fig. 2: the amount of entrapped argon de
creases with increasing sputtering pressure. This is interpret
ed as the increase pressure resulting in a decrease in both the
flux of argon ions and of argon neutrals with energies > 100
eV that arrive at the film surface. However, our Il!-icrostruc
tural evaluation indicates that variation in Ar content alone
is insufficient to funy account for the film stress. The impact
of argon ions and neutrals has a strong influence on film
morphology as well. Figure 7 is a composite of transmission
micrographs from films having extremes of stress as indicat
ed in Fig. 6. Micrographs 7 (a) and 7 (b) are low-stress sam
ples and micrographs 7 (c) and 7 (d) are high-stress samples
(stress and resistivity values are designated in Figs. 3 and 4).
Differences in the surface condition and in the microstruc
ture between the stress states are apparent. The low-stress
samples have a columnar or fibrous structure with a rough
surface and large, open-grain boundary areas. The higher
stress samples have columnar grains of approximately the
same size but the surfaces are smoother. The low-stress films
have only slight preferred orientation (texture) as shown by
the selected area diffraction patterns inset into each micro
graph. The samples with highly compressive stresses have
significantly different diffraction patterns than the slight
texture shown at low stress. The sample with the highest
stress [Fig. 7(d)] has a completely random texture while
the sample in Fig. 7 (c) has the strongest texture.
The rough surface and columnar structure of the low
stress films can be explained by the sputtering model of Mov
chan and Demchishin (M-D) 21 for films which lie in Zone 1.
Zone I includes the deposition conditions of low-homolo
gems melting temperature (T /Tm) where the mobility of
deposited atoms on the surface is too low to anow diffusional
growth processes to overcome the directionality of the depo
sition process. The result is a fibrous microstructure with
open areas beside the grains that originate from shadowing
effects. Thornton22•23 has shown that the M-D model is ap
plicable to sputtered films in the absence of substrate bias
and has expanded the model to incorporate the effects of
sputtering gas pressure. Increases in the sputter gas pressure
extend the range of temperature for which the fibrous, rough
structure characteristic of Zone I can be observed and it is
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reasonable to expect that with a melting point of TiN listed
as 3223 K, all films of this investigation were deposited un
der conditions that lie in Zone I. The surface roughness and
the open regions adjacent to grains shown in Figs. 7(a) and
7 (b) are consistent with the M-D deposition model. Fur
thermore, the smooth surfaces observed in Figs. 7 (c) and
7 (d) can be explained by the effects of the impact of argon
neutrals, argon ions and sputtered titanium atoms on the
film surface. The impingement of energetic atoms and ions
imparts energy to the film through an atom "peening" pro
cess that enhal1ces the surface mobility of the deposited
atoms and counteracts the directionality of the deposition
process. The result is a smoother surface and a more dense
structure that is characteristic of Zone T behavior in the
modified M-D model.
The role of argon in generating stress is subject to debate.
If the incorporation of argon per se were the stress causing
process, then one might expect a unique value of stress for a
given argon concentration. Because Fig. 6 contradicts this
idea, then more complex effects of the argon incorporation
process must lead to stress generation. It has been suggested
that the stress in films is the result of the peening action of the
incident atoms or ions which causes lattice damage resulting
in compressive stress. This argument was originated for
films in which no sputter gas was incorporated.24,26 Even
when residual gas is found, the argument has been made that
the incorporation of argon is a by-product of the stress gener
ation process and not the cause of the compressive stress.
This argument implies that the peening action of the incident
argon ions and neutrals causes the stress, and that the argon
becomes embedded in the lattice following the collision pro
cess. Ifwe accept this argument, then it appears from the two
different stress versus argon dependences shown in Fig. 6
that argon neutrals reflected by the cathode and reaching the
substrate at low pressure Ce) may be more effective at gen
erating stress than argon ions accelerated by the substrate
bias (0); the amount of argon retained per unit stress is
J. Vac. Sci. Techno!. S, Vol. 5, No.6, Nov/Dec 1987 1728
FIG. 7. Micrographs of TiN films having ex
tremes of stress (sec Fig. 6) with electron
diffraction patterns inset. Ca) Low-stress
sample from high-total pressure-low-bias
conditions; (b) low-stress sample from
moderate pressure-low bias conditions; (c)
high stress from low pressure-low bias con
ditiolls; (d) high stress from moderate pres
sure-high bias conditions.
lower for the case oflow bias-low pressure. Note, however,
that the texture of the high-bias samples is random, indicat
ing that some recrystallization may be occurring as the result
offilm heating, thus adding other dimensions to the interpre
tation of what conditions are most effective at stress genera
tion. However, we can conclude that the stress related to
argon incorporation is not a simple function of the concen
tration but is related to the processing variables causing ar
gon incorporation and causing the differences in film micro
structure. More careful experiments must be undertaken
before the influence of sputter gas incorporation on stress
can be detailed.
Figure 8 is the data from a range of conditions plotting
resistivity as a function of the O/Ti ratio. This data spans the
entire range of total pressures, Nz/ Ar ratios, dc target pow
ers and rf substrate powers that were investigated. The data
in Fig. 8 are from TiN films of stoichiometry from 0.98 to
1.12 and from stress values from -2 X 109 to 5 X 1010 dynes/
! ! ! I ! ! I I I , !
0.20 0.25 0.30
OXYGEN/TITANIUM RATiO
FIG. 8. The resistivity is plotted as a functioll of the O/Ti ratio.
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cm2• The argon concentration in the films varies by more
than a factor of 10 and the films are aU crystalline TiN. The
dependence of resistivity on the oxygen content of the film is
clearly monotonic and is presented in. Fig. 8 by a linear
regression analysis. Note that extrapolation of this data to a
TiN film totally free of oxygen would yield a resistivity
between 10 and 20 f1n em. Such low values have been re
ported for high purity polycrystalline19 and single-crystaI2
!)
TiN. The implication is that any resistivity greater than -20
flo' cm is the result of incorporated oxygen.
The incorporation of oxygen in the TiN films appears
from Figs. 3 and 4 to be the result of impurity contamination
of the system as discussed for nitrogen. Most models predict
that the incorporation into the film of any impurity from the
sputtering gas should be proportional to the partial pressure
of the impurity and inversely proportional to the deposition
rate. 14, 17 The predictions by such a model are qualitatively
observed for oxygen incorporation as a function of total
pressure in Fig. 3. Additionally, the decrease of oxygen con
tent in the film as substrate bias increases (Fig. 4) is consis
tent with models of bias sputter removal of impurities, 17
However, Fig. 7 shows clearly that there are microstructural
changes which can affect both the oxygen incorporation and
the resistivity. The oxygen that was interpreted from RBS as
uniformly distributed through the films may be oxygen that
reacted with the surface of the fibrous microstructure [for
example, Fig. 7(a)]. This interpretation is consistent with
the dependence of oxygen content on sputtering conditions
and with the inverse relationship between argon content and
oxygen content; i.e., the same conditions which lead to high
oxygen contamination also produce the most fibrous struc
tures. Furthermore it would explain why no change in lattice
parameter was observed as a function of oxygen content; the
amount of oxygen in the TiN lattice can remain virtually
unchanged while large differences in oxygen are detected by
RRS. Our conclusion is that the correlation of resistivity
with O/Ti ratio may very well be coincidental and not causal
as is implied by Fig. 8. In this interpretation, the Zone I
microstructure causes increases in resistivity through
changes in effective cross-sectional area which then in
creases the surface area that can react with the environment
(before or after removal from the reactor) to increase the
detected oxygen level.
Vo CONCLUSIONS
The incorporation of argon, oxygen, and nitrogen into
sputtered TiN films has a strong dependence on the depo
sition variables of total pressure, substrate bias, and cathode
power. The increased incorporation of argon correlates with
increases in the compressive stress of the films and the
amount of incorporated oxygen correlates with the in
creased resistivity of the TiN. However, the explanation of
these correlations lies in the effect of argon bombardment on
the film microstructure: under deposition conditions that
yield a low flux of argon impingement upon the surface, the
J. Vac. ScI. Technol. El, Vol. 5, No.6, Nov/Dec 1987 1729
deposited film has a fibrous microstructure characteristic of
Zone I of the Movchan-Demchishin sputtering model. This
microstructure itself should result in low stresses and a high
resistivity, Moreover, as a by-product of this microstructure,
a high concentration of oxygen can result because of the high
surface to volume ratio of the fibrous structure. Under depo
sition conditions that yield a higher flux of argon upon the
surface, the film surface is made smoother and the film den
sity is higher because of the peening action of the argon neu
trals and ions. As a result, the resistivity is lower, the stress is
higher and the detected argon content is higher while the
oxygen content is lower. Thus, we conclude that the mea
sured physical and chemical properties of the films are large
ly a consequence of this peening action on the film micro
structure, Finally, the formation of the nitride film appears
to foHow an impurity incorporation model involving the re
action of nitrogen with Ti at the film surface.
ACKNOWLEDGMENT
We gratefully acknowledge the x-ray diffraction work of
J. M. Vandenberg.
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271. A. Thornton J. Vac. Sci. TechnoL 11,666 (1974),
23J, A, Thornton, J, Vac, Sci. Techno!' 12,830 (1975),
24D. W. Hoffman and J, A. Thornton, Thin Solid Films 40,355 (1977).
251. A. Thornton and D. W. Hoffman, 1. Vae. Sci. Techno!. 14, 164 (1977).
26D. W. Hoffman and J. A. Thornton, Thin Solid Films 45,387 (1977).
27J._E. Suudgren, R-o. Johansson, and S.-E. Karlsson, Thin Sulid Films
105,353 (1983).
28J,·E. Sundgren, B.-O, Johansson, S.-E. Karlsson, and H. T. G. Hentzell,
Thin Solid Films 105, 367 (1983).
29J,_E. Sundgr(!ll, B.-O, Johansson, H. T. G. Hentzell, and S.-E. Karlsson,
Thin Solid Films 105, 385 (1983).
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1.341434.pdf | Interactions of thin Ti films with Si, SiO2, Si3N4, and SiO x N y under rapid thermal
annealing
A. E. Morgan, E. K. Broadbent, K. N. Ritz, D. K. Sadana, and B. J. Burrow
Citation: Journal of Applied Physics 64, 344 (1988); doi: 10.1063/1.341434
View online: http://dx.doi.org/10.1063/1.341434
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/64/1?ver=pdfcov
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24Interactions of thin Ti films with SI, SiO:z, Si3N4, and SiOx Ny under rapid
thermal annealing
A. Eo Morgan, Eo K. Broadbent, K. N. Ritz, D. K. Sadana,a) and B. J. Burrow
Philips Research Laboratories Sunnyvale, Signetics Corporation, Sunnyvale, California 94088-3409
(Received 4 December 1987; accepted for pUblication 19 February 1988)
Thin Ti films sputter deposited onto single-crystal Si, thermal Si02, and low-pressure chemical
vapor deposited Si3N4 and SiOx Ny ex:::::y::::: 1) substrates have been rapid thermal annealed in
N2 or Ar, with and without an amorphous 8i overlayer, and the reactions followed using
Auger elecron spectroscopy, transmission electron microscopy, electron diffraction, and sheet
resistance measurements. A multilayer film is created in practically every case with each layer
containing essentially a single reaction product, viz.,TiSix, TiOx, 8-TiN, or TiNxOl _ x' The
results are discussed in light of published Ti-Si-O and Ti-Si-N phase diagrams.
I. INTRODUCTION
A self-aligned silicide ("salicide") technology using
TiSiz has been proposedl-3 for metal-oxide-semiconductor
(MOS) devices to simultaneously reduce the sheet resis
tance of the gate and source/drain regions. TiSi2 is chosen
for its low resistivity, high-temperature stability, and good
compatibility with current MOS processing. A standard sa
lieide process involves (1) deposition of a thin Ti film onto
an MOS transistor structure having oxide sidewall spacers
around the polysilicon gate, (2) a low-temperature
( < 700°C) anneal to induce silicidation over the exposed Si
areas of the source, drain, and gate, (3) removal of the Ti
over oxide regions with a selective wet chemical etch, and
finally (4) an 800-900°C homogenization anneal to com
plete the silicide reaction and minimize the sheet resistance.
An Nz ambient is essentiaf-5 for the initial anneal to sup
press lateral diffusion of Si into the Ti deposited on the
sidewall spacers which could cause short circuiting between
adjacent gate and source/drain regions. Rapid thermal an
nealing (R T A) is preferred over furnace annealing to more
easily avoid oxidation of Ti during the initial anneal, which
would hinder nitrogen incorporation and prevent Ti wet
etching.6 Several studies of the reaction between thin Ti films
and Si substrates during furnace3,5,7,8 or rapid thermal an
nealing9-14 in an N2 ambient have been reported.
During the low-temperature anneal in N2 interaction of
Ti with Si02 should be limited, otherwise silicide residues
could remain on the oxide spacers. In an extension of the
salicide process,]5 the Ti layer over selected oxide regions is
masked after the initial anneal for protection during the sub
sequent selective etch. The succeeding high-temperature an
neal is then also performed in N2 to convert this residual Ti
into local interconnects, thereby much improving the pack
ing density over conventional processing. Interaction
between Ti and SiOz at higher temperatures in N2 now also
becomes of interest. Phase formation in the Ti/Si02 reaction
has been investigated using furnace annealing in Nz (Refs. 7
and 15) and inertlO,16 ambients, or RTA also in N2 (Refs. 10,
12, and 14) and inert 12, 17 ambients.
In an alternative variation,18 a blanket layer of amor-
oj Present address: IBM Thomas J. Watson Research Center, Yorktown
Heights, NY 10598. phous silicon (a-Si) is deposited immediately after Ti depo
sition and then patterned so that local silicide strap intercon
nects will be formed over certain oxide areas during the
salicide process. Also, a very thin a-Si layer covering the
entire Ti layer has been used19 in the conventional salicide
process to prevent oxidation and nitridation ofTi during the
initial anneaL Interactions in the a-SiiTi/Si and a-SilTi!
SiOz systems in an Nz ambient now come into play. Prelimi
nary studies using furnace annealing in N2 have been report
ed,7 while in an investigation of the epitaxial growth ofTiSi2
onto SiC 111), vacuum furnace annealing of a-Si/Ti/Si was
examined.20
Future technology could employ S13 N4 rather than
Sial spacers since these could easily be disposed of by etch
ing after salicide formation. TilSi3 N4 and a-SiiTilSi3 N4
interactions would then become relevant. The former has
been examined under R T A in Ar (Ref. 21 ) and N 2 (Refs. 14
and 21) and under vacuum annealing,22 and the latter under
furnace annealing in N 2 .7
For the present studies, thin Ti layers have been sputter
deposited onto Si, Si02, Si3 N4, and SiO, Ny substrates, and
sometimes capped with a thin a-Si layer. The phases formed
after RTA at various temperatures in N2 or Ar ambients
have been characterized using mainly Auger electron spec
troscopy, cross-sectional transmission electron microscopy
(TEM), electron diffraction, and sheet resistance measure
ments.
II. EXPERIMENT
The substrates used were 17-33 n cm, lO-cm-diam, p
type ( 100) Si wafers, sometimes covered with a layer of ther
mally grown Si02 or low-pressure chemical vapor deposited
Si3N4 or SiOxN y containing approximately equiamounts
of all three elements. All substrates were dipped in dilute HF
before immediate insertion into a Balzers BAK 600 vacuum
system equipped with a 99.91 % pure Ti and a 99.999% pure
Si (lightly doped with B to facilitate dc sputtering) conical
magnetron sputter sources. The system was evacuated to
< 1.5 X 10 -7 Torr before backfilling with ultrahigh-purity
Ar to a pressure of 3.0 mTorr. An in situ sputter dean to
remove the equivalent of 2-3 nm Si02 using low-energy
bombardment to minimize sample damage preceded Ti de
position. a-Si deposition was initiated immediately upon
344 J. Appl. Phys. 64 (1). 1 July 1988 0021-8979/88/130344-10$02.40 @ 1988 American Institute of Physics 344
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24cessation of the latter. Typical deposition rates were 6 nrn
Tilmin and 2-3 nm a-Si/min.
Samples were rapid thermal annealed in an A. G. Asso~
dates heatpuise halogen lamp annealer. Temperatures were
measured with a thermocouple attached to a neighboring
piece of 8i of similar resistivity. Sheet resistances were ob
tained using a four-point probe.
Auger sputter profiling was performed in a Physical
Electronics 590 spectrometer using a 3-keV, I-p,A, 30· inci~
dent electron beam rasteredoverO.Ol mm2 and peak~tc-peak
modulations of 1-6 V, along with a 2-keV, O.6-p,A, 60· inci~
dent Ar + beam rastered over 3 mm2• Sensitivity factors for
Nand Si (92 eV) relative to Ti (418 eV) were obtained from
TiNx and TiSi2 standards, respecti.vely. Peak overlap with
Ti prevents an accurate determination of N,23 and the Si
value could differ with other titanium silicides on account of
preferential sputtering. Atomic concentrations of 0 and C
are also only approximate since handbook sensitivity factors
were employed. Furthermore, Ti peak shape changes upon
oxidation, nitridation, and silicidation introduce further un~
certainties. The spectrometer incorporates a double-pass cy
lindrical mirror analyzer and a double~anode MgKa x-ray
source to permit electron spectroscopy for chemical analysis
(ESCA) measurements. Spectra were recorded using a
pulse counter and an analyzer pass energy of 25 e V.
Cross-sectional specimens for transmission electron mi
croscopy (TEM) were prepared by sawing, lapping, polish
ing, and Ar + sputter etching to a final thickness of 0.05-0.2
11m. The TEM micrographs were taken at an accelerating
voltage of 120 kV in a Philips 400ST microscope. Microdif
fraction patterns were recorded in cross section using an
electron beam of about 4 nm in diameter. Electron diffrac~
tion patterns were also obtained from planar TEM samples.
m. RESULTS AND DISCUSSION
A. Tl/singlemcrystal Si
For the sake of completeness and clarity, Fig. I sum
marizes our previous observationsl2 plus some additional
analytical data on 28-75 nm Ti films deposited on undoped
8i substrates and annealed at 400-1100 °C for 10 s in N2• Ti
initially becomes contaminated with ° (solid solubility limit
;:::; 34 at. %, Ref. 24) from the annealing ambient before be
coming nitrided at the surface and silicided at the interface.
The 0 (along with any C) is eventually expelled from the
growing silicide into the face-centered cubic 8-TiN layer
forming at the surface, thus causing the nitride reaction front
to cease. At < 700 cC, the silicide layer of ;:::; 30-nm mean
diameter grains contains the metastable, high resistivity,
C49 TiSi2 phase25 together with a small amount of TiSi. At
higher temperatures, conversion into large grain (;:::; 2 ,urn),
15 ,un em, C54 TiSi2 occurs. 0 is absent from the silicide
apart from a small amount close to but not at the TiSi2/Si
interface coinciding with the presence of voids. The 15-20
nm TiNx01 _ x surface layer provides a good diffusion bar
rier against Al junction spiking.26 The low resistivity
TiN,,01_x/TiSi2 bilayer film is also formed at 1100"C.
However, during extended annealing at this temperature,
first the 0 in the surface layer is replaced by N and then TiSi2
345 J. Appl. Phys., Vol. 64. No.1, 1 July 1988 FI G. I. Schematic of Ti/Si reaction pl"Oducts at various R T A temperatures
in N2•
becomes completely converted into 8~TiN with the rejected
Si growing epitaxially on the single-crystal substrate.
The Ti-Si-N phase diagram at 700-1000 °C27 shows that
the TiN~TiSi2 -Si three~phase region is at equilibrium. The
presence of the TiN-TiSi2 tieline demonstrates that TiN
rather than Si3 N4 is the stable nitride on TiSiz. Thus, during
silicide nitridation on Si substrates, TiN should form on top
of TiSi2 and the liberated Si diffuse through the remaining
TiSi2 to become bonded to substrate Si.
B. TitSIO:;;
The experiments were perfonned using lO~s anneals in
Ar or N 2 of28-nm Ti/280-nm Si02 lSi samples. At tempera~
tures < 700 °C (Fig. 2) a very thin reacted layer was present
at the Ti/Si02 interface, and the unreacted Ti contained
dissolved 0 mainly originating from the annealing ambient.
The N2 anneal created a TiNxOt _ x surface layer in addi~
tion, and N also diffused into the unreacted Ti.
A 900 °C anneal in Ar generated a 20-nm TiOJ2S~nm
TiSix film of 51-H/D sheet resistance. The TEM micrograph
[Fig. 3(a) 1 indicates that the oxide region might in fact
contain two distinct layers. The C peak in the Auger profile
[Fig. 3(b)], would then be situated at the interface between
these oxide layers. Figure 3(b) was derived using relative
sensitivity factors from oxidized Ti for the upper part of the
film. A diffraction analysis revealed TiOz and Tis Si3 (20 nm
average grain size) with no clear evidence of any other titan
ium oxide. However, using TiO, Ti2 °3, and Ti02 reference
powders, ESCA and also Auger line shape2R analyses sug
gested that the oxide comprised TiO with Ti02 towards the
FIG. 2. Schematic of Ti/Si02 reaction products at various RT A tempera
tures in AT or N,. ambients.
Morgan et al. 345
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:2428nm Ti/Si02
60 900" C, lOs, Ar
50 (Ti
f-// ----...
z / /-.. ~ LlJ 40 I u
Cl: / .,/ , w a..
u / ~ 30 0 \ ~
20 \ \
10 \ /C \ \ , ........ ,
\,. .. ",4> <oo~_ ........ __ .... _---.... 0 0 4 8 12 16 20 24
SPUTTER TIME (min)
FIG. 3. (a) TEM cross section and (b) Augcrctcpth profile after 900 "C, lO
s anneal of 28-nm Ti/SiOz in Ar.
surface. Ion-beam sputtering is known29 to reduce Ti02 to a
mixture ofTi0 2, Ti2 °3, and TiO. However, the ESCA data
showed a much higher concentration of TiO than expected
from ion-induced reduction of Ti02• ESCA also showed
that the 0 in the Tis Si3 layer was bound to Tio
Thus, in agreement with Ting et al.,16 Ti reacts with
Si02 to produce Tis Si3 with the liberated 0 mostly migrat
ing into Ti to eventually form an oxide surface layer. Ac
cording to electron and x-ray diffraction, fcc TiO is formed
at 950°C in the absence 0[0 contamination from the anneal
ing ambient.27 The Ti-Si-O ternary-phase diagram has thus
been constructed27 to show the Tis Si3 -TiO-SiOl three-phase
region at equilibrium.
A 900°C, lO-8 anneal of a similar sample in N2 genera
ted an ;::; 8-nm interfacial Tis Si3 layer and a 24-nm surface
layer containing Ti, N, and ° (Fig. 4). The sheet resistance
of 33 n/o corresponded to a composite film resistivity of
100 pf'l cm. The electron diffraction pattern from the upper
layer suggested 8-TiN with no evidence of either Ti2 N or Ti
containing dissolved N (solid solubility limit ;::;23 at.%,
Ref. 24). The 8-TiN phase exists as the N aCl structure with
compositions ranging from TiNo.s to TiN 1.1' the fcc lattice
parameter increasing only slightly with N content. How
ever, electron diffraction cannot distinguish 8-TiN from fcc
TiO which crystallizes in the same structure with only a
slightly smaner lattice spacing. In fact, these compounds
form a continuous series of solid solutions at elevated tem-
346 J. Appl. Phys., Vol. 64, No.1, 1 Ju:y 1988 f-z
I.L;
U
Il: w
Q..
Sd
:2
0
~
w
" w
z 70
60
50
40
30
469 2 4 6 8 10 12 14 16
SPUTTER TIME (min)
464
ELECTRON BINDING ENERGY, eV (c)
MIN.
1
3
4
7
9
449
FIG. 4. (al TEM cross section, (b) Auger depth profile, and (c) Ti 2p
ESCA spectra at various depths in the surface layer [sputter times corre
spond roughly to those in (b) 1 after 900 °C, 10-8 anneal of 28-nm Ti/SiO,
inN,.
peratures ranging from TiO to TiOo4No6.30 At higher N
content, TiN coexists with Ti004 No.6,
ESCA scans from the Ti-N-O surface layer are shown in
Fig. 4 (c). While the Ti peak height decreased somewhat
with increasing depth, the Nand 0 Is peaks decreased and
increased 1.8 and 2.6 times, respectively. Near the surface
the Ti 2p binding energy indicated TiNx while the (barely
visible) satellite structure on the high binding energy side of
the Ti 2p doublet suggested a near stoichiometric composi
tion.31 The binding energy decreased slightly with depth and
the satellite structure became somewhat less pronounced.
No peak splitting into separate TiN and TiO components
was apparent. A likely interpretation is the increasing re
placement with depth ofN by 0 atoms at substitutional sites
in the TiN lattice.
Morgan et al. 346
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24100
80
60
40
r /-
B
~ 20
u.;
C> z
<! I-en
in w
0::
I-w w
I en 10
8
6~
4
2
t as
dep. 400 53nm a;-Si/28nm Ti/Si(100)
RTA, iOs, N2
500 600 700 800 900
RTA TEMPERATURE (·C ) 1000
FIG. 5. Sheet resistance of53-nrn a-Si!2S-nrn Ti/Si after 10-s anneals in N,
at various temperatures.
c. ctaSi/Ti/Si
An a-Si layer approximately 53 or 83 nm thick was de
posited onto 28-nm Ti/Si and a 1O-s anneal performed in N2
at a plateau temperature between 400 and 1000°C. Sheet
resistances of the thinner a-Si samples are given in Fig. 5.
After a slight increase from the room-temperature value, the
sheet resistance decreased slowly with increasing tempera
ture, leveled off between 600 and 825°C, dropped sharply to
reach a value of2.6 n/D at 875 ·C, and thereafter remained
constant up to l000°C. Similar values were found with the
B3-nm a-Si samples.
Figure 6 summarizes the results of the compositional
studies. The as-deposited a-Si layers contained a few at. %
O. Silicidation occurred at both interfaces with the a-Si layer
preventing contamination of the Ti by ambient 0 or N. After
annealing at 400°C, ::;:: 7 nm of a-Si diffused into the upper Ti
creating a 14-nm amorphous TiSix layer, Si from the sub
strate diffused into the lower part forming an 1I-nm amor
phous TiSiy layer, and 17-nm Si-free Ti remained in between
ex-S!
FIG. 6. Schematic of a-Si/Ti/Si reaction products at various RTA tem
peratures in N,..
347 J. Appl. Phys., Vol. 64, No.1, 1 July 1988 [Fig. 7 (a) ]. Auger profiling showed that the Si content in
these amorphous layers decreased with increasing distance
from the a-Si overlayer or from the single-crystal Si sub
strate. Average values of x::;:: 1.5 and y::;:: 1.3 were derived in
good agreement with those determined by scanning TEM
coupled with energy dispersive x-ray analysis. Amorphous
Ti-Si alloy formation at low annealing temperatures has
been observed previously. 32
No unsilicided Ti was left at 500 "C, and two poly
crystalline silicide layers were formed. The 30-nm TiSi,
(x;::::; 1.8) upper layer grew from ::;::40-nm a-5i and con
tained grains as large as 30 nrn across. The 23-llm TiSiy
(y;::::; 1.2) lower layer was made up of much smaller grains.
The diffraction pattern from the overall silicide film revealed
C49 TiSi2 and Tis Si3 with some TiSi. Coupled with the Au
ger data, this would indicate that the upper layer was com
prised of essentially C49 TiSi2, and the lower layer of both
C49 TiSi2 and Tis Si3 •
The 600 °C anneal generated a 70-nm, 88-,ufl em film
again separated into two distinct layers but now of similar
size grains [Fig. 7 (b) ] . A small amount of a-Si remained on
the surface (;::::; 30 nm with the thicker sample). The Auger
profile now showed a uniform silicide of approximate com
position TiSi1.8' Electron diffraction phase identification
suggested C49 TiSi2 with a trace of TiSi. The thicker upper
layer, 47 versus 23 nm, would at first suggest a faster diffusi
vity ofSi into Ti from an amorphous as opposed to a crystal
line source. However, the relative amount of contamination
at the a-Si/Ti and Tilsingle-crystal 5i interfaces could have
also influenced the diffusi.on rate.
A uniform TiSi2 film was found at 900 °C [Fig. Sea) J
with some patches of nitrided Ti at the surface. 0 and C were
absent from the silicide, apart from the usual sman amount
of 0 close to the TiSi2/Si interface. The TEM micrograph
showed a large-grain polycrystalline layer with grain boun-
FIG. 7. TEM cross s~ctions after a lO-s anneal of 53-nrn a-Si/2g-Bm Tl/Si
in N, at (at400"C and (\1) 600 "C. In (a), part of the (l-Si layer has been
removed during sample preparation.
Morgan eta!. 347
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24Ti~ ...l-__
N
5 15 20
SPUTTER TIME (min)
FIG. 8. Ca) Augcrdepth profile and (b) TEM cross section after9()() °C, lO
s anneal of 53-nm a-Si/28-nm Ti/Si in N,.
daries perpendicular to the substrate surface. Stacking faults
traversing the film [Fig. 8 (b)] were visible at isolated areas
along its entire length, These defects were never visible with
Ti/Si samples and presumably are a consequence of trans
forming the two intennediate silicide layers into the final
single-grain layer. The 18-fl!1 cm resistivity exceeded the
hitherto 15 fin cm probably due to the presence of these
stacking faults.
The 900°C anneal of the 83-nm a-Si sample (Fig. 9)
again generated a 70-nm, 18.un cm, C54 TiSi2 layer with
stacking faults but now capped by a 20-nm Si layer still con
taining some amorphous regions in its lower part. 0 origi
nating from the as-deposited a-Si was found in this Si layer
concentrated at the Si/TiSi2 interface. No N was apparent in
the Auger profile even at the surface of the residual Si layer,
indicating that that shown in Fig. 8 (a) was indeed bound to
Ti and not incorporated into the Si02 surface layer. Thus, a
sufficiently thick a-Si deposit can completely prevent nitri
dation of Ti. Due to inadequate cleaning of the sputter
source, the Ti layers prepared for the thicker samples were
contaminated with 0 and particularly C. Therefore, C and
trace 0 peaks were visible in the depth proflles from the
lower temperature anneals situated at the interface between
the silicide layers, and were also found at a similar depth in
the 900°C film [Fig. 9(a)]. This illustrates that any 0 or C
in the as-deposited Ti can end up trapped at the intersection
of the two silicide reaction fronts.
348 J. Appl. Phys., Vol. 64, No.1, 1 .July 1988 100~--~-----'-----'----~----~--~
>-60 !r'\. ..
z
t5 60
0::
W
Cl..
U
~ 40 o
~
5 o (a)
10 15 20
SPUTTER TIME (min)
PI G. 9. (a) Auger depth profile and (h) TEM cross section after 900 'C, lO
s anneal of 83-nm a-Sil28-nm Ti/Si in No.
D, aaSi/TilSi02
The experiments of Sec. III C were duplicated on 0.25-
pm Si02 lSi substrates. The sheet resistance behavior in Fig.
10 roughly paralleled that shown in Fig. 5. With 83-nm a-Si,
the lowest sheet resistance was reached at 900°C but the
thinner deposit required at least 1000 °C and a somewhat
higher minimum value was found.
100
80
60
40
e 20
q
u.:
~ 10
~ 8
(f)
(i) 6 w
0::
I-4 w w
en <
I >
/
/ // // // If
2-
as 400
dsp. ""\
o 53nmJ' .. a: -S;/28nm TI/S,02 • 83nm
RTA, 10s, N2 i !
-i :
500 600 700 800 900 1000
RTA TEMPERATURE (oC)
FIG. 10. Sheet resistance of53-nm a-Sil28-nm TilSi02 and 83-nm a-Sil28
nm TiiSiO, after lO-s anneals in No at various temperatures.
Morgan et at. 348
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24At lower temperatures, reactions proceeded indepen
dently at the a-Si/Ti and TilSi02 interfaces, as described in
Sees. III C and III B, respectively. Si from the a-Si layer
diffused into the upper Ti first giving an amorphous silicide
and then predominantly C49 TiSi2, and 0 from the con
sumed a-Si piled up at the a-Silsilicide interface. A very
thin, metal-rich silicide layer was formed on the substrate
and ° from decomposed Si02 mostly accumulated in the
adjacent nonsilicided Ti.
The Auger profile and TEM cross section from the
900 "C annealed thinner sample are contained in Fig. 11. The
50-nm upper layer comprised 60-nm grains of C54 TiSi2 and
some distinct D-TiN surface particulates, fonowed by an
;::::; 8-nm intermediate TiO layer apparently bridged by sili
cide in some areas, and an ;::::; 8-nm small-grain interfacial
layer of Tis Si3• Not enough a-Si had been deposited to con
vert the upper Ti completely into TiSi2, and so the excess Ti
became nitrided. The film resistivity was 34 f.-LH em at
900 "e, presumably decreasing to 26 f.-Ln em at 1000"C. If
the sheet resistance at 1000 °C was determined essentially by
50-nm TiSi2, the resistivity of the latter would be 20 f.-LH cm.
The thicker sample after annealing at 900 "C is shown in
Fig. 12. The 80-nm, 24-f.-L!l em film contained large-grain
C54 TiSiz devoid of stacking faults, covered in most areas by
up to 20 nm residual Si. The Si was partially crystallized,
particularly towards the surface. Since the silicide layer
SPUTTER TIME (min)
FIG. 11. (a) Auger depth profile and (h) TEM cross section after 900"C.
lO-s anneal of 53-nrn a-Si128-nrn Ti/Si02 in N2,
349 J. Appl. Phys., Vol. 64. No.1, 1 July 1988 f
Z
W 50
~ 40
I.t! 0..
U
~ o 30
!;(
20 I Ti\ r------------
12 16 20 24 28
SPUTTER TIME (min)
FIG. 12. (a) Auger depth profile and (b) TEM cross section after 900 'C,
10-s anneal of 83-nrn a-Si/2S-urn TiiSiO, in N2•
thickness varied between 60 and 80 nm, its surface was
rough although the overall film possessed a smooth surface.
The interface to Si02 was more irregular than hitherto. 0
from decomposed Si02 was dispersed as void like features
(presumably TiO) in the lower portion of the TiSi2 layer.
Thus, deposition of sufficient a-Si converts any Tis Si3
formed from the TiiSiOz reaction into TiSi2 and also pre
vents TiO layer formation.
Eo Ti/SiaN4
90~nm Ti were deposited onto a 332-nm Si3 N4 layer and
annealed for 30 s in Ar at a temperature between 400 and
1100 cC. The sheet resistance (Fig. 13) peaked at around
600 "C, decreased abruptly from 12 OlD at 900"C to 2.6
HID at 1000 "C, and increased to 3.9 O/D at 1100"C.
Previously we examined2! phase formation using much
thinner Si3 N4 layers where interpretation was complicated
by Ti interacting with the Si or Si02 underlying the nitride.
In the current investigation, the Auger depth profiles be
came distorted by sample charging upon reaching the thick
Si3 N4 layer.
The compositional information is summarized in Fig.
14. A too-nm film was formed at 800·C containing a well
defined IS-nm interfacial 8-TiN interfacial layer. The Auger
depth profile suggested a 50-nm surface Ti layer uniformly
contaminated with about 10 at. % 0 from the annealing am
bient and very approximately 10 at. % N from decomposed
Morgan et al. 349
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24100
80
60
40
0
"-20 q
W ()
Z 10
~ (j) 8
i75 w 6 cr::
I-
lU 4-w
I (j)
2· ,// .,
as
dep. ./ 90nm Ti/332nm Si3N,lSi
RTA, 30s, Ar
./
400 600 800 1000
RTA TEMPERATURE ("(;) 1200
FIG. 13. Sheet resistance of90-nm Ti/332-nm Si,N'./Si after 30-5 anneals
in Ar at various temperatures.
Si3 N4 plus a small amount ofSi on the surface, and a 35-nm
intermediate Tis Si3 layer practically free of 0 but contain
ing a few at. % N. Diffraction analysis confirmed the pres
ence orTis Si3 and indicated some 15-TiN in the surface layer
in addition to elemental Ti. The TEM cross section provided
no dear evidence of two layers in the upper 85 nrn of the film.
However, a row of distinct grains of Tis Si3 appeared to be
developing immediately adjacent to the interfacial 0-TiN
layer.
A 11O-nm, 130-,uH em film was found at 900°C (Fig.
15). The 20-nm interfacial /5-TiN layer was topped by an ill
defined 25-nm larger-grain Ti5 Si3 layer. The 25-nm
TiNx01 x surface layer appeared to be made up of several
thin layers each of uniform thickness so that the grain boun
daries between were parallel to the film surface. Similar to 0,
C was swept out of the silicided Ti into this layer. The lattice
parameter of fcc TiN x Cv is in fact close to that of 0-TiN. Si
was again detected on the surface. The region below the sur
face layer appeared to comprise both TiN x 01 x and Ti5 Si3 .
The resistivity of the 120-nm film formed at 1000°C
decreased to 3 I ,un cm. A three-layer structure developed,
Fig. 16, viz., 30-nm TiN,,01_x/40-nm C54 TiSiz/SO- nm 0-
FIG. 14. Schematic of Ti/Si3 N4 reaction products at various RTA tem
peratures in N2•
350 J. Appl. Phys., Vol. 64, No.1, 1 July 1988 70r-----.------r-----.------,---~
(a)
60
50
20
20 30 40 50
SPUTTER TIME (min)
FIG. 15. (a) Auger depth profile and (b) TEM cross section after 'lOOT,
30-s anneal of90-nm Ti/332-nm Si3N./Si ill Ar.
TiN/Si3 N4• The film/substrate interface was very rough,
unlike that at lower temperatures [Fig. 15(b)] or in
Ti/Si02 interactions [Fig. 3 (a) ] . The uppedayer contained
some TiSi2 and C, the middle layer some TiN x 01 _ x' and the
lower layer some TiSi2. Note that the only O-free region was
the lower 8-TiN layer. This grew as a result of Ti diffusing
into Si, N4 whereas the others were formed by Si and N
diffusing into O-contaminated Ti. The 0 was subsequently
expelled from TiSi2 regions but remained as TiNx01_x in
nitrided areas. The upper layer was again stratified, possibly
on account of the variation of x with depth. Diffraction and
Auger analyses of the 1100 °C annealed film indicated less
TiSi2 formation and the presence of elemental Si particularly
in the lower part of the film.
The most striking feature of Fig. 16 is the large increase
in thickness of the interfacial 8-TiN layer. According to the
ternary-phase diagram,27 Ti should react with Si3 N" to give
TiN and Si since TiSix is unstable in the presence of Si3 N4.
Apparently then, direct reaction of Ti with Si3 N 4 generates
an interfacial o-TiN layer, and the Si and excess N diffuse
through into unrcacted Ti where the faster diffuser N con
centrates towards the surface. At low temperatures, the
amount of Ti available for reaction is limited bv diffusion
thereby restricting interfacial a-TiN formation ~nd freein~
Morgan et al. 350
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24SPUTTER TIME (min)
PIG. 16. (a) Auger depth profile and (b) TEM cross section after 1000 T.
30-s anneal of90-nm Ti/332-nm Si, N4/Si in Ar.
90nm Ti/332nm Si"N"/Si (a)
60 900" C. 305, N2
~~'" A~ 50
fO~ V
f-40 Z
W u
0:: w
Il.. 30 u
~
0
~ 20
i Si~ .. \
......-Si
10 ;/
0 0 W 20 30 40 50 60
SPUTTER TIME (min)
FIG. 17. Ca) Auger depth profile and (b) TEM cross section after 900 'C,
30-s anneal of90-nm Ti/332-nm Si, N./Si in N2.
351 J. Appl. Phys., Vol. 64, No.1, 1 July 1988 most of the N to diffuse into the outer Ti and form b-TiN
once the solid solubility limit ofN in Ti is exceeded. Si diffu
sion creates the Ti-rich silicide Tis Si3. Proportionally more
Ti is available for direct reaction at the higher temperatures,
the interfacial 8-TiN layer becomes thicker, and Si diffusion
leads to TiSi2•
A 900°C anneal in N2 caused direct nitridation of the
outermost Ti so that the 0 expelled from siJicided Ti became
trapped in the bulk oftne film [Fig. 17(a)]. A llO-nm, 63-
j.lfl. em film resulted [Fig. 17 (b) ] containing 5-15 nm strata
throughout, hut in some areas surface bulging practically
doubled the film thickness. A very uneven reaction front
with Si3 N4 was indicated.
F, a-Si/TUSi3 N¢
The experiments of Sec. HI E were repeated with a 50-
nm a-Si layer on top of the Ti. At 600°C, (Fig. 18) aU of the
a-Si diffused into the upper Ti giving a 75-nm TiSi, surface
layer containing a trace of 0 throughout, separated into tv<'O
distinct layers of similarly sized small grains. The upper 50-
om layer comprised TiSi and the lower 2S-nm layer Tis Si3 •
Beneath this was a 30-nm layer of elemental Ti containing
::::::; 10 at. % N and some 0 and C, and a lO-nm interfacial
layer of Ti/Si, N4 reaction products. The overall resistivity
of the lIS-urn, 13-ft/D film was 140,uH em.
At 900°C (Fig. 19) a 140-nm, L6-H/D, 22-j.lfl cm, bi
layer film was generated. The SO-nm upper layer comprised
large-grain C54 TiSi2 free of 0, C, and N. The 60-nm lower
layer contained 8-TiN plus some TiSi2, and its resistivity
would be 60 f-ln em if that of the TiSi2 layer was 15 f..tH cm.
About 4()-nm Sil N4 were consumed in a very uneven fash-
100
50nm a; -Si/90nm Ti/332nm Si3N4/Si
600"0, ,0', A, /\ 80 (a)
f-
Si~ TJ \ z
l.<.J u 60 0::
W r----~ .. a..
/r-~. u
~ 40 / 0 f-\ <Z I \ /··C N-, : ,0
\' ·L f
10 20 30 40
SPUTTER TIME (min)
FrG. 18. (a) Auger depth profile and (ll) TEM cross section after 600 'C,
30-s anneal of 50-nm a-Si/90-nm Ti/332-nm Si, N./Si in Ar.
Morgan et al. 351
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:2470~--~-----.----~---,-----r----c
50nm ex: -Si/90nm Ti/332nm Si3N4/Si
r-·~/.. 9000 C, 305, Ar
60 ~ \
II Si~ /~ (a)
50
I
Z
ILl
U 40 0:
ILl
0...
u
~ 30 o
~
10 V \
Tiy\
,----""'" ',--
X
N~ \ .I
/' '. / '--.,
.j
10 20 30 40 50
SPUTTER TIME (min) 60
FIG. 19. (a) Auger depth profile and (h) TEM cross section after 90!) °c,
30-s anneal of 50-nm a-Si/90-mn Ti/332-nm Si, N./Si in Ar.
ion, Thus, these results imply that Ti reacts with Si3 N4 to
give D-TiN and most of the liberated Si joins with the a-Si in
creating a TiSi2 surface layer,
G. Ti/SiO ... Ny
30-or 60-nm Ti were deposited onto a 48-nm SiO"Ny
layer (x:::::y::::: 1) and annealed at 900 DC for 10 s in AI, With
the thicker deposit, a 71-nm, 28-0,/0, 200-pn em trilayer
film was formed on top of 12-nrn unreacted SiO¥N~, (Fig.
20), A trace of Si was detected at the very surface of the
upper 35-nm Ti layer which was heavily contaminated with
o plus some N and a little C. The intermediate 2S-nm layer
comprised Tis Si) and the interfaciaill-nm layer 8-TiN. No
unreacted Ti remained with the thinner sample, the outer
layer of the 45-nrn, 45-HID, 200-pH cm trilayer film now
comprising TiN x 01 __ .~ with x < 1. The whole structure thus
appeared to be a supposition of the Ti/Si02 and Ti/Si3 N4
reaction products,
A further 1000°C, lO-s anneal was performed to com
plete the reaction with the 60 nm deposit. As shown by the
TEM cross section in Fig, 21, not enough silicon oxynitride
was present to prevent Ti from diffusing through into the Si
352 J. Appl. Phys., Vol. 64, No, 1, 1 July 1988 fz w 70
1E 40 w
(L
20 -
10
L---5~----:~"":"--:1-::-5--=2"::0~-'_·~'5----3LO-'-"""-.J35
SPUTTER TIME (min)
Ti
FIG. 20. (a) Auger depth profile and (b) TEM cross section after 900 0c,
to-s anneal of60-nm Ti/48-mn SiOxNyfSi in AL
substrate and forming TiSi2 precipitates, A similar phenom
enon occurs with thin 5i3 N4 iayers,21
IV. SUMMARY AND CONCLUSIONS
Thin Ti films deposited onto Si, Si02, Si3 N4, and
SiOxN y substrates, with and without an a-Si overlayer,
achieve minimum sheet resistance after a 10-30 s rapid ther
mal annealin N2 or Ar at a temperature of900-1000 0c. The
final film is made up of distinct layers each containing most
ly a single reaction product. The exclusive or predominant
phase is listed in the following summary:
FIG. 21. TEM cro~s section after a further lOOO T, 10-8 anneal in Ar of the
sample shown in Fig. 20.
Morgan et al. 352
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155.33.16.124 On: Thu, 27 Nov 2014 19:01:24N,
(a) Ti/Si-TiNx01_xIC54 TiSi2/Si,
Ar
->
(b) Ti/SiO, -N,
-> TiNxOI _ x1Ti5Si3/Si02,
. '/S' N, 8-TiN/C54 (c) a-Sl/Tt 1-Si/C54 (deficient a-Si),
TiSi2/Si (excess a-Si),
. . S'O N'D-TiN/C54 TiSizlTiOlTisSi3/SiOz (deficient a-SO,
Cd) a-Sl/T!1 1 2-+ Si/C54 TiSi2/Si02 (excess a-Si),
Ar
(e) Ti/Si3NC+ TiN,,01_JC54 TiSizI8-TiN/Si 3N4,
Ar
(£) a-SilTi/ShN 4 -C54 TiSizI8-TiN/Si 3N4,
Ar
(g) Ti/SiO_1 N",\ -+ TiNxOl_xITisSi3/8-TiN/SiO",\ N",\.
Phases formed at lower temperatures in reaction (c) are
amorphous TiSi" at 400°C, Tis Si3 and C49 TiSiz at 500 ·C
and C49 TiSi1 at 600 °C [the latter also in reaction (a)}. In
reaction (e), Tis Si, is the low-temperature silicide phase
while above lOOO ·C, elemental Si is generated and less C54
TiSi2• An upper TiSilTis 8i3 bilayer is formed rather than
TiSiz at 600 ·C in reaction (f).
The reaction products are, in general, in accordance
with predictions based on Ti-Si-O and Ti-Si-N phase dia
grams. ° contamination of Ti, essentially derived from the
annealing ambient, is responsible for the formation of the
TiNxOI_x layers in reactions (a) and (e), and will influ
ence the value of x in reactions (b) and (g). In the absence of
this contamination, reaction of Ti with Si02 in Ar would
very probably lead to a TiO surface layer.
ACKNOWLEDGMENTS
The expert assistance of H. Shishido, G. de Groot, D.
Stadtler, M. Norcott, and A. Reader (Philips Eindhoven) in
sample preparation and data acquisition is very gratefully
acknowledged.
Ie. K. Lau, Y. C. See, D. B. Scott, J. M. Bridges, S. N. Perna, and R. D.
Davies, IEDM Tech. Dig. 82, 714 (1982).
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VLSI Science and Technology/1982, edited by C. J. Dell'Oea and W. M.
Bullis (The Electrochemical Society, Pennington, NJ, 1982), p. 224.
3M. E. Alperin, T. C. Holloway, R. A. Haken, C. D. Gosmeyer, R. V. Kar
naugh, and W. D. Parmantie, IEEE Trans. Electron Devices ED-32, 141
( 1985). ·c K. Lau, Electrochem. Soc. Ext. Abst. 83·1, 569 (1983 l.
5S. S. Iyer, C.-Y. Ting, and P. M. Fryer, J. Electrochem. Soc. 132,2240
(1985).
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(1985).
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and Materials, Tokyo, (1985), p. 325.
12 A. E. Morgan, E. K. Broadbent, and A. H. Reader, Mater. Res. Soc.
Symp. Proc. 52, 279 (1986).
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chern. Soc. 133, 1451 (1986).
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Electrochemical Society, Pennington, NJ, 1986), p. 316.
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Soc. 131, 2934 (1984).
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J. Vac. Sci. Technol. A 4,993 (1986).
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Amano, and K.oY. Chiu, IEDM Tech, Dig. 84,118 (1984).
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(1986).
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( 1985).
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1236 (1986).
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App!. Phys. Lett. 50, 953( 1987).
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4,2463 (I986).
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Metals, Metals Park, OH, 1986), Vol. 2.
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Norcott, IEEE Electron Device Lett. EDL-6, 59 J (1985).
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12K. Holloway and R. Sinclair, J. Appl. Phys. 61,1359 (1987).
Morgan et al. 353
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1.342837.pdf | Photoluminescence study of the annealing behavior of transmuted impurities in
neutrontransmutationdoped semiinsulating GaAs
M. Satoh, K. Kuriyama, and Y. Makita
Citation: Journal of Applied Physics 65, 2248 (1989); doi: 10.1063/1.342837
View online: http://dx.doi.org/10.1063/1.342837
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/6?ver=pdfcov
Published by the AIP Publishing
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155.33.16.124 On: Thu, 27 Nov 2014 21:07:49Photoluminescence study of the annealing behavior of transmuted
impurities in neutron ... transmutation .. doped semi .. lnsulating GaAs
M. Satoh and Ko Kuriyama
College of Engineering and Research Center of Ion Beam Technology, Hosei University, Koganel:
Tokyo 184, Japan
Y. Makita
Electrotechnical Laboratory, Umezono 1-1-4, Tsukubashi, Ibaraki 305, Japan
(Received 17 August 1988; accepted for publication 4 November 1988)
In neutron-transmutation-doped GaAs irradiated with various fast neutron fluences, the
annealing behavior of band-germanium acceptor [Ge(B-A)] transitions has been evaluated
using the photoluminescence technique. In the fast neutron irradiation of <7.0X 1017 cm-2, a
few percent of transmuted Ge atoms behave as acceptors in As sites and more than 98% of the
transmuted Ge atoms activate as donors in Ga siteso In the fast neutron irradiation of
3.7 X 1018 cm--z, the shift of Ge(B-A) transitions towards lower energies originates from the
band-edge distortion. Removing the band-edge distortion by annealing above 790°C leads to
the increase in the Ge acceptor, accompanied by an increase ofthe peak intensity of Ge (B-A)
transitions. The lower electrical activation oftransmuted impurities ( -75%) arises from the
high-temperature annealing required to remove the radiation damage. On annealing out the
radiation damage, the peak shift of Ge(B-A) transitions based on the increase in the free
carrier is discussed using the Burstein-Moss model.
I. INTRODUCTION
Neutron-transmutation doping (NTD) is a useful tech
nique for obtaining a uniform distribution and a precise con
centration of the dopant. The NTD process for GaAs has
been studied by severa] workers. I~ In the NTD process,
however, the defect clusters involving the As antisite defect
(AsGa) (Ref. 7) and the Ga vacancy (Vaa) (Refs. 8 and 9)
are created by the primary knock~on (PKO) due to the fast
neutron. These defects disturb the electrical activation of the
NTD-induced impurities.6 Fast neutron irradiation of"> 1017
cm--2 induces hopping conduction between the defect elus
ters.6. 10. I I Moreover, in photoluminescence studies,4.5 it has
been reported that part of the transmuted Ga atoms activate
as acceptors in As siteso The evaluation of the annealing be
havior of the Ge acceptor is important to obtain more de~
tailed information about the activation of transmuted im
purities since the existence of the Ge acceptor restricts the
electrical activity as donors of transmuted impurities. In
particular, there is a great interest in the relationship
between the electrical activation of Ge acceptors introduced
by the NTD process and the removal of radiation damage
introduced by the fast neutron irradiation. In the present
paper, we report the annealing behavior of a Ge acceptor in
neutron-transmutation-doped GaAs irradiated with various
fast neutron fluences using the photoluminescence (PL)
technique.
II. NEUTRON TRANSMUTATION DOPING OF Gaits
The compound semiconductor GaAs contains the natu
ral isotopes 69Ga(natural abundance of 60,2%),
71Ga( 3908%), and 75As( 100%). When GaAs is bombarded
with thermal neutrons, the unstable isotopes are transmuted
from these isotopes and subsequently decay to stable iso
topes in accordance with their half-lives. Consequently, 70Ge, 72Ge, and 76Se isotopes are introduced into GaAs as
impurity spedes.2 Ifboth Ge and Se isotopes are maintained
in the lattice sites where they are introduced, an the three
reaction products would behave as donors in GaAs. The
doping concentration (N NTD ) is determined precisely by the
thermal neutron flux (if!) and the exposure time(t) as fol
lowsl2:
NNTD = O.16¢t. (1)
Unfortunately, after the nuclear reactions, the transmuted
atoms are usually not in their original positions but are dis
placed into interstitial position due to the recoil produced by
the rand f3 rays in the nuclear reactions. In addition, the
defects 13 induced by the fast neutron irradiation disturb the
electrical activation of transmuted impurities.6
ill. EXPERIMENT
Starting materials used in this study are undoped semi~
insulating GaAs (p=2X 107 n em), grown by the liquid
encapsulated Czochralski method to clear the electrical acti ~
vation of impurities introduced by NTD. Neutron
irradiations were performed at three positions (P 1, P 2, and
P3) in the Kyoto University Reactor (KUR), which is a
light-water moderated research reactor, as described in our
previous paper. 12 Table I lists the irradiation condition and
carrier concentration predicted theoretically. P 1 and P 2 are
the water channel between the fuel and the graphite reflector
and the center of the core in KUR, respectively. P 3 is the
thennal column using the graphite reflector. Fast neutron
fluxes at P 1 and P 2 are comparable to thermal neutrons in
each position, while fast neutrons at P 3 are considerably re
duced by the graphite reflector in comparison with thermal
neutrons. It is expected that the annealing and electrical be
haviors for GaAs irradiated at P 3 are different from crystals
2248 J. Appl. Phys. 65 (6), 15 March 1989 0021-8979/89/062248-06$02.40 (c) 1989 American Institute of Physics 2248
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155.33.16.124 On: Thu, 27 Nov 2014 21:07:49TABLE 1. The irradiation condition.
Irradiation position Pl P2 P3
Thermal neutron 4.7XlO" 8.2X 10" g.OX 10"
flux (n/cm2/s)
Fast neutron lAX 1Ol3 3.9X 10" < lOS
flux (n/cm2/s)
Thenna! neutron j.3xlO'9 1.5 X 10'" 2.2X 1017
fluence (n/cm2)
Fast neutron 3.7X 10'" 7.DX ]017 < 1O'4
fluence (n/cm2)
Nn(/cm,)a 2.1 X 101" 2.4 X 1017 3.5 X 10'"
a The net donor concentration predicted theoretically in the NTD process.
irradiated at other positions. The energy distribution of neu
trons at each position also has been described in our previous
paper. 12
The annealing of irradiated samples was performed by
placing the two GaAs wafers 14 in N 2 flow for 30 min at sever
al temperatures. To eliminate the decomposed layer by in
congruent evaporation of arsenic, a few p.m of material was
removed from the surface by chemical etching after each
annealing stage. I This procedure was an important process
to obtain reproducible data. The resistivity and Hall mea
surements were carried out at room temperature using the
van der Pauw method. The photoluminescence spectra were
recorded using the 514.5 nm of an Ar+ laser as an excitation
source, a grating spectrometer, and a cooled photomultiplier
tube having a GaAs photocathode. The PL spectra present
ed here were recorded at just below 2 K.
IV. RESULTS AND DISCUSSION
Figure 1 shows the resistivity of the neutron irradiated
samples as a function of annealing temperature for each irra
diation position. There was a remarkable difference in the
recovery process between samples irradiated at P 1 (or P 2)
108 ~~2 F --', , ,
lOs
E
'" 01 104
> l-
'> r:: 102
\I)
iii
II.!
IX
ANNEAliNG TEMPERATURE (Oc)
FIG. 1. Roomotemperature resistivity as a function of annealing tempera
ture for various irradiation conditions (see Table I): open circles represent
PI, open triangles represent P 2, open squares represent P 3, and the reversed
triangle represents the starting material.
2249 J. Appl. Phys., Vol. 65, No.6, 15 March 1989 and P 3. The difference in the recovery process is concerned
with whether or not defect clusters involving ASOa exist. The
resistivity of samples irradiated at P 1 and P 2 is based on the
tunneling-assisted hopping conduction between defect c1us~
ters induced by the PKO events. 6.13 The hopping conduction
was observed at annealing temperatures up to 500 ·C. In par
ticular, the resistivity of the unannealed sample irradiated at
P 1 was reduced from 2 X 107 to 8 X 105 !l cm by the hopping
conduction. In the irradiation at P 1 and P 2 the abrupt
change in resistivity was observed around 600·C with a
slight change around 400°C. The drastic decrease in resistiv
ity around 600·C corresponds to the annihilation of ASGa
defects. (, Moreover, the annealing stage around 400 ·C origi
nates from the enhancement in the hopping conduction due
to the activation ofNTD-induced impurities.6 On the other
hand, the samples irradiated at P 3 did not show the hopping
conduction because of the irradiation with a small amount of
fast neutrons. In the irradiation at P 3 the gradual decrease in
resistivity around 300·C is based on the activation of the
NTD-induced impurities.
Figure 2 shows the carrier concentration as a function of
reciprocal annealing temperature. The activation energies
for samples irradiated at P 1 (or P 2) and P 3 were estimated
to be about 0.9 and 0.3 eV, respectively. The activation ener
gy of 0.9 eV corresponds to the annihilation of ASGa defects,
as described in our previous paper.6 On the other hand, the
activation energy of 0.3 eV may be based on the recovery of
radiation damage induced by the y and {:J rays in the nuclear
reactions. In the irradiation of P 2 and P 3, the predicted car
rier concentration was achieved by annealing at 700 and
600 °C, respectiveiy. This s.uggests that more than 98% of
the transmuted Ge atoms activate as donors in Ga sites.
However, in the irradiation at PI with the fast neutron
fiuence of 3.7X 1018 cm-2, the expected carrier concentra
tion was not achieved even at 850"C. The activated carrier
concentration was abou.t 75%. This fact suggests the exis-
TEMPERATURE (oe i
10'9 800 600
I
"" 's
10'9 -
\~ ~ -
Z
Q
.~ -0-
<t ll: 0-z 1017
- !OJ u z 0 ~ (,)
a: 1"-3
w
Ci: 10'6 !- - a:
<It u
FIG. 2. Roomo!emperature carrier concentration as a function ofl'ecipTOca1
temperature: open circles represent P 1, open triangles represent P2, and
open squares represent P 3.
Satan, Kuriyama, and Makita 2249
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155.33.16.124 On: Thu, 27 Nov 2014 21:07:49tence of a remaining lattice defect. The Hall mobility for
carrier concentrations achieved at each irradiation position
are 1900 cm2jV s for lAX 1018 cm-3 (P 1, for annealing at
850 ·C), 3000cm2/V 8for2.3 X 1017 cm--3(Pl, 700 Qq, and
4050 cm2jV s for 3.4X 1016 cm-3 (P3, 600 ·C), respective
ly.
Figure 3 shows the photoluminescence spectra obtained
from an unirradiated sample, The emissions at around 820
nrn are associated with donor and acceptor bound exci
tons.S•IS The emissions at 830 and 831 nm have been attribut
ed to band-carbon acceptor [C(li-A) J and donor-carbon ac
ceptor [C( D-A)] transitions involving residual carbon
impurities, and unidentified donors present in starting mate
ria1.4•16 The corresponding phonon replicas of C{B-A) and
C(D-A) transitions (fllilw = 36 meV) are observed around
850nm.
Figure 4 shows the PL spectra obtained from samples
irradiated atP3. Labels (a), (b), and (c) denote the samples
annealed at 700,600, and 500 "C, respectively. The emission
originated from band-Ge acceptor [Ge(B-A}} transi
tions4•5,]6 was observed at 838 urn in addition to C(B-A)
transitions. The corresponding phonon replica of Ge(B-A )
transitions (muw = 36 meV) was observed at 859 nm. The
appearance ofGeCB-A) transitions suggests that some of the
transmuted Ge atoms occupy the As sublattice sites because
of the recoil produced by the f3 fu'ld r rays3 i.n the nuclear
reactions and the subsequent annealing. No apparent vari
ation of Ge(B-A) transitions was observed in annealing
between 500 and 700 cC. This annealing behavior of the PL
emission is correlated with the lower activation of impuri
ties, as shown in Fig. 2 (P 3). In the irradiation at P 1 and P 2,
however, the PL emission was not observed in samples indi
cating the hopping conduction.
Figure 5 shows the PL spectra recorded for samples ir
radiated at P 2. Labels (a) and (b) denote the samples an
nealed at 600 and 700 ·C, respectively. C(B-A) transitions
were not observed in the irradiation at P 2. These transitions
are concealed by the broad main emission because of the
existence of the Ge acceptors exceeding the carbon concen
tration. The very weak bound exciton was also observed at
around 820 nm (indicated by arrows in the figure). The peak
energy of the main emission is corresponding to that of
Ge(B-A) transitions. However, the fun width at half maxi-
Undoped GaAs 2K
{AO-X}
I !
810 820 C(B-A)
)(10
~ \ .
/ I\-'~J
830 340 850 360
WAVELENGTH (nm)
FIG. 3. Photoluminescence spectrum taken at 2 K of unirradiated semi
insulating GaAs.
2250 J. Appl. Phys., Vol. 65. No.6, 15 March 1989 FIG. 4. Photoluminescence spectra taken at 2 K of samples ilTadiated at P 3.
Annealing temperatures: (a) 700, (b) 600, and (c) 500 ·C.
mum (FWHM) of this emission (~13 urn) was larger than
that of Ge(B-A) transitions (see Fig. 4) observed for sam
ples irradiated at P 3 ( ~ 4 nm) < This large FWHM suggests
the large contribution of donor-Ge acceptor transitions
[Ge(D-A)] in addition to Ge(B-A) transitions. In anneal
ing at 600 "C, a broad emission was observed at around 860
nm, but in the irradiation at P 3 it was not obtained. This
broad emission is not identified as the phonon replica of
Ge(B-A) transitions because its intensity is much larger
than that of the phonon replica of Ge(B-A) transitions, as
shown in Fig. 4. In general, the intensity of phonon replica is
about 10 times smaller than that of its zero-phonon transi
tions. The broad emission at around 860 nm disappeared as
the annealing temperature increased from 600 to 700 ·C. We
speculate that this emission is based on the peak shift of
Ge(D-A) transitions which has been observed for the low
excitation intensity.!? The measurement of the excitation
intensity dependence of Ge(D-A) transitions is necessary to
confirm this speculation, but we cannot clarify the origin of
this emission at present. However, this emission may be cor
related with a certain radiation damage induced by the fast
neutron irradiation of 7.0X 1017 cm-2• In annealing at
700 °C, the peak of the main emission was shifted to higher
energy ( -3 nm). This shift may originate from the increase
in carrier concentration.
In samples irradiated at P 1, the main emission shifted
from 860 to 820 nm as the annealing temperature increased
from 600 to 850 cC, as shown in Fig. 6. Labels (a), (b), (c),
P-2
2K
'-_-'-_ ......... _--'-, (b)
~ __ ~~~~-L~~~~ __ ~ __ --L (a)
810 850 870
WAVELENGTH (urn)
FlG. 5. Photoluminescence spectra taken at 2 K of samples irradiated at P 2.
Annealing temperatures: (a) 600 and (b) 700"C. At the wavelength indi
cated by the arrow, the very weak bound excitons arc observed.
Satoh, Kuriyama, and Makita 2250
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155.33.16.124 On: Thu, 27 Nov 2014 21:07:49Ip-1
, 2K
__ ,/ ~(d) r<;;.sX5
-'-- ' ~5 ~C) ,
x5 (b)
WAVELENGTH (nm)
FIG. 6. Photoluminescence spectra iaken at 2 K ofsamples irradiated at P 1.
Annealing temperatures: (a) 850, (b) 790, (c) 700. and (d) 600 'CO
and Cd) denote the samples annealed at 850, 790,700, and
600 ·C, respectively. The emissions for samples annealed at
600 and 700 ·C were observed at 860 and 843 nm, which are
lower energies than Ge (B-A) transitions obtained in the
irradiation at P 3. It has been reported that donor-acceptor
transitions in the strongly compensated insulating GaAs
layer fabricated by the ion implantation shift to lower ener
gies with increasing the impurity concentration.17 On the
other hand, NTD GaAs annealed at 600 and 700·C were
conductive and their carrier concentrations were 1.2 X 1017
and 4.7X 1017 cm-3, respectively. Therefore, the peak shift
observed in the samples annealed at these temperatures is
associated with a certain radiation damage introduced by the
fast neutron irradiation of 3.7 X 10 18 em -2 rather than do
nor~acceptor transitions as observed in the compensated
crystal. This radiation damage is confirmed by the near-in
frared absorption measurements, as described later. The
shrinkage of the optical band gap, which arises from the
lattice distortion induced by the fast neutron irradiation, was
observed in the samples annealed at 600 and 700"C. The
shrinkage at these temperatures were estimated to be 39 and
8 meV, respectively, in comparison with the original position
of Ge(B-A) transitions in the unirradiated crystal. 16
To evaluate the origin for the shift of emission in Fig. 6,
the near-infrared absorption measurements at 77 K were
performed for the samples irradiated at P 1. Figure 7 shows
the near-infrared absorption spectra obtained from the sam-
WAVELENGTH 1"-1
17K
FIG. 7. Near-infrared absorption spectra obtained from the P I irradiation
samples annealed at (II) 550, (b) 600, and (c) 700"C These spectra were
taken at 77 K.
2251 J. Appl. Phys., Vol. 65, No.6, 15 March 1989 pIes annealed at (curve a) 550, (curve b) 600 and (curve c)
700 ·C. The newly appeared optical absorption lay at the
wavelength ranging from ~ 830 to -865 nm for annealing
at 550 "c. As the annealing temperature i.ncreased from 550
to 600 ·C, the low-energy side of this absorption varied from
-865 to -840 nm. Therefore, it is suggested that the band
edge distortion is induced by the fast neutron irradiation. In
the samples annealed at 600 ·C, the difference in absorption
edge between the irradiated and unirradiated (-820 nrn)
GaAs is in good agreement with the shift of the PL emission
between these samples, as mentioned above. The PL emis
sions observed at lower energies must be based on the transi
tions from the distorted band edge to Ge acceptors. This
absorption disappeared on annealing at 700 ·C, but the slight
shift (-5 nm) of the PL emission suggests the existence of
the residual radiation damage< With the increase of the an~
neaHng temperature, the band-edge distortion was almost
removed and then the peak shifted to the original position
(838 nm) of Ge(B-A) transitions with increasing the elec
tron concentration. Moreover, in annealing at 600 "C, the
broad emission around 860 nrn was also observed in the irra
diation at P 1 and P 2. It is suggested that in the fast neutron
irradiation of> 7<OX 1017 em -2, the local radiation damage
disturbs the band edge.
In order to estimate the recovery of the band~edge dis
tortion in samples irradiated at P 1, we calculated the energy
shift of Ge(B-A) transitions. The asymmetry in the spectra
of Fig. 6 indicates that indirect (B-A) transitions without k
selection dominates the emission across the optical gap. 18
The emissions for samples annealed at 790 and 850°C were
observed at higher energy than GeCB-A) transitions ob
tained from unirradiated crystal. According to Burstein and
MOSS,19 this shift results from the filling of the conduction
band. The Burstein-Moss shift has been observed at the elec
tron concentration of> -5 >< t017 em -3 (Ref. 18). The car
rier concentration for samples annealed at 790 and 850°C
are L2x 1018 and 1.44 X 1018 cm-3, respectively. Therefore,
we performed the calculation using the Burstein-Moss mod
el. although this model has been usually applied to the emis
sion at higher energy than the forbidden band gap. Figure 8
shows the intensity distribution of the spontaneous recombi-
1<0
WAVELENGTH
FIG. 8. Calculated intensity distribution of spontaneous emission (indi
rect) from n-type GaAs as a function of electron concentration [(a)
L44X 10'", (b) 1.20X 10'", and (c) 4.7 X 1OI7cm·-3] considering the
shrinkage of band gap due to the band tailing.
Satoh, Kuriyama, and Makita 2251
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155.33.16.124 On: Thu, 27 Nov 2014 21:07:49nation spectra of indirect (B-A) transitions in n-type GaAs
calculated with the following equation 18;
I(E) 0:: (E -Eg + EA ) 1/2
X{l +exp[(E-Eg +EA -E:;")/kT]}--'< (2)
In this equation, E( = fuu) is the energy of the emitted pho
ton, Eg is the band gap ofGaAs (1.519 eV at 2 K), EA is the
ionization energy of the Ge acceptor (0.0404 e Vat 2 K), and
E ~ is the quasi-Fermi level for electrons, respective1y< The
other symbols in Eq. (2) have the usual meaning. The quasi
Fermi level is estimated as fonows:
(3)
where n is the electron concentration, Equation (3) is modi
fied by the corrections of Reymod, Roverts, and Bernard,20
and the nonparabolicity of the conduction band is consid
ered. With increasing electron concentration, the develop
ment ofa density-of-states tail in the energy gap due to inho
mogeneous impurity distribution and potential fluctuations
becomes more important for the radiative recombination
process in heavily doped semiconductors. This development
has been identified in the crystal grown by the molecular
beam epitaxy technique. 18 The NTD GaAs with the doping
level of> -5X 1017 cm--3, however, the band-edge distor
tion is induced not only by the fluctuation of impurity distri
bution, but also simply by the fast neutron irradiation as
shown in Fig. 7. The localized states in the band tail induced
by the increase in electron concentration can be treated as
acceptorlike centers distributed above the top of the valence
band, as proposed by Levanyuk and OsipOV.21 Therefore, in
the heavily doped GaAs (> ~ 5 X 1017 cm-3), the energy of
the photoexcited holes in the density-of-state tail (ET) is
accounted as foUows18:
ET = 2rrli2(e2/e)al/4n5J12. (4)
The value of E T correlates directly with the effective narrow
ing of the optical band gap. The electron concentrations esti
mated from Hall measurements are used in these calcula~
tions. The calculated spectra shown in Fig. 8 indicate a
smooth slope on the low-energy side and a steep slope on the
high-energy side. These features coincide with the PL spec
tra obtained from samples irradiated at P 1. The measured
and calculated peak wavelengths are listed in Table II. The
estimated values for samples annealed at 850 and 790 ·C are
in good agreement with the experimental results, but the
peak wavelength for the sample annealed at below 700 "C is
smaller than that of Ge(B-A} transitions observed in the
irradiation at P 1. Therefore, the band-edge distortion in-
TABLE II. The experimental and calculated peak wavelength for irradia
tion at P l.
Annealing Peak wavelength (nm)
temperature Carrier concentration
CC) Experiment Calculation (1018 cm -l)"
850 821.5 821.6 1.44
790 824.0 824.1 1.20
700 843.0 833.1 0.47
a Values obtained from Hall measurements.
2252 J. Appl. Phys., Vol. 65, No.6, 15 March 1989 duced by the fast neutron irradiation of 3.7X 1018 cm-2 is
removed by annealing between 700 and 790·C. However,
the annealing temperature above 790·C is required to re
move the residual radiation damage,
In samples irradiated at P 2 and P 3, the predicted NTD
carrier concentrations are achieved by annealing at 700 and
600 ·C, respectively, even if the transmuted Ge atoms acti
vate as acceptors in As sites, as observed in PL measure
ments. These facts suggest that the Ge acceptors are a few
percent of the donors introduced by NTD. However, in the
irradiation at PI (fast neutron fluence = 3.7x 1018 cm--2),
the Ge(B-A) emission intensity in the sample annealed at
850·C is about five times larger than other annealed sam
ples, as shown in Fig. 6. It is suggested that the part of Ge
atoms that migrates to As sites by annealing above 790 ·C
required to remove the radiation damage is introduced by
the fast neutron irradiation. Therefore, the electrical activa
tion of the NTD-induced impurities is reduced by increasing
the Ge acceptor.
V. CONCLUSION
In the photoluminescence measurements for NTD
GaAs, it was found that the shift of Ge(B-A) transitions
towards lower energies originates from the band-edge distor
tion introduced by the fast neutron irradiation of 3.7 X 1018
cm-2• The shrinkage of the optical band gap due to the lat
tice distortion was estimated to be 39 me V in the sample
annealed at 600 ·C, in comparison with the original position
of Ge (B-A) transitions in the unirradiated crystal. Remov
ing the band-edge distortion by annealing above 790°C led
to the increase in the Ge acceptor, accompanied by an in~
crease ofthe peak intensity ofGe(B-A) transitions. The exis
tence of the Ge acceptor was correlated with the lower elec
trical activation (-75%) of transmuted impurities. In the
fast neutron irradiation of ~7.0 X 1017 em --2, a greater part
of transmuted Ge atoms behaved as donors in Ga sites with
the electrical activity of >98%.
ACKNOWLEDGMENTS
The authors wish to express thanks to 1. Kimura, T.
Kawakubo, and K. Yoneda of Kyoto University Research
Reactor Institute for the neutron irradiation, M. Mori for
assistance of PL measurements, and C. Kim for providing
the starting material.
'P. D. Green. Solid State Commun. 32, 325 (1979).
2J. E. Mueller, W. Kellner, H. Kniepkamp, E. E. Haas, and G. Fischer, J.
App\. Phys. 51, 3178 (1980).
elM, A. Vesaghi, Phys. Rev. B 25, 5436 (1 Y82).
<J, Garrido, J. L Castano, J. Piqueras, and V. Alcober, J. Appl. Phys. 57,
2186 (1985).
'T. S. Low, M. H. Kim, B. Lee, R J. Skromme, T. R. Lepkowski, and G. E.
Stillman, J. Electron. Mater. 14.477 (1985).
DM. Satoh, K. Kuriyama, M. Yahagi, K, {wamura, C. Kim, T. Kawakubo,
K. Yoncda. and I. Kimura. AppL Phys. Lett. SU. 580 (1987).
7R, Waner. U. Kaufman, and J. Shneider. App!. Phys. Lett. 40, 141
(1982).
"A. Goltzene, H. Meyer, and C. Schwab. J. App!. Phys. 57.1332 (1985).
OR. B. Beall, R. Co Newman. and J. E. Whitehouse, J. Phys. C 19, 3745
(1986).
Satoh, Kuriyama, and Makita 2252
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155.33.16.124 On: Thu, 27 Nov 2014 21:07:49lOR, Coates and E. W, J. Mitchell, J, Phys. CS, LlB (1972).
IJR. Coates and E. W. I. Mitchel!, Adv. Phys. 24. 593 (1975),
11M. Satah, H. Kawahara, K. Kuriyama, T. Kawakubo, K. Yoneda, and I.
Kimura, J. App!. Phys. 63,1099 (1988).
13K. Kuriyama, M. Satoh, M. Yahagi, K. Iwamura, C. Kim, T. Kawakubo,
K. Yoneda, and I. Kimura, NueL Instrum. Methods B 22, 553 (1987).
'4B. Molnar, App!. Phys. Lett. 36, 927 (1980).
"D. J. Ashen, P. J. Dean, D. T. J. Hurle, J. B. Mullin, A. M. White, and P.
D. Green, J. Phys. Chern. Solids 36, 1041 (1975).
2253 J. Appl. Phys., Vol. 65, No.6, 15 March 1989 16D. W. Kisker, H. Tews, and W. Rehm, J. App!. Phys. 54,1332 (1983).
Hp. W. Yu, J. App!. Phys. 48,5043 (1977).
ISJ. De-Sheng, Y. Makita, K. Ploof, and H. J. Queisser, J. App!. Phys. 53,
999 (1982).
19E. Burstein, Phys. Rev. 83,632 (1954); T. S. Moss, FlOC. Phys. Soc. Lon
don Sec. B 67,775 (1954).
2OA, Reymod, J. L. Roverts, and C. Bernard, J. Phys. C 12. 2289 (1979).
21A. P. Levanyuk and V. V. Osipov, SOy. Phys. Semicond. 7, 721 (1973).
Satoh, Kuriyama, and Makita 2253
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1.4898791.pdf | III International Workshop on Point-contact Spectroscopy
Citation: Low Temperature Physics 40, 893 (2014); doi: 10.1063/1.4898791
View online: http://dx.doi.org/10.1063/1.4898791
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On: Sat, 20 Dec 2014 02:45:20III INTERNATIONAL WORKSHOP POINT-CONTACT SPECTROSCOPY (PCS-2014)
KHARKIV, UKRAINE 8-11 SEPTEMBER, 2014
III International Workshop on Point-contact Spectroscopy
(Submitted September 25, 2014)
Fiz. Nizk. Temp. 40, 1144–1146 (October 2014; revised online December 3, 2014)
Kharkiv, Ukraine, September 8–11, 2014
On the Fortieth Anniversary of Yanson’s Point-contact
Spectroscopy
In 1974, the “Journal of Experimental and Theoretical
Physics,” published an article by I. K. Yanson, called“Nonlinear Effects in the Electroconductivity of Point
Contacts and the Electron-Phonon Interaction in Normal
Metals.”
1This work laid the foundation for a new method of
studying physics, hereinafter referred to as point-contact
spectroscopy (PCS). The essence of the method is that if the
size of the point contact becomes less than the length of themean free path of the conduction electron, then, as they go
through the contact, the electrons obtain an excess energy
equal to eV, where Vis the voltage applied to the contact,
and eis the electron charge. The non-equilibrium electrons
energized in this manner relax, giving off their excess energy
to the lattice (i.e., phonons). This type of electron scatteringby phonons causes an increase in the contact resistance at
typical phonon energies, and correspondingly, leads to a
non-linear current-voltage characteristic (CVC). The pointcontacts studied by I. K. Yanson that had the necessary size
were formed in the dielectric layer of a film tunnel junction.
As a result, as was found by I. K. Yanson, the second deriva-tive of the CVC for such contacts, directly reflects a known
function of electron-phonon interaction, a
2F(e), where F(e)
is the phonon density of states, and a2is a slightly smoother
dependence that takes into account the strength of the elec-
tron interaction with a particular group of phonons.
In the following year, 1975, I. K. Yanson reported his
original results at the International Low Temperature
Physics Conference in Helsinki (Finland). The report caused
a wide resonance, and a number of foreign laboratoriesbecame interested in this method. We should note a group of
Dutch scientists, headed by the President of the Netherlands
Physics Society, Professor P. Wyder, who, along with hisgraduate student, A. G. M. Jansen, were the first to apply the
PCS method of creating point contacts from bulk electrodes
in the needle-anvil geometry.
2This method significantly
simplified the methodology of creating point contacts, used
by I. K. Yanson, and almost indefinitely expanded the range
of the objects that could be studied. In particular, it enabledfor the possibility of using the superior single-crystal sam-
ples instead of polycrystalline films, and studying the effects
of anisotropy.
3
Decisive contributions to the understanding of the proc-
esses occurring in the ballistic contacts, and to the establish-
ment and further progress of the PCS method, were made bythe pioneer studies from Kulik, Omelyanchouk, and
Shekhter, leading to the creation of a fundamental PCS
theory.
4The next important step in the development of PCS
theory was the examination of the diffusion regime ofcurrent flow across point contacts.5It was shown that PCS
allows us to obtain spectral information for systems with asmall elastic mean free path of electrons,
6which gave the
basis for using the PCS method practically for all conductive
alloys and compounds. van Gelder, also from the aforemen-tioned Dutch group, presented his own independent version
of the PCS theory,
7which in the end led to findings that
were analogous to those in Ref. 4. As a result of the experi-
mental and theoretical studies conducted at the end of the
70s, it became clear that point contacts were full-scale tools
of physics studies, and PCS became entrenched as themethod.
It also became clear, that PCS was not limited to study-
ing the process of electron scattering by phonons, but couldbe expanded to include the interaction of electrons with other
quasi-particles, or other mechanisms of relaxation of ener-
gized electrons. This is where studies of electron-magnoninteraction,
8Kondo effect,9,10two-level systems,11electric
crystal field effects,12spin fluctuations,13etc., began.
In the process of searching for effects of electron-
magnon interaction in simple ferromagnetic metals, a giant
CVC nonlinearity was discovered, at energies significantly
higher than those belonging to phonons,14,15which, as a
result, led to the development of a theory of thermal regime
for contacts,15wherein the inelastic length of the electron
mean free path becomes less than the contact, and Jouleheating causes a rise in contact temperature proportional to
the applied voltage.
A high-frequency point-contact spectroscopy
16,17was
also developed for the study of kinetics of relaxation for
quasi-particle excitations in solids: non-equilibrium pho-
nons, two-level systems, internal crystal field levels, etc.
It should be noted that in parallel to using point contacts
for the purposes of PCS at the start of the 1980s, point con-
tacts were also used to study energy gaps in superconductingmaterials, using the so-called Andreev-reflection spectros-
copy.
18Even though the physical processes at the basis of
PCS and Andreev-reflection spectroscopy are different, theyhave a relationship based on the common methodology for
creating point contacts, and the synergy of spectroscopic
data.
19
As a result of the development of nanophysical studies
at the end of the last century, researchers using PCS began to
apply their expertise in this area, since microcontacts are infact, nano objects. In particular, microcontacts are capable of
reaching a huge current density of an order 10
10A/cm2and
higher. Accordingly, using ferromagnetic materials, one canreach high densities of spin-polarized current, which is im-
portant in conducting spin-valve research in the field of spin-
tronics, for example.
20,21Developments in the field of PCS
became valuable in the analysis of quantum effects in the
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On: Sat, 20 Dec 2014 02:45:20conductivity of single-atom contacts and nanowires.22It is
necessary to also note the promising results achieved in the
area of applying metal contacts to sensorics.23
To summarize, it can be said, that for the last 40 years,
significant progress has been made in the area of PCS, with
the publication of nearly five hundred scientific papers, and a
number of reviews and books.24–30PCS became not only the
new and popular method for the physics studies of elemen-
tary excitations in solids, but also found its place in a series
of applications in nanophysics.
The studies published in this issue of the journal are
based on reports presented at the International Workshop on
PCS Challenges, which was held in the PCS method’s home-land, at the B. Verkin Institute of Low Temperature Physics
and Engineering of the National Academy of Sciences of
Ukraine, in September 2014. The publications largely reflectcurrent trends and directions in the PCS method. This applies
to spin-dependent phenomena in the conductivity of point
contacts, studies of nontraditional mechanisms of electronpairing in composite compounds, processes of electron trans-
port at the boundary of a normal metal–superconductor, and
a number of nanophysics studies, etc. All of this points to afurther fruitful development of the PSC method, its rele-
vance, and wide application in many areas of solid-state
physics research.
1I. K. Yanson, Zh. Eksp. Teor. Fiz. 66, 1035 (1974) [Sov. Phys. JETP 39,
506 (1974)].
2A. G. M. Jansen, F. M. Mueller, and P. Wyder, Phys. Rev. B 16, 1325
(1977).
3I. K. Yanson and A. G. Batrak, Zh. Eksp. Teor. Fiz. 76, 325 (1979) [Sov.
Phys. JETP 49, 166 (1979)].
4I. O. Kulik, A. N. Omelyanchouk, and R. I. Shekhter, Fiz. Nizk. Temp. 3,
1543 (1977) [Sov. J. Low Temp. Phys. 3, 840 (1977)].
5I. O. Kulik and I. K. Yanson, Fiz. Nizk. Temp. 4, 1267 (1978) [Sov. J.
Low Temp. Phys. 4, 596 (1978)].
6A. A. Lysykh, I. K. Yanson, O. I. Shklyarevskii, and Yu. G. Naydyuk,
Solid State Commun. 35, 987 (1980).
7A. P. van Gelder, Solid State Commun. 25, 1097 (1978).
8A. I. Akimenko and I. K. Yanson, Pis’ma Zh. Eksp. Teor. Fiz. 31, 209
(1980) [JETP Lett. 31, 191 (1980)].9A. G. M. Jansen, A. P. van Gelder, P. Wyder, and S. Str €assler, J. Phys. F:
Met. Phys. 11, L15 (1981).
10Yu. G. Naidyuk, O. I. Shklyarevskii, and I. K. Yanson, Fiz. Nizk. Temp.
8, 725 (1982) [Sov. J. Low Temp. Phys. 8, 362 (1982)].
11A. I. Akimenko, N. M. Ponomarenko, I. K. Yanson, S. Jano /C20s, and M.
Reiffers, Sov. Phys. Solid State 26, 1374 (1984).
12K. S. Ralls and R. A. Buhrman, Phys. Rev. Lett. 60, 2434 (1988).
13Yu. G. Naidyuk, M. Reiffers, A. G. M. Jansen, P. Wyder, I. K. Yanson, D.
Gignoux, and D. Schmitt, Int. J. Mod. Phys. 7, 222 (1992).
14B. I. Verkin, I. K. Yanson, I. O. Kulik, O. I. Shklyarevski, A. A. Lysykh,
and Yu. G. Naydyuk, Solid State Commun. 30, 215 (1979).
15B. I. Verkin, I. K. Yanson, I. O. Kulik, O. I. Shklyarevski, A. A. Lysykh,
and Yu. G. Naidyuk, Izv. Akad. Nauk SSSR, Ser. Fiz. 44, 1330 (1980).
16R. W. van der Heijden, H. M. Swartjes, and P. Wyder, Phys. Rev. B 30,
3513 (1984).
17I. K. Yanson, O. P. Balkashin, and Yu. A. Pilipenko, Pis’ma Zh. Eksp.Teor. Fiz. 41, 304 (1985) [JETP Lett. 41, 373 (1985)].
18G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys. Rev. B 25, 4515
(1982).
19Yu. G. Naidyuk and K. Gloos, Solid State Commun. 184, 29 (2014).
20I. K. Yanson, Yu. G. Naidyuk, D. L. Bashlakov, V. V. Fisun, O. P.
Balkashin, V. Korenivski, A. Konovalenko, and R. I. Shekhter, Phys. Rev.
Lett. 95, 186602 (2005).
21I. K. Yanson, Yu. G. Naidyuk, V. V. Fisun, A. Konovalenko, O. P.
Balkashin, L. Y. Triputen, and V. Korenivski, Nano Lett. 7, 927 (2007).
22N. Agrait, A. L. Yeyati, and J. M. van Ruitenbeek, Phys. Rep. 377, 81 (2003).
23G. V. Kamarchuk, O. P. Pospelov, A. V. Yeremenko, E. Faulques, and I.
K. Yanson, Europhys. Lett. 76, 575 (2006).
24A. G. M. Jansen, A. P. van Gelder, and P. Wyder, J. Phys. C: Solid State
Phys. 13, 6073 (1980).
25I. K. Yanson, Fiz. Nizk. Temp. 9, 676 (1983) [Sov. J. Low Temp. Phys. 9,
343 (1983)].
26I. K. Yanson and O. I. Shklyarevskii, Fiz. Nizk. Temp. 12, 899 (1986)
[Sov. J. Low Temp. Phys. 12, 509 (1986)].
27A. Duif, A. G. M. Jansen, and P. Wyder, J. Phys.: Condens. Matter 1,
3157 (1989).
28Yu. G. Naidyuk and I. K. Yanson, J. Phys.: Condens. Matter 10, 8905
(1998).
29A. V. Khotkevich and I. K. Yanson, Atlas of Point-Contact Spectra of
Electron–Phonon Interaction in Metals (Kluwer Academic Publishers,
Boston, 1995).
30Yu. G. Naidyuk and I. K. Yanson, Point-Contact Spectroscopy , Springer
Series in Solid-State Sciences (Springer Science þBusiness Media, Inc,
2005), Vol. 145.
Yu. Naidyuk, Guest Editor
Translated by A. Bronskaya894 Low Temp. Phys. 40(10), October 2014 III International Seminar of Microcontact Spectroscopy
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On: Sat, 20 Dec 2014 02:45:20 |
1.4897298.pdf | Synthesis and characterization of large-grain solid-phase crystallized polycrystalline
silicon thin films
Avishek Kumar, Felix Law, Goutam K. Dalapati, Gomathy S. Subramanian, Per I. Widenborg, Hui R. Tan, and
Armin G. Aberle
Citation: Journal of Vacuum Science & Technology A 32, 061509 (2014); doi: 10.1116/1.4897298
View online: http://dx.doi.org/10.1116/1.4897298
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/32/6?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20Synthesis and characterization of large-grain solid-phase crystallized
polycrystalline silicon thin films
Avishek Kumara)
Solar Energy Research Institute of Singapore, National University of Singapore, 7 Engineering Drive 1,
Block E3A, #06-01, Singapore 117574; Department of Electrical and Computer Engineering,
National University of Singapore, Singapore 117583; and Institute of Materials Research and Engineering,A*STAR (Agency for Science, Technology and Research), 3 Research Link, Singapore 117602
Felix Law
Solar Energy Research Institute of Singapore, National University of Singapore, 7 Engineering Drive 1,Block E3A, #06-01, Singapore 117574
Goutam K. Dalapatia)and Gomathy S. Subramanian
Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research),3 Research Link, Singapore 117602
Per I. Widenborg
Solar Energy Research Institute of Singapore, National University of Singapore, 7 Engineering Drive 1,Block E3A, #06-01, Singapore 117574
Hui R. Tan
Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research),3 Research Link, Singapore 117602
Armin G. Aberle
Solar Energy Research Institute of Singapore, National University of Singapore, 7 Engineering Drive 1,Block E3A, #06-01, Singapore 117574 and Department of Electrical and Computer Engineering,
National University of Singapore, Singapore 117583
(Received 19 June 2014; accepted 25 September 2014; published 13 October 2014)
n-type polycrystalline silicon (poly-Si) films with very large grains, exceeding 30 lm in width, and
with high Hall mobility of about 71.5 cm2/V s are successfully prepared by the solid-phase crystal-
lization technique on glass through the control of the PH 3(2% in H 2)/SiH 4gas flow ratio. The
effect of this gas flow ratio on the electronic and structural quality of the n-type poly-Si thin film is
systematically investigated using Hall effect measurements, Raman microscopy, and electron back-
scatter diffraction (EBSD), respectively. The poly-Si grains are found to be randomly oriented,
whereby the average area weighted grain size is found to increase from 4.3 to 18 lm with increase of
the PH 3(2% in H 2)/SiH 4gas flow ratio. The stress in the poly-Si thin films is found to increase above
900 MPa when the PH 3(2% in H 2)/SiH 4gas flow ratio is increased from 0.025 to 0.45. Finally, high-
resolution transmission electron microscopy, high angle annular dark field-scanning tunnelingmicroscopy, and EBSD are used to identify the defects and dislocations caused by the stress in the
fabricated poly-Si films.
VC2014 American Vacuum Society .[http://dx.doi.org/10.1116/1.4897298 ]
I. INTRODUCTION
Thin-film polycrystalline sili con (poly-Si) is a promising
semiconductor material for a variety of large-area elec-
tronic applications ranging from thin-film transistors
(TFTs),1active matrix type liquid-crystal displays,2,3and
three-dimensional (3D) vertical NAND flash memories4to
photovoltaics (PV).5–10The thin-film poly-Si solar cell
technology7,8,11–14received significant attention after the
promising device efficiencies reported by SANYO in the
1990s.5Among various poly-Si technologies,7,8,15the thin-
film poly-Si on glass solar cell prepared by solid-phasecrystallization (SPC) is one of the most innovative technolo-
gies that combines the robustness of the c-Si wafer-based
technology with the advantages of thin films.
11In 2006, CSGSolar was the first company that attempted to commercialize
this technology.16CSG Solar achieved an efficiency of 10.4%
for a 94-cm2minimodule using a simple single-junction diode
structure in a superstrate configuration.17This single-junction
device is believed to have an energy conversion efficiency
potential of more than 13%.18
It has been hypothesized that an enhancement in the grain
size of the poly-Si thin film could lead to further improve-
ments in the performance of solar cells,19and a high field
effect mobility as required for TFTs.20However, recent
reports suggest that the efficiency of hydrogen-passivated
poly-Si thin-film solar cells does not necessarily depend on
the grain size, but might depend more on intragrain defectsand dislocations.
21,22Thus, to consider poly-Si thin films for
future large-scale electronic applications, it is desirable to
better understand the effect of grain size and grain bounda-ries on the structural and electrical qualities of the poly-Si
thin film. a)Authors to whom correspondence should be addressed; electronic
addresses: avishek.kumar@nus.edu.sg and dalapatig@imre.a-star.edu.sg
061509-1 J. Vac. Sci. Technol. A 32(6), Nov/Dec 2014 0734-2101/2014/32(6)/061509/9/$30.00 VC2014 American Vacuum Society 061509-1
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20Matsuyama et al .5,23reported that n-type poly-Si thin
films with large grains can be fabricated by controlling thephosphorus dopant density in the film, but not much infor-
mation was given about grain size distribution, orientation,
and crystal quality of the film. Recently, our group reportedthat large-grain n-type SPC poly-Si films can be formed by
increasing the concentration of phosphorus [P] in the film.
24
This finding differs from the results previously reported by
SANYO,5where the average grain size was reported to be
inversely proportional to the [P] concentration. Furthermore,
we also observed from UV reflectance measurements thatthe crystal quality deteriorates with increasing grain size of
the poly-Si film.
24However, the mechanism behind the
increase of the grain size and the deterioration of the crystalquality of the poly-Si film with increasing PH
3flow was still
unclear and required further experimental investigation.
In this work, we evaluate large-grain n-type poly-Si films
prepared by SPC of hydrogenated amorphous silicon
(a-Si:H). The effect of an increasing PH 3(2% in H 2)/SiH 4
gas flow ratio on the phosphorus [P] doping concentration
and the carrier mobility of the poly-Si thin film is studied
using Hall effect measurements. Further, its impact on grain
size, orientation, and the crystal quality of the n-type poly-Si
film is investigated in detail using Raman and electron back-
scatter diffraction (EBSD) measurements. Finally, high-
resolution transmission electron microscopy (TEM) and highangle annular dark field scanning tunneling microscopy
(HAADF-STEM) are used to investigate the intragrain
defects and to reveal the dislocations in the poly-Si films.
II. EXPERIMENTAL DETAILS
About 500 nm thick n-type SPC poly-Si thin films with
varying doping concentrations were prepared for this study.
First, the a-Si:H films were deposited onto a SiN
x(/C2470 nm)
coated planar glass sheet (Schott, Borofloat) in a PECVD(plasma-enhanced chemical vapor deposition) cluster tool
(MVSystems, USA). The n-type doping of the a-Si:H films
was obtained by in-situ doping with phosphorus [P] from the
PH
3(2% in H 2) gas mixed with SiH 4during the PECVD pro-
cess. The nþa-Si:H thin films were deposited using different
PH3(2% in H 2)/SiH 4gas flow ratios, as summarized in
Table I.A n /C24100 nm thick SiO xcapping layer was thendeposited onto the a-Si:H films. The SiN xfilm acts as an
antireflection coating and diffusion barrier to impuritiesfrom the glass substrate,
15,25while the sacrificial SiO xlayer
acts as a barrier for impurities from the ambient during the
SPC process as well as the subsequent rapid thermal anneal-ing (RTA) process.
25,26The deposited a-Si:H films were
then annealed (Nabertherm, N 120/65HAC furnace,
Germany) at 610/C14Ci naN 2atmosphere for a duration of
12 h to achieve solid phase crystallization of the film. A
rapid thermal anneal (RTA, CVD Equipment, USA) for 1
min at a peak temperature of 1000/C14Ci nN 2atmosphere was
then used to remove crystallographic defects from the SPC
poly-Si thin films and to activate the dopants. Subsequently,
the samples were cleaned in a diluted (5%) HF solution toremove the capping SiO
xlayer, rinsed in DI water and then
dried with a nitrogen gun. The n-type poly-Si samples were
then characterized for its crystal properties, grain size andorientation maps using x-ray diffraction (XRD, D8, Bruker)
and EBSD system (Bruker Quantax EBSD CrystAlign,
Germany) attachment onto a SEM (Carl Zeiss, Germany).The poly-Si material quality was then determined using UV
reflectance measurements
27–29(PerkinElmer, Lambda 950,
UV/Vis/NIR spectrometer) and Raman spectroscopy30,31
measurements (Witec Alpha 300R confocal Raman micro-
scope equipped with a 532 nm Nd:YAG laser), whereby the
samples were always measured from the air side. Further,TEM (CM300, Philips) was used to examine the microstruc-
ture, thickness, and dislocations
22in the poly-Si films. The
defects and dislocations in the poly-Si films were further vali-dated and quantified using HAADF STEM.
32The majority
carrier mobility and the doping concentration of the n-type
poly-Si films were evaluated using Hall effect measurementsystem (model HL5500 from Accent). The Hall effect meas-
urements were conducted at a magnetic field of 0.32 T and
temperature of 300 K and the system was calibrated using ac-Si reference sample at the identical magnetic field.
III. RESULT AND DISCUSSION
A. Impact of PH 3(2% in H 2)/SiH 4gas flow ratio on the
electronic properties of the SPC poly-Si films
The effect of the PH 3(2% in H 2)/SiH 4gas flow on the
electronic properties of the nþpoly-Si films were evaluated
using a Hall effect measurement system. Figure 1shows the
carrier concentration of the nþpoly-Si films for four differ-
ent PH 3(2% in H 2)/SiH 4gas flow ratios (0.025, 0.125, 0.25,
and 0.45). As expected, the majority carrier concentration
was found to increase from 2.36 /C21019to 3.90 /C21020cm/C03
as the PH 3(2% in H 2)/SiH 4gas flow ratio was increased
from 0.025 to 0.45. Further, the Hall mobilities of the nþ
poly-Si films were extracted at various doping concentra-
tions. Figure 2shows the Hall mobilities of the nþpoly-Si
films at various doping concentrations. Also, for comparison,
the Hall mobility of [P] doped single-crystal Si (Ref. 33)a sa
function of the doping concentration (thick solid line) is pre-
sented. The electrical properties such as Hall mobility and
resistivity of phosphorus doped single-crystal n-type Si were
extracted from the literature.33,34The Hall mobility ofTABLE I. Experimental details used for the PECVD of the SiN x/nþa-Si:H/
SiO xfilms.
Process condition SiN x nþa-Si layer SiO x
SiH 4(sccm) 12 40 10
2% PH 3:H2(sccm) 0 1–20 0
NH 3(sccm) 20 0 0
N2(sccm) 143 0 0
N2O (sccm) 0 0 50
Time (s) 636 2000 200Deposition rate (A ˚/s) 1.1 2–3 5
Substrate temperature (
/C14C) 350 410 350
Pressure (Pa) 80 106 80RF power density (mW/cm
2) 8 34 8061509-2 Kumar et al. : Synthesis and characterization of large-grain solid-phase crystallized poly-Si thin films 061509-2
J. Vac. Sci. Technol. A, Vol. 32, No. 6, Nov/Dec 2014
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20n-type poly-Si prepared by the SPC method decreases as the
majority carrier concentration increases and follows a trend
similar to that of single-crystal Si. The decrease in the Hall
mobility with the increase in the carrier concentration is dueto the enhanced carrier scattering.
34,35A Hall mobility of
71.6 cm2/V s was obtained for n-type poly-Si fabricated with
aP H 3(2% in H 2)/SiH 4gas flow ratio of 0.025, which is
equivalent to a carrier concentration of 2.36 /C21019cm/C03.
The Hall mobility of /C2471.6 cm2/V s obtained for the poly-Si
film is approximately 76% of the Hall mobility of c-Si at thesame doping concentration. The reason for this 24% drop
observed in Hall mobility for the poly-Si film with respect to
that of single-crystal Si could be due to the presence of grainboundaries, grain orientation, and the structural defects in
poly-Si. However, the mobility of the n-type poly-Si thin
films decreased drastically to 36.8 cm
2/V s as the carrierconcentration increased to 3.9 /C21020cm/C03. This is approxi-
mately 48% of the single-crystal Si Hall mobility at thatsame doping concentration. This sharp drop in Hall mobility
of the poly Si thin film by 52% as compared to single-crystal
Si is a strong indication of the increase in defects and disor-der in the poly-Si thin film with the increase in the PH
3(2%
in H 2)/SiH 4gas flow ratios to 0.45.
B. Stress and crystal quality characteristics of the
SPC poly-Si films
Then-type poly-Si thin-film samples were further charac-
terized using Raman spectroscopy to evaluate the effect of
the PH 3(2% in H 2)/SiH 4gas flow ratios (doping concentra-
tion) on the crystal quality of the poly-Si films. Raman char-acterization is a powerful, nondestructive, and fast technique
that can be conveniently used to characterize stress and
defects in polycrystalline silicon.
36–38Figure 3shows the
Raman spectra acquired from the visible (532 nm) laser line
for the selected poly-Si thin films fabricated with different
PH3(2% in H 2)/SiH 4gas flow ratios. As a reference, the
Raman spectrum was also obtained for an intrinsic single-
crystal FZ double side polished Si (100) wafer, (solid line).
A strong peak at a frequency x0of about 521 cm/C01is
observed for the c-Si wafer. This peak position value of c-Si
may slightly vary from experiment to experiment, depending
on the calibration of the spectrometer and monochromator.Furthermore, the Raman spectra reveal that there is a shift in
the peak position of the poly-Si thin film toward lower wave
numbers with respect to c-Si as the PH
3(2% in H 2)/SiH 4
flow ratio is increased, indicating the presence of tensile
stress in the poly-Si film.39,40Stress in poly-Si thin films is
an area of great concern, as a high stress can lead to bending,buckling, cracks, and in some cases even peeling of the
poly-Si films,
37,41,42which are detrimental effects for micro-
electronic applications and thus need to be controlled. The
FIG. 1. Majority carrier concentration of nþpoly-Si films as a function of the
PH3(2% in H 2)/SiH 4gas flow ratio. The dashed lines are guides to the eye.
FIG. 2. (Color online) Hall mobility of SPC nþpoly-Si films as a function of
the majority carrier concentration. The solid line indicates the Hall mobility
of single-crystal n-type Si (Refs. 33and34). The dashed lines are guides to
the eye.
FIG. 3. (Color online) Measured Raman spectra of n-type poly-Si thin films
fabricated with four different PH 3(2% in H 2)/SiH 4gas flow ratios. Also
shown, for comparison, is the Raman spectrum measured for a polished FZ
single-crystal Si (100) wafer (solid black lines).061509-3 Kumar et al. : Synthesis and characterization of large-grain solid-phase crystallized poly-Si thin films 061509-3
JVST A - Vacuum, Surfaces, and Films
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20stress level in a poly-Si film can be determined from the
wave number shift obtained in the Raman measurement,using the following equation:
36,37,43
r¼/C0 ð 250 MPa cm Þ/C2Dx; (1)
where rstands for stress and Dxis the shift in the Raman
peak position (wave number) of the poly-Si film compared
to that of unstressed single-crystal Si.
Further, detailed analysis of the Raman spectra (see Fig.
3) reveals that the full width at half maximum (FWHM) of
the poly-Si film increases with increasing PH 3(2% in H 2)/
SiH 4flow ratio. The FWHM is an excellent indicator of the
crystal quality of the poly-Si film. An increasing defect den-
sity and disorder in Si thin films leads to the broadening ofthe peak (FWHM).
30,36,38A Raman quality factor (R Q)i s
defined here as the ratio between the FWHM of single-
crystal Si to that of the poly-Si film ( RQ¼FWHM c–Si
FWHM poly–Si)t o
quantify the defects in the poly-Si film relative to a (stress-
free) single-crystal Si wafer.
Figure 4shows the calculated Raman quality factor and
stress behavior of the poly-Si thin film as a function of the
PH3(2% in H 2)/SiH 4flow ratio. From the trend in Fig. 4,i t
is observed that the stress in the poly-Si thin film increases,
while the crystal quality decreases, when the PH 3(2% in
H2)/SiH 4gas flow ratio increases. The increase of tensile
stress in the poly-Si thin film with the increase of phospho-
rous [P] concentration is in good agreement with the earlier
reported results by Nickel et al.,44but not much information
was given about the impact of stress on the crystal quality of
the poly-Si thin film. Stress in the poly-Si film could be due
the combination of several factors, such as internal micro-structure (grain size, orientation, shape, etc.), different
expansion coefficients of materials, and defects in the crys-
talline matrix during the formation of poly-Si films.
36
Raman spectroscopy confirms that the defect density in then-type poly-Si thin film increases with the increase of PH 3
(2% in H 2)/SiH 4gas flow ratio or [P] concentration.
However, since all the parameters in this experiment except
the PH 3(2% in H 2)/SiH 4gas flow ratio were kept constant,
we suspect the internal microstructure such as crystallinity,grain size, grain orientation, and misorientation could be the
major factors for stress in the poly-Si thin films. Thus, the
poly-Si thin films were further analyzed using the XRD andEBSD characterization techniques to study the effect of the
PH
3(2% in H 2)/SiH 4gas flow ratio (doping concentration)
on the phase transformation, crystallinity, grain size, crystal-lographic orientation, and intra- and intergrain defects in the
poly-Si thin film.
C. Grain size enlargement, crystallographic
orientation, and defects in the SPC poly-Si thin film
Figure 5shows the XRD spectra of poly-Si thin films fabri-
cated with different PH 3(2% in H 2)/SiH 4gas flow ratios.
Three distinct strong diffraction peaks were observed at 2 h
values of 28.4/C14,4 7 . 3/C14,a n d5 6 . 2/C14corresponding to the Si
(111), Si (220), and Si (300) planes, respectively.4,45–47These
three sharp peaks are a good indication of complete crystalli-
zation of a-Si:H films after the RTA process and are in goodagreement with the above Raman measurements results.
These well-developed peaks also suggests that the Si thin film
obtained after SPC process are of good quality and polycrys-
talline in nature with no preferred orientation.
48XRD is a
powerful technique that can provide excellent informationabout the phase of the material under test. However, it fails to
give specific information about individual grain orientations,
shape, deformation, grain boundaries and phase distribu-tions.
49Hence, the n-type poly-Si thin films were further ana-
lyzed using the EBSD characterization technique.
Figure 6shows an EBSD grain orientation map of the
poly-Si thin film for four different PH 3(2% in H 2)/SiH 4gas
FIG. 4. (Color online) Crystal quality factor (Q R) and stress characteristic of
then-type poly-Si thin film as obtained from Raman spectroscopy as a func-
tion of the PH 3(2% in H 2)/SiH 4gas flow ratio. The dotted lines are guides
to the eye. Inset: Schematic view of the poly-Si thin film under test.
FIG. 5. (Color online) XRD spectra of n-type poly-Si thin films fabricated
with four different PH 3(2% in H 2)/SiH 4gas flow ratios (0.025, 0.125, 0.25,
and 0.45).061509-4 Kumar et al. : Synthesis and characterization of large-grain solid-phase crystallized poly-Si thin films 061509-4
J. Vac. Sci. Technol. A, Vol. 32, No. 6, Nov/Dec 2014
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20flow ratios (0.025, 0.125, 0.25, and 0.45). Each color in the
orientation map represents a specific crystallographic orien-tation. A color triangle representing the different crystal ori-
entation is shown in the inset of each figure. The grains of
then-type poly-Si thin films were found to be randomly ori-
ented and the grain size increased with increasing PH
3(2%
in H 2)/SiH 4gas flow ratio. The average grain size was found
to increase from 4.32 to 18.1 lm. The increase in the grain
size could be due to the enhanced growth rate from the
increased [P] dopant concentration.50,51Further, detailed
analysis of EBSD data reveals that the percentage of coinci-dent side lattice (CSL) grain boundaries in the n-type poly-
Si thin films increases with increasing PH
3(2% in H 2)/SiH 4
gas flow ratio. Figure 7shows the CSL grain boundary map
of the n-type poly-Si thin film fabricated with three different
PH3(2% in H 2)/SiH 4gas flow ratios (0.025, 0.25, and 0.45).
It can be observed from CSL maps that the first orderP3
(red) and the second orderP9 (purple) grain boundaries
predominantly appear on all the fabricated n-type poly-Si
thin film. However, third orderP27 (yellow) grain bounda-
ries tends to appear in the poly-Si thin film produced with
PH3(2% in H 2)/SiH 4gas flow ratio of 0.45 (see Fig. 7). An
increase in CSL grain boundaries in the n-type poly-Si is an
indicator of an increasing density of crystallographic defects
in the poly-Si film.15
To understand the impact and mechanism behind the deg-
radation of the poly-Si material quality with increasing grainsize, a further analysis of the EBSD data was carried out to
obtain qualitative and quantitative information about misor-ientation and strain present in the grain at microscopic level
that could affect the poly-Si film quality. EBSD is quite sen-
sitive and can map intragrain misorientation (plastic defor-mation) in polycrystalline films subjected to strain
gradients.
52–55Figure 8shows the grain average misorienta-
tion (GAM) map for the n-type poly-Si thin films as a func-
tion of the PH 3(2% in H 2)/SiH 4gas flow ratio (0.025, 0.125,
0.25, and 0.45). The accumulated orientation changes rela-
tive to the average orientation within a grain can be meas-ured from a GAM map, and thus, it allows the visualization
of misorientation gradients within the material (plastic defor-
mation).
52,53,56A color map from blue (0/C14) to red (5/C14)i s
used here to measure the misorientation between the refer-
ence pixel and every other pixel, within each grain. In Fig. 8,
blue color represents a small degree (0/C14–0.5/C14) of intragrain
misorientation/lattice rotation (little deformation), while red
color denotes higher degree ( /C244/C14–5/C14) of intragrain misorien-
tation (plastic deformation). It can be clearly seen that themajority of the grains in the poly-Si thin film produced with
aP H
3(2% in H 2)/SiH 4gas flow ratio of 0.025 has negligible
misorientation (0/C14–0.5/C14) (dominated by the blue compo-
nent), while a few grains can be seen with a slightly higher
degree of misorientation (1/C14–2/C14) represented by green color
[see Fig. 8(a)]. Even higher degree of misorientation (3/C14–4/C14)
represented by yellow color starts to appear in very few
FIG. 6. (Color online) EBSD grain size and orientation maps of the n-type poly-Si thin film as a function of the PH 3(2% in H 2)/SiH 4gas flow ratio.061509-5 Kumar et al. : Synthesis and characterization of large-grain solid-phase crystallized poly-Si thin films 061509-5
JVST A - Vacuum, Surfaces, and Films
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20grains of the poly-Si thin film when the PH 3(2% in H 2)/SiH 4
gas flow ratio is increased to 0.125 [see Fig. 8(b)]. The num-
ber of grains with higher degree of misorientation (green and
yellow color component) increases when the PH 3(2% in
H2)/SiH 4gas flow ratio is increased from 0.025 to 0.45 [see
Figs. 8(a)–8(d) ]. In addition, the degree of intragrain misor-
ientation reaches up to 5/C14(red) in few grains of poly-Si thin-
films produced with a PH 3(2% in H 2)/SiH 4gas flow ratio of
0.25 and 0.45, respectively [see Figs. 8(c) and8(d)], which
is nearly four times higher than for the film produced with a
flow ratio of 0.025 [Fig. 8(a)]. A detailed observation of
Figs. 8(c)and8(d) reveals that the number of grains with a
higher degree of misorientation (red color) increases when
the PH 3(2% in H 2)/SiH 4gas flow ratio is increased from
0.25 to 0.45. Thus, from the trend in Figs. 8(a)–8(d) it can be
inferred that the overall intragrain misorientation increases
with increasing PH 3(2% in H 2)/SiH 4gas flow ratio. This
increase in plastic deformation (misorientation/strain) in thegrains of poly-Si thin film could be responsible for the
increase of tensile stress in the film (see Fig. 4). The high
degree of misorientation (plastic deformation) is also an in-
dication of the presence of geometrically necessary disloca-
tions (GNDs),56which are detrimental for the application of
the poly-Si thin films in solar cells and other devices.
EBSD is an excellent technique that provides detailed in-
formation about the grain orientation, distribution andboundary characterization of a polycrystalline film but is
limited to the surface region of the film and hence fails to
give a detailed overview of the entire film. Furthermore, tohave a better understanding for deterioration of the poly-Si
thin film quality with increasing [P] concentration, cross-
sectional TEM and HAADF-STEM studies were performedon selected poly-Si thin-film samples. TEM was used to get
detailed information about the microstructural changes in the
poly-Si films as a function of the PH
3(2% in H 2)/SiH 4gas
flow ratio, while HAADF-STEM was used to reveal the dis-
locations in the poly-Si films.32,56
Figures 9(a)and9(b) show cross-sectional TEM images
of the nþpoly-Si thin films prepared with a PH 3(2% in
FIG. 7. (Color online) CSL maps projected on the top of the EBSD band contrast of the n-type poly-Si thin film fabricated with three different PH 3(2% in H 2)/
SiH 4gas flow ratios (0.025, 0.25, and 0.45).
FIG. 8. (Color) GAM maps of the n-type poly-Si thin film as a function of
the PH 3(2% in H 2)/SiH 4gas flow ratio (0.025, 0.125, 0.25, and 0.45).
FIG. 9. Cross-sectional bright field TEM image of the n-type poly-Si thin
film fabricated with a PH 3(2% in H 2)/SiH 4gas flow ratio of (a) 0.025,
(b) 0.45.061509-6 Kumar et al. : Synthesis and characterization of large-grain solid-phase crystallized poly-Si thin films 061509-6
J. Vac. Sci. Technol. A, Vol. 32, No. 6, Nov/Dec 2014
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20H2)/SiH 4flow ratio of 0.025 and 0.45, respectively. It can
be clearly seen from these images that there is a deteriora-
tion of the structural quality of the poly-Si film with
increasing PH 3(2% in H 2)/SiH 4gas flow ratio. Further
detailed observations of the TEM images revealed the for-
mation of white precipitates in the heavily [P] doped poly-
Si film. It has been reported in the literature that an excessphosphorus concentration in cry stalline Si results in the
formation of phosphorus-rich precipitates
57,58and thus the
white precipitate seen in the TEM image of Fig. 9(b) could
be due to the formation of phosphorus-rich precipitates,
which in turn could produce defects in the poly-Si thin film
during heat treatment.57Further analysis was carried out
on the same specimens using weak beam dark-field
(WBDF) TEM (Ref. 59) to identify the nature of the
defects and dislocations in the poly-Si films as a functionof the [P] concentration. Disl ocations in a poly-Si thin film
can, under certain diffraction conditions, be imaged using
WBDF TEM.
59Figure 10shows the cross-sectional
WBDF TEM images of the nþpoly-Si thin films prepared
with a PH 3(2% in H 2)/SiH 4gas flow ratio of (a) 0.025 and
(b) 0.45. Clear dislocations (white lines) are observed inthe poly-Si film prepared with a PH
3(2% in H 2)/SiH 4gas
flow ratio of 0.025. These dislocations could be a combina-tion of statistically stored dislocations (SSDs) that are
formed during the grain growth,56,60and the GNDs. The
dislocation density seems to increase drastically when the
PH3(2% in H 2)/SiH 4gas flow ratio is increased to 0.45
[see Fig. 10(b) ]. The increase in dislocations as observed
in Fig. 10(b) could be due the formation of additional
GNDs. GNDs are extra defects in addition of SSDs which
are formed due to the presence of strain gradient in crystal-line material
60and hence need to be minimized. Selected
specimens were further analyzed using HAADF-STEM,
whereby the samples were tilted at the zone axis. In thisconfiguration, atoms close to the core of dislocations dis-
play a high contrast in HAADF images.
32In addition,
STEM images are formed by collecting most of the scat-tered electrons on the ADF de tector whereas only a frac-
tion of the scattered electrons is permitted to enter the
objective aperture for the formation of dark-field (DF)TEM images.
59Thus, HAADF-STEM is more capable of
providing detailed information about defects and disloca-
tions in poly-Si thin films. Figure 11shows cross-sectional
HAADF-STEM images of nþpoly-Si thin films prepared
with a PH 3(2% in H 2)/SiH 4gas flow ratio of (a) 0.25 and
(b) 0.45. It can be seen that dislocations are present (whitelines) in the poly-Si thin produced with a low flow ratio of
0.025. It is possible to make a rough estimate of the dislo-
cation density by counting the number of line (white lines)over a selected area. Detailed observation of Figs. 11(a)
and11(b) reveals that in comparison to the poly-Si thin
produced with a low flow ratio of 0.025, the dislocationdensity (white dots) seems to increase significantly and
looks like distributed over the entire film for the sample
p r e p a r e dw i t hah i g hfl o wr a t i oo f0 . 4 5[ s e eF i g . 11(b) ].
From HAADF-STEM, it appears t hat the film quality dete-
riorates significantly when the PH
3(2% in H 2)/SiH 4gas
flow ratio is increased to 0.45. These additional disloca-tions could act as charge carrier recombination centers,
which would be detrimental in solar cell applications. This
interpretation of dislocati ons in the poly-Si films as a func-
tion of the PH
3(2% in H 2)/SiH 4gas flow ratio from TEM
and HAADF-STEM is in good agreement with the results
obtained from EBSD (see Fig. 8).
FIG. 10. Cross-sectional WBDF TEM image of the n-type poly-Si thin film
fabricated with a PH 3(2% in H 2)/SiH 4gas flow ratio of (a) 0.025, (b) 0.45.
FIG. 11. Cross-sectional HAADF-STEM image of the n-type poly-Si thin film fabricated with a PH 3(2% in H 2)/SiH 4gas flow ratio of (a) 0.025, (b) 0.45.061509-7 Kumar et al. : Synthesis and characterization of large-grain solid-phase crystallized poly-Si thin films 061509-7
JVST A - Vacuum, Surfaces, and Films
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Sat, 20 Dec 2014 20:05:20IV. CONCLUSION
In conclusion, large-grain ( >10lm)n-type SPC poly-Si
thin films with high Hall mobility of about 71 cm2/V s
were successfully fabricated. The experimental resultsshowed that the doping concentration and the grain size of
the SPC poly-Si films increased with increasing PH
3(2%
in H 2)/SiH 4gas flow ratio, whereas the crystalline quality
of the material deteriorated. The average grain size of the
poly-Si films was found to increase from 4.3 to 18 lma s
the PH 3(2% in H 2)/SiH 4gas flow ratio was increased from
0.025 to 0.45, with some grains even exceeding 30 lmi n
width. It was shown that the stress in the large-grain poly-
Si thin films fabricated with a high PH 3(2% in H 2)/SiH 4
gas flow ratio could be the likely cause for the deteriora-
tion of the material quality. The stress in the poly-Si films
was found to be in excess of 900 MPa, which leads todefects (for example dislocat ions) in the poly-Si films. The
increased dislocation density with increasing PH
3(2% in
H2)/SiH 4gas flow ratio was also observed in the HAADF-
STEM and EBSD studies performed in this work. With
respect to device applications, it is thus desirable to control
the phosphorus concentration in the poly-Si films throughthe control of the PH
3(2% in H 2)/SiH 4gas flow ratio, to
strike the right balance betw een the grain size and the ma-
terial quality of the poly-Si thin film.
ACKNOWLEDGMENTS
The Solar Energy Research Institute of Singapore
(SERIS) is sponsored by the National University of
Singapore (NUS) and the National Research Foundation(NRF) of Singapore through the Singapore Economic
Development Board (EDB). This work was sponsored
by NRF grant NRF2009EWT-CERP001-046. A.K.acknowledges a Clean Energy Programme Office (CEPO)
Ph.D. scholarship from the EDB.
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1.4898063.pdf | Surfactant role of Ag atoms in the growth of Si layers on Si(111) √ 3 × √ 3 -Ag
substrates
Tsuyoshi Yamagami, Junki Sone, Kan Nakatsuji, and Hiroyuki Hirayama
Citation: Applied Physics Letters 105, 151603 (2014); doi: 10.1063/1.4898063
View online: http://dx.doi.org/10.1063/1.4898063
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/15?ver=pdfcov
Published by the AIP Publishing
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155.33.16.124 On: Fri, 28 Nov 2014 17:22:56Surfactant role of Ag atoms in the growth of Si layers on Si(111) /H2088133/H208813-Ag
substrates
Tsuyoshi Y amagami, Junki Sone, Kan Nakatsuji, and Hiroyuki Hirayamaa)
Department of Materials Science and Engineering, Tokyo Institute of Technology, J1-3, 4259 Nagatsuda,
Midori-ku, Yokohama 226-8502, Japan
(Received 25 July 2014; accepted 2 October 2014; published online 13 October 2014)
The growth of Si layers on Si(111) /H208813/C2/H208813-Ag substrates was studied for coverages of up to a few
mono-layers. Atomically flat islands were observed to nucleate in the growth at 570 K. The top
surfaces of the islands were covered in Ag atoms and exhibited a /H208813/C2/H208813 reconstruction with the
same surface state dispersions as Si(111) /H208813/C2/H208813-Ag substrates. These results indicate that the Ag
atoms on the substrate always hop up to the top of the Si layers. VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4898063 ]
Much attention has been paid recently to the epitaxial
growth of silicene on Ag(111) substrates. Silicene is a two-dimensional (2D) Si material that has a single atomic-layer
thick hexagonal lattice.
1,2It is anticipated as a new material
with Dirac electron dispersion that is fully compatible withconventional Si device technology. However, Si does not
have a graphene-like layered crystal structure and thus cannot
be obtained by exfoliation, unlike graphene. Instead, epitaxial
growth of silicene has been examined on several substrates.
In particular, silicene growth has been studied intensively onAg(111) substrates
3–7because the Ag(111) surface is unreac-
tive with Si and has the same three-fold rotational symmetry
as the silicene lattice. However, a recent experimental studysuggested that the Ag(111) surface is not ideally stable and
does not remain intact during silicene growth.
8The Ag atoms
readily exchange with Si atoms at the Ag(111) surfaces, mak-ing the growth process complicated and difficult to control.
In this study, we therefore examined the epitaxial
growth of Si layers on Si(111) /H208813/C2/H208813-Ag substrates. The
Si(111) /H208813/C2/H208813-Ag substrate surface is fully covered by one
mono-layer (1 ML
Si(111) ) of Ag atoms.9,10(Here, we define
1M L Si(111) as the number density of Si atoms at the top of
ideal Si(111) surface, ca. 7.3 /C21014Ag atoms/cm2.) The Ag
atoms are fixed on the top layer by a strong chemical bond
with the underlying Si layers. This is expected to make theSi(111) /H208813/C2/H208813-Ag surface robust against Ag-Si exchange
during growth. In addition, the Ag atoms are arranged in a
three-fold rotational symmetry. The dangling bonds are per-fectly terminated by Ag atoms, making the surface inert.
11
The surface supports a free-electron like surface state12–16
the same as Ag(111).17,18All these characteristics are
expected to be advantageous for epitaxial growth of silicene.
Here, we experimentally investigated the growth of Si on
Si(111) /H208813/C2/H208813-Ag surfaces at 570 K, which is a suitable
temperature for the growth of silicene on Ag(111) surfaces.
The Ag atoms were found to play a surfactant role even in Si
growth on Si(111) /H208813/C2/H208813-Ag surfaces.
Experiments were carried out using two ultra-high-vac-
uum (UHV) apparatuses. One was equipped with a scanning
tunneling microscope (STM) unit,8while the other wasequipped with low energy electron diffraction (LEED) optics
and a hemispherical electron energy analyzer for X-ray photo-electron spectroscopy (XPS) and angle-resolved photoelectron
spectroscopy (ARPES).
19Si(111) substrates were cleaned by
flashing at 1470 K for 15 s and subsequent slow cooling toroom temperature (RT). The Si(111) /H208813/C2/H208813-Ag substrates
were prepared by depositing 1 ML
Si(111) of Ag atoms on the
clean Si(111) substrates at 770 K, or at RT with subsequent
annealing at 770 K. The Ag-induced /H208813/C2/H208813 reconstruction
was confirmed by STM or LEED in each apparatus. Si atomswere deposited on the Si(111) /H208813/C2/H208813-Ag substrates from a
resistively heated Si wafer. The growth of Si was conducted
at 570 K because this temperature is known to be suitable forthe epitaxial growth of silicene in the case of Ag(111) sub-
strates.
3–7The growth process was followed by repeated depo-
sition of a small amount of Si and subsequent STM, LEED,XPS, and ARPES measurements at RT. A bias voltage was
applied to the substrate during STM. An Al K ax-ray source
and a He I a(21.22 eV) uv-source were used in the XPS and
ARPES measurements, respectively. The photoelectrons were
detected in the surface normal direction in the XPS study. In
the LEED, XPS, and ARPES experiments, the deposition rateof Si on the substrate was calibrated by the saturation behav-
ior in the reduction of XPS Ag 3 dcore level intensity as a
function of Si deposition time at RT. The amount of Si at thebreak in the slope was defined as 1 ML
Si(111).
Figure 1shows LEED patterns (a) before and (b) after
deposition of 1.25 ML Silicene. Here, we define 1 ML Silicene as
FIG. 1. LEED pattern of (a) a pristine Si(111) /H208813/C2/H208813-Ag substrate and
(b) after the growth of 1.25 ML Silicene thick Si layers at 570 K. Electron
energy was 75 eV.a)Electronic mail: hirayama.h.aa@m.titech.ac.jp
0003-6951/2014/105(15)/151603/4/$30.00 VC2014 AIP Publishing LLC 105, 151603-1APPLIED PHYSICS LETTERS 105, 151603 (2014)
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155.33.16.124 On: Fri, 28 Nov 2014 17:22:56the number density of Si atoms in the silicene honeycomb
lattice, ca. 1.5 /C21015Si atoms/cm2. (Note that 1 ML Silicene is
twice as large as 1 ML Si(111). ) Sharp diffraction spots indi-
cated the /H208813/C2/H208813 periodicity in both LEED patterns. The in-
tensity of the diffraction spots did not decay even after the
deposition of 1.25 ML Silicene of Si. This result suggests that
the top of the Si layers also maintained the /H208813/C2/H208813
reconstruction.
The tops of the Si layers were directly observed to ex-
hibit the /H208813/C2/H208813 reconstruction by STM. Figure 2shows
STM images of the pristine Si(111) /H208813/C2/H208813-Ag substrate ((a)
and (b)), and the surfaces after the deposition of 0.65ML
Silicene ((c) and (d)) and 2.6 ML Silicene ((e) and (f)) of Si at
570 K. A wide (240 /C2240 nm2) STM image of the pristine
Si(111) /H208813/C2/H208813-Ag substrate (Fig. 2(a)) revealed a maze-like
pattern on the terraces with a series of steps running from the
upper left to the lower right. This maze-like pattern is char-
acteristic of the Si(111) /H208813/C2/H208813-Ag reconstruction that is
accompanied by pairs of Si(111) one double-layer height
(ca. 0.31 nm) deep “hole” and high “island” regions.20–22
The /H208813/C2/H208813 reconstruction was observed across virtually the
entire substrate, as can be seen in the magnified (8 /C28n m2)
STM image in Fig. 2(b). Many small islands nucleated on
the terraces after deposition of 0.65 ML Silicene of Si (Fig.
2(c)). The tops of the islands were atomically flat and exhib-
ited the /H208813/C2/H208813 reconstruction (Fig. 2(d)). The /H208813/C2/H208813reconstruction was also observed in the gap regions between
islands. The surface morphology of the Si layers did not
change significantly with further Si growth. The top surface
was covered by atomically flat, small islands as can be seenin the STM images of the 2.6 ML
Silicene thick Si layer (Figs.
2(e)and2(f)). The appearance of the islands in terms of size
and distribution was almost the same as the 0.65 ML Silicene
thick Si layer. The /H208813/C2/H208813 reconstruction was still observed
at all locations.
XPS measurements revealed that the Si layers were cov-
ered in Ag atoms. Figure 3shows the Ag 3 dand Si 2 pcore
level spectra before and after the Si layer growth on theSi(111) /H208813/C2/H208813-Ag substrates at 570 K. Both Ag and Si core
levels showed no significant shift in energy after the Si layer
growth. Furthermore, the intensities were almost identical tothe pristine Si(111) /H208813/C2/H208813-Ag substrate except for a reduc-
tion of ca. 15% in the Ag 3 dpeak after Si growth. This indi-
cates that the tops of the Si layers remained covered in Agatoms. The coverage of Ag atoms on the Si layer was almost
the same as for the Si(111) /H208813/C2/H208813-Ag substrate. These
results indicate that the Ag atoms on the substrate segregatedto the top surface of the Si layers and formed the same Ag-
induced /H208813/C2/H208813 reconstruction as on the substrate.
Existence of the Ag-induced /H208813/C2/H208813 reconstruction on
the Si layers was also confirmed by observation of the surface
state dispersions. Figure 4shows the surface band dispersions
on (a) pristine Si(111) /H208813/C2/H208813-Ag substrate and (b) the grown
Si layers in the ARPES measurements. As reported in previ-
ous studies,
12–16theS1surface state with a downward convex
dispersion, the less dispersive S2surface state, and the upward
convex dispersing S3surface state were observed on the
Si(111) /H208813/C2/H208813-Ag substrate (Fig. 4(a)). All these characteris-
tic surface states were also observed in the dispersion of the1.25 ML
Silicene thick Si layers (Fig. 4(b)). This indicates that
the Si layers support the same surface electronic structure as
the Si(111) /H208813/C2/H208813-Ag surface. Although the S1band was
slightly upward shifted in energy on the 1.25 ML Silicene thick
Si layers, the bottom of the S1band is known to be sensitive
to the amount of excess Ag atoms on the Si(111) /H208813/C2/H208813-Ag
surfaces.23–25The Si(111) /H208813/C2/H208813-Ag reconstruction is com-
pleted by 1 ML Si(111) of Ag atoms. However, it is possible for
excess Ag atoms to exist as adatoms on the Si(111) /H208813/C2/H208813-
Ag surface without breaking the reconstruction. Since these
Ag adatoms migrate on the /H208813/C2/H208813 surface swiftly, they can-
not be detected by LEED and STM. However, the Ag
FIG. 2. STM image of (a) and (b) pristine Si(111) /H208813/C2/H208813-Ag substrate,
(c) and (d) 0.65 ML Silicene thick Si layer, and (e) and (f) 2.6 ML Silicene thick
Si layer. The Si layers were grown at 570 K. The STM images were taken at
room temperature. Image sizes are 240 /C2240 nm2in (a), (c), and (e), and
8/C28n m2in (b), (d), and (f). Sample bias voltage was þ2.0 V and tunneling
current was 0.1 nA.
FIG. 3. (a) Ag 3 dand (b) Si 2 pcore level spectra. Solid and dashed lines
indicate spectra before and after growth of a 1.25 ML Silicene thick Si layer on
the Si(111) /H208813/C2/H208813-Ag substrate at 570 K. Photoelectrons were detected in
the direction normal to the surface.151603-2 Y amagami et al. Appl. Phys. Lett. 105, 151603 (2014)
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155.33.16.124 On: Fri, 28 Nov 2014 17:22:56adatoms act as dopants that donate electrons to the S1surface
state, which causes a downward shift in the S1band.
Tentatively, we attribute the upward shift of the S1band to
the deficiency of Ag adatoms on the Si layers. Although thisis consistent with the small decrease in the Ag 3 dcore spec-
trum intensity (Fig. 3(a)), it is not clear where the lost Ag
atoms became located in this study.
The present results indicate that Ag atoms in
Si(111) /H208813/C2/H208813-Ag substrate serve as surfactants for the
growth of Si layers. The Ag atoms at the substrate always hopto the top of the Si layers during the growth of Si on
Si(111) /H208813/C2/H208813-Ag substrates at 570 K. Energetically unfavor-
able dangling bonds are left on the Si surface, while the dan-gling bonds are fully terminated by Ag atoms at the
Si(111) /H208813/C2/H208813-Ag surface.
9,10We regard this as the basic
driving force for the surface segregation of the Ag atoms. Inorder for segregation to occur, it is necessary for the Ag atoms
to exchange with deposited Si atoms during growth. The
exchange process decreases the diffusivity of the Si atoms andenhances the nucleation of islands.
26This is consistent with
the nucleation of many small islands during Si growth on
Si(111) /H208813/C2/H208813-Ag substrate.
The persistence of the Ag-induced /H208813/C2/H208813 reconstruction
during Si layer growth is of interest in the debate regarding the
structure of double-layer and multilayer silicene on Ag(111)substrates. Double-layer and multilayer silicene exhibit the
/H208813/C2/H208813 reconstruction of the silicene 1 /C21l a t t i c e .
27,28Since
interaction with the Ag substrate is greatly reduced by theunderlying first layer of silicene, the second layer of silicene is
expected to reveal the intrinsic Dirac electron dispersion.
Observation of “Dirac dispersion” has been reported in STMand ARPES studies.
27,29,30Several buckled silicene structures
have been proposed as a model for the second layer of /H208813s i l i -
cene,27,29,31but Shirai et al. reported in their detailed LEED I-
V analysis32that /H208813 silicene is actually the Si(111) /H208813/C2/H208813-Ag
surface. They further suggested that the S1band of the
Si(111) /H208813/C2/H208813-Ag surface could be fitted by a linear disper-
sion in the unoccupied states. The linear slope of the S1band
gives a Fermi velocity close to that one in the STM study of
/H208813 silicene,27although the effective mass (0.59 m0;m0is therest mass of electron) of the dispersion of the /H208813 silicene in
ARPES30,32was larger than that of the intrinsic S1band
(0.13 m0)o ft h eS i ( 1 1 1 ) /H208813/C2/H208813-Ag surface.33Even though the
present study was conducted at the Si(111) /H208813/C2/H208813-Ag surface
instead of the Ag(111) surface, the results indicate that once
the/H208813/C2/H208813-Ag reconstruction has been established, Ag atoms
always segregate and form a /H208813/C2/H208813-Ag reconstruction at the
top of the Si layers in the subsequent growth of Si at tempera-
tures suitable for the epitaxial growth of silicene on Ag(111)
surface. From this viewpoint, we also suggest that the /H208813s i l i -
cene could be the Si(111) /H208813/C2/H208813-Ag surface.
In summary, we examined the growth of Si layers on the
Si(111) /H208813/C2/H208813-Ag substrate at 570 K. LEED and STM
revealed that the /H208813/C2/H208813 reconstruction was persistent on
the surface of the Si layers with many small 2D islands. Thereconstruction was verified to be due to Ag atoms that segre-
gated from the substrate to the Si layer surface by XPS and
ARPES. These results were attributed to the stability of theSi surface terminated by Ag atoms. This caused Ag-Si
exchange-induced surface segregation of Ag atoms and a
decrease in the diffusivity of surface migrating Si atoms.
We thank Professor F. Komori for the opportunity to use
the apparatus equipped with photoelectron spectroscopy
under the Visiting Researcher’s Program of the Institute for
Solid State Physics, The University of Tokyo. This studywas financially supported by a Grant-in-Aid for Scientific
Research from the Japan Society for the Promotion of
Science (Grant No. 2628604). It was also partly supportedby grant-in-aids from the Murata Science Foundation and
Toray Science Foundation.
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FIG. 4. Surface state dispersions along the /C22C-/C22Mline in the /H208813/C2/H208813 surface
Brillouin zone as measured by ARPES for (a) pristine Si(111) /H208813/C2/H208813-Ag
substrate and (b) 1.25 ML Silicene thick Si layers grown on the substrate at
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1.4896967.pdf | Contribution of alloy clustering to limiting the two-dimensional electron gas mobility in
AlGaN/GaN and InAlN/GaN heterostructures: Theory and experiment
Elaheh Ahmadi, Hamidreza Chalabi, Stephen W. Kaun, Ravi Shivaraman, James S. Speck, and Umesh K.
Mishra
Citation: Journal of Applied Physics 116, 133702 (2014); doi: 10.1063/1.4896967
View online: http://dx.doi.org/10.1063/1.4896967
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/13?ver=pdfcov
Published by the AIP Publishing
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155.33.16.124 On: Mon, 01 Dec 2014 01:10:18Contribution of alloy clustering to limiting the two-dimensional electron gas
mobility in AlGaN/GaN and InAlN/GaN heterostructures: Theory and
experiment
Elaheh Ahmadi,1Hamidreza Chalabi,2Stephen W. Kaun,3Ravi Shivaraman,3
James S. Speck,3and Umesh K. Mishra1
1Electrical and Computer Engineering Department, University of California, Santa Barbara,
California 93106, USA
2Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
3Materials Department, University of California, Santa Barbara, California 93106, USA
(Received 18 June 2014; accepted 22 September 2014; published online 2 October 2014)
The influence of alloy clustering on fluctuations in the ground state energy of the two-dimensional
electron gas (2DEG) in AlGaN/GaN and InAlN/GaN heterostructures is studied. We show that
because of these fluctuations, alloy clustering degrades the mobility even when the 2DEGwavefunction does not penetrate the alloy barrier unlike alloy disorder scattering. A comparison
between the results obtained for AlGaN/GaN and InAlN/GaN heterostructures shows that alloy
clustering limits the 2DEG mobility to a greater degree in InAlN/GaN heterostructures. Our studyalso reveals that the inclusion of an AlN interlayer increases the limiting mobility from alloy
clustering. Moreover, Atom probe tomography is used to demonstrate the random nature of the fluctu-
ations in the alloy composition.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4896967 ]
I. INTRODUCTION
In recent years, AlGaN/GaN and InAlN/GaN hetero-
structures have attracted attention from industries requiringhigh-power and high-frequency high-electron-mobility tran-
sistors (HEMTs).
1–3One of the key factors in determining
the quality of HEMTs is the mobility of the two-dimensionalelectron gas (2DEG). Therefore, analysis of the individual
scattering mechanisms limiting the 2DEG mobility is para-
mount. The scattering mechanisms originating from acousticand optical phonons, interface roughness, threading disloca-
tions,
4,5and ionized impurities have been studied extensively
in the literature.6,7In heterostructures with an alloy channel
or barrier, alloy disorder scattering adds to all above-
mentioned mechanisms to reduce the mobility. The scatter-ing of electrons in an alloy occurs as a result of random
disorder in the alloy composition, which is a well-known
phenomenon.
8,9In the case of heterostructures with a binary
compound semiconductor as the channel, like InAlN/GaN
and AlGaN/GaN, the 2DEG is confined mainly in the binary
material. However, the tail of the wavefunction still pene-trates the ternary barrier because of the finite depth of the
quantum well.
10,11The mobility of the electrons that pene-
trate the barrier are influenced by alloy disorder scattering.In addition, an alloy barrier can also affect the mobility of
electrons in the binary material via alloy clustering. Alloy
clustering, which is generally a consequence of differencesin adatom diffusivities during growth, makes the barrier
composition non-uniform and locally alters the polarization
and conduction band discontinuities along the channel(Fig. 1). This leads to fluctuations in the energy levels of the
channel, which behave as a perturbation potential and scatter
the electrons in the 2DEG.
12
Decreasing the gate length of a HEMT is essential to
improving its high-frequency operation. As the gate length isreduced, the vertical distance between the gate and channel
needs to be reduced to maintain effective gate control.13
However, minimizing the barrier thickness in conventionalGa-face AlGaN/GaN heterostructures decreases the chargedensity in the channel, which consequently results in highersheet resistance. Therefore, the Al content of the barrierneeds to be increased as the barrier thickness is reduced tomaintain a high charge density in the channel. Experimentaldata in the literature reveals a poor 2DEG mobility inAlGaN/GaN heterostructures with high Al content.
14,15This
is contrary to what we expect from calculations of alloy dis-order scattering. Despite an increase in interface roughnessscattering with higher 2DEG charge density, mobility shouldnot significantly degrade since alloy disorder scattering isreduced. As the Al content of the AlGaN barrier increases,the probability of finding electrons in the alloy barrierdecreases, so the mobility of the 2DEG should improve due
to reduced alloy disorder scattering. However, increasing the
Al content in the AlGaN barrier increases the likelihood ofalloy clustering, which can explain the discrepancy betweenexperimental data and calculations.
InAlN barriers are a promising alternative to AlGaN
barriers. In
0.18Al0.82N presents the advantage of being
lattice-matched to GaN and exhibiting a high spontaneous
polarization charge, making it suitable for use as the barrier
layer in ultra-scaled HEMTs.16However, InAlN needs to be
grown at lower temperatures than AlGaN, which reduces
adatom diffusivity and increases the probability of alloy
clustering.
In this article, we drive a model to calculate the 2DEG
mobility limited by alloy clustering scattering. We then use
atom probe tomography (APT) to demonstrate the randomnature of the fluctuations in the alloy composition. The limit-
ing mobility from alloy clustering is also calculated for
0021-8979/2014/116(13)/133702/6/$30.00 VC2014 AIP Publishing LLC 116, 133702-1JOURNAL OF APPLIED PHYSICS 116, 133702 (2014)
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155.33.16.124 On: Mon, 01 Dec 2014 01:10:18various fluctuation amplitudes and cluster sizes. Moreover,
the effect of alloy clustering on limiting the 2DEG mobility
is compared for both InAlN/GaN and AlGaN/GaN
heterostructures.
II. DERIVATION
In order to model the contribution of alloy clustering to
limiting the 2DEG mobility, we followed the approach thatwas used by Sakaki et al.
17to calculate interface roughness
scattering. In the case of interface roughness, changes in the
width of quantum well cause fluctuations in the energy levelsof the 2DEG, whereas in the case of alloy clustering, varia-
tions in the depth of the quantum well change the energy
levels. Therefore, a local change in the composition ( DXðrÞ)
results in a local variation in the ground state energy
(DE
0ðrÞ), as shown in Eq. (1)
DE0rðÞ¼@E0
@XDXrðÞ; (1)
where rrefers to the position in the heterointerface. It should
be noted that we have assumed all electrons in the channel
are accumulated in the first subband. Therefore, only local
variations in the ground state energy are considered.
The composition fluctuations can be characterized using
the auto-covariance (AC) function, which measures theprobability that the compositions at r0andrare the same.
Due to the random nature of the fluctuations in composition,
this probability should decrease as the distance r/C0r0
increases. Following similar works on interface roughness,17
we assume the AC function can be estimated by a Gaussian
function as shown in Eq. (2)
hDXðrÞDXðr0Þi ¼D2exp /C0r/C0r0 ðÞ2
f2 !
; (2)
where Dand fare the amplitude of fluctuations and AC
length, respectively.
Alloy composition fluctuations can be quantified with
APT. APT is a destructive technique through which the 3D
atomic distribution of heterostructures is mapped.18To
extract the parameters of the Gaussian distribution shown in
Eq.(2), we followed the work done by Goodnick et al.19in
which high-resolution transmission electron microscopy wasused to determine interface roughness parameters. Hence,
the scattering matrix elements of the perturbation potential
can be expressed as
M
2
k0k¼ð
expðj~k0/C1~rÞDE0ðrÞexpð/C0j~k/C1~rÞd3; (3)
which can be simplified to the following equation according
to the Fourier transform of a Gaussian function:
M2
k0k¼p@E0
@X/C18/C192
D2f2exp /C0f2q2
4/C18/C19
; (4)
where ~q¼~k/C0~k0is the 2D scattering wave vector. In the
relaxation time approximation, the momentum relaxation
time sis given by
1
sEðÞ¼1
4p2/C18/C19
2p
/C22h/C18/C19ð
jMk0kqðÞj21/C0cosh ðÞ dEk0
0/C0Ek
0/C16/C17
d2k0:
(5)
The energy of the electron is assumed to remain unchanged
after scattering. The scaling factor (1 /C0cosh) takes into
account that large-angle scattering has a greater impact on
momentum relaxation. Contrary to calculations done bySakaki et al. ,
17we did not use the Thomas-Fermi screening
factor in our calculations. Large angle scattering is dominant
since small angle scattering does not significantly decreasethe mobility. However, large angle scattering occurs at wave
vectors near 2k
F. These wave vectors correspond to wave-
lengths comparable to the inter-electron spacing. Screeningis unlikely to be effective at these distances. Moreover, the
Thomas-Fermi approximation to the dielectric constant of
the electron gas is a quasi-static approximation which is ap-plicable only at long wavelengths (q/k
F/C281).20Therefore,
this is only relevant if we are trying to screen the long-range
part of Coulomb interaction.21Although, as explained intui-
tively in the following paragraph, the charge density along
the channel rearranges itself as a result of quasi electric field
caused by variations in the ground state. This rearrangementcan moderate the electron scattering from fluctuations in the
barrier composition.
FIG. 1. (a) Band structure of an AlGaN/GaN heterostructure showing the
fluctuations in barrier height as a result of fluctuations in the barrier compo-
sition. (b) Schematic of ground state fluctuations along the channel. The
Fermi level is assumed to be pinned at the surface and is constant along the
channel.133702-2 Ahmadi et al. J. Appl. Phys. 116, 133702 (2014)
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155.33.16.124 On: Mon, 01 Dec 2014 01:10:18Fluctuations in the ground state (E 0) generate a varying
quasi-electric field that provides a driving force for electrons
to move along the channel. Since the 2DEG charge density(n
s) is proportional to the difference of the Fermi level and
the ground state (E f-E0), the charge density fluctuates with
changes in E f-E0. The gradient in charge density generates a
diffusion current in opposition to the drift current generated
by the quasi-electric field. Figure 1(b)is a simple illustration
of these two currents in the channel. The value of E f-E0is
larger at x 1than x 2which results in higher charge density at
x1. Because of the lower energy state at x 1, electrons at x 2
prefer to move toward x 1. In addition, the gradient in the
charge density causes electrons to diffuse from x 1to x 2.
These two currents cancel each other out to balance the driv-
ing forces from the quasi-electric field and charge densitygradient. The direction and magnitude of this electric field
depends on which current is dominant. Depending on the
direction of the generated electric field, the conduction band(and consequently the ground state) at x
2will be either low-
ered or raised, which results in the screening or exacerbation
of fluctuations in the ground state, respectively. The driftcurrent (I
drift) and diffusion current (I diff) that result from the
quasi-electric field and gradient in the charge density along
the channel, respectively, are defined by the following:
Idrif t¼ltotDE0
DL;
Idiff¼DqDns/C2d
DL¼lkBT
qqDns/C2d
DL
¼ltotkBTDns/C2d
DL; (6)
where ltotis the total 2DEG mobility considering all scatter-
ing mechanisms, DLis the lateral distance between two
points with different ground states (assumed to be equal to
the AC length ( f)), d is the channel thickness which can be
defined as full width at half maximum of the 2DEG wave-
function in AlGaN/GaN heterostructures. To examine the
extent to which this electric field can screen or aggravate thefluctuations in the ground state, we calculated the diffusion
and drift currents for a specific variation in the AlGaN com-
position. As calculated by BandEng,
22a 2% change in the Al
mole fraction in the barrier of Al 0.27GaN/GaN heterostruc-
ture causes a change of 0.0032 eV for E 0-Efand
3/C21011cm/C02for the charge density. The I driftand I diffcorre-
sponding to these values are 0 :0032 ltot=DLand
0:003ltot=DL, respectively. Hence, these opposing currents
are effectively equal, and the screening effect can be safelyignored.
We then calculate the limiting mobility using
l¼e
m/C3hsðEÞi¼ð
sEðÞE@f0EðÞ
@EdE/C18/C19 /C30ð
E@f0EðÞ
@EdE/C18/C19
;(7)
where eandm/C3are the electron charge and effective mass,
respectively, and f0ðEÞis the Fermi-Dirac distribution func-
tion. As an intuitive explanation, the E@f0EðÞ
@Eterm in Eq. (7)
originates from averaging the momentum relaxation timeover the energy of electrons in an attempt to calculate the
current density of electrons.
23Equation (7)can be simplifiedtol¼esðEFÞ=m/C3in the case of a 2DEG because all elec-
trons are assumed to move very close to the surface of the
Fermi sphere. It should be noted that the mobility limited byalloy clustering is temperature-independent, much like the
mobility limited by interface roughness.
17
III. ATOM PROBE TOMOGRAPHY
To determine the amplitude and distribution of random
composition fluctuations, APT was performed on theAl
0.15Ga0.85N electron blocking layer of a commercial
c-plane (0001) GaN LED. The in-plane Al distribution in the
Al0.15Ga0.85N layer was reconstructed by averaging the Al
mole fraction over 3 nm along the c-axis. To obtain a signifi-
cant number of sampling points, a 60 /C260 nm2in-plane
composition map (Fig. 3(a)) was generated by combining
four 30 /C230 nm2composition maps extracted from different
regions in the AlGaN layer as shown in Fig. 2.
The above-mentioned digitalized data were then used to
calculate the 2D AC as demonstrated in Fig. 3(b). The root
mean square (rms) value of Al composition fluctuations ( D)
was obtained from the zeroth coefficient of the 2D ACsequence and was estimated to be 1.14%. To estimate the
AC length, the composition profile was taken along the
directions shown in Fig. 3(a), and the AC function was
calculated for each profile. Since the Fourier transform of the
AC function (the power spectrum) is included in the relaxa-
tion time formula (Eq. (5)) rather than the AC function itself,
it is preferable to estimate the power spectrum. Fast Fourier
transform can be used to calculate the power spectrum.
However, it leads to severe fluctuations around the actualpower spectrum as demonstrated in Fig. 3(c). Therefore, the
Autoregressive (AR) model was used for this purpose.
19The
AC lengths ( f) were then obtained by fitting a Gaussian func-
tion to the power spectrums of the 1D composition sequen-
ces that were taken along the directions indicated by the
arrows in Fig. 3(a)The distribution of f-values was charac-
terized by a log-normal function and is plotted in Fig. 3(d).
The AC length was estimated to be 12.3 nm from the expec-
tation value of the log-normal distribution fit.
IV. SIMULATIONS
To study the effect of the aforementioned composition
fluctuations on limiting the 2DEG mobility, we assumed an
FIG. 2. To obtain a significant number of sampling points, a 60 /C260 nm2in-
plane composition map was generated by combining four 30 /C230 nm2com-
position maps extracted from different regions in the AlGaN layer.133702-3 Ahmadi et al. J. Appl. Phys. 116, 133702 (2014)
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155.33.16.124 On: Mon, 01 Dec 2014 01:10:18average In (Al) mole fraction of 0.18 (0.27) for InAlN
(AlGaN) in our calculations. As mentioned previously, the
In0.18Al0.82N/GaN heterostructure is particularly attractive
for HEMTs since it is a nominally stress-free heterostructure
and yields a high-density 2DEG. The Al mole fractions of
AlGaN barriers in state-of-the-art AlGaN/GaN HEMTs are
generally between 0.2 and 0.3, due to the trade-off in charge
and mobility.24
To calculate @E0=@X, we solved the Schrodinger-
Poisson equation self-consistently using BandEng software.22
The parameters used in calculations for each heterostructure
are reported in Table I. The ground state energy of the 2DEG
in AlGaN/GaN (InAlN/GaN) were calculated as a function of
Al (In) mole fractions around 0.27 (0.18), as shown in Fig. 4.
@E0=@Xwas then determined from the slope of the
curve to be /C00.5 eV and 1.85 eV for Al 0.27Ga0.73N/GaN
and In 0.18Al0.72N/GaN, respectively. By entering these
values in Eq. (4), we calculated the mobility limited by alloy
clustering for different AC lengths and fluctuation
amplitudes.
FIG. 3. (a) 2D III-site composition
map of the in-plane Al distribution in
an Al 0.15Ga0.85N layer (Black arrows
illustrate the directions along whichthe AC lengths were calculated). (b)
AC sequence of digitized data shown
in part (a). (c) An example of the
power spectrum calculated using both
the FFT and AR methods and the fitted
Gaussian function. (d) Histogram of
AC lengths obtained from differentareas on the 2D III-site composition
map.
TABLE I. Materials parameters used in BandEng to calculate the ground
state energy. m/C3
e=meis the ratio of the electron effective mass to the electron
mass. Eg,DEc, and /C15rare bandgap, conduction band discontinuity with
respect to GaN, and the relative permittivity, respectively.
GaN Al xGa1/C0xNI n xAl1/C0xN
m*
e=me 0:20 :2þ0:2x 0:4/C00:29x
Eg(eV) 3 :42 3 :42þ1:86xþ1x26:28/C08:51xþ3x2
DEc(eV) … 1 :24xþ0:66x21:9/C05:56xþ1:96x2
/C15r 8:98 :9þ0:4x 8:5þ6:8x
FIG. 4. Ground state energy of the 2DEG as a function the alloy composi-
tion calculated using BandEng for (a) Al 0.27Ga0.73N/GaN and (b)
In0.18Al0.82N/GaN.133702-4 Ahmadi et al. J. Appl. Phys. 116, 133702 (2014)
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155.33.16.124 On: Mon, 01 Dec 2014 01:10:18Figure 5demonstrates the mobility limited by alloy clus-
tering as a function of fluctuation amplitude for different AClengths. The mobility limited by alloy clustering decreases
as the fluctuation amplitude increases, as expected. Also,
from the dependence of matrix elements M
2
k0konfshown in
Eq.(4), we expect the mobility to first decrease with increas-
ing AC length until it reaches a minimum and then start
increasing. However, in this work we only calculated thelimiting mobility for the AC lengths in the range of 4 to
18 nm, which are more likely to be experimentally observed.
We then compared the significance of alloy clustering
to mobility limitation between In
0.18Al0.82N/GaN and
Al0.27Ga0.73N/GaN heterostructures in Fig. 6. Since the
bandgap and polarization difference between AlN and InN ismuch higher than that between AlN and GaN, fluctuations in
InAlN composition affect the mobility more significantly
than fluctuations in AlGaN composition. As a result, the lim-iting mobility for the same fluctuation amplitude and AC
length is lower for the InAlN/GaN heterostructure in com-
parison with the AlGaN/GaN heterostructure. It should benoted that due to the large difference in the atomic size
between In and Al and difference in the bonding energy
between Al-N and In-N,
25lower growth temperatures are
required for InAlN than AlGaN. Poor Al adatom diffusion atlow growth temperatures can lead to severe clustering in
InAlN which has been shown to result in a honeycombmicrostructure in certain conditions.
26–28
In AlGaN/GaN and InAlN/GaN heterostructures, insert-
ing a thin AlN interlayer at the heterointerface effectivelysuppresses the penetration of the 2DEG wavefunction into
the barrier, consequently enhancing the 2DEG mobility.
29In
this work, we investigated the influence of AlN interlayer onreducing the scattering from alloy clustering. As shown in
Fig.7, including a 3-nm-thick AlN layer between the channel
and the InAlN barrier enhances the limiting mobility by a fac-tor of 1.6. The barrier height in an InAlN/AlN/GaN HEMT
structure is defined solely by the conduction band discontinu-
ity between GaN and AlN. However, the charge density inthe channel depends on the composition of InAlN barrier.
Thus, variations in InAlN composition can change the charge
density in the channel of InAlN/GaN heterostructure and con-sequently create fluctuations in the ground state energy.
V. CONCLUSION
In conclusion, we calculated the contribution of alloy
clustering to limiting the mobility of 2DEG for various struc-tures. Comparisons were also made between limiting
mobility of alloy clustering between Al
0.27Ga0.73N/GaN and
In0.18Al0.82N/GaN heterostructures, demonstrating that alloy
clustering has more influence on limiting the 2DEG mobility
in InAlN/GaN heterostructures in comparison to AlGaN/
GaN heterostructures for the same auto-correlation lengthand amplitude of composition fluctuations. We also showed
that inserting a thin AlN interlayer between the barrier and
the channel increases the mobility limited by alloy cluster-ing. However, the AlN interlayer cannot completely elimi-
nate the scattering from alloy clustering.
ACKNOWLEDGMENTS
The authors appreciate fruitful discussions with Dr.
Chetan Nayak. This work was supported by the funding
from the Office of Naval Research (Dr. Paul Maki, programmanager), the Center for Energy Efficient Materials
(CEEM), and the NSF MRSEC at UCSB.
FIG. 5. Plot of the mobility limited only by alloy clustering in the barrier as
a function of the mean amplitude of fluctuations in mole fraction ( D) for var-
ious cluster sizes. This limit is independent of temperature.
FIG. 6. Comparison of the effect of alloy clustering on the mobility of
2DEG between AlGaN/GaN and InAlN/GaN heterostructures. The x-axis is
the mean amplitude of fluctuations in mole fraction.
FIG. 7. Plot of 2DEG mobility limited by alloy clustering as a function of
the mean amplitude of fluctuations in mole fraction ( D) for different AlN
interlayer thicknesses in InAlN/AlN/GaN structures.133702-5 Ahmadi et al. J. Appl. Phys. 116, 133702 (2014)
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155.33.16.124 On: Mon, 01 Dec 2014 01:10:18 |
1.4897353.pdf | Surfactant-directed synthesis of mesoporous films made single-step by a tandem
photosol-gel/photocalcination route
Héloïse De Paz-Simon, Abraham Chemtob, Céline Croutxé-Barghorn, Séverinne Rigolet, Laure Michelin,
Loïc Vidal, and Bénédicte Lebeau
Citation: APL Materials 2, 113306 (2014); doi: 10.1063/1.4897353
View online: http://dx.doi.org/10.1063/1.4897353
View Table of Contents: http://scitation.aip.org/content/aip/journal/aplmater/2/11?ver=pdfcov
Published by the AIP Publishing
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Surfactant-directed synthesis of mesoporous films made
single-step by a tandem photosol-gel/photocalcination
route
Héloïse De Paz-Simon,1Abraham Chemtob,1,aCéline Croutxé-Barghorn,1
Séverinne Rigolet,2Laure Michelin,2Loïc Vidal,2and Bénédicte Lebeau2
1Laboratory of Macromolecular Photochemistry and Engineering, ENSCMu, University
of Haute-Alsace, 3 bis rue Alfred Werner, 68093 Mulhouse Cedex, France
2Institut de Science des Matériaux de Mulhouse, UMR-CNRS 7361, University
of Haute-Alsace, 3 rue Alfred Werner, 68093 Mulhouse Cedex, France
(Received 6 August 2014; accepted 16 September 2014; published online 15 October 2014)
In view of their technological impact in materials chemistry, a simplified and more
efficient synthetic route to mesoporous films is highly sought. We report, herein,
a smart UV-mediated approach coupling in a one-stage process sol-gel photopoly-
merization and photoinduced template decomposition /ablation to making meso-
porous silica films. Performed at room temperature with a solvent-free solution
of silicate precursor and amphiphilic poly(ethylene oxide)-poly(propylene oxide)-
poly(ethylene oxide) block copolymer, the synthesis relies on photoacid generation
to induce the fast formation ( ≈10 min) of mesostructured silica /surfactant domains.
Continuation of UV exposure for three additional hours enables subsequent and com-
plete photodegradation of the polyether copolymer, resulting in ordered or disordered
mesoporous silica film. One of the most attractive features is that the one-step proce-
dure relies on a continuous illumination provided by the same conventional medium-
pressure Hg-Xe arc lamp equipped with a 254 nm reflector to enhance the emission of
energetic photons <300 nm. In addition to X-ray di ffraction and transmission elect-
ron microscopy, time-resolved Fourier transform infrared spectroscopy has proved
to be a powerful in situ technique to probe the di fferent chemical transformations
accompanying irradiation. Photocalcination strengthens the inorganic network, while
allowing to preserve a higher fraction of residual silanol groups compared with ther-
mal calcination. A polyether chain degradation mechanism based on oxygen reactive
species-mediated photo-oxidation is proposed. C2014 Author(s). All article content,
except where otherwise noted, is licensed under a Creative Commons Attribution 3.0
Unported License. [http: //dx.doi.org /10.1063 /1.4897353]
Since the first report of mesoporous silicate and aluminosilicate in the early 90s, mesoporous
materials have been the subject of intense scientific and technological interest.1What makes them
particularly attractive is this unique combination of high interfacial area and controlled mesopore
topology /size distribution. The first e fforts focused on powder2amenable to catalysis3and adsorp-
tion4applications. More recently, sol-gel-derived synthetic pathways were adjusted to the shaping
of mesoporous materials as thin films, thereby extending the scope of their applications.5The most
emblematic methodology is the Evaporation Induced Self-Assembly (EISA), which has given rise
to a host of highly ordered mesoporous films employed as interlayer dielectrics, sensors, mem-
branes, or photonic devices.6Despite the success of this approach, the main caveat is a complex
processing which has dampened somewhat the industrialization of these applications.7,8
aAuthor to whom correspondence should be addressed. E-mail: abraham.chemtob@uha.fr. Tel.: +33 3 8933 5030. Fax: +33
3 8933 5034.
2166-532X/2014/2(11)/113306/7 2, 113306-1 ©Author(s) 2014
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In a typical EISA synthesis, a multicomponent mixture, including organic surfactant, hydro-
lyzed low-polymerized inorganic precursor, acid catalyst, water, and large excess of a volatile
solvent, is cast on a substrate. When performed under appropriate environmental conditions, the
film deposition results, after the gradual evaporation of the volatile components, in the formation
of a solid sol-gel film with ordered organic-inorganic mesoscopic domains. After post-treatment
to stabilize the oxide network, the template is eventually removed to liberate porosity. Obviously,
the numerous steps and compounds of this methodology, as well as the high concentration of
solvent (>90 vol. %) have made scaling-up di fficult. As a result, one of the current frontiers in
materials chemistry has been to devise a facile, e fficient, and environmentally compliant route for
synthesizing mesoporous films.
To this end, we describe, herein, the first one-step templated method to synthesize mesoporous
silicate films. Our approach departs from nonhydrolyzed precursor film and exploits UV light’s
versatility to drive both (i) self-assembly and (ii) subsequent surfactant degradation in a single and
continuous stage. Note that these two photochemical reactions were already reported separately9–11
but have never been combined together to form a single route relying on the same UV lamp.
Figure 1 outlines our procedure performed at room temperature and obviating solvent, and even
water. Unlike EISA method, we begin with a fully alkoxylated oligomeric inorganic precursor
(polydimethoxysiloxane, PDMOS, ABCR) mixed with an amphiphilic poly(ethylene oxide) (PEO)
poly(propylene oxide) (PPO) triblock copolymer (PEO 19-b-PPO 69-b-PEO 19, P123, BASF) surfac-
tant and a photoacid generator ( Φ2I+PF−
6, PAG, Sigma-Aldrich). The resulting homogeneous and
nonvolatile solution has been deposited as a stable liquid film on a silicon wafer having a thickness
of 10 ±1µm (Altisurf 500 workstation profilometer, Altimet). Then, a polychromatic UV radia-
tion spanning 185–2000 nm is provided during 190 min to the film sample placed approximately
3 cm lower, at a relative humidity (RH) of approximately 30%. For UV exposure, a conventional
medium-pressure mercury-xenon arc lamp (L8252, 254 nm reflector, Hamamatsu) connected to a
flexible light-guide system (LC6, Hamamatsu) is employed to focus light on the sample.
In this process, the role of UV light is twofold:
(i) First, to trigger the fast photolysis of the PAG. The released photoacids (H+PF−
6) can then
catalyze the silicate precursor sol-gel polymerization. As demonstrated previously, hydro-
lysis of PDMOS increases polarity. Such change in solvation properties is thought to be the
driving force behind the formation of mesostructured surfactant /silica film.9,12–14
(ii) UV light may not only promote sol-gel reactions but also organic matter degradation. This
second strength may permit the subsequent elimination of the copolymer template. As early
FIG. 1. Schematic setup for the preparation of mesoporous silica films via dual light induced self-assembly and calcination.
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as 2000, the concept of photochemical calcination was reported as an alternative method for
the removal of surfactant by the teams of Hozumi10,15–18and Parikh11,19,20using mainly sil-
ica nanocomposite films prepared by the EISA process. A monochromatic excimer lamp ( λ:
172 nm) and low-pressure mercury arc lamp ( λ: 185-254 nm) were implemented, respectively.
Unlike thermal calcination or solvent extraction, photoablation limited mesostructure damage
and made feasible surface patterning and the use of solvent or thermally sensitive substrate.
To make this process one-step, irradiance (400 mW cm−2), emission range (185-2000 nm), and
exposure duration (190 min) must be carefully selected, in order to favor a “stepwise” mechanism,
starting ideally with a fast photoacid-induced mesostructuration and ending with a slower degrada-
tion of the surfactant, so that the latter can play its structuring role before significant UV-induced
cleavages have altered its self-assembling properties. Here, we demonstrate the proof-of-concept for
this one-step generation of mesoporous silica film, but our approach should be also applicable to
other oxide or functionalized mesostructured films as well as patterning applications. In our study,
the dual UV-driven mesostructuration-calcination process is assessed by real-time Fourier transform
infrared spectroscopy in transmission (RT-FTIR, Bruker Vertex 70), X-ray di ffraction (XRD, Philips
X’pert Pro PANalytical), and transmission electron microscopy (TEM, Phillips CM200).
FT-IR spectra of the PDMOS /P123/PAG (1 /0.5/0.02 wt. ratio or 1 /0.009 /0.005 mol. ratio) film on
a silicon wafer substrate before and after two di fferent exposure times (10 and 190 min) are displayed
in Figure 2. Before UV irradiation (t =0, black trace), the broad massif of methylene and methyl
C—H stretching modes in the 2800-3000 cm−1range reflects both the PEO and PPO blocks of copol-
ymer surfactant and the methoxysilyl groups of the precursor. In this set of overlapping bands, the
well-resolved sharp νsym(C—H) stretching mode at 2848 cm−1is distinctively assigned to SiOCH 3
hydrolyzable moities.21The featureless aspect of the IR spectrum between 3000 and 3800 cm−1
supports the absence of silanol groups and the integrity of these methoxysilyl functions before irra-
diation. This spectral characteristic is consistent with the fact that hydrolysis has not started and that
the sol-gel process is mediated exclusively by UV light.
After 10 min exposure, the occurrence of a photoacid-catalyzed sol-gel is supported by several
substantial changes in the IR spectrum (red trace, Figure 2). First, there is a complete disappearance
of theνsym(C—H) feature of the methoxysilyl groups at 2848 cm−1, indicative of a full hydro-
lysis. Second, two new bands emerge clearly: the characteristic ν(Si-O )stretch of silanol groups
at 930 cm−1and the broad OH stretching band centered at 3400 cm−1suggesting the formation of
hydrogen-bonded silanols (interacting with adsorbed water molecules). As expected, conversion of
SiOCH 3groups a ffects significantly the C—H (2800-3000 cm−1) and C—O symmetric stretching
bands (842 cm−1) (and in less extent, the weaker CH 3deformation and rocking modes at 1460 cm−1
and 1190 cm−1, respectively). However, the persistence of these bands after hydrolysis suggests
FIG. 2. FTIR spectra of PDMOS /P123 film before UV exposure (black trace), after 10 min (red trace), and 190 min (blue
trace) of irradiation.
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that a significant fraction of surfactant may be maintained after this short exposure time ( vide
infra ). Moreover, photopolymerization accompanied by the release of methanol byproducts causes
a significant film thickness decrease from 10 ±1µm to 7 ±1µm. Evidence for mesostructuration
of the as-prepared surfactant /silica hybrid film (t =10 min) is given by XRD measurements. The
XRD pattern (red trace, Figure 3) reveals a single broad di ffraction peak assigned to a disordered
mesostructure, which is consistent with our previously reported work.9The corresponding TEM
image exhibits consistently a bicontinuous vermicular structure resulting from elongated micelles
locked in by inorganic cross-linking before the onset of ordering. The d-spacing of 8.1 nm furnished
by XRD cannot be indexed to a particular topology but corresponds rather to a constant pore-pore
distance. Self-organization requires that the surfactant has not undergone significant degradation.
Therefore, these evidences of mesostructured silica film formation confirm indirectly that pho-
todegradation has not progressed very far after 10 min and that longer exposure times may be
required for a complete surfactant removal.
After an extended exposure period of 190 min, the FT-IR spectrum (blue trace, Figure 2)
exhibits again several discernible changes. All C—H stretching (2800-3000 cm−1) and bending
(1300-1500 cm−1) modes have disappeared below the noise detection level (0.001 a.u.), which is
in agreement with a complete decomposition and removal of P123. Concomitantly, the decrease of
the broad envelope around 3400 cm−1and theν(Si-O )stretch at 930 cm−1suggest an enhanced
condensation taking place concomitantly with photodegradation. There is additionally a signifi-
cant decrease of the intense spectral feature spanning 1000-1250 cm−1, which incorporates (after
hydrolysis) both the Si—O—Si asymmetric stretching and the C—O stretch of the deteriorating
polyether surfactant. After this extended UV exposure causing template degradation, there is a new
reduction of film thickness estimated at 5 ±1µm. The XRD pattern (blue dotted trace, Figure 3)
and TEM image displayed in Figure 3 show a preservation of the mesostructure after calcination.
The only di fference between nanocomposite (t =10 min) and mesoporous silica films (t =190 min)
is a slight shrinkage, as exemplified by a d-spacing which has decreased by ∼10% due to further
photoinduced condensation. The resultant calcined films display a good adhesion on silicon wafer
substrate but are easy to scratch. Regarding chemical resistance, they can withstand several hours of
immersion in a number of common organic solvents.
Additionally, FTIR spectra were monitored continuously and in real-time during the UV illu-
mination. Figure 4 shows the temporal evolution of four characteristic vibrational spectral features.
FIG. 3. XRD patterns of the P123 /PDMOS film irradiated during 10 min (solid curve) and 190 min (short-dashed curve).
The corresponding TEM images are also depicted in the right part of the figure.
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νsym(CH )of SiO—CH 3,ν(Si—OH ), andν(OH )are used as makers of hydrolysis-condensation
while theν(C—H )assigned to the C—H stretching mode of the copolymer assesses the kinetics
of photocalcination. As seen graphically, the consumption of the Si—OCH 3functions is achieved
in less than 8 min and accompanied consistently by a marked growth of the two vibrational bands
due to silanols. Upon longer UV exposure times, these latter absorption modes gradually and
simultaneously decrease in intensity, reflecting continuous condensation reactions. Nevertheless,
an important fraction of silanol is present in the film after template elimination (approximately
50%), thus remaining available for subsequent functionalization reactions. Integrated intensities
for theν(C—H )(calculated only after 10 min irradiation to get rid of any contribution from
SiOCH 3) show a progressive and continuous loss of hydrocarbon chains throughout the irradiation.
Noteworthy is that more than 90% of P123 is removed within the first 120 min. In addition to
RT-FTIR, carbon elemental analysis using X-ray photoelectron spectroscopy (XPS) could be im-
plemented to assess the photocalcination process. To further support the potential of this method, a
one-step procedure was carried out to synthesize periodically ordered mesoporous silica film from
a PDMOS /P123/PAG/film (1/0.35/0.02 wt. ratio or 1 /0.006/0.005 mol. ratio). As established in a
previous study,14the film was irradiated for 40 min at lower irradiance (60 mW cm−2) and higher
humidity (RH =50%) to promote organization and yield an hexagonally packed hybrid mesostruc-
ture. Three additional hours at higher irradiance (400 mW cm−2, RH =30%) were then necessary
for a complete surfactant removal. RT-FTIR, XRD, and TEM data (Figures S1-S3) are described in
the supplementary material.22
Furthermore, our single-step UV process was compared with a more conventional two-step
procedure involving, first, the synthesis of a mesostructured hybrid silica film under short UV expo-
sure (10 min) as demonstrated previously, followed by a thermal calcination in the dark (heating
rate at 2◦C min−1up to 250◦C during 180 min). In this case, Figure 5 shows several di fferences
in the temporal evolution of the previous IR absorption bands used again as diagnostic markers of
chemical transformations. A detailed analysis of the CH 2and CH 3stretching bands shows a sharp
and fast decline above a threshold temperature of 180◦C whereas their decay is gradual and contin-
uous in photocalcination (Figure 4). Additionally, the IR data demonstrate that C—H modes’ decay
is pronounced but incomplete; longer heating or higher temperature may be required to remove the
≈10% surfactant residue. The spectral features attributed to silanols ( ν(Si—OH )andν(OH )) are
FIG. 4. Normalized integrated IR band absorbance during irradiation time: νsym(C—H) of SiO—CH 3(■, 2848 cm−1),
ν(Si—OH )(•, 930 cm−1),ν(O—H )(N, 3000-3600 cm−1), and ν(C—H )modes (solid curve, 2800–3000 cm−1). The inset
shows the temporal evolution of the first three modes during the sol-gel-induced mesostructuration step within 10 min
illumination.
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FIG. 5. Plot of normalized integrated IR absorbance (left axis) for νsym(C—H) of SiO—CH 3(■),ν(Si—OH )(•),ν(O—H )
(N), and ν(C—H )modes (solid curve), as well as the evolution of temperature (right axis) during the two-step synthesis: UV
irradiation (10 min) as well as thermal calcination (180 min).
no longer visible after 180 min of heating indicating an extensive thermally induced condensation.
In Figure 5, TEM pictures before (t =10 min) and after thermocalcination (t =190 min) reveal
mesostructure conservation with resolution loss compared to the photocalcination process.
The UV-induced decomposition and ablation of the block copolymer were also studied. Pure
polyethers exhibit a very limited absorption range above 180-200 nm. As a result, direct photolysis
of C—C or C—O bonds is unlikely under our irradiation conditions.23However, polyethers, such
as PEO or PPO, are known to be highly prone to photo-oxidative degradation in air through an
extensively investigated mechanism.24,25Photoinitiation proceeds by α-H abstraction from methy-
lene groups adjacent to ether oxygen ( β-H abstraction of CH (CH 3)in PPO seems to less favoured
photochemically26,27) yielding alkyl radicals (R•) involved in hydroperoxidation reaction. As shown
below, the photodecomposition of the resulting secondary hydroperoxide (ROOH) produces alkoxy
radicals (RO•), which are preferentially decomposed in formate species (RCHO) by β-scission
mechanism.
Such transient species have been detected by RT-FTIR through a weak band centered at
1725 cm−1consistent with carbonyl (C =O) absorption mode visible during the first 30 min of
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irradiation. FTIR detection of the carbonyl IR mode during the irradiation (Figure S4) is shown
in the supplementary material.22During photodegradation, there is a progressive decomposition of
the polyether chains into smaller (often gaseous) fragments. Since smaller molecules have a lower
density, irradiated volume expands rapidly and can escape from the film. For wavelengths larger
than 300 nm, the process is slow but requires only chromophoric impurities (for initiation) and air
atmosphere. In our case, photodegradation may be substantially accelerated through the mediation
of oxygen reactive species.20Irradiation at wavelengths of 175-210 nm can promote the dissociation
of O 2to produce ozone (O 3). After UV absorption, ozone behaves as a precursor for atomic oxygen
O, singlet oxygen1O2as well as hydroxy HO•, and hydroperoxy H 2O•radicals, which are highly
efficient oxidative species. As a first clue, limiting the emission wavelength above 300 nm with a
filter greatly slows calcination (data not shown).
In summary, a smart single-step route to mesoporous silica film was investigated in details,
in particular, through RT-FTIR. By extending applicability to photopatterning and precursors of
various compositions, we believe that this UV-driven method could have a significant potential to
expand applications of mesoporous materials. The description of this method was complemented
by a qualitative discussion on the photodegradation mechanism of the polyether template. Nev-
ertheless, it remains unclear in particular the influence of film thickness and the doping e ffect of
photolyzed PAG residue28in order to make the process even more e fficient. More systematic studies
on the poloxamer photo-oxidation are also necessary including its wavelength, irradiance, block
composition, and molecular weight dependence, as well as reaction intermediates, volatile spe-
cies characterization (mass spectrometry and gas chromatography) compatible with decomposition
mechanism.
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1.4897084.pdf | On The Sensitivity Of 4 Different CPV Module Technologies
To Relevant Ambient And Operation Conditions
César Domínguez and Pierre Besson
CEA-LITEN, LCPV, cesar.dominguez@cea.fr
Institut National de l’Energie Solaire, 50 Avenue du lac Léman, 73375 Le Bourget du Lac, France.
Abstract. The sensitivity of four different CPV module techno logies to most operating conditions relevant to CPV
systems has been studied, namely DNI, spect rum, cell and lens temperature and clear ness of the sky. In order to isolate
the influence of a single operation parame ter, the analysis of long-term outdoor m onitoring data is required. The effect
of lens temperature on cell current has been found to vary greatly between modules due to the different optical
architectures studied. Maximum sensitivity is found for silicone-on-glass primary lenses. The VOC thermal coefficient
was found to vary between module techno logies, probably due to differences in maximum local effective concentration.
Keywords: solar concentrator, CPV performance, multi-junction cells, I-V curve, operating conditions
PACS: 88.40.F, 88.40.fc, 88.40.ff, 88.40.jp, 92.60.Wc
INTRODUCTION
A good knowledge of the sensitivity of PV system
performance to changing operating conditions is a basic requirement for producing realistic models of
their power output, accurate predictions of their energy
yield or outdoor power rating with a low uncertainty. However, while the performance of flat-plate PV
depends mainly on irradiance and cell temperature, the
performance of multi-junction cell-based CPV systems is affected by a larger set of operation conditions [1],
namely irradiance, spectral distribution[2], circumsolar
radiation[3], cell and lens temperature[4,5], and tracking accuracy. This work shows an experimental
analysis of the sensitivity of 4 different CPV module
technologies to most relevant operation conditions. All of them use MJ cells and a high concentration ratio,
but they feature different optical architectures and
materials.
EXPERIMENTAL
Outdoor Test Bench And Relevant
Operation Parameters
The measurements presented here were performed
at the CEA outdoor test bench for CPV modules at the Institute National de l’Énergie Solaire site (see Fig.1).
It consists of a high-accur acy 2-axis tracker (azimuth-
elevation) and an electronic bench able to measure the
IV curve and backplane te mperature (4-wire PT-100
sensors) of up to 12 modules automatically. The
measurement of each module can take up to 10 seconds, so all meteo parameters are measured simultaneously with each IV-curve. The pointing error
of the tracker both in azimuth
Az and elevation El are
registered as well through a Black Photon BPI-TA1.
FIGURE 1. CPV outdoor characteriz ation bench at INES
site (Le Bourget du Lac, France). The IV curves of up to 12
modules can be taken automati cally, simultaneously with the
relevant operating conditions.
The meteo station, which is located besides the
CPV tracker, monitors irradiance and environmental
conditions relevant to CPV systems – a larger set than that of flat-plate PV. The largest differences between
CPV and Si flat-plate PV arise from the large spectral
sensitivity of multi-junction (MJ) cells (due to current mismatch between sub-cells ) and the narrow angular
transmittance of concentrat or optics. Any change in
the state or alignment of the optical stages will change the intensity and the spatial, spectral and angular
distributions of the light transmitted to the solar cell,
10th International Conference on Concentrator Photovoltaic Systems
AIP Conf. Proc. 1616, 308-312 (2014); doi: 10.1063/1.4897084
© 2014 AIP Publishing LLC 978-0-7354-1253-8/$30.00
308which w i
mismatch
silicone-o n
temperatu r
attributes d
glass and s
of silico n
temperatu r
operation the narro
w
significan t
given thro
Thus,
Irradiance temperatu
r
relative h
effective D
to a latti c
cell DNI T
Spectro- H
other par a
in order t o
The a v
the Spectr a
ratio of t
compone n
where SMR
a spectral b
The DN
of the cle a
the futur e
also as a r
the highes
FIGURE 2
equivalent
is estimate d
real lens te m
the convec
function o f
lens parqu e
elevation h aill in turn v a
and series re s
n-glass (So G
re can have
due to therma l
silicone and t h
ne refractive
re has to b e
parameter in C
w angular acce p
t sensitivity to
ugh the circu m
the meteo st a
DNI, Global
re Tair, wind s
humidity, at m
DNI given by c
ce-matched G
Top, DNI Middle
eliometer IC U
ameters and fi g
o better analyz e
vailable light
al Matching R a
the effective
nt cells.
mi top SMR /(
MR(top/middle)
balance equiv a
NI to GNI rati
arness of the s
e IEC 62670-3
rough probe o f
t the DNI to G
2. Thermal mo d
lens temperatur e
d through mod u
mperature meas u
tive heat trans f
fwind speed (in
et, for which wi n
ave to be consid
ary its photo c
sistance losse s
G) lenses, t
a large infl u
l expansion m i
he large tempe r
index [6, 7
e considered
CPV character i
ptance of CPV
the clearness o
msolar ratio (C S
ation records
Normal Irra d
speed Wvel and
mospheric pr e
component cel l
GaInP/GaAs/G e
and DNI Bottom
U-3J35). Up o
gures of merit
e CPV perfor m
spectrum is a
atio, which is d
DNI given b
MidT
DNIDNIiddle)
= SMR(top/b o
alent to AM1. 5
io is then use d
sky as specifie
norm. It mi g
f the circums o
GNI ratio, the l o
del used for th e
e for each CPV
ule dimensions
urements. R th,con v
fer coefficient o
directions affe c
nd speed and m o
ered).
current, curr e
s. In the case
their operati n
uence on the
ismatch betwe e
rature sensitiv i
7]. Thus, le n
also as a k e
ization. Besid e
optics implie s
of the sky, oft e
SR) [8].
Direct Nor m
diance GNI, a
d direction W d
essure and t h
ls correspondi n
e triple-juncti o
(through S A
on them, ma n
are construct e
mance:
assessed throu g
derived from t h
by any pair
ddleTop (1
ottom) = 1 mark
5D.
d as an indica t
d in the draft
ght be regard e
olar ratio (CS R
ower the CSR.
e estimation of
module. R th,inte r
or fitted throu g
vection is defined b
of air, which is
cting the air at t h
odule azimuth a n
ent
of
ng
se
en
ity
ns
ey
es,
s a
en
mal
air
dir,
he
ng
on
AV
ny
ed
gh
he
of
)
ks
tor
of
ed
R):
an
rnal
gh
by
a
he
nd Reg
simpl e
first,
measu r
measu r
for al l
apertu r
ambie n
wind s
has n o
it is u s
on th e
ambie n
We
main
operat i
Howe v
differ e
effect o
The
a bro a
under
of the range
then e
v
of this
No
perfor m
derive d
ISC/DN
apertu r
moduloptica
l
be dir e
solar c
The
the m o
be el e
(differ
lenses )
TAB L
Tec
In
from t
modul
them
Three
which garding lens t e
e thermal mo d
it was not
urement perio d
urement of thi s
l types of mo d
re. The mode l
nt and backpl a
speed, quantiti e
ot been validat e
sed in this st u
e effect on l e
nt or module t e
e have theref o
module per f
ing conditio n
ver, these are o
ent extents) so
of each magni t
e long measu r
ad range of v a
study. We us e
independent v
and study the
valuate the ex i
trend.
ot only the mai
mance indicat o
d from them l i
NI ratio. The l
re area to al l
es, and it is t a
l efficiency of
ectly compare d
cell, provided a
e ratio (ISC-IMP
odule mismatc h
ectrical (diff e
rent optical e
).
LE 1. Optical st a
chnology
1
2
3
4
CPV T e
this study w e
the long-term
e technologie s
with a high- c
of the m com p
will have a p remperature, w e
del to estimate
regularly m e
d for all mod u
s magnitude m
dules without
l estimates le n
ane temperatu r
es which are m
ed for all mo d
udy only to pr o
ens temperat u
emperature.
ore studied th e
formance pa r
ns –the inde
often correlat e
there is the n
tude separatel y
rement period
alues for mos
e this large va r
variables to a
effect of var y
istence of a tr e
in IV paramet e
ors (ISC, VOC, F
ike the electri c
latter is norm a
low direct c o
aken as an ind
fthe module ( a
d to the curre n
all technologie s
PP)/IMPP is use
h between cel l
erent cell re s
efficiency or
ages of the tech n
Primary lens
SoG
SoG
SoG
PMMA
echnolo gies
e have consi d
outdoor moni t
s installed o n
concentration
prise SoG prim
rimary influene have constr u
it for two re a
easured durin g
ules and seco n
might not be p o
shading the o
ns temperatur e
res and the ef f
measured anyw
dule technolog i
ovide better i n
ure than just
e dependence o
rameters to
ependen t var i
ed between th e
need of isolati n
y.
considered pr o
t of the para m
riability to fix
particular sett i
ying the othe r
end and the li n
ers are conside
FF…) but also
cal efficiency
alized to the o
omparisons b e
dicato r of the o
as the magnitu d
nt density of a
s use similar c e
d as an indic a
ls, whose caus e
sponse) or o
alignment b e
nologies studie d
SOE
DTIR C
XTP
-
RTP
Studied
dered IV-curv e
toring of 4 di f
n the tracker,
ratio (300-1 0
mary lens pa r
ce on the sen sucted a
asons:
g the
nd, the
ossible
optical
e upon
fect of
ays. It
ies, so
nsights
using
of the
these
iables.
em (to
ng the
ovides
meters
some
ing or
rs. We
nearity
red as
others
or the
optical
etween
overall
de can
a bare
ells).
ator of
es can
optical
etween
d
C
e data
fferent
all of
000X).
rquets,
sitivity
309of optical
each one
element ( S
the varia b
technolog y
homogeni z
angular a
optical ef f
Table
stands fo r
RTP for r
DTIRC i s
parabolic c
TABL E
to improve
Mete
SMR
SMR
D
DNI fl u
prev
Device-r e
Backpl
Lens
E
(ISC
(VOC
D
In ord e
the datase t
to the ac q
(e.g. nega t
or the eff e
(partial s h
lens…). T
used as fil t
The d e
carried o u
(MATLA B
RE
The m
given D N
subcells.
happen o u efficiency t o
uses a differ e
SOE), which i n
bility of the p r
y uses PMM A
zer as SOE.
and lens tem p
ficiency can be
1 summarizes
r reflective tr u
refractive tru n
s a compact
concentrator, a
E 2. Baseline fi l
the quality and s
eo parameter
DNI
Tair
R(top/middle)
R(top/bottom)
DNI/GN I
uctuation during
vious 30 min
elated paramet
ane temperature
s temperature
Efficiency
ISC/DNI
C-IMPP)/IMPP
C-VMPP)/VMPP
Az, El
Data Filter i
er to improve t
t to study, a b
quired data in o
tive value of i r
ects of events
hading, soilin g
able 2 summa r
ters in this stu d
escribed filteri n
ut by means o f
B environmen t
ESULTS A N
Effect O
main influenc e
NI) is on the c
Therefore, c u
utside perfect co lens temper a
ent optic as s e
nvolves differ e
rimary lens. A
A Fresnel len s
Therefore, di f
perature sensi t
expected.
all architectu r
uncated invert e
ncated inverte d
variation of
a nearly ideal c
lters applied to
significance of t h
Va
700 –
0°C
0
0
er Va
0° C
0°C
0.8*medi a
1.2*m e
0.7*medi a
1.3*m e
x < 1.3* m
x < 1.3* m
ng And An a
the quality an d
asic filtering h
order to remo v
rradiance), tra n
outside the sc o
g, water cond e
rizes the range
dy.
ng and subseq u
f in-house de v
t).
ND DISCU S
Of Spectru m
on spectral
current misma t
urrent losses a
current matchi nature. Howev e
econdary opti c
ent tolerances
A fourth mod u
ses and a gl a
fferent spectr a
tivities of th e
res, where X T
ed pyramid a n
d pyramid. T h
the compou n
oncentrato r.
the whole data s
he data
lid range
1100 W/m2
C – 40°C
.7 – 1.2
.7 – 1.2
>0.7
<10%
lid range
C – 80°C
C – 50°C
an(dataset ) < x <
edian( dataset )
an(dataset ) < x <
edian( dataset )
median( dataset )
median( dataset )
±0.5°
alysis
d significance
has been appli e
ve incoherenci
nsient respons
ope of the stu d
ensation on t h
s of valid val u
uent analysis a
veloped softw a
SSION
m
changes (for
tch be tween M
are expected
ng. This effect er,
cal
to
ule
ass
al,
eir
TP
nd
he
nd
set
<
<
of
ed
es
es
dy
he
ues
are
are
a
MJ
to
is show n
top-to -
propor
with v a
match i
to sho w
data p
efficie n
can be
particu
sharp e
FIGU R
functio n
Color m
the tre n
FIGU R
functio n
matchi n
techno l
In
modultempe
r
ratio n
direct curren
t
achie v
(equiv„SoG
+
n in Fig. 3, wh e
-middle sp e
rtionality bet w
arying spectru m
ing conditions
w values of e s
point (a par a
ncy), one can
e achieved if t
ular range of l e
est trend is giv e
RE 3. Propor t
n of spectrum
mapping shows
nd dispersion.
RE 4. A n i n d i
n of spectral b a
ng condition, w h
logies.
Fig. 4, a si m
e technology
rature variatio n
normalized to
comparison b
nt matching is m
ved reasonably
valent to AM1. 5
+ No SOE“ t e
ere the ISC/DNI
ectral balan c
ween ISC and D
um, and has a m
. However, if
stimated lens t
ameter that
note that lo w
the dataset is f
ens temperatu r
en for tempera t
tionality betwe e
(shown here f o
the influence o
icator of optic a
alance. Peak v a
hich varies sign i
milar plot is p
after filteri n
ns. However, t
lens area has
between mod u
marked for ea c
close to a va l
5D) only fo r „
echnologies. H
NI ratio is plot v
ce (SMR):
DNI is not c o
maximum for c
a color map i s
temperature fo r
influences o
wer dispersion
further filtere d
res (in this ca s
tures above 37
en ISC and DNI
or a sample m o
of lens tempera t
al efficiency pl o
alues mark the c
ificantly betwee n
presented for
ng for ~5 ° C
this time the IS
been used t o
ules. The poi n
ch module, w h
lue of SMR equ
„PMMA + RT P
However, the c
versus
the
onstant
current
s used
r each
optical
trends
d for a
se, the
°C).
NI as a
odule).
ture on
ot as a
current
n CPV
every
C lens
SC/DNI
o have
nt for
hich is
uals 1
P“ and
current
310matching
strongly s h
lens temp
with its s
Fig. 5: th e
effective D
cells as a
with the l o
(blue - le f
module c u
subcell is
with the f a
found un d
FIGURE 5
subcells fo
efficiency f
lower tha n
mismatch u
FIGURE 6
temperatur e
shown in c o
temperatur e
lowering d i
Effec t
The re l
is well k n
instrumen t
are open cannot b
e
probe), b u
for the „S o
hifted to red-r i
erature range
subcells-limit a
e proportiona l
DNI given b y
function of t h
ow slopes sho w
ft) or middle (
urrent. The f a
much lower t h
act that the to p
er red-rich sp e
5. Subcell-limit
for the “SoG +
for the spectral
n that of the t o
under reference s
6. Masured VO
e (sample modu
olor through th e
e coefficient, s
ispersion.
t Of Cell A n
lationship bet w
nown for bare
tation issue at
on how to es
e directly c o
ut in our work w
oG + DTIRC“
ich spectra ( SM
considered. T
ation diag ram
lity between c
y top and mi d
he spectrum. T
w the regions w
red - right) s u
act that the r
han for top su b
-to-middle cu r
ectra.
ation diagram fo
+ DTIR” mod u
region of the
op cell, which
spectrum.
C as a function
le). The conce n
e ISC) affects bo t
o it has to b e
nd Lens Te m
ween VOC and
cells, but it r e
the module le
timate cell te m
ontacted with
we have esti m
technology
MR ≈ 0.9) for t h
This is coher e
[9], shown
current and t h
ddle compon e
The linear tren d
where either t o
ubcell is limiti n
ratio for mid d
bcell is coher e
rrent matching
for top and mid d
ule. The opti c
middle subcell
creates a curr e
of estimated c e
tration level (h e
th the VOC and t h
e filtered out f
mperature
cell temperat u
emains a thor n
vel. Discussio n
mperature (as
a temperat u
mated it using t h
is
he
ent
in
he
ent
ds
op
ng
dle
ent
is
dle
cal
is
ent
ell
ere
he
for
ure
ny
ns
it
ure
he VOC-ISC
refere n
The d
with t h
the daaroun
d
Result
0.18%
this la r
be par
peak c
the ce
cells w
the da t
FIGU R
estima t
to the v
FIGU R
temper a
variabi l
Theref o
order t
respon s
As
efficie n
the ISC/
tempe r
A col o
the lat t
large
additi o
C method [1 0
nce level, whi c
dVOC/dT coeffi
he concentrati
ataset has bee n
d 850 W/m2.
ting thermal c o
%/K. As all mo d
rge variation w
rtly explained
concentration l
ell. This impli
within the mod u
tasheet.
RE 7. Relat i
ted cell tempera t
value under 70 ° C
RE 8. ISC to
ature for a sam p
lity introduce d
ore the latter s h
to analyze the e
se.
the lens tem p
ncy, we have
C/DNI ratio. If w
rature of the m
or map for the
ter in the disp e
effect on cu r
onal filtering
0] (we used t
ch was measu r
icient is well
ion level (as s
n filtered for 3
This gives t
oefficients var y
dules use latti c
was not expect e
by difference s
level achieve d
es the therm a
ule might diff e
ionship betwe e
ture. The volta g
C for easier co m
o DNI ratio v
ple module, whe r
d by SMR v a
hould be fixed
effect of lens t e
perature has a
analyzed its i m
we plot it vers u
module, a very n
SMR values s
ersion found ( s
rrent mismatc h
of the datase
the VOC at S T
red indoors at C
known to de c
shown in Fig.
3% variations
the plot in F
y from -0.11% /
ce-matched 3 J
ed, although it
s in the avera g
d by each mo d
al coefficient o
er from that gi v
en module V O
ge has been nor m
mparison.
versus estimate d
re it is shown th
ariation (color
to a narrow r a
emperature on c
an effect on o
mpact again t h
us the estimat e
noisy trend is f
shows the im p
see Fig. 8), du e
h losses. Th u
t for a rang e
TC as
CEA).
crease
6), so
of ISC
Fig. 7.
/K to -
J cells,
might
ge and
dule at
of the
ven in
OC and
malized
d lens
e large
map).
ange in
current
optical
hrough
ed lens
found.
pact of
e to its
us, an
e of a
311maximum
variation
clear trenFig. 9 for
to lens a
r
show the
probably
sensitivit y
temperatu r
thermal c o
with a D
tolerance t
with a P M
sensitivit y
FIGURE 9
as a funct i
module tec h
have been f
Filteri n
has been
sensitivit y
values. H o
of the C S
found cle a
this ratio CSR sho
u
efficiency .
“SoG + D T
ratio incr e
at slices o f
The s e
technolog i
has been s
single op e
have to b e
to assure a
5% variatio n
of DNI/GNI r
ds are then r
all modules i n
rea): “SoG + N
largest sen s
due to the
y of “SoG + X
re is about 1
oefficient of t h
DTIRC secon d
to SoG temp e
MMA primar y
y (within uncer t
9. An indicator
ion of the esti m
hnology, for w h
fixed to a narro w
Effec
ng for a parti c
proven usef u
y to other qua n
owever, it see m
SR and asses s
ar trends betw
for all techn o
uld result in
. Nevertheles s
TIRC” techn o
eases significa n
f constan t DNI
CON C
ensitivity of
ies to the mos t
studied. In ord
eration parame t
e properly tun e
a broad range o
n in SMR(top/ m
ratio (very si m
revealed. The y
n terms of ( ISC/
No SOE” an d
sitivity to le n
silicone-on-g
XTP” module
0 times high
he bare solar c
dary optic ac h
rature variati o
y lens show s
tainty).
of the optical e f
mated lens tem p
hich the SMR an
w range.
ct Of CSR
cular range o f
ul for analyzi n
ntities with lo w
ms to be too r o
sing its effect s
een the optic a
ologies, while
a clear inc r
s, we show t h
ology, for wh i
ntly with DNI/
I making use o f
CLUSIONS
four differen t
t relevant ope r
er to isolate t h
ter, filters for
ed. Long-term
of values for al l
middle) and 3
milar clearnes s
y are shown
/DNI normaliz e
d “SoG + XT P
ns temperatu r
lass lens. T h
current to le n
er than the I
cell. The mod u
hieves a lar g
ons. The mod u
s no signific a
fficiency is sho w
perature for ea
nd DNI/GNI rati
f DNI/GNI rat
ng performan c
wer dispersion
ough as a pro b
s. We have n
al efficiency a n
the decrease
ease in opti c
his trend for t h
ich the ISC/DN
/GNI if we lo o
f the color ma p
t CPV mod u
rating conditio n
he influence o f
the rest of th e
data is requir e
l quantities.
%
s),
in
ed
P”
re,
he
ns
ISC
ule
ger
ule
ant
wn
ch
ios
tio
ce
of
be
not
nd
of
cal
he
NI
ok
p.
ule
ns
f a
em
ed The
photoc
tempe r
primar
SOE i s
betwe e
differ e
The
be con
real o p
FIGU R
increas
interva l
Thi
Com m
28379 8
1. T. G
T. L
Pub
2. G. P
158
3. I. R
Pho
4. G.
Bet
5. H. C
Pho
6. T. S
Gom
Pla
7. S. A
Ant
201
8. C. A
201
9. C. D
Pho
10. E. S
No.
e main the r
current has b e
rature rather t
ry lenses are
s present). VOC
en module t
ent effective c o
e sensitivity t o
nsidered when m
perating condi t
RE 10. For th e
es with DNI/G N
l (color).
ACKN O
is work has b
mission throug h
8) and SOPHI A
RE
Gerstmaier, S. v a
Lejeune, and E.
blishing, 2010), p
Peharz, G. Sief e
88 (2009).
R. Cole, T.R. Be t
otovolt. 2, 62 (2 0
Peharz, J.P. Fe r
tt, Prog. Photov o
Cotal and R. Sh e
otovolt. Energy C
Schult, M. Neu b
mbert, in 2nd In
ants Opt. Desin g
Askins, M. Vict o
tón, and G. Sala
11), pp. 57–60.
A. Gueymard, in
10), pp. 316–31 9
Domínguez, I. A
otovolt. Res. Ap p
Sanchez and G. L
. 8, 817 (1982).
rmal coeffic i
een found to
than cell tem p
considered ( a
C thermal coef f
technologies,
oncentrations a
o all the para m
modeling CP V
tions.
e “SoG + DTI R
NI ratio (clearn e
OWLEDGE M
been supporte
h the projec ts
A (Ref. N: 26 2
EFERENC E
an Riesen, A. G
Duminil, in AIP
pp. 183–186.
er, and A.W. Be t
tts, and R. Gotts
012).
rrer Rodríguez, G
olt. Res. Appl. 19
erif, in IEEE 4t h
Convers. (2006)
bauer, Y. Bessle r
t. Workshop Co n
g Grid Connect. (
oria, R. Herrero,
a, in AIP Conf. P
n AIP Conf. Pro c
9.
Antón, G. Sala, a
pl. n/a (2012).
L. Araujo, Solid
ient for the
be related t o
perature, whe n
and no appr o
ficient found t o
probably d u
at the cell.
meters studied h
V performance
RC”, the ISC/DN
ess) for any giv e
MENTS
d by the Eu r
s NGCPV (R e
2533).
ES
ombert, A. Mer m
P Conf. Proc. (AI
tt, Sol. Energy 83
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G. Siefer, and A
9, 54 (2011).
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), pp. 845–848.
r, P. Nitz, and A
nc. Photovolt. P
(Darmstadt, 200
C. Domínguez,
Proc. (AIP Publi s
c. (AIP Publishi n
and S. Askins, P r
State Electron. 2
cell
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n SoG
opriate
o vary
ue to
has to
under
NI ratio
en DNI
ropean
ef. N:
moud,
IP
3,
.W.
.
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rog.
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Conference
Proceedings
is
copyrighted
by
AIP
Publishing
LLC
(AIP).
Reuse
of
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content
is
subject
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1.4876234.pdf | Continuously-tuned tunneling behaviors of ferroelectric tunnel junctions based on
BaTiO3/La0.67Sr0.33MnO3 heterostructure
Xin Ou, Bo Xu, Changjie Gong, Xuexin Lan, Qiaonan Yin, Yidong Xia, Jiang Yin, and Zhiguo Liu
Citation: AIP Advances 4, 057106 (2014); doi: 10.1063/1.4876234
View online: http://dx.doi.org/10.1063/1.4876234
View Table of Contents: http://scitation.aip.org/content/aip/journal/adva/4/5?ver=pdfcov
Published by the AIP Publishing
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All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/
Downloaded to IP: 192.231.124.91 On: Fri, 12 Dec 2014 04:46:54AIP ADV ANCES 4, 057106 (2014)
Continuously-tuned tunneling behaviors of ferroelectric
tunnel junctions based on BaTiO 3/La0.67Sr0.33MnO 3
heterostructure
Xin Ou,1Bo Xu,1,aChangjie Gong,2Xuexin Lan,2Qiaonan Yin,1
Yidong Xia,1Jiang Yin,1and Zhiguo Liu1
1National Laboratory of Solid State Microstructures and Department of Materials Science
and Engineering, Nanjing University, Nanjing 210093, People’s Republic of China
2National Laboratory of Solid State Microstructures and Department of Physics,
Nanjing University, Nanjing 210093, People’s Republic of China
(Received 28 March 2014; accepted 1 May 2014; published online 9 May 2014)
In this work, we fabricate BaTiO 3/La 0.67Sr0.33MnO 3(BTO/LSMO) ferroelectric tun-
nel junction on (001) SrTiO 3substrate by pulsed laser deposition method. Combining
piezoresponse force and conductive-tip atomic force microscopy, we demonstrate ro-bust and reproducible polarization-controlled tunneling behaviors with the result-
ing tunneling electroresistance value reaching about 10
2in ultrathin BTO films
(∼1.2 nm) at room temperature. Moreover, local poling areas with different
conductivity are finally achieved by controlling the relative proportion of up-
ward and downward domains, and different poling areas exhibit stable trans-
port properties. C/circlecopyrt2014 Author(s). All article content, except where otherwise
noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
[http://dx.doi.org/10.1063/1.4876234 ]
I. INTRODUCTION
Since polarization reversal does not induce a chemical alteration and is an intrinsically fast
phenomenon,1some novel and significant applications based on ferroelectric polarization have been
revealed in recent years. One of the most promising aspects is ferroelectric tunnel junction (FTJ)
which consists of an ultrathin ferroelectric material as the insulating barrier sandwiched between two
metallic electrodes. If the ferroelectric film is sufficiently thin, conduction electrons can pass throughthe ferroelectric barrier according to quantum mechanics theory.
2It has been theoretically3–5and
experimentally2,6,7proved that the tunneling resistance and transport property of the FTJ depend
on the orientation of the ferroelectric polarization. This phenomenon is known as the tunnelingelectroresistance (TER) effect.
6,8A schematic diagram of FTJ was presented by Tsymbal et al. who
attributed the resistive switching in ferroelectric tunnel junction to the electrostatic, interface and
strain effects.4By totally or partly switching the polarization of the ferroelectric barrier, it is possible
to change the electronic potential energy profile and further control the TER values and transport
properties.8,9
Almost all FTJs have been considered for binary data storage due to the stable of the ferroelectric
polarization. There are two resistance states (i.e., a high resistance state (HRS) and a low resistance
state (LRS)) which can be converted by switching the polarization direction, and the resistancebetween HRS and LRS changes up to 2 orders of magnitude at room temperature. Recent research
reported by Wen et al. has demonstrated very large TER value that can reach up to 10
4.2These
results overcome the nondestructive readout at a sub-100 nm scale10and suggest that the FTJ is a
promising candidate for non-volatile resistive memories. Furthermore, in another type of the memory
resistor called memristor, the conductance can be continuously tuned in an analogous manner by
aElectronic mail: xubonju@gmail.com
2158-3226/2014/4(5)/057106/6 C/circlecopyrtAuthor(s) 2014
4, 057106-1
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controlling the relative proportion of up and down domains.11Such a result is achieved by applying
the writing voltage pulse of varying amplitudes and durations. Thus the polarization reversal canmodulate the potential energy profile gradually, and also play an important role in the transport
property of ferroelectric devices. With the advantage of non-destructive readout and simpler device
architecture,
11the FTJs have been emerging as next generation non-volatile memories.
Although the concept of a polar switch involving a switching thin film based on ferroelectric
material has been proposed in 1971,12the FTJ and TER effect have only been recently reported
by experiment. Realization of FTJ relies on thermodynamic stability and switching in ultrathin
ferroelectric films.8The study of FTJs mainly focuses on the theoretical calculation and analysis,
due to the difficulty of obtaining the low thickness film with high quality and polarization stability.13
With the development of advanced thin film growth techniques, good ferroelectricity can be achieved
in a few nanometers ferroelectric barrier layer. Besides some organic ferroelectric materials such as
poly-vinylidene fluoride, the traditional ferroelectric materials including BaTiO 3, BiFeO 3, PbTiO 3
and Pb(Zr ,Ti)O 3are widely used in barrier layer.7,9,14,15Recently, Yuan et al. demonstrated a FTJ
based on ultrathin Bi 3.15Nd0.85Ti3O12films which established a novel concept for FTJ through the
strain effect.16For all these materials, BaTiO 3is one of the most stable ferroelectric materials and
reveals the high structural quality even if the thickness of the film reduces down to several nanometers.
In fact, highly strained BaTiO 3films with thickness of 1 nm have shown robust ferroelectricity by
Garcia et al.6Thus, we choose BaTiO 3as the tunnel barrier to fabricate the FTJ.
In this letter, the BaTiO 3(∼1.2 nm)/La 0.67Sr0.33MnO 3(∼10 nm) (BTO/LSMO) heterostructures
were epitaxially grown on (001) SrTiO 3single-crystal substrates by pulsed laser deposition (PLD).
Combining piezoresponse force microscopy (PFM) and conductive-tip atomic force microscopy
(C-AFM), we have obtained local ferroelectric and transport properties of the BTO/LSMO FTJ.
Moreover, a correlation between the polarization reversal and the tunneling conductance has beenconfirmed. After poling by a series of positive and negative DC biases of various amplitudes, the FTJ
exhibits resistive switching behaviors with the gradual change and quasi-continuous modulation.
In addition, the multi-resistance states of our FTJ were achieved by varying the amplitude of thewriting bias and can be kept for 100 s. These results suggest that the BTO/LSMO FTJ has a potential
application in non-volatile and high-density memory.
II. EXPERIMENTAL
The BTO/LSMO heterostructures were epitaxially deposited on (001)-oriented SrTiO 3(STO)
substrates by PLD (KrF excimer laser ( λ=248 nm), fluence of 2.5 J cm−2, repetition rate of 1 Hz).
LSMO bottom electrode was grown at 780◦C with an oxygen pressure of 15 Pa. BTO film was
subsequently grown at 780◦C with an oxygen pressure of 10 Pa. The sample was annealed in oxygen
atmosphere ( ∼104Pa) at 750◦C for 20 min and then allowed to cool to room temperature. The
cross-sectional morphology of the heterostructures was prepared for the high-resolution transmission
electron microscopy (HR-TEM) (FEI Tecnai F20) observation. The local piezoelectric responses,domain switching and electronic transport properties were performed by a commercial atomic
force microscopy (Cypher, Asylum Research) equipped with dual AC resonance tracking switching
spectroscopy piezoresponse force microscopy (DARTSS-PFM). The Olympus AC240TM Pt/Ticoated silicon cantilevers were adopted in the PFM measurements. Phase images were recorded
in single-frequency PFM mode. Phase and Amplitude loops were measured under the DARTSS-
PFM mode and the measurements were repeated to improve the signal-to-noise ratio and verifyreproducibility. Current map and current-voltage ( I-V) curves were recorded under C-AFM mode
with a conductive diamond-coated tip (CDT-NCHR, NanoWorld), and the current-limiting value
always kept at 20 nA. In the measurement of current maps and local I-Vcurves, the voltage was
applied to the LSMO bottom electrode and the tip which was regarded as top electrode was grounded.
III. RESULTS AND DISCUSSIONS
Fig. 1(a) shows the cross-sectional morphology of the BTO/LSMO/STO heterostructure by
TEM. The LSMO and BTO layers are fully commensurate with the STO substrates. The thickness
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FIG. 1. (a) Cross-sectional high resolution transmission electron microscopic (HR-TEM) image of the BTO/LSMO/STO
heterostructure. (b) Surface topography of the BTO ultrathin film by AFM.
of LSMO bottom electrode and BTO film is about 10 nm and 1.2 nm, respectively. The result shows
an atomically flat surface and the film is essentially free of nanodroplets. It is possible to find some
atomically smooth areas for the AFM measurement. In Fig. 1(b), the surface topography of the BTO
ultrathin film over 3 ×3μm2scan size exhibits atomically flat surface, and the corresponding root
mean square (RMS) roughness is about 103.5 pm.
To demonstrate the local ferroelectricity in BTO film with the thickness of ∼1.2 nm grown
on LSMO buffered (001) STO substrate, the ferroelectric domain structure and correlation between
polarization reversal and resistance switching behavior of BTO ultrathin film were investigated
through PFM and C-AFM mode. Before these measurements, PFM hysteresis loops were recordedunder DC bias with a triangular waveform at room temperature in order to confirm the local
ferroelectric nature. Fig. 2(a) shows the out-of-plane phase and amplitude responses of the ultrathin
BTO film, respectively. The phase loop changing from 0
◦to 180◦indicates the 180◦phase contrast
and antiparallel polarization of the two domains. The amplitude loop indicates a typical well-shaped
butterfly loop with the local coercive voltage being about −1.8 V and ±2.2 V , respectively. Note that
the phenomenon for asymmetric loops is attributed to the presence of an internal built-in electric
field at the BTO/LSMO interface.17–19In Fig. 2(b), the central area of 1 ×1μm2was switched to
upward by −3 V DC bias while the remaining square region in the 3 ×3μm2area was switched
to downward by +3 V DC bias. The obvious phase contrast indicates the antiparallel polarization
of the ferroelectric domains in the film, which is a direct evidence of the ferroelectricity in ultrathin
BaTiO 3film.
We examine the polarization controlling resistive switching behavior of the BaTiO 3films by
using a C-AFM technique. A typical current map over the polarization-patterned area is acquired by
C-AFM mode with a +0.3 V reading tip bias, as shown in Fig. 2(c). It shows the resulting current
pattern within the poling area where variations of contrast correspond to different conductivity. The
region of downward polarization exhibits larger conductivity than that of upward polarization, in
agreement with other reports.8,20Besides, the phase image and the current map show little change
after hours, which suggest robust polarization and stable conductivity behavior in the BTO/LSMO
FTJ. To further quantify the TER effect, two current-voltage ( I-V) curves were measured by setting
the conductive diamond tip at a selected point on the downward and upward polarization region inthe current map, carried out by applying a sweep voltage ranging from −0.5 V to +0.5 V , as shown
in Fig. 2(d).I-Vcurves are plotted in a logarithmic scale in order to clearly show the nonlinear
tunneling behavior and robust TER effect in our FTJ. The same experimental curves in a linear scale
are shown in the inset of Fig. 2(d). The experimentally obtained I-Vcurves have been fitted with the
WKB
21approximation model in Ref. 8assuming a trapezoidal potential barrier to obtain information
about the average barrier height. The black solid lines in Fig. 2(d) show the simulated I-Vcurves
for both HRS and LRS. As clear, the experimental points match well with the theoretical fitting.
It indicates that the transport property is a tunneling effect. According to these results, the reversal
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FIG. 2. (a) Phase loop and amplitude loop of the BTO ultrathin film, both indicate the typical loops with the local coercive
voltage being about ±2 V . (b) PFM out-of-plane phase image after poling the central area of 1 ×1μm2by−3 V bias and the
remaining region in the 3 ×3μm2area by +3 V bias, respectively. (c) Current map obtained after the same poling method
as PFM image, the reading bias is +0.3 V . (d) Two I-Vcurves in a logarithmic scale measured after poling at +3Va n d
−3 V , respectively, corresponding to LRS or HRS. Solid lines show the fitting of the experimental data by the WKB model
for both HRS and LRS. The inset is the same experimental I-Vcurves in a linear scale. (e) Resistance ratio between HRS and
LRS as a function of different biases in the range of −0.5 V to +0.5 V . (f) Resistance ratio for all the 10 samples measured
at 0.2 V and 0.5 V , respectively.
of polarization changes the potential energy difference between HRS and LRS across the BaTiO 3
barrier from 0.22 to 0.06 eV . This change of 0.16 eV is due to the change in the electrostatic potential
associated with ferroelectric polarization reversal and associated reorientation of the depolarizing
field.8Fig. 2(e) shows the resistance ratio between HRS and LRS as a function of different biases.
The resistance ratio always keeps a value of up to 102which is comparable to other results reported
before,8,14and shows no significant change in the range from −0.5 V to +0.5 V . Furthermore, we
have measured 10 different sample points for both HRS and LRS, and calculated the resistance ratio
for all the 10 points measured at 0.2 V and 0.5 V respectively, as shown in Fig. 2(f). This result
suggests that the BTO/LSMO FTJ has good reproducibility and stability.
To further investigate how resistive switching behavior of the BTO/LSMO FTJ was affected
by different poling biases, spatially resolved images of polarization and corresponding current mapwere measured by applying biases ranging from −4Vt o +4 V on the block including in the dashed
lines, while the region outside the block corresponding to as-grown area was not polarized by any
biases, as shown in Fig. 3(a) and Fig. 3(b). The scanning area is larger than the poling area in order to
observe the contrast between the regions with the poling and those without the poling. For Fig. 3(a),
the blue and yellow tones stand for up and down direction of the polarized domains, respectively.
Similarly, the dark and bright tones in tunneling current map show small and large current at the
fixed area, respectively. As the bias increasing from −4Vt o +4 V , the area of yellow tones increases
gradually, while the area of blue tones decreases step by step, as shown in Fig. 3(a). This indicates
that the proportion of upward or downward polarization domains can be gradually modulated by the
poling bias. Corresponding to the contrast map in Fig. 3(a), the tunneling current map performed by a
±0.3 V scanning bias shows different conduction properties under different poling biases, indicating
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FIG. 3. Spatially resolved correlation between the domain switching (a) and the electrical conductance (b), obtained after
poling at +4V ,+2V ,0V , −2V ,−4 V , respectively. The reading bias in the current map is +0.3 V . (c) A series of I-Vcurves
of the FTJ measured in the range from −0.5 V to +0.5 V after the application of different poling voltages: +4V ,+2V ,0V ,
−2V ,−4 V . (d) Data retention of the FTJ carried out by measuring the current values of all 5 different poling areas for 100 s.
that the potential energy profile at the interface can be continuously tuned.11,22Thus, the transport
property of the FTJ is controlled by the barrier height which can be modulated by the polarization
direction of the BTO film. This is an unambiguous demonstration of the ferroelectric nature of the
resistive switching.
As different poling biases make the local regions show different conduction properties, a series
of local I-Vcurves measured from −0.5 V to +0.5 V were obtained by positioning the conductive
probing tip at a selected area after it had been poled by different biases of various amplitudesranging from ±4Vt o −4 V , as shown in Fig. 3(c). It is obviously seen that the conductivity of
BTO/LSMO FTJ can be continuously tuned by varying the poling bias, and eventually several
different states have been achieved. This fact suggests that the BTO/LSMO FTJ in this work has
a potential application as multi-resistance state memory. Through controlling the proportion of
upward or downward polarization domains, the poling bias can gradually modulate the potentialenergy profiles at the interfaces between the ferroelectric barrier and the electrode, and further lead to
the continuously-tuned resistive switching behaviors. Based on this special property, data retention
of the FTJ was carried out by applying a +0.2 V reading bias on the conductive tip to measure the
current values of these different poling areas for 100 s, as shown in Fig. 3(d). All data retention
curves after poling by varying biases show stable results with little decay. Besides, the resistance
ratio between two different poling areas is changeable and the largest resistance ratio can reach 10
2,
which is consistent with the result in Fig. 2(e). The stable and multivalued TER effect we have
obtained provides the possibility of replacing traditional ferroelectric random access memories by
this simple device architecture. According to the new concept of high-density data storage reportedby V . Garcia et al. , the nanoscale ferroelectric dot arrays have been achieved by applying pulses.
6If
the multi-resistance state of our FTJ can be applied to the arrays, the higher storage density per unit
area will be realized.
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IV. CONCLUSION
In summary, we have demonstrated polarization-depengdent resistive switching behavior based
on BTO/LSMO heterostructures by pulsed laser deposition. A correlation between polarization
reversal and transport property has been established with resistance ratio between the two polarizationstates reaching about 10
2. By controlling the relative proportion of upward and downward domains
through changing the amplitude and direction of the poling bias, several local regions with different
conductivities are finally obtained. The multi-resistance states under different poling biases withstable retention suggest a potential application in high-density data storage.
ACKNOWLEDGMENTS
This work was supported by a grant from the State Key Program for Basic Research of
China (2012CB619406), the National Natural Science Foundation of China (11174135, 51372111,
and 11134004), the Fundamental Research Funds for the Central Universities (1095021336 and
1092021307) and a Project Funded by the Priority Academic Program Development of JiangsuHigher Education Institutions.
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1.4897552.pdf | Ductile-to-brittle transition in spallation of metallic glasses
X. Huang, Z. Ling, and L. H. Dai
Citation: Journal of Applied Physics 116, 143503 (2014); doi: 10.1063/1.4897552
View online: http://dx.doi.org/10.1063/1.4897552
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Published by the AIP Publishing
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30Ductile-to-brittle transition in spallation of metallic glasses
X. Huang,1,2Z. Ling,1and L. H. Dai1,3,a)
1State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences,
Beijing 100190, China
2Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang, Sichuan 621999, China
3State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 10081,
China
(Received 31 July 2014; accepted 29 September 2014; published online 9 October 2014)
In this paper, the spallation behavior of a binary metallic glass Cu 50Zr50is investigated with
molecular dynamics simulations. With increasing the impact velocity, micro-voids induced by ten-
sile pulses become smaller and more concentrated. The phenomenon suggests a ductile-to-brittletransition during the spallation process. Further investigation indicates that the transition is con-
trolled by the interaction between void nucleation and growth, which can be regarded as a competi-
tion between tension transformation zones (TTZs) and shear transformation zones (STZs) at atomicscale. As impact velocities become higher, the stress amplitude and temperature rise in the spall
region increase and micro-structures of the material become more unstable. Therefore, TTZs are
prone to activation in metallic glasses, leading to a brittle behavior during the spallation process.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4897552 ]
I. INTRODUCTION
Due to the unique disordered microstructures, metallic
glasses (MGs) have many excellent properties and receive
much attention in recent years.1–8It is well known that me-
tallic glasses usually exhibit a brittle behavior like a glass at
macroscopic scale, but show different capability of plastic
deformation at microscopic scale.9–13Thus, two distinct
morphologies are usually observed on the fracture surfaces
of MGs. For brittle fracture, the fracture surfaces are flat
with nano-scale periodic corrugations or dimple struc-tures;
13–15but for ductile fracture (not globally), much
coarser patterns are found, such as river-like and cellular pat-
terns as well as honeycomb structures.16,17
The fracture behavior of MGs is sensitive to their com-
position, and Mg-based and Fe-based MGs are usually much
more brittle than Zr-based MGs.13,18,19The fabrication pro-
cess is also important. The longer the annealing time is, the
more brittle MGs are.9Besides, different loading conditions
may lead to various fracture behaviors. During plate-impactexperiments, Gupta and coworkers
20,21found that spallation
of a Zr-based MG exhibits a ductile-to-brittle transition.
With increasing the impact velocity, the pull-back velocityslope increases monotonically, which indicates that the
loading-unloading response of the MG at macroscopic scale
is more brittle. Further examination show that the spalledsurfaces at microscopic scale agree with the macroscopic
phenomenon.
21,22Smoother morphologies are observed at a
higher impact velocity, while much coarser patterns areobserved at a lower impact velocity.
To answer the question of what controls the ductile-to-
brittle behavior in MGs, extensive works have been madeover the past decades. On one hand, some researchers triedto find the macroscopic mechanical parameters that dominate
the ductile-to-brittle transition process. In 1975, Chen et al.
23
found that Poisson’s ratio is closely correlated with plasticity
of MGs. Schroers and Johnson24further proved that the
larger the Poisson’s ratio, the better is the plasticity of MGs.
Equivalent with Poisson’s ratio, another parameter l=j
revealed by Lewandowski et al.25is a key parameter control-
ling the ductile-to-brittle transition of MGs, where lis the
shear modulus representing the resistance to plastic deforma-tion, and jis the bulk modulus or the resistance to dilation.
A lower l=jor larger Poisson ratio implies more ductile
behavior. It is noted that MGs usually exhibit a significanttension-compression plasticity asymmetry and shear-induced
dilation. Considering these intrinsic characters, Chen
et al.
10,11recently took the intrinsic strength of the material
into consideration, and proposed a shear-to-normal strength
ratio aand a strength-differential factor bto characterize the
ductile-to-brittle behavior in MGs. A smaller aimplies
enhanced plasticity, while a larger bindicates brittle fracture
under tensile loading. On the other hand, researchers
intended to find the answer at atomic scale. Based on a over-view of fracture patterns, Jiang et al.
14argued that the duc-
tile-to-brittle transition of MGs is controlled by competition
between shear transformation zones (STZs)26–28and tension
transformation zones (TTZs)7,9,14,21,29at microscopic scale.
In contrast to STZs that are corresponding to shape distor-
tions of atomic clusters under shear stresses, TTZs areregarded as the fundamental carriers of bulk dilations under
negative pressures.
7,14When TTZs dominate, more brittle
facture behavior is expected. This view is supported byrecent impact toughness tests
21and spallation experiments.9
In these tests, typical brittle fracture patterns are observedsuch as nm-sized vein patterns
21and nanosized corruga-
tions,9and TTZs are thought to be the reason for the phe-
nomenon. More recently, Murali et al .30,31studied the
fracture behavior of two typical MGs (FeP and CuZr) viaa)Author to whom correspondence should be addressed. Electronic mail:
lhdai@lnm.imech.ac.cn
0021-8979/2014/116(14)/143503/8/$30.00 VC2014 AIP Publishing LLC 116, 143503-1JOURNAL OF APPLIED PHYSICS 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30atomistic simulations. It is revealed that even a brittle frac-
ture is dominated by nucleation and growth of voids in MGs,
and a higher degree of spatial fluctuation induces more brittlebehavior during the fracture process. Despite extensive
investigations, the atomistic scale mechanism that governs
the ductile-to-brittle transition in MGs is still unclear.
To reveal the ductile-to-brittle transition mechanism
during a spallation process, we present molecular-dynamic
(MD) simulations of a binary MG Zr
50Cu50in this paper. By
using a flyer-target configuration, the spallation behavior is
studied at different impact velocities from 600 m/s to
1800 m/s, with emphasis on the damage evolution process. Itis found that as the impact stress increases, a ductile-to-brit-
tle transition occurs, which agrees well with the available ex-
perimental results. Further investigation reveals that theinteraction between void nucleation and growth, which can
be interpreted as the competition between TTZs and STZs at
atomic scale, controls the ductile-to-brittle transition duringthe spallation process.
II. MD SIMULATIONS OF SPALLATION
During the MD simulations, a simple binary MG
Zr50Cu50is selected as the model material. To model the
atomic interactions in the Zr-Cu system, we adopt the
Finnis-Sinclair type interatomic potential with parameters
given by Mendelev et al.32Calculations are carried out with
the open source code LAMMPS.33Glass samples are pre-
pared via a melting-and-quenching process. The initial sys-
tem is a fcc lattice with the sites randomly occupied by Zrand Cu atoms in accordance with the nominal composition.
It consists of /C24440 000 atoms arranged in a cubic shape, and
three-dimensional periodic boundary conditions with ambi-ent pressure are applied. To obtain the Zr
50Cu50glass, simu-
lations are performed in the constant number of particles,
pressure, and temperature (NPT) ensembles with a time stepof 1 fs. Temperature gradually increases from 1 K to 2500 K,
equilibrates for 100 ps and cools down to 300 K, with the
same heating and cooling rate of 5 K/ps. After a furtherrelaxation for 100 ps, a glass sample is prepared with dimen-
sions of /C2420/C220/C220 nm
3.
In simulations of spallation, we construct the traditional
flyer-target configurations.34,35The flyer plate consists of
/C242 200 000 atoms with dimensions of /C24100/C220/C220 nm3,
and the target has the same cross-section area (20 /C220 nm2)
but its thickness is twice as that of flyer. To obtain such a
large system, the 400 000-atom glass ( /C2420/C220/C220 nm3)i s
replicated along the X direction, and equilibrates for another100 ps to remove possible artifacts from the replication pro-
cess.
34In fact, we have also explored the flyer-target system
with a cross-section area of /C2410/C210 nm2to examine the
size effect on spallation and the results are similar. In our
simulations, the loading direction is along the X axis, so the
nonimpact sides of flyer and target normal to the X axis arefree surfaces. But along the Y and Z axes, the periodic
boundary conditions are maintained to mimic one-
dimensional (1D) strain shock loading. Here, we denote thedesired impact velocity as V. The flyer plate and target are
assigned initial velocities of 2 V=3 and /C0V=3 beforeimpacting, so that the flyer-target system has a center-of-
mass velocity of 0. Shock simulations adopt the constant
number of particles, volume, and energy (NVE) ensembles.The time step for integrating the equations of motion is 1 fs,
and the run duration is 120 ps.
To obtain the physical properties of plates, the 1D bin-
ning analysis is used. The simulation cell is divided into fine
bins along the X axis by neglecting the heterogeneities in the
transverse directions, and we obtain the average physicalproperties such as density ( q), stresses ( r
x), particle velocity
(up), and temperature ( T) profiles. To characterize the atomic
configuration, we use the Voronoi tessellation analysis.36
And the plastic deformation is identified by the nonaffine
displacement D2
minproposed by Falk and Langer.27
III. RESULTS
During the shock simulations, the thickness of flyer
plates and targets are not changed. To achieve shock loadingwith different amplitudes, we choose impact velocities Vof
600, 900, 1200, 1500, and 1800 m/s, respectively. Figure 1
illustrates the free surface velocity histories on the targetside, similar to that measured by a velocity interferometer
system for any reflector (VISAR) in plate-impact experi-
ments.
20,37,38As shown in Fig. 1, typical “pull-back” waves,
which are signatures for spallation, are observed in all cases,
except for the case of V ¼600 m/s. It indicates that spallation
occurs in the cases of V ¼900, 1200, 1500, and 1800 m/s.
Besides, as the impact velocity increases, the pull-back ve-
locity slope also increases. It agrees well with the experi-
mental results,20which indicates a ductile-to-brittle
transition behavior. To compare the spallation behaviors
under different loading amplitudes, the cases of V ¼900 and
1500 m/s are further characterized.
Figure 2shows the density evolution in a conventional
x-t diagram at impact velocities of 900 and 1500 m/s. With
color coding based on the local atomic number density, thewave propagation and interaction process is illustrated,
which is related to the shock, release, tension, and spallation.
As shown in Fig. 2, the red color represents regions with a
higher density, while the blue color represents regions with a
lower density. A deeper blue color implies a larger amount
FIG. 1. Free surface velocity histories on the target side at different impact
velocities.143503-2 Huang, Ling, and Dai J. Appl. Phys. 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30of spallation damage. According to the process of wave
propagation, the tensile stress duration needed for spallationat the lower impact velocity is much longer than that at the
higher velocity. It is obvious that the distribution of spalla-
tion damage is different between these two impact velocities.In the case of V ¼900 m/s, damage is scattered over the spall
plane. But in the case of V ¼1500 m/s, it is more
concentrated.
The corresponding stress profiles ( r
x) at different times
before and after spallation at V ¼900 and 1500 m/s are
shown in Fig. 3. It is seen that the tensile region is formed
due to the interaction of two release waves reflected from the
free surfaces of flyer and target. As micro-damage nucleates
and grows, recompression waves are generated in the spalledregion and propagate toward the free surface. The recom-
pression wave is registered in the free surface velocity profile
as a “pull-back” wave. Compared with the case ofV¼1500 m/s where there is only one recompression wave,
two recompression waves are observed near the spall plane
at V¼900 m/s, which imply that a multi-spall occurs. The
result is in accordance with the scattered distribution of spal-
lation damage at a lower impact velocity, as shown in Fig. 2.
Next, we examine the damage evolution process in the
spalled region (where the recompression wave is generated)
at different impact velocities. Figures 4(a)–4(c) show the
spallation damage at the impact velocity of 900 m/s, andFigs. 4(d)–4(f) show the damage at V ¼1500 m/s. As the
impact velocity varies, the rate of damage evolution is differ-
ent. Thus, in the case of 900 m/s, a time spacing of 5 ps isused to track the spall process, while 3 ps is adopted at
V¼1500 m/s. As shown in Fig. 4, spallation of Cu
50Zr50
glass undergoes the process of nucleation, growth, and coa-
lescence of micro-voids. At a lower impact velocity, only a
few large voids (actually only one in the slice) dominate thedamage evolution process. In contrast, a large number of
voids can be observed at a higher impact velocity. The voidsare small and begin to coalesce. The damage characteristics
imply a smoother morphology on the fracture surfaces at a
higher impact velocity.
IV. DUCTILE-TO-BRITTLE TRANSITION MECHANISM
According to the results of plate-impact experiments,20–22
there are two typical characteri stics at different impact veloc-
ities, which suggests a ductile-to -brittle transition during spalla-
tion of MGs: (1) at macroscopic scale, the pull-back velocity
slope increases with increasing the impact velocity; and (2) at
microscopic scale, it is frequent to observe a smoother morphol-ogy on the fracture surfaces of the spalled samples at a higher
impact velocity, while much coar ser patterns are observed at a
lower impact velocity. Our results generally agree with the ex-perimental results,
20–22as shown in Figs. 1and3.
In the MD simulations, the most obvious difference
between the fracture phenomena at different impact veloc-ities is the change of generated void numbers. With increas-
ing the impact velocity, there are much more voids observed
to nucleate and grow on the spall plane. The larger the voidnumber is, the smaller the void sizes are before coalescence.
Then the fracture surface is smoother, which is a typical
characteristic in brittle fracture. This interesting phenomenonhas also been observed in other works. For example, during
the MD simulations of the fracture behavior of two typical
MGs (FeP and CuZr),
31more smaller voids are observed in
brittle FeP MG, while one bigger void is found in ductile
CuZr MG. As the fracture behavior (brittle or ductile) is
determined by the plastic deformation at microscopic scale,this phenomenon implies that the plastic deformation is
impeded when more voids are generated. Now the question
FIG. 2. The x–t diagram for shock
loading of Cu 50Zr50: (a) V ¼900 m/s;
and (b) V ¼1500 m/s.
FIG. 3. The stress profiles at different
time: (a) V ¼900 m/s; and (b)
V¼1500 m/s.143503-3 Huang, Ling, and Dai J. Appl. Phys. 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30is, why the plastic deformation is impeded in the case with
more and smaller voids.
A. Competition of TTZs and STZs
In order to reveal the factors that influence the plastic
deformation during spallation, we explore the process of
void nucleation and growth. Figure 5shows the nonaffine
displacement during the void nucleation and growth atV¼900 m/s. Here, the critical size for void nucleation is
determined to be /C241 nm in diameter.
22,39Thus, according to
the void size, Figs. 5(a)–5(c) illustrate the nucleation pro-
cess, and Figs. 5(d)–5(e) exhibit the growth process. As
shown in Figs. 5(a)–5(c) , during the void nucleation process,atoms with a larger nonaffine displacement are randomly dis-
tributed in the material. With increasing the time interval
(the reference configuration is the same at t ¼81 ps in Fig.
5), the number of atoms with a larger nonaffine displacement
increases. There is no apparent difference observed between
the void nucleation location and other region. It implies that
the nonaffine displacement is induced by temperature (orstructural relaxation) instead of stresses. However, duringthe void growth process, nonaffine displacement of atoms in
the region around the void is much larger than that away
from the void. It indicates that plastic deformation of the ma-terial is mainly induced by void growth, there is nearly no
contribution from void nucleation.
FIG. 4. Damage evolution process at
different impact velocities: (a)–(c)
V¼900 m/s; and (d)–(f) V ¼1500 m/s.
The colors indicate the normalized
local atomic number density.
FIG. 5. Snapshots of void nucleationand growth at V ¼900 m/s: (a)–(c)
Nucleation of voids; and (d)–(f)
Growth of voids. The colors represent
the value of D
2
mincalculated from the
same reference configuration at t ¼81
ps.143503-4 Huang, Ling, and Dai J. Appl. Phys. 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30Further investigation reveals that the nucleation and
growth of voids is closely related to the fundamental unit-processes of collective atomic motion in MGs. Figure 6
shows some close-up views of the atomic cluster motion
around the void. As shown in Fig. 6(a), during the nucleation
process, transformation of the atomic structure at the centre
of the void is similar to the picture of a TTZ.
14But during
the growth process as shown in Fig. 6(b), the motion of the
atomic cluster at the edge of the void is close to the picture
of a STZ.26We know that TTZs are corresponding to bulk
dilations of atomic clusters, but STZs arouse shape distor-tions (the accompanied dilations are very small). As STZs
are mainly activated during the void growth process, plastic
deformation induced by damage evolution in the material isattributed to the void growth process.
Now the question is, as the impact velocities increase,
why does plastic deformation decrease? Because plastic de-formation is closely related to the void growth process, void
growth at different impact velocities is examined. We com-
pare the diameter history of the biggest voids at V ¼900 and
1500 m/s, as shown in Fig. 7. At a lower impact velocity, we
see that the void grows continuously with a gradually
increasing growth rate. But at a higher impact velocity, thevoid grows fast at the initial stage, but the growth rate
decrease a lot after a short time of /C244 ps. The difference can
be explained by the damage evolution process as shown inFig.4. As there are more voids at the higher impact velocity,
a growing void quickly interacts with the surrounding voids,
leading to a coalescence process. This impedes the furthergrowth of voids. However, as there is only one void at the
lower impact velocity, it can grow continuously without con-
finements of other voids. Based on the above results, wethink that the plastic deformation during spallation of MGs
is controlled by competition of two rate processes at micro-
scopic scale. On one hand, the void growth process promotesplastic deformation in the material. According to the conven-
tional void growth mechanism,
40–42the plastic zone around
the void is proportional to the void volume. Bigger voids
induce a larger region of the material to undergo plastic de-
formation. Thus, the larger the voids grow, the more exten-sive plastic deformation the material undergoes. On the other
hand, the void nucleation process impedes plastic deforma-
tion in the material. As void growth is bounded by the spac-ing between two nucleation sites, a higher nucleation rate
which decreases the spacing between voids impedes the
growth process. Therefore, plastic deformation in the mate-rial is slight.
In fact, the interaction between nucleation and growth
can be interpreted as a competition between the fundamentalunit-processes of collective atomic motion in MGs. Since
void nucleation is related to the activation of TTZs, and
growth is induced by STZs around the voids, the damageevolution process is intrinsically a competition between
FIG. 6. Motion of atomic clusters dur-
ing the damage evolution process at
V¼900 m/s: (a) nucleation; and (b)
growth.
FIG. 7. Diameter of the biggest void at different impact velocities.143503-5 Huang, Ling, and Dai J. Appl. Phys. 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30TTZs and STZs. To characterize the competition process,
here we propose a non-dimensional number composed of
two time scales:
Ia¼TSTZ
TTTZ; (1)
where TSTZand TTTZare the characteristic time scales for
activation of STZs and TTZs, respectively. As to a larger Ia,
TTZs are more dominant than STZs. To determine the twotime scales, we estimated the activation rates of TTZs and
STZs.
According to the STZ models,
27,43the activation rate of
a single potential STZ is written as
vSTZ¼1
TSTZ¼v1exp/C0DF1/C0s/C1c0/C1X0
kh/C18/C19
; (2)
where vSTZis the STZ activation rate, v1is an attempt fre-
quency of order of the Debye frequency, sis the local shear
stress, c0is the characteristic shear strain with the order of
/C240.1,X0is the STZ volume, kis the Boltzmann constant, h
is the temperature, and DF1is the activation barrier.
For TTZs, they are similar in size to STZs, and are acti-
vated by high hydrostatic tensile pressure. In the same way,we can estimate the activation rate of a single TTZ as
v
TTZ¼1
TTTZ¼v2exp/C0DF2/C0p/C1ev/C1X0
kh/C18/C19
; (3)
where vTTZis the TTZ activation rate, v2is an attempt fre-
quency, pis the hydrostatic tensile pressure, evis the charac-
teristic volumetric strain, and DF2is the activation barrier,
which is mainly related to the dissipated energy forming new
surfaces.14Thus,
Ia¼v1
v2expDF1/C0s/C1c0/C1X0
DF2/C0p/C1ev/C1X0/C18/C19
; (4)
where v1,DF1,c0,X0are material parameters according to
STZ models. If v2,DF2, and evare also regarded as material
parameters, Iaare determined by local stress states.
Further analysis indicates that the local stress states
change before and after voids are nucleated. When there is no
void in the material during spallation, it is the 1D strain condi-tion and the ratio of shear stress sto tensile pressure pis
s
p¼l
j; (5)
where lis the shear modulus and jis the bulk modulus.
For Cu 50Zr50,l/C2522 GPa and j/C25123 GPa, therefore,
s=p/C250:18. Since the shear stress is much smaller than the
tensile pressure, TTZs may play a dominant role according
to Eq. (4). However, after voids are nucleated, the local
stress states are completely changed. Although the tensilepressure pis nearly the same, the ratio of stoparound the
void increases to 0.75 (as a rough estimate, the asymmetry of
the loading and initial void shape is not taken into account).Thus, I
awill decrease, and STZs may play a dominant role.
Note that only around the void’s surrounding where stressconcentration takes place, Iais smaller. For the region that is
not influenced by the void, Iais still relatively large and
TTZs is the dominant collective atomic motion.
B. Mechanism resulting in dominance of TTZs
If MGs undergo brittle spallation, it is obvious that
TTZs must dominate the fracture process. According to Eq.(3), factors such as stresses, temperature, and the activation
barrier can influence the activation of TTZs in the material.
In order to find the reason that results in dominance of TTZs,we further compare the evolution of the above factors at dif-
ferent impact velocities.
Figure 8shows a comparison of the stress profiles at the
beginning of the damage evolution process. With increasing
the impact velocity, the stress amplitude near the spall plane
is slightly higher. According to Eq. (3), a higher tensile stress
can increase the work done by the system, and decreases the
energy barrier of TTZs, thus a higher activation rate is
expected. Besides, it should be noted that micro-inertiamight have influence on the competition between STZs and
TTZs. As the impact velocity increases, the loading rate is
higher and micro inertial effects on void growth becomemore important. Activation of STZs around the voids may be
impeded by micro inertial effects, leading to a decrease of
void growth rate.
The history of material temperature near the spall plane
is illustrated in Fig. 9(a). The temperature keeps constant at
first, then increases sharply as the flyer impacts the target,and finally decreases a little when the region of tension is
created. Compared with the case with V ¼900 m/s, the mate-
rial temperature is apparently higher at V ¼1500 m/s. As
higher temperature implies that atoms have a higher chance
of getting enough energy from thermal fluctuation to over-
come the free energy barrier, it contributes to a higher activa-tion rate.
For the activation barrier, it is determined by local
atomic structures at the potential TTZ sites. Here, the degreeof local fivefold symmetry (LFFS) is used as a key factor to
characterize the local atomic structures.
44In the Voronoi tes-
sellation analysis, each atom is indexed with the Voronoiindices hn
3;n4;n5;n6; :::i, where n3,n4,n5, and n6represent
FIG. 8. Stress profiles at the beginning of the damage evolution process: (a)
V¼900 m/s; and (b) V ¼1500 m/s.143503-6 Huang, Ling, and Dai J. Appl. Phys. 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30the number of triangles, tetragons, pentagons, and hexagons
on the Voronoi polyhedron, respectively, and the degree of
LFFS is defined as the fraction of the number of pentagons
(LFFS ¼n5=P
ini). The average degree of LFFS in the
region near the spall plane is shown in Fig. 9(b). It is clear
that the average degree of LFFS increases under compres-
sion and decreases under tension at both impact velocities.But at the time just before voids begin to nucleate, the aver-
age degree of LFFS can decrease to lower amplitude at the
higher impact velocity. Since a lower LFFS indicates thatthe structural configuration of atoms is packed more loosely
and has higher potential energy, the local structure is more
unstable and it is easier for transformation of local atomicclusters.
Further examination indicates that TTZs are prone to
activation from the region with a lower average LFFS. Asshown in Fig. 10, at the impact velocity of 900 m/s, the aver-
age degree of LFFS of the atomic cluster that void originates
from is 0.422, while that of the entire slice near the spallplane is 0.472. As the impact velocity increases to 1500 m/s,
the average degree of LFFS of the atomic cluster that the
biggest void originates from (0.431) is also smaller than thatof the entire slice (0.464). It indicates that TTZs are indeed
easier to be activated in the region with a lower degree of
LFFS. As a previous work has shown that STZs prefer to beinitiated in regions with a lower degree of LFFS too, it is
obvious that a lower degree of LFFS means a loweractivation barrier for transformation of atomic clusters. As
the average degree of LFFS in the spall region is smaller at a
higher impact velocity, there are more potential sites for acti-
vation of TTZs. Thus, the activation rate is higher.
V. CONCLUSION
We have studied the ductile-to-brittle transition phe-
nomenon during spallation of a binary MG Zr 50Cu50with
MD simulations. Our results show that as the impact velocity
increases, the distribution of spallation damage becomesmore concentrated and the fracture patterns are smoother,
which agrees well with experimental observations in recent
works. The ductile-to-brittle transition in spallation is relatedto extra fracture energy dissipation at a lower impact veloc-
ity and impedance of plastic deformation at a higher impact
velocity. Plastic deformation during the damage evolutionprocess is controlled by the interaction of two microscopic
rate processes (i.e., void nucleation and growth), which can
be interpreted as the competition of STZs and TTZs atatomic scale. As the impact velocity increases, TTZs domi-
nates the fracture process and spallation exhibits a brittle
behavior. Further investigation shows that with increasingthe impact velocity, the tensile stress amplitude and material
temperature is higher in the spall region, and the atomic
structure is more unstable. All these reasons induce a largervoid nucleation rate or the dominance of TTZs.
FIG. 9. The history of material temper-
ature and average LFFS near the spall
plane at different impact velocities of
900 m/s and 1500 m/s: (a) temperature
and (b) LFFS.
FIG. 10. Atomic configuration beforevoid nucleation showing the LFFS of
atoms. The colors represent value of
LFFS at (a) V ¼900 m/s and (b)
V¼1500 m/s.143503-7 Huang, Ling, and Dai J. Appl. Phys. 116, 143503 (2014)
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137.149.200.5 On: Sat, 29 Nov 2014 12:29:30ACKNOWLEDGMENTS
Financial support was from the National Key Basic
Research Program of China (2012CB937500), the NSFC
(Grants Nos.: 11272328, 11472287, and 11402245), and theCAS/SAFEA International Partnership Program for Creative
Research Teams.
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1.4898712.pdf | Does water dope carbon nanotubes?
Robert A. Bell, Michael C. Payne, and Arash A. Mostofi
Citation: The Journal of Chemical Physics 141, 164703 (2014); doi: 10.1063/1.4898712
View online: http://dx.doi.org/10.1063/1.4898712
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130.237.165.40 On: Tue, 11 Aug 2015 04:46:45THE JOURNAL OF CHEMICAL PHYSICS 141, 164703 (2014)
Does water dope carbon nanotubes?
Robert A. Bell,1Michael C. Payne,1and Arash A. Mostofi2
1Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge, United Kingdom
2Department of Materials and Department of Physics, and the Thomas Young Centre for Theory and
Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
(Received 30 June 2014; accepted 8 October 2014; published online 27 October 2014)
We calculate the long-range perturbation to the electronic charge density of carbon nanotubes (CNTs)
as a result of the physisorption of a water molecule. We find that the dominant effect is a charge re-
distribution in the CNT due to polarisation caused by the dipole moment of the water molecule. Thecharge redistribution is found to occur over a length-scale greater than 30 Å, highlighting the need
for large-scale simulations. By comparing our fully first-principles calculations to ones in which the
perturbation due to a water molecule is treated using a classical electrostatic model, we estimate thatthe charge transfer between CNT and water is negligible (no more than 10
−4e per water molecule).
We therefore conclude that water does not significantly dope CNTs, a conclusion that is consistent
with the poor alignment of the relevant energy levels of the water molecule and CNT. Previous cal-culations that suggest water n-dopes CNTs are likely due to the misinterpretation of Mulliken charge
partitioning in small supercells. © 2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4898712 ]
I. INTRODUCTION
The unique electronic properties of carbon nan-
otubes (CNTs) make them a promising material for novelapplications
1including highly sensitive chemical sensors,2,3
light-weight electrical wires,4–6and nanoscale electronic
devices.1,7,8
Optimal performance of these devices often requires the
CNTs to have a particular electronic character, whether semi-
conducting or metallic, which is determined by the CNT
chirality. The control of chirality during CNT synthesis is
challenging, which has led to the development of alternativein-solution techniques for separating bulk-grown CNT sam-
ples with respect to electronic type. Examples include density
gradient ultracentrifugation,
9,10polymer wrapping,11,12and
chromatography.13,14
As a consequence of this post-processing, residual wa-
ter may remain adsorbed to the CNTs. Therefore, it is vitalto understand the influence that water has on the electronic
structure of CNTs.
Experimental investigations of the effect of water vapour
on the conductivity of mats and fibres of CNTs have been con-
tradictory with both increases
15–19and decreases20–22in con-
ductivity observed. The lack of agreement may be attributableto an abundance of factors, including the CNT sample com-
position and purity, the presence of impurities and their
composition, contact resistances with external electrodes and
between the CNTs themselves, and the alignment and con-
nectivity of CNTs in the mat/fibre network. The relative con-tribution of these factors, and their dependence on local wa-
ter concentration, may be significantly different between the
different samples used in the reported experiments, and aredifficult to isolate.
Theoretical calculations based on density functional the-
ory (DFT)
23,24have shown that water interacts weakly with
CNTs, binding through physisorption.21,25–28This weak inter-action has been shown to cause little scattering, and the con-
ductance of individual CNTs when hydrated is little changedfrom when dry.
26,29
Charge transfer analyses, also performed within DFT,
have suggested that water may n-dope CNTs.21,25–28The con-
ductance of semiconductor CNTs is sensitive to the amount of
doping, and in Ref. 19a mechanism based on charge transfer
between water and CNTs has been proposed to explain the
experimental observations.
There are, however, several issues with the charge trans-
fer analyses used to determine this mechanism. Most funda-
mentally, there is no unique formalism to partition the DFT-
derived ground-state charge density among different speciesin a system. The magnitude of charge transfer is sensitive
to the details of the calculations, including the choice of
functional for exchange and correlation,
30the basis set,31–33
and the partitioning method used.31,33Changing the partition-
ing method will often alter the computed partial charges by
0.1 e or more,32,33which is comparable to the proposed wa-
ter/CNT charge transfer.21,25–28These theoretical calculations
may still, therefore, be consistent with no charge transfer or
even p-doping. Indeed, it has been suggested that there is no
overall charge transfer.20,27,34
Regardless of the method used to determine the charge
partitioning, it is also not clear that charge doping can be de-
termined by considering only the total partial charge of the
CNT, as used in previous studies.21,25–28In principle, doping
is manifested by additional or reduced electron charge den-
sity, as compared to the bulk, far from the defect that may
be causing the doping, such that all electrostatic perturba-tions have been screened. Only this delocalised charge trans-
fer can result in doping and contribute to conductance; lo-
calised charge transfer will in fact act to scatter current anddecrease the conductance. Accordingly, the long-range spatial
distribution of the electron charge density must be considered
to determine whether doping occurs.
0021-9606/2014/141(16)/164703/7/$30.00 © 2014 AIP Publishing LLC 141, 164703-1
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Neither experiment nor theory, therefore, has reached
agreement over the interaction between CNTs and water and
further analysis of the calculated charge transfers is requiredto support a doping hypothesis. In this work, we revisit the
problem of charge transfer between water and CNTs. Working
directly with the charge density, derived from first-principlescalculations, we calculate the long-range perturbation to the
CNT charge density due to the water molecule. Our main re-
sult is that the interaction is a long-ranged electrostatic po-larisation that arises due to the dipole moment of the water
molecule which cannot be fully captured within a small sim-
ulation cell. We isolate the contribution to the density per-
turbation due to the water dipole moment by using a simple
classical model for the water electrostatics. This allows us toestimate the residual charge transfer between a CNT and wa-
ter molecule which we find to be negligible. We therefore con-
clude that water does not n-dope CNTs.
The remainder of this paper is organised as follows: we
first give details of our methods; Sec. IIIanalyses the elec-
trostatic interaction between the CNT and water molecule;we then discuss the wider context of these conclusions
in Sec. IV.
II. METHODS
We consider supercells containing a single water
molecule adsorbed on one of two CNT structures: 16 unit-
cells of a semiconducting (10, 0) CNT; and 28 unit-cells ofa metallic (5, 5) CNT. The overall length of each supercell is
68.5 Å and 69.1 Å, respectively.
Electronic structures are calculated using the
ONETEP
linear-scaling DFT code,35which uses a small set of localised
numerical orbitals called non-orthogonal generalised Wannier
functions (NGWFs).36In this work, we use four NGWFs per
carbon and oxygen atom and one per hydrogen atom. Each
NGWF is represented in terms of an underlying basis of psinc
functions,37equivalent to a set of plane-waves, that enables
them to be optimised in situ for their unique chemical envi-
ronment as the calculation proceeds. Throughout this work,
we use a localisation radius of 5.3 Å for the NGWFs in order
to capture charge polarisation accurately.
Equivalent plane-wave kinetic energy cutoffs of 1000 eV
and 4000 eV are used for the psinc basis sets represent-
ing the NGWFs and charge density, respectively, and the
Brillouin zone is sampled at the /Gamma1point only. Core elec-
trons are described using norm-conserving pseudopotentials
in Kleinman-Bylander form.38
In this work, all calculations employ the PBE generalised
gradient approximation for exchange and correlation;39our
conclusions are unchanged when equivalent calculations are
performed using the local density approximation (LDA).40
Periodic boundary conditions are used along the CNT
axis, which is denoted as the z-direction; directions perpen-
dicular to the axis are treated with the supercell approxima-tion with at least 12 Å separating periodic images.
The atomic structures of the CNT unit cells are deter-
mined using the plane wave DFT package
CASTEP .41A fully
converged Brillouin zone sampling scheme of 16 and 28
equally spaced k-points, including the /Gamma1point, for the (10, 0)and (5, 5) CNTs, respectively. The states sampled are equiva-
lent to those sampled in the larger supercell. The same pseu-
dopotentials and parameter set, as far as possible, are used asfor the
ONETEP calculations.
After relaxation, the maximum residual forces and stress
are 5 meV/Å and 0.02 GPa, respectively. Calculated C–Cbond lengths are 1.424 Å and 1.432 Å for the (10, 0) CNT,
and 1.429 Å and 1.431 Å for the (5, 5) CNT; and the re-
laxed periodic unit cell lengths are 4.279 Å and 2.469 Å,respectively.
The water molecule is similarly relaxed in isolation in
a 22 Å cubic simulation cell within the supercell approxi-
mation. Previous calculations have shown that the change to
the structure of CNT and water is negligible when water isadsorbed,
28therefore the geometry of the composite structure
is not relaxed further. We have verified for a selection of struc-
tures that our conclusions are unaffected by this choice.
Maximally localised Wannier functions (MLWFs)42,43
used for the point charge model of Sec. III A are calculated us-
ing the Q UANTUM ESPRESSO44interface to W ANNIER 90.45
III. RESULTS AND DISCUSSION
A. Computing the CNT charge polarisation
Our key result is given in Fig. 1where we show the long-
range electron density redistribution for a (10, 0) semicon-ducting CNT with a single water molecule adsorbed (solid
lines). The supercell is 68 Å in length along the CNT axis
and the oxygen ion of the water molecule is directly above a
carbon site, at a distance of 3.20 Å which is approximately
the average equilibrium binding distance of these orienta-tions, and is positioned at the centre of the CNT supercell
(z≈34 Å). The water molecule is oriented such that the nor-
mal to the atomic plane makes an angle θto the radial vector
of the CNT as shown in Fig. 2. The four panels show dif-
ferent orientations of the water molecules that are thermally
FIG. 1. The laterally integrated density difference profile for a 68 Å (10, 0)
CNT supercell with a single water molecule adsorbed (full DFT calculation,
solid lines). Also shown (dashed lines), the corresponding induced polarisa-tion when the water molecule treated as classical Wannier charges (see main
text). The angle θcorresponds to the angle between the water dipole vector
and the normal to the CNT surface as shown in Fig. 2.
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FIG. 2. The structure of the water molecule adsorbed on a (10,0) CNT. The
water oxygen ion is situated 3.20 Å above a carbon, with the water dipole
making an angle θto the CNT axis. Shown here is θ=90◦. Only the part
of the CNT closest to the water molecule is shown, the CNT extends for an
additional ≈30 Å in both directions to form the full supercell.
accessible at room temperature. As we will show shortly, the
precise CNT/water geometry does not strongly affect the in-
teractions present, precluding the need for a detailed thermo-dynamic analysis.
The induced density polarisation is calculated through
the charge density difference, defined as the difference be-tween the density for the CNT and water combined n
1,2(r),
and the isolated CNT and water molecule alone n1(r),n2(r)
/Delta1n(r)=n1,2(r)−n1(r)−n2(r). (1)
Three separate calculations per configuration are performed
to determine the density difference. The periodicity due to theunderlying atomic lattice is smoothed out by convolving this
quantity with a window function w(z) with width equal to the
CNT unit cell length L
uc. In order to smooth out the large
variations due to the underlying ionic lattice, we integrate this
quantity over planes perpendicular to the CNT axis defining
an electron density difference per unit length,
λ(z)=/integraldisplay
/Delta1n(x/prime,y/prime,z/prime)w(z−z/prime)dx/primedy/primedz/prime, (2)
w(z)=/braceleftBigg1/Luc|z|<Luc/2
0 otherwise. (3)
The charge redistribution shown in Fig. 1is remarkably
long-ranged, occurring over a length-scale greater than 30 Å.
As this is much larger than the CNT unit cell, this long-range
polarisation cannot be observed in the smaller supercells usedin previous calculations.
21,25–28
The form of the charge polarisation is strongly depen-
dent of the orientation of the water molecule, but correlates
well with the direction of the water dipole. For example, at
θ=0◦, the dipole points away from the CNT and electrondensity is repelled; at θ=180◦, the dipole is towards the
CNT and electron density is attracted. Equivalent calculations
(not presented here) show similar behaviour when varying thewater-CNT binding distance.
The dominant effect of the water molecule on the CNT
appears to be purely electrostatic in origin. In order to demon-strate this more rigorously, we calculate the charge polari-
sation of the system using a purely electrostatic model for
the water molecule, i.e., without explicit inclusion of the realelectron density of the water molecule in the system. The
water molecule is treated as a set of point charges, whose
influence appears as a correction to the local Kohn-Sham
potential
47
δVloc(r)=/summationdisplay
iqi
|r−ri|, (4)
where riand qiare the position and magnitude, respectively,
of each point charge. Positive (ionic) charges are located at the
ionic positions with magnitudes given by those of the corre-sponding pseudo-ions. For the negative (electronic) charges,
the positions are the centres of the MLWFs
42,45obtained by
subspace rotation of the manifold of occupied eigenstates ofan isolated water molecule.
46The magnitude of each elec-
tronic charge is then the integrated charge density of each
MLWF. Due to the unitarity of the Wannier transformation,this gives −2 e, with the factor of two being a result of spin de-
generacy. In practice, to prevent unphysical “charge-spilling”
into the deep Coulombic potential, these point charges aresmeared with a Gaussian function of half-width 0.16 Å.
47The
geometry of the MLWF centres in relation to the ionic posi-
tions is shown in Fig. 3(bottom left). Our method is similar
in spirit to that of Ref. 48, but differs in that the procedure is
parameter free and requires no fitting.
The difference in electronic density induced by this clas-
sical electrostatic model for the water molecule can be cal-
culated using the equivalent of Eq. (1)and is shown in
Fig. 1(dashed lines). The agreement with the full DFT
calculation (solid lines) is excellent for all configurations.
Additional calculations (not shown) modifying the bindingdistance show that the Wannier charge model accurately de-
scribes charge redistribution for thermally accessible geome-
tries. To achieve a large difference in the long-range densitydifference in the θ=0
◦orientation, for example, the water
molecule must have a binding distance less than 2.5 Å. Such
small separations, however, incur a serious energy penalty ofat least 200 meV (or 8 k
BTat ambient temperature) and there-
fore the contributions from these configurations can be ne-
glected under the ambient conditions that experiments are per-formed. The success of the MLWF model can be explained by
comparing the long-range electrostatic potential correspond-
ing to the MLWF model and that of the water molecule fromDFT. This comparison is shown in the top two panels of
Fig. 3. The classical model reproduces the potential to high
accuracy, with only small differences very close to the wa-
ter molecule where the detailed charge density distribution is
important. Equivalent calculations (not shown) performed ona metallic (5, 5) CNT produce similar results, providing evi-
dence for the general applicability of our model.
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FIG. 3. Top panels: a comparison between the electrostatic potential (lo-
cal ionic and Hartree) for the isolated full DFT water molecule (left), and
the classical Wannier charge representation (right). Contours are in steps of
20 meV , in the plane 3.20 Å below the water molecule, where the surface of
the CNT would be when the water is in the 90◦orientation. The water oxygen
ion is located at the origin. The inset in the bottom right panel gives the dif-ference between the two potentials in the region indicated by the dashed box.
Contours are in steps of 5 meV , and the shading gives the absolute difference
between 0 meV (white) and 50 meV (black). Outside the region shown, thedifference between the potentials is less than 5 meV . Bottom panel, left: the
positions of the Wannier charge centres (blue spheres) and oxygen/hydrogen
ions.
It is interesting to note that simpler models for the wa-
ter electrostatics also well reproduce the density polarisation.
In Fig. 4, we compare the density polarisation induced in a
metallic (5, 5) CNT within three different models. The left
panel gives the Wannier charge model which most accuratelyreproduces the DFT induced polarisation. The central panel
FIG. 4. Comparison of the different electrostatic models for the water
molecule adsorbed on a (5, 5) CNT in the θ=45◦orientation. Left panel:
point charge (MLWF) model for the water molecule; centre panel: dipole
model for the water molecule; right panel: classical conducting cylinder
model (see main text for details). In all cases, the dashed blue line gives the
full DFT result.uses a classical dipole model for the water potential, with clas-
sical charges of magnitude ±8 e at the centres of positive and
negative charge of the isolated water molecule; the CNT isstill treated using DFT. The agreement between this model
and the DFT induced polarisation is still excellent, however
differences between the classical and DFT electrostatic po-tential in the near-field produce a small lateral shift in the po-
larisation along the z-direction. The right panel shows the in-
duced charge density for the simplest model where the CNT istreated as a classical conducting cylinder. The water molecule
is described as a series of classical point charges as in the
Wannier charge model, with the induced density calculated
by solving the classical Poisson equation, as detailed in the
Appendix. We note that the classical induced polarisation cal-culated by this crude final model captures well the main form
of the full DFT induced polarisation supporting the conclu-
sion that the dominant interaction is electrostatic.
Similar results (not shown) are obtained for the (10, 0)
CNT, including for the classical conducting cylinder model
despite the CNT being semiconducting.
Finally, we note that we do not expect that our conclu-
sion will change in the presence of multiple water molecules.
The shallow binding energy between CNT and water shouldnot change with additional water molecules as the dominant
interaction in this case is not the relatively weak physisorp-
tion between CNT and water, but instead the much strongerhydrogen bonding between the individual water molecules
themselves. The short ( <2.5 Å) binding distances required
to potentially achieve charge transfer will remain thermally
inaccessible at ambient conditions in this case as well.
B. Estimating the residual charge transfer
In any calculation of the electronic density, the difference
in charge density given by Eq. (1)consists of both charge
polarisation /Delta1np(r) and charge transfer /Delta1nt(r) components,
/Delta1n(r)=/Delta1np(r)+/Delta1nt(r). (5)
A convincing indicator of charge transfer would be ad-
ditional charge delocalised in the CNT, far from the water
molecule. As shown by the results above, however, the chargepolarisation induced by the water dipole moment is very
long-ranged. In principle, the charge transfer contribution
could be determined by increasing the system size to screenthe electrostatic perturbation, and considering regions where
/Delta1n
p(r)→0.50Such an approach is impractical, especially
for low-dimensional systems such as CNTs in which the rel-atively weak screening necessitates the use of very large sys-
tems. The larger the system size, the more accurately the
charge densities must be determined as any charge trans-
fer/Delta1Qbecomes delocalised over a larger volume V, and
the associated density difference becomes smaller: /Delta1n
t(r)
∼/Delta1Q/V . Discerning small amounts of charge transfer ac-
curately in this way is challenging from a computation point
of view.
Instead, we approximate the polarisation contribution to
the charge density difference in the full DFT calculation
/Delta1np(r) (Fig. 4, dashed lines) as exactly the density difference
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calculated by the Wannier charge model /Delta1nWF(r) (Fig. 4,l e f t
panel, solid line) in which the charge density difference is due
entirely to electrostatic polarisation: i.e., /Delta1np(r)≈/Delta1nWF(r).
The residual charge transfer is then approximated as
/Delta1nt(r)≈/Delta1n(r)−/Delta1nWF(r). (6)
Summing /Delta1nt(r) over the unit cell furthest from the water
molecule provides an estimate of the charge transfer betweenthe CNT and the water molecule, which we find to be no
more than |/Delta1Q|/lessorsimilar10
−4e, independent of orientation. This is
three orders of magnitude lower than the value calculated byMulliken population analysis, and shows that there is negligi-
ble charge transfer in this system.
C. Considerations of the electronic energy
level alignment
Finally, we consider the evidence for charge transfer in
terms of the energy levels of the CNT and water systems.
Previous calculations have shown that water interacts
weakly with a CNT.21,25–28As there is little chemical bond-
ing, the eigenstates of the isolated water and CNT are ex-
pected to be little perturbed.
This is confirmed in Fig. 5, which compares the density
of states of a 16 unit cell (10, 0) semiconductor CNT and a
water molecule when mutually isolated, and the correspond-
ing CNT/water local density of states (LDOS)49with the wa-
ter adsorbed. Indeed, the LDOS/DOS of the CNT are indistin-
guishable. Equivalent calculations surrounding the CNT witha cluster of water molecules result in the same conclusion.
For significant charge transfer between CNT and water to
occur, charge must transfer from the highest occupied molec-ular orbital (HOMO) of the water molecule to the CNT con-
duction band. As the water HOMO lies almost 4 eV below
the CNT conduction band, this transfer would involve a large
FIG. 5. A comparison of the density of states (LDOS) for a (10,0) CNT
and water molecule when isolated (dashed red/blue, respectively), and the
local density of states of the CNT and water molecule (solid red/blue) when
the water is adsorbed 3.20 Å above the CNT in the 90◦configuration. A
Gaussian smearing of 0.1 eV has been used. The CNT LDOS and DOS are
indistinguishable. For each calculation, energies have been aligned by the
potential far into the vacuum.energy penalty, the magnitude of which is dependent on the
CNT band gap.
The energy penalty for metallic CNTs is smaller than
for semiconducting CNTs, and so calculations for these sys-
tems should show a large difference in either the binding
energy or the charge transferred to the CNT. As neither ofthese effects are observed in calculation,
25,28we conclude
that if charge transfer occurs then it must be very small, con-
sistent with our estimation from Sec. III B . We also con-
clude that the Mulliken population analysis reported in previ-
ous calculations21,25–28is not suitable for determining charge
transfer in this system.
Whilst the energy levels calculated by Kohn-Sham DFT
do not correspond to the true quasi-particle energy levels,the many-body correction to the energy levels is likely to
be smaller than the large difference between water and CNT
states. Moreover, the correction to the DFT band gap willincrease the energy difference between the occupied water
states and the CNT conduction band. Therefore, we do not
believe that this conclusion will change under a higher levelof theory. For other adsorbed molecules, significant charge
transfer would be possible if the molecular levels better align
with the CNT states. For example, molecular oxygen in thetriplet spin state has been calculated to have an unoccupied
molecular level that sits within the CNT band gap.
51We there-
fore do not dispute the conclusion that oxygen may p-dope
semiconductor CNTs.34,52
IV. CONCLUSIONS
Using linear-scaling density-functional theory, we have
calculated the long-range electronic effects of a water
molecule adsorbed onto a CNT. We have shown that the inter-
action is described very well with classical electrostatics: thepermanent dipole moment of the water molecule induces a po-
larisation of the electronic charge density of the CNT that is
remarkably long-ranged, occurring over a length-scale greaterthan 30 Å.
By comparing our full DFT calculations with ones in
which the water molecule is treated as a classical charge dis-
tribution defined by its Wannier charge centres, we estimate
that the charge transfer between CNT and a water molecule isno more than 10
−4e. We therefore conclude that water does
not significantly dope CNTs. This conclusion is supported by
the poor alignment of the relevant energy levels of the watermolecule and the CNT, and contrasts with previous results,
based on Mulliken charge partitioning in small supercells, that
suggest much greater charge transfer.
As a consequence of the lack of charge transfer and the
weak interaction between CNT and water, we conclude that
water has a very weak effect on the conductivity of individual
CNTs.
26,29In order to understand the origin of the humidity-
dependent conductivities observed in experiments on CNT fi-
bres and mats, therefore, it is vital to go beyond the effect ofwater on individual CNTs, and also consider the effect of wa-
ter on the conductivity of networks of CNTs, i.e., on the con-
ductivity between CNTs. For example, in Ref. 53we recently
proposed a mechanism that greatly improves the conduc-
tance between different CNTs through momentum-resonant
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130.237.165.40 On: Tue, 11 Aug 2015 04:46:45164703-6 Bell, Payne, and Mostofi J. Chem. Phys. 141, 164703 (2014)
scattering. The resonance can be achieved using a weak, long-
ranged perturbation to the CNTs, which may be provided, for
example, by water molecules weakly adsorbed to the CNTsurface.
Finally, it is worth emphasising that our results highlight
the importance of using supercells that are sufficiently largeto capture long-ranged charge polarisation effects and that en-
able the disentanglement of charge polarisation from charge
transfer. Beyond the immediate application to water on CNTs,these ideas are relevant more generally to the determination
of charge polarisation and charge transfer resulting from ad-
sorption of molecular species on bulk surfaces and layered
materials.
ACKNOWLEDGMENTS
The authors would like to thank N. D. M. Hine for use-
ful discussions. This work was performed using the Dar-win Supercomputer of the University of Cambridge High
Performance Computing Service funded by Engineering and
Physical Sciences Research Council (U.K.) (EPSRC(GB))under Grant No. EP/J017639/1. R.A.B. acknowledges fi-
nal support from British Telecommunications and EPSRC;
M.C.P. acknowledges support from EPSRC under Grant No.EP/J017639/1; and A.A.M. acknowledges support from the
Thomas Young Centre under Grant No. TYC-101.
APPENDIX: CLASSICAL ELECTROSTATIC MODEL
In Sec. III A , we model the interaction between a CNT
and an adsorbed water molecule as a classical conducting
cylinder interacting with point charges.
The cylinder radius is set as the radius of the CNT. The
water molecule is modelled as point charges placed at the cen-
tres of the Wannier/ionic charges, as described in Sec. III A .
We calculate the charge density profile induced in the
conducting cylinder due to the classical charges.
The electric potential is calculated by solving for the
Green’s function to the Poisson equation subject to the con-stant potential Dirichlet boundary condition on the cylinder
∇
2φ(r)=4π/summationdisplay
iqiδ(r−ri), (A1)
where we have adopted atomic units.
In the limit of an infinite radius cylinder, the conductor
becomes an infinite conducting plane and the solution is ob-tained using the method of images in a simple analytic form.
For a single charge a position r
i=(xi,0,0) above a conduc-
tor in the yzplane, the potential is
φ(r)=q
|r−ri|−q
|r−rm
i|, (A2)
where rm
i=(−xi,0,0) is the position of the mirror charge if
the conductor lies on the yz-plane.
The surface charge of the conductor is calculated using
Gauss’ law giving σ(y,z)=1/(2π)Ex|x=0, where Ex|x=0is
the electric field perpendicular to the plane, evaluated at the
plane. The charge density per unit length of CNT is given bythe sum of the surface charge along a direction perpendicular
to the CNT axis, i.e.,
λ(z)=/integraldisplay
dy σ (y,z)=q
πxi
z2+x2
i. (A3)
The charge density due to multiple charges is generated
through superposition. To compare to the charge polarisationderived from the DFT calculations, this quantity is convolved
with the same window function given in Eq. (3).
Whilst the shape of the induced density calculated using
this model is in excellent qualitative agreement with our DFT
calculations, the amplitude is an order of magnitude too large.Heuristically, this can be understood to arise from the differ-
ence in screening in the metallic cylinder as compared to a
real CNT. We account for this by including a single param-eter to the model that scales all the classical charges by the
same factor, and choose its value such that the best fit to the
DFT data is obtained. For the calculation shown in the rightpanel of Fig. 4, the fitted scaling factor is 0.13.
Treating the finite radius of the CNT explicitly by calcu-
lating the Green’s function for the cylindrical geometry
54is
found to little change the form of the induced density profile.
This observation is reasonable as the CNT diameter ( ≈8Å )i s
much larger than the distance between point charges and CNTsurface (3.20 Å). Regardless, we find that the classical model
captures well the main features of the charge polarisation due
to the water molecule.
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1.4883259.pdf | Electric field-induced magnetic switching in Mn:ZnO film
S. X. Ren, G. W. Sun, J. Zhao, J. Y. Dong, Y. Wei, Z. C. Ma, X. Zhao, and W. Chen
Citation: Applied Physics Letters 104, 232406 (2014); doi: 10.1063/1.4883259
View online: http://dx.doi.org/10.1063/1.4883259
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/23?ver=pdfcov
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131.156.59.191 On: Thu, 11 Sep 2014 12:27:29Electric field-induced magnetic switching in Mn:ZnO film
S. X. Ren,1,2G. W. Sun,1J. Zhao,1J. Y. Dong,1Y. Wei,3Z. C. Ma,3X. Zhao,1
and W. Chen1,a)
1Key Laboratory of Advanced Films of Hebei Province, College of Physics Science and Information
Engineering, Hebei Normal University, Shijiazhuang 050024, China
2School of Material Science and Engineering, Shijiazhuang TieDao University, Shijiazhuang 050043, China
3College of Chemistry and Material Science, Hebei Normal University, Shijiazhuang 050024, China
(Received 30 April 2014; accepted 30 May 2014; published online 11 June 2014)
A large magnetic modulation, accompanied by stable bipolar resistive switching (RS) behavior,
was observed in a Mn:ZnO film by applying a reversible electric field. A significant enhancement
of the ferromagnetism of the film, to about five times larger than that in the initial (as-grown) state
(IS), was obtained by switching the film into the low resistance state. X-ray photoelectronspectroscopy demonstrated the existence of abundant oxygen vacancies in the IS of the film. We
suggest that this electric field-induced magnetic switching effect originates with the migration and
redistribution of oxygen vacancies during RS. Our work indicates that electric switching is aneffective and simple method to increase the ferromagnetism of diluted magnetic oxide films. This
provides a promising direction for research in spintronic devices.
VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4883259 ]
Diluted magnetic oxides (DMOs) have attracted increas-
ing attention for their possible applications in spintronics
devices.1Following theoretical predictions by Dietl2and
Sato,3extensive studies have been carried out over the past
decade to search for room temperature ferromagnetism in
various transition metal (TM)-doped and undoped binary
metal oxides.4,5To date, however, the ferromagnetism of
TM-doped and undoped DMOs reported in most investiga-
tions has still been very weak, which remains one of the
main problems limiting their practical applications.
Recently, resistive switching (RS) behavior in
TM-doped and undoped binary metal oxides has received
considerable attention due to its potential applications innonvolatile memory devices. It has been widely proposed
that oxygen vacancies in these DMO films play an important
role in their RS behavior.
6Bogle and co-workers7have sug-
gested that the migration of oxygen vacancies under an
applied voltage results in RS in Co-doped TiO 2films. Xu
et al.8proposed that the low resistance state (LRS) in
TiN/ZnO/Pt devices could be attributed to electron hopping
through filament paths consisting of oxygen vacancies. Since
the oxygen vacancies can be manipulated through the RSprocess, and the origin of the observed ferromagnetism in
DMO films is mostly associated with oxygen vacancies,
5,9it
seems reasonable that the magnetic properties might bemodulated merely by applying an electric field sufficient to
induce RS. In other words, the RS effect caused by the
movement of oxygen vacancies under an applied electricfield might well be accompanied by magnetic switching.
Based on the above considerations, in this work, we
fabricated metal/insulator/metal sandwich structures withMn-doped ZnO as the central functional layer. We found
experimentally that not only the electric properties but also
the magnetism of the films could be switched in a controlledmanner by applying an external electric field. We also found
that the magnetic moment of the films were, in some cases,
as much as five times larger than that in the Initial State (IS,
i. e., the as grown film) when the devices were switched tothe LRS by applying an electrical bias field. The magnetiza-
tion of the films in the LRS was found to be much higher
than in previous reports.
10
ZnO films doped to a Mn concentration of 5 at. %
(Mn:ZnO films) with various thicknesses were deposited
using the pulsed laser deposition (PLD) technique. Thebeam of a KrF excimer laser ( k¼248 nm) with a repetition
rate of 3 Hz and an energy density of 2.0 J/cm
2was focused
onto a rotating Mn:ZnO target. After the base pressure ofthe deposition chamber was pumped below 10
/C05Pa, the
films were grown on Pt/Ti/SiO 2/Si substrates of approxi-
mately 5 mm /C23m m/C20.5 mm under an oxygen pressure of
15 mTorr at 400/C14C. For later measurements of electric and
magnetic properties, 45 Ti electrodes with diameters of
200lm were deposited on the Mn:ZnO films. The electro-
des covered approximately 10.6% of the film area. The crys-
tal structure and morphology of the films were investigated
using X-ray diffraction (XRD, X’pert PRO MPD) with CuKaradiation ( k¼0.15406 nm) and scanning electron mi-
croscopy (SEM, Hitachi S-4800). The current-voltage ( I-V)
characteristics were measured using a semiconductor char-acteristic system (Keithley 2612A source meter). Hysteresis
loops were measured using a physical property measurement
system (PPMS-6700), with the magnetic field applied paral-lel to the films. During all sample manipulations, we used
Teflon tweezers to handle all the samples so as to reduce
possible contamination of the samples. The elemental com-position and chemical states were characterized using X-ray
photoelectron spectroscopy (XPS, PHI5000Versa Probe)
with monochromatic Al K aradiation (1486.6 eV) as the
X-ray source. The C
1sbinding energy (284.6 eV) of carbon
contamination was used as a calibration to compensate for
charging effects.a)Author to whom correspondence should be addressed. Electronic mail:
chen07308@mail.hebtu.edu.cn.
0003-6951/2014/104(23)/232406/4/$30.00 VC2014 AIP Publishing LLC 104, 232406-1APPLIED PHYSICS LETTERS 104, 232406 (2014)
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131.156.59.191 On: Thu, 11 Sep 2014 12:27:29The XRD pattern of a representative as-grown Mn:ZnO
film is shown in Fig. 1. It may be seen that a strong (002)
peak appears, showing that the as-grown film has a c-axis
preferred orientation. No diffraction peaks related to second-
ary Mn metal or its oxide phases were observed within theXRD detection limit. The cross-sectional SEM image, shown
in the inset of Fig. 1, shows that the thickness of the film is
about 50 nm and that the grains grew with a columnar struc-ture which is apparently related to the c-axis preferential
growth orientation on the substrate.
To further investigate the elemental composition and
chemical states of the as-grown film, XPS analysis was car-
ried out. The results are shown in Fig. 2. The extended scan
for the as-grown film (see Fig. 2(a)) reveals that only O, Zn,
and Mn were detected except for the C that was used for cali-
bration. Fig. 2(b) shows the XPS spectrum for O1s with
Gaussian fitting. It was found that O1s can be fitted withthree peaks. Apart from lattice oxygen ions (centered at
around 530.0 eV)
11in the ZnO structure and chemically
adsorbed oxygen (centered at around 532.0 eV)12on the sur-
face, the peak at 530.6 eV is attributed to the presence of
abundant oxygen vacancies12in the IS of the film. Fig. 2(c)
shows the Zn 2p 3/2XPS spectrum. The core level for Zn2þ
centered at around 1021.80 eV, which is lower that thestandard data of zinc oxide (1022.2 eV),13indicates less oxy-
gen ions binding with Zn2þions. This result is consistent
with the XPS analysis of O1s as shown in Fig. 2(b). The core
level for Mn2p 3/2centered at approximately 640.85 eV as
shown in Fig. 2(d). It indicates that the dominant chemical
state of Mn in the IS is Mn2þ,13which is in agreement with
the EELS study for Mn-doped ZnO.14
Fig.3(a)shows a schematic of the device layout and the
measurement configuration. All the driving voltages were
applied to the top electrode (TE) with the Pt bottom electrode
(BE) being grounded. A positive bias was defined such that
the current flowed into the films through the TE and out ofthe BE. Fig. 3(b) shows a representative I-Vcharacteristic of
the Ti/Mn:ZnO/Pt device for 10 consecutive cycles. The volt-
age was swept in the sequence 0 !positive !0!negative !0
with a compliance current of 100 mA to protect the device
from hard breakdown. It should be noted here that a Forming
process was not required for the device. The lack of such aprocess can be ascribed to the presence of a large number of
preexisting oxygen vacancies in the as-grown film as shown
in Fig. 2(d). These vacancies contribute to the rapid formation
of conducting filament paths without the need for generating
them in a Forming process.
8The above argument is strongly
reinforced by the temperature dependence of the resistance ofthe film in the LRS as shown in the inset of Fig. 3. The
increase of the resistance upon cooling over the range
300–10 K indicates a semi-conductive rather than metalliccharacter in the LRS, implying the formation of conducting
filaments based on oxygen vacancies.
10
To clarify the effects of RS on the magnetism of
Mn:ZnO films under an applied electric field, we first meas-
ured the hysteresis loops of the device in the IS at room tem-
perature. Subsequently, we switched the device to the LRSand high resistance state (HRS) by applying voltages of 0.4 V
and/C00.4 V, and measured the hysteresis loops of the film in
the LRS and HRS. Finally, the signal from the commerciallyobtained Pt/Ti/SiO
2/Si substrates (shown in the inset of Fig.
4(a)) was subtracted. Fig. 4(a)shows the hysteresis loops of
the film in the IS, LRS, and HRS for the first cycle. Weak fer-romagnetism was found in the IS at room temperature. The
saturation magnetism ( M
s) in the IS was only about
3.82 emu/cm3, which is in good agreement with previous
reports for Mn-doped ZnO.15The values of the Msfor both
the LRS and HRS, but especially for the LRS, increased. The
value of Msin the LRS reached 22.3 emu/cm3, which is 5.8
times larger than that in the IS.
In order to check the reversibility of the magnetism dur-
ing RS, the hysteresis loops in the LRS and HRS were meas-ured for three consecutive cycles, as shown in the inset of
Fig.4(a). The figure shows that the maximum and minimum
values of M
swere reversibly switchable between the HRS
and LRS. To check the retention of the strong magnetism of
the film in the LRS, we re-measured the hysteresis loops of
the film after exposing the film to atmosphere for 24 and 48h. We found that the magnetic moment of the film dropped
very little, as shown in Fig. 4(b), indicating the excellent
magnetic retention properties of the film. Similar resultswere obtained with a series of Ti/Mn:ZnO/Pt devices where
the thickness of the Mn:ZnO film was between 30 and
70 nm.
FIG. 1. XRD patterns of an as-grown Mn:ZnO film in the initial state depos-
ited on a Pt/Ti/SiO 2/Si substrate. The inset shows a cross-sectional SEM
image of the film.
FIG. 2. XPS spectra for the as-grown Mn:ZnO film in the initial state:Extended scan (a), O1s (b), Zn2p
3/2(c). and Mn2p 3/2(d).232406-2 Ren et al. Appl. Phys. Lett. 104, 232406 (2014)
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131.156.59.191 On: Thu, 11 Sep 2014 12:27:29Recently, a few studies have reported a similar effect in
Mn-doped ZnO,16Co-doped ZnO,10and Mn-doped TiO 2.17
However, there are clear advantages in our study. The mostimportant one is that the LRS value of M
sin our work
reached about 22.3 emu/cm3. This value is about 1.6 and 4
times larger than the maximum values of 14 emu/cm3
reported by Wang et al.16and 5.5 emu/cm3reported by Chen
et al.10It is worth mentioning that the areas of the cells in
our device that were actually subjected to the bias electric
fields covered only 10.6% of the total film surface area,which is 6 times less than the corresponding area of 65%used in the study of Co-doped ZnO.
10Much stronger ferro-
magnetism can be expected in our device if more area is
switched to the LRS. One reason for this result may be that
abundant oxygen vacancies preexisted in our Mn:ZnO films,as indicated in Fig. 2(d). Another reason is probably that the
chemically active Ti top electrode acts as a reservoir for oxy-
gen ions
18,19in our device so that a large number of vacan-
cies remained in the film when a positive bias was applied to
the top electrode. Similar magnetic switching phenomena
have been observed with an Ag electrode. However, themagnetization of the film with an Ag electrode is not as high
as that with the Ti electrode when the film is switched into
LRS. We know that Ag is not as active as Ti, so this resultindicates that the active electrode Ti may be of some assis-
tance for the magnetic switching since the active Ti electrode
makes it is easier to absorb and reserve oxygen ions, thusincreasing the strength of the ferromagnetism in the Mn:ZnO
film.
To date, several related models have been proposed to
explain the mechanism behind the ferromagnetism observed
in DMO films including carrier modulation ferromagnetism,
2
bound magnetic polarons (BMPs),20and an F-center
model.21Many experimental and theoretical studies22sup-
port the BMP theory in TM-doped DMOs. This theory can
also account for the weak ferromagnetism observed in thiswork when the films were in the IS. We propose that the
magnetization change between the HRS and LRS involves a
migration and redistribution of oxygen vacancies along theapplied electric field.
7When a positive electric field is
applied to the top electrode, oxygen vacancies near the elec-
trode migrate toward the bottom electrode and form conduct-ing filaments between the electrodes, thus leading to the
LRS. The formation of filaments results in a tremendous
increase in the density of vacancies along the filaments, andmore magnetically active polarons produce stronger global
ferromagnetism. When a negative electric field is applied,
the vacancies move back to the top electrode and combinewith the reservoir of oxygen ions held by the Ti electrode.
This leads to a reduction in the number of vacancies and
eventually to the rupture of the conducting filaments. This isaccompanied by a dramatic reduction in the number of polar-
ons as well as a decline in the magnetic ordering and weaker
magnetism when the film is in the HRS.
We note also that the results of photoluminescence (PL)
spectra (not shown here) indicate that the relative content of
F-center in the form of singly ionized oxygen vacancies in
FIG. 3. A schematic structure of the
Ti/Mn:ZnO/Pt device (a), and 10 cycles
of RS behavior of the Ti/Mn:ZnO/Pt
device with the compliance current lim-
ited to 100 mA (b). The arrows indicate
the voltage sweeping directions. The
inset in Fig. 3(b)shows the temperature
dependence of the resistance of the film
in the LRS.
FIG. 4. Ferromagnetism modulation behavior of the/Ti/Mn:ZnO/Pt device.(a) M-H curves in the IS, HRS, and LRS. The top inset shows the M-H curve
of the Pt/Ti/SiO
2/Si substrate. The bottom inset shows the reversible change
in Ms accompanying the RS effects. (b) M-H curves of the film in the LRS
after atmospheric exposure for 24 and 48 h.232406-3 Ren et al. Appl. Phys. Lett. 104, 232406 (2014)
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131.156.59.191 On: Thu, 11 Sep 2014 12:27:29the LRS is much higher than in the IS, which provides favor-
able conditions for the formation of magnetically active
polarons.20
In summary, electric field-induced magnetic switching,
accompanied by resistive switching, was observed in a series
of Mn:ZnO films with thicknesses between 30 and 70 nm.
The saturation magnetism of the films in the low resistancestate was about five times larger than that in the initial state.
The strong ferromagnetism of the film could be maintained
for more than 2 days under ambient conditions. We suggest
that the formation of conductive filaments based on oxygen
vacancies under a positive electric field results in strong fer-romagnetism due to a dramatic increase in the number of the
bound magnetic polarons. Our work provides an effective
and simple way to increase the ferromagnetism of dilutemagnetic oxide films using an external electric field.
The work described in this paper was supported by the
Natural Science Foundation of Hebei Province (Grant Nos.
A2013205149 and E2013210133) and Hebei Education
Department (Grant Nos. ZH2012067 and 2011170). Theauthors are grateful to Professor Norm Davison for critical
reading of the manuscript.
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1.4896418.pdf | High quantum efficiency ultrananocrystalline diamond photocathode for photoinjector
applications
Kenneth J. Pérez Quintero , Sergey Antipov , Anirudha V. Sumant, , Chunguang Jing , and Sergey V. Baryshev,
Citation: Appl. Phys. Lett. 105, 123103 (2014); doi: 10.1063/1.4896418
View online: http://dx.doi.org/10.1063/1.4896418
View Table of Contents: http://aip.scitation.org/toc/apl/105/12
Published by the American Institute of PhysicsHigh quantum efficiency ultrananocrystalline diamond photocathode
for photoinjector applications
Kenneth J. P /C19erez Quintero,1,2Sergey Antipov,3,4Anirudha V. Sumant,1,a)
Chunguang Jing,3,4and Sergey V. Baryshev3,4,b)
1Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
2Department of Physics, University of Puerto Rico, R /C19ıo Piedras Campus, San Juan, Puerto Rico 00931, USA
3Euclid TechLabs, Solon, Ohio 44139, USA
4High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
(Received 6 August 2014; accepted 10 September 2014; published online 22 September 2014)
We report results of quantum efficiency (QE) measurements carried out on a 150 nm thick nitrogen-
incorporated ultrananocrystalline diamond terminated with hydrogen; abbreviated as (N)UNCD:H.
(N)UNCD:H demonstrated a remarkable QE of /C2410/C03(/C240.1%) at 254 nm. Moreover, (N)UNCD:H
was sensitive in visible light with a QE of /C245/C210/C08at 405 nm and /C245/C210/C09at 436 nm.
Importantly, after growth and prior to QE measurements, samples were exposed to air for about 2 h
for transfer and loading. Such design takes advantage of a key combination: (1) H-termination pro-ven to induce negative electron affinity on the (N)UNCD and to stabilize its surface against air expo-
sure; and (2) N-incorporation inducing n-type conductivity in intrinsically insulating UNCD.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4896418 ]
The photocathode is a key component of the electron
injectors in synchrotrons, free electron lasers, linear acceler-ators (linacs), and ultrafast electron systems for imaging and
diffraction. Choice of a photocathode is application specific,
and there is always a trade-off: quantum efficiency (QE) vs.lifetime/robustness vs. response time vs. emittance. It is gen-
erally accepted that if a technology providing a high QE pho-
tocathode operating at moderate vacuum conditions existed,it would greatly benefit the field of photoinjectors R&D.
1
Semiconductor photocathodes still hold records in terms
of QE. These are low work function (WF) alkali/multialkalibased materials which are either used in a form of thin films
to absorb light and emit electrons
2or in a form of ultrathin
layers to activate traditional metal photocathodes.3Activation
of heavily doped p-Si or p-GaAs surfaces with alkali Cs has
led to a special photocathode type with negative electron af-
finity (NEA). NEA is a unique circumstance, when electronsinjected to the conduction band can be emitted directly into
the vacuum. Such NEA photocathodes are bright electron
sources because of their high QE and low emittance, whichdecreases as the NEA value increases.
4The NEA value is a
measure of how low vacuum level locates with respect to the
conduction band minimum. Nevertheless, the main drawbackof alkali-based photocathodes remains the same—they
require a vacuum base pressure /C2010
/C010Torr for synthesis,
handling, and operation.
Wide bandgap ( >5 eV) semiconductors are another class
of NEA materials. This includes AlN, BN, and diamond.5,6In
diamond, NEA can be either an inherent surface property7or
an engineered one8via surface treatment in a hydrogen envi-
ronment. Since the first experiment which demonstrated a re-
markable quantum yield from a NEA diamond surface undervacuum UV illumination,
7there was more interest generated
in using diamond for photocathode applications andprototypes of solar blind high efficiency photocathodes for
space research detectors have been introduced.9–11High pu-
rity H-terminated synthetic diamond has been found to be an
excellent electron amplifier, where the primary electrons
from a standard QE photocathode (e.g., Cu) accelerated to akeV energy get multiplied upon transmission through a thin
diamond film. Chang et al.
12have demonstrated gain coeffi-
cients as high as 200. In most of the previous studies, eitherhigh purity (undoped) diamonds or boron doped ( p-type con-
ductivity) diamonds were used in the UV wavelengths
(/C20200 nm) range. Boron p-doping did not play a significant
role
13as the boron level is only 0.4 eV above the top of the
valence band in diamond. Importantly, a comparison between
single-, micro-, nano-, and graphite-like nano-crystalline dia-mond films was carried out.
11It has been demonstrated that
graphite-like nano-crystalline diamond had a better perform-
ance compared to the others in terms of having QE of 10/C03in
a spectral range extended to 200 nm. Finally, the same group
has also demonstrated identical significant QE of 10/C03at
200 nm for microcrystalline diamond films.14However, none
of these films showed good performance at wavelengths
>200 nm.
In order to take advantage of NEA of diamond towards
the near UV and visible spectral ranges, which then could be
of great interest to the photoinjectors community, one should
introduce electron states in the band gap closer to the conduc-tion band minimum. A way to do so would be by n-doping.
Relatively recent progress in n-doping of micro-, nano-, and
ultranano-crystalline diamond offers a few options: sulfur(activation energy 0.4 eV (Ref. 15)), phosphorous (activation
energy 0.6 eV (Ref. 16)), and nitrogen (activation energy
1.7 eV (Ref. 17)). Given that the electron affinity induced by
hydrogen can be as low as /C01 eV (NEA value ¼1 eV),
18all
aforementioned dopants are capable of promoting visible
light photoemission. To date, there is one experimental reportshowing (N)UNCD:H is sensitive to visible light. Sun et al.
19
reported a measurable external quantum effect at rooma)sumant@anl.gov
b)sergey.v.baryshev@gmail.com
0003-6951/2014/105(12)/123103/4/$30.00 VC2014 AIP Publishing LLC 105, 123103-1APPLIED PHYSICS LETTERS 105, 123103 (2014)
temperature between 400 and 480 nm; but no QE values were
presented. With this letter, we report proof-of-concept QE
measurements suggesting that n-doped UNCD:H is an emer-
gent air resistant NEA photocathode. QE measurements werecarried out in the near UV range 250–270 nm, standard for
many photocathode applications, and in the visible range at
405 and 436 nm. The cathode was exposed to air for about2 h for transfer and loading; QE was measured at base pres-
sure/C2410
/C06Torr.
(N)UNCD films were synthesized on polycrystalline mo-
lybdenum substrates in a 915 MHz microwave-assisted
plasma chemical vapor deposition (MPCVD) reactor(Lambda Technologies, Inc.) Growth of UNCD on non-
diamond substrates requires a nanodiamond (ND) pre-seeding
treatment prior to deposition to promote rapid nucleation andgrowth of the UNCD thin film.
20Slurry of ND particles from
Ad/C19amas Technologies was used. The average particle size of
the seeds was 5–10 nm. Mo substrates were immersed into theND slurry and subjected to ultrasonic treatment in the solution
for 20 min. Subsequent growth of the (N)UNCD films was
carried out under following conditions: substrate temperature850
/C14C; operation chamber pressure 56 Torr; microwave
power 2.3 kW; and individual gas flows in the precursor gas
mixture were 3 sccm CH 4/160 sccm Ar/40 sccm N 2.F i g . 1(a)
shows a scanning electron micrograph (SEM) of a deposited
film taken by an FEI Nova 600 NanoLab. A uniform needle-
like nanostructure, typical for (N)UNCD, was observed.21
Fig.1(b)represents a visible Raman spectrum recorded by a
Renishaw InVia Raman Microscope using a He-Ne laser
(k¼633 nm). The shoulder around 1140 cm/C01corresponds to
the/C231(C-H in-plain bending) vibrational mode of trans-
polyacetylene and the broad peaks at 1340 and 1540 cm/C01
correspond to the D and G bands of diamond, respec-
tively.22,23An expected resulting carrier concentration in the
(N)UNCD films was /C241020cm/C03.21As a final step, the sam-
ples underwent the H-termination procedure for 15 min. Itwas accomplished in the same MPCVD reactor at substrate
temperature of 750
/C14C. H 2gas flow was 200 sccm at chamber
pressure 15 Torr, and the microwave power was 2 kW. Afterthe plasma treatment, the samples were left to cool down to
room temperature naturally.
WF and QE measurements of the synthesized samples
were performed in a commercial Kelvin probe (KP) instru-
ment (KP6500 from McAllister Technical Service) with cus-
tom in-house modifications so that the WF and QE can beobtained in the same experimental run. Before or after termi-
nation, all samples were taken from the synthesis chamber
and transported to the KP chamber under ambient condi-
tions; total exposure time was about 2 h. The KP chamber inall measurements was evacuated to a base pressure of
/C2410
/C06Torr. Fig. 2(a)represents a schematic of the experi-
mental setup. A voltage of þ300 V was applied to a small
aluminum anode plate, and a current of photoelectrons to the
ground was collected by the same source/ammeter (Keithley
6487) with a threshold sensitivity of 610 fA. The anode
plate was introduced into the KP chamber at an angle such
that it did not interfere with the light beam and the tipassessing the WF. The sample holder actuator and the KP tip
are both retractable, and ideal positions can be found for QE
and WF measurements independently. WFs for (N)UNCDsamples were determined by the KP with respect to its cali-
brated tip (WF ¼4.6 eV) before and after they underwent H
2
plasma treatment. A sample holder made of standard poly-
crystalline copper was used as a reference. All deduced WF
values are plotted in Fig. 2(b). WF dependence on time is a
standard representation for KP. This is to estimate the signal’snoise and drift to get a confident measurement of a WF.
Surprisingly, the WFs of (N)UNCD:H films were still
quite high, between 3 and 3.1 eV. For NEA UNCD films, anexpected effective WF value is an activation energy of a
dopant in use (1.7 eV for N), as no upward band bending is
expected on the surface.
19Even though sometimes KP is
considered a tool insensitive to changes of surface chemis-
try,24following QE results suggest that in the present
study, the WF values were somewhat higher than 1.7 eV. H-termination process optimization and comparison to ultravio-
let photoelectron spectroscopy measurements are necessary
subsequent steps to achieve a systematic and conclusiveinsight into the UNCD surface chemistry.
QE measurements were performed using an arc broad-
band Hg lamp (Spectra-Physics/Newport Oriel Instrumentsseries 66900) as a light source. A light spot size from the
source was adjusted by an aperture and focused by a lens;
spot size on sample’s surface was /C241m m
2. A number of
Newport filters were used to define a spectral dependence of
(N)UNCD QE before and after H-termination, namely, 254,
313, 365, 405, and 436 nm. The output power of the lampPðkÞat each filtered wavelength was assessed by a calibrated
power meter (Ophir Nova II), equipped with a calibrated
photodiode (Ophir PD300-UV). The photoelectron current
FIG. 1. (a) SEM surface topography
and (b) visible Raman spectrum typical
for (N)UNCD films on molybdenum.123103-2 P /C19erez Quintero et al. Appl. Phys. Lett. 105, 123103 (2014)IphotoðkÞwas recorded at each wavelength. QEs were calcu-
lated as QE ðkÞ¼Nelectrons ðkÞ
Nphotons ðkÞ, where N electrons ðkÞper second is
IphotoðkÞ=eand number of photons per second is
PðkÞ½eV=s/C138=ðh/C1/C23Þ½eV/C138with ebeing the elementary electron
charge and h/C1/C23being a single photon energy,
PðkÞ½eV=s/C138¼PðkÞ½W/C138=e, and h/C1/C23½eV/C138¼1240
k½nm/C138.IphotoðkÞ½A/C138
and P ðkÞ½W/C138are experimentally measured quantities. All
numbers are compiled and plotted in Fig. 3.
As expected, upon n-doping and H-termination, UNCD
sensitivity shifted toward near UV/visible wavelengths. There
are two main features in Fig. 3we would like to stress. The
first feature is QE in the band 250–270 nm, which is of com-
mon interest to the photocathode community. QE of the origi-
nally grown (N)UNCD was 5.3 /C210/C06. Given the measured
WF of 3.6 eV, it is a quite moderate effect compared to the
single crystal Cu (100) QE of 5 /C210/C05with WF ¼4.2 eV.25
Remarkably, the QE was enhanced by a factor of 140 upon
H-termination, placing (N)UNCD at the low boundary of a
QE range of alkali-based photocathodes. Second, diamond
films were responsive in visible blue. KP results suggest thatin all cases, the photoemission was in the sub-WF regime. For(N)UNCD at 365 and 405 nm and for (N)UNCD:H at 436 nm,
this seems to be a plausible conclusion. It can be explained byenhanced emission from grain boundaries with a lowered WF,
caused by the local environment,
26accounted also for strong
field emission from flat polycrystalline diamond surfaces.27
Photoemission from (N)UNCD:H in visible blue at 405 nm is
most probably a regular threshold process—photon energy of
3.06 eV versus WF 3.07 60.01 eV and 3.15 60.01 eV as
determined by KP (light green and olive solid lines in Fig.
2(b)). In any of the two regimes, incorporation of nitrogen
leads to sustainable currents /C2410 pA from UNCD surfaces
using blue light.
In conclusion, by combining n-type doping with surface
hydrogen passivation, a proof-of-concept was demonstratedthat ultrananocrystalline diamond is an emergent robust high
efficiency photocathode. This was accomplished by meas-
uring a QE dependence on wavelength of primary photons.(N)UNCD:H films of 150 nm thickness had a QE of /C2410
/C03
at 254 nm, and were sensitive in the visible range (between
405 and 436 nm). A QE /C245/C210/C08of the (N)UNCD:H at
405 nm is at the low boundary of a QE range of copper-
based photocathodes operated at 250–270 nm. It is reasona-
ble to expect that QE in near UV and sensitivity in the visi-ble, toward 532 nm, can be further increased. A route to
achieve this requires detailed investigation and optimization
of: (1) UNCD thickness for the best photon absorption; (2)defect engineering in the band gap to find the best trade-off
between donors’ activation energy and donors’ concentration
affecting simultaneously the density of states and electronlifetime; and (3) defect engineering on the surface to avoid
any possible upward band bending and to obtain work func-
tions compared with n-dopant’s activation energies.
Hydrogen termination procedure should be optimized by sys-
tematically varying hydrogen pressure/flow rate, substrate
temperature and microwave power.
The authors thank Robert Nemanich and Franz Koeck
(ASU) for valuable discussions, and Eric Wisniewski and
Zikri Yusof (IIT) for partial technical assistance. EuclidTechLabs LLC acknowledges partial support from the DOE
SBIR program, Grant No. DE-SC0009572. This work was
performed, in part, at the Center for Nanoscale Materials, aU.S. Department of Energy, Office of Science, and Office of
Basic Energy Sciences User Facility under Contract No. DE-
AC02-06CH11357. Funding was provided, in part, by
FIG. 2. (a) A crude schematic top view
of the modified Kelvin probe chamber;
(b) WF values measured for (N)UNCD
before and after H-termination (two
measurements for each case), and a
copper WF as a reference.
FIG. 3. Summary of the experimental QEs from the (N)UNCD samples: one
measurement before termination and two measurements after termination.
Some reference data are plotted to clearly emphasize the QE effects in the
(N)UNCD:H system. Black and red dotted lines are WFs determined for
(N)UNCD and (N)UNCD:H by KP, respectively. The symbols superscriptedas “a,” “b,” and “c” in the figure represent Ref. 2, Ref. 25, and Ref. 28,
respectively.123103-3 P /C19erez Quintero et al. Appl. Phys. Lett. 105, 123103 (2014)NASA EPSCoR (Grant No. NNX13AB22A) and NASA
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1.4869125.pdf | Anomalous large electrical capacitance of planar microstructures with vanadium
dioxide films near the insulator-metal phase transition
V. Sh. Aliev, S. G. Bortnikov, and I. A. Badmaeva
Citation: Applied Physics Letters 104, 132906 (2014); doi: 10.1063/1.4869125
View online: http://dx.doi.org/10.1063/1.4869125
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Appl. Phys. Lett. 92, 162903 (2008); 10.1063/1.2911745
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129.120.242.61 On: Wed, 03 Dec 2014 19:28:11Anomalous large electrical capacitance of planar microstructures with
vanadium dioxide films near the insulator-metal phase transition
V . Sh. Aliev,a)S. G. Bortnikov, and I. A. Badmaeva
Rzhanov Institute of Semiconductor Physics, Siberian Branch of the Russian Academy of Sciences,
13 Lavrentyev Ave., 630090 Novosibirsk, Russia
(Received 31 January 2014; accepted 8 March 2014; published online 3 April 2014)
The temperature dependence of electrical capacitance of planar microstructures with vanadium
dioxide (VO 2) film near the insulator-metal phase transition has been investigated at the frequency
of 1 MHz. Electrical capacitance measurements of the microstructures were performed by thetechnique based on the using of a two-terminal resistor-capacitor module simulating the VO
2layer
behavior at the insulator-metal phase transition. At temperatures 325–342 K, the anomalous
increase in microstructures capacitance was observed. Calculation of electric field in themicrostructure showed that VO
2relative permittivity ( e) reaches /C24108at the percolation threshold.
The high value of ecan be explained by the fractal nature of the interface between metal and
insulator clusters formed near the insulator-metal phase transition. VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4869125 ]
The polycrystalline vanadium dioxide (VO 2) film under-
goes the insulator-metal phase transition (IMPT) under heat-
ing,1,2mechanical stress,3applied electric field,4and optical
radiation.5IMPT is accompanied with an abrupt change in
the electrical resistance of VO 2film that is applied in bolom-
eters,6,7high-speed optical shutters,8,9modulators of tera-
hertz radiation,10memristors,11and metamaterials.12Near
the IMPT, the VO 2film is known to be a disordered hetero-
geneous system consisting of a mixture of high-resistance
insulating and low-resistance metal phases.13For such heter-
ogeneous systems, a large increase in the static dielectric
constant is observed at the percolation threshold due to
Maxwell-Wagner polarization.14,15As the dynamic charac-
teristics of devices based on VO 2films depend on their elec-
trical capacitance, the VO 2permittivity investigation at the
percolation threshold is of practical interest.
High-frequency (1010–1013Hz) permittivity of VO 2
films is usually measured by optical methods.16The
low-frequency (103–107Hz) permittivity is determined from
out-of-plane-type structures (sandwich type) impedance
measurements. With the measuring of VO 2films impedance,
the measurement resolution limit is caused by a low resist-ance of a sandwich structure at IMPT. For example, the re-
sistance of Metal/VO
2(90 nm)/Metal sandwich structure of
104lm2area can be less than 0.001 Xat IMPT. Such a low
resistance of the sandwich structure makes an experimental
measurement of electrical capacitance impossible. To over-
come this limitation, the high-resistance buffer layers areembedded into sandwich structures. In Si-sub/VO
2/Pd sand-
wich structure,17the Schottky barrier served as buffer layer,
and in n-Si-sub/HfO 2/VO 2/HfO 2/Ti/Au structure,18the HfO 2
layer placed under the metal electrodes played the same role.
In measurements for sandwich structures, the applied electric
field is perpendicular to the layers plane. Using the planarstructures in which the electric field is directed along the
VO
2layer, instead of sandwich structures, the film electricresistance in the metal state can be increased up to a few
Ohms. For example, the microstructure with a VO 2film of
0.1lm in thickness, 50 lm wide metal electrodes, and a
3lm interelectrode gap has a resistance of about 5 Xin the
metal state. While keeping the electrodes width constant, the
resistance of planar microstructure can be increased with
increasing the interelectrode gap width. However, in thiscase, the electrical capacitance of the microstructure will
also decrease. Planar impedance spectroscopy,
19in which
the electric field is applied parallel to the layer plane, wasused for measuring the electrical capacitance of the VO
2
layer at IMPT.20These results, however, raise doubts since
the physical interpretation of impedance measurementsrequired inductance to be added to the equivalent VO
2layer
circuit.
In this Letter, we present a method for measuring elec-
trical capacitance of the planar microstructure based on the
using of a standard resistor-capacitor two-terminal module
(RCM) that simulates the VO 2layer at IMPT. This method
allowed us to investigate the temperature dependence of
VO 2planar microstructures electrical capacitance near the
phase transition and to explain the obtained results withoutadding any inductance to the equivalent circuit.
20
VO 2films were grown in the vacuum chamber of unit
SOURCERER (Veeco-Ion Tech, Inc.) by the ion beamsputtering-deposition method on sapphire (0001) substrate at
821 K in the presence of O
2. The film crystal structure was
investigated by RHEED revealing polycrystalline VO 2in
monoclinic phase (PDF Card No. 44-0252). The film thick-
ness (h), determined with quartz crystal microbalance, was
90 nm. The resistance ratio at room temperature and atT¼358 K exceeded 3 orders of magnitude, indicating a good
film quality.
Shown in Fig. 1, three microstructures types with different
electrode widths Land interelectrode gaps A(Table I)w e r e
fabricated by using a typical photolithography and plasma
etching with freon-12. Measurements of electrical capacitancewere carried out at the frequency of 1 MHz using Agilent
B1500A semiconductor device parameter analyzer with
a)Author to whom correspondence should be addressed. Electronic mail:
aliev@isp.nsc.ru
0003-6951/2014/104(13)/132906/4/$30.00 VC2014 AIP Publishing LLC 104, 132906-1APPLIED PHYSICS LETTERS 104, 132906 (2014)
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129.120.242.61 On: Wed, 03 Dec 2014 19:28:11resonant-type Multi Frequency Capacitance Measurement Unit
B1520A MFCMU. Tungsten probes provided a contact to themicrostructures. Before measurements, the standard calibration
was performed to eliminate parasitic capacitances and induc-
tances: the phase correction, and correction with open and
shortened probes.
The complexity of experimental measurements was in a
simultaneous abrupt change in active and reactive compo-nents of microstructures impedance in a narrow temperature
range. In addition, with a low microstructures resistance near
IMPT, their electric capacitances were out of the measure-ment range of B1500A device.
21Therefore, to improve the
measurements accuracy and reliability, the RCM was used
consisting of a parallel variable capacitor and resistor [Fig.2(a)], which values of electrical capacitance Cpd and resist-
ance Rdoverlapped possible changes of microstructures
capacitances and resistances. Since the B1520A unit is of theresonant-type,
22an enhance in its operating stability was
achieved connecting the capacitor of 120 pF parallel to
probes [Fig. 2(b)]. The B1500A device readings in parallel
parameters "Cp-G" measurement mode,21when measuring
RCM, with capacitance value Cpd being fixed 120 pF, and
resistance value Rdbeing varied (simulation of the drop in
VO 2layer resistance at the percolation threshold), are pre-
sented in Fig. 3. It is seen that, with reducing resistance Rd,
fixed capacitance 120 pF changed according to the B1500Adevice readings, as if it decreased.
The electrical capacitance measurement technique was
in matching of B1500A device readings for the alternatelyconnected microstructure and RCM. At each temperature
point, with measuring the Rx(T) andCx(T) dependences, the
readings of B1500A device connected to the microstructurewere recorded. Then probe needles were switched from the
microstructure to the RCM, with RCM resistance set equal
to microstructure resistance at this temperature point,Rpd¼Rx(T) . Further, the RCM electrical capacitance Cpdwas tuned so as B1500A device readings to coincide with
these ones when the microstructure was connected. The
RCM electrical capacitance thus obtained was assumed to be
equal to the microstructure electrical capacitance,Cx(T)¼Cpd. The measurements were verified to be repro-
ducible by probes multiple switching from the microstruc-
ture to RCM. Moving from one temperature point to another,the temperature dependences of the microstructures resist-
ance and capacitance were obtained during the IMPT.
The temperature dependences of capacitance and resist-
ance for different microstructures types, measured at fre-
quency of 1 MHz are shown in Fig. 4. Sloping parts of
electrical capacitance in the range of 296–330 K were deter-mined, obviously, not by microstructures electrical capaci-
tance, but by the parasitic capacitance of B1500A probes and
RCM. This parasitic capacitance was about 2 pF being thesame for three types of microstructures. Using BETAFields
software, microstructures capacitances Cxat room tempera-
ture were calculated from their geometry and electric fielddistribution in microstructures (Table I). When calculated
relative permittivity e
VO2was taken to be 36 at room temper-
ature.18Indeed, as it turned out, the values of microstructures
capacitances did not exceed 70 fF, being negligible in com-
parison with parasitic capacitance. In the temperature range
of 330–337 K, the abrupt increase in microstructures electri-cal capacitances occurred by more than 4 orders of magni-
tude. The saturation of Cx(T) dependencies took place at
TABLE I. The microstructures electrical capacitances calculated and
measured.
No. A(lm)aL(lm) h(nm) Cxcal(fF)bCxexp(nF) d(nm)c
#1 3 35 90 27.6 6.33 7.1
#2 3 84 90 66.2 16.05 7.0
#3 56 100 90 29.2 25.3 /C210/C03446
aA, L, h —geometrical parameters of microstructures.
bCx cal,Cx exp—calculated ( T¼296 K, e¼36) and measured at T¼356 K
electrical capacitances.
cd—estimated gap width between metal clusters at the percolation threshold.
FIG. 2. Equivalent circuits: (a)—of resistor-capacitor module; (b)—of the
VO 2-microstructure and the capacitor of 120 pF connected in parallel.
Pr—tungsten probes. Rd,Cpd—variable resistor and capacitor of the
module.
FIG. 1. Microstructures types (highlighted): Ni/Au electrodes (yellow),
90 nm VO 2film (green), sapphire substrate (gray). Interelectrode gaps
3lm—for #1 and #2 types, 56 lm—for #3, and electrode widths 35, 84, and
100lm, respectively.
FIG. 3. Curve 1—B1500A device readings ( CandR) at the frequency of 1
MHz connected to the resistor-capacitor module with fixed capacitance
120 pF and variable resistance overlapping possible changes of microstruc-tures resistances. For example, curve 2—temperature dependences of resist-
ance for microstructure #1.132906-2 Aliev, Bortnikov, and Badmaeva Appl. Phys. Lett. 104, 132906 (2014)
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129.120.242.61 On: Wed, 03 Dec 2014 19:28:11temperatures above 337 K. Temperature dependences Cx(T) ,
as well as Rx(T) , were hysteretic.
Within the formal approach, it is necessary to assume that
a change in microstructure capacitance is determined by a
change in the VO 2film relative permittivity. The electrical ca-
pacitance of microstructure #1 increased from 27.6 fF to 6.33nF, i.e., more than 2.3 /C210
5. However, the experimentally
observed increase was by only the factor of 3 /C2103due to par-
asitic capacitance 2 pF. Similar ly, the capacitance of micro-
structure #2 increased by the factor of 2.4 /C2105and that of
microstructure #3—8.7 /C2102. To estimate a relativepermittivity change from the capa citance change, it is neces-
sary to calculate the electric field distribution in the microstruc-
ture. The BETAFields program calculations for microstructure
#1 are shown in Fig. 5. In order to obtain the capacitance
equal to the experimental one (6.33 nF), it was necessary
to take e¼2.2/C2108in calculations. In sandwich struc-
tures17,18Si-sub/VO 2/Pd and Si-sub/HfO 2/VO 2/HfO 2/Ti/Au,
the obtained VO 2dielectric constant value was of /C24105.I ti s
interesting to note that the capacitance of microstructure #3
cannot be represented as /C2419 (56 lm–3 lm) microstructures
#2 connected in series (taking into account the ratio of electro-
des widths).
The structural phase transition in VO 2single crystals is
known to be observed at the temperature of 341 K accom-
panied by an abrupt change in crystal resistivity,1with the
crystal system changing from monoclinic to tetragonal. The
low-temperature monoclinic phase exhibits insulating prop-
erties, and the high-temperature tetragonal phase is a metal.Structural phase transition is also observed in polycrystal-
line VO
2films.2The abrupt change in film resistivity at the
phase transition is explained in terms of the percolationtheory
14or the percolative-avalanche model.23With an
increasing temperature, the metallic phase fraction in the
film increases to form electrically connected metal clus-ters.
24When clusters sizes become comparable to a micro-
structure interelectrode gap the percolation occurs.
According to the theoretical concepts,14,15the "polarization
catastrophe" takes place at th e percolation threshold, when
the low-frequency dielectric constant tends to infinity. At
the percolation, the metal clusters in the film form anextended (fractal) surface, with a high surface area deter-
mining anomalous behavior of the electrical capacitance.
24
The VO 2film near the percolation point is schematically
represented in Fig. 6as two metal clusters, electrically con-
nected to the left and right electrodes. There is an insulat-
ing gap between the clusters (VO 2film in the insulating
state). The electric field is concentrated in the insulating
gap, and the capacitance of the structure is determined by
its width and interface area between the clusters. Since thefilm thickness is significantly smaller than the interelec-
trode gap (e.g., 0.09 lma n d3 lm for the microstructure
#1), we assume that the area of the interface between theclusters is a product of the clusters fractal boundary lengths
in surface plane of the film ( K) and in section plane ( H). In
this case, the electrical capacitance of the microstructure isdefined as
FIG. 5. The electric field distribution in the microstructure at room temperature (a) and near the phase transition (b). Interelectrode voltage was se t 10 mV.
FIG. 4. Temperature dependences of electrical capacitances Cxand resistan-
cesRxat the frequency of 1 MHz for (a)—#1, (b)—#2, and (c)—#3 micro-
structures types. Red dots—heating, blue—cooling. The dashed lines
represent anticipated capacitances behavior. The values of 27.6, 66.2, and
29.2 fF are Cxlevels calculated at room temperature. PP—percolation point.132906-3 Aliev, Bortnikov, and Badmaeva Appl. Phys. Lett. 104, 132906 (2014)
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129.120.242.61 On: Wed, 03 Dec 2014 19:28:11Cx¼e/C2e0/C2K/C2H
d; (1)
where
K¼L/C2A
2d; (2a)
H¼h/C2A
2d; (2b)
where Ais the interelectrode gap width, Lis the Ni/Au elec-
trode width, dis the average width of insulating gap between
the metal clusters, and e0is the vacuum permittivity.
Substituting experimental values of Cxand geometrical pa-
rameters ( L,h) into Eq. (1), insulating gap width dwas cal-
culated (Table I). Average gap width dis a physical
parameter characterizing the high surface area of metal clus-ters at the percolation threshold, and its value should be the
same for all microstructures types. Actually, the values of d
for microstructures #1 and #2 are almost the same, but theydiffer from the value obtained for microstructure #3. It
means that Eqs. (2a)and(2b)are incorrect for #3. The fractal
geometric objects are self-similar.
25For our microstructures,
the criterion for self-similarity is ratio h/A. This criterion is
significantly smaller for microstructure #3 than for #1 and
#2. Microstructure #3 would be comparable to #1 and #2, ifthe VO
2film thickness for #3 was equal to 1680 nm.
In this Letter, the anomalous electrical capacitance was
first investigated in planar microstructures with a VO 2layer
near the insulator-metal phase transition. The results of our
research work are of practical importance for the analysis of
the processes occurring in metamaterials12and terahertz
radiation modulators10based on VO 2films. Capacitance
measurements for planar microstructures were performed by
the technique using the two-terminal resistor-capacitor mod-ule that simulated the VO
2layer near the phase transition.Estimation of the relative permittivity obtained by the calcu-
lation of electric field distribution in the microstructure
revealed that eVO2reaches /C24108at the percolation threshold.
Anomalous electrical capacitance can be explained consider-ing the fractal structure of the metal clusters formed at the
phase transition.
The authors are grateful to V. A. Voronkovsky for his as-
sistance in data preprocessing, L. D. Pokrovsky for the films
RHEED measurements, and Y. A. Zhivodkov for his assis-tance in impedance measurements at the "Nanostructures"
Collective Use Center (ISP SB RAS, Novosibirsk).
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FIG. 6. The schematic representation of metal clusters structure in the VO 2
film at the phase transition. A—interelectrode gap width, L—Ni/Au elec-
trode width, h—VO 2film thickness.132906-4 Aliev, Bortnikov, and Badmaeva Appl. Phys. Lett. 104, 132906 (2014)
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129.120.242.61 On: Wed, 03 Dec 2014 19:28:11 |
1.4876769.pdf | Epoxidized Natural Rubber: Exploring the Potential of an
Old Elastomer
Leno Masciaa, Pietro Russob, Marino Lavorgnac, Letizia Verdolottic, Jane Clarkea,
Adriano Vignalid and Domenico Aciernod
aDepartment of Materials, Loughborough University, Loughborough LE11 3QL, UK
bInstitute of Chemistry and Technology of Polymers, Nati onal Council of Research, Via Campi Flegrei 34, 80078
Pozzuoli, Naples, Italy
cInstitute of Composite and Biomedical Materials, National Council of Research, P.le E. Fermi, 80055 Portici,
Naples, Italy
dDepartment of Chemical, Materials and Production
Engineering University of Naples Federico II P.le V.Tecchio, 80,
80125, Naples Italy
Abstract. A study was carried out to evaluate the efficiency of dodecyl succinic anhydride as a curing agent for
a commercial grade of natural rubber that had been epoxidized to approximately 50 %mol (ENR50). It was shown that the maximum achievable gel content for this system is about 87 - 88 %wt due to the presence of non-
functionalized species. The incorporation of unmodified natural rubber in the mix reduced the gel content in direct
correlation with the d ilution of the epoxidized component. Mixing the system, even under “mild” thermal conditions
induces rapid gelation due to the high functionality of EN R50. The catalytic effect of N,N-Dimethylbenzylamine
was confirmed by both thermal analysis and the curometer evaluations. A quantitative analysis of the latter data has
shown that mixing under severe conditions can lead to an increase in reactivity in the subsequent curing step.
Keywords: Epoxidized natural rubber, anhydrid e, OD Curometer, thermal analysis
PACS: 81.05.Lg, 81.70.Pg, 83.80.Jx
INTRODUCTION
Epoxidized natural rubber (ENR) has been known for so me time and is commercia lly available in different
grades, up to 50 mol% epoxidization level. Epoxidation of natural rubber (NR) can be carried out either in solution
or from the latex using specific amounts of peroxy formic acid to control the degree of conversion.
The presence of epoxy groups in the chain increases the pola rity, giving rise to enhanced adhesion characteristics
and oil resistance, but also to an increase in glass tran sition temperature up to -24 oC for systems epoxidized at 50%
level. Due to the small size of the oxirane ring ENR reta ins the cis 1,4 configuration of NR and can undergo strain
induced crystallisation, which is largely responsible for the high tensile strength and elongation, as well as a high
resistance to crack growth [1]. Furthermore, the epoxy groups sited along the polymer chains enhance the compatibility of ENR with polar polymers, such as polyvi nyl chloride and polyamides for the production of blends
[2].
Although conventional sulphur-based vulcanization, or peroxide curing, is normally used in industrial practice,
mainly because ENR is usually blended with other el astomers, researchers have evaluated the efficacy of
vulcanization achieved through esterifi cation reactions, using ENR with differe nt epoxide content and dodeca nedioic
acid as curing agent [4]
ENR elastomers are expected to play an important role for the development of biodegradable elastomers due to
the large number of epoxy groups along the chain, which are capable of being converted to vicinal di-hydroxyl units.
At 50 % epoxidization this would give a nominal alternating copolymer of trans-polysoprene and methyl oxy-butene, as shown in Figure 1. It can be expected that, in combination with biodegradable polymers and/or
Times of Polymers (TOP) and Composites 2014
AIP Conf. Proc. 1599, 26-29 (2014); doi: 10.1063/1.4876769
© 2014 AIP Publishing LLC 978-0-7354-1233-0/$30.00
26
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220.225.230.107 On: Fri, 16 May 2014 06:37:41biodegradable fillers, ENR can be induced to undergo extensive chain scission through the formation of aldehyde
groups, which is assisted by the presen ce of tertiary H atoms attached to the same C atom. Some studies along these
lines have already been report ed involving the use of poly (caprolactone) and chitosan, which can both be grafted on
the ENR chains through reactions with the epoxy groups [5,6].
In this paper the authors examine th e use of dodecyl succinic anhydride (D DSA) as a cross linking agent for
ENR. The pendant dodecyl segments from the DDSA present in the resulting cr oss-links are expected to provide
also internal plasticization, through a sc reening effect on polar groups within th e chains. The groups that are likely to
be found in the cross-links are shown in Figure 1.
FIGURE 1 . Left. Structure of repeating units in Epoxidized ENR at 50mol%. Right: Cross-links formed from reactions
between epoxy groups in ENR and dodecyl succinic anhydride.
EXPERIMENTAL
Materials
Epoxidized Natural Rubber (Epoxyprene 50) and Natural Rubber (SMR CV 60) were donated by the Tun Abdul
Razak Research Centre, Dodecyl succinic anhydride (DDSA) and N,N-Dimethylbe nzylamine (DMBA) were
obtained from Sigma-Aldrich.
Mixing procedure
The amount of DDSA (13 %wt) used was calculated to produce one cross-link per 100 C atoms in the backbone
of the polymer chains. An accelerator for the esterification reactions, DMBA, wa s used at 2 parts per hundred parts
(polymer + anhydride) in all cases. Th e DMBA was premixed with amorphous s ilica powder, at 1: 0.7 weight ratio,
to facilitate handling of this liquid during the preparation of the blends. With the ultimate aim to produce TPV type
systems, partially pre-cured systems were prepared by melt mixing the components, giving a total weight of 50 g, in
a Haake Rheomix laboratory internal mixer fitted, with Banbury rotors, at 160oC and 80 rpm and a total mixing
cycle of 15 minutes. An ad-hoc mix was produced at 80 oC and 80 rpm over 10 minutes in order to examine the
effect of a “mild” thermal history in the mixi ng stage of the prepar ation of the reactive.
Characterization techniques
A Wallace precision cure analyzer was used to study the po st-mix curing behaviour of systems by monitoring the
torque evolution with respect to time at 200oC with 1.7 Hz frequency and 0.44 strain setting. This procedure was
used to determine the residual curability of the mixes as a means of estimating the additional vulcanization
requirements to complete the reactions.
Since the increase in modulus during cu ring is proportional to the rate of cross-linking reactions, the process can
be described by the following equation:
ܩሺ௧ሻൌܩ ሾܩஶെܩሿ൫1െ݁ିఏ௧൯, which can be re-written as ீಮିீ
ீಮିீሺሻൌ݁ఏ௧ …………..Equ. 1
27
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220.225.230.107 On: Fri, 16 May 2014 06:37:41where G(t)= shear modulus at time t, G∞= shear modulus at full reaction, Θ = reactivity factor for curing
reactions, G0= shear modulus at t = 0.
Since the shear modulus G is directly proportional to the torque ( Γ), measured in the curing experiments, a plot
of logሺ்ಮି்
்ಮି்ሺሻሻ against ‘time’ would yield a linear relationship with the gradient of the curve corresponding to the
reactivity factor ഇ
మ.యబయ. The term Γ∞ refers to the torque at th e plateau (full reaction) in the torque-time curve, while
Γ(t) is the torque at time t.
Solvent extractions, utilizing boiling xylene, were used to determine the gel content of the blends after mixing
without any further thermal treatment. As xylene is a suitable solvent also for dissolving all individual components
i.e. ENR, DDSA and NR, it can be pres umed that the resultant gel content only consists of insoluble cross-linked
DDSA/ENR, considering that the amounts of silica and accelerator used are small and within the expected
experimental error.
A Mettler Toledo DSC 1 apparatus in nitrogen atmosphere was used to produce thermograms at different heating
rates for samples mixed at 160 °C.
RESULTS AND DISCUSSION
The gel content of samples mixed under mild conditions was around 81 – 83 % and up to 88 % for samples
mixed under sever thermal conditions. The gel content was re duced with the addition of natural rubber in proportion
to the concentration, which indicated that the formation of the gel was entirely due to cross-links produced from the
reactions with the anhydride, without any significan t contribution by collateral free radical reactions.
In Figure 2 are shown semi-logarithm plots for the evolution of the normalized torque for samples produced
under “severe” thermal conditions. These confirm the valid ity of the relationship for the evolution of the shear
modulus represented by equ.1 and show that the reactivity parameter Θ increases by approximately 30 % with the
addition of the DMBA catalyst. Similar results were obtained for the samples produced under “mild” thermal
conditions and have displayed a reduction in reactivity by about 20 % relativel y to the values obtained for mixes
produced under “severe” conditions.
FIGURE 2 . Plot of ܗܔሺಮି
ಮିሺሻሻ against time for tests at 200oCfor samples prepared under severe mixing conditions
In Figure 3 are shown the DSC thermograms for scans carried out at different heating rates on samples prepared
under “severe” thermal conditions. Again these show the cata lytic effect of the DMBA a dditive. In this case it was 00.20.40.60.811.21.41.61.8
0 500 1000 1500 2000Log(T∞/(T∞‐T(t))
Time(seconds)93ENR/7DDSA
93ENR/7DDSA (withoutDMBA)
28
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220.225.230.107 On: Fri, 16 May 2014 06:37:41difficult to quantify the effect of the DMBA due to the occurrence of extensive degradation reactions at the upper
side of the thermogram. This aspect is under scrutiny for future work in this area.
FIGURE 3 . DSC thermograms for samples produced under “sever e” mixing conditions, obtained with scans at 1 and 5oC/min for
both systems (i.e. with and without DMBA catalyst).
CONCLUSION
Mixtures of epoxidized natural rubber (ENR50) and dodecyl succinic anhydride (DDSA) were produced in a
Haake rheometer in proportions that would give 1 cross-link for every 100 C atoms in the backbone of the polymer
chains at full esterification. For the mixing conditions used in the preparation of the samples the gel content was found to be in the range 81 – 88 w%. The reactivity factor, θ, which is synonymous with the rate constant for the
curing reactions, was obtained from plots of
logሺ்ಮି்
்ಮି்ሺሻ against time. Higher θ values (around 30 %) were
obtained for mixes prod uced under “severe” thermal conditions than the corresponding systems that received a
“mild” thermal treatment and, irrespective of the thermal cond itions used in the preparing the mixture, an increase of
about 20 -25 % in reactiv ity was observed by the addition of DBMA as an accelerator for the curing reactions. The
catalytic effect of DMBA was confir med by the thermal analysis study.
REFERENCES
1. S. Toki, T. Fujimaki, M. Okuyama Polymer , 41, 5423 (2000).
2. M. Narathichat, C. Kummerlöwe, N. Vennemann, K. Sahakaro, C. Nakason, Adv. Polym. Techn . 3, 118 (2012).
3. S. Mukhopadhyay, S.K. De, J. Appl. Polym. Sci. , 42, 2773 (1991).
4. M. Pire, S. Norvez, I. Iliopoul os, B.L. Rossignol, L. Leibler, Polymer , 52, 5243 (2011).
5. Joy K. Mishra, Y.-W. Chang, D.-K. Kim, Materials Letters , 61, 3551 (2007).
6. M.R.H. Mas Haris, G. Raju, eXPRESS Polymer Letters , 8, 85 (2013).
29
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220.225.230.107 On: Fri, 16 May 2014 06:37:41AIP
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1.4893986.pdf | Type I and type II band alignments in ZnO/MgZnO bilayer films
Arpana Agrawal, Tanveer Ahmad Dar, D. M. Phase, and Pratima Sen
Citation: Applied Physics Letters 105, 081603 (2014); doi: 10.1063/1.4893986
View online: http://dx.doi.org/10.1063/1.4893986
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/8?ver=pdfcov
Published by the AIP Publishing
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147.188.128.74 On: Tue, 26 Aug 2014 04:54:57Type I and type II band alignments in ZnO/MgZnO bilayer films
Arpana Agrawal,1,a)Tanveer Ahmad Dar,1D. M. Phase,2and Pratima Sen1
1School of Physics, Devi Ahilya University, Takshashila Campus, Indore 452001, India
2UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore 452001, India
(Received 28 May 2014; accepted 13 August 2014; published online 25 August 2014)
We report the change in the type of band alignments due to an increase in the dopant (Mg)
concentration in pulsed laser deposited ZnO/MgZnO bilayer film. The band offset measurements
were carried out from the core level shifts as well as valence band maxima in the single as well asthe bilayer films. The change in the type of band alignment is attributed to the surface enrichment
of Mg at the heterojunction.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4893986 ]
Semiconductor heterostructures (SHs) are the key ele-
ments for making optoelectronic devices. The dynamics of
charge carriers in the SHs depends on the potential barrier
heights experienced by electrons/holes at the heterojunction.The conduction/valence band offset at the heterojunction
being the measure of the potential barrier. In type I SHs, both
electrons and holes experience the presence of the potentialbarrier, while in type II structure either of the charge carrier
types experiences the potential barrier at the heterojunction.
Suitability of type I structure is well established in designingsemiconductor lasers, while type II structure can be a good
candidate material for making avalanche photodetectors
where only one type of carrier acceleration is preferred.
1For
optical communication systems, InGaAsP SHs are designed
in the wavelength range of 1.33–1.55 lm, while in optical
memory storage devices the storage capacity can be increasedmanifold if the heterostructures are designed at shorter wave-
lengths. Accordingly, ZnO based heterostructures can be pre-
ferred because of its wide band gap (3.3 eV) and largeexciton binding energy (60 meV).
2–6
It is well known that Cd doping in ZnO causes lowering
of the band gap,7while Mg doping gives rise to an increase
in the band gap.8,9MgZnO/ZnO/MgZnO may be useful as
SHs for optoelectronic devices working at shorter wave-
lengths. Recently, Zhang et al.10reported type I band align-
ment in MgZnO/ZnO heterojunctions. The same group has
also studied the Mg composition dependent band offsets of
MgZnO/ZnO heterojunctions prepared by plasma-assistedmolecular beam epitaxy (PAMBE) method and found a strad-
dling (type I) structure.
11Band offset measurement and mag-
netotransport studies in TiO 2/LaSrMnO 3heterostructure have
also been reported.12Very recently, we have reported band
bowing as well as the observation of magnetoresistance in
MgZnO films.9,13
In view of the above discussion, we report the experi-
mental results of band offset measurements in pulsed laser
deposited ZnO/MgZnO heterostructures. We have intention-ally chosen moderate (9%) and high (21%) Mg concentration
in our studies and found that at lower concentration, the band
offset exhibit type I band alignment, while at higher concen-tration the type II band alignment is observed. The present
study may be of significant usefulness in making ZnO/MgZnO based monolithic circuits where one needs same ma-
terial for making various devices on the same chip.
Five samples, namely, three Mg
XZn1/C0XO( x¼0.0, 0.09,
and 0.21) films and two ZnO(2–3 nm)/Mg XZn1/C0XO
(300–400 nm) (x ¼0.09 and 0.21) bilayers were grown on
quartz substrate by pulsed laser ablation technique using KrF
excimer laser ( k¼248 nm) from sintered ceramic targets of
ZnO and MgZnO. The details of deposition are given else-
where.13Structural analysis and energy band gap estimation
have been performed using x-ray diffraction (XRD) techniqueand ultraviolet-visible spectroscopy (UV-Vis), respectively.
The core levels (CLs) have been explored using x-ray photo-
electron spectroscopy (XPS) with Al-K a(k¼0.834 nm) lab
source whereas the valence levels are studied via valence
band spectroscopy (VBS) at 41 eV using photoelectron beam-
line at Indus I synchrotron radiation source of Raja RamannaCenter for Advanced Technology (RRCAT), Indore (India).
As XPS is a surface sensitive technique with a low penetration
depth, we keep the upper layer thinner (2–3 nm) for the pur-pose of probing the heterojunction. Prior to XPS measure-
ments, all the samples were subjected to a surface clean
procedure by Ar
þsputtering for 5 min at 500 V. In order to
check the damage that might occurred due to Arþsputtering,
we had taken the XPS data before and after the sputtering and
found that this process resulted only in the reduction of C con-tent accumulated on the film surface due to the exposure of
the samples in the atmosphere. The estimation of energy reso-
lution for the VBS measurements dependent on photon energywas done by aligning the Fermi edge of the sample with
respect to the Fermi edge of Au/Ag foil and was found to be
/C250.05 eV, whereas for the XPS all the CLs were fitted using
Touguard background and Voigt profile and were carefully
corrected by a correction factor arising from the C 1 s
(284.6 eV) CL shift. We have also performed the electricaltransport measurements (Resistance vs Voltage (R-V)) pref-
erably at low temperature (5 K). This issue will be discussed
later in the manuscript.
Fig.1(a)exhibits XRD patterns of the samples (plotted
in logarithmic scale) to identify any small peak that may
arise due to the impurity phases. Appearance of the domi-nant (002) peak along with the absence of peak that corre-
sponds to either MgO or any other impurity confirms the
single phase of the grown films with wurtzite structure ofZnO.
a)Electronic mail: agrawal.arpana01@gmail.com
0003-6951/2014/105(8)/081603/4/$30.00 VC2014 AIP Publishing LLC 105, 081603-1APPLIED PHYSICS LETTERS 105, 081603 (2014)
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147.188.128.74 On: Tue, 26 Aug 2014 04:54:57The energy band gap of the samples was calculated
using UV-Vis spectroscopy. Figure 1(b)displays ( ah/C23)2ver-
sus (h /C23) plot of pure ZnO and MgZnO films where (h /C23)i s
the incident energy and ais the absorption coefficient. The
band gaps obtained by extrapolating the spectrum to
(ah/C23)¼0 for pure ZnO, Mg 0.09Zn0.91O, and Mg 0.21Zn0.79O
films were found to be 3.24, 3.37, and 3.49 eV, respectively.
The blue shift in energy band gap subsequent to Mg doping
can be attributed to lower electronegativity of Mg comparedto Zn.
13Such an increase in band gap with increasing Mg
concentrations has also been reported by Ohtomo et al.8
We now focus our attention on band offset measurements
at ZnO/MgZnO heterojunction using the method suggested by
Kraut et al.14Here, we need to determine the shifts of CLs in
single and bilayer films as well as the valence band maxima(VBM) of the single layers. The detailed narrower scan of Zn
and Mg 2p-CL spectra were recorded using XPS technique.
Figure 2shows the Mg 2p-CL spectra of Mg
XZn1/C0XOfi l m s
and ZnO/Mg XZn1/C0XO heterostructures (x ¼0.09 and 0.21).
The CL peak positions are given in Table I.F r o mF i g u r e 2
and the CL values given in Table I, one can notice that the
Mg 2p-CLs get shifted to higher energy in the bilayer films ascompared to their corresponding MgZnO films. Similarly, the
detailed narrower scan of Zn 2p-CL spectra shown in Figure 3
for pure ZnO and ZnO/Mg XZn1/C0XO heterostructures
(x¼0.09 and 0.21) exhibits shift in each film (for Zn 2p-CLs
of Mg XZn1/C0XO( x¼0.09 and 0.21) single layer films refer to
Ref. 15). These CL shifts should be carefully understood in
single as well as bilayer films while determining the valence
band offset. It is interesting to note that Zn 2p-CL occurringat 1021.66 eV in pure ZnO film shifts to higher energy
(1021.76 and 1021.91 eV) in 9% Mg doped single and bilayer
films, respectively. In case of 21% Mg doped films, the Zn2p-CL peak rises to higher energy (1021.93 eV) in single layer
film whereas it lowers down to 1021.56 eV in the bilayer film.
Such an unusual behavior can be attributed to the occurrenceof surface enrichment in the bilayer film. At the interface of
the films, due to the change in the chemical environment,
some random distribution of Mg/Zn takes place leading tochange in the potential due to the neighbouring atoms. This
will significantly affect the position of the CLs in the bilayer
films.
16,17Such a surface enrichment effect at the interface
may complicate the assignment of the VBM as well as the
CLs of the bilayer films as their measurement gives rise to an
averaged value. However, in case of single layer films, we donot consider surface enrichment effect.
The VBM is determined by linear extrapolation of lead-
ing edge of valence band spectra (shown in Figure 4) (for
VBS of ZnO/Mg
XZn1/C0XO( x¼0.09 and 0.21) bilayer films
refer to Ref. 15). Experimentally observed VBM values
(Table I) show that VBM shifts downwards as the Mg con-
tent increases. It is well known that the valence band is
mainly contributed by the O 2p and Zn 3d states. Because of
the weakened p-d coupling resulting from the absence of Mg3d electrons, the VBM in Mg
XZn1/C0XO is pulled down with
respect to that of ZnO.18This effect can be more promi-
nently seen in the MgZnO sample doped with larger Mgconcentration.
Considering the shift of the CLs of Mg and Zn in the
bilayers and their VBM, the valence band offset DE
vvalue
has been calculated using the following relation:14
DEv¼DECLþEZnO
Zn2p/C0EZnO
VBM/C16/C17
/C0EMgZnO
Mg2p/C0EMgZnO
VBM/C16/C17
:
(1)FIG. 1. (a) X-ray diffraction pattern of grown samples; (i), (ii), and (iii)
show the pattern of Mg XZn1/C0XO for x ¼0.0, 0.09, and 0.21; and (iv) and (v)
show the pattern of ZnO/Mg XZn1/C0XO( x¼0.09 and 0.21) heterostructures,
respectively; (b) ( ah/C23)2versus h /C23plot of the grown films.
FIG. 2. Detailed narrower scan of Mg 2p-CL in the grown samples; (a) and
(b) show the Mg 2p-CL in Mg 0.09Zn0.91O and ZnO/Mg 0.09Zn0.91O samples
and (c) and (d) shows the Mg 2p-CL in Mg 0.21Zn0.79O and ZnO/
Mg0.21Zn0.79O samples.TABLE I. XPS CL and VBM positions in pure ZnO, Mg XZn1/C0XO( x¼0.09
and 0.21) films, and ZnO/Mg XZn1/C0XO( x¼0.09 and 0.21) heterostructures.
Sample State Binding energy (eV)
ZnO Zn 2p 1021.66
VBM 3.21
Mg0.09Zn0.91O Zn 2p 1021.76
Mg 2p 49.69
VBM 3.30
Mg0.21Zn0.79O Zn 2p 1021.93
Mg 2p 49.75
VBM 3.36
ZnO/Mg 0.09Zn0.91O Zn 2p 1021.91
Mg 2p 49.92
ZnO/Mg 0.21Zn0.79O Zn 2p 1021.56
Mg 2p 49.85081603-2 Agrawal et al. Appl. Phys. Lett. 105, 081603 (2014)
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147.188.128.74 On: Tue, 26 Aug 2014 04:54:57Here,DECLdenotes the energy separation between Mg 2p and
Zn 2p CL peaks in ZnO/Mg XZn1/C0XO heterojunction. The sec-
ond and third terms are the VBM energies with reference tothe CL peaks in pure ZnO and MgZnO films, respectively.
Substituting the peak positions of CLs and VBM (Table
I) in Eq. (1), the valence band offset DE
vis found to be
0.07 eV and 0.35 eV for ZnO/Mg 0.09Zn0.91O and ZnO/
Mg0.21Zn0.79O heterojunctions, respectively. In both the
cases, a positive value of DEvshows the possibility of hole
confinement at the heterojunction.
To explore the possibility of electron confinement, we
use the change in band gap due to Mg doping in the samplesand obtained the conduction band offset via the relation
7,19
DEc¼DEg/C0DEv; (2)
DEgbeing the energy band gap difference of Mg XZn1/C0XO
(x¼0.09 and 0.21) and ZnO films. From UV-Vis spectra,
DEgis found to be 0.13 eV and 0.25 eV for 9% and 21% Mg
doping, respectively. The corresponding values of DEcare
found to be þ0.06 eV and /C00.10 eV for ZnO/Mg 0.09Zn0.91O
and ZnO/Mg 0.21Zn0.79O heterojunctions, respectively. The
negative sign of DEcin the later case suggests that the con-
duction band of Mg 0.21Zn0.79O is at lower energy than that
of ZnO. The change in sign of DEcsignatures the different
types of band alignment in the grown SHs.The overall schematic of energy band alignments in
ZnO/Mg XZn1/C0XO( x¼0.09 and 0.21) heterojunctions using
the values of DEvandDEcis shown in Fig. 5(a). The striking
feature in Fig. 5(a)is: At 9% doping, the band alignment is
type I (straddling) structure (left) showing the possibility of
confinement of both electrons and holes, while at 21% dop-ing the band alignment is type II (straddling) structure (right)
and show that only hole will be confined at the heterojunc-
tion. We attribute the cause of this change to the surfaceenrichment of Mg at the heterojunction in 21% Mg doped
bilayer film. Previously, the MgZnO/ZnO bilayer films
grown by PAMBE exhibited type I band alignment for 10%,15%, and 20% Mg concentrations only.
11The present work
could have been extended for an additional data point to con-
solidate the concentration dependence of band alignmentwhich will be a part of our future work. In the present Letter,
we restrict ourselves to the observation of the change of the
type of band alignment and assign its probable cause in thesurface enrichment. The comparable values of band offsets
(DE
v¼0.07 eV and DEc¼0.06 eV) in ZnO/Mg 0.09Zn0.91O
suggest that the barrier height to transport electron across theheterojunction is slightly lower than that for hole, while in
ZnO/Mg
0.21Zn0.79O heterostructure only hole is confined
with larger barrier height ( /C250.35 eV).
We have carried out the R-T (Resistance vs temperature)
measurements in single layers of ZnO ( /C2564Xat 5 K) andFIG. 3. Detailed narrower scan of Zn
2p-CL in the grown samples; (a), (b),
and (c) represent the Zn 2p-CLs in
pure ZnO film and ZnO/Mg XZn1/C0XO
heterostructures (x ¼0.09 and 0.21),
respectively.
FIG. 4. Valence band spectra of the
films; (a), (b), and (c) show the valence
band spectra of Mg XZn1/C0XO( x¼0.0,
0.09, and 0.21) films, respectively.081603-3 Agrawal et al. Appl. Phys. Lett. 105, 081603 (2014)
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147.188.128.74 On: Tue, 26 Aug 2014 04:54:57Mg0.21Zn0.79O(/C2525023 Xat 5 K) films (not shown here)
and found that due to Mg doping, the resistance of the film
increases manifold.15We also observed that the resistance of
Mg0.21Zn0.79O single layer film is strongly temperature sen-
sitive, while the ZnO/Mg 0.21Zn0.79O bilayer as well as ZnO
single layer films show better stability towards the tempera-ture.
15In order to examine the role of band offset at the inter-
face, we have carried out R-V measurements at 5 K for both
positive as well as negative values of the applied potentialacross the junction of the bilayer film (Figure 5(b)). In pure
ZnO film, changing polarity of the field does not change theresistance, while in bilayer film the change in polarity of the
field causes increase/decrease in the resistance of the film.
This observation suggests that in one case (negative polarity,
say), the charge transport experiences potential barrier acrossthe interface while the potential barrier disappears for oppo-
site polarity and confirms the presence of the band offset at
the interface.
Fruitful discussions with Professor P. K. Sen from
S.G.S.I.T.S, Indore is thankfully acknowledged. The authors
are grateful to Dr. Mukul Gupta and Dr. R. Rawat fromUGC-DAE-CSR, Indore, for providing XRD and electric
transport measurement facilities. They are also thankful to
Mr. A. Wadikar for helping in XPS and VBS measurements.The financial supports from UGC-DAE CSR, Indore and
SERB, New Delhi are acknowledged herewith.
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15See supplementary material at http://dx.doi.org/10.1063/1.4893986 for Zn
2p-CLs of MgZnO (Mg ¼0.09, 0.21) single layer films, VBM of ZnO/
MgZnO (Mg ¼0.09, 0.21) bilayer films, and R-T data of ZnO, MgZnO,
and ZnO/MgZnO (Mg ¼0.21) films.
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Curr. Appl. Phys. 14, 171 (2014).
FIG. 5. (a) shows the schematic of energy band alignment of ZnO/
Mg XZn1/C0XO( x¼0.09 and 0.21) heterostructures; type I band alignment in
ZnO/Mg 0.09Zn0.91O heterostructure (left) and type II band alignment in
ZnO/Mg 0.21Zn0.79O heterostructure (right). The central part represents the
bands in the pure ZnO thin film; (b) shows the resistance Vs voltage meas-
urements in pure ZnO single layer and ZnO/Mg 0.21Zn0.79O bilayer films at
5K .081603-4 Agrawal et al. Appl. Phys. Lett. 105, 081603 (2014)
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1.4872795.pdf | Acetone sensor based on zinc oxide hexagonal tubes
Anita Hastir, Onkar Singh, Kanika Anand, and Ravi Chand Singh
Citation: AIP Conference Proceedings 1591, 898 (2014); doi: 10.1063/1.4872795
View online: http://dx.doi.org/10.1063/1.4872795
View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1591?ver=pdfcov
Published by the AIP Publishing
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128.112.200.107 On: Tue, 11 Aug 2015 12:50:17Acetone Sensor Based on Zinc Oxide Hexagonal Tubes
Anita Hastir *, Onkar Singh, Kanika Anand, and Ravi Chand Singh.
Department of Physics, Guru Nanak Dev University, A mritsar-143005, Punjab, India
*E-mail: anitahastir@gmail.com
Abstract. In this work hexagonal tubes of zinc oxide have be en synthesized by co-precipitation method. For stru ctural,
morphological, elemental and optical analysis synth esized powders were characterized by using x-ray di ffraction, field
emission scanning microscope, EDX, UV-visible and F TIR techniques. For acetone sensing thick films of zinc oxide
have been deposited on alumina substrate. The fabri cated sensors exhibited maximum sensing response to wards acetone
vapour at an optimum operating temperature of 400 oC.
Keywords: Gas sensors, Structure, Precipitation.
PACS: 07.07.Df, 61.66.-f, 81.20.F
INTRODUCTION
Volatile organic compounds (VOC) are considered
to be the most unsafe indoor pollutants, whose
inhalation may be critically harmful to the human
body. Among the VOCs, acetone is widely used, it is
colourless flammable liquid used as a solvent, an
extracting reagent in research laboratories, in nai l
polish removers, paints, varnishes, adhesives, etc.
Acetone evaporates readily and its high concentrati on
above 1000 ppm in the air may cause irritation of e yes,
throat and nausea [1]. In diabetes, acetone can be used
as biomarker since it can be found in the exhaled
breath of the diabetes patient [2]. Metal oxide
semiconductors have been popular candidates for
sensor materials for the past several years. For ga s
sensing application, zinc oxide has been proven a
promising material and it is eco-friendly too [3]. The
gas sensors are based on the mechanism of interacti on
between the test gas molecules and adsorbed oxygen
molecules on the metal oxide surface. The amount of
absorbed oxygen is strongly dependent on morphology
and structure of sensing material [4].
In this present work we are reporting the acetone
sensors based on zinc oxide hexagonal tubes. The
sensing response of synthesized zinc oxide thick fi lms
towards acetone vapour at different temperatures ha s
been investigated.
EXPERIMENTAL
For synthesis of zinc oxide powder we have
adopted co-precipitation technique. To get precipit ate of zinc hydroxide, 0.2 M zinc acetate was dissolved in
distilled water and ammonia solution was added drop
wise with constant stirring at room temperature. Th e
pH of the solution had been fixed to 8 to get a
particular morphology. The precipitates thus obtain ed
were filtered and washed thoroughly with distilled
water. Drying of powder was done in an oven at a
temperature of 120 oC. The dried powder was ground
and calcined in a furnace at a temperature of 500 oC for
three hours.
The crystal structure of the prepared powder was
characterized by powder x-ray diffraction (XRD) usi ng
Cu-Kα radiation with Shimadzu 7000 Diffractometer
system. Morphology of the synthesized samples was
analyzed by field emission scanning microscope
(FESEM) with Carl Zeiss SUPRA 55. Energy
dispersive X-ray analysis (EDX) was employed to
determine elemental analysis of powder sample.
Optical and FTIR studies have been investigated by
using Shimadzu UV-2450 spectrophotometer and
C92035 Perkin Elmer Spectrometer respectively.
For sensing measurements we have used a home
built apparatus consisting of potentiometeric
arrangement, a 40L test chamber in which a sample
holder, a small temperature controlled oven, and a
mixing fan was installed. Variation of real time
voltage signal across a resistance connected in ser ies
with a sensor was recorded with Keithley Data
Acquisition Module KUSB-3100 connected to a
computer, reported elsewhere [5]. The magnitude of
sensing response was determined as Ra/Rg, where Ra
and Rg are the resistances of sensor in air ambienc e
and air-gas mixture, respectively.
Solid State Physics
AIP Conf. Proc. 1591, 898-900 (2014); doi: 10.1063/1.4872795
© 2014 AIP Publishing LLC 978-0-7354-1225-5/$30.00
898
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128.112.200.107 On: Tue, 11 Aug 2015 12:50:17RESULTS AND DISCUSSIONS
XRD Analysis
The xrd pattern of prepared zinc oxide powder is
shown in Fig 1. The peaks obtained were compared
with standard data confirming the hexagonal wurtzit e
structure of zinc oxide with no impurity phase. Sha rp
peaks are obtained showing highly crystalline natur e
of synthesized sample.
20 30 40 50 60 70 80 (202) (004) (201) (112) (200) (103) (110) (102) (101) (002) (100) Intensity (a.u.)
2θ(D egree s)
FIGURE 1. X-ray diffraction pattern of zinc oxide powder.
FESEM & EDX Analysis
At room temperature and pH 8 of the solution we
have got hexagonal tubes of zinc oxide. The driving
force for the one dimensional hexagonal tubes is th e
decrease in its Gibbs free energy because of low
supersaturation. Figure 2(a) shows FESEM image of
the prepared zinc oxide powder. It is clear from th e
image that the zinc oxide has morphed into hexagona l
tube like structures. Figure 2(b) shows the element al
analysis of synthesized sample which indicates the
purity of synthesized zinc oxide. The elements pres ent
are zinc and oxygen with no other impurities.
FIGURE 2(a). FESEM image of synthesized zinc oxide.
FIGURE 2(b). EDX image of synthesized zinc oxide.
Optical Properties
Fig. 3(a) shows the plot of absorbance as a functio n of
wavelength, where the maximum absorption was
observed at wavelength of 375 nm. From Fig 3(b) the
calculated optical band gap of zinc oxide is 3.0 eV ,
which indicates the semiconductor behaviour of
synthesized zinc oxide.
300 400 500 600 700 0.00 0.04 0.08 Absorbance (a.u)
Wavelength (nm) 375nm
2.0 2.4 2.8 3.2 0.00 0.04 0.08 0.12
hν (eV) Eg = 3eV (αhν)2
3(a) 3(b)
FIGURE 3. (a) Absorbance Vs wavelength (b) Absorption
coefficient square Vs photon energy for zinc oxide.
FTIR Analysis
The FTIR spectrum of the prepared zinc oxide
shown in Fig. 4 indicates the Zn-O absorption band at
491.10 cm -1.The peaks at 3401.94 cm -1 and 1508.95
cm -1 corresponds to the O-H and the C=O stretching
mode, probably due to atmospheric moisture and
carbon dioxide respectively. V. Parthasarathi and c o-
workers have reported the similar results [6].
4 0 0 0 3 5 0 0 3 0 0 0 2 5 0 0 2 0 0 0 1 5 0 0 1 0 0 0 5 0 0 % Transmittance
W a v e n u m b e r ( c m -1 )
FIGURE 4. FTIR spectra of synthesized zinc oxide.
899
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Sensing properties
Zinc oxide being an n-type metal-oxide shows a
decrease in resistance with the injection of aceton e
vapour into a test chamber. This is because when zi nc
oxide sensor is exposed to air, oxygen molecules
adsorb on the surface of the materials to form O 2-, O -,
O2- ions by capturing electrons from the conduction
band. This results in high resistance in air. On
exposure of metal oxide sensors to the reducing gas es,
the gas molecules react with adsorbed oxygen and as a
result release the captured electrons to the conduc tion
band. This increases the conductivity of metal oxid e
based sensors. The sensing response of the zinc oxi de
towards 250 ppm of acetone vapour was checked at
various temperatures in order to determine the
optimum operating temperature as shown in Fig. 5. I t
is found from the figure that the maximum sensing
response is observed at an operating temperature of
400 oC. The low response at low temperature is
explained as the reaction rate between absorbed
oxygen species on the surface and the acetone vapou r
under test is low, which is due to the high activat ion
energy of the surface reaction. At an optimum
operable temperature, a large number of gas molecul es
possess required energy, to overcome the potential
barrier and react with adsorbed oxygen resulting in
change in conductance of sensing element. At higher
temperatures the absorbed oxygen may desorbs from
the surface resulting in decrease of sensing respon se.
Figure 6 shows the sensing response of zinc oxide
thick film towards 250 ppm of acetone vapour at an
operating temperature of 400 oC. The sensor shows a
maximum sensing response of 10 with very quick
response time of 4 s and a fast recovery time of 25 s.
The reason for significantly higher sensing respons e of
zinc oxide thick films towards acetone is high surf ace
to volume ratio of hexagonal tubular morphology.
200 250 300 350 400 450 0246810 12 Sensing Response
Operating Temperature
FIGURE 5. Sensing response Vs Operating temperature for
zinc oxide thick film for 250 ppm of acetone vapour . -10 0 10 20 30 40 50 60 70 80 90 100 110 120 0246810 Sensing Response
Time (sec) Gas in Gas Out
FIGURE 6. Sensing response versus time for zinc oxide
thick film to 250 ppm of acetone at 400 oC.
CONCLUSION
In conclusion, we have successfully synthesized
hexagonal tubular shaped zinc oxide micro-crystals by
co-precipitation technique. XRD results confirmed t he
hexagonal wurzite structure of zinc oxide. From
optical properties we determine the band gap of 3.0 eV
with the maximum absorption at 375nm wavelength.
The prepared zinc oxide sensor showed maximum
sensing response towards acetone vapour at an
operating temperature of 400 oC with a quick response
time and a fast recovery time of 4 and 25 s
respectively.
ACKNOWLEDGMENTS
One of the authors Ms. Anita Hastir would like to
thanks Department of Science & Technology for
awarding INSPIRE Fellowship.
REFERENCES
1. N. H. Al-Hardana, M. J. Abdullahb and A. Abdul Aziz,
Appl. Surf. Sci. 270 , 480-485 (2013).
2. E. H. Oh, H. S. Song and T. H. Park, Enzyme Microb
Technol 48 , 427-437 (2011).
3. P. Mitra, A. P. Chatterjee and H. S. Maiti, Mater. Lett.
35, 33 (1998).
4. O. Singh, M. P. Singh, N. Kohli and R.C.Singh, Sens.
Act. B, 166-167 , 438-443 (2012).
5. O. Singh and R. C. Singh, Mat. Res. Bull. 47 , 557-561
(2012).
6. V. Parthasarathi and G. Thilagavathi, Int Pharm Pharm
Sci. 3, 392-398 (2011).
900
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1.4893647.pdf | An interchangeable scanning Hall probe/scanning SQUID microscope
Chiu-Chun Tang, Hui-Ting Lin, Sing-Lin Wu, Tse-Jun Chen, M. J. Wang, D. C. Ling, C. C. Chi, and Jeng-Chung
Chen
Citation: Review of Scientific Instruments 85, 083707 (2014); doi: 10.1063/1.4893647
View online: http://dx.doi.org/10.1063/1.4893647
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/8?ver=pdfcov
Published by the AIP Publishing
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130.159.70.209 On: Sun, 14 Dec 2014 16:49:57REVIEW OF SCIENTIFIC INSTRUMENTS 85, 083707 (2014)
An interchangeable scanning Hall probe/scanning SQUID microscope
Chiu-Chun Tang,1Hui-Ting Lin,1Sing-Lin Wu,1Tse-Jun Chen,2M. J. Wang,2D. C. Ling,3
C. C. Chi,1,4and Jeng-Chung Chen1,4
1Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
2Institute of Astronomy and Astrophysics, Academia Sinica, Taipei 10617, Taiwan
3Department of Physics, Tamkang University, Tamsui Dist., New Taipei City 25137, Taiwan
4Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University,
Hsinchu 30013, Taiwan
(Received 8 April 2014; accepted 11 August 2014; published online 26 August 2014)
We have constructed a scanning probe microscope for magnetic imaging, which can function as a
scanning Hall probe microscope (SHPM) and as a scanning SQUID microscope (SSM). The scan-
ning scheme, applicable to SHPM and SSM, consists of a mechanical positioning (sub) micron-XYstage and a flexible direct contact to the sample without a feedback control system for the Z-axis.
With the interchangeable capability of operating two distinct scanning modes, our microscope can
incorporate the advantageous functionalities of the SHPM and SSM with large scan range up to mil-limeter, high spatial resolution ( ≤4μm), and high field sensitivity in a wide range of temperature
(4.2 K-300 K) and magnetic field (10
−7T-1 T). To demonstrate the capabilities of the system, we
present magnetic images scanned with SHPM and SSM, including a RbFeB magnet and a nickel gridpattern at room temperature, surface magnetic domain structures of a La
2/3Ca1/3MnO3thin film at
77 K, and superconducting vortices in a striped niobium film at 4.2 K. © 2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4893647 ]
I. INTRODUCTION
A variety of microscopies for imaging micron or sub-
micron magnetic structures have been developed, including
scanning electron microscopy,1magneto optics microscopy,2
magnetic force microscopy,3scanning Hall probe microscopy
(SHPM),4and scanning superconducting quantum interfer-
ence device (SQUID) microscopy (SSM).5–8Among these
imaging techniques, SHPM and SSM are known as highly
sensitive and non-invasive instruments to probe local (sub)
micron-sized surface magnetic profiles.9
SHPM and SSM share several common characteristics in
operations. Both microscopies incorporate a magnetometer,
a SQUID sensor for SMM, and a miniature Hall-bar sensorfor SHPM, which is placed in close proximity to the sample
and is raster-scanned over the sample surface by means of a
dedicated scanner. The spatial images of magnetic features onthe sample surface are obtained by recording the output signal
of sensor with its local registration.
For the operation of a conventional SHPM system, a
feedback technique is often used to maintain a close con-
tact between the Hall probe and the sample, e.g., scan-
ning tunneling microscopy (STM)
4,10or atomic force mi-
croscopy (AFM).11,12Both the STM- and AFM-tracking SH-
PMs require complicated electronic circuit, a sophisticated
Hall probe, and delicate operations. In contrast, SSM can be
functioned in a mechanical scanning scheme without a feed-
back control system.5,13,14
The spatial resolution of SHPM, which is about ≤1μm
in most of the designs as defined by the size of conductive
channels on Hall junctions,4,10is in principle limited by the
active region of the Hall cross and by the separation between
the probe and the sample surface rather than by the scanningtechniques. Alternatively, the spatial resolution of SSM is lim-
ited to the size of the pick-up loops; the line-width of the pick-up loops cannot be smaller than the penetration depth of the
superconducting material. Although a pick-up loop made of
Al and Nb less than 1 μm has been lithographically fabri-
cated, the field sensitivity of the small probe is greatly de-
graded and accompanied with undesirable hysteresis.
15
SSM is currently the most sensitive magnetic field imag-
ing microscopy.9The SQUID sensor measures local magnetic
flux through a micron-sized pick-up loop and yields superiorfield resolution of ∼10
−10T/Hz1/2.5,13Nb-based SQUID of-
fers sensitivity of one order of magnitude better than High-
TcSQUIDs with equivalent spatial resolution and is more
commonly used in SSM for its reliable junction quality and
good SQUID performance. Nevertheless, the SQUID sensor
used for SSM has to be kept at a stable temperature suffi-ciently below its superconducting transition temperature T
c,
which restricts the operation of the Nb-based SSM at a cryo-
genic temperature below 7 K. On the other hand, the perfor-mance of a semiconductor Hall probe, although inferior to
SQUID in field sensitivity, is relatively insensitive to temper-
ature changes in a wide temperature range from above roomtemperature to the lowest reachable temperature.
To date, much effort has been devoted to improving the
functionalities of SHPM and SSM separately.
9,16–21From
a practical point view, an instrument capable of operating
both SSM and SHPM in one system would be very de-sirable. In this paper, we demonstrate a feasible scheme
of an interchangeable SHPM-SSM system, which holds the
advantageous functionalities of both microscopes. Our de-signs accommodate several merits for magnetic imaging:
First, a variable-temperature operation ranging from room
0034-6748/2014/85(8)/083707/8/$30.00 © 2014 AIP Publishing LLC 85, 083707-1
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temperature down to liquid helium temperature for SHPM
and a variable temperature below 8 K for SSM. Second, a
wide range of ambient magnetic fields from ≈1×10−6Tt o
several Tesla for SHPM and from 1 ×10−8Tt o1 ×10−3
T for SSM. Third, a temperature-insensitive mechanical scan-
ning scheme adapted to reliably provide millimeter scan rangewith sub-micrometer step resolution. Fourth, a cantilever de-
sign adapted for both SHPM and SSM to enable sensors to
follow the contour of the sample surface without a feedback
electronics. Finally, an innovative Hall probe fabrication de-
veloped for effectively reducing the separation between thesensor and the sample to about ≈1μm.
II. INSTRUMENT DESIGN
A. Mechanical design and scanning method
of the scanning probe microscope
Figure 1(a) shows a schematic diagram of the micro-
scope, which was primarily constructed by incorporating acustom two-axis translation stage controlled by dc stepper
motors. The translation stage is made up of one stage on top
of another with a centered hole for the accommodation of vac-
uum bellow, as shown in Fig. 1(b). A long stainless steel rod,
with a diameter of 5 mm, is to transmit the transverse andlongitudinal motions of the translation stages, located on the
top of the microscope, to the bottom sample mount. A flexi-
ble cantilever is to maintain light contact between the sensorand the sample surface. The sample is attached to a copper
mount, which is screwed to the bottom end of the rod. The
top end of the rod, which passes through a flexible stainlessvacuum bellow, is fixed to a z-axis linear actuator (Huntington
Mechanical Laboratories, Inc. L2251-1). The z-axis actuator
is connected to the X-Y stage with a top plate, and movesalong with the X-Y stage. A cutaway view of the connection
is illustrated in Fig. 1(c). The z-direction actuator, with a nom-
inal maximum extension of ∼2.5 cm and a minimum step
∼0.1μm, is used for the vertical movement of the sample
to approaching the sensor. For the transverse movement, two
motors (Oriental Motor Co. DRL28PA1-03NF) are employed
to drive a mechanical X-Y stage. The translation stage moves
1μm per full step, 0.1 μm per micro step. The bottom end
of the rod is connected to a copper mount. At ∼20 cm above
the copper mount, the rod slides through a stainless washer
with three ball plungers, as shown in Fig. 1(d). The rod func-
tions as a scan lever and the washer serves as a pivot point
to directly transmit the motion of the X-Y stage to the sam-
ple and simultaneously allows the rod to shift vertically. Byproperly choosing the position of the pivot point, the trans-
verse motion of the sample is thus further reduced by a factor
of 6.5 from the motion of the X-Y stage. This scheme notonly further improves the transverse scanning resolution but
also minimizes the effects of external vibrations. The maxi-
mum scan range of present design is approximately 1 mm;this value is limited by the restoring force of the vacuum bel-
low against atmospheric pressure. The scan range could be
significantly increased by either the relocation of the washer
or the use of a flexible bellow. We note that in our scanning
scheme the movement of the scan lever might tilt a small an-electrical
feedthro ughx motorz motortranslation
stage
washer plank O-ring to fit
vacuum tube
20 cmscan le ver
sample
areascan le ver
pivoting
pointwasher
plankxyz
bellow
pumping
port z motor head
supporting
rodx yz
x motor y motor
y motor
ball pl unger
sensor
cantile ver
brass n ut
copper
basecold fingercopper
mountsampleheater thermometer(a)
(d)(c)(b)
5 cm
3 cm Top plate
Bottom plate
FIG. 1. (a) Schematic of the scanning magnetic probe microscope. (b) Top
view of the X-Y translation stage. (c) Sketch of the interior of the translation
stage from the side. (d) Enlarged sketch of the sample area.
gle and induce a height variation of the sample position in z
direction. For a 1-mm scan range, the tilt angle is estimated as
0.3◦=arctan(1 mm/20 cm), which corresponds to the height
variation of ∼3μm. This small variation is no concern be-
cause the flexible cantilever ensures a direct contact of the
sensor to the sample surface during scans.
The three-axis actuators driven by stepper motors at room
temperature can be controlled by a personal computer. To
achieve optimal repeatability, a raster-scan scheme was de-
veloped. For each scan line, the sample is swept left-to-rightalong the x-axis at a steady rate; the sample is then raised
vertically, moved back to the left, moved one step in the y-
position, and lowered vertically, and the next line is swept out.
The maximum speed of the linear actuators is approximately
24 mm/s. However, to avoid sudden jerky movements of the
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rod due to hasty stopping, the X-Y stage is typically operated
at∼100μm/s. With the time spent in mechanical movement
and in electronic measurements, it takes approximately 0.2 to0.6 s to acquire a data point. As a result, a 60 ×60 pixel scan
would take approximately 30 min to complete. With a proper
electrical isolation, no electronic noise component or a falsesignal induced from the mechanical movement of the stages
is found.
The microscope is approximately 170 cm in length and
30 kg in weight. To minimize the mechanical vibration in-
duced noise, the microscope is suspended from the ceiling.The sample area, the scanning lever, and the interconnected
parts from the vacuum bellow to the z-axis actuator dis-
played in Fig. 1(c)are vacuum sealed with a housing tube. To
achieve measurements under low-temperatures and magnetic
fields, the housing tube with a diameter of ∼4 cm was de-
signed to be accommodated into either a liquid-helium cryo-stat with superconducting magnets (Oxford SMD8VS Dewar)
or a non-magnetic helium storage Dewar. The sample can be
cooled through the introduction of helium exchange gas intothe housing tube while the microscope is immersed in liquid
helium. The temperature of the sample is monitored with a
carbon-glass thermometer and is varied by controlling the cur-rents through a heater rod, which is embedded in the copper
mount. The sensor, which is mounted on a cantilever attached
to a copper base, remains at ≈5 K though a direct contact with
the cold fingers.
For low-field measurements with sensitivity of ∼10
−6
T for SHPM and ∼10−8T for SSM, a 20-cm long μ-metal
cylinder can be implemented to cover the sample area and to
shield the ambient fields to less than 1 ×10−7T. A hand-
wound solenoid inside the cylinder can be employed to ap-
ply a magnetic field of ≤2×10−4T. For low-field ex-
periments, the measurement is performed in a non-magneticDewar; whereas for high-field measurements with magnetic
fields up to a few Tesla, the microscope is fitted into a typical
4He cryostat equipped with a superconducting magnet, which
has a bore size greater than 5 cm. The components assembled
in the sample area were designed to be easily exchangeable
and were made with non-magnetic metals; therefore, the Hallsignals are not contaminated by possible stray field residuals
induced in the metal parts after the application of high mag-
netic fields.
B. Sensor-sample alignment
Figure 2(a) illustrates an expanded view of the sensor
region of the microscope shown in Fig. 1(c). The sensor is
mounted onto a 300 μm-thick quartz plate which is attached
to a flexible metallic cantilever. The cantilever dimensions
are 12 mm ×6 mm (length ×width). It is found that the
cantilever is best made of either 25 μm-thick copper foil or
10μm-thick aluminum foil. The quartz plate, which was tai-
lored to be similar in size to the cantilever, is used to sup-port the sensor. The purpose of the plate is to maintain the
flatness of the arm surface without twisting or bending. The
initial alignment of the sample and sensor can be monitored
with a charge-coupled device (CCD) microscope camera at
room temperature. The initial approach procedure is to move
I+I-V+
V-20μm
1.2μm(f)
(b)
(e)0 200 400 -200T = 4.2K
Height ( μm)Approaching
contact0.06
0.00
-0.06metal shield
no shield
ΔRxy(Ω)
chip corner(a)quartz plate
~5osensor
V+
V-I-
I+
Vin Voutgold wire
xz
I+V-I-V+(c) (d)
Hall ChipSQUID Chip
5 mm5 mm
FIG. 2. (a) Schematic diagram of a sensor mounted on a flexible foil can-
tilever and a gauge circuit to sense the contact point of the sample and the
chip tip. (b) The change in the Hall resistance /Delta1Rxyas a function of the sam-
ple height measured during the approach process. (c) and (d) Photos of theHall chip and the SQUID chip mounted on cantilevers. (e) and (f) Scanning
electron micrographs (SEM) of the Hall probe.
the sample toward the corner of the chip until the cantilever
just begins to bend. To precisely ensure the contact point in
the dark, we designed a simple gauge circuit, as shown in
Fig. 2(a). A small piece of gold wire with a diameter of
100μm is inserted inside the wedge and is electrically con-
nected to a bias voltage and a current-limited resistor. When
the sample is in contact with the sensor tip, the cantilever armis deflected downward into contact with the Au wire. It makes
the circuit suddenly conductive. With knowledge of the con-
tact position of the sample, we can therefore finely adjust thecontact height between the sample and the sensor tip within
a few microns, while maintaining a gentle contact force less
than≤10
−5N. As a result, the sample can be quickly swept
while in contact with the sensor without severely scratching
the fragile chip, which can be verified by examining the probesurface after the experiments. To employ the gauge circuit, we
drive the close-loop circuit with a bias current of 1 μA, which
would generate magnetic field of only ∼10
−8T at the center
of the single-turn close loop. The magnetic field on the sample
is far weaker than 10−8T and would not possibly magnetize
the samples.
We note that, in the direct contact scheme, the Hall probe
not only responds to the local perpendicular magnetic field
but also responds to signals induced by environmental elec-tric fields.
22As shown by the solid triangles in Fig. 2(b),t h e
measured change in the Hall resistance abruptly varies imme-
diately after contact is made, and it irregularly varies as theHall probe descends further. This type of errant Hall voltage
becomes most pronounced in the scanning process. The inter-
fering signal may originate from friction-induced charging as
the Hall probe is dragged over the sample surface. To screen
out the accumulated charges, we deposited a thin gold film
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with thickness of ∼10 nm over the entire Hall cross to act as
a screening gate. By employing this technique, the errant Hall
voltage disappears, as shown by the open squares in Fig. 2(b).
For the operation of SSM, the single-chip dc SQUID
magnetometer can be mounted on the cantilever and be di-
rectly contacted to the sample. The approaching procedure issimilar to that of SHPM, as described earlier. The SQUID out-
put voltage shows an abrupt change as the chip just touches
the sample surface. At low temperatures, the touchdown posi-
tion routinely deviates about 100 to 150 μm from the value set
at room temperature, which is attributed to the thermal con-traction of the scan rod and the cantilever at low temperatures.
C. Micro-Hall chip fabrication and characteristics
The Hall probe was manufactured on a two-dimensional
electron gas (2DEG) 105 nm beneath a GaAs/Al0.3Ga0.7As
heterostructure surface. The electron density of a typical
wafer is approximately n=2.0×1011cm−2and the mobility
isμ=5.1×105cm2/Vs. The Hall coefficient RH, represent-
ing the field sensitivity, is calibrated to be 3000 /Omega1/T at 4.2 K
and 2000 /Omega1/T at 300 K. In the present design, the junction
area of the Hall bar patterned by photolithography is 5 μm
×5μm. The spatial resolution of the SHPM is mainly dom-
inated by two factors: the area of the Hall junction and thedistance r
zbetween the Hall junction and the targeted sam-
ple surface. Technically, the junction size can be reduced to
sub-micron scale by electron-beam lithography techniques.For Hall sensors made on a semiconductor heterostructure,
the distance r
zincludes the depth of the 2DEG. To minimize
rz, it would be desirable to implement the Hall cross as close
as possible to the chip corner; this construction requirement
significantly increases the fabrication difficulty and degrades
the reliability of the Hall probe because of the brittle nature ofthe GaAs crystal. We overcame this problem by simply etch-
ing a deep mesa while defining the Hall junction. Here, the
etching depth Dis approximately 1.2 μm and the Hall cross is
∼20μm away from the corner of the cleaved chips, as shown
in Figs. 2(e) and2(f). This approach posses several advan-
tages for the contact-mode scanning scheme in SHPM. First,
it is easier to make the contact height small in typical oper-
ations. Second, the junction area can be further reduced be-cause of anisotropic sidewall etching. For example, the orig-
inal junction area was reduced to ∼3.5×3.5μm
2,a ss h o w n
in Fig. 2(e). Finally, the deeply etched Hall chip performs as
well as those in previous studies, and the fabrication complex-
ity is greatly reduced.
The field resolution, the minimum detectable magnetic
field change /Delta1Bmin, of the Hall probe is restricted by the in-
trinsic noise of the materials. /Delta1Bminis related to the Hall volt-
age noise Vnthough /Delta1Bmin=Vn/IbiasRH. Here, Ibiasis the
applied bias currents. For the Hall probe fabricated on the
GaAs/AlGaAs heterostructure, /Delta1Bminis known to be domi-
nated by low-frequency 1/ f-like noise.19Figures 3(a)and3(b)
showVnas a function of frequency under various Ibiasat tem-
peratures of T=300 K and 77 K, respectively. Figures 3(c)
and3(d) are the corresponding /Delta1Bminas a function of fre-
quency under optimal bias currents. Vnfollows a 1/ fγpower
law with γ≈1f o r f≤fcwhere fcis the cross-over frequency,10 1000
Freq uency (Hz)10-710-3T = 77K
I = 20 μA(c) (d)
1 10 100 1000 100Bmin (T/Hz 1/2)
Vn (V/Hz 1/2)10-7
10-8
1/f 20μA(b)
60μA
10-6
Bmin (T/Hz 1/2)T = 300K
I = 2 μA10-5
10-6(a)
1/fVn (V/Hz 1/2)T = 300K
2 μA
1 μA
0.6 μAT = 77K
FIG. 3. Hall voltage noises Vnspectra at (a) 300 K and (b) 77 K under var-
ious bias currents. Minimum detectable magnetic field change /Delta1Bminas a
function of frequency at (c) 300 K and (d) 77 K.
which is marked with a dash line. For f>fc, we found that
Vnbecomes less insensitive to Ibiasin the limit of the ab-
sence of Joule heating, and Vnis dominated by white noise.
The magnitude of the white noise was found to be on scale
of the Johnson noise associated with the Hall leads. ForSHPM, we generally drive the Hall probe at 1.5 kHz si-
nusoidal wave and measure the Hall signals with a stan-
dard lock-in technique with a time constant of approximately100 ms which is chosen in comparable to the time spent in me-
chanical movement. It should be noted that V
nis affected by
the circuit noise as well. In our present setup, the voltage noiseof the home-made voltage amplifier, which was constructed
from instrumentation amplifier Analog AMP01, is approxi-
mately 5 nV/Hz
1/2atf=1.5 kHz. Table Isummarizes the
characteristics of the Hall probe over the temperature range
from 300 K to 4.2 K. The field sensitivity, RH, is found to be
insensitive to temperature variation; in contrast, the field reso-lution significantly decreases at the lower temperature. /Delta1B
min
saturates at ∼0.6×10−7T/Hz1/2at 4.2 K and is primarily
limited by the amplifier noise.
D. SQUID chip characteristics
The magnetometer fabricated by our own Nb-AlOx-
Nb technology is composed of an integrated dc SQUID
TABLE I. Characteristics of typical Hall probes at various operating tem-
peratures. Ibiasdenotes the bias current, Rsis the parasitic resistance, /Delta1Bmin
is the field resolution, and RHis the Hall coefficient, which represents the
field sensitivity.
300 K 77 K 4.2 K
Ibias(μA) 2 20 20
Rs(k/Omega1)8 0 1 0 2 . 5
RH(/Omega1/T) 2000 3000 3000
/Delta1Bmin(10−4T/Hz1/2)3 . 51 . 1 ×10−30.6×10−3
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(a)
0.0 50 -500.0
-0.1
-0.2
-0.3T = 4.2K(c)
(d)
0 -0.2 -0.4 0.20 20 40
I (mA)
V(μV)
Imod (mA)
V(μV)(b)(i)10 μm
(ii)
(iv)
(v)(iii)
FIG. 4. (a) and (b) Optical micrographs of the pick-up region of a scanning
SQUID chip and the SQUID loop centered with a modulation coil. The com-
ponents are labeled as (i) pick-up loop, (ii) modulation coil, (iii) SQUID loop,(iv) Josephson junctions, and (v) shunted resistors. (c) A representative I-V
trace of the SQUID chip. The critical current I
cis approximately 100 μA.
(d) Output voltage as a function of modulation current Imodfor different bias
currents of 50, 70, 90, and 120 μA.
sensor with a pick-up loop, as shown in Figs. 4(a) and4(b).
Figure 4(a) shows the octagonal pick-up loop, which has an
area of 80 μm2and is serially coupled to a SQUID loop
through a 1-mm long stripline. The spatial resolution limited
by the diameter of the signal coupling loop is about 10 μm.
The SQUID loop consists of a single-turn flux modulation coiland two Nb-AlO
x-Nb (100/6/100 nm) junctions shunted by
two 2/Omega1resistors R. The junction is with critical current J0of
∼560 A/cm2,a na r e ao f3 ×3μm2, and a capacitance Cof
0.13 pF. The optimal hysteresis parameter βc=2πI0RC//Phi10
is approximately 0.1. The hole-inductance Lof the SQUID
loop is estimated to be ∼17 pH.23The screening parameter
βL=2LI0//Phi10with a value of ∼0.9 is designed to fit the low
flux noise requirement.24
A representative bias current-to-output voltage character-
istic of our SQUID chip is shown in Fig. 4(c). Flux modula-
tion is accomplished by passing current Imodthrough the mod-
ulation coil around the square washer. As shown in Fig. 4(d),
the magnetic field generated by Imodof∼160μA corresponds
to one flux quantum. The flux-to-voltage transfer coefficientV
/Phi1is maximized as bias current is driven near Ic, and the cor-
responding modulation amplitude is ≈24μV . To operate a
SSM, the SQUID chip is driven at a modulation frequency of100 kHz and a I
modfor a maximum V/Phi1. The noise amplitude
of the device at 100 kHz is around 10 μ/Phi10/Hz1/2, correspond-
ing to a field noise of ≈2.6×10−10T/Hz1/2.
III. DEMONSTRATION OF PERFORMANCE OF SHPM
AND SSM WITH EXAMPLES OF SCANNED IMAGES
The first example demonstrates the feasibility of our
scanning scheme for SHPM operated in a large scan range
at room temperature. To demonstrate the capability of a
millimeter-range scan of our microscope, we have imaged
the field contrast of a RbFeB magnet at room temperature by
RbFeB
0.5
0
FIG. 5. A 1 ×1m m2scan of the magnetic image of the edge of a RbFeB
strong magnet a pixel size of 10 ×10μm2, taken at room temperature. The
scale bar represents the variation of the field strength and the dashed line
marks the boundary of the magnet.
SHPM. Figure 5shows a 1 ×1m m2scan area of an edge of
the magnet. The GaAs/AlGaAs Hall probe is rather fragile,
and could be easily damaged by large-range scan and fast-
scan rate in order to keep a reasonable scanning time. There-fore, we operate the Hall probe 50 μm above the magnet dur-
ing scans and choose RbFeB magnet with strong magnetic
field as the investigated sample.
For the second example, we use patterned magnetic Ni
film as the target feature for the imaging. Micron-size pho-
toresist patterns were first transferred onto the GaAs substrateby conventional optical lithography, and this transfer is fol-
lowed by the deposition of a Ni film with a thickness of ap-
proximately 200 nm by thermal evaporation follows. After a
lift-off procedure, the Ni square-grid and stripe patterns were
defined as shown in Figs. 6(a)and6(b), respectively. To facil-
itate the measurements, the Ni patterns were placed under a
permanent magnet for several days to pre-align the magnetic
moment before the images are acquired. Figure 6(c)shows a
400μm×400μm scan area of the Ni grid pattern with a pixel
size of 4 μm×4μm. Comparing Fig. 6(c) with Fig. 6(a),
we can readily assure that the images acquired by themechanical setup show no apparent geometrical distortion,
100 μm(c) (d)
30 μmT = 300K(a)
NiGaAsNi
100 μm 30 μm(b)GaAs
10ΔB(mT)
0
FIG. 6. Optical microscopy images of the patterned Ni-films studied: (a) Ni-
square grid, (b) Ni-stripe. (c) A 400 ×400μm2scan of the magnetic image
of the Ni-grid sample with a pixel size of 4 ×4μm2.( d )A7 0 ×70μm2scan
of the magnetic image of the Ni-stripe with a pixel size of 0.7 ×0.7μm2.
Both samples are imaged at 300 K. The scale bar represents the variation of
the measured field strength. Note that images (c) and (d) are original raw data
without any image correction.
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nonlinearity, or the effect with hysteresis, even up to a
400-μm scan range. Figure 6(b) shows a crack along the Ni
stripe and a few scattered small particles on the GaAs sub-strate; these particles were identified as residue resist by op-
tical inspection. By comparison with Fig. 6(b), Figure 6(d)
emphasizes the authentic mapping of the magnetic structurebut not the non-magnetic debris.
After showing the capability of our system to detect ar-
tificial magnetic structures, the third example is the imag-
ing of the intrinsic magnetic domains in a La
2/3Ca1/3MnO3
(LCMO) thin film at 77 K. LCMO is a well-known colossal
magnetoresistive material, which exhibits an intriguing phase
transition from a paramagnetic insulator to a ferromagnetic
metal as the temperature decreases below a transition temper-ature T
C.25The 75 nm-thick LCMO film studied was grown
by pulsed laser deposition on a 500- μm-thick single crystal
SrTiO3(STO) (100) substrate. The temperature dependence
of the sample resistivity ρis displayed in Fig. 7(a).I ts h o w s
that TCis approximately 215 K, which is consistent with the
previous report of thin LCMO films.26The LCMO film was
then milled into a 30 μm-wide stripe pattern. Figure 7(b)
shows an image at 77 K after the sample was field cooled
under an ambient field of ∼5×10−5T. With respect to the
background signal of the STO substrate, sporadic magnetic
domains with an imaged spatial size of ≤10μm are observed
in the LCMO/STO stripes. Note that the adjacent magnetic
domains exhibit an opposite field polarity, which is likely as-
sociated with the magnetic poles for the in-plane magnetiza-tion. The general features of the magnetic domains revealed
far below T
Care similar to those shown in an earlier report
on La0.65Ca0.35MnO3thin films, which were studied by low-
temperature magnetic force microscopy.27
The fourth example is the magnetic images of supercon-
ducting vortices scanned with SHPM and SSM. The magneticfield penetrating through a thin type-II superconducting film
cooled below the superconducting transition temperature T
c
is known to form flux bundles. Each superconducting vortex
contains a single magnetic flux quantum /Phi10=hc/2e(20.7
×10−4T-μm2). Suppose that the origin of the coordinate
system is at the center of the vortex on the film surface, thez-component of the field distribution of a vortex at a position
0.25
00.20
03 0 0 25020015010050
T (K)ρ (Ω-cm)La2/3Ca1/3MnO 3
75 nm (a)
0.15
0.10
0.05
0.00(b)
20 μmSTOLCMO/STO
TC~215 K-0.25 ΔB(mT)
FIG. 7. (a) The temperature dependence of the resistivity ρof the
La2/3Ca1/3MnO3/SrTiO3(LCMO/STO) film. The LCMO film is 75 nm thick
with a transition temperature TCof around 215 K. (b) A 60 ×60μm2scan
of the magnetic image of the LCMO stripes at 77 K with a pixel size of 1 ×1
μm2. The image was taken after the cooling of the sample in an ambient field
of∼5×10−5T. The dashed lines mark the borders of the stripe pattern. The
red/blue color represents the magnetic moment lying out-of-/in-planes of thesurface on the STO substrate.zabove the film surface is defined as Bz(x,y,z). In the limit of/radicalbig
x2+y2+z2/greatermuchλ,Bzcan be expressed as4,28,29
Bz(x,y,z )=/Phi10
2πz+λeff
[x2+y2+(z+λeff)2]3/2, (1)
where λis the magnetic penetration depth, λeff
=λcoth(t/2λ), and tis the thickness of the superconducting
thin film. To correctly consider the field distribution measured
by the Hall probe below, Fig. 8(a)depicts the relative position
of the Hall probe relative to the vortex field sensed. The mea-sured B
zextracted from the Hall signal actually corresponds
to an averaged Bzover the sensing area of Hall junction
through Bz(av)(x,y,z )=(1/w2)/integraltexty+w
2
y−w
2/integraltextx+w
2
x−w
2Bzdxdy , where
w2is the junction area. Figure 8(b) shows simulated curves
ofBz(0, 0, z) (dashed line) and Bz(av)(0,0,z) (solid lines)
for different junction sizes of the Hall probe as a function
ofz. The relevant parameters adopted in the simulation are
chosen to fit the experimental conditions, as discussed below.
It is clear that Bz(av)decays rapidly as zandw2increase.
Therefore, the imaging of the vortex feature can be viewedto be a stringent evaluation of the field sensitivity and a
delicate inspection of the mechanical aberrations of our
SHPM setup. Meanwhile, the spatial resolution of scanning
0.02
0.00(e)
0
x(μm)0.04
0.06
modeldata00.14(c)
NbNb
30μm5μm(d)
Si
SiΔB(mT)
0.07
00.040.080.12
0.00
z (μm)(b)
yx23 4 5611
3.5
5
10Bz rz
wNb(a)
Si(Not in scale)
GaAsD
θ
Bz(av)(mT) Bz(av)(mT)w =0 . 5 μm
-2 2 4 6 -4-6t
ΔB(mT)
FIG. 8. (a) A schematic drawing of the cross-section of the Hall junction
and the field profile of a vortex in a superconducting Nb film with the contact
scheme. (b) Simulated curves of the z-component of the magnetic field distri-
bution of a vortex as a function of z: a genuine vortex Bz(red dashed line) and
Bz(av)(solid lines) for different junction sizes w, obtained from the average
of the flux penetrating through the Hall junction area. (c) A 70 ×105μm2
scan of patterned Nb stripes at 4.2 K after a field-cooled process in 1 ×10−5
T, the pixel size is 1 ×1μm2.( d )A2 0 ×16μm2scan of the unpatterned Nb
film at 4.2 K with a pixel size of 0.6 ×0.6μm2. Each black spot represents an
individual vortex with magnetic flux quanta. The diameter of the vortex im-
age is estimated approximately 3.2 μm, which is roughly comparable to the
junction size of our Hall probe. (e) The field profile of a isolated vortex along
a line scan indicated by a blue dashed line in (d). The black squares represent
the data, and the red line is the best-fit theoretical model for a single vortex
field.
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probe microscopies can be estimated by the full-width at
half-maximum (FWHM) of a vortex profile.
The Nb thin film investigated was deposited by dc mag-
netron sputtering on a pure Si substrate. The thickness tis ap-
proximately 300 nm, and the corresponding penetration depth
is known to be λ=80 nm at 4.2 K.30T h eN bfi l mw a st h e ni o n
milled into 30 μm-wide stripes. The sample with Tcof∼9K
was slowly cooled down to 4.2 K while an external magnetic
field perpendicular to the sample surface is applied by passing
current through a hand-wound solenoid. A μ-metal can was
used to cover the entire sample area and the solenoid.
Figures 8(c) and8(d) show the SHPM magnetic images
of a Nb stripe film and an unpatterned Nb film, respectively.
The individual vortices, shown as black spots, can be clearlyidentified. The size of each imaged vortex is ∼3.2μm, which
is comparable to that of the Hall junction. The flux penetrat-
ing through the Nb stripes in Fig. 8(c) is approximately 14
/Phi1
0, which is consistent with the estimated number of 14 vor-
tices trapped in 10−5T after a field-cooled process. To obtain
a detailed field profile of a single vortex, a line scan alongthe x axis across a chosen vortex was performed, as shown in
Fig. 8(e). The black squares in Fig. 8(e) are the experimen-
tal data with a pixel spacing of ∼280 nm. The field pro-
file of a single vortex can be fitted by B
z(av)(z), where zis
the only fitting parameter. The red line shown in Fig. 8(e)
is the best-fit result for z=1.5μm. The spatial resolution
of the SHPM estimated by the FWHM of the vortex profile is
about 4 μm.
We noted that the field profile severely smears out as z
increases. For z=5μm, the vortex features can no longer be
resolved experimentally. For z=1.5μm, the deduced con-
tact angle θis 7.4◦, which is slightly larger than the set value
of∼5◦as identified by optical microscopy at room temper-
ature. The discrepancy may result from thermal contractionof the scan rod and cantilever during the cooling. Despite the
micron-sized Hall probe and the simple scan scheme, the ac-
curacy and resolution of our SHPM is still sufficient to imagethe features of the vortices.
To demonstrate the functionality of our SSM, we have
imaged the vortex distributions in a Nb stripe over an areaof 150 ×150μm
2by SSM, as shown in Fig. 9.T h es a m p l e
was slowly cooled down to below Tcwith a small magnetic
field of 5 ×10−6T perpendicular to the sample surface be-
fore images were taken. The trapped vortices at local pinning
sites were clearly resolved as shown in Fig. 9(a). To discrimi-
nate the variation of the pinning force among certain vortices,
an external pulse current of 100 mA with a current density
Jof 5×105A/cm2was applied to the Nb stripe. It exerts
a driving Lorentz force on the vortices and its corresponding
force per unit length f=J×/Phi10is estimated to be 11 μF/m.
Few vortices marked by arrows and labeled by numbers traveldifferent distances in a three-second time interval, which is
due to the fact that the driving Lorentz force is larger than
the pinning force of these vortices. Figure 9also illustrates
the presence of any spatial inhomogeneity in the investigated
Nb film, which may result from impurities, grain boundaries,
etc. More importantly, the snapshots of the scanned images bySSM provide a direct visualization of the temporal and spatial
correlation of the vortex dynamics. Similar to SHPM we use5
0
x(μm)1015Bz(av) (μT)
10 -10modeldata
0
40 m0 s
(b) 1 s
(c) 2 s
(d) 3 s(a) (e)
xy
13
0ΔB(μT)
FIG. 9. (a) SSM images of vortices trapped in a 60- μm wide Nb stripe,
which were scanned in an area of 150 ×150μm2with a pixel size of 3
×3μm2. The sample was field-cooled down to 4.2 K in a small magnetic
field of 50 mG. (b), (c), and (d) show images taken after a current pulse of
100 mA with a duration time of 1 s, 2 s, and 3 s respectively. The vortices
driven by the pulse current are indicated by the arrows and numbers. (e) TheB
zprofile of a vortex extracted along the blue dashed line in (a). The black
squares are the data, and the red line is the best theoretical fit.
the FWHM of a superconducting vortex to evaluate the spa-
tial resolution of the SSM. Figure 9(e) shows the Bzprofile
of a single vortex extracted from Fig. 9(a), indicated by the
blue dashed line. The black squares are the experimental data
with a pixel spacing of 3 μm and the red line is the simulated
Bz(av). The spatial resolution of the SSM indicated FWHM of
the vortex profile is about 9 μm.
IV. CONCLUSIONS
In summary, we have developed an interchangeable
SHPM/SSM system for passive magnetic imaging. The me-chanical positioning stage enables us to keep the advantages
of a large-area scan and sub-micron spatial resolution in a
wide temperature range (4.2 K-300 K) without mechanicalaberrations. The cantilever design adapted for both SHPM
and SSM reliably ensures a direct contact between the sensor
and sample investigated. The sensitivity of the micron Hallprobe is greatly improved with a fruitful fabrication process.
The functionality of the SHPM and SSM is demonstrated
by imaging a RbFeB magnet, and artificial magnetic micro-
structures in Ni films at room temperature, surface magnetic
domain structures in La
2/3Ca1/3MnO3films at 77 K, and indi-
vidual superconducting vortices in Nb films at 4.2 K.
ACKNOWLEDGMENTS
We acknowledge A. M. Chang, J. R. Kirtley, and Deng-
Sung Lin for helpful discussions, and Kuang-Cheng Lin and
Yu-Tien Shen for assistance with the experiments. This work
is supported by Department of Natural Science at NationalScience Council under Grant No. NSC 101-2628-M-007-002-
MY3, Taiwan.
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Sci.138–139 , 40 (1999).
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T. Y . Chang, Europhys. Lett. 20, 645 (1992).
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1.4870577.pdf | Phase transitions in delafossite CuLaO2 at high pressures
Nilesh P. Salke, Alka B. Garg, Rekha Rao, S. N. Achary, M. K. Gupta, R. Mittal, and A. K. Tyagi
Citation: Journal of Applied Physics 115, 133507 (2014); doi: 10.1063/1.4870577
View online: http://dx.doi.org/10.1063/1.4870577
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/13?ver=pdfcov
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32Phase transitions in delafossite CuLaO 2at high pressures
Nilesh P . Salke,1Alka B. Garg,2Rekha Rao,1,a)S. N. Achary,3M. K. Gupta,1R. Mittal,1
and A. K. Tyagi3
1Solid State Physics Division, Bhabha Atomic Research Center, Mumbai 400 085, India
2High Pressure & Synchrotron Radiation Physics Division, Bhabha Atomic Research Center,
Mumbai 400 085, India
3Chemistry Division, Bhabha Atomic Research Center, Mumbai 400 085, India
(Received 6 February 2014; accepted 25 March 2014; published online 3 April 2014)
Structural stability of a transparent conducting oxide CuLaO 2at high pressures is investigated
using in-situ Raman spectroscopy, electrical resistan ce, and x-ray diffraction techniques. The
present Raman investigations indicate a sequenc e of structural phase transitions at 1.8 GPa and
7 GPa. The compound remains in the first high pressure phase when pressure is released.Electrical resistance measurements carried out at high pressures confirm the second phase
transition. These observations are further supported by powder x-ray diffraction at high
pressures which also showed that a-axis is more compressible than c-axis in this compound.
Fitting the pressure dependence of unit cell volume to 3
rdorder Birch-Murnaghan equation of
state, zero pressure bulk modulus of CuLaO 2is determined to be 154(25) GPa. The vibrational
properties in the ambient delafossite phase of CuLaO 2are investigated using ab-initio
calculations of phonon frequencies to complement the Raman spectroscopic measurements.
Temperature dependence of the Raman modes of CuLaO 2is investigated to estimate the
anharmonicity of Raman modes. VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4870577 ]
INTRODUCTION
Transparent conducting oxides (TCO) of the delafossite
family AMO2(A¼Cu, Ag; M¼Al, Sc, Ga, In) have many
unusual physical properties leading to technological applica-tions in devices, such as solar cells, touch panels, as electro-
des in flat panel displays ultraviolet-emitting diodes.
1While
there are many n-type TCOs, p-type conductivity in transpar-
ent semiconductors is rare and essential for applications in
p-njunctions.2Copper delafossites can be made p-type semi-
conductors either by doping or creating non-stoichiometry.The origin of positive carriers in undoped delafossites is ei-
ther due to excess oxygen in the interstitials or copper vacan-
cies. Engineering of optical and electronic band structure bydoping in copper delafossites makes them useful as photoca-
talyst to produce hydrogen by water splitting.
3Catalytic ac-
tivity of copper delafossites also finds applications indecomposition of toxic waste gases.
4Some members of the
delafossite family have attracted interest due to the multifer-
roic properties exhibited by them;5,6wherein ferroelectricity
is induced by magnetic ordering.
Delafossite type of crystals have layered structure with
hexagonal P63/mmc or rhombohedral R/C223mspace group,
with a general formula AMO2, in which monovalent cations
A(A¼Cu, Ag) are linearly coordinated with two oxygen
ions along the c-axis and the trivalent cations Mare octahe-
drally coordinated to oxygen atoms.7Delafossite com-
pounds, where the trivalent ion is magnetic, have been
studied with the interest of magnetic transitions exhibited bythem. Both CuCrO 2and CuFeO 2show antiferromagnetism
below 24 and 14 K respectively.8,9Though earlier magneto-
striction studies indicated a structural transition in CuCrO 2,8
similar to the ferroelastic transition in CuFeO 2,9no anomaly
in either of them has been observed in low temperature
Raman spectroscopic studies.5This suggests that the ferroe-
lastic transitions are not driven by Raman active modes.
Due to widely different coordination of the cations,
delafossites are expected to have a rich phase diagram,especially many pressure induced phases. Earlier, high
pressure investigations of some of the members of this fam-
ily of compounds have revealed interesting phase transi-tions. X-ray diffraction studies along with M €ossbauer and
x-ray absorption spectroscopy at high pressure have
revealed a sequence of reversible structural/electronic-mag-netic transitions in CuFeO
2.10CuFeO 2transforms from
R/C223mtoC2/c at 18 GPa, while CuCrO 2transforms from
R/C223mtoP21/mat 26 GPa.10,11Contrary to usual trend
observed for a class of materials under pressure, these com-
pounds do not seem to follow any specific trend in terms of
phase transition sequence; various copper delafossitesbehave differently under pressure except in the case of
CuGaO
2and CuAlO 2where they seem to follow a trend.
From Raman spectroscopic and x-ray diffraction measure-ments, it has been reported that both CuAlO
2and CuGaO 2
transform to unresolved structures above 34 and 26 GPa,respectively.
12–15In both CuAlO 2and CuGaO 2,in-situ
Extended X-ray Absorption Fine Structure measurements
have confirmed that the transition involves change in cop-
per environment.14,15Both CuAlO 2and CuGaO 2are indi-
rect band gap semiconductors. One common feature of all
the copper delafossites belonging to R/C223mis that under higha)Author to whom correspondence should be addressed. Electronic mail:
rekhar@barc.gov.in
0021-8979/2014/115(13)/133507/7/$30.00 VC2014 AIP Publishing LLC 115, 133507-1JOURNAL OF APPLIED PHYSICS 115, 133507 (2014)
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32pressure, a-axis was found to be more compressible than
thec-axis resulting in more regularization of oxygen octa-
hedra compared with the distorted octahedra at ambientconditions.
14–17There have been several computational
studies on these compounds to understand their high pres-
sure behavior. Ab-initio calculations of phonon frequencies
under pressure have indicated that pressure induced phase
transitions in CuGaO 2and CuAlO 2are initiated by dynami-
cal instability of a transverse acoustic phonon.12,13
Electronic structure calculations have predicted change in
band gap with pressure in CuAlO 2with the compound
remaining an indirect band gap semiconductor up to36 GPa, even though its smallest direct band gap decreases
with pressure.
18Recent first principles calculations of crys-
tal structures determined the critical pressure of transitionfor delafossite CuAlO
2to a leaning delafossite with a
higher bandgap to be 60 GPa.19Optical absorption studies
and ab-initio calculations of electronic structure on
CuScO 2, a direct band gap semiconductor, reported changes
in electronic band structure, with direct gap abruptly
decreasing with increase in pressure at 18 GPa.20Among
other copper delafossites, CuLaO 2is a direct gap semicon-
ductor with a band gap of 2.77 eV and p-type conductiv-
ity.21Due to its lower band gap, CuLaO 2is expected be a
better candidate as a photoelectrode for hydrogen produc-
tion than other copper delafossites.22
Recently, negative thermal expansion (NTE) has been
reported in some members of the delafossite family.7
Interestingly, CuLaO 2exhibits NTE along both a-and
c-axes at low temperatures and it shows nearly isotropic vol-
ume thermal expansion, though its structure is anisotropic.
Neutron diffraction studies from 30 to 600 K range reported
that while a-axis shows positive expansion above 100 K,
c-axis contracts in the temperature range 30–200 K and
expands at higher temperatures up to 600 K.7NTE in copper
delafossites in which Cu is two-fold coordinated, is attrib-uted to the vibrational motion of Cu atom perpendicular to
the linear chain of O-Cu-O which is along the c-axis.
23
High pressure investigation of NTE materials reveals a
variety of interesting phenomena, such as softening of pho-
nons, phase transitions, and also amorphization. High pres-
sure investigation of Raman spectrum gives informationabout the mode Gr €uneissen parameter, useful for understand-
ing the thermal expansion behavior. Though Raman spec-
troscopy gives information about only the zone-centerphonons, it is quite useful in understanding the contribution
of different vibrations to the thermal expansion. Earlier pre-
liminary Raman spectroscopic studies on CuLaO
2at high
pressures reported pressure dependence of mode frequencies
in the ambient phase and a phase transition at 1.8 GPa.24
Here, we report detailed Raman spectroscopic studies, x-ray
diffraction, electrical transport, and ab-initio calculations of
phonon frequencies of CuLaO 2at high pressures.
EXPERIMENTAL DETAILS
The compound CuLaO 2was synthesized by solid state
reaction of Cu 2O and La 2O3. The sample was characterized
using powder x-ray diffraction technique. Unit cellparameters and atomic coordinates obtained by Rietveld
refinement of x-ray powder diffraction data confirmed it to
be a delafossite structure with space group R/C223mand lattice
parameters are in agreement with literature values.25Raman
spectroscopic measurements at high pressure were carried
out from inside a diamond anvil cell (DAC) (Diacell B-05)in back-scattering geometry, with 4:1 methanol-ethanol mix-
ture as pressure transmitting medium which remains hydro-
static up to 10 GPa.
26Spectrum of polycrystalline sample of
CuLaO 2was excited using 532 nm (2.33 eV) laser line of
power /C2415 mW. Pressure was measured using the ruby fluo-
rescence technique.27Scattered light was analyzed using a
home built 0.9 m single monochromator,28coupled with an
edge filter and detected by a cooled CCD. Entrance slit was
kept at 50 lm, which gives a spectral band pass of 3 cm/C01.
Raman measurements in the temperature range 77–600 K
were carried out using the temperature stage from Linkam
(Model-THMS 600), also in back-scattering geometry.
The electrical resistance measurements under high pres-
sure were carried out on CuLaO 2in an opposed Bridgman
anvil setup. Bridgman assembly consists of 12 mm face diame-ter tungsten carbide (WC) anvil pairs, two 0.2 mm thick pyro-
phylite (alumino silicate Al
2O3.2SiO 24H2O) gaskets with
central hole of diameter 3 mm and steatite as pressure transmit-ting medium with in-situ bismuth pressure calibration. Initially,
the powdered sample was pressed between WC anvils to a load
of 3 ton. The well compacted material was then trimmed to1.5 mm width and 2.5 mm length pieces with a thickness of
0.2 mm, for electrical resistance measurements. For four probe
resistance measurements, stainless steel wires of 40 lmd i a m e -
ter were used. For each pressure point, 2 min pressure soaking
time was given before recording the resistance.
In-situ high pressure x-ray diffraction measurements
were carried out at the powder x-ray diffraction beam line of
Elettra synchrotron source, Italy. The data were collected in
angle dispersive x-ray diffraction (ADXRD) mode, in thetransmission geometry. The wavelength of the x-ray
employed and the sample to image plate (IP) distance were
calibrated using CeO
2diffraction pattern. Sample to detector
distance in the high pressure XRD set-up was 153.52 mm.
Hardened stainless steel gasket with a central hole of diame-
ter 150 lm and thickness 50 lm contained the sample. For
high pressure measurements, finely powdered CuLaO 2along
with gold as pressure calibrant and methanol–ethanol (4:1)
mixture as pressure transmitting medium were loaded in aMao–Bell-type DAC with diamond anvils of culets size
400lm. X-ray powder patterns at various pressures were
collected employing x-ray of wavelength 0.5997 A ˚colli-
mated to 80 lm diameter. Typical exposure times of 15–20
min were employed for measurements at high pressures.
Images of the powder diffraction rings were read from theMAR345 image plate detector with a resolution of
100/C2100lm
2pixel size. The images thus obtained were
integrated using the program FIT2D.29
COMPUTATIONAL DETAILS
The first principles density functional theory methods
(DFT) for total energy and phonon calculations were carried133507-2 Salke et al. J. Appl. Phys. 115, 133507 (2014)
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32out using Vienna ab-initio simulation package (VASP)30,31
software. The generalized gradient approximation (GGA)
exchange correlation given by Perdew, Burke, andErnzerhof
32,33with projected–augmented wave method has
been used. The plane wave pseudo-potential with plane
wave kinetic energy cutoff of 780 eV is used in the calcula-tion. The integrations over the Brillouin zone were sampled
on a 8 /C28/C22 grid of k-points generated by Monkhorst-pack
method.
34The above parameters are found to be sufficient
for total energy convergence of less than 0.1 meV. Density
functional perturbation theory has been used for zone centre
phonon calculation implemented in VASP. The convergencecriteria for the total energy and ionic forces were set to
10
/C08eV and 10/C05eV A˚/C01, respectively.
RESULTS AND DISCUSSION
Raman spectroscopy
In the delafossite structure R/C223m, primitive unit cell con-
sists of four atoms resulting in 12 normal modes which trans-
form as C¼A1gþEgþ3A2uþ3Euof which EgandA1gare
Raman active modes. Movement in the direction of Cu-O
bonds along the hexagonal c-axis is represented by Amodes,
whereas Emodes correspond to vibrations in the perpendicu-
lar direction. In the absence of single crystals, Raman modes
were identified by comparing the Raman spectra of analo-
gous compounds like CuAlO 2and CuGaO 2,12,13as well as
by using ab-initio calculations.
Figure 1shows the evolution of Raman spectra of
CuLaO 2under high pressures. At ambient conditions (phase
PI), it consists of two modes at 318 and 652 cm/C01identified
asEgandA1g, respectively. An asymmetry on the low fre-
quency side of the Egmode and a few weak modes around
200 cm/C01are also observed at ambient conditions, which
could be non-zone center modes observed due to relaxation ofRaman selection rules due to copper vacancies or interstitial
oxygen, similar to those observed in CuAlO
2/CuGaO 2.12,13
The frequencies of both the Raman modes are found toincrease monotonically with pressure. Above 1.8 GPa, several
new modes appear in the low frequency region. On further
pressurization, the low frequency component of Egmode
increased in intensity accompanied by softening of both the
components. Appearance of new modes and changes in the
pressure dependence of mode frequencies indicate a phasetransition to a phase PII. Above 1.8 GPa, the A
1gmode could
not be followed. Appearance of many new modes in PII indi-
cates lower symmetry of the high pressure phase. Nature ofchanges observed in the Raman spectra at 1.8 GPa are similar
to the observations in the Raman spectra of other delafossite
members CuAlO
2and CuGaO 2, which show high pressure
transitions at 34 and 26 GPa, respectively.12,13Higher phase
transition pressures in CuAlO 2and CuGaO 2could be attrib-
uted to the difference in ionic radii and polarizability of thecounter cations. Lanthanum has larger ionic radius and higher
polarizability compared with Al or Ga, the deformation of
coordination polyhedra and delocalization of electron densityaround lanthanum can be expected at lower pressure. Thus,
the pressure induced transitions in these are related to the dif-
ferences in the bonding and electronic structure. This is fur-ther supported from the behaviour of CuLaO
2at still higher
pressures. The Raman intensity of all the modes reduced dras-
tically above 7 GPa and the sample becomes opaque indicat-ing drastic reduction in the band gap. The absence of any
detectable Raman spectra above 7 GPa could be due to phase
transition to a phase with no Raman active modes, amorphousphase or the lack of Raman intensity could be due to change
in electronic band structure leading to increase in absorption.
Of these possibilities, the last possibility looks more feasiblesince the sample becomes opaque. Finally, on complete
release of pressure from 8 GPa, sample remains in phase PII.
Figure 2indicates the pressure dependence of Raman mode
frequencies. The pressure coefficient of all the modes in the
PI and PII phases is given in Table I. Frequencies of modes
that appear only in the phase PII are extrapolated to zero pres-sure. Among the modes that appear in PII, the modes at
112 cm
/C01and the two split components of Egmode in the am-
bient phase around 318 cm/C01show softening with increase in
pressure whereas all the other modes show usual hardening.
FIG. 1. Raman spectra of CuLaO 2at various pressures. Red bars represent
the Raman mode frequencies as obtained from ab-initio calculations. Note
the appearance of new modes above 2 GPa.FIG. 2. Pressure dependence of Raman mode frequencies of CuLaO 2. The
solid lines are linear fit to data in a particular phase.133507-3 Salke et al. J. Appl. Phys. 115, 133507 (2014)
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32Ab-initio calculations of phonon frequencies were carried
out to assign the Raman modes. The vertical bars in Figure 1
show the calculated Raman frequencies in the phase PI, fromab-initio calculations. Both calculated Raman frequencies
and the pressure dependence of Raman frequencies are given
in Table I. It may be noted that the frequencies of both the
modes as well as their pressure dependencies are found to be
under-estimated as compared with the experimental values.
The temperature dependence of Raman modes is investi-
gated to extract information about the anharmonicity of
Raman modes which plays an important role in the thermal
expansion of a material. Figures 3(a) and 3(b) show the
Raman spectra at various temperatures and Figure 4shows
the temperature dependence of Raman modes in the range
77–593 K. There are no discontinuous changes in thistemperature range indicating absence of any phase transition.
Both the modes show normal anharmonic behavior with lin-
ear dependence indicating predominantly three phonon decayprocess. Beyond 593 K, we did not observe any Raman
modes due to darkening of the sample, which may be prob-
ably due to the transformation of the sample to CuLaO
2.62.35
The temperature dependence of phonon frequency arises
due to thermal expansion of the lattice and anharmonic inter-
actions between them. For an isotropic system, phonon fre-quency can be considered as a function of volume and
temperature. The change in phonon frequency as a function
of temperature can be separated into a quasiharmonic contri-bution which arises only due to change in volume, also
called “implicit anharmonicity” and a purely anharmonic
contribution (explicit anharmonicity) which arises due tochanges in vibrational amplitude.
36Raman spectroscopic
studies at high pressures and temperature are useful in sepa-
rating these two parts. At a particular pressure, the totalchange in phonon frequency due to temperature can be
expressed as follows:
@xi
@T/C18/C19
p¼@xi
@V/C18/C19
T@V
@T/C18/C19
pþ@xi
@T/C18/C19
V: (1)
This can also be written as
1
xi@xi
@T/C18/C19
p¼/C0aciTþ1
xi@xi
@T/C18/C19
V(2)
where ciT¼/C0@lnxi
@lnV/C16/C17
T¼B0
xi/C16/C17
@xi
@P/C16/C17
Tis the isothermal
Gr€uneissen parameter, ais the volume thermal expansion
coefficient, and B0is bulk modulus.
The left-hand side of Eq. (2)gives the temperature de-
pendent isobaric frequency shift, which is the total anharmo-nicity effect as measured in temperature dependent Raman
experiments. The first term on the right-hand side is theTABLE I. Experimental and calculated Raman mode frequencies at room pressure and their pressure coefficients, experimental temperature coefficient s and
the anharmonicity calculated using a Bulk modulus of B0¼154 GPa and thermal expansion coefficient a¼1.07/C210/C05K/C01. The numbers with “a” in the first
column indicate the new modes that appear in the high pressure phase PII which are obtained by extrapolation of high pressure data to ambient pressure.
PI
Mode
frequency, (cm/C01)@xi
@T/C16/C17
p
(cm/C01K/C01)@xi
@P/C16/C17
T
(cm/C01GPa/C01)Total
anharmonicity
(10/C05K/C01)Implicit
(pure-volume)
(10/C05K/C01)Explicit
(pure-temperature)
(10/C05K/C01)PII@xi
@P/C16/C17
T
(cm/C01GPa/C01)
114a…… … … … /C00.9(3)
116a… … … … … 1.6(1)
147a… … … … … 0.9(2)
191a… … … … … 2.4(3)
273 ( EgCal.) … 4.1 … … … …
318(Eg) /C00.0056(8) 5.0(7) /C01.76 /C02.59 0.83 /C01.4(2)
324a…… … … … /C03.0(8)
409a… … … … … 4.4(8)
620 ( A1gCal.) … 6.5 … … … …
652(A1g) /C00.005(1) 9(1) /C00.77 /C02.27 1.50 …
695a… … … … … 1.2(9)
748a…… … … … /C00.7(2)
FIG. 3. (a) and (b) Raman spectra of CuLaO 2at various temperatures.133507-4 Salke et al. J. Appl. Phys. 115, 133507 (2014)
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32implicit anharmonicity arises due to isothermal frequency
shift as a function of pressure. This is the volume contribu-
tion to the frequency shift. The second term on the right-
hand side of Eq. (2)is the explicit anharmonic contribution
to the frequency shift which is the pure-temperature effect.
The results as summarized in Table I, separate the total fre-
quency shifts into the pure-volume and pure-temperaturecontributions of Raman active modes. We have used experi-
mental value of bulk modulus B
0¼154 GPa obtained from
our high pressure x-ray diffraction experiments on CuLaO 2,
which will be discussed later. Volume thermal expansion
coefficient a¼1.07/C210/C05K/C01in the range 300 K to 600 K
is used from Ref. 7. Though ideally, this formalism can be
applied only for isotropic systems, where the phonon fre-
quency is considered to be a function of volume and temper-
ature x(V, T), it has been applied for uniaxial systems,
where the phonon frequency depends also on c/aratio.37The
volume contribution so calculated has been found to differ
from the accurately calculated value as in Ref. 38obtained
using formalism for uniaxial systems by about 10%. This is
because the relative change in c/ais an order of magnitude
less than the relative change in volume with pressure or tem-perature.
37In the present case, in the absence of uniaxial
pressure data, the anharmonicity is estimated using the
expressions for cubic systems. As seen in the Table I,
pure-volume or the implicit contribution is dominant for
both the modes.
Resistance measurements
Figure 5shows the pressure dependence of resistance for
CuLaO 2. Since the measurements were done on compactedpolycrystalline sample along with electrical contacts via pres-
sure, initial value of resistance was quite high ( >20 MX).
Hence, we have plotted the data above 2 GPa. As pressure isfurther increased, the resistance of the sample decreases at a
rate of 0.34 K X/GPa up to 5.3 GPa; beyond that the resistance
drops by three orders of magnitude indicating abrupt changesin the material. This is around the pressure region of second
high pressure transition, where the intensity of Raman modes
is found to vanish. An abrupt change in resistance in a semi-conductor under pressure mainly arises from a change in the
energy band gap, as the applied pressure changes the elec-
tronic band structure thereby changing the number of elec-trons in the conduction band and holes in the valence band.
39
Thus, the sharp decrease in the resistance beyond 5.3 GPa isan intrinsic nature of the sample and can be attributed to theabrupt decrease in band gap with increase in pressure. On fur-
ther increase of pressure up to 10 GPa (the highest pressure
reached in the present investigations), the resistance contin-ued to decrease but with much slower rate. The pressure de-
pendence of electrical resistance correlates well with the
second high pressure phase transition involving decrease inband gap at around the same pressure as disappearance of
Raman bands. The differences in transition pressures by two
techniques could be due to the presence of quasihydrostaticconditions of resistance measurements where solid medium is
used as pressure transmitting medium.
High pressure X-ray diffraction
In order to confirm the phase transitions observed by
Raman spectroscopy, in situ x-ray diffraction experiments
were carried on CuLaO 2up to high pressures of 12 GPa.
Figure 6shows the ADXRD pattern of CuLaO 2at various
pressures. Above 2.0 GPa, two new peaks appear in the pat-tern in the low angle region indicative of a structural transition
corroborating the results obtained by Raman spectroscopy.
Beyond 7 GPa, there is a broadening of all the sample peaksand a redistribution of intensity indicating onset of disorder.FIG. 4. Variation of Raman mode frequencies with temperature.
FIG. 5. Variation of electrical resistance of CuLaO 2with pressure.FIG. 6. Evolution of the diffraction pattern of CuLaO 2as a function of pres-
sure. * indicates the peaks due to the pressure marker. Arrow marks indicate
the new peaks that appear after transition to PII.133507-5 Salke et al. J. Appl. Phys. 115, 133507 (2014)
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32These observations are again consistent with the results of
Raman spectroscopic measurements. Rietveld analysis of the
x-ray diffraction data in the ambient phase reveals that as in
other delafossites, c/aratio increases with pressure, as shown
in Figure 7(a). Figure 7(b)shows the variation of normalized
lattice parameter with pressure. The axial compressibility Ka
and Kcobtained using equation K¼/C01
V/C0/C1ð@V
@PÞTare
2.5(1) /C210/C03GPa/C01and 1.04(7) /C210/C03GPa/C01, respectively.
Similar to other delafossites, a-axis is found to be more com-
pressible than c-axis resulting in increase in c/awith pressure
which may make system unstable and lead to phase transition.
The unit cell volumes at different pressures were fitted with
the 3rdorder Birch-Murnaghan equation of state (BM-EOS)
and are shown in Figure 7(c). Error in the volume is negligible
hence it cannot be seen in the figure, though it is plotted. The
zero pressure volume, bulk modulus, and pressure derivativeof bulk modulus obtained from the BM-EOS are 217.3(2) A ˚
3,
154(25) GPa, and 4.8, respectively. The error in estimated
bulk modulus is quite high due to coexistence of phases andthe small pressure range of stability of the ambient phase. As
in the case of other delafossites like CuAlO
2and
CuGaO 2,14,15we could not index the diffraction peaks corre-
sponding to the high pressure daughter phase and hence the
structures of high pressure phases could not be determined.
From the observed diffraction peaks of high pressure phasePII, it can be mentioned that its structure is different from the
known high pressure phase of other delafossites like CuFeO
2and CuCrO 2.10,11As we do not have close data points in x-ray
diffraction measurements, the phase transition pressures are
estimated from Raman spectroscopy data. Phase transitionpressure as measured by x-ray diffraction measurements is in
general slightly higher, as compared to that Raman spectro-
scopic measurements, due to the fact that Raman spectroscopyis a local probe whereas x-ray diffraction is a bulk tech-
nique.
40Note that changes in optical properties occur
at similar pressures as observed in the structural and vibra-tional measurements, suggesting a correlation between all
phenomena.
In order to recover large volume of high pressure meta-
stable phase PII, we have also used the large volume
Bridgman anvil press to pressurize sufficient quantity of
sample with no pressure transmitting medium. The XRDdata were collected on as-synthesized sample and recovered
sample from non-hydrostatic compression of 10 GPa using
a standard diffractometer. Figure 8shows XRD pattern of
CuLaO
2ambient phase and pressure quenched from
10 GPa, recorded with Mo K awith k¼0.7107 A ˚.P r e s e n t
non-hydrostatic experiments show the same signatures ofthe first high pressure phase as in hydrostatic, synchrotron
based XRD data confirming the absence of role of devia-
toric stresses in this phase transition. However, due to theappearance of only two new clear peaks, coexistence of dif-
fraction peaks and broadening of all the peaks from ambient
structure, it was not possible to solve the high pressurestructure. The recovery of first high pressure phase after
pressure release has potential technological applications in
synthesis of new materials with tailored physical properties.
In order to understand the high pressure behavior of
delafossite compounds, the compressibility data of CuLaO
2
obtained from present studies are compared with the reported
data of other delafossite compounds and they are presented
in Table II. It is noted that the physical parameters like bulk
modulus obtained experimentally for CuLaO 2agree well
with that of the other members of the delafossite family. The
anisotropic nature of compressibility in CuLaO 2is in tune
with that of other delafossites. The present results also give aclue to systematic understanding of high pressure behavior
of copper delafossites. As proposed earlier
24in the family ofFIG. 7. (a) Variation of c/awith pressure in the ambient phase. (b) Variation
of normalized lattice parameters. (c) Variation of cell volume with pressurein the ambient delafossite phase. Square symbols are experimental data
points and solid line is the fitted data to the third order Birch–Murnaghan
equation of state.
FIG. 8. XRD pattern of CuLaO 2, as-synthesized (blue) and pressure
quenched from 10 GPa (red), recorded with Mo K awith k¼0.7107 A ˚.
Arrow marks indicate the diffraction peaks due to the first high pressure
phase.133507-6 Salke et al. J. Appl. Phys. 115, 133507 (2014)
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158.109.139.195 On: Fri, 19 Dec 2014 05:22:32delafossites Cu MO2(forM¼Al, Ga, and La), the variation
in the first transition pressure can be correlated to the ionic
radii of trivalent cation M3þ. The first transition pressure
decreases from 34 GPa in CuAlO 2to 1.8 GPa in CuLaO 2as
the radius increases from 0.54 to 1.03 A ˚. We observe that the
first transition pressure is inversely proportional to the ionicradius of M
3þin this class of delafossites Cu MO2. Thus, a
general inference of the pressured induced phase transition is
related to the deformation of bonding and electronic struc-ture around the of M
3þion and hence the transition can be
attained at lower pressure for larger and highly polarizable
ions. Furthermore, the observation of phase transitionaccompanied by a change in band gap in CuLaO
2, at moder-
ate to lower pressure, will have merit to envisage applica-
tions like touch panel and sensors.
CONCLUSION
Raman spectroscopic studies point out towards two
phase transitions in CuLaO 2at 1.8 GPa and 7 GPa which are
further supported by electrical resistance and x-ray diffrac-
tion measurements. There is an increase in anisotropy with
pressure in the ambient phase, typical of delafossite familyof compounds. From x-ray diffraction measurements, bulk
modulus of CuLaO
2is determined to be 154(25) GPa. The
changes in the resistance at the second high pressure transi-tion are indicative of a band gap collapse. The first transition
pressure is found to vary inversely as the ionic radius of M
3þ
in copper delafossite Cu MO2.
ACKNOWLEDGMENTS
The authors thank Dr. S. L. Chaplot and Dr. R.
Mukhopadhyay for support and encouragement. N.P.S.acknowledges Department of Atomic Energy, India for
financial support.
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CuLaO 2CuAlO 2
(Ref. 14)CuGaO 2
(Ref. 13)CuFeO 2
(Ref. 17)CuCrO 2
(Ref. 16)
B0(GPa) 154(25) 200(10) 202(15) 156 126.8
Ka(10/C03GPa/C01) 2.5(1) 2.06(5) 1.96(5) 2.58(4) 2.30(6)
Kc(10/C03GPa/C01) 1.04(7) 0.83(4) 0.75(4) 0.65(2) 0.39(9)133507-7 Salke et al. J. Appl. Phys. 115, 133507 (2014)
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1.4890347.pdf | Thermal transport properties of metal/MoS2 interfaces from first principles
Rui Mao, Byoung Don Kong, and Ki Wook Kim
Citation: Journal of Applied Physics 116, 034302 (2014); doi: 10.1063/1.4890347
View online: http://dx.doi.org/10.1063/1.4890347
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/3?ver=pdfcov
Published by the AIP Publishing
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131.217.6.8 On: Mon, 01 Sep 2014 21:31:20Thermal transport properties of metal/MoS 2interfaces from first principles
Rui Mao, Byoung Don Kong,a)and Ki Wook Kimb)
Department of Electrical and Computer Engineering, North Carolina State University, Raleigh,
North Carolina 27695-7911, USA
(Received 9 June 2014; accepted 4 July 2014; published online 15 July 2014)
Thermal transport properties at the metal/MoS 2interfaces are analyzed by using an atomistic phonon
transport model based on the Landauer formalism and first-principles calculations. The considered
structures include chemisorbed Sc(0001)/MoS 2and Ru(0001)/MoS 2, physisorbed Au(111)/MoS 2,a s
well as Pd(111)/MoS 2with intermediate characteristics. Calculated results illustrate a distinctive
dependence of thermal transfer on the details of interfacial microstructures. More specifically, the
chemisorbed case with a stronger bonding exhibits a generally smaller interfacial thermal resistancethan the physisorbed. Comparison between metal/MoS
2and metal/graphene systems suggests that
metal/MoS 2is significantly more resistive. Further examination of lattice dynamics identifies the
presence of multiple distinct atomic planes and bonding patterns at the interface as the key origins ofthe observed large thermal resistance.
VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4890347 ]
I. INTRODUCTION
Transition-metal dichalcogenides (TMDs) have emerged
as key candidates for the beyond-graphene, two-dimensional
(2D) or van der Waals crystals due to their distinctive electri-cal, optical, and thermal properties.
1,2In each case, the bulk
material is formed by a stack of 2D monolayers through the
weak van der Waals interactions as in graphene, while theintralayer binding is much stronger. For instance, monolayer
of molybdenum disulfide (MoS
2)—a prototypical example—
consists of one Mo plane sandwiched between two S planesvia the covalent bonding that is arranged in a trigonal pris-
matic network.
2Consistent with its diatomic nature, MoS 2
exhibits a non-zero energy gap whose magnitude depends on
the layer thickness.2–4Successful fabrication of a transistor
with a large on/off ratio (as high as 108owing to the large
gap)5has made this material an early focus of investigation
among the TMDs.
As in the metal/graphene (metal/Gr) cases, it was
recently found that the metal/MoS 2interfaces can be classi-
fied into two categories—physisorption and chemisorp-
tion.6,7The former generally has a smaller binding energy
and a larger interfacial separation than the latter. Since thecontacts with metallic electrodes comprise a crucial compo-
nent of the high-performance electronic devices, consider-
able efforts have been devoted to investigate the electricaltransport properties of the metal/MoS
2structures.8,9In com-
parison, thermal transport has received much less attention.
Nonetheless, the impact of efficient heat transfer on the oper-ation of 2D crystal devices is significant when considering
the inevitable presence of heterogeneous interfaces and sub-
sequent joule heating in the layered structures.
10–12
Accordingly, a comprehensive understanding of thermal
properties at the interface with the metallic contacts is cru-
cial from the perspective of both fundamental low-dimensional physics and practical applications of this emerg-
ing material system.
In this paper, we present a detailed theoretical analysis
of interfacial thermal resistance in the metal/MoS 2system
via phonon transport. The sample structures are chosen to
reflect the range of typical interfaces from chemisorption to
physisorption. For an atomistic description of lattice dynam-ics at the interface, our theoretical approach adopts a first-
principles method based on density functional theory (DFT)
and density functional perturbation theory (DFPT).
13,14Then
the phonon/thermal transport characteristics are determined
via the Green’s function techniques15–17in the Landauer for-
malism.18The calculation results are examined in terms of
interfacial microstructures and force constants to identify the
key contributors to the disparate thermal properties at theconsidered interfaces. Comparison is also made with those
of the corresponding graphene based structures.
19
II. THEORETICAL MODEL
Thermal conduction across the heterogeneous metal/
MoS 2interface is characterized by the interfacial resistance
or the so-called Kapitza resistance.20,21In the phonon trans-
port calculation, we consider a three parted system where the
central interface region (i.e., the region of interest) is con-
nected to the thermal reservoirs on the left and the right withtwo semi-infinite leads (labeled LandR), often known as the
lead-conductor-lead configuration.
17,22In the nanoscale, the
Kapitza resistance can be evaluated by extending theLandauer formalism for electrons to phonons. Then, the ther-
mal current density can be written as
JT
L;TRðÞ ¼/C22h
2pðþ1
0dxxTphxðÞnT L;xðÞ /C0nT R;xðÞ ½/C138 ;
(1)
where nðTL;R;xÞis the equilibrium Bose-Einstein distribu-
tion for phonons, TL;R¼T6DT=2 is the temperature in thea)Present address: U.S. Naval Research Laboratory, 4555 Overlook Avenue,
Washington, District of Columbia 20375, USA.
b)Electronic address: kwk@ncsu.edu
0021-8979/2014/116(3)/034302/5/$30.00 VC2014 AIP Publishing LLC 116, 034302-1JOURNAL OF APPLIED PHYSICS 116, 034302 (2014)
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131.217.6.8 On: Mon, 01 Sep 2014 21:31:20left or right thermal reservoir, and TphðxÞis the phonon
transmission function through the structure. In the limit of
small DT, the phonon contribution to the thermal conduct-
ancejphðTÞ¼JðTÞ=DTis then given by
jphTðÞ¼1
2p/C22hðþ1
0d/C22hxðÞTphxðÞ/C22hx@nT ;xðÞ
@T/C20/C21
:(2)
The thermal resistance (normalized to the cross-sectional
area of the interface) is then obtained by inverting Eq. (2).
The phonon transmission function TphðxÞcan be calculated
by adopting a real-space Green’s function approach, similar
to the one used for electronic transport.17In particular, one
can take advantage of the following analogy between the
electronic and phononic systems: EelI$x2MphandHel$
Kph:Here, HelandEelare the Hamiltonian and the eigen-
energy in the electronic system, whereas KphandMphdenote
the matrix of the interatomic force constants (IFCs) and the
diagonal matrix corresponding to the mass of the atoms.14,23
Additionally, Isymbolizes the identity matrix and xthe pho-
non frequency. Further details on the theoretical formulation
can be found in Refs. 23and19.
In the present treatment, the IFCs (thus, Kph) are calcu-
lated fully from the first principles within the DFT/DFPT
framework that allows accurate consideration of the micro-scopic geometry as well as the chemical and electronic mod-
ification at the interface without resorting to
phenomenological or ad hoc models.
13,23Specifically, the
QUANTUM-ESPRESSO package24is used with ultrasoft
pseudopotentials in the generalized gradient approximation
(GGA). A semiempirical van der Waals force correction isalso added to the density functional calculation (GGA þD)
to obtain more accurate interlayer distances.
25,26It has been
verified that the GGA þD routine provides the optimal
results for layered MoS 2structures in comparison to other
approaches such as the nonlocal exchange-correlation func-
tional treatment and the local density approximation.27A
minimum of 50 Ry is used for the energy cut-off in the plane
wave expansion along with the charge truncation of 600 Ry.
In addition, the Methfessel-Paxton first-order spreading withthe smearing width of 0.01 eV is employed. The momentum
space is sampled on a 6 /C26/C22 Monkhorst-Pack mesh in the
first Brillouin zone. The realistic interface structures areobtained through geometry optimization, where the total
energy and atomic force are minimized. The energy conver-
gence threshold is chosen at 10
/C08Ry and the maximum
forces acting on each atom is relaxed below 10/C04Ry.
III. RESULTS AND DISCUSSION
In order to achieve the maximum orbital overlap (i.e., a
good electrical contact), it is highly desirable to minimize
the lattice constant mismatch between the metallic material
and MoS 2. In addition, the work function of metal species
must be close to that of the conduction band minimum or the
valence band maximum for a small Schottky barrier,
although the Fermi-level pinning may affect the final barrierheight.
28,29Following these criteria, the metal/MoS 2struc-
tures selected for the current investigation are Au(111)/MoS 2, Pd(111)/MoS 2, Ru(0001)/MoS 2, and Sc(0001)/MoS 2.
The lattice constant of MoS 2is fixed at the optimized value
3.22 A ˚. The 1 /C21 unit cell of face-centered cubic Sc(0001)
is commensurate with the 1 /C21M o S 2with only a 2.4% lat-
tice mismatch, whereas the 2 /C22 unit cell is needed for
Au(111), Pd(111), and Ru(0001) to make the lattice mis-match below 3.4% against theffiffi ffi
3p
/C2ffiffi ffi
3p
R30 8unit cell of
MoS
2. Figure 1shows the resulting interfacial structures of
the considered material combinations after geometry optimi-zation. In accord with earlier studies,
7,28our calculation
clearly illustrates that Ru and Sc form strong bonding with
MoS 2at the interface (i.e., chemisorption) resulting in a rela-
tively small interfacial separation (2.20 A ˚and 2.02 A ˚, respec-
tively). On the other hand, Au is physisorbed on MoS 2
through weak van der Waals bonding with a larger interlayer
distance (2.77 A ˚). As for Pd(111)/MoS 2, the interfacial sepa-
ration of 2.18 A ˚is obtained in close agreement with a recent
DFT calculation (weak chemisorption).28These interfacial
structures serve as the central region in the previously men-
tioned lead-conductor-lead configuration. Two leads consist-
ing of respective bulk materials (i.e., bulk metal and bulkMoS
2) are connected seamlessly to the interface region and
modeled separately. No appreciable mismatch (i.e., resist-
ance) exists between the leads and the conductor.
Phonon transport through the different metal/MoS 2
interfaces is calculated in Fig. 2by using the theoretical
model described earlier. The results are plotted only up to100 cm
/C01in order to illustrate clearly the contributions of
dominant low-lying acoustic branches. The impact of high-
frequency optical phonons is negligible while not shown ex-plicitly. As evident from the figure, the transmission function
of the physisorbed Au/MoS
2interface exhibits more resonant
features than those of the chemisorbed cases. This is due tothe fact that the Au and S atoms are bonded through the
weak van der Waals force, leading to limited hybridization
FIG. 1. Side view of the metal/MoS 2systems under consideration: (a)
Sc(0001)/MoS 2, (b) Ru(0001)/MoS 2, (c) Pd(111)/MoS 2, and (d) Au(111)/
MoS 2. Two upper layers represent MoS 2.034302-2 Mao, Kong, and Kim J. Appl. Phys. 116, 034302 (2014)
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131.217.6.8 On: Mon, 01 Sep 2014 21:31:20of vibrational modes at the interface. Accordingly, phonon
transmission is more selective with certain frequenciesblocked almost completely (i.e., nearly zero transmission).
On the other hand, the strong interactions at the chemisorbed
interfaces (e.g., Sc/MoS
2and Ru/MoS 2) result in substan-
tially mixed properties between the corresponding metal and
MoS 2. Hence, phonon propagation encounters a more grad-
ual barrier with much less hindrance over a broader fre-quency spectrum [see Figs. 2(b) and2(c)]. As for the Pd/
MoS
2contact, the transmission function in Fig. 2(d) resem-
bles those of chemisorbed cases although to a lower degree.The bonding between the Pd and S atoms appears to be not
as strong as the other two cases, particularly the Sc/MoS
2
structure. Such intermediate characteristics were also
observed when Pd is paired with graphene.19The Pd/Gr
interface was deemed a mixture of chemisorption and physi-
sorption with only weak, incomplete hybridization.
Figure 3shows the interfacial thermal resistance
obtained as a function of temperature. Since the total resist-
ance of the structure contains the contribution from the leadsas well, the intrinsic thermal resistance at the junction is
deduced by subtracting this portion in a manner analogous to
electrical transport.
16The results exhibit the 1/T dependencein the low temperature region, while staying almost invariant
between 200 K and 450 K. The dashed vertical line marks
the values at room temperature, which are 5.8 /C210/C08Km2/
W, 1.9 /C210/C08Km2/W, 3.1 /C210/C08Km2/W, and 1.2 /C210/C07
Km2/W for Au/MoS 2, Sc/MoS 2, Ru/MoS 2, and Pd/MoS 2,
respectively. Consistent with the expectation from the trans-mission function comparison, the chemisorbed interfaces
(Sc/MoS
2and Ru/MoS 2) show the lowest thermal resistances
among the considered. Of the two chemisorbed examples,Sc/MoS
2provides a smaller value than Ru/MoS 2that can be
understood, in part, by the difference in the interfacial sepa-
ration (2.02 A ˚versus 2.20 A ˚) as the interatomic distance
tends to indicate the strength of the bonding between the
atoms. In this regard, Pd/MoS 2provides an exception with
the largest resistance even though it is supposed to be chemi-sorption albeit weakly. The physisorbed Au/MoS
2is actually
placed in between the Pd/MoS 2and the (strongly) chemi-
sorbed cases. A similar feature was reported in the Pd/Grstructure earlier.
19
Considering their seeming resemblance, a detailed com-
parison between the metal/MoS 2and metal/Gr systems could
provide an insight into the lattice dynamics at the 2D crystal
heterojunctions. The most crucial finding is that the metal/
MoS 2interfaces exhibit considerably larger resistances than
the metal/Gr counterparts. For instance, Ni/Gr that is a typi-
cal chemisorbed metal/Gr interface can reach a low thermal
resistance of 3.9 /C210/C09Km2/W, while the lowest value for
the chemisorbed metal/MoS 2is about five times higher at
1.9/C210/C08Km2/W. This difference suggests strong depend-
ence of the Kapitza resistance on the specifics of the interfa-cial microstructures. To further illustrate this point, two
essential factors—the atomic scale morphology and IFCs—
are carefully examined at the boundaries.
The schematics in Fig. 4highlight the dissimilarity in the
interfacial structures of Ni/Gr and Ru/MoS
2. Unlike grapheneFIG. 2. Phonon transmission function vs. frequency at the interface in the
metal/MoS 2structures under consideration. The magnitude of the transmis-
sion function can be larger than 1 since it also reflects the number of avail-
able modes.
FIG. 3. Interfacial thermal resistances vs. temperature for (a) Au/MoS 2, (b)
Sc/MoS 2(c) Ru/MoS 2, and (d) Pd/MoS 2. The vertical dashed lines mark the
resistances at room temperature (300 K).
FIG. 4. Schematic view of the interfacial nanostructure for Ni/Gr and Ru/MoS
2with the atomic mass listed for the compositional atoms (in the unified
atomic mass unit u). The red solid box highlights the difference between gra-
phene and MoS 2in the atomic configuration and morphological arrange-
ment. The dashed blue box shows the mass disorder introduced by the sulfur
layer.034302-3 Mao, Kong, and Kim J. Appl. Phys. 116, 034302 (2014)
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131.217.6.8 On: Mon, 01 Sep 2014 21:31:20that is formed by a single plane of C atoms, each layer of
MoS 2consists of one monatomic Mo plane sandwiched
between two monatomic S planes. This multi-layer structure
of MoS 2damps the phonon vibrations across the interface.
Additionally, the Mo and S atoms are much heavier than C
atoms (S-32.065 u, Mo-95.96 u vs. C-12.01 u in the unified
atomic mass unit), which also contributes significantly to thereduced phonon transfer. In fact, experimental investigations
have observed the low thermal conductivity in both bulk and
thin-film TMDs due to the high average mass, atomic com-plexity, and weak bonding.
12A closer scrutiny shows that the
larger mass variation may be yet another reason for the larger
thermal resistance of metal/MoS 2. When phonons propagate
through the interface region, they encounter a drastic change
in the atomic mass. In the case of Ru/MoS 2, for instance, it
varies from 101.07 u to 32.065 u then to 95.96 u or vice versa.
In other words, the relatively lighter S atoms sandwiched
between the heavy Mo and contact metal atoms serve as anextra scattering layer due to the mass disorder. In this regard,
the case of metal-S-Mo
2is analogous to the hydrogen termi-
nated SiC on graphene (SiC-H/Gr), where the H adatoms pro-vide an additional scattering mechanism.
30On the other hand,
the conditions are much more straightforward in the metal/Gr
cases, with only the metal/carbon interaction at the interface;the phonons experience only a single alteration in terms of
mass (from 58.69 u to 12.01 u for Ni/Gr).Analyzing the impact of the second factor (i.e., the
IFCs), Fig. 5provides the interlayer force constants for the
two chemisorbed cases, Ru/MoS
2and Ni/MoS 2, deduced
from the DFPT calculation. The height of each bar symbol-
izes the interaction strength between two neighboring layers.
For example, the first bar on the left denotes the interactionbetween layers 1 and 2; the next bars are for layers 2 and 3,
and so on. In both of these plots, the metallic layers are up to
layer 5. For MoS
2, layers 6 to 8 correspond to the covalently
bonded S-Mo-S planes (i.e., the first monolayer from the
interface). Accordingly, the S atoms in layer 9 belong to the
second monolayer of MoS 2. On the other hand, layers 6 to
10 represent the first through fifth graphene layers from the
interface that are held together by the van der Waals force.
We focus on the force constants between layers 5 and 6,where the physical interface of two heterogeneous materials
is located. The magnitudes of these force constants indicate
the interaction strength between the metal atoms and eitherthe S or C atoms. As shown, the force constant between Ru
and MoS
2is around 0.03 a.u. that is much smaller than the
corresponding quantity of approximately 0.1 a.u. between Niand graphene (where a.u. denotes atomic Rydberg units).
The suggested weaker interaction between the metal and the
S atoms is further verified by the analysis of electronic bind-ing energy for the chemisorbed interfaces available in the lit-
erature.
7,9Clearly, it is not unreasonable to anticipate lower
phonon/thermal transmission at an interface with the lesseffective bonding and the more complex morphology.
In the case with Au or Pd, the physical picture appears
to be somewhat different. Our calculation as summarized inTable Iindicates that the Au/MoS
2and Pd/MoS 2contacts ex-
hibit interfacial force constants similar to the corresponding
Au/Gr and Pd/Gr cases. In fact, those with MoS 2are slightly
larger than the graphene counterparts.6,7With the binding
interaction much weaker than the chemisorbed, the distin-
guishing factor for the thermal resistance at these interfacesmay be the mass variation/disorder rather than the magnitude
of force constant. Accordingly, MoS
2again shows a larger
resistance than graphene when interfaced with Au or Pd.Nonetheless, the relatively muted differences between metal/
MoS
2and metal/Gr in the physisorbed (and the intermediate)
cases can be attributed to the comparable bonding strengths.
IV. SUMMARY
Thermal transport in the metal/MoS 2heterostructures is
investigated by using an atomistic model based on the DFT
FIG. 5. Interlayer force constants for Ru/MoS 2and Ni/Gr. The height of each
bar represents the interaction strength between two layers, where a.u. standsfor atomic Rydberg units. In both plots, the metallic layers are up to layer 5
(i.e., 1–5). The dashed-dotted line indicates the physical interface with the
metal as MoS
2(in the S-Mo-S order) or graphene starts from layer 6.
TABLE I. Thermal properties at the relevant metal/MoS 2and metal/Gr interfaces. a.u. denotes atomic Rydberg units.
Bonding characteristics Interfacial separation (A ˚) Interfacial forceconstant (a.u.) Thermal resistance (Km2/W)
Sc/MoS 2 Chemisorption 2.02 0.043 1.9 /C210/C08
Ru/MoS 2 Chemisorption 2.20 0.034 3.1 /C210/C08
Au/MoS 2 Physisorption 2.77 0.005 5.8 /C210/C08
Pd/MoS 2 Mixed 2.18 0.0136 1.2 /C210/C07
Ni/GraChemisorption 2.02 0.103 3.9 /C210/C09
Au/GraPhysisorption 3.31 0.004 1.7 /C210/C08
Pd/GraMixed 2.43 0.0125 3.4 /C210/C08
aReference 19.034302-4 Mao, Kong, and Kim J. Appl. Phys. 116, 034302 (2014)
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131.217.6.8 On: Mon, 01 Sep 2014 21:31:20formalism and the Green’s function approach. The obtained
characteristics indicate generally more effective thermal
transfer at the chemisorbed surface owing to the strongerinteraction with MoS
2. One exception is Pd/MoS 2with a
hybrid bonding at the interface that actually shows the larg-
est interfacial thermal resistance among the considered.Comparison with metal/Gr reveals that metal/MoS
2interfa-
ces are more resistive in terms of phonon/thermal transport.
A detailed examination of interfacial geometry and the lat-tice dynamics identifies the difference in atomic scale mor-
phology, composition, and interaction strength as the main
origins of resistive nature in the metal/MoS
2system. More
specifically, the three-plane structure with heavy atoms, the
mass disorder introduced by the light-massed sulfur plane as
well as the different bonding forces at the interface, all con-tribute to phonon scattering and subsequently a large interfa-
cial thermal resistance. As these features are not unique to
MoS
2, other TMDs are expected to be similarly resistive in
heat transfer when interfaced with a metal.
ACKNOWLEDGMENTS
The authors would like to thank Cheng Gong for useful
discussions. This work was supported, in part, by SRC/NRISWAN.
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131.217.6.8 On: Mon, 01 Sep 2014 21:31:20 |
1.4896697.pdf | Electricity access in urban slum households
of Bangladesh: A case of Dhaka
Molla Shahadat Hossain Lipu1,a)and Arif Md. Waliullah Bhuiyan2
1Department of Electrical and Electronic Engineering, University of Asia Pacific,
Dhaka 1209, Bangladesh
2Energy and Environmental Management, Europa-Universit €at Flensburg, Flensburg 24943,
Germany
(Received 6 January 2014; accepted 15 September 2014; published online 29 September 2014)
Dhaka, the capital city of Bangladesh, is one of the fastest growing cities in
Southern Asia, having population of more than 13 million, and is expected to
accommodate more than 20 million by 2025. This growth has been accompanied
by the growth of urban slums and the subsequent challenges to access basic urbanservices like water, sanitation, clean energy, and transport for the urban poor.
Despite its importance for basic survival, electricity supply is not recognized as a
basic urban service, as a result of which, the poverty alleviation and basicinfrastructure provision programs have not addressed this issue completely. On the
basis of a stakeholder interaction approach, following a set of logically sequenced
questions to assess the availability, accessibility, affordability, reliability andcontinuity of usage of electricity, this study assesses the current status of electricity
access in an urban poor area of Dhaka and identifies barriers to electricity access
from both demand and supply side. Barriers specific recommendations are alsosuggested based on the experiences from field visit and the best practices outside
Bangladesh are also identified.
VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4896697 ]
INTRODUCTION
With the rapid urbanization taking place in the world, it is expected that 59.7% of the
world population (4.9 billion) will live in cities in 2030.1This increase is even more striking in
the Asian countries, where the population in urban areas has increased from 22.7% to 37.1%
during 1970–2000, and is expected to rise to 54.1% in 2030.1In developing countries, the com-
bination of high population density, poverty and limited resources supports the rapid growth ofslum areas, mainly in the cities.
2With the rapid rise of slums around the world, the number of
slum dwellers is expected to rise to 2 billion by 2022.3Dhaka, the capital city of Bangladesh,
with an estimated 37% of its total 9 million population (2005) living in slums4is a prime exam-
ple of unprecedented growth of informal settlements where the dwellers mostly live below the
poverty line in terms of low living standards, productivity, and basic services.5Slums world-
wide share a number of common problems which are unauthorized and unsafe habitation with-out the access to government services.
3Governments have chronically failed to deal with the
growth of slums until the development became entrenched and as a consequence roads and
other infrastructures have not been planned well enough.
In recent years, there has been a growing interest in the issues of access of the poor to
energy supply.6–8Just as energy is instrumental for socio-economic development, equally appa-
rent is the issue of short supply of electricity that depresses economy, increases unemploymentthereby compromising development prospects.
9There are approximately 1.4 billion people who
lack access to electricity.10The necessity to establish and sustain electricity service in slum
a)Author to whom correspondence should be addressed. Electronic mail: lipuhossain@gmail.com. Tel.: þ8801781628171.
1941-7012/2014/6(5)/053112/14/$30.00 VC2014 AIP Publishing LLC 6, 053112-1JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 6, 053112 (2014)
areas may not always be recognized and allowed. Historically, electric utilities have experi-
enced or expected low or negative returns from expanding service to low income customers,
given their relatively low consumption levels and the added problems and costs of electrifying
these mostly informal areas. The companies strive to increase net revenue to improve their fi-
nancial viability as well as fulfill universal service policies that are increasingly being imposed
by regulators. In addition, slum consumers have very poor internal wiring, no ground fault pro-tection or circuit breakers and very long and often undersized wires or cables connecting them
to the electricity grid or to a neighbor. In these cases, risks of electrocution and fires are high,
further dragging families and communities down the economic ladder. The slum electrificationcan be an opportunity to increase revenues, albeit a risky one, that requires appropriate policy,
careful planning and execution and a sustained presence in the community for success.
Presently, 62% of the total population (including renewable energy) of Bangladesh have
access to electricity and per capita generation is 321 kWh, which is very low compared to other
developing countries.
11Most of the studies on electricity in Bangladesh are focused in urban
and rural areas with limited information and study on the electricity access in slum areas ofDhaka. Due to the lack of explicit policies, laws, and regulations on slum settlements, very of-
ten slum dwellers do not come into the picture of the national strategic plans and programs.
12
About 90% households in urban poor areas of Dhaka city have access to electricity.4However,
the slum areas have very limited access to electricity supply in terms of affordability, availabil-
ity, and reliability. Though the urban poor have access to electricity, most often it is used ille-
gally at extorted prices. There is a lack of effective monitoring practice by the utility companiesincluding purchasing power, quality control, transparent approach in the allocation, and optimal
resource utilization.
13Moreover, Dhaka city is suffering from scarcity of power supply.
Frequent load shedding is very common in summer-time with a 40% deficit of supply.14In the
absence of electricity, kerosene lamps called “Kuppi” and “Hurricane” are the major appliances
used by the urban poor to meet their lighting needs. These are very inefficient appliances which
have very low level of lighting emitting lots of smoke. Besides, these lamps have a high risk offire and negative impact on health.
The understanding of electricity access status could provide a base for future decisions on
electricity related planning for the poor in Dhaka. A better understanding of electricity accesscan inspire the design and development of pro-poor policies and pricing of modern energy serv-
ices to reduce energy poverty.
15Therefore, this paper aims to assess the electricity access status
of urban poor in Dhaka. The objectives of this research are:
1. To assess the current level of access to electricity in a slum area of Dhaka.
2. To identify supply side and demand side barriers for electricity access to the urban poor of
Dhaka.
3. To provide specific recommendations and identify best practices to overcome the barriers to
promote electricity access for the urban poor of Dhaka.
The paper is organized as follows. First, the methodology section describes the procedures used
to address the research questions of the study. Second, the current status of electricity access, includ-
ing household fuel consumption pattern in an urban poor area of Dhaka is presented next. Third, wehighlight both the supply side and demand side barri ers to electricity access. Finally, the paper con-
cludes with barriers specific recommendations and policy implications on electricity access.
METHODOLOGY
Korail slum32was chosen as the study area for the purpose of carrying out the research
and to attain the objectives. This slum was purposely selected since it has the largest slum com-munities of Dhaka considering population, area, and the number of years people have lived
there. The area is located under wards 19 and 20 of Dhaka and shares its borders with two
wealthy neighborhoods, Banani and Gulshan. The Korail slum in Dhaka sits on over 90 acresof the government land owned by the state-owned Bangladesh Telecommunications Company
Limited, the Public Works Department and the Ministry of Information and Communication.053112-2 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)The population of Korail slum is about 100 000 and generally consists of 5 persons per family.4
Therefore, 100 families were surveyed with a 10% limited error.33
A random sampling was applied to select samples in each slum community in which an individ-
ual household was taken as a unit of the sample in this study. Random sample means all possible
samples of households in the study area have the equal chance of being selected. The random sam-
pling technique was chosen to avoid any kind of bias in the study. Usually, the random sampling is
done either by using a random number table or a com puter program. For this study, first, total sam-
ple size was determined using sampling equation. In formation on slum identification (ID) along with
address, map and number of households were coll ected from the Center of Urban Studies (CUS).
The random number was created against each of the slum using Excel RAND functions.
Both primary as well as secondary data on energy access of the urban poor were collected.
The data collection took place during November and December, 2012. The duration time of aninterview was about 30 min on average. The interviews were recorded and transliterated for fur-
ther analysis. Primary information was collected through reconnaissance surveys, direct observa-
tions, key informant interviews, household surveys, and focus group discussions. Secondary dataand information were collected from various sources like annual reports, previous theses,
research papers, journals, recognized websites and documents available in different agencies like
Bangladesh Bureau of Statistics (BBS), Local Government Engineering Department (LGED),Bangladesh Institute of Development Studies (BIDS), Bangladesh Rural Advancement
Committee (BRAC) NGO, Nagar Daridra Basteebashir Unnatan Sangstha (NDBUS) NGO,
Dhaka City Co-operation (DCC), National Housing Authority (NHA), Petro Bangla, BangladeshEnergy Regulatory Commission (BERC), Dhaka Power Distribution Company (DPDC) and
Dhaka Electricity Supply Company Limited (DESCO), and other concerned agencies. Detailed
map of each slum area along with slum ID in each ward, total number of population and house-holds was collected from the CUS. Some international articles (UNDP, World Bank) regarding
energy and poverty of Bangladesh were also reviewed. These data and information were utilized
to understand the socioeconomic background, livelihood operation, electricity related issues.Besides, the data and information were also used to cross check with current survey results.
The data collected from different sources and methods were analyzed both quantitatively
and qualitatively. After completion of household survey, the data were compiled and analyzedwith the help of Microsoft Excel and Statistical Package for the Social Science (SPSS) software.
General information such as demographic data, household sizes, income, occupation patterns,
type of houses, house ownership patterns as well as electrification rates, percentage of differentfuel usage for lighting, average consumption of different fuels were assessed by using descrip-
tive statistics such as frequency, percentage, average, standard deviation, and cross tabulation.
To measure the user satisfaction on electricity, Weighted Average Index (WAI) was
used.
16Level of satisfaction is ranked from 1 to 5 where 1 indicates the lowest level of satis-
faction and 5 the highest level of satisfaction.
Strongly dissatisfied Dissatisfied Neutral Satisfied Strongly satisfied
12 3 4 5
The equation shows the formulating of WAI using level of satisfaction,
WAI ¼½ ffSTS ð5ÞþfSð4ÞþfNeð3ÞþfDSð2ÞþfSDS ð1Þg/C138=N; (1)
where WAI is the weighted average index, fSTS is the frequency of strongly satisfied, fS is the
frequency of satisfied, fNe is the frequency of neutral, fDS is the frequency of dissatisfied,
fSDS is the frequency of strongly dissatisfied, and N is the total number of observations.
In order to know how slum households are electrified, there were questions on electricity
connection status of the households, such as whether they are serviced by the utility company053112-3 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)or from other sources. In addition, there were questions on mode of payment to know whether
they pay electricity bill by meter or by other methods. Some questions also included to know
the type of appliances used and their specifications (rating, capacity) as well as operating hours.
ANALYSIS AND KEY FINDINGS
Although 100% households in Korail slum have a ccess to electricity, it does not mean that
each and every slum household has an individu al metered electricity connection. Many slum
households are electrified through a single met er which is located at pole called pole meter. The
DESCO is responsible to provide electricity supp ly in Korail slum through pole meters regardless
of the illegal status of the slum area, by taking a hi gh amount as an advance electricity bill (as se-
curity deposit). The meter is authorized under the name of the slum representative/local leader/
area committee of the slum areas. Banks17stated that different government agencies that are re-
sponsible to provide energy services in the slum a reas do not get involved directly with slum com-
munities. The local leader called “Maastan” take s the responsibilities who acts as intermediary
between service provider and slum dwellers. As the services are only delivered by “Maastan” in
the slum areas, they take this opportunity by charging slum dwellers an exorbitant price. The first
reason for accessing this type of connection is the ir illegal status. A legal individual connection
requires a set of documents which urban poor living in the slum areas do not have. The second
reason is the high upfront cost of connection which consists of security deposit, meter cost, and in-
stallation cost including labor charge and wiring cost. The observations from the survey also indi-cated that urban poor pay a fixed amount electric ity bill either by equipment type or by agreed
sum through negotiation depending on the type of appliances used which is shown in Table I.
The level of access to electricity can also be estimated by ownership of electrical appliances.
Due to limited power supply available at house s as well as limited income, it is expected that
urban poor in Dhaka has limited access to different types of electrical appliances. The survey of
100 households indicated that the majority of t hem use one lamp for lighting and one fan for cool-
ing as the minimum basic need. Table Ishows that a total of 83% slum households own Compact
Fluorescent Lamp (CFL) (25 W), 38% own incandescent bulb (60 W), 11% own fluorescent tube
light (40 W). Fans are used by all income group s (77%). Television (TV) is usually owned by
middle income groups (34%), while the refrigerator is owned by high income households (3%).
User satisfaction on electrical system
WAI method was applied to measure the user satisfaction on electricity system. A total of
100 users were interviewed to know the users’ perception about electricity supply in slum areas.TABLE I. Unit price and percentage of households owning different appliances in Korail slum, Dhaka.
Name of appliance Incandescent lamp Fluorescent tube light CFL TV Fan Refrigerator
Percentage of households—users (%) 38 11 83 34 77 3
Unit price (BDT/month) 150 150 150 150 150 300
TABLE II. Electricity supply index-quality level for households [code: 1 ¼strongly dissatisfied, 2 ¼dissatisfied,
3¼neutral, 4 ¼satisfied, 5 ¼strongly satisfied].
Satisfaction parameterLevel of satisfaction
Mean SD 12 3 4 5
The amount of electricity supplied by the utility company 1 35 21 35 0 3.06 0.908
Time of hours of electricity supplied by the system 2 54 29 7 0 2.63 0.761Electricity bill 1 60 12 27 0 2.65 0.892Quality of power supply 1 9 63 27 0 3.16 0.615
Safety of the power supply 2 9 49 36 0 3.19 0.734053112-4 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)Users’ opinion on various characteristics with their mean and standard deviation (SD) is listed
in Table II.
The amount of electricity supplied by the system
The users were neither happy nor unhappy with the amount of electricity supplied by the
utility company. The mean value for this satisfaction parameter is 3.06 with a standard devia-
tion of 0.908. Although they have access to electricity, they have limited access to use all theappliances irrespective of their affordability. Slum dwellers live as a tenant with very less facil-
ity of electricity services. They pay the electricity bill by equipment type and most of the
houses have minimum two electrical points for using electrical appliances where one source isused for lighting purposes and another source to run a fan. Regardless of their interest or buy-
ing capacity to use other appliances, house owners do not allow slum dwellers to use more than
two electric sources due to limited capacity load of the pole meter.
Time of hours of electricity supplied by the system
Dhaka city is suffering from shortage of power supply. Frequent load shedding is very
common in summer-time. Load shedding occurs for 6–7 h in a day in cities and for 12 h in vil-
lages at regular intervals in a day.14During the survey, it was found that slum dwellers are suf-
fering due to not only limited access of power supply, but also the unavailability of the powersupply. Out of 100 households surveyed, 54 correspondents showed dissatisfaction towards
availability of electricity provided by the utility company. Some correspondents also reported
that the power line is cut off without giving any prior notice. Sometimes, the contractor fails to
pay the electricity bill to the utility office regularly. Besides, poor people use secondary fuels
like kerosene, candles, and rechargeable batteries during the time of load shedding which meansurban poor are not only charged for using electricity but also for secondary fuels to get a con-
tinuous supply of electricity.
Electricity bill
It is estimated that urban poor pay more per kWh (three times higher) compared to domestic
tariff rate34set by the BERC. In addition, due to unplanne d distribution of poor quality electric
cables, occurrence of a short circuit is common phenomena which cause a fire hazard. Therefore,
the users were not satisfied about the electr icity bill with an average score of 2.65 (SD ¼0.892).
Quality of power supply
About 63% correspondents were neutral ab out quality of power supply. About 9% slum
dwellers were not satisfied with the frequent vo ltage drop of the power supply which happens
repeatedly during the summer season. They claimed that the level of lighting in the summer periodis very low which hampers the study of their children. However, 27% correspondents were happy
with the quality of power supply. Overall, the p oor people were quite happy with the quality of
power supply with a score of 3.16 (SD ¼0.615) in spite of voltage up and down in the summer.
Safety of the power supply
Users were happy about the safety feature of the power supply with an average score of
3.19 and standard deviation of 0.734. Around 36% correspondents showed satisfaction towards
the safety of the power supply as no major accidents have occurred so far. Besides, around 9%
users were dissatisfied with the distribution of extension cords which originate from pole meter/shared meter. In addition, a small fraction of around 2% users were strongly dissatisfied regard-
ing the safety of the power supply. They reported that the electric cables which are used to sup-
ply power to the households have very poor quality. In fact, some users complained about the
occurrence of short circuit which causes a fire hazard from these low quality cables. Women
and children are the most vulnerable to this threat, who can have an electric shock by the loose053112-5 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)cable. As the majority of slum households is flimsy structured, it will be very difficult to con-
trol the fire.
Patterns of household energy use
The primary source of energy used for lighting in the slum households in Korail is elec-
tricity. In addition to providing household lighting, electricity is increasingly used to operatean array of household appliances (e.g., televisi on sets, refrigerator, and fans). However, in the
absence of electricity during the time of load shedding, slum dwellers use kerosene, candles,
and rechargeable batteries as a secondary fuel for lighting purposes. So, the unavailability ofelectricity not only hampers the daily life of the slum dwellers but also penalizes them with
extra payment for using secondary fuel for lighting. The average monthly expenditure for
electricity is 557 BDT which accounts 54% of total energy expenditure. The average monthlyexpenditure for kerosene is 134 BDT (67 BDT/l) and candles are 150 BDT (5 BDT/candle).
The most common kerosene lamp used by the slum dwellers is traditional wick lamps
(“Kuppi” and “Hurricane”). To assess the energy use, the average values [The values areaveraged for all households (not only for the users)] for slum households are considered
w h i c hi ss h o w ni nT a b l e III.
Household energy use not only depends on fuel type, availability, nature of its use but also
on the type of appliances, therefore the total energy may not give an actual energy consumption
pattern of slum households. As a consequence, end use energy needs to be taken into considera-
tion. To convert end use energy from total energy, O’Sullivan and Barnes
18considered fuel
type and efficiency of end use appliances. For example, kerosene is burnt in traditional “Kuppi”
or “Hurricane” which has very low end use efficiency of 15%. To get useful energy from elec-
tricity, a value of 95% is considered as end use efficiency. Candlepower is used to obtainenergy from one candle which is the radiating power of a light with the intensity of one candle
[One candlepower is equal to about 0.981 candela which is defined to be the luminous intensity
of a light source. One candela is equal to 18.3988 mW ( http://www.onlineconversion.com/ )].
The rechargeable battery is used in a torch light or rechargeable light [Usually, three AA
Lithium Ion rechargeable batteries is used in a rechargeable light where each battery has
capacity of 11 050 J ( http://www.allaboutbatteries.com/Energy-tables.html )]. The batteries have
chemical energy which is changed to electrical energy whereby it is converted to the light
energy. Useful energy consumption shown in Table IIIsuggests that electricity is the highest
consumer followed by kerosene, rechargeable batteries, and candles.
Household income and energy consumption
Understanding the relationship between income and energy requires a deeper analysis of
household energy consumption in the context of a varying composition of energy sources and
their implication for useful energy consumed.19The energy consumed is always less than the
total available energy from the physical sources used. The capacity of a physical source todeliver useful energy depends on the fuel type, the nature of its use, and available means and
TABLE III. Monthly household energy-use patterns.
Energy useType of fuel
Electricity Kerosene Rechargeable batteries Candle
Household users (%) 100 55 13 52
Energy used (kgOE/HH/month) 4.32 0.24 0.07 0.001
Share of total energy (%) 93.28% 5.18% 1.51% 0.02%
Energy cost (BDT/HH/month) 557 134 200 150Price paid (BDT/kgOE/month) 129 558 2857 150000
Share of total expenditure (%) 54% 13% 19% 14%053112-6 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)technology used to deliver the energy services. Since these factors vary across households, fo-
cusing on only total energy available from various sources, may not do justice to the analysisof energy-consumption patterns of slum households. As a consequence, we examined both total
and end-use household energy consumption.
As expected, a household’s end-use energy in reality is only a fraction of the total energy
consumed. The survey indicated that only about two-third of total energy is converted to useful
energy. Figure 1shows the household energy consumption
35against household income decile36
where it was found that that as income goes up, households’ total energy as well as end use
energy consumption also increases, which is the result of the adoption of electricity by the
higher income households. For example, at the first decile, the ratio of end-use to total energy
is only half, whereas it is about two-third and double at the fifth and tenth decile, respectively.For total energy, electricity constitutes an overwhelmingly large share of energy use, and this
pattern is consistent for all households. The total amount of energy usage per household has
increased consistently, especially beyond the sixth decile income group due to the use of highernumber of electrical appliances as well as kerosene by higher income households. The result
shows that end-use energy patterns reflect the actual energy service that consumers receive
because they are based on the energy content used for a particular task. Thus, the role of elec-tricity gains prominence owing to its higher efficiency levels. On the other hand, kerosene
energy consumption also increases with income; but as far as end-use energy is concerned, ker-
osene constitutes a lower percentage of total energy consumption as income rises.
BARRIERS TO ELECTRICITYACCESS
Supply side barrier
Energy policy barrier
The government has introduced several energy policies since 1996, but none of the policies
highlighted the need of energy for the urban poor as a part of the basic service. The key ele-
ments of energy policies are summarized in Figure 2. Besides, wide-ranging policy on urbaniza-
tion specifically urban poverty is missing. Also, there is no policy in relation to improvingenergy efficiency. The government has set up policies which concentrate more towards expand-
ing electrification rather than being focused on end uses or energy applications.
12However, the
interview with key informants (Interview by the author with Engr. Imdadul Haque, Chairman,BERC, Dhaka, November 2, 2012) also supported the literature which means there is no
explicit energy policy for the urban poor.FIG. 1. Trend in household’s total and end-use energy consumption by household income decile.053112-7 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)UNDP12also reported that policies for each sub- sector, such as Power Policy, Petroleum
Policy, Private Sector Policy, and now the Draft Renewable Energy Policy have no linkages with
the policies and programs of other sub-sectors wh ich means that there is no coordination in poli-
cies and programs in the functioning of sub-agen cies or companies under the ministries of these
sub-sectors. For instance, sub-sectors such as ene rgy and minerals do not coordinate their policies
and programs with each other, but they do coordi nate with the power sector independently. As a
result, lack of collaboration among the institutio ns with several policies not only lead to policy
confusion in the energy sector but also undermine the regulatory environment.
Housing policy barriers
Legal settlement is a pre-requisite for acquiring legal electricity services. In order to have
legal electricity access, the provision of affordable housing for urban poor should be empha-
sized first. The government has already emphasized the need for providing affordable housing
for urban poor and, therefore, has introduced several policies in order to establish housing rightsfor the urban poor. The National Housing Policy (NHP) was first introduced in 1993. After a
long time break, the government came forward to modify the NHP (1993) in 2004. However,
the modified version is still in the draft stage and awaiting for the government’s final approval.Hence NHP, 1993 is considered to be the available approved official policy for housing provi-
sion. The key policy statement under the NHP, in line with housing for the urban poor, is “The
urban poor will be given the advantages in receiving the housing rights where different priceswill be offered according to their affordability”. But in reality, the strategic provisions of the
NHP (1993) have not been executed. There are no regulatory laws or legislations which have
been enacted to support NHP (1993). As a result, no government has been successful in estab-lishing housing rights and preparing plans that truly take care of the affordable housing needs
of the urban poor living in the slums of Dhaka.
20
However, consultations with key informant (Interview by the author with Engr. Md. Nurul
Huda, Chairman, Rajdhani Unnayan Kartripakkha (RAJUK), Dhaka, November 6, 2012) also
gave information on various policies and programs regarding housing rights of the urban poor.
But the major problems reported by the key informant in implementing the policies are the lim-ited availability of resource land and the high price of land in Dhaka city. Also, a huge number
of urban poor make it difficult for proper rehabilitation.
Institutional barriers
There are no centralized institutions which can truly take care of the electricity services in
the slum areas. In the early 1990s, DCC established a Slum Development Department with an
aim to improve the physical infrastructure in the slum areas of Dhaka. But there are no linkagesbetween the slum development department of DCC and electricity service providers at national
or local levels, thereby hindering the growth of slum electricity services. However, the key in-
formant (Interview by the author with Anwar Hossain Patwary, Chief Slum DevelopmentOfficer, DCC, Dhaka, November 7, 2012) stated that the only program that the department has,
related to electricity access of slum areas is to improve street lighting. But there is no explicit
FIG. 2. The key energy policies of Bangladesh.12053112-8 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)plan and program for improving energy access in terms of providing clean fuels, meter electric-
ity connection, etc., at an affordable price. The key informant also mentioned that one of the
major problems of the department that has delayed the execution of programs is the lack of
funding. Besides, other agencies who are responsible to take care the urban development do not
address slum electricity needs.
Islam et al.21mentioned that urban policy gets conflicted due to dual metropolitan power
and control between DCC and other agencies. Although the DCC is an autonomous body, it is
controlled by the Ministry of Local Government, which means that there are sufficient control
and leadership of municipal government over municipal affairs. The DCC alone cannot provideservices to the urban poor related to electricity supply, but has to depend on DPDC, DESCO
for their acknowledgment and support in their final decision making to implement the plan. The
overall scenario results in poor urban governance causing major urban problems. Due to thisproblem, DCC has been unable to make a fruitful plan and program to improve the electricity
accessibility in slum areas.
Institutionally, there is little or no understanding/appreciation of the relationship between
energy and poverty. Energy sector institutions behave autonomously and interact little among
themselves, and thus their policies and programs are non-synergistic and often contradict with
each other. Moreover, the institutional management structure is highly centralized where deci-sion making is top-down, which inhibits participation of private sector players and other
stakeholders.
12
Lack of infrastructure
Scarcity of electricity has always been a severe problem since the country got its independ-
ence in 1971. Bangladesh has not become self-sufficient so far to deliver quality electricity sup-ply continuously due to low plant efficiencies and high system losses. The government has
taken steps to install new power plants having generation capacities of 2350 MW in 2015,
2800 MW in 2016 and 12 450 MW between 2015 and 2020 to ensure electricity for all by2021.
22However, the fundamental problems associated with lack of power generation are the
inadequate supply of modern fuels, constraints of adequate foreign exchanges, budget con-
straints for making large investments to generate electricity, inadequate institutional and person-nel capacity to implement policies and lack of appropriate national and regional partnerships.
Power sector reforms have been carried out over the years but, in practice, these are not hap-
pening in effective measures.
12According to the DESCO,14load shedding occurs at least 6–7 h
daily in cities and 12 h in the villages. The existing demand is nearly 2000 MW in Dhaka city,
but around 1000–1200 MW of electricity is supplied. As a result, load shedding takes place at
regular intervals in a day. Now, the question has left to answer is whether these inefficientpower plants can meet the demand of slum areas, even though it has already failed to deliver
quality electricity services to residential, commercial, and industrial areas.
Lack of monitoring and evaluation system
The utility companies do not get directly involved with slum communities, but rather they
work via medium known as “Maastans” The responsibility of the utility companies is restrictedonly to sanction a pole meter. “Maastans” takes control of the pole meter and provides electric-
ity supply from pole meter to households where they charge slum dwellers very high price for
using different appliances. The utility company do not concern about the billing methods (pay-ment by equipment type) of urban poor. The above scenario clearly suggests that there is a lack
of effective monitoring practice as well as transparent approach by the utility companies includ-
ing purchasing power, ensure quality control, and optimal resource utilization.
Moreover, there is no central agency which can review the electricity use in the slum areas.
Besides, identification of influencing parameters related to electricity, assessment of energy sav-
ing opportunities, an adaptation of a strategic approach to improve energy efficiency and opti-mization of energy supply in slum areas are also missing. Also, there is no energy management
system that can provide information on energy in slum areas regarding planning, monitoring,053112-9 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)and implementing measures to improve energy performance. Besides, there is no baseline data-
base which can be used as a benchmark to make plans for future initiatives.12
Demand side barrier
Illegal settlement
Legal recognition of the settlement is the pre-requisite for a household to access legal
energy services like electricity. The key informant [Interview by the author with Eng. Sha
Alam, Director (Engineering), DESCO, Dhaka, 5 December 2012] reported that due to the ille-
gal nature, urban poor automatically get excluded from the formal delivery services as they donot have a valid residence address and other pre-requisite documents. Barrett and Dunn
23found
that 80% of the land is authorized by 30% of the city’s population, while the remaining 70% of
the population have access to only 20%. The result suggests that accommodating land to all the
city dwellers in Dhaka would be a serious challenge for the government. As majority of poor
migrates from rural areas for economic reasons, most of them have very little assets which can-not help them to afford a legal tenureship. Bari and Efroymon
24also noticed that the land price
in residential areas, especially in the central zones of Dhaka is increasing at an alarming rate,
which forces the slum and squatter communities to be moved towards the city’s peripheries insearch for cheap shelter.
Financial barriers
The most significant barrier to access electricity among the poor is the application fee.
Currently, a high amount of application fee, 33,921 BDT [US$ 424, 1 US$ ¼80 BDT,
(November, 2012)] and 277 days are required to get estimation and load requirement for solarpanels from DESCO.
25This amount is equivalent to about 5–6 months’ estimated household
monthly income of urban poor in Dhaka city. However, despite of the illegality, DPDC and
DESCO allow them to apply for legal electricity connection through the pole and shared meter.But to sanction a pole meter, a high amount of advanced electricity bill (3–4 month) is needed
as a security deposit which is quite difficult for slum dwellers to afford.
Physical barriers
As observed from the survey that the physical constraint of the poor communities are usu-
ally very crowded with narrow walkways, poor quality of housing material often causes diffi-
culty in the installation, delivery and monitoring of electricity services.
Lack of awareness
It was observed that most of the slum dwellers are uneducated and very few of them have
completed primary school. They are more concentrated on economic benefits rather than healthbenefits. So, the low level of education and limited awareness regarding health and financial
benefits of clean and efficient fuels resist the slum dwellers to use energy efficient appliances.
Moreover, with limited awareness levels and lack of sufficient knowledge of the urban poor onavailable electricity costs, options, and efficient utilization, most often, their demand cannot
receive priority to the higher authority.
RECOMMENDATIONS AND POLICY DIRECTIONS
The government has already introduced some policies for the urban poor. But these policies
only concentrated on the improvement of slum infrastructure. Some policies also focused on
slum resettlement, but none of them have highlighted electricity access. So, it is necessary that
the policy should target the urban poor specifically in the field of energy access. Also, itrequires proper coordination among various sub agencies in order to avoid any policy confu-
sion. It requires the proper collaboration among various institutions in order to make the regula-
tory environment effective and strong. It is also suggested to change or revise the policies053112-10 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)related to slum development. The best practice can be learnt by following the Integrated
National Electrification Program (INEP), South Africa.26A white paper energy policy was
introduced in 1998 which emphasized to provide affordable energy services to the urban poor
by improving energy governance and economic stimulation. The success behind the electrifica-
tion program was the widespread energy policies, the effective role of the government, encour-
age the private sector players to invest in electrification program.
The illegal status of slum settlement and lack of valid residence address were found as two
of the major barriers to access electricity. Access to legal energy services is inherently linked
with valid residence address. So, it is recommended that the government should give emphasison this issue with high priority. To address this issue, it is required to recognize the slum settle-
ments and give them the authorization of permanent status as a first step. But, in case if it is
difficult to give legal status, tenure regulation can be achieved by issuing temporary residentialproof which make them eligible to apply for legal energy services. Another solution would be
the relaxation in requirements for new connections by the supply agency for the urban poor. A
similar approach has been introduced in Mumbai, where the community, with the help of localNGOs, held a series of negotiations between the Mahila Milan and the service provider
Bombay Electricity Supply and Transport (BEST).
27A government letter was issued after the
negotiations, declaring that the dwellings would not be demolished for one-and-a-half years.This served to reassure the service provider, who wanted assurance that its supply of electricity
to the pavement dwellers would neither place the company in breach of its own rules, nor
would it be seen to symbolize security of land tenure for the pavement dwellers. Through stepby step negotiations that occurred in several stages, the tenureship and other requirements
demanded by the service provider and community were met.
As discussed earlier, NHP was introduced in 1993, with an aim to provide the affordable
housing to the urban poor. But the government is unsuccessful to establish the housing rights
for the urban poor. As affordable housing is a compulsory need for the urban poor, so it is sug-
gested that the government can introduce the affordable housing to the urban poor for longtime installment basis. At the same time it needs to implement NHP and also needs revision
based on the current situation. However, implementing affordable housing to the urban poor
will be a difficult task, therefore a temporary household ID can be provided. A similar policyhas been introduced by the government of Thailand, where Quasi housing identity was initiated
in slum areas to help the poor population of the cities.
28The Housing Registration Act was for-
mulated in 1992 in order to have better access to infrastructure. Housing registration was classi-fied into two types. One was permanent type and another was the temporary housing registra-
tion, which was called quasi-household ID. The Quasi households ID not only helped the urban
poor to apply for legal energy services like electricity, water but also reduced illegal electricityconnections (connection through a neighbor).
The electricity connection fee is too high for slum dwellers. In this regard, subsidized con-
nections by the supply agency along with efficiency improvement measures can be delivered tourban poor to reduce energy consumption and charges. All the facilities can be provided
through “community agents.” In Salvador, the service provider Companhia de Electricidade do
Estado do Bahia (COELBA) subsidized the installation of new connections and theft resistantmeters and facilitated community registration into a social tariff program run by the govern-
ment to further facilitate affordability.
29COELBA also worked to negotiate affordable payment
plans with their low-income clients, particularly those who had payment defaults or outstandingdebts. Apart from this, a combined approach of information and energy efficiency improve-
ments, delivered by Community Agents, aided in reducing energy consumption, bringing the
energy bills under the affordability bracket of the poor households and avoiding non-payment.Supporting energy efficiency in the target urban poor communities also facilitated energy
affordability in some cases. In Salvador, the appliance exchange was an initiative that helped
overcome affordability issues faced in the community by helping them exchange energy ineffi-cient appliances for newer ones that would result in less energy consumption.
Urban poor are charged three times more than domestic electricity tariff rate. Besides, physi-
cal constraints of the poor communities which ar e usually very crowded with narrow walkways053112-11 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)often causes difficulty in the installation, deliver y and monitoring of electricity services. So it is
recommended that urban poor be charged on the unit basis by providing them with prepaid meter
connection. The metered electricity connectio n would help the urban poor not only in reducing
electricity bill but also create a wareness about its careful consumption. As the renovation of slum
infrastructure will require a long term effective plan, therefore the installation of prepaid electricity
meters would be an appropriate option. In South Afr ica, under the INEP, prepaid electricity meters
were implemented with an objective to substitute “conventional” credit meters to reduce the
monthly electricity cost.26At first, credit meters were hung on the external walls of residential
buildings. But suspicion was raised extensively that the meters were accessed by unauthorizedusers. Hence, for security conc ern, prepaid meters were mounted inside dwellings. It has the
advantages by giving consumers the opportunity not only to monitor the consumption of the appli-
ances they used but also to reduce the problem of non-payment.
Lack of education and limited awareness regarding health and financial benefits of clean
and efficient fuels is one of the main hindrances to promote electricity services in slum areas of
Dhaka. Educational, training program and workshop should be arranged to raise awareness touse electricity within budgetary limits, including how to monitor usage and reduce consump-
tion; and at the same time engage slum dwellers to participate in community activities to pre-
pare for electrification and assist in policing of illegal activities threatening the scheme. In NewDelhi, INDCARE Trust worked with the slum community to raise awareness of the safety risks
of illegal electrification and the benefits of legal connections.
27Following their empowerment
through education and awareness, the community recognized the risks of illegal electricalaccess and was taught to voice its demands and take the necessary steps to overcome issues
such as illegality in order to achieve legal electrification. Innovative means were used to engage
and raise awareness in the community surrounding the risks of illegal electrification. Creativemethods were also used to conduct community based research and included tools like knowl-
edge, attitude and performance (KAP), participatory learning and action (PLA), and the main-
streaming of urban poor women in design for resource assessment (MUDRA) tool that helpedthe program effectively target the needs of the community to ensure engagement and success.
Street performances and poster campaigns were also used to raise awareness and help teach the
community how to negotiate to demand and achieve their rights.
Urban poor were also found to use inefficient app liances. In the absence of electricity, kero-
sene is the major fuel used by urban for lighting a nd it is used inefficiently by burning it in tradi-
tional “Kuppi” or “Hurricane” which emits a lot sm oke. As load shedding occurs frequently three
to four times in day and usage of secondary fuel for lighting is necessary fo r household needs, so
it is recommended that usage of kerosene can b e replaced by a recharge able light emitting diode
(LED) lamp or solar photovoltaic (PV). Solar en ergy has already been proven to be a very promis-
ing resource to improve the ongoing electricity s hortage in Bangladesh. The solar PV project spe-
cifically Solar Home System (SHS) has already go t an acceptance among the people all over the
country, particularly in rural areas through i nnovative financing options. The government of
Bangladesh is already one step closer to deliver a reliable supply of electricity through solar PV
by introducing a “Draft Renewable Energy Policy” in 2008 where emphasis has been given to
renewable energy, particularly solar power and biogas.
30In order to disseminate solar PV project
in slum areas of Dhaka, it should make easier for poor households to pay, including subsidies and
convenient payment facilities, and improving local pa rticipation that facilitates discussion and iden-
tification and resolution of any problems early on . It is also recommended to involve slum com-
munities, as they are crucial to the success of a ny scheme. The key activities for communities
include support for the effort, set up activities for communication among the key stakeholders to
help in understanding community needs and issu es and how the solar PV electrification scheme
will work, set up a self-policing function; and con tinue to work with stakeholders to keep the solar
PV scheme working after implementation. A sim ilar method was applied in Sri Lanka, where a
project called Energy Services Delivery (ESD) was proposed to minimize the gap resulting from a
serious shortage of investment in the energy sector.31ESD project successfully installed 21 000 so-
lar home systems within 6 yr. ESD project provided benefits for its stakeholders by no longer
using kerosene, and improved affordability by not having to pay monthly electricity bills. With the053112-12 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)help of this project, the renewable energy sector continued to flourish in Sri Lanka with hundreds
of organizations and thousands of people directly involved in making or se lling renewable energy
equipment.
Finally, it is recommended that slum development department of DCC should focus on pro-
viding electricity services to the urban poor by proper coordination between Dhaka city cooper-
ation and electricity service provider in planning and dealing effectively the electricity issues ofurban poor. It needs to strengthen the performance of RAJUK and DCC. DCC should have suf-
ficient control and power over DPDC and DESCO, Petro Bangla so that plans and programs
can be introduced on improving the electricity access in the slum areas with proper coordina-tion. It is also recommended that proper co-ordination should be established between DCC and
RAJUK as well as planning ministries in urban development project in Dhaka.
CONCLUSION
The initial assessment in the study provides a clear picture about access to electricity, its
connection status, household energy use pattern in urban poor households and the structured
policy analysis brings to light the lack of responsiveness and proactive sectorial policies (urbanplanning, poverty alleviation, energy) to address the lack of access to electricity for the urban
poor. On the other hand, barrier specific actions identified in the recommendation directly
address challenges associated with electricity access, the same need a strong backing at themacro level in terms of strategic energy planning policies/plans.
As observed from the study, there is no comprehensive energy policy which relates to
urban poverty. Besides, there are no centralized institutions which look after energy accessissues in the slum areas. Lack of sufficient control and power by DCC over various national
utility agencies like DPDC, DESCO, and Petro Bangla has resulted poor urban governance.
Moreover, due to the illegal nature, urban poor cannot apply for legal energy services. NGOsfind difficulties to work in slum areas due to illegal settlements of slums and interference of
middlemen. Also, lack of awareness does not help the urban poor to learn about financial and
health benefits of electricity.
The paper also gives an idea about the barriers specific recommendations based on the
experiences obtained from field visit. It was found from the field survey that poverty is not the
only main cause for limited electricity services in the slum areas. The policy failure, bad gover-nance, and ineffective legal and regulatory framework, corruption and lack of political will are
also the major hindrances to provide electricity in the slum areas. Therefore, to provide appro-
priate suggestions and recommendations to address the different barriers related to electricityaccess is a very complex task. To address the barriers, the government should come forward to
closer look into each barrier and at the same time initiate fruitful plans, programs, and policies
to solve the problems. Also, it would be beneficial to learn from best practices related to elec-tricity issues from other regions/countries. Best practices could be taken as recommendations/
suggestions to address different barriers in slum areas of Dhaka.
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11Power Division, Ministry of Power, Energy and Mineral Resources, See http://www.powerdivision.gov.bd/user/brec1/30/1
for present status of electricity access in Bangladesh, 2014; accessed 22 March 2014.
12UNDP, Asia Pacific Regional Centre, Energy and Poverty in Bangladesh: Challenges and the Way Forward (United
Nations Development Program, 2007).
13S. F. Rashid, “Strategies to reduce exclusion among populations living in urban slum settlements in Bangladesh,”
J. Health, Popul., Nutr. 27, 574–586 (2009).
14DESCO, See https://www.desco.org.bd/index.php?page=annual-reports for annual reports, 2011; accessed 15 July 2012.
15S. R. Khandker, D. F. Barnes, and H. A. Samad, “Are the energy poor also income poor? Evidence from India,” Energy
Policy 47, 1–12 (2012).
16L. Chen, S. K. Soliman, E. Mao, and M. N. Frolick, “Measuring user satisfaction with data warehouses: An exploratory
study,” Inf. Manage. 37(3), 103–110 (2006).
17N. Banks, “A tale of two wards: political participation and the urban poor in Dhaka City,” Environ. Urbanization 20,
361–376 (2008).
18K. O’Sullivan and D. F. Barnes, Energy Policies and Multitopic Household Surveys: Guideline for Questionnaire Designin Living Standard Measurement Surveys, Energy and Mining Sector Board, Discussion Paper No.17, World Bank,Washington, DC, 2006.
19D. F. Barnes, S. R. Khandker, and H. A. Samed , “Energy poverty in rural Bangladesh,” Energy Policy 39(4), 894–904 (2010).
20M. M. Rahman, Government and housing for the poor. Policy and Implementation in Bangladesh. East West Journal of
Humanities, Dhaka: East West University (2009).
21N. Islam, A. Q. M. Mahbub, and N. I. Nazem, Urban Slums of Bangladesh (Center for Urban Studies, Dhaka, 2009).
22MoF (Ministry of Finance), Finance Division, Government of People’s Republic of Bangladesh, See http://mof.gov.bd/
en/budget/11_12/power/power_energy_en.pdf for Power and energy sector road map: An update; accessed 26 March
2014.
23A. Barrett and K. Dunn, Reaching the MDGs in urban Bangladesh. World Bank Workshop: Towards a strategy forachieving MDG outcomes in Bangladesh. Session 5: Challenges facing the urban poor, Dhaka, 2006.
24M. Bari and D. Efroymon, Detailed Area Plan (DAP) for Dhaka Metropolitan Development Plan (DMDP): A Critical
Review (WBB Trust, Dhaka, 2009).
25World Bank Group, Doing Business, Economy Profile: Bangladesh, see http://www.doingbusiness.or g/data/exploreeconomies/~/
media/giawb/doing%20business/documen ts/profiles/country/BGD.pdf?ver=2 , 2014 for Getting Electricity; accessed 23
September, 2014.
26B. Bekker, A. Eberhard, T. Gaunt, and A. Marquard, “South Africa’s rapid electrification program: Policy, institutional,
planning, financing and technical innovations,” Energy Policy 36, 3125–3137 (2008).
27NESD, Country report (India). Urban and Per i-urban energy access III. Report prepared for the global network on energy for
sustainable development by The Energy and Resources Institute (TERI), 2013, see http://www.gnesd.org/~/media/Sites/GNESD/
Publication%20pdfs/Urban%20 Peri-Urban%20Theme/UPEA% 20III%20-%20Newly%20Edited/TERI_final.ashx ; accessed
February 20, 2014.
28GNESD, Country report (Thailand). Urban and Peri-urban ener gy access III. Report prepared f or the Global Network on Energy
for Sustainable Development by The Asia n Institute of Technology (AIT) (2013), see http://www.gnesd.org/~/media/Sites/
GNESD/Publication%20pdfs/Urban%20Peri-Urban%20Theme/UPEA%20III%20-%20Newly%20Edited/AIT_Final.ashx ;
accessed 20 December 2013.
29ESMAP, See http://www.esmap.org/sites/esmap.org/files/FINAL_EA-Case%20Studies.pdf for innovative approaches to
energy access for the urban poor, 2011; accessed 12 March 2012.
30Power Division, See http:// www.powerdivision.gov.bd/user/brec1/30/1 for Renewable Energy policy Bangladesh,
Ministry of Power, Energy and Mineral Resources, Government of the People Republic Bangladesh, 2008; accessed 22September 2012).
31I. M. Drupady and B. K. Sovacool, Harvesting the Elements: The Achievements of Sri Lanka’s Energy Services Delivery
Project (Lee Kuan Yew National University of Singapore/Centre on Asia and Globalization, Singapore, 2011).
32In Bangladesh, the definition of slum by the Bangladesh Bureau of Statistics (BBS) is “Predominantly very poor housing
structure, Jhupri, Tong, chhai, tin shed, semi-pucca flimsy structure, dilapidated building in bad condition, very high
housing density, grow on govt./semi govt. vacant land and public owned places, abandoned buildings/places or by the
side of the road, having poor sewage and drainage or even it has no such facilities, inadequate, unhealthy drinking watersupply, prevailing unhealthy atmosphere, insufficient or absence of street lighting, little or no paved street, inhabited bypoor, uneducated and below poverty level people.”
33Sample size, n ¼N
ðN/C2e2Þþ1, where, n ¼sample size, N ¼Total number of households, and e ¼Limited error ¼10%.
34Consider a typical slum house where a 25 W CFL and a 70 W ceiling fan is used for monthly fee of 150 (light) þ150
(fan) ¼300 BDT. Considering 10 hours daily usage time and 30 days a month, a typical slum house consumes
{(25 W /C210 h/C230 day/1000) kWh/month þ70 W /C210 h/C230 day/1000) kWh/month)} ¼28.5 kWh/month which means
urban poor pay (300 BDT/month /C428.5 kWh/month) ¼10.5 BDT/kWh, but the domestic tariff rate is 3.33 BDT per unit
(0–75 unit) which means slum residents pay more than 3 times higher than normal tariff rate set by the BangladeshEnergy Regulatory Commission (BERC).
35Regarding energy use, first, the average value of end use energy of each fuel (electricity, kerosene, rechargeable batteries,
and candles) in each decile group is determined. Then the average end use energy of all the fuels in each decile group is
added to estimate the total end use energy consumption.
36To draw the graph, the per capita monthly income of the urban poor household is organized according to the order of theirincome and then divided into ten groups of equal size, so that each decile then has 10 percent of the households. For this
study, 100 households have been considered which means each decile has 10 households.053112-14 Hossain Lipu and Waliullah Bhuiyan J. Renewable Sustainable Energy 6, 053112 (2014)Journal
of
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1.4891276.pdf | Anisotropic magnetoresistance of individual CoFeB and Ni nanotubes with values of
up to 1.4% at room temperature
Daniel Rüffer, Marlou Slot, Rupert Huber, Thomas Schwarze, Florian Heimbach, Gözde Tütüncüoglu, Federico
Matteini, Eleonora Russo-Averchi, András Kovács, Rafal Dunin-Borkowski, Reza R. Zamani, Joan R. Morante,
Jordi Arbiol, Anna Fontcuberta i Morral, and Dirk Grundler
Citation: APL Materials 2, 076112 (2014); doi: 10.1063/1.4891276
View online: http://dx.doi.org/10.1063/1.4891276
View Table of Contents: http://scitation.aip.org/content/aip/journal/aplmater/2/7?ver=pdfcov
Published by the AIP Publishing
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Anisotropic magnetoresistance of individual CoFeB and Ni
nanotubes with values of up to 1.4% at room temperature
Daniel R ¨uffer,1Marlou Slot,1Rupert Huber,2Thomas Schwarze,2
Florian Heimbach,2G¨ozde T ¨ut¨unc¨uoglu,1Federico Matteini,1
Eleonora Russo-Averchi,1Andr ´as Kov ´acs,3Rafal Dunin-Borkowski,3
Reza R. Zamani,4,5Joan R. Morante,5Jordi Arbiol,4,6
Anna Fontcuberta i Morral,1and Dirk Grundler2,7,a
1Laboratoire des Mat ´eriaux Semiconducteurs, Institut des Mat ´eriaux,
Ecole Polytechnique F ´ed´erale de Lausanne, 1015 Lausanne, Switzerland
2Lehrstuhl f ¨ur Physik funktionaler Schichtsysteme, Physik-Department,
Technische Universit ¨at M ¨unchen, D-85747 Garching bei M ¨unchen, Germany
3Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons
and Peter Gr ¨unberg Institute, Forschungszentrum J ¨ulich, D-52425 J ¨ulich, Germany
4Institut de Ci `encia de Materials de Barcelona (ICMAB-CSIC), Campus de la UAB,
08193 Bellaterra, CAT, Spain
5Catalonia Institute for Energy Research (IREC), Barcelona 08930, Spain
6Instituci ´o Catalana de Recerca i Estudis Avanc ¸ats (ICREA), 08019 Barcelona, CAT, Spain
7Institut des Mat ´eriaux, ´Ecole Polytechnique F ´ed´erale de Lausanne, 1015 Lausanne,
Switzerland
(Received 25 March 2014; accepted 15 July 2014; published online 30 July 2014)
Magnetic nanotubes (NTs) are interesting for magnetic memory and magnonic ap-
plications. We report magnetotransport experiments on individual 10 to 20 μm long
Ni and CoFeB NTs with outer diameters ranging from 160 to 390 nm and film
thicknesses of 20 to 40 nm. The anisotropic magnetoresistance (AMR) effect studied
from 2 K to room temperature (RT) amounted to 1.4% and 0.1% for Ni and CoFeB
NTs, respectively, at RT. We evaluated magnetometric demagnetization factors of
about 0.7 for Ni and CoFeB NTs having considerably different saturation magne-tization. The relatively large AMR value of the Ni nanotubes is promising for RT
spintronic applications. The large saturation magnetization of CoFeB is useful in
different fields such as magnonics and scanning probe microscopy using nanotubesas magnetic tips. © 2014 Author(s). All article content, except where otherwise
noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
[http://dx.doi.org/10.1063/1.4891276 ]
Ferromagnetic nanostructures with tubular shape are fascinating objects for fundamental re-
search as well as for applications. Due to their hollow structure, theory predicts the existence of
Bloch-point free vortex states and domain walls.
1–3The motion of vortex domain walls in nanotubes
is expected to occur at very high velocities,4,5possibly fast enough to generate a Cherenkov-type
spin wave excitation.6Such magnetic properties and high velocities could be beneficial in future
low-power and high-speed memory applications.7For this, polycrystalline or even better amorphous
materials, being soft-magnetic and magnetically isotropic, represent a very promising basis. While
soft-magnetic behavior allows for mobile domain-walls, isotropic magnetic properties are key forthe formation of the characteristic magnetic states predicted for tubes. Molecular beam epitaxy
and epitaxial growth as reported for GaMnAs, MnAs, and Fe
3Si nanotubes recently10–12intro-
duce however magnetocrystalline anisotropy. Magnetron sputtering as a technologically relevantdeposition technique has not been reported for the fabrication of magnetic nanotubes yet. Instead
aElectronic mail: dirk.grundler@ph.tum.de
2166-532X/2014/2(7)/076112/8 © Author(s) 2014
2, 076112-1
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ferromagnetic nanotubes were first fabricated by electrodeposition into nanoporous membranes.13,14
Various other methods were developed such as hydrogen reduction of porous alumina templates
preloaded with metallic salts15or decomposition of polymers containing a metallo-organic pre-
cursor wetting such templates.16Different deposition techniques including atomic layer deposi-
tion (ALD) were employed to fabricate tubes in nanopores17,18or as shells onto semiconductor
nanowires.8,10,17,19Early magnetic characterization was restricted to large ensembles of nanotubes.
In the last years, the investigation of individual nanotubes became technologically feasible.9,20–24
The role of both magnetocrystalline9,24and shape anisotropy19has been discussed but the relevant
magnetometric demagnetization factor for individual nanotubes has not yet been addressed. For Ni
nanotubes anisotropic magnetoresistance (AMR) data presented recently revealed a technologicallyunfavourable relative AMR effect of only 0.3% at 4 K.
21Here we report on the structural char-
acterization of polycrystalline Ni and amorphous CoFeB nanotubes. Studying their AMR over a
broad temperature range we obtain a large relative effect of up to 1.4% for the Ni nanotubes at roomtemperature. For both types of nanotubes, we evaluate a consistent magnetometric demagnetization
factor N
⊥of about 0.7. Thereby we account for the different fields Hdneeded to saturate the Ni and
CoFeB nanotubes in transverse ( ⊥) direction. Correspondingly, the magnetic anisotropy is argued to
be dominated by the shape. Large room-temperature AMR values are interesting if one thinks about,
e.g., sensor applications or transport studies on magnetic configurations predicted for nanotubes.1–3
The nanotubes from CoFeB are expected to advance both nanomagnonics and magnetic sensing.
Their large saturation magnetization favors fast spin dynamics25and provides one with large stray
fields from nanoscopic tips, respectively, helping to improve magnetic microscopy.26
Magnetic nanotubes were fabricated from either Ni or CoFeB by depositing the ferromagnetic
shells around bottom-up grown GaAs nanowires.27,28The nanowires, which were grown using Ga
droplets as catalysts, had lengths between about 10 and 20 μm. Their diameters ranged from 100
to 150 nm.27,28A list of relevant geometrical parameters is given in the table in the supplementary
material.29The Ni was deposited by ALD,21,23while the CoFeB was obtained by magnetron
sputtering using Xenon gas at room temperature.25In the ALD process, we intentionally produced
an intermediate Al 2O3layer in order to vary the inner diameter of the supporting core before
depositing the ferromagnetic shell. For magnetron sputtering of CoFeB, we mounted the Si (111)
substrate containing the GaAs nanowires on a rotatable sample holder facing a Co 20Fe60B20(CoFeB)
target that was positioned under an angle of 35◦with respect to the substrate normal. Intentionally
choosing ensembles of nanowires with rather large nanowire-to-nanowire separation, the substrate
rotation allowed us to obtain nanotubes showing homogeneously thick CoFeB shells.
Annular Dark Field (ADF) Scanning Transmission Electron Microscopy (STEM) images were
obtained in order to determine the morphology and thicknesses of the Ni [Fig. 1(a)] and CoFeB shells
[Figs. 1(b) and 1(c)]. The Ni shells were found to exhibit a surface roughness with peak-to-peak
values of about 10 nm.21,23The magnetron-sputtered CoFeB shells were much smoother. Atomic-
resolution ADF STEM analyses as those presented in Fig. 1(d) evidenced a zinc-blende structure
of the GaAs core that grew along one of the [111]B directions as demonstrated recently.27,30Cross
sections of the core/shell systems were prepared by means of Focused Ion Beam showing that the
hexagonal cross-section of the core was transferred to the CoFeB shell [Fig. 1(c)]. This was not
observed for the Ni shells due to the larger surface roughness21,23[Fig. 1(a)]. The Ni consisted of
grains being ellipsoids with a long (short) axis of roughly 30 nm (10 nm). The conformal CoFeB
shell appeared instead amorphous. The amorphous structure is provoked by adding B to the CoFealloy.
31The columnar structure seen in Fig. 1(d) is attributed to local variations in the density of the
material. These might be caused by directional deposition on the rotating nanowires. This peculiar
feature is under further investigation. Electron Energy Loss Spectroscopy (EELS) spectrum imageswere obtained in STEM mode in order to study the composition. The nanowire cores are composed
of GaAs. Shells are shown to be Ni rich in the inset of Fig. 1(a) and Fe and Co rich in Figs. 1(g) and
1(h), respectively. EELS analyses performed on the CoFeB shell provided a relative composition of
Fe 77% (at. %), Co 20%, and Xe 3%. Note that the content of B could not be obtained as the energy
range of the B in the EELS spectra falls far from the Fe and Co signal. The upper bound for the
oxygen content in the shell is determined to be 2%. The values are consistent with energy dispersivex-ray analysis performed on planar films.
25Remarkably, the catalyst seed for nanowire growth is
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FIG. 1. (a) Low-magnification ADF STEM image of Ni nanotubes; the inset shows an EELS Ni map obtained on the same
region of the tube. (b) ADF STEM image of a CoFeB nanotube shell covering the GaAs nanowire template as well as theGa tip used for bottom-up growth. (c) Cross-section ADF STEM view showing the hexagonal prismatic morphology of theGaAs core template and the CoFeB nanotube shell. (d) Atomic resolution ADF STEM image showing the crystallinity ofthe GaAs and the amorphous CoFeB shell. The CoFeB exhibits a columnar morphology. The inner ADF detector semi-angleused was 78 mrad. (e)-(h) EELS chemical maps corresponding to Ga, As, Fe, and Co, respectively, obtained on the squaredregion in (b).
composed of pure Ga covered with a slight thin shell containing As. The CoFeB layer coats the
seed as well. In contrast to Refs. 8,9, and 19, we do not find an epitaxial relationship between the
magnetic shells and the semiconductor cores. For polycrystalline Ni and amorphous CoFeB25,32
prepared on planar substrates a magnetocrystalline anisotropy was not observed.
The core/shell systems were released in isopropanol using sonication and transferred to Si
wafers covered with 200 nm thick silicon oxide. The absolute position of nanotubes was determinedusing prepatterned gold alignment markers, optical microscopy, and an in-house developed software
for image recognition.
33In situ plasma etching was performed before sputtering electrical contacts
from 5 nm thick titanium and 150 nm thick gold [Fig. 2(b)]. The separation between voltage probes
Lcontact [Fig. 2(c)] was varied between 6.5 and 13.2 μm depending on the investigated nanotube.
The Ni nanotubes have a thickness of 40 nm (NiL1, NiL2) and 20 nm (NiM). By inserting an Al 2O3
layer between the ferromagnetic shell and the GaAs core, we achieved different outer diameters of
about 350 nm (large, “L”) and 220 nm (middle, “M”). The CoFeB nanotubes considered here have
thicknesses of 30 nm (CFBM1, CFBM2) and 20 nm (CFBS1, CFBS2) where “S” (small) indicates
an outer diameter of about 180 nm. The CoFeB nanotubes stick to the substrate with one of theirside facets.
Magnetotransport experiments were performed on wire-bonded samples mounted on a rotatable
stage in a bath cryostat with a superconducting magnet providing a magnetic field μ
0Hof up to
9 T. The resistance R(H,θ) as a function of the magnetic field and the rotation angle θwas
measured in a four-point-probe configuration [Fig. 2(d)] using a nanovoltmeter in combination
with a programmable current source and a three-step current operated at 25 Hz to compensate for
thermovoltages. The data from the bath cryostat were corrected for thermal drifts and the field
dependent characteristics of the temperature sensor. To compare different nanotubes when rotatinga fixed field H, we consider the relative resistance change /Delta1R(θ)=(R(θ)−min ( R))/min ( R) where
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FIG. 2. Scanning electron microscopy images of a small segment of sample (a) NiS1 and (b) CFBS1. (c) Overview of sample
CFBS1 with electrical contacts. (d) Measurement configuration.
||/
||
FIG. 3. Normalized resistance change /Delta1R(H)//Delta1Rmaxas a function of |H|for sample (a) NiS1 and (b) CFBS2 at room
temperature. Magnetic field sweeps in both directions and field polarities are shown for field parallel (top) and perpendicular(bottom) to the long axis. We define H
das the field at which most of the magnetization saturates and /Delta1R(H)//Delta1Rmaxis smaller
than the noise level. For CFBS2, the saturation occurs at very small fields for the parallel field configuration.
min ( R) is the minimum resistance value. The AMR ratio is defined as AMR =R/bardbl−R⊥
R⊥where R/bardbland
R⊥are the absolute maximum (max ( R)) and minimum (min ( R)) resistance values for a magnetic
field Hbeing parallel and perpendicular, respectively, to the current Iand being larger than the field
Hdat which most parts of the magnetization saturate.34Furthermore, we utilize the normalized
resistance /Delta1R(H)//Delta1Rmax=(R(H)−min( R))/(max( R)−min( R)).
Before discussing the electrical properties and magnetoresistance of the nanotubes in detail, we
determine Hd.34Magnetic field sweeps can be found in Fig. 3for sample NiS1 (a) and CFBS1 (b) with
Hbeing parallel (top) and perpendicular (bottom) to the long axis (see supplementary material for fur-
ther experimental data29). In the parallel configuration, only small fields were needed to saturate the
nanotubes. CoFeB was in particular soft magnetic. In the perpendicular configuration, we extracted
μ0Hd(black arrow) to be 0.35 ±0.05 T for the Ni nanotube. This value was much smaller compared
to the CoFeB nanotube for which we found 1.2 ±0.2 T. We attribute this observation to different de-
magnetization fields. If we consider Ms≈375 kA/m for Ni,22we estimate the magnetometric demag-
netization factor34to be N⊥(Ni)=|Hd(Ni)/Ms(Ni)|≈0.7.35If we assume N⊥(CoFeB) =N⊥(Ni)
and take the saturation magnetization of 1430 kA/m measured for our CoFeB when magnetron-
sputtered on a planar substrate,32we calculate μ0Hd=μ0N⊥(CoFeB) ×Ms(CoFeB) ≈1.3T .T h i s
value is consistent with the experimental value of μ0Hd=1.2±0.2 T observed for the CoFeB
nanotube in Fig. 3(b). We do not expect the hexagonal shape of the smooth CoFeB nanotubes to
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vary significantly the effective component of the demagnetization factor compared to the rougher
and thereby more circular Ni nanotubes. The different values Hdthus reflect the different saturation
magnetization values of Ni and CoFeB. Note that a large and thin film is expected to exhibit N⊥of
1.0 whereas an infinitely long (full) cylinder acquires N⊥=0.5. The extracted effective demagneti-
zation factor of 0.7 for the nanotubes being hollow cylinders is in between these values and seems
reasonable to us. The specific shape of the nanotubes reduces the overall demagnetization effect
compared to a film, but still provides a larger effective demagnetization effect compared to a fullcylinder. The nanobar-magnet behavior reported in Ref. 19is consistent with the shape anisotropy
provided by the relatively large N
⊥≈0.7 extracted here.
We now present the electrical properties and magnetoresistance of the nanotubes. Figure 4(a)
shows the temperature dependent resistance R(T) of a Ni nanotube (NiL1) at zero magnetic field.
Rdecreases from 40.9 /Omega1at room temperature down to 15.8 /Omega1at 2 K. The behavior is expected
for a polycrystalline metallic material. Using the geometrical parameters,29we calculate a specific
resistivity ρ=R·A/Lcontact of 18μ/Omega1cm and 7 μ/Omega1cm for room and low temperature, respectively
(Ais the cross-section of Ni). Our values of ρare in relatively good agreement with values measured
on nanostripes fabricated from thermally evaporated Ni36,37indicating a good electrical quality of the
ALD-grown metal. The temperature dependent R(T) for two CoFeB samples is shown in Fig. 4(b).
Here, we obtain specific resistivities of ρ=1−2×103μ/Omega1cm at room temperature. As a function of
Twe do not observe the typical metallic behavior. For sample CFBS1, the resistance decreases from
room temperature down to 140 K and then increases. In case of CFBM1, the resistance increases
monotonously with decreasing temperature. The measured resistances range from 7.63 to 7.79 k /Omega1
and 7.35 to 7.79 k /Omega1for CFBS1 and CFBM1, respectively. The semi-logarithmic plot suggests R(T)
to exhibit a logarithmic dependence on 1/ TforT<Tmin≈130 K (190 K) for CFBS1 (CFBM1),38
albeit a small deviation can be found for CFBM1 at T<10 K.
Figure 4(c) shows the resistance change of Ni tubes as a function of the rotation angle θat
different temperatures. We rotated a field H>Hdto saturate the tubes at all angles. R(θ) follows
a cos2(θ) dependence remodelled by solid lines in Fig. 4(c). This is expected for ferromagnetic
conductors displaying the AMR. Relative AMR values are shown in Fig. 4(d) as a function of T.
Between 3 and 220 K, the AMR is found to increase linearly with Tfrom about 0.35% to 1.2%.
Then, up to 295 K, the AMR stays almost constant for sample NiL1. The low-temperature valueis consistent with data obtained previously on different Ni nanotubes.
21At room temperature, we
now find a much larger value of up to 1.4% for NiS1 and NiM [Fig. 4(d)]. In Refs. 36and 37,
stripes from thermally evaporated Ni were studied and the authors provided values of 1.6% and1.8%, respectively. We attribute the slightly smaller AMR effect of our nanotubes compared to the
planar stripes mainly to the influence of the nanotube roughness. We assume the roughness-induced
scattering of electrons to enhance the resistivity and thereby to reduce the overall AMR effect(compare considerations on boundary scattering in Ref. 39).
R(θ) of CoFeB nanotubes CFBS1 (triangles) and CFBM1 (squares) shown in Fig. 4(e) also
follows a cos
2(θ) dependence consistent with the AMR effect. The AMR effect is found to di-
minish with increasing T[Fig. 4(f)]. This is different from the Ni nanotubes. For CFBM1, we get
AMR =0.18% at 2 K and 0.08% at room temperature being more than an order of magnitude
smaller than Ni. We attribute this to the amorphous structure of our unannealed CoFeB leading to a
short electron mean free path and reducing the MR ratio.40The measured CoFeB resistivity of 1 −
2×103μ/Omega1cm is one order of magnitude larger compared to the best values given in literature for
CoFeB alloy films with a comparable thickness.41,42ForR(T), we do not find a T3/2dependence in
the accessible temperature range and rule out magnetic contributions to R(T).43The characteristic
minima in R(T) [Fig. 4(b)] have been reported for many amorphous and granular alloys with interme-
diate resistivities44,45including CoFeB.46,47The following dependencies have been discussed for the
low-temperature Rwhen considering Coulomb interaction in disordered systems: exp(√T0/T),48a
power law 1/ Tαor ln ( T0/T)38(T0is a characteristic temperature and 0 <α/lessmuch1). The first (latter)
occurs for systems with high (intermediate) resistivity.38,46,49,50Following Ref. 38, we attribute
the logarithmic behavior of R(T)i nF i g . 4(b) forT<Tminto electron-electron interaction in the
disordered and amorphous material. The role of the columnar structure is not yet fully clear andunder further investigation. Despite the complex R(T) dependence, the AMR value of up to 0.18%
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FIG. 4. Resistance Ras a function of the temperature Tfor (a) the Ni nanotube NiL1 (circles) and (b) the two different
CoFeB nanotubes CFBM1 (squares) and CFBS1 (triangles). For CoFeB, Ris more than two orders of magnitude larger and
shows a different temperature dependence (note the different axes) compared to the metallic Ni. (c) Resistance variation as afunction of the angle θdisplayed as /Delta1R(θ) for NiL1 (circles) and NiS1 (stars) at 3 T and 2 T, respectively. The field values
Hwere chosen such that H>H
satand magnetic saturation was achieved for all angles θ. (d) AMR ratios as a function
of temperature for NiL1 (circles). For NiS1 (star) and NiM (triangle) room-temperature AMR ratios are given. (e) R(θ)o f
CFBS1 at 5 T at two temperatures (triangles) and CFBM1 at 2 T and 283 K. The data for CFS1 were taken in two-pointconfiguration. (f) AMR ratios of samples CFBM1 (squares), CFBS1(triangles), and CFBS2 (diamond) at room temperature.The AMR effect of CFBM1 was extracted from magnetic field sweeps performed at different θ.
29Solid lines in (c) and (e)
indicate a cos2(θ) relationship. The maximum AMR ratio is one order of magnitude smaller for CoFeB compared to Ni.
that we observe for CoFeB nanotubes at small Tis slightly larger than the value of 0.12% obtained
by DFT simulations.51
The large room-temperature AMR ratios of up to 1.4% for Ni are encouraging for possible
applications of nanotubes and, in general, magnetic devices on curved surfaces7prepared by ALD.
Still there is room for improvement as the AMR ratio of bulk Ni is known to be 2%.52We expect an
improved AMR ratio after reducing the surface roughness of the nickel. The smooth side facets of theCoFeB nanotubes make the integration of magnetic tunnel junctions
53feasible, thereby enhancing
the perspectives of nanotube-based sensing and local detection of domain walls.
In conclusion, we prepared nanotubes from Ni and CoFeB on non-magnetic nanotemplates
using two different technologically relevant deposition techniques, i.e., atomic layer deposition
and magnetron sputtering, respectively. Structural analysis of the CoFeB proved the shell to beamorphous. For polycrystalline Ni and amorphous CoFeB, the magnetic anisotropy was argued
to be dominated by the shape. Both the relatively small resistivity and large AMR ratio of 1.4%
obtained for Ni indicated a good electrical performance of the ALD-grown metal at room temperature.Magnetron-sputtered CoFeB nanotubes exhibited a much smoother surface but a smaller AMR effect
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attributed to the amorphous structure and thereby enhanced electron scattering. The materials are
highly eligible for magnetotransport studies on individual domain walls in nanotubes and nanotube-based sensing or logic applications. For room temperature spintronic applications, the relatively
large AMR of Ni is promising. The larger saturation magnetization makes the CoFeB nanotubes
favorable as magnetic tips in scanning probe microscopy.
The work has been supported by the DFG via GR1640/5-1 in SPP1538 “Spin caloric transport.”
Funding through the Swiss National Science Foundation NCCR QSIT and FP7 ITN Nanoembrace
are greatly acknowledged. We acknowledge financial support from the European Union under a
contract for an integrated Infrastructure Initiative 312483 - ESTEEM2 project that facilitates the useof advanced electron microscopes at ER-C J ¨ulich. The authors would like to thank D. Meertens for
the preparation of FIB lamellas. J.A. acknowledges the funding from the Spanish MICINN project
MAT2010-15138 (COPEON), and Generalitat de Catalunya 2009 SGR 770. R.R.Z. acknowledges
the former. The authors would also like to thank the TEM facilities in CCiT from Universitat de
Barcelona.
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1.4900843.pdf | Effect of viscosity contrast on gravitationally unstable diffusive layers in porous media
Don Daniel and Amir Riaz
Citation: Physics of Fluids (1994-present) 26, 116601 (2014); doi: 10.1063/1.4900843
View online: http://dx.doi.org/10.1063/1.4900843
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54PHYSICS OF FLUIDS 26, 116601 (2014)
Effect of viscosity contrast on gravitationally unstable
diffusive layers in porous media
Don Daniel and Amir Riaza)
Department of Mechanical Engineering, University of Maryland, College Park,
Maryland 20742, USA
(Received 2 December 2013; accepted 15 September 2014;
published online 7 November 2014)
We investigate the effect of viscosity contrast on the stability of gravitationally un-
stable, diffusive layers in porous media. Our analysis helps evaluate experimental
observations of various diffusive (boundary) layer models that are commonly used to
study the sequestration of CO 2in brine aquifers. We evaluate the effect of viscosity
contrast for two basic models that are characterized with respect to whether or not
the interface between CO 2and brine is allowed to move. We find that diffusive layers
are in general more unstable when viscosity decreases with depth within the layercompared to when viscosity increases with depth. This behavior is in contrast to the
one associated with the classical displacement problem of gravitationally unstable
diffusive layers that are subject to mean flow. For the classical problem, a greaterinstability is associated with the displacement of a more viscous, lighter fluid along
the direction of gravity by a less viscous, heavier fluid. We show that the contrasting
behavior highlighted in this study is a special case of the classical displacement prob-
lem that depends on the relative strength of the displacement and buoyancy velocities.
We demonstrate the existence of a critical viscosity ratio that determines whether theflow is buoyancy dominated or displacement dominated. We explain the new behav-
iors in terms of the interaction of vorticity components related to gravitational and
viscous effects.
C/circlecopyrt2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4900843 ]
I. INTRODUCTION
Transient, diffusive boundary layers in porous media play an important role in a wide range
of geophysical flows.1This study in particular is motivated by carbon dioxide sequestration in
subsurface saline aquifers.2,3When supercritical CO 2is injected into a brine-saturated aquifer, the
lighter CO 2rises up and accumulates under an impervious layer, as shown in Figure 1.C O 2then
dissolves into the underlying brine across the two-phase interface and forms a diffusive boundary
layer. This boundary layer is unstably stratified and transitions to natural convection in the form of
unstable, sinking plumes. The process of natural convection greatly enhances the dissolution of CO 2
into brine.
Diffusive boundary layers associated with CO 2sequestration have been studied widely with the
help of various simplified models. These models often assume that CO 2dissolves into brine across
a two-phase interface at constant pressure and temperature. The concentration of dissolved CO 2at
the interface is therefore taken to be constant. The interface motion resulting from dissolution is
further considered to be small by one popular model, compared with other relevant time scales inthe problem. The position of the interface is therefore considered fixed. We refer to this model as the
fixed interface model.
4–6Another model of the diffusive boundary layer attempts to incorporate the
motion of the interface by considering a diffused layer that separates two initially quiescent, miscible
fluids. For this model, a non-monotonic density-concentration relationship is used to produce both
stable and unstable regions within the boundary layer.7–10The overall result is the apparent motion
a)Author to whom correspondence should be addressed. Electronic mail: ariaz@umd.edu
1070-6631/2014/26(11)/116601/17/$30.00 C/circlecopyrt2014 AIP Publishing LLC 26, 116601-1
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54116601-2 D. Daniel and A. Riaz Phys. Fluids 26, 116601 (2014)
FIG. 1. Sketch of CO 2sequestration. Dissolution of CO 2into brine occurs across the two-phase interface, indicated by
pairs of counter-pointing arrows. The gravitationally unstable CO 2layer within brine plays a vital role in determining the
interfacial dissolution rate.
of the diffusive layer after the onset of nonlinear convection. We refer to this setup as the moving
interface model. Because of the relative ease of laboratory setup, the moving interface model hasgained more popularity with experimental studies compared with the fixed interface model. The
moving interface model however has not been studied with the help of linear stability analysis and
a fundamental insight regarding the physical behavior is lacking. Moreover, it is unclear how the
stability characteristics of the two models are related.
From a practical stand point, the viscosity difference between the CO
2-brine solution and the
CO 2-free brine is small.11,12However, the practical selection of experimental fluids often results
in very different viscosity contrasts in the laboratory than what is expected in practice. In some
cases, the viscosity of the experimental fluid representing the CO 2-brine solution is about 20 times
greater than the viscosity of the fluid representing the CO 2-free brine.8Therefore, the effect of the
viscosity contrast on the stability behavior needs to be understood to properly interpret experimental
observations. In order to facilitate such an understanding, we consider the closely related, classicalproblem of a diffusive layer displaced by a mean flow. For the classical displacement problem, the
effects of viscosity contrast, density difference, and the mean flow, all compete to influence the
stability behavior.
13The moving interface model is a special case of the displaced interface problem
with zero mean flow. The transition from the classical case to the moving interface model involves
the transition from the mean flow dominated regime to the buoyancy dominated flow regime. The
evaluation of this transition is thus expected to facilitate a deeper understanding of the role ofviscosity contrast for both the moving and the fixed interface models. Moreover, such a transition
has not been studied in detail previously for the classical displacement problem.
The objectives of this study thus are twofold: (i) To investigate the effect of the viscosity contrast
for the fixed and the moving interface models and (ii) to study the interaction of mean flow, density
difference, and viscosity contrast for understanding the transition from mean flow dominated tobuoyancy dominated behavior. For the purposes of this analysis, we define the viscosity contrast,
R, as the natural logarithm of the ratio of viscosities of the heavier to the lighter fluid. We show
that the fixed interface model generally predicts more instability than the moving interface modelwhen Ris greater than about 1.8. On the other hand, the moving interface model is more unstable
for smaller values of R. We also show that the two models can be made to yield similar results by
altering the non-monotonic density profiles or by selecting fluids with specific viscosity contrasts.This can facilitate the translation of results between the two models.
The previous understanding of the classical problem suggests that the displacement of a more
viscous fluid by a less viscous fluid is more unstable compared with the displacement of a lessviscous fluid by a higher viscosity fluid. We find that this behavior reverses depending upon the
viscosity contrast and the relative strengths of the displacement, and buoyancy related velocities.
A similar effect has also been observed by Meulenbroek et al.
14To characterize this phenomenon,
we define a critical viscosity ratio, Rc.F o r R<Rc, instability increases with a decrease in R.T h e
classical behavior of an increase in instability with an increase in Ris recovered when R>Rc.W e
show that Rcis a function of the relative magnitudes of the mean flow and buoyancy velocity. We
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54116601-3 D. Daniel and A. Riaz Phys. Fluids 26, 116601 (2014)
show further that when the relative magnitude exceeds a threshold value, these qualitatively different
behaviors are separated by an intermediate stable region. The new behavior associated with R<Rc
occurs for both the fixed and moving interface models. We explain this new phenomenon in terms
of the interaction of vorticity components related to gravitational and viscous effects. We show thatthis previously unrecognized phenomenon is a general feature of gravitationally unstable, variable
viscosity diffusive layers.
A quasi-steady-state (QSSA) eigenvalue approach
5in self-similar space is used to study the
linear stability problem. The suitability of this approach is suggested by the recent findings of Tilton
et al.15The authors demonstrate that QSSA and other optimization methods based on linear operators
in non self-similar space, give rise to nonlocal perturbation structures that cannot lead to nonlinear
convection in finite time. Tilton et al.15show that perturbations inside the boundary layer, such as
those related to the QSSA modes in self-similar space, are responsible for the onset of nonlinearconvection. A recent study by Daniel et al.
16finds that QSSA modes in self-similar space coincide
with optimal boundary layer perturbations that lead to the earliest onset of nonlinear effects.
The work is divided as follow. The geometries and governing equations are explained in
Sec. II. The results are discussed in Sec. IIIalong with conclusions in Sec. IV.
II. GOVERNING EQUATIONS
In order to evaluate experimental setups based on the moving interface (MI) model of the
diffusive boundary layer, we use a non-monotonic density profile, ρ∗, of the form illustrated in
Figure 2(a). This density profile can be represented as
ρ∗=ρ0+/Delta1ρF(c), (1)
where the function F(c)=/summationtext4
n=1ancn, determines how density varies with concentration c. The end
point densities related to c=0 and c=1a r eρ0andρ1, respectively, and ρmis the maximum density.
Note that the fluid with c=1 lies above the fluid with c=0. The quantity, /Delta1ρ=ρm−ρ0, indicates
the strength of unstable density stratification. The function F(c) is normalized to the maximum value
of one. The density profile is linear when a1=1 and an=0f o r n=2, 3, 4. Following previous
works, we employ a monotonic viscosity profile illustrated in Figure 2(b),
μ∗=μ1exp(R(1−c)), (2)
where R=ln(μ0/μ1) is the log mobility ratio, μ1is the viscosity of the fluid with c=1, and μ0is
the viscosity of the fluid with c=0.
For the experimental study of Backhaus et al.8based on the moving interface model, water
and propylene glycol were used as the lighter and heavier fluids, respectively. For that system, the
location of the density peak occurs at a concentration of c≈0.38. A log mobility ratio, R≈− 3, fits
FIG. 2. (a) Non-monotonic density-concentration profile employed in a MI model. (b) Monotonic viscosity-concentration
profiles for various log mobility ratios, R=ln(μ0/μ1).
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FIG. 3. Concentration base-states for Rayleigh number, Ra=500, at various instants of time t. (a) Base-state for FI model,
cF
b=erfc(z√Ra/4t). (b) Base-state for MI model, cM
b=0.5 erfc( z√Ra/4t).
the viscosity-concentration relationship at a temperature of 120◦F. Neufeld et al. ,7MacMinn et al. ,9
and Ehyaei and Kiger10also employ a moving interface model, using methanol/ethylene glycol
(MEG) mixtures and water as the lighter and heavier fluids, respectively. The location of the density
peak and the viscosity differences depend on the composition of the MEG mixture. Typical values ofthe peak density vary in the range, 0.2 <c<0.55,
17while the log mobility ratios vary approximately
in the range, −1.5<R<1.9Another experimental study by Slim et al.18employs a setup that
is closer to the fixed interface model. The authors employed potassium permanganate (KMnO 4)i n
water as an analogous model for CO 2in brine. The KMnO 4-water mixture approximately satisfies a
linear density profile and a log mobility ratio of R≈0.04 fits the viscosity-concentration relationship
at 77◦F.19
In this study, we consider an isotropic and homogeneous porous aquifer of infinite horizontal
extent and depth H. The vertical coordinate, z, is positive in the direction of gravity, g. The porous
medium is characterized by permeability, K, dispersivity, D, and porosity, φ. We use characteristic
values of Hfor length, μ1for viscosity, K/Delta1ρg/μ1for velocity, μ1H/K/Delta1ρgφfor time and /Delta1ρgH
for pressure. Using these characteristics values we obtain the following non-dimensional governingequations:
μ(c)v+∇p−F(c)e
z=0,∇·v=0,∂c
∂t+v·∇c−1
Ra∇2c=0. (3)
The Rayleigh number is defined as Ra=K/Delta1ρgH/φDμ1. The symbol v=[u,v,w ] is the nondimen-
sional velocity vector, and pis the nondimensional pressure obtained from the dimensional pressure
ˆpthrough the relation p=(ˆp−ρogz)//Delta1ρ gH. The symbol ezis the unit vector in the z-direction.
The boundary conditions for (3)depend on the model. For the fixed interface (FI) model, the
boundary conditions for (3)are
c/vextendsingle/vextendsingle
z=0=1,∂c
∂z/vextendsingle/vextendsingle/vextendsingle/vextendsingle
z=1=0,w/vextendsingle/vextendsingle
z=0=w/vextendsingle/vextendsingle/vextendsingle
z=1=0. (4)
Equations (3)and(4)admit the concentration base state, cF
b(z,t)=erfc(z√Ra/4t), see Figure 3(a)
for illustration. The velocity base-state is vb=0.
For the MI model, we use boundary conditions that allow diffusion in two opposite directions,
∂c
∂z/vextendsingle/vextendsingle/vextendsingle/vextendsingle
z=−1=∂c
∂z/vextendsingle/vextendsingle/vextendsingle/vextendsingle
z=1=0,w/vextendsingle/vextendsingle/vextendsingle
z=−1=w/vextendsingle/vextendsingle/vextendsingle
z=1=0. (5)
Equations (3)and(5)admit the base-states, cM
b(z,t)=erfc(z√Ra/4t)/2, see Figure 3(b), and
vb=0. These expressions of the base-states, cF
bandcM
b, are valid as long as the boundary layer is
far from the boundary at z=1 for the FI model and z=± 1 for the MI model, respectively. This
holds true when√Ra/4t>3.5
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The linear stability of various diffusive boundary layer models is studied with respect to small
wavelike perturbations of the form,
/tildewidec=/hatwidec(z,t)ei(αx+βy),/tildewidev=/hatwidev(z,t)ei(αx+βy), (6)
where i =√
−1,αandβare wavenumbers in the x- and y-directions, respectively, and /hatwidec(z,t) and
/hatwidev(z,t) are time-dependent perturbation profiles in the z-direction. We substitute c=cb+/tildewidecand
v=vb+/tildewidevinto Eq. (3), subtract out the base state and linearize to obtain the following initial value
problem for perturbations, /hatwidecand/hatwidew,
/parenleftbigg∂
∂t−1
Ra∂2
∂z2−k2/parenrightbigg
/hatwidec+∂cb
∂z/hatwidew=0, (7)
/parenleftbigg∂2
∂z2−R∂cb
∂z∂
∂z−k2/parenrightbigg
/hatwidew+Gk2/hatwidec=0, (8)
where k=/radicalbig
α2+β2,G=1/μ(cb)∂F(cb)/∂cb+URandcbrefers to the appropriate base state.
Homogeneous Dirichlet boundary conditions are specified for the perturbations at z=1 and z=± 1
for the FI and MI models, respectively.
The velocity, U=U∗μ1/K/Delta1ρg, refers to the fluid displacement velocity, U∗, scaled with the
buoyancy velocity, K/Delta1ρg/μ1. It indicates the relative strength of the mean flow with respect to
buoyancy velocity and is relevant only for R/negationslash=0 and U∗/negationslash=0. When U=0, Eqs. (7)and(8)represent
either the FI or MI models. When U/negationslash=0, these equations represent the displaced interface problem,
which is a generalization of only the MI model. Note that the counterpart of the FI model with
nonzero Uis not considered in this study. The displaced interface problem is formulated in the
coordinate system that moves with velocity, Uez. The associated linearized equations are obtained
by first performing coordinate transformations to Eqs. (3)and(5)before carrying out an expansion
using normal modes. Note that with the coordinate transformation, the boundary conditions and theresulting base-state for the displaced interface problem are the same as for the MI model.
13
We solve Eqs. (7)and(8)using a QSSA eigenvalue formulation in the self-similar ( ξ,t) space,
where ξ=azanda=√Ra/4t.5The resulting eigenvalue problem can be expressed as
σce=ξ
2∂ce
∂ξ+1
Ra/parenleftbigg
a2∂2
∂ξ2−k2/parenrightbigg
ce−a∂cb
∂ξwe, (9)
/parenleftbigg
a2∂2
∂ξ2−a2R∂cb
∂ξ∂
∂ξ−k2/parenrightbigg
we=−Gk2ce, (10)
with homogeneous Dirchlet boundary conditions for the eigenmodes, ceandwe, and the eigenvalue,
σ, represents the growth rate. The least stable perturbation is defined as the eigenmode with the
maximum real value for σ. The growth rates obtained in the self-similar space ( ξ,t) are equivalent to
the growth rates calculated in the regular space ( z,t) when perturbation amplitudes are based on the
L∞norm. In the case of other norms, explicit transformations are required.15Equations (9)and(10)
are discretized using standard second-order finite difference schemes. For given parameters of k,t,
andRa, the generalized eigenvalue problem is solved using function “eig” in MATLAB . We define
the onset time for linear instability, t=to, as the time at which the growth rate of a perturbation
eigenmode first becomes positive. The corresponding wavenumber is called the critical wavenumber,
k=ko.
III. RESULTS AND DISCUSSION
We discuss the effect of viscosity contrast on the onset of instability for the fixed and moving
interface models. The effect of different non-monotonic density profiles will be investigated for
the moving interface model. We will also explore the effect of mean flow and viscosity contrast
for the classical, displaced interface problem. We will investigate how stability features transition
from displacement dominated to buoyancy dominated behavior. Throughout the study, the Rayleigh
number will be fixed at Ra=500. Linear stability behavior at other value of Ra>50 can be obtained
by a simple rescaling.5,15
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FIG. 4. Isocontours of σ=0 produced by a FI model. Arrows point toward the unstable region, σ> 0. Solid dots mark the
critical points, ( ko,to).
A. The fixed interface model
Following previous studies, we employ a linear density profile, F(c)=c, for the FI model.
Figure 4illustrates the isocontours of the growth rate, σ=0, in the ( k,t) parameter plane for log
mobility ratios of R=− 1 (solid line), R=0 (dashed line), and R=1 (dashed-dotted line). The
arrows point toward the unstable zone where the growth rates are greater than zero, σ> 0. For small
times, all perturbation wavenumbers are stable. Later, a band of wavenumbers become unstable. The
lowest point on the σ=0 isocontour corresponds to the critical parameters ( ko,to). For R=− 1, the
critical point is at (66.8, 0.1). The case, R=0, is the previously described5constant viscosity case
with the critical point at (34.7,0.3). The R=0 case has a smaller band of unstable wavenumbers
compared to R=− 1. The unstable region shrinks further when the viscosity ratio is increased to R
=1, resulting in smaller koand larger to. This decrease in instability with increasing Rrepresents
the non-classical stability behavior with respect to the affect of viscosity contrast.
To further describe the effect of the viscosity contrast, Fig. 5(a) plots the temporal evolution
of the maximum growth rate, σmax,f o r R=− 1 (solid line), R=0 (dashed line), and R=1
(dashed-dotted line). The maximum growth rate is defined as
σmax(t)=sup
0≤k<∞σ(t,k). (11)
Figure 5(a) shows that the largest values of σmaxfor all times result for the case of R=− 1, followed
byR=0 and R=1. When t<1, the R=− 1 perturbations attain growth rates as large as σmax≈6.
In contrast, the R=1 perturbations are stable for the same time period with σmax<0. Figure 5(b)
FIG. 5. Results produced by FI model. (a) Maximum growthrates, σmax,v s .t. (b) Dominant wavenumbers, kmax,v s .t.T h e
solid points represent the critical point of instability, ( ko,to).
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TABLE I. V orticity values and growth rate produced by the FI model for k=30 and t=0.2.
RI 1 I2 I1+I2 σ
−3 12.67 −5.40 7.27 23.39
−25 . 3 7 −1.75 3.63 8.99
−12 . 4 9 −0.45 2.04 1.70
0 1.26 0.00 1.26 −2.23
1 0.68 0.13 0.80 −4.41
2 0.38 0.13 0.51 −5.59
3 0.23 0.09 0.32 −6.21
illustrates the dominant wavenumbers, kmax, that are associated with σmax,f o r R=− 1 (solid line),
R=0 (dashed line), and R=1 (dashed-dotted line). We observe that kmaxdecreases monotonically
in time for all R.T h e R=− 1 perturbations have larger values of kmaxcompared to the R=1
perturbations. Thus, from Fig. 5we gather that both σmaxandkmaxincrease when Ris lowered,
which indicates that smaller viscosity contrasts lead to greater instability.
We find that the phenomenon of greater instability associated with smaller values of Ris directly
correlated to the instantaneous vorticity field
/Omega1e=k
μ(cb)ce−R
k∂cb
∂z∂we
∂z. (12)
To measure vorticity components, we define the integral,
I=/integraldisplay
/Omega1edz=I1+I2, (13)
where
I1=k/integraldisplay
exp[−R(1−cb)]cedz,I2=−R
k/integraldisplay∂cb
∂z∂we
∂zdz. (14)
The eigenmodes are normalized such that the maximum value of ceis one. The first integral, I1,
measures the contribution to vorticity arising from gravitational effects and is positive for ce>0.
The second integral, I2, depends on the gradients of the base-state and velocity perturbation. The
instantaneous magnitude of both the concentration and velocity perturbations is determined by their
coupled evolution given by Eqs. (9)and(10).
Table IlistsI1,I2, andσ,f o rRranging from −3 to 3. Larger values of the total vorticity integral,
I=I1+I2, are associated with higher growth rates. Table Iindicates that I1increases with an
increase in the viscosity of the heavier fluid (decreasing R) whereas I2decreases with deceasing
R. Table Ifurther indicates that I2makes a positive contribution to total vorticity when R>0 and
a negative contribution when R<0. The contribution of I1is always positive and increases with
decreasing R. Overall, we gather from Table Ithat instability increases (larger values of σ) with an
increase in the viscosity of the heavier fluid ( R<0) and that the destabilizing contribution comes
mainly from vorticity related to buoyancy, signified by the I1integral.
In order to understand the role of individual contributions to the total vorticity, I1+I2,w e
examine the perturbation eigenmodes. Figure 6illustrates the base-state, cF
b(solid line), the concen-
tration eigenmode, ce(dashed line), and the vertical velocity eigenmode, we(dashed-dotted line) for
R=− 1.5 (panel a) and R=1.5 (panel b), respectively. The numbers along the top axis represent
the spatial distribution of viscosity values based on μ=exp ( R(1−cF
b)). When R=− 1.5, the
magnitudes of weandceare similar. The ratio of the maximum values of weandceis 0.92. For a
larger value of R=1.5, Fig. 6(b) indicates a substantial weakening of we. The ratio of the maximum
values in this case drops to 0.13. The magnitude of the velocity perturbation is smaller for R=1.5
because the velocity perturbation peaks in the boundary layer region where viscosity is greater ascompared to R=− 1.5. Physically, this implies more viscous resistance to fluid flow in the case
of the larger value of R=1.5. Velocity perturbations thus tend to concentrate more in regions of
lower viscosity. Note that the classical behavior of greater instability associated with larger values
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FIG. 6. Base-state and least stable eigenmodes produced by the FI model as a function of self-similar coordinate, ξ,f o rk=
30, and t=0.2. Viscosity values are presented at the top axis. (a) R=− 1.5. (b) R=1.5
ofRis due to an additional source of vorticity arising from the background mean flow. This will be
explained in more detail in Sec. III D .
B. The moving interface model
In order to characterize the MI model, we employ a density profile that corresponds to an
aqueous propylene glycol mixture. Figure 7(a) illustrates the concentration-density function F(c)
FIG. 7. Comparison between MI and FI models. (a) Nonmonotonic function Fas a function of concentration c,s e eE q . (1).
The coefficients of F(c)a r e : a1=1.06, a2=17.31, a3=− 39.35, a4=12.28. (b) cM
bvs.zfort=10. The density gradients
are destabilizing only when z>γ (arrow). (c) tovs.R.( d ) kovs.R.
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FIG. 8. Agreement between FI model with R=0 (solid line) and MI model with R=0.48 (dashed line). (a) σmaxvs.t.
(b)kmaxvs.t.( c )ce//bardblce/bardbl∞vs.ξfork=30 and t=1. (d)we//bardblwe/bardbl∞vs.ξfork=30 and t=1.
defined in Eq. (1). The concentration, c, is scaled with the maximum concentration of the propylene
glycol solution and c=0 refers to pure water. The positive density gradient for c<0.38 represents
the unstable density stratification that promotes the formation of instability. Figure 7(b) illustrates
the location of the zone of unstable stratification within the diffusive layer. Unlike the FI model,
where the entire boundary layer is unstable, the unstable density gradients in the MI model exist
only for z>γ(t)( o rξ> 0.21), where γ(t)=0.21√4t/Ra.
Figure 7(c) illustrates the onset time, to, as a function of the log mobility ratio, R,f o rt h e
MI (circles) and FI (crosses) models. As expected, the onset time predicted by the two modelsincreases with increasing R. However, Fig. 7(c) indicates a large difference in the onset times for
small values of R. When R=− 2,t
ois about an order of magnitude greater in the case of the FI
model. With increasing R, the difference in the onset times produced by the two models decreases. For
R≈1.8, both models predict identical onset times. Beyond this point, the FI model is relatively more
unstable and predicts earlier onset times. Figure 7(d) illustrates the associated critical wavenumbers,
ko,v e r s u s Rfor the MI (circles) and FI (crosses) models. As expected, kodecreases with increasing
R.F o r R<1.36, the MI model predicts smaller unstable wavelengths.
Figure 7(c) shows that the onset times predicted by the two models coincide at a specific value
ofR≈1.8. It is further obvious from Fig. 7(c) that the two models also predict the same value of
the onset times for different values of R. For example, an onset time of to≈0.1 is predicted by both
the MI and FI models with R=0 and R=0.48, respectively. For these values of R, we find that the
corresponding growth rates and perturbation profiles are also in relatively good agreement for t>to.
This is depicted in Figure 8where the temporal evolution of the dominant growth rate, σmax, (panel
a) and the dominant wavenumber, kmax, (panel b) are plotted for the FI model with R=0 (solid
line) and the MI model with R=0.48 (dashed line). Furthermore, Figure 8(c) illustrates ce//bardblce/bardbl∞
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FIG. 9. Eigenmodes associated with the MI model (a) Base-state, cM
b(solid line), least stable ce(dashed line), and we
(dashed-dotted line) at critical point ( ko,to)w h e n R=0. The vertical line is drawn at the location of maximum (turning
point) in the density profile. (b) Normalized weprofiles at k=15 and t=1 for log mobility ratios, R=0 (solid line), R=1
(dashed line), and R=2 (dashed-dotted line). The dots emphazise the points where we=0.
versus ξfork=30 and t=1. The ceprofile produced by the MI model (dashed line) for R=0.48 is
identical to that produced by the FI model (solid line) for R=0 except for a narrow region around
ξ=0. The FI domain (solid line) does not exist for ξ< 0. Figure 8(d) illustrates the corresponding
normalized weprofiles for k=30 and t=1, which are also similar for ξ> 0. For the MI domain
(dashed line), the region associated with we<0 is stabilizing, according to the term, we∂cb/∂z,i n
Eqs. (9)and(10).
In order to illustrate the instability mechanism for the MI model, Figure 9(a)shows the base-state,
cM
b(solid line) and the profiles of the most unstable eigenmodes, ce(dashed line) and we(dashed-
dotted line), for t=toandR=0. The vertical line represents the location of peak density, ξ=0.21
orz=γ, where the density gradient is zero. The destabilizing stratification occurs to the right side of
this point. The perturbation peaks occur in the destabilizing zone where we>0. Note that we/negationslash=0a t
peak density location, ξ=0.21. This suggests that there is a net upward momentum transport across
the horizontal isosurface of peak density values. Figure 9(b) depicts the normalized weprofiles for
k=15,t=1 and log mobility ratios, R=0 (solid line), R=1 (dashed line), and R=2 (dashed-dotted
line). With increasing R, there is less momentum transport across the location of peak density at ξ
=0.21. Consequently, the solid dots move to the right.
We can now explain why the MI model is more unstable at small Rand less unstable at large
R, compared to the FI model, as depicted in Figure 7(c). Unlike the FI model, we find that for
the MI model, momentum transport occurs across the boundary separating the zones of stable
and unstable density stratification at z=γorξ=0.21 (indicated by the dashed vertical lines in
Figure 9). This mechanism is absent in the FI model. The upward momentum transport in the MI
model at small Rallows the formation of stronger instabilities within the boundary layer. For larger
values of the viscosity ratio, the destabilizing effect of momentum transport is countered by thegreater negative velocity perturbation, as observed in Fig. 9. The negative velocity perturbation
represents an additional set of counter rotating vortices that produce a stabilizing effect. This results
in lesser instability for the MI model at large R, as depicted in Figure 7(c).
C. Effect of non-monotonic density profiles
We now consider the effect of the density profile on the stability behavior associated with the
MI model. The density profile used in Sec. III B is referred to as ρA. To investigate how varying the
location of the maximum density may affect the onset times, we define two new profiles, ρBandρC,
by modifying the function F(c) defined in Eq. (1). Figure 10(a) illustrates F(c) for density profiles, ρA
(circles), ρB(crosses), and ρC(squares). The maximum value of density occurs at c=0.38, c=0.5,
andc=0.25 for the density profiles, ρA,ρB, andρC, respectively. The density associated with the
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FIG. 10. Three different non-monotonic density profiles in the MI model. (a, b) Effect of changing the location of the
maximum value of density. (c, d) Effect of changing the density values of the saturated fluid, c=1.
maximum concentration is held constant. As the maximum value of density moves closer to c=1,
Figure 10(a) shows that the zone of unstable stratification expands and the zone of stable stratification
shrinks.
Figure 10(b) illustrates the onset time, to, versus log mobility ratio, R, obtained using the MI
model with density profiles, ρA(circles), ρB(crosses), and ρC(squares). The onset times produced
by all three density profiles increase with increasing R, as expected. When R=− 2, the onset time,
to, produced by ρBis about 1.8 times greater than the one produced by ρC.F o r R≈− 0.2, all
three density profiles produce about the same value of to. With increasing R,t h eρCprofile tends to
produce the largest onset time.
Figure 10(c) illustrates two more density profiles for which the location of the maximum density
is fixed at c=0.375 (solid dot) and the density at c=1 is different. This amounts to varying the slopes
in the stable part of the density profile, as shown in Fig. 10(c) . The density profile, ρE(squares), has
a larger gradient compared to ρA(circles) and ρD(crosses). Figure 10(d) plots the corresponding
onset time as a function of R. Interestingly, the onset times for all three density profiles are very
similar. This shows that the magnitude of the density gradient in the stable part of the density profile
is not particularly relevant to the stability behavior.
The stability characteristics observed in Figures 10(b) and 10(d) can be explained by exam-
ining the profile of the velocity eigenmode, we, with respect to the spatial variation of viscosity.
Figure 11(a) illustrates weversus ξforR=0,k=30,t=1, and density profiles, ρA(solid line),
ρB(dashed line), ρC(dashed-dotted line). The viscosity values are mentioned along the top axes in
Figure 11. Crosses denote the location of the maximum value of density. Perturbations are predom-
inantly concentrated in the unstable regions to the right of the crosses. Compared with the case of
ρA, the peak of weshifts to the right for ρBand to the left for ρC. Though the perturbations produced
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FIG. 11. Effect of density profiles on velocity eigenmode wefork=30 and t=1. The top axis represents viscosity at the
corresponding depthwise coordinate ξ. The location of the maximum density associated with each profile is marked with a
cross. (a) R=0, (b) R=− 2, (c), R=2, and (d) R=0.
by the three density profiles are concentrated at different locations, the corresponding onset times
forR=0, shown in Figure 10(b) , are similar.
The location of the peaks play an important role in explaining the instability characteristics
for non-zero values of R. Figure 11(a) is repeated for R=− 2 in Figure 11(b) and for R=2i n
Figure 11(c) .F o r R=− 2, we find that the shift in wefields is similar to the case for R=0s h o w n
in Figure 11(a) . Because viscosity decreases with depth when R<0, the perturbations produced
byρCare located in the lower viscosity regions compared to perturbations produced by ρAorρB.
Consequently, perturbations produced by ρCare more unstable and lead to earlier onset times when
R<0, see Figure 10(b) . In the case of R=2, we find that perturbations produced by ρBprofiles are
located in the lower viscosity regions, and therefore, have earlier onset times. Figure 11(d) shows
that the density profiles, ρDandρE, do not have a significant effect on the corresponding perturbation
structures. Consequently, the onset times shown in Figure 10(d) are not sensitive to such density
profiles.
D. Effect of uniform flow
In Secs. III A –III C , we found that gravitationally unstable diffusive layers are less unstable for
larger values of R. This behavior contrasts with the behavior of the classical displacement problem
where the instability increases with R. To explain this contrast, we consider the displaced interface
problem, which is a generalization of the MI model. The displaced interface problem considered
here relates to the gravitationally unstable displacement of the lighter fluid by a heavier fluid with a
uniform velocity, U, along the direction of gravity. For U=1, the dimensional displacement velocity
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FIG. 12. Effect of viscosity contrast for the displaced interface problem with a linear density profile. (a) Onset time tovs.R.
(b) Critical wavenumber kovs.R. (c) Critical viscosity ratio, Rc,v s . U(diamond). Results for density profiles, ρA(circles),
ρB(crosses), ρC(squares), are also shown for comparison. (d) Various flow regimes as a function of RandU, for a linear
density profile. The shaded region in ( R,U) space represents the stable flow regime.
is equal to the buoyancy velocity, K/Delta1ρg/μ1, see Sec. IIfor details. To facilitate comparison with
previous studies related to the displacement problem,13we first consider a linear density profile and
later also evaluate the non-monotonic density profiles, such as the ones illustrated in Figure 10(a) .
Figure 12(a) plots the onset time, to, versus the log mobility ratio, R, for displacement velocities,
U=0( c i r c l e s ) , U=0.5 (squares), and U=1(crosses), using a linear density profile. As expected,
when U=0,toincreases with increasing R.F o r U=0.5,toincreases with Runtil it attains a
maximum value at R≈0. Beyond this value of R,todecreases with R. When U=1, the maximum
value of tooccurs at R=− 1. Figure 12(b) illustrates the corresponding critical wavenumbers, ko,
versus RforU=0 (circles), U=0.5 (squares), and U=1(crosses). For U=0,kodecreases
monotonically with R.F o r U=0.5,kodecreases with increasing Runtil it reaches a minimum at R
=0 and increases thereafter. For U=1, the minimum point occurs at a lower value of R. Similar
qualitative trends can also be obtained for the non-monotonic density profiles.
Figures 12(a) and12(b) depict the existence of qualitatively different stability behaviors for the
critical parameters, toandko.T h ev a l u eo f Rat which the instability characteristics undergo the
qualitative switch, is referred to as the critical viscosity ratio, Rcas shown in Figure 12(a) . When
R<Rc,toincreases with an increase in R. This behavior is in contrast to the classical displace-
ment behavior and is similar to the behavior of the buoyancy driven instabilities considered in the
Secs. III A –III C . When R>Rc,todecreases with an increase in R, depicting the dominance of
displacement-related instabilities. We find that although the values of Rat the points of maximum to
and minimum kodepicted in Figures 12(a) and12(b) do not coincide, they are close. The small dif-
ference could perhaps be due to numerical artifacts associated with the measurement of perturbation
quantities at small times, t<O(to).15
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TABLE II. V orticity integral values and growth rates for U=1,k=30,t=0.2, and Ra=500.
RI 1 I2 I3 I1+I2+I3 σ
−3 15.90 −3.29 −4.89 7.71 19.79
−27 . 1 6 −0.76 −3.55 2.85 4.88
−13 . 4 8 −0.11 −1.92 1.44 0.85
0 1.90 0.00 0.00 1.90 3.0011 . 1 9 −0.07 1.86 2.97 7.36
20 . 8 2 −0.31 3.66 4.18 12.17
30 . 6 2 −0.74 5.43 5.31 16.59
Figure 12(c) illustrates Rcversus Ufor density profiles, ρA(circles), ρB(crosses), ρC(squares),
along with the linear density profile (diamonds), for mean flow in the range, 0 <U<2. In all cases,
when the displacement velocity tends to zero, U→0, the critical log mobility ratio, Rc, approaches
infinity, Rc→∞ . With increasing U,Rcdecreases. The rate at which Rcdecreases is highest for the
linear density profile followed by the density profiles, ρB,ρA, andρC, respectively. This suggests
that the rate of decay is proportional to the width of the zone of unstable density stratification within
the boundary layer, see Sec. III C . By increasing the displacement velocity beyond U=2, we find
thatRcsplits into two branches. This is depicted in Figure 12(d) for a linear density profile. The split
atU≈2.7 is due to the formation of a stable region when Uis larger than a certain critical value.
ForU>2.7, the boundary layer is buoyantly unstable for negative values of R. With increasing R,
the boundary layer becomes more stable and the onset time, to→∞ , as the shaded stable region
is approached. With further increase of R, the boundary layer becomes susceptible to displacement
dominated instabilities and finite values for toare again observed.
To gain a deeper insight into relevant physical mechanisms, we examine the instantaneous
perturbation vorticity field,
/Omega1e=k
μ(cb)ce−R
k∂cb
∂z∂we
∂z+kRUc e. (15)
We integrate (15) to obtain a measure of the vorticity field given by
I=/integraldisplay
/Omega1edz=I1+I2+I3, (16)
where
I1=k/integraldisplay
exp(−R(1−cb))cedz,I2=−R
k/integraldisplay∂cb
∂z∂we
∂zdz,I3=kRU/integraldisplay
cedz. (17)
Compared to Eq. (13) in Sec. III, an additional source of vorticity production, I3, arises that de-
pends on the uniform flow, U.F o r R>0,I3is positive and destabilizing and for R<0,I3
is negative and stabilizing. The effect of the uniform flow is negligible when Rtends to zero,
R→0.
Table IIlists the values of vorticity integrals, I1,I2, and I3, and the growth rate, σ, for a linear
density profile for U=1,k=30, and t=0.2. The eigenmodes are normalized such that the maximum
value of ceis one. The smallest values of Iandσare observed when the log mobility ratio is close to
its critical value, R=− 1(R≈Rc). The growth rate increases with an increase in Rfor large values
ofR, and with a decrease in Rfor small values of R. In the latter case, the major contribution to
vorticity comes from the buoyancy term, I1, while for larger values of R,I3, is the primary source of
vorticity. For small R, although both I2andI3are stabilizing, the combined stabilizing effect is not
enough to overcome the unstable effect represented by the buoyancy term, I1.
The vorticity integrals also help explain the presence of the stable zone in Figure 12(d) . Within
the stable zone where R<0 and U>0, the stabilizing effect represented by I3, overcomes the
destabilizing buoyancy effect represented by I1. The stabilizing effect of Uwhen R<0 has also
been previously reported by Manickam and Homsy.13The three regimes of displacement dominated,
buoyancy dominated, and stable flows are observed only when U>0. When U<0 (not considered
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54116601-15 D. Daniel and A. Riaz Phys. Fluids 26, 116601 (2014)
FIG. 13. Effect of displacement velocity on the velocity eigenmode we. Viscosity values are mentioned at the top. The
crosses denote the location of the maximum in the density profile, ρA.( a )we//bardblwe/bardbl∞vs.ξforR=− 1,k=30, and t=1.
(b) Same as in panel (a) for R=1.
in this study), the instability characteristics are similar to buoyancy dominated flows except for the
stable regions in the ( U,R) space when R>0.
In the case of non-monotonic density variation, displacement dominated mechanisms also affect
the transport of momentum across the interface. Recall that the interface in this case is defined as the
point of zero gradient of density. Figure 13(a) illustrates the normalized vertical velocity profiles,
we//bardblwe/bardbl∞,f o rU=0 (solid line), U=1 (dashed line), and U=2 (dashed-dotted line) when R=−1,
k=30, and t=1. The crosses correspond to the peak density location at ξ=0.21 for the ρAdensity
profile. With increasing values of U, the strength of the wefields associated with R=− 1 decreases
due to the stabilizing effect of uniform flow associated with R<1. As a result, the momentum
transport across ξ=0.21 also decreases. On the other hand, R>0 results in greater momentum
transport. This is illustrated in Figure 13(b) forR=1. In this case the velocity perturbations gain
strength due to the increased destabilizing effect of the uniform flow.
Finally, we show that the critical value of Rcis also a useful indicator for t/greatermuchto, even though
it is defined with respect to to. To demonstrate this, Figure 14(a) illustrates σmaxvsRforU=0.5
using a linear density profile. The vertical dashed line represents R=Rc. The solid dots denote the
points at which ∂σmax/∂R=0. Across this minima, there is a reversal of instability characteristics
associated with σmax. We find that at t=0.1,σmaxhas a nonmonotonic behavior as a function of R
with the local minima at R=0. At t=1 and t=10, the local minima also occur at R=0. In all
cases, the local minima coincide with Rc. Figure 14(b) repeats Figure 14(b) forU=2. Large values
oftwere used because of smaller perturbation growth rates. The locations of local minima (solid
FIG. 14. Time invariance of the critical viscosity ratio Rc(solid dots). (a) Maximum growth rates, σmax,v s . Rfor a linear
density profile when U=0.5. (b) Same as in panel (a) for U=2.
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54116601-16 D. Daniel and A. Riaz Phys. Fluids 26, 116601 (2014)
dots) are within 10% of Rceven for times as late as t=1000. The critical value is thus a useful
indicator of the dominant instability mechanism even at late times.
IV. CONCLUSION
In this study we investigated the effect of viscosity contrast on the stability behavior of grav-
itationally unstable diffusive layers. To interpret experimental observations, we considered twophysical models characterized by specific depthwise concentration profiles and different density-
concentration relationships. If laboratory studies are carried out for R≈0, our study indicates that
the MI model predicts earlier onset times. For R<0, the MI model is even more unstable. The two
models can however be made to yield similar results by using fluids with different values of Ras
well as different profiles of the density-concentration relationship.
We demonstrated that diffusive layers are more unstable in general when viscosity decreases
with depth within the layer compared to when viscosity increases with depth. This contrasts with
the behavior of gravitationally unstable diffusive layers in displaced flow. We explained the contrast
in terms of the interaction of vorticity components associated with gravitational and viscous effects.We have further shown how this interaction gives rise to a critical value of the log mobility ratio
that depends on the displacement velocity. Below the critical point, instability is governed by
buoyancy effects and decreases with an increase in R. Above the critical point, the background flow
is the dominant mechanism and instability increases by increasing R. We also found that when the
magnitude of the displacement velocity exceeds a certain threshold, the critical curve, in the space of
log mobility ratio and displacement velocity, splits into two branches giving rise to an intermediatestable zone.
Available data on the viscosity-concentration relationship for the CO
2-water system indicates
some uncertainty with regards to whether the viscosity of the mixture would increase or decrease
upon dissolution of CO 2. Different studies report both positive and negative values of R.11,12,20
Though all studies report viscosity differences to be small, R≈O(0.1). It is hence fairly likely that
such viscosity contrasts would not substantially affect the stability behavior under actual conditions.
However, the viscosity contrast between the solution and the solvent in experimental studies is large.
For example, the experimental study of Backhaus et al.8was based on the moving interface model
where the viscosity contrast was about R≈− 3. This implies a much greater level of instability
compared with the case of R≈0. For the experimental study of Slim et al.18based on the fixed
interface model, on the other hand, R≈0.04, which is closer to what is expected in practice.
However, it is uncertain whether the model employed in that study exactly corresponds to either the
fixed or the moving interface models. A range of critical times, 60/ Ra<to<160/Ra, are reported
by Slim et al.18which makes it difficult to conclude as to which model is applicable. In general,
theoretical estimates based on the assumption of R=0 cannot be used directly to interpret results
from experimental observations of systems with a large viscosity contrast. Stability analysis for such
systems is needed to account for the effect of viscosity.
Most experimental studies report the time for the onset of nonlinear convection. Fully resolved
nonlinear simulations21–23demonstrate that the time for the onset of nonlinear effects depends
on both the amplitude of initial perturbations and Ra, and is usually much greater than to.O u r
characterization of linear instability as a function of viscosity contrast and various models would
facilitate the study of the onset of nonlinear convection in such systems. Finally, the degree towhich either the fixed, or the moving interface model corresponds to an actual two-phase flow
experiment with mass transfer remains to be determined. This requires quantitative measurement of
the perturbation flow field. Some developments in this area have been reported recently by Ehyaeiand Kiger.
10
ACKNOWLEDGMENTS
The authors would like to acknowledge insightful discussions with Professor Nils Tilton at
Colorado School of Mines and Professor Hamdi Tchelepi at Stanford University. This study was
supported through a research grant from the Petroleum Institute, Abu Dhabi.
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54116601-17 D. Daniel and A. Riaz Phys. Fluids 26, 116601 (2014)
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geometry,” Phys. Rev. Lett. 106, 104501 (2011).
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in vertically confined, horizontal aquifers,” Water Resour. Res. 48, W11516, doi:10.1029/2012WR012286 (2012).
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(30-60) C and (10 to 20) MPa,” J. Chem. Eng. Data 49, 1328–1332 (2004).
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Mech. 288, 75–102 (1995).
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of a diffusive interface between aqueous and gaseous CO 2,”Phys. Fluids 25, 074103 (2013).
15N. Tilton, D. Daniel, and A. Riaz, “The initial transient period of gravitationally unstable diffusive boundary layers
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media,” J. Fluid Mech. 727, 456–487 (2013).
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128.235.251.160 On: Sat, 20 Dec 2014 16:13:54 |
1.4875855.pdf | Revisiting single photon avalanche diode current-voltage modeling and transient
characteristics
M. Javitt , V. Savuskan, , T. Merhav , and Y. Nemirovsky,
Citation: Journal of Applied Physics 115, 204503 (2014); doi: 10.1063/1.4875855
View online: http://dx.doi.org/10.1063/1.4875855
View Table of Contents: http://aip.scitation.org/toc/jap/115/20
Published by the American Institute of PhysicsRevisiting single photon avalanche diode current-voltage modeling
and transient characteristics
M. Javitt,1V. Savuskan,1,a)T. Merhav,1and Y . Nemirovsky1,2,b)
1Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
2Kinneret College on the Sea of Galilee, Israel
(Received 24 January 2014; accepted 29 April 2014; published online 23 May 2014)
A model for the current-voltage and transient behavior of Single Photon Avalanche Diodes (SPADs)
based on device physics is presented. The results of the model are compared to actual measurementsand a reasonable fit is seen. Additionally, the model provides a useful tool for designing quenching
circuitry and determining optimal operation conditions of the SPAD.
VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4875855 ]
I. INTRODUCTION
Single Photon Avalanche Diodes (SPADs) have been
studied extensively over the last 40 years1due to the wide
range of their potential applications.2In the last decade, the
focus of research has shifted to CMOS SPAD sensors andimagers.
3–10In order to achieve the lucrative potential appli-
cations, several issues are still under investigation: optimal
design of quenching circuitry,11–14transient behavioral
modeling15–18as well as current-voltage characteristics
above breakdown based on rigorous physical approaches.19
An analytical, physical quench model would thus prove valu-
able towards the improvement of future SPAD devices and
imagers.
Similarly to Avalanche Photodiodes (APDs), SPADs are
PN junction devices fabricated with doping profiles that
emphasize reverse-bias avalanche breakdown over Zener
(tunneling) breakdown.20When these structures are reverse-
biased at sufficiently high voltage, a high electric field active
region develops with sufficient energy to allow electron-hole
pair generation through impact ionization, providing amplifi-cation of current injected into the junction. The current gain
rises sharply with the applied voltage until the breakdown
voltage where the gain becomes “infinite,” that is, limitedexclusively by resistance serial to the junction: any voltage
applied beyond this point will produce a current equal to the
difference between applied voltage and breakdown voltage(termed the “excess voltage”) divided by the serial resist-
ance. While APDs are designed to be biased near but below
the junction breakdown voltage so as to allow finite meangain, SPADs are biased sufficiently above this voltage where
the gain is “infinite.” In this way, a single electron-hole pair,
generated either thermally or optically, can trigger a macro-scopic current through the junction with a corresponding
macroscopic voltage drop across the resistance serial to the
junction. Since the source of the electron-hole pair is virtu-ally irrelevant with regards triggering of the device, keeping
minimal the non-photon generated rate of events, termed theDark Count Rate (DCR), is paramount in fabricating an
effective device.
21–23
While true breakdown voltage was defined in Ref. 19,
breakdown may be defined as the measured voltage wherethe avalanche process is self-sustaining. This distinguishes
the SPAD from the APD as APDs are operated below break-
down, while SPADs are operated above breakdown. Asmobile charge carrier generation in the junction occurs
through impact ionization, from a steady state perspective,
the current in the device can potentially exist in two pseudo-stable states: breakdown, with large current providing the
mobile charge carriers to maintain said current; and zero
current with zero charge carriers to generate current. As aresult, if through some induced or statistical fluctuation all
the charge carriers exit the active region at a given moment
while in the breakdown state, then the current through thejunction will cease (termed “quench”) and the device will
transition back into the zero current state.
SPADs are ultimately transient-governed devices in that
photon sensitivity is achieved through detecting the abrupt
transition between zero current and breakdown states
brought on by the optically generated electron-hole pair thattriggered breakdown. As a result, the temporal stability of
each state, that is, likelihood of the state to persist over time,
is of the highest importance. The stability of the zero currentstate is relatively straightforward to consider and is simply a
function of the rate of events, photo- or thermally generated.
The stability of the high current state is less clear, and it ishere that an accurate and well founded model can provide
particularly valuable insight. It is clear that for a device to be
effective this high-current state must be relatively unstable,as while in this state the device will be unable to detect addi-
tional incident photons. Thus, the amount of time that the
device is in this state with the addition of the transition timeback to the zero current state is collectively termed the
“deadtime.” The model presented in this study refers to
breakdown which ends due to statistical fluctuations but intheory could continue indefinitely. “Stability” refers to the
propensity for this state NOT to end.
In order to increase breakdown state instability, negative
feedback must be incorporated in the device design. This can
be done either actively
24or passively.25In active quenching,a)Author to whom correspondence should be addressed. Electronic mail:
savuskan@tx.technion.ac.il.
b)Fellow, IEEE.
0021-8979/2014/115(20)/204503/9/$30.00 VC2014 AIP Publishing LLC 115, 204503-1JOURNAL OF APPLIED PHYSICS 115, 204503 (2014)
control circuitry detects the transition of the device into
breakdown and acts to directly decrease biasing below the
breakdown voltage. After quench, the junction bias isrestored to the above breakdown voltage rapidly, shortening
the deadtime. In passive quenching, a simple resistance serial
to the junction converts the current flow into a voltage reduc-tion across the PN junction effectively acting as negative
feedback during breakdown, which increases that state’s
instability. With this method, there is no need to implementcontrol circuitry on-pixel, saving valuable space. The price
of this, however, is in the requirement to calibrate the single
resistance value to be simultaneously high enough to quenchthe device effectively while at the same time low enough to
allow for quick junction recharge times, as will be shown
later. Modeling the relationship between load resistance andquench time could provide valuable tools for design and for
optimizing the operation of SPADs.
This study presents a physically rigorous modeling of
SPADs focusing on breakdown state stability. The previous
attempt to model the breakdown state directly
15,16yielded a
non-exponential quench time distribution and predicted aninfinite mean quench time, both in contrast to typically
reported results. A further attempt to predicate quench on
dynamic negative feedback to the quench resistance pre-dicted an oscillatory behavior of the breakdown current.
While such behavior has been observed in some devices and
at some biasing conditions, it has not been shown to be aconstant fixture of all devices and biasing conditions and
thus focusing on the breakdown state directly still holds
promise. The model presented in this paper is based primar-ily on a physical model taking into account the dynamic
nature of the charge carriers’ multiplication within the active
region. It aims to explain the nature of the SPAD DC I-Vcurve and provides a potential tool to optimize the transient
performance of the device. The model of this study presents
the probability per unit of time for the avalanche process tocease. One of the model inputs is the value of the quenching
resistance. Accordingly, the practical implementation of the
proposed model is to allow circuit designers to correctlyselect the optimal passive quencher resistance for minimiz-
ing the overall “deadtime” value.
II. MODEL DERIVATION AND ANALYSIS
The approach of the current model is to first compute
the spatial steady-state mobile charge carrier distributionduring breakdown and only then consider the temporal fluc-
tuations of this distribution. The ultimate goal is to find a
probability for the given breakdown state to quench per unittime. With this result, the temporal stability of the break-
down state and thus the temporal behavior of the device can
be evaluated. To that end, the following assumptions weremade:
1. Classical model for impact ionization—the charge carrier
concentration distributions are computed based on the
local field model presented by McIntyre in 1966.
26In this
model, the probability for impact ionization at a givenpoint is a function only of the mobile charge carrier type
(electron or hole) and the electric field at that location.This model is both analytically simple and well-
established, and allows relationships between device
parameters and breakdown state stability to be clearly
understood.
2. Independent charge carriers—it is assumed that the
mobile charge carriers do not affect one another. As a
result, the effect of the mobile charge on the electric fieldin the junction is neglected. Additionally, the probability
for each mobile charge carrier to ionize (produce a new
electron-hole pair) is considered independent of all othermobile charge carriers.
3. Self-sustaining avalanche during breakdown—the junc-
tion is biased at breakdown, the voltage at which the mul-tiplication gain of the device is “infinite” with all excess
voltage falling across the serial resistance. Since there is
infinite multiplication, the influx of mobile charge carriersinto the junction must be zero otherwise the total current
would not be finite. Instead, mobile charge carriers are
generated within the junction through impact ionizationand exclusively exit the junction. As a result and since
electrons and holes travel in opposite directions under the
influence of an electric field, at one end of the device thecurrent will consist only of electrons exiting the junction,
while at the other end the current will be comprised only
of holes exiting the junction. From a mathematical per-spective, this means that the hole current density at x ¼0
will be zero (J
p(0)¼0), while at the other end of the
device, x ¼L, the current density of electrons will be zero
(Jn(L)¼0). This does not contradict that the value of the
current is dictated externally by the choice of excess volt-
age and serial resistance; rather, this assumption providesborder conditions that together with the overall current
value dictate the mobile charge carrier distribution.
4. Constant field—for the simplicity of the derivation, it is
assumed that the field is constant in the active region,
assuming the value of the high field PN interface where
the impact ionization occurs.
5. Pure drift current—due to the extremely high electric field
in the active region, it is assumed that any diffusion cur-
rent is negligible.
6. Equal drift velocity—due to the extremely high electric
field in the active region, it is assumed that each carrier
travels at its saturation velocity (v
sat) and that these veloc-
ities are approximately equal.
The parameters used in the model are: the current
through the PN junction ( I), the electron charge ( q), the time-
of-flight of an injected charge carrier from one end of the
junction to the other ( TOF), the ionization probability ratio
between electrons and holes ( k), and a unit-less model fitting
parameter used to fit the data to measurements.
A. Spatial behavior
Based on the assumptions listed above (specifically,
pure drift current at saturation velocity), for electron density
n(x) and hole density p(x), the current density for each car-
rier in the multiplication region is given by
JnxðÞ¼qn xðÞvsatJpxðÞ¼qp xðÞvsat: (1)204503-2 Javitt et al. J. Appl. Phys. 115, 204503 (2014)The current must be constant in the entire junction under
steady state conditions, so
J¼JnxðÞþJpxðÞ¼qvsatnxðÞþpxðÞ ðÞ ;
nxðÞþpxðÞ¼J
qvsat¼N¼const : (2)
The ionization generation coefficients (a,b) of units
1/length are functions of the electric field. However, under
the assumption listed above of a constant field, these coeffi-cients will be constant as well. Generation from impact
ionization,
GxðÞ¼1
qa/C1JnxðÞþb/C1JpxðÞ/C0/C1¼avsatnxðÞþbvsatpxðÞ:(3)
We can insert this result into the steady-state continuity
equation to determine the mobile carrier distributions n(x)and p(x) from the set of differential equations
dJnxðÞ
dx¼/C0qG xðÞ!dn
dx¼/C0GxðÞ
vsat¼/C0a/C1nxðÞ/C0b/C1pxðÞ;
dJpxðÞ
dx¼qG xðÞ!dp
dx¼GxðÞ
vsat¼a/C1nxðÞþb/C1pxðÞ:(4)
Using the constant nature of the total charge carriers
shown above, these equations can be rewritten as regular dif-
ferential equations
dn
dx¼b/C0aðÞ nxðÞ/C0bN;
dp
dx¼b/C0aðÞ pxðÞþaN:(5)
With solutions
nxðÞ¼b
b/C0aNþn0exp b /C0aðÞ x ðÞ ;
pxðÞ¼/C0a
b/C0aNþp0exp b /C0aðÞ x ðÞ :(6)
Since the device is in breakdown, there is zero influx
current so JP(0) ¼Jn(L)¼0. From Eq. (1), this means that
p(0)¼n(L)¼0, where L is the junction length referring to
the width of the high field region where multiplication
occurs. Using these boundary conditions yields the final
distributions
nxðÞ¼b
b/C0aN1/C0exp b /C0aðÞ x/C0LðÞ/C0/C1/C0/C1
;
pxðÞ¼/C0a
b/C0aN1/C0exp b /C0aðÞ x ðÞ/C0/C1
:(7)
As previously mentioned, the density of total charge car-
riers at any point must be constant.
N¼nxðÞþpxðÞ¼NþN/C1ða/C0b exp a /C0bðÞ L ðÞ Þ
b/C0a
/C2expððb/C0aÞxÞ;
[exp a /C0bðÞ L ðÞ ¼a
b: (8)For convenience, we can define a parameter k,
k¼b
a!k¼exp k /C01ðÞ aL ðÞ : (9)
This is the same breakdown condition achieved by
McIntyre26where the breakdown voltage is the voltage
where a, which increases with the electric field and thusthe applied voltage, is large enough for this condition to
occur.
B. Temporal behavior
With the steady-state spatial distribution curves previ-
ously found, one can investigate the nature of the distribution
as it develops over time. After a time twhere no impact ioni-
zation has occurred, the distribution curve will have shifted
by distance vsattsince all carriers are travelling at the identi-
cal velocity vsat. The probability for a hole to not ionize over
time dtfrom that point will be the product of the probabil-
ities for each hole still present in the high field region to not
ionize
Phtþdtjt ðÞ ¼Y
xexp/C0bvsatdt ðÞAp xðÞdx
¼exp/C0Abv satdtðL/C0vsatt
0pxðÞdx0
B@1
CA: (10)
The exponent is the probability that there will be no ion-
ization over time dtper hole, while the term Ap(x)dxis the
number of holes located between point xandxþdx(Ais the
cross sectional area of the junction).
Computing the integral
ðL/C0vsatt
0pxðÞdx¼N
1/C0kL/C0vsatt/C01
k/C01ðÞ a/C20
/C2ðexp k/C01ðÞ aL/C0vsatt ðÞ/C0/C1
/C01Þ/C21
:(11)
This result can be simplified using Eq. (9) and
TOF¼L=vsat,
ðL/C0vsatt
0pxðÞdx¼N
1/C0kL1/C0t
TOF/C01
lnkðÞ/C20
/C2exp ln kðÞ 1/C0t
TOF/C18/C19/C18/C19
/C01/C18/C19 /C21
:(12)
The result
Phtþdtjt ðÞ ¼exp/C0Akav satdtN
1/C0kL1/C0t
TOFþ1
lnkðÞ/C20 /C18
/C21/C0exp ln kðÞ 1/C0t
TOF/C18/C19/C18/C19/C18/C19 /C21/C19
: (13)
Simplifying once again and noting that ANv sat¼I=q,204503-3 Javitt et al. J. Appl. Phys. 115, 204503 (2014)Phtþdtjt ðÞ ¼expI
qklnkðÞ
1/C0kðÞ21/C0t
TOFþ1
lnkðÞ/C20
/C21/C0exp ln kðÞ 1/C0t
TOF/C18/C19/C18/C19/C18/C19 /C21
dt/C19
:(14)
This is the probability for no hole-induced ionization to
occur over time dtgiven that no ionization has occurred for
time t. For electrons, the result is fundamentally the same
and can be achieved simply via the conversion k!1=k,
Petþdtjt ðÞ ¼exp/C0I
qklnkðÞ
1/C0kðÞ21/C0t
TOF/C01
lnkðÞ/C20
/C21/C0exp/C0lnkðÞ 1/C0t
TOF/C18/C19/C18/C19/C18/C19 /C21
dt/C19
:(15)The total probability for there to not be an ionization event
over time dtis the product of that for electrons and holes,
PTOTtþdtjt ðÞ
¼Petþdtjt ðÞ /C1Phtþdtjt ðÞ
¼expI
q2k
1/C0kðÞ21/C0cosh ln kðÞ 1/C0t
TOF/C18/C19/C18/C19/C20/C21
dt !
:
(16)
With this result, one can compute the probability for no
ionization to occur from some time to some later time. Of par-
ticular interest is the prob ability for a total of time T OFto elapse
assuming a starting point of a given time T. This is because after
time T OFhas elapsed all mobile charge carriers will have exited
the junction and as a result the device will have quenched:
PTOTTOFjTðÞ ¼ expI
q2k
1/C0kðÞ2ðTOF
T1/C0cosh ln kðÞ 1/C0t
TOF/C18/C19/C18/C19/C20/C21
dt0
B@1
CA
¼expI
q2k
1/C0kðÞ2TOF/C0T/C0TOF
lnkðÞsinh ln kðÞ 1/C0T
TOF/C18/C19/C18/C19 /C20/C21 !
: (17)
While this result is significant, it does not on its own
provide the deadtime of the device. The source of current inthe SPAD is generation through impact ionization in the ava-
lanche region. As such, the average time T
AVbetween gener-
ation events during breakdown will be equal to the charge ofthe electron divided by the current,
T
AV¼q
I: (18)
If the time between any two consecutive generation
events during breakdown reaches T OF, then all carriers will
have exited the region leaving none to produce any further
electron-hole pairs. As a result, the current will quench.Since on the average the time between these events will be
T
AV, the probability to quench will be the probability for the
charge carriers to make it to time T OFfor a given T AV
(PQ¼PT(TOF|TAV)). As a consequence of this, for I <q/T OF,
the current is by definition unstable (probability to
quench ¼1). In general,
PQ¼PTOTTOFjTAV ðÞ
¼exp2k
1/C0kðÞ2TOF
TAV/C01/C0TOF
TAVsinh ln kðÞ1/C0TAV
TOF/C18/C19/C18/C19
lnkðÞ2
643
750
B@1
CA:
(19)
For convenience, one can define
y¼1/C0TAV
TOF¼1/C0q
I/C1TOF: (20)Substituting
PQ¼exp2k
1/C0kðÞ2y
1/C0y1/C0sinh ln kðÞy/C0/C1
lnkðÞy"# !
: (21)
This is the probability to quench. To account for the
simplistic nature of the model and to fit results to data, a
model parameter gcan be incorporated to scale the argument
of the exponent,
PQ¼exp g2k
1/C0kðÞ2y
1/C0y1/C0sinh ln kðÞy/C0/C1
lnkðÞy"# !
;
y¼1/C0q
I/C1TOF: (22)
This is the desired equation: the probability for the cur-
rent to quench as a function of the various device parameters.The nature of the fitting parameter gis now evident: it
accommodates the simplified model assumptions (see also
Sec.IV).
As can be seen from the above expression, there are
three significant physical parameters that dictate quench
probability: the ionization coefficient ratio k, the charge car-
rier time-of-flight T
OF, and the breakdown current I(via its
effect on y). The model parameter gis needed to accommo-
date the simplified model assumptions and its effect is ratherapparent: the smaller this value is, the closer the argument of
the exponential term is to zero and thus the closer that P
Q
will be to 1. Therefore, decreasing this parameter increases
the probability to quench. As will be seen later, a similar204503-4 Javitt et al. J. Appl. Phys. 115, 204503 (2014)result can be achieved by replacing the other parameters
by effective values as they too influence the breakdown
probability.
The contribution of the ionization coefficient ratio is
less obvious. For both extremes of k,
lnPQk!0 ðÞ /2k
1/C0kðÞ2y
1/C0y1þ1
2kyylnkðÞ/C20/C21
!0;[PQk!0¼1;
lnPQk!1ðÞ /2k
1/C0kðÞ2y
1/C0y1/C0ky
2ylnkðÞ/C20/C21
!0;[PQk!1¼1:
(23)
This result is not altogether unexpected: for avalanche
breakdown to be self-sustaining, both carriers must partici-
pate. Specifically, positive feedback is provided throughoppositely charged carriers traveling in opposite directions.
If one of those carriers does not participate in the process
(k!0 for electrons and k!1 for holes) then the ava-
lanche breakdown cannot occur. Nonetheless, this result runs
contrary to the model derived in Ref. 15. Based on the model
presented here, the probability to quench will be lowest atk¼1 and will symmetrically rise around this minimum for
the conversion k!k
/C01shown graphically in Figure 1.
From a design and materials perspective, this would
imply that the avalanche pulse at breakdown will be less sta-
ble for greater ionization coefficient disparity. Since pulse
stability can be a limiting element in operation frequency, infuture applications intended for higher frame rates it may
prove necessary to transition to either more imbalanced
materials or more complex doping profiles that dispropor-tionately enhances the ionization rate of one carrier.
As stated above, an additional element in determining
pulse stability is the T
OFterm. As the carriers clear the junc-
tion faster (lower T OF), probability to quench also increases,
shown graphically in Figure 2. This can be accomplished ei-
ther by reducing junction dimensions or by increasing carriervelocity. Both approaches, however, are limited. Overly
reducing junction dimensions increases the field at break-
down, which at some point will result in band-to-bandtunneling carrier generation (Zener breakdown) causing
prohibitively high DCR. Carrier velocity alternatively is pri-
marily limited by material parameters and generally cannotrise above a material-defined saturation value.
The final significant parameter influencing quench prob-
ability is the breakdown current:
Figure 3shows the relationship between quench proba-
bility and breakdown current and it can be seen that the prob-
ability transitions relatively abruptly between high and lowvalues as a result of the current. As opposed to the other
parameters, the operational breakdown current can be con-
trolled external to the device and is not determined solely byfabrication (both kand T
OFare determined by junction
parameters and material constants). This can be utilized for
active quenching, where the effective serial resistance can betransitioned from a low value pre-breakdown to a high value
post-breakdown. This allows for both abrupt device recharg-
ing (low resistance) and abrupt device quenching (highresistance–low breakdown current). However, active
quenching requires additional circuitry in each pixel,
decreasing fill factor and increasing complexity.
FIG. 1. Model derived quench probability (P Q) by ionization coefficient ra-
tiok. Parameters: I ¼1lA, T OF¼1 ps, and g¼1.
FIG. 2. Model derived quench probability (P Q) by time-of-flight. Parameters:
I¼1lA, k¼0.3, and g¼1.
FIG. 3. Model derived quench probability (P Q) by breakdown current.
Parameters: k ¼0.3, T OF¼1 ps, and g¼1.204503-5 Javitt et al. J. Appl. Phys. 115, 204503 (2014)III. MODEL APPLICATIONS
The model, and specifically the model derived quench
probability P Q, allows for modeling and predictions with
regards to the transient and DC behavior of the device. Inorder to verify the success of the model, predicted results
were compared to measurements performed on SPADs fabri-
cated in a commercial 180 nm CMOS Image Sensors pro-cess.
27,28To show the versatility of the model, SPADs were
selected from opposite ends of the performance spectrum:
one with a breakdown voltage of /C2411 V with very high DCR
(a “poor” SPAD), and the other with a breakdown voltage of
/C2420 V showing very low DCR (a “good” SPAD).
To be useful, the quench probability must be converted
into units of time. This can be done by envisaging the propa-
gation of the breakdown pulse as a geometric series of gener-ation events, where one event not occurring causes quench.
Based on this, the probability for a “failure” to quench is
1/C0P
Qand the probability for the breakdown pulse to sur-
vive exactly nsuch events is P Q(1/C0PQ)n.
The “event” in this case is impact ionization induced
charge carrier generation, such that the average time betweenevents, T
AV, would be the inverse of the generation rate as
stated above in the derivation section. The time associated
with surviving nevents can thus be approximated as nTAV.
Under this approximation, the probability for a breakdown
pulse to quench at time twould be
PtðÞ¼PQ1/C0PQ ðÞt
TAV: (24)
The model, therefore, predicts that quench-time will fol-
low an exponential distribution (Fig. 4). This distribution,
however, accounts only for the pseudo-steady state lifetime
of the pulse and does not include even more transient aspectslike junction discharge and recharge times during which the
current can be significantly higher and thus more stable.
19
As such, the measured distribution will be shifted by a con-
stant time to account for these additions.
Based on this distribution, another curve can be pre-
dicted: the DC current of the SPAD. The DC current of theSPAD will be the average current over time since the actual
current is transient by nature (breakdown pulses and quench-
ing). This can be found by considering the total amount ofcharge that flows through the device per cycle (breakdown
of the device, quench, and recharge).The average breakdown
pulse lifetime can be extracted from the distribution (or byenvisaging a series of Bernoulli experiments) and is easily
shown to be T
AV/PQ. As a result, the mean amount of
pseudo-steady state charge collected per pulse is
Qss¼I/C1TAV
PQ: (25)
PQis a function of a number of variables; however, the
only one that is influenced by choice of bias is the current I.
From here on, therefore, P Qwill be replaced with P Q(I) to
reinforce its dependence on biasing conditions.
Prior to breakdown, the capacitance of the junction is
charged to the excess voltage (V e) above breakdown,
whereas during breakdown it is discharged to the breakdownvoltage. Additionally, any capacitance parallel to the load
resistance will charge to the excess voltage during break-
down as this is the voltage that falls across the load resist-
ance. Post quench, these capacitances will charge anddischarge back to their original values. As a result, added to
the steady state charge collected will be the capacitance
induced charges, proportional to the excess voltage:
Q
c¼C/C1Ve: (26)
The average current will be these two accumulated
charges times the event frequency known as DCR. Asserting
I¼Ve/R and adding an offset current due to device
leakage, etc.,
IDC¼IOSþmin DCR/C1CVeþVe
RTAV
PQVe
R/C18/C190
B@1
CA;Ve
R0
B@1
CA:(27)
Theminfunction was added to account for the fact that
the measured current can only approach V e/R and not exceed
it even when the lifetime exceeds the mean time between
breakdown events.
In Figure 5, the model was fit to measurements per-
formed on actual SPADs, one with a breakdown voltage
(BV) of /C2411 V with corresponding high DCR, while the
other with a breakdown voltage of /C2420 V with correspond-
ing low DCR. More information with regards these SPADs
can be found in Ref. 27. For the low BV device, the measure-
ment was performed with a serial resistor of 5 k X, while no
additional resistor was added for the high BV device. The
curves were produced with the following shared parameters:
FIG. 4. Measured quench time histogram. On the low breakdown voltage
SPAD the measurement was performed at 1 V excess voltage with a 15 k X
serial resistor, while on the high breakdown voltage SPAD the measurement
was performed at 1.3 V of excess voltage with a 29 k Xresistor. Shown as
well is the fit to an exponential distribution and the r-square coefficient. By
the result, it can be seen that excellent fit is found. The timescale shown
(microseconds) is much larger than what is expected for typical integrateddevices (nanoseconds). This is due to the use of external rather than inte-
grated resistors responsible for bringing the capacitive load to the /C24100 pF
range rather than the typical /C24100 fF for integrated devices. Additionally,
resistance values were selected to produce meta-stability and thus a discerni-
ble quenchtime distribution, whereas in actual devices resistance values are
selected specifically to minimize the meta-stability of the breakdown state.204503-6 Javitt et al. J. Appl. Phys. 115, 204503 (2014)C¼100 pF, k ¼0.05, and T OF¼1 ps. The capacitance was
selected to correspond to the capacitive load provided by thesetup used to attain the measurements caused in part by the
use of an external resistor. Integrated pixels are expected to
have a capacitance on the order of 100 fF. For the low BVSPAD, I
OS¼0.3 nA and g¼0.121, while for the high BV
SPAD, I OS¼0.06 nA and g¼0.157. The offset current, ca-
pacitance, and model parameter were chosen empirically,
while the ionization ratio coefficient and time-of-flight were
set based on the device material (Si) and junction dimen-sions. For both devices, the serial resistance was extracted
from the linear portion of the measurement curve and was
found to be R /C255.7 kXfor the low BV device (correspond-
ing to the 5 k Xserial resistor with the addition of an internal
/C24700Xresistance) and R /C252.7 kXfor the high BV device.
Additionally, for the low BV device the DCR was assumedto be of the form DCR V
eðÞ¼aðexpbVeðÞ /C01Þwith values
ofa¼60 Hz and b¼11.1 V/C01. The exponential nature of
the DCR was determined due to the low breakdown voltageof the device and thus the propensity for band-to-band tun-
neling, which produces an exponential current dependence
on voltage. For the high BV device, the DCR was assumedto be of the form DCR V
eðÞ¼aVewith a value of
a¼50 Hz V/C01. The linear nature of the DCR was determined
due to the higher breakdown voltage of the device whereband-to-band tunneling is unlikely to occur, and based on
results reported in Ref. 27.
While modeling the DC curve does have significance,
modeling of transient behavior is more useful, as the appli-
cation is ultimately transient. For this, the model proves
useful as well, especially when it comes to passivequenching designs. Assuming a constant resistance, the
model can be applied to find the optimal load resistance
for overall device performance. The total pulse time iscomprised of the steady-state time, dictated by operating
point pseudo-stability, and the junction recharge time dic-
tated by the serial resistance and the junction capacitance.The maximum time it will take for ppercent of pulses to
quench will beT
p:XTp
TAV
n¼0PQ1/C0PQ ðÞn¼p!Tp¼TAVln 1/C0pðÞ
ln 1/C0PQ ðÞ/C01 !
:
(28)
At low resistances, the probability to quench will be
much lower than 1 and so ln 1 /C0PQ ðÞ /C25/C0PQ. Since P Qis
approximately exponentially dependent on R, for low resis-
tances a near-exponential dependence is expected. Figure 6
provides an example of the overall recovery time (deadtime)of a SPAD using the same values as the DC simulation for
the low BV SPAD, with the exception of the capacitance
taken to be 100 fF to correspond to typical capacitances of
integrated CMOS SPAD pixels. The junction recharge time
constant was taken to be 3RC, and the curve was generatedfor 1 V excess voltage.
From the recovery time simulation (Figure 6), it can be
seen that there is a clear optimal resistance. It is also appa-rent that due to the exponential nature of quench time but
only the linear nature of junction recharge time, there is
asymmetry around this minimum: reducing the resistanceonly slightly yields a significant increase in the duration of
the pulse, while increasing the resistance has a much weaker
influence. This is in agreement with empirical results, mostnotably in Ref. 19.
To fit the model presented here to experimental data, a
fitting parameter, g, was necessary though this could also
have been accomplished via the use of effective value k
effor
TOF,eff . This is likely due to the inexact nature of the break-
down model, which is based on simplifying assumptionssuch as uniform field, equal saturation velocities for elec-
trons and holes, etc. These assumptions are obviously not
met in the CMOS SPAD, where retrograde wells are appliedand the nature of the SPAD junction is very narrow but
neither abrupt nor fully graded. Furthermore, the model
FIG. 5. Model derived DC I-V relationship and measured data points for a
low breakdown voltage SPAD and a high BV SPAD.
FIG. 6. Predicted recovery time by serial resistance at 1 V excess voltage.The two curves represent the average result and the maximum time that
accounts for 99.9% of predicted results. Below /C2425 kXthe time is domi-
nated by the pulse lifetime and is strongly dependent on the serial resistance.
Above this resistance, the pulse lifetime is insignificant relative to the
recharge time of the junction capacitance and the curve rises linearly
(/RC).204503-7 Javitt et al. J. Appl. Phys. 115, 204503 (2014)disregards charge carrier history, an assumption not fully
valid at small junction dimensions which all SPADs have.
Charge carrier history has been found to change impact ioni-zation probabilities and thus charge carrier distribution. This
has resulted in newer models for breakdown that have
attempted to account for this effect.
29–32It is possible that
deriving a more accurate spatial distribution based on these
methods will decrease the need for a fitting parameter. At the
same time, given that the fitting parameter can be extractedfrom steady state data and applied to transient performance
analysis it is not overly burdensome to the application of the
model.
IV. SUMMARY
A model explaining SPAD transient behavior has been
presented. It is based on a well-established physical and
mathematical approach to avalanche breakdown, allowing
for a simple and easily applied model. The model providesvaluable insight into the physical operation of SPADs and
has achieved a good fit to empirical data. Elucidating the
parameters that significantly affect device performance ( k,
T
OFand bias point) allows for higher performing devices to
be fabricated in the future and allows for devices to be oper-
ated optimally. For example, the model can be used to pre-
dict the optimal serial resistance and calculate the optimal
deadtime. This can be used to determine if active quenchingis required with its necessitating complexity or if high
enough resolution can be achieved via much simpler passive
quenching.
The model also predicts that what primarily determines
the deadtime of the device is the current during breakdown.
Based on the model and especially the sharp relationshipbetween deadtime and current, the current at apparent break-
down of the DC curve can be used to approximate a suffi-
cient resistor. As a rule of thumb, a resistor that brings thecurrent to 1/2 to 1/3 of the current at apparent breakdown
will produce a sufficiently short deadtime. This principle
could also lead to new designs that limit the current moreeffectively than a serial resistor (which is excess voltage
dependent) without the complexity of active quenching, such
as realizing a constant current limiter in pixel.
The model was successfully applied and fit to measure-
ments performed on two different CMOS SPADs fabricated
in a standard nanometer technology but with different break-down voltage levels (and thus very different DCR). The
model reproduced the DC curve measured for both devices
and correctly predicted the deadtime probability distributionfunction. In addition to elucidating the nature of the curve
between the true breakdown voltage and the apparent break-
down voltage (defined in Ref. 19), successfully modeling the
DC curve is an important achievement because finding the
correct parameters ultimately allows for the deadtime vs se-
rial resistance curve to be generated. This allows for the opti-mal load resistance to be found. Optimizing the SPAD as
well as knowing the optimal result itself (or for example
knowing the worst case deadtime for 99.9% of detections)allows one to determine if active quenching, with its more
complex fabrication and space requirements, is necessary.Additionally, optimizing passive quenching allows for appli-
cations where active quenching is not feasible to nonetheless
be achievable. It should be noted of course that the optimalload resistance only relates to the process of quenching and
recharging of the device. In practice, other parameters may
also contribute to the choice of optimal resistance, such asafterpulsing tendency. While the model was only compared
to CMOS SPADs, it is generalizable to all technologies and
materials providing that the proper constants are selected.Likely each structure will produce a different fitting parame-
ter indicating its variance from the simplified assumptions
that formed the basis of the model. Nonetheless, the underly-ing structure will likely remain the same with only modifica-
tions to the relevant parameters being necessary.
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1.4895661.pdf | Silicon fiber with p-n junction
D. Homa, A. Cito, G. Pickrell, C. Hill, and B. Scott
Citation: Applied Physics Letters 105, 122110 (2014); doi: 10.1063/1.4895661
View online: http://dx.doi.org/10.1063/1.4895661
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/12?ver=pdfcov
Published by the AIP Publishing
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On: Thu, 11 Dec 2014 10:17:49Silicon fiber with p-n junction
D. Homa, A. Cito, G. Pickrell, C. Hill, and B. Scott
Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University,
312 Holden Hall, Blacksburg, Virginia 24060, USA
(Received 11 July 2014; accepted 27 August 2014; published online 24 September 2014)
In this study, we fabricated a p-n junction in a fiber with a phosphorous doped silicon core and
fused silica cladding. The fibers were fabricated via a hybrid process of the core-suction and melt-
draw techniques and maintained overall diameters ranging from 200 to 900 lm and core diameters
of 20–800 lm. The p-n junction was formed by doping the fiber with boron and confirmed via the
current-voltage characteristic. The demonstration of a p-n junction in a melt-drawn silicon core
fiber paves the way for the seamless integration of optical and electronic devices in fibers. VC2014
AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4895661 ]
The p-n junction is one of the fundamental building
blocks of the electronic technologies that are ingrained into ev-
ery fabric of modern society. In turn, the element that makes
up the majority of these electronic devices is silicon, often inthe form of wafers for current microelectronics. On a length
scale of millimeters to centimeters, the rigid wafers were more
than sufficient for the innovations and products of the 20th andearly 21st centuries. It is these electronic devices that are now
becoming a prerequisite for a functioning society and must
evolve into the new functions that will inevitably be required.
As discussed by He et al ., the extension of electronic
functions to longer and more flexible forms has become
almost inevitable in applications such as power generation,sensing, imaging, telecommunications, and medical devi-
ces.
1–5The integration of electronics and fiber optics has
been proposed as the catalyst to meet these demands forexpanded functionality. The fibers can increase electronic
function from meters to kilometers and can be exploited in
3D arrays to dramatically improve the performance of cur-rent electronics as well as those yet to be explored.
1,5,6
The potential of electronic fibers has prompted a number
of researchers to begin fabricating these types of fibers andbuilding the devices to demonstrate basic feasibilities.
5–7
The two fiber synthesis routes that have garnered the most
attention have been fiber drawing and high pressure chemicalvapor deposition (HPCVD).
8–10Briefly, in HPCVD, a chem-
ical precursor is injected into nanoscale or microscale pore(s)
in an optical fiber or capillary tube and heated to induce dep-osition of the desired materials. Conversely, in the fiber draw
process, the selected material such as a semiconductor is
inserted into a glass tube and simply drawn into a fiber viatraditional fiber optic equipment processes and equipment.
Although both approaches have their advantages and disad-
vantages as described extensively in the noted references,high temperature drawing is well suited for the fabrication of
very long lengths of fiber (kilometers vs. meters) and can be
readily adapted to currently available and proven opticalfiber manufacturing technologies.
1–10These proven techni-
ques and associated expertise can be leveraged to fiberize
semiconductor materials such as silicon in a fashion that isboth scale-able and cost effective.
In this letter, we demonstrate a p-n junction in a drawn
silicon fiber, as seen in Figure 1. The phosphorous dopedsilicon core fiber was doped with boron via a solution doping
technique and confirmed by the current-voltage characteristic.
The phosphorous doped silicon core fibers were pre-
pared on a traditional glass working lathe, as seen in Figure2. Simply, a core-suction technique was used to fabricate the
doped silicon core preform that was then drawn into a fiber
via a melt-draw technique. The synthesis route was an amal-gam of processes discussed in our previous publications.
12–16
First, a fused silica substrate tube (GE214, O.D. ¼8m m ,
I.D.¼3 mm) was fused to a processing tube (GE214,
O.D.¼12.75 mm, I.D. ¼10.5 mm). The phosphorous doped
silicon powder was then pushed into the processing tube with
a fused silica rod (O.D. ¼10 mm), but not into the substrate
tube. The doped powder was produced from Motorola N-
Type silicon wafers that were fractured and ground into pow-
der with an alumina mortar and pestle. The starting wafersmaintained a resistivity of 0.024–0.034 Xcm with a h100i
orientation. The processing tube was then collapsed onto the
rod to create a seal and a vacuum pump was connected to theinlet of the substrate tube. The doped silicon powder was then
melted via an oxygen-hydrogen torch and the vacuum pump
was turned on to “pull” the molten doped silicon into the sub-strate tube and allowed to solidify, as seen in Figure 2(a).T h e
process tube was then separated from the preform and another
FIG. 1. Performance of p-n junction in a silicon fiber. The p-n junction was
formed by doping a phosphorus doped silicon fiber (n-type) with boron on a
fiber endface via a solution doping technique.1Contacts on the ends of the
p-n junction were made with nickel conductive glue.
0003-6951/2014/105(12)/122110/3/$30.00 VC2014 AIP Publishing LLC 105, 122110-1APPLIED PHYSICS LETTERS 105, 122110 (2014)
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On: Thu, 11 Dec 2014 10:17:49fused silica rod (O.D. ¼12 mm) was joined to the doped sili-
con core preform. Finally, the preform was drawn into a fiber
via a technique similar to the Taylor process, as seen inFigure 2(b).
16–18
Fiber core diameters in the range of 50–600 lm and
overall diameters of 100–950 lm were routinely fabricated
on a glass working lathe. The maximum achievable fiber
lengths were limited to 120 cm by the working distance of
the lathe. Fiberization via the glass working lathe allows fora preliminary evaluation of material compatibility and feasi-
bility of synthesis. It is anticipated that the fundamental
processes can be translated to a more traditional draw towerstructure to manufacture fiber lengths on the order of
kilometers.
19,20
Polished fiber cross sections were characterized with a
scanning electron microscope (SEM, LEO 1550). The micro-
structure of a selected phosphorus doped silicon core fiber
cross section is shown in Figure 3(a). The fiber maintained a
fused silica cladding diameter of approximately 300 lm and
a phosphorous doped silicon core diameter of 40 lm. Energy
dispersive spectroscopy (EDS) was also performed to deter-mine chemical composition and elemental mapping with an
attached IXRF system, Inc., Iridium Microanalysis System at
an accelerating voltage of 20.0 kV. As shown by the EDSmapping images in Figure 3(b), the distinct core-cladding
profile of the preform was maintained upon fiberization, and
there was limited oxidation of the silicon core. Phosphorous(and boron) were not detected with the EDS because the con-
centration were below the detection limit. The phosphorous
and boron concentration were determined via secondary ionmass spectroscopy. The bulk phosphorus and boron concen-
trations of the p-n junction at the fiber end face 2.932 /C210
17
atoms/cm3and 4.708 /C21018atoms/cm3, respectively. We
plan to further investigate the effect of processing conditions
on the dopant profiles in an effort to further improve per-
formance, as well as to fabricate other types of devices suchas n-p-n transistors and p-i-n diodes.
A p-n junction was fabricated in a phosphorous doped
silicon fiber via boron incorporation by a boric acid solutiondoping technique.
11First, boric acid ( >99.9% Alfa Aesar)
was mixed with deionized water to produce solutions atselected concentrations. The fiber endface was immersed in a
10% HF aqueous solution for 3 minutes to remove the native
oxide layer on the silicon core . The exposed silicon core sur-
face was then treated in a 1:1:5 solution of NH
4OH:H 2O2:H2O
at 80/C14C for 10 minutes to make it hydrophilic. The boric acid
solution was then disposed on the endface of phosphorousdoped silicon fiber and heat treat ed in a quartz tube furnace.
Above temperatures of 130
/C14C, a mixture of boron oxide
hydrates was formed and then converted to anhydrous B 2O3as
the temperature exceeded 250/C14C. At 350/C14C, the concentration
of B 2O3was in excess of 90 wt. % of the mixture. Finally, the
B2O3reacted with the silicon core to form SiO 2and B, which
then diffused into the silicon at high temperatures ( >900/C14C).
The borosilicate glass layer that formed during this process
was removed by etching in 10% HF solution at ambient tem-perature for 3 min.
The current-voltage characteristic of the doped core fibers
was verified via the basic circuit shown in Figure 4.AH P
Hewlett Packard Agilent, 6633A System was utilized as the
direct current supply and ammeter. An Agilent, 34405A, 5 1/2
Digit Multi-meter was connected in parallel with the p-n junc-tion fiber. Electronic contacts were made by coating the fiber
end faces with nickel (MG Chemicals 841 Super Shield
Nickel Conductive Coating-Pen) and heat treating at 200
/C14C
for 30 min.
The current voltage characteristics of n-type (phospho-
rous) doped silicon fibers with and without a p-n junctionwere compared to validate the performance of the fiber p-n
junction, as shown in Figure 5(a). As expected, the doped
fiber with the p-n junction exhibited a reverse bias in contrast
FIG. 2. Fabrication process for silicon and phosphorous doped silicon core
fiber on glass working lathe. (a) First, the preform was formed via a core-
suction technique by melting doped or un-doped silicon granules and
“pulling” into the substrate tube. (b) The doped or un-doped silicon core pre-
form was then fiberized by a modified melt-draw technique on a glass work-
ing lathe.
FIG. 3. (a) SEM image of a phosphorus doped silicon (n-type) fiber with a
40lm core and overall diameter of 300 lm. X-ray dot mapping of (b) silicon
(red) and (c) oxygen (green).122110-2 Homa et al. Appl. Phys. Lett. 105, 122110 (2014)
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On: Thu, 11 Dec 2014 10:17:49to the linear relationship between current and voltage exhib-
ited by the doped silicon fiber. Furthermore, the performance
of the fiber p-n junction was compared to a p-n junction fab-ricated in the silicon wafer that provided the raw material for
the fiber core, as shown in Figure 5(b). The forward bias cur-
rent was higher in the p-n junction in the polycrystalline sili-con core than the single crystal silicon wafer. It is suspectedthat the grain boundaries acted as traps and recombination
centers that decreased lifetimes in the polycrystalline silicon
fiber p-n junction fiber.
21The efficiency of the fiber p-n junc-
tion can be improved by fabrication of fibers with singlecrystal silicon cores or polycrystalline silicon cores with
larger grain boundaries.
9
The demonstration of a p-n junction in a silicon core
fiber fabricated via high temperature fiber drawing processes
is the first step in the development of truly efficient and cost
effective fiber electronics. These results are only a prelude to
the development of devices with improved performance and
more complicated designs in other semiconductor corefibers. Furthermore, these results are very promising for the
potential realization of a truly scale-able approach to the fab-
rication of electronic devices in fiber and integration of thesedevices with other technologies.
The authors would like to acknowledge Adam Floyd
and Edward Liang for their assistance with our
experimentation.
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FIG. 4. Schematic of test setup to evaluate the voltage-current characteristic
of the fiber and wafer p-n junctions. Please note that the same setup was
used to test the n-type silicon core fiber.
FIG. 5. (a) Current-voltage characteristics of a phosphorous doped silicon
fiber with and without a p-n junction. (b) Current-voltage characteristics of a
phosphorous doped silicon fiber and wafer, each with a p-n junction. The p-
n forward and reverse bias is clearly demonstrated for p-n junctions in both
the wafer and silicon fiber. Conversely, the silicon fiber demonstrates a lin-
ear relationship between voltage and current.122110-3 Homa et al. Appl. Phys. Lett. 105, 122110 (2014)
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On: Thu, 11 Dec 2014 10:17:49 |
1.4896357.pdf | Hofstadter butterflies and quantized Hall conductance in quasi-one dimensional
organic conductors
Xiao-Shan Ye
Citation: Journal of Applied Physics 116, 123902 (2014); doi: 10.1063/1.4896357
View online: http://dx.doi.org/10.1063/1.4896357
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/12?ver=pdfcov
Published by the AIP Publishing
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131.181.251.130 On: Sun, 23 Nov 2014 17:11:53Hofstadter butterflies and quantized Hall conductance in quasi-one
dimensional organic conductors
Xiao-Shan Y e
College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China
(Received 30 July 2014; accepted 9 September 2014; published online 23 September 2014)
We explore the structure of the energy spectra of quasi-one dimensional organic conductors sub-
jected to the field-induced spin-density-wave (FISDW) state. We show that the structure of theenergy spectra can exhibit Hofstadter butterfly, which is generally believed to appear in two dimen-
sional systems. The phenomenon of the quantized Hall conductance due to FISDW is also investi-
gated. We find that the Hall number L, which is defined by L¼r
xy/(e2/h), coincides with the
number described by FISDW order parameter. The sign reversal of the quantized Hall conductance
is discussed theoretically. VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4896357 ]
I. INTRODUCTION
Over the past decades, much attention has been
focused on the electronic properties under a uniform mag-
netic field. One of the interesting properties is the energyspectrum. The exquisite structure of the energy diagram of
a tight-binding electron system on a two-dimensional
square lattice subjected to a uniform perpendicular mag-netic field was first elucidated by Hofstadter. It exhibits
multifractal properties and the band spectrum for rational
values of magnetic flux looks just like a butterfly.
1For in-
depth understanding of such an intricate spectral structure,
the Hofstadter butterfly spectrum has been calculated for a
variety of lattices, such as triangular,2honeycomb,3and
kagom /C19e lattices.4Some new approaches such as non-
commutative geometry,5pseudo-differential operators,6
functional analysis,7and renormalization group approach8,9
are also developed to further theoretical investigations of
Hofstadter’s problem. Recently, some physicists considerdifferent magnetic fields to investigate the Hofstadter but-
terfly (such as fields that are spatially sine or cosine modu-
lated,
10–12staggered-modulated, and strip modulated13–15).
But observation of the butterfly spectra in real systems is
still very difficult. For the experimental realization of the
butterfly with ordinary lattice spacing, magnetic field ofabout 1000 Tis required. Recently, there are some sugges-
tions to observe the butterfly spectra using the recent
advances in artificial periodic structures techniques such aslateral superlattices produced with high-quality shallow het-
erostructures, superconducting wire networks,
16and optical
lattices with confined cold atoms.17,18
So far, most of these schemes are concentrated on two-
dimensional systems under a perpendicular magnetic field.
We would address a question: Can the Hofstadter butterflybe produced in quasi-one dimensional system with special
modulated order parameter? In this paper, we will respond
to this question by analyzing the energy spectrum of aquasi-one dimensional lattice subjected to FISDW. We will
show that the modulated FISDW order parameters can
make the energy spectrum show Hofstadter butterfly. Weemphasize that this Hofstadter butterfly energy spectrum is
caused by the FISDW potential. It is not like the casecaused directly by the magnetic field in two-dimensional
lattice system. We also find that the FISDW state makes
the system show quantum Hall effect (QHE). The mecha-nism of the QHE is different from the ordinal QHE in two-
dimensional system subjected to a perpendicular magnetic
field. Our research is based on the quasi-one dimensionalorganic compounds.
II. HOFSTADTER BUTTERFLY ENERGY SPECTRUM
Organic metals of the ( TMTSF )2Xfamily, where TMTSF
is an abbreviation for tetramethyltetraselenafulvalene andX
represents an inorganic anion, are quasi-one-dimensional
crystals that consist of parallel conducting chains. The over-
laps of the electron wave functions are the highest in thedirection of the chains (the adirection) and are much smaller
in the bdirection perpendicular to the chains. ( TMTSF )
2X
materials exhibit very interesting behaviors when a strongmagnetic field is applied perpendicular to the a–b plane.
There is a phase transition from the metallic state to a spin-
density wave state.
19This state is referred to as the FISDWs.
As the magnetic field is increased further, a sequence of
phase transitions between different FISDWs is observed. We
will discuss the FISDW effect on the energy spectrum of thesystem. For simplicity, compounds TMTSF
2Xare character-
ized by a simple electron spectrum: /C15(kx,ky)¼2ta
coskxþ2tbcoskywhere ta/tb¼10. Each “quantized”
FISDW is characterized by an order parameter DGNðrÞ
¼DexpðiGNrÞwhere Nis an integer.20,21The parameter
Dcharacterizes the strength of the order parameter.
GN¼(NG,p/b),bis the lattice spacing of the yaxis,
G¼ebH =/C22hc, where eis the electron charge and cis the ve-
locity of light. A magnetic field H¼(0, 0, H) is applied per-
pendicular to the conducting chains of a quasi-one-
dimensional compound. Then, aG¼2p/=/0;/¼abH is
the flux per unit cell a/C2b,/0¼hc=eis the flux quantum.
Considering a charge particle hopping between nearest
neighbor with hopping amplitude tin the presence of
FISDW, we obtain the following Hamiltonian:
H¼/C0X
ijrtijCþ
irCjrþX
ir½rDeðiGNrÞ/C0l/C138Cþ
irCir:(1)
0021-8979/2014/116(12)/123902/4/$30.00 VC2014 AIP Publishing LLC 116, 123902-1JOURNAL OF APPLIED PHYSICS 116, 123902 (2014)
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131.181.251.130 On: Sun, 23 Nov 2014 17:11:53In the absence of the FISDW, the corresponding energy
spectrum of the Hamiltonian is shown in Fig. 1. As for exam-
ple, we choose Nx¼Ny¼10. Six energy levels are contained
in the spectrum. In this quasi-one system, the dimerization
will produce a periodic potential self-consistently in order tolower the total energy of the system. When the FISDW
appears, the energy spectrum begins to show some particular
structures. In Fig. 2(a), we show the band structure in the
presence of FISDW with a small FISDW strength ( D¼0.2).
Each band is broadened and there are two sine or cosine
modulated forms in it. The bands broaden are bigger atG¼(2p/5) * n(n¼0, 1, 2, 3, 4). There are energy gaps near
these points in each broaden band. That is, each band is split
into two sub-bands due to the FISDW order parameter. Wecall one conductance sub-band and the other value sub-band.
This band structure can be understood with the help of sim-
ple quantum mechanics: Once the dimerization appears inthe system, it modulates the charge density of the electrons,
producing a charge density wave (CDW) with the wave vec-
torQ
x. Now, suppose that a FISDW potential is present in
the system, so the electrons experience two periodic poten-
tials with the wave vectors QxandG. If the two wave vec-
tors can be treated as commensurate, the energy spectrumchanges dramatically at the wave vectors k¼ðQ
x6GÞ.
This is why we see the broaden bands are bigger at some par-
ticular wave vectors. With increasing the strength of theFISDW ( D¼0.6), the energy bands begin to touch each
other. The energy gaps near commensurate wave vector
points increase bigger. When D¼2, all these energy gapedges in each band touch each other. The energy spectrum
versus different Gis presented in Fig. 2(b). We can find that
it has a similar structure of the two-dimensional lattice sys-tem Hofstadter butterfly. If we consider the effect of inter-
particle short range on-site interaction Uon the spectrum, we
find that the spectrum is divided into two butterflies withincreasing the strength of the interaction U(Fig. 2(c)).
When we increase the strength of the FISDW, the sys-
tem changes continually from metal state into insulator state.To give a clear image, we investigate the structure of the
eigenfunctions of the system for different strength of the
FISDW. From Fig. 3, we can see that when the strength of
the FISDW is small ( D¼0.2), the eigenfunctions are quasi-
extended over the size of the system. When the strength of
the FISDW is big ( D¼2), all these energy gap edges in each
band touch each other and the energy spectrum shows struc-
ture of the Hofstadter butterfly, the eigenfunctions are local-
ized. The system changes into insulator state. With furtherincreasing the strength of the FISDW, the butterfly begins to
change. The energy gaps for different bands near commensu-
rate wave vector points connect each other and grow up tobe a linked gap. The crisscross structures are disappeared
completely. In Fig. 4, we show the structure of the energy
spectrum for the strength of the FISDW ( D¼8).
Interestingly, this structure looks like the structure of the
energy spectrum of the system under a uniform perpendicu-
lar magnetic field without the FISDW (Fig. 4(b)). This par-
ticular structure of the energy spectrum of the quasi-one
dimensional system under a uniform perpendicular magnetic
field implies that the magnetotransport property of the sys-tem shows a different character from the two dimensional
lattice. Next, we will discuss the QHE in this system.
III. QUANTUM HALL EFFECT AND DISCUSSION
The discovery of the quantization of the Hall conduct-
ance in two dimensional electron system exposed to a strongmagnetic field has led to a number of theoretical studies of
the problem. It has been concluded that a noninteracting
electron gas has a Hall conductance, which is a multiple ofe
2/hif the Fermi energy lies in a gap between Landau levels.
In quasi-one dimensional organic ( TMTSF )2X, the QHE is
observed and is closely related to the FISDW observed inthese materials.
21–24However, there is an unexpected phe-
nomenon in Hversus rdiagram: the sign reversal of the
quantized Hall conductivity r(H)¼Le2/h(Lcan take bothFIG. 1. Energy levels for quasi-one dimensional organic ( TMTSF )2Xmateri-
als with ta/tb¼10.
FIG. 2. Energy varying with the wave vector Gof the FISDW for ( TMTSF )2Xmaterials with ta/tb¼10 and the FISDW strength D¼0.2 (a), D¼2 (b),D¼2,
andU¼2 (c).123902-2 Xiao-Shan Y e J. Appl. Phys. 116, 123902 (2014)
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131.181.251.130 On: Sun, 23 Nov 2014 17:11:53signs) as a function of H. In the following, we will explain
this abnormal property with our model. To obtain the longi-
tudinal and transverse conductivities, we use the Kuboformalism which is briefly outlined below.25The general
expression for electrical conductivity is written in the follow-
ing form:
rkl¼ie2/C22h
NX
aX
b6¼aFa/C0Fb ðÞhwaj_vkjwbihwbj_vljwai
Ea/C0Eb ðÞ2þg2þe2/C22h
NX
aX
b6¼aFa/C0Fb ðÞ
Ea/C0Ebg
Ea/C0Eb ðÞ2þg2hwaj_vkjwbihwbj_vljwai;(2)
where g!0þ. Here, the indices kandlcan be xory. For
k¼l¼x, we get rxx, the so-called longitudinal conductivity,
while for the other case, we have the transverse conductivity
rxy. The states jwaiandjwbiare the eigenstates of the
Hamiltonian (Eq. (1)), corresponding to the energy eigenval-
uesEaandEb, respectively, and N¼NxNyrepresents the size
of the sample. _vðkÞis the velocity operator along k-th (xory)
direction and Fa¼1=½1þeðEa/C0EFÞ=kBT/C138is the Fermi distribu-
tion function at absolute temperature Twith Fermi energy
EF.
We use this formula to investigate the two-dimensional
square lattice with non-interacting electrons subjected to a
uniform magnetic field in a direction perpendicular to the lat-tice plane. The integer QHE has emerged for the two-
dimensional square lattice model. When we consider the
anisotropic system with the hopping matrix elementst
a/C29tb(ta/tb¼10), the integer QHE is almost absent. This
can be understood from the structure of the energy spectrum
of the system under a uniform perpendicular magnetic field(Fig. 4). From the discussion above, we calculate the eigen-
functions of the system and find that they are nearly local-
ized, so the system is a bad metal in this case. In fact, weknow that in real one dimensional system, there is no integer
QHE. When there is a phase transition from the metallic state
to FISDW state, we calculate the Hall conductivity and find
that it is zero. This result gives a clear picture for theobserved integer QHE in this system: When a strong mag-
netic field is applied perpendicular to the a–bplane of the
(TMTSF )
2Xmaterials, there is a phase transition from the
metallic state to FISDW state. Within each FISDW phase,
the value of the Hall resistance remains constant, independ-
ent of the magnetic field. Once the boundary of anotherFISDW phase is crossed, the value of the Hall resistance
jumps to a new value, which remains constant until the next
phase boundary is crossed. That is the QHE in this system.So, the quantized Hall conductivity can be written as:
r
xy¼L(e2/h), where Lis integer and it is determined by the
quantized FISDW phase. This result is exactly consistentwith the experimental observation. In the above calculation,
we assume the system is half-filled, and each band is split
into two sub-bands due to the FISDW order parameter. Theelectrons only occupy the value sub-band. For the strong
FISDW potential case, the split upper conductance sub-band
of one band will gradually overlap the low value sub-band ofFIG. 3. Spatial variations of the eigen-
functions of the system for the strength
of the FISDW D¼0.2 (a) and D¼2
(b).
FIG. 4. Energy varying with the wavevector G of the FISDW for
(TMTSF )
2Xmaterials with ta/tb¼10
and the FISDW strength D¼8 (a).
Energy varying with the magnetic flux
/=/0for the ( TMTSF )2Xmaterials (b).123902-3 Xiao-Shan Y e J. Appl. Phys. 116, 123902 (2014)
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131.181.251.130 On: Sun, 23 Nov 2014 17:11:53the other band. So, there is Hall conductivity again, but the
sign of the Hall conductance is reversed due to the electrons
now occupy the conductance sub-band (Fig. 5). This result
accounts for the sign-reversal phenomenon, which was
observed with X¼C104,22PF6,21andReO.24
IV. SUMMARY
In summary, we explore the structure energy spectrum
of the quasi-one dimensional organic conductors subjected
to the FISDW state. We find that the structure energy spec-trum can exhibit Hofstadter butterfly. The phenomenon of
the quantized Hall conductance due to FISDW is also inves-
tigated theoretically. We find that the mechanism of QHE inthis system is different from the normal QHE found in two
dimensional electron system subjected to a magnetic field. It
is caused by the FISDW order parameter. The sign reversalof the quantized Hall conductivity can appear when theFISDW is big enough to make the split bands overlap each
other.
ACKNOWLEDGMENTS
We thank Yi-Fei Wang and Shun-Li Yu for useful
discussions. This work was supported by the National NatureScience Foundation of China (Grant No. 11147029).
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70, 144524 (2004).
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53, 1845 (1984).
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25P. Dutta, S. K. Maiti, and S. N. Karmakar, J. Appl. Phys. 112, 044306 (2012).FIG. 5. The Hall conductance varying with the strength of the FISDW.123902-4 Xiao-Shan Y e J. Appl. Phys. 116, 123902 (2014)
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131.181.251.130 On: Sun, 23 Nov 2014 17:11:53 |
1.4895838.pdf | Strain mediated coupling in magnetron sputtered multiferroic PZT/Ni-Mn-In/Si thin film
heterostructure
Kirandeep Singh, Sushil Kumar Singh, and Davinder Kaur
Citation: Journal of Applied Physics 116, 114103 (2014); doi: 10.1063/1.4895838
View online: http://dx.doi.org/10.1063/1.4895838
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/11?ver=pdfcov
Published by the AIP Publishing
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25Strain mediated coupling in magnetron sputtered multiferroic
PZT/Ni-Mn-In/Si thin film heterostructure
Kirandeep Singh,1Sushil Kumar Singh,2and Davinder Kaur1,a)
1Functional Nanomaterials Research Lab, Department of Physics and Centre of Nanotechnology, Indian
Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
2Functional Materials Division, Solid State Physics Lab (SSPL), DRDO, Lucknow Road, Timarpur,
Delhi 110054, India
(Received 26 June 2014; accepted 5 September 2014; published online 16 September 2014)
The strain mediated electrical and magnetic properties were investigated in PZT/Ni-Mn-In
heterostructure deposited on Si (100) by dc/rf magnetron sputtering. X-ray diffraction pattern
revealed that (220) orientation of Ni-Mn-In facilitate the (110) oriented tertragonal phase growth ofPZT layer in PZT/Ni-Mn-In heterostructure. A distinctive peak in dielectric constant versus tem-
perature plots around martensitic phase transformation temperature of Ni-Mn-In showed a strain
mediated coupling between Ni-Mn-In and PZT layers. The ferroelectric measurement taken at dif-ferent temperatures exhibits a well saturated and temperature dependent P-E loops with a highest
value of P
sat/C2455lC/cm2obtained during martensite-austenite transition temperature region of Ni-
Mn-In. The stress induced by Ni-Mn-In layer on upper PZT film due to structural transformationfrom martensite to austenite resulted in temperature modulated Tunability of PZT/Ni-Mn-In hetero-
structure. A tunability of 42% was achieved at 290 K (structural transition region of Ni-Mn-In) in
these heterostructures. I-V measurements taken at different temperatures indicated that ohmic con-duction was the main conduction mechanism over a large electric field range in these heterostruc-
tures. Magnetic measurement revealed that heterostructure was ferromagnetic at room temperature
with a saturation magnetization of /C24123 emu/cm
3. Such multiferroic heterostructures exhibits
promising applications in various microelectromechanical systems. VC2014 AIP Publishing LLC .
[http://dx.doi.org/10.1063/1.4895838 ]
I. INTRODUCTION
Multiferroics are materials that exhibit simultaneously
different ferroic orders such as (anti) ferromagnetism, (anti)
ferroelectricity, and ferroelasticity.1Multiferroic materials
are classified into two broad category namely “Intrinsic or
natural” multiferroic single phase compounds and “extrinsic
or artificial” multiferroic heterostructures. The utilization ofmultiferroics in practical applications required the presence
of strong coupling between two ordered parameters along
with relatively high magnetic or ferroelectric critical temper-atures. However, the scarcity and low temperature magneto-
electric response of single phase multiferroic materials
hinders their use in practical devices.
2Artificial multiferroic
heterostructures with high quality and sharp interfaces fur-
nish an alternate route for achieving strong magnetoelectric
coupling above room temperature. This approach provides alarge pool of ferroelectric and magnetic group of materials
for optimizing magnetoelectric strength and other system
properties. The coupling mechanism in artificial multiferroicheterostructures thus far rely on: (i) strain mediated elastic
coupling at the interface (ii) exchange bias interaction
between antiferromagnetic multiferroic and ferromagneticcomponent (iii) electric field modulated carrier charge den-
sity of ferromagnetic layer.
3Strain mediated and exchange
bias mediated coupling operate by modification of magneticanisotropy and saturation magnetization, respectively;4,5
whereas charge modulated exchange bias coupling changes
the exchange interaction in the ferromagnetic layer.6The
interaction length scale differs for different mechanism, for
example, charge density modulation is limited to interface
(1–2 unit cells) in case of metal and to few nanometers inmagnetic semiconductors, whereas elastic interaction can
extends upto 100s of nanometers, while exchange bias propa-
gates through the whole ferromagnetic layer.
7Interfacial
strain has been used extensively for obtaining a strong cou-
pling between two ferroic orders. Fabrication of artificial het-
erostructures by procedures like tape-casting and sinteringtogether thick polycrystalline films
8suffers from major draw-
backs like poor mechanical coupling between the layers and
impurities formation due to interfacial diffusion at high tem-perature. Therefore, for obtaining strong coupling between
ferroelectric and ferromagnetic layers in artificial heterostruc-
tures, it is desirable to grow the epitaxial ferroelectric thinfilms on an elastically and magnetically functional substrates
or bottom layers.
9This additive advantage gives the in-plane
elastic coupling in the heterostructures. Such a substrate orbottom layer should have: (i) giant anisotropy magnetostric-
tion,
10(ii) good in-plane lattice matching to the ferroelectric
layer, and (iii) a good electrical conductivity that rules out thepossibility for separate bottom electrode.
Ferromagnetic shape memory alloys (FSMAs) are multi-
functional materials, which show the existence of ferromag-netism and shape memory effect simultaneously.
11Recently,
a family of Ni-Mn-X (X ¼In, Sb, Sn, and Ga) FSMAs havea)Author to whom correspondence should be addressed. E-mail: dkaurfph@
iitr.ernet.in. Tel.: 91-1332-2285407; FAX: 91-1332-273560
0021-8979/2014/116(11)/114103/9/$30.00 VC2014 AIP Publishing LLC 116, 114103-1JOURNAL OF APPLIED PHYSICS 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25provoked the greatest interest due to their promising physical
properties, such as large magnetic field induced strain12
greater than any piezoelectric, magnetostrictive and electro-
strictive materials, faster frequency response than conven-
tional shape memory alloys (SMAs),13giant magnetocaloric
effect,14large magnetoresistance, and Hall effect.15,16These
materials undergo a phase transformation from parent cubic
structure (austenite) to low symmetric martensitic structure.
This transition is driven by Jahn-Teller distortion and resultedin a large strain in transformation course due to unit cell vol-
ume reduction.
17The large magnetic field and temperature
driven strain makes FSMAs promising candidate for practicalapplications. In the current study, Ni
50Mn35In15alloy have
been used because it exhibits ferromagnetism at room tempe-
rature, its martensitic temperature is close to room tempera-ture,
18and it exhibits large magnetic field induced strain in
the temperature regime across martensite to austenite phase
transition. Room temperature tetragonal structured PbZrTiO 3
has been chosen as a top ferroelectric layer. It is well a studied
material, which exhibits room temperature ferroelectricity
with large saturation and remnant polarization.
The aim of this work was to fabricate highly oriented
PZT/Ni-Mn-In multiferroic heterostructure and to investigate
the effect of temperature driven strain during martensite toaustenite phase transformation on its electrical and magnetic
properties. To the best of our knowledge, no report is avail-
able in the literature about magnetron sputtered PZT/Ni-Mn-In thin film heterostructure. This type of study provide us a
possibility to fabricate novel multiferroic materials, which
exhibit properties of ferroelectricity, ferromagnetism, shapememory effect, and strong M-E coupling at room tempera-
ture while keeping the function of each material. Such novel
multiferroic heterostructures could prove useful in spin-tronics and could lead to new types of memory devices,
switching devices, magnetic field and stress sensors, trans-
ducers, and actuators.
II. EXPERIMENTAL DETAILS
PZT/Ni-Mn-In thin film heterostructure was fabricated
on Si (100) substrate by dc/rf magnetron sputtering system
(Excel Instruments, India) using high purity (99.99%)Ni
50Mn35In15[Ni-Mn-In] and a Pb(Zr 0.52Ti0.48)O3[PZT] tar-
gets. The PZT and Ni-Mn-In targets used for sputtering were
50 mm in diameter and 3 mm in thickness. Initially the Si(100) substrates were cleaned thoroughly with a mixture of
distilled water and trichloroethylene in an ultrasonic bath
and then washed with boiled acetone. The Ni-Mn-In andPZT layers in PZT/Ni-Mn-In heterostructure were grown ex-
situand prior to deposition of these layers sputtering system
was evacuated to a base pressure of 3 /C210
/C06Torr for 6 h.
The complete heterostructure was fabricated at a constant
substrate temperature of 550/C14C and at constant working
pressure of 10 m Torr. The target to substrate distance wasfixed to 4 cm. Ni-Mn-In films were deposited for 20 min at a
dc power of 110 W in pure argon atmosphere, while PZT
films were prepared by a rf power of 100 W in the presenceof 90% (Ar) þ10% (O
2) mixture. No post annealing was per-
formed after deposition. The synthesis of similar kind of Ni-Mn-X (X ¼Sn) sputtered thin films on Si (100) at 550/C14sub-
strate temperature was reported by Vishnoi et al .19
Relatively low substrate temperature (550/C14C) for the fabri-
cation of heterostructure ensures the formation of sharp and
abrupt interface between PZT and Ni-Mn-In layer. The phase
formation and crystallographic orientation of the heterostruc-tures were analyzed using a Burker advanced diffractometer
of CuK a(1.54 A
/C14) radiations in h–2hgeometry at a scan
speed of 1/C14/min. The surface morphology and the cross sec-
tional micrograph of PZT/Ni-Mn-In heterostructure was ana-
lyzed by FEI quanta 200F model field emission scanning
electron microscope (FESEM). To measure the dielectricand ferroelectric properties of PZT/Ni-Mn-In heterostruc-
ture, 0.2 mm diameter Pt dots was sputter deposited onto
PZT layer through a shadow mask at room temperature. Thedc power was typically set at 80 W for Pt target. The bottom
electrode was made available by partially masking the Ni-
Mn-In coated Si substrate during the PZT deposition. Thefrequency, electric field, and temperature dependence of
dielectric constant were recorded using HP4294A impedance
analyzer. The temperature dependent leakage current charac-teristic and ferroelectric properties of the heterostructure
were characterized using RT66A ferroelectric tester (Radiant
Technologies, USA) attached to temperature controlledchamber. The magnetic hysteresis loops of the samples were
recorded in 61 Tesla magnetic field at different temperatures
using a vibrating sample magnetometer (VSM).
III. RESULTS AND DISCUSSIONS
Fig. 1shows the XRD pattern of Ni-Mn-In, PZT, and
PZT/Ni-Mn-In samples deposited on Si (100) substrate. An
appearance of (311) super lattice reflection along with domi-
nant (220) fundamental peak in Fig. 1(a) authenticate the
cubic structure of Ni-Mn-In, whereas Fig. 1(b)shows the sin-
gle perovskite tetragonal phase with (110) preferred orienta-
tion of PZT. XRD pattern of PZT/Ni-Mn-In heterostructureis shown in Fig. 1(c). The XRD pattern shows the formation
of bilayer structure, which is confirmed by the presence of
(110), (102) orientation of PZT, and (220) phase of Ni-Mn-In. Moreover, form Fig. 1(c), it can also be realized that
(220) oriented Ni-Mn-In thin film serves as a good seed crys-
tal for the growth of (110) dominated top PZT layer. The ab-sence of any side phases like Ti
3Ni4or TiNi 3in X-ray
diffraction pattern of PZT/Ni-Mn-In indicates that no chemi-
cal interaction takes place at the interface of PZT and Ni-Mn-In. The strain present in PZT layer due to underneath
Ni-Mn-In film in PZT/Ni-Mn-In heterostructure and sub-
strate imposed strain in PZT/Si and Ni-Mn-In/Si sampleswere calculated using the following formula:
e¼½ ðd/C0d
oÞ=do/C138/C2100; (1)
where “ d”is the lattice spacing of the strained films calcu-
lated from XRD pattern and “ do”is the lattice spacing corre-
sponds to bulk values of strained films. The strain and other
parameters calculated from XRD patterns have been sum-
marized in Table I. The value of strain is positive in all the
samples, which indicate the nature of strain is tensile. The
large strain in PZT/Ni-Mn-In heterostructures is due to large114103-2 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
128.193.164.203 On: Sat, 20 Dec 2014 23:11:25lattice mismatch between Ni-Mn-In and PZT layer. This
large strain promotes the elongation of out of plane latticeparameter “c” and hence increases the tetragonal distortion
“c/a ratio” of PZT layer in PZT/Ni-Mn-In heterostructure.
The tetragonal distortion, which is a measure of ferroelec-tricity, mainly results from the competition between lattice
mismatch induced stress and thermal expansion coefficient
difference between bottom and top layer.
20,21Figs. 2(b) and
2(c)showed the surface morphologies and thicknesses of Ni-
Mn-In/Si, PZT/Si, and PZT/Ni-Mn-In/Si samples measured
by FESEM. The morphologies were very dense, smooth, andpore free. Spherical shaped grains with average grain size of
55 nm, 61 nm, and 72 nm were observed in Ni-Mn-In/Si,
PZT/Ni-Mn-In, and PZT/Si samples, respectively. The crosssectional micrographs (Fig. 2(c)) show sharp and abruptinterface between PZT and Ni-Mn-In layer, which indicates
that no inter-diffusive layer is present in PZT/Ni-Mn-In het-erostructure. It also revealed that lattice mismatch generated
stress in the film was not detrimental to the film adhesion.
The fabrication schematic of Ni-Mn-In/Si, PZT/Si, and PZT/Ni-Mn-In/Si samples are shown in Fig. 2(a).
Fig.3(a)shows frequency dependent dielectric constant
(e) and dielectric loss (tan d) of PZT/Ni-Mn-In heterostruc-
ture in 1 kHz to 1 MHz frequency range. The measurements
were done at room temperature with an oscillation level of
500 mV. The dielectric constant ( e) and dielectric loss (tan d)
were found to be 513 and 0.07, respectively, at a frequency
of 1kHz. There is a decrease in dielectric constant ( e) with
increasing frequency. This fall occurs from the fact thatcharge possesses inertia due to which the polarization doesFIG. 1. X-ray diffraction pattern of Ni-
Mn-In, PZT, and PZT/Ni-Mn-In sam-ples deposited on Si (100) substrate.
TABLE I. Different parameters calculated from X-ray diffraction patterns and FE-SEM images of Ni-Mn-In, PZT, PZT/Ni-Mn-In samples.
Samples a (nm) c (nm) c/a ratio Strain (%) Crystallite size (nm) Grain size (nm) Thickness (nm)
PZT/Ni-Mn-In 0.4243 0.8520 2.008 5.5 37 61 1120
PZT 0.4269 0.8489 1.988 5.1 40 72 370
Ni-Mn-In 0.5920 0.5920 1.0 0.23 20 55 750114103-3 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25not occur instantaneously with application of electric field.
Moreover, a sharp decrease in dielectric constant at lowerfrequency could be due to low frequency charge accumula-
tion effect. Such a strong dispersion is referred as low fre-
quency dielectric dispersion and it is a common feature ofthose ferroelectrics which are associated with non-negligible
ionic conductivity.
22Inset of Fig. 3(a) shows the procedure
for measuring the ferroelectric properties of thin filmheterostructure. Fig. 3(b) shows the variation of dielectric
constant ( e) as a function of temperature (T) in PZT/Ni-Mn-
In heterostructures at 1 MHz frequency and 300 mV magni-
tude of an applied oscillating electric field. An occurrence of
distinctive hump in the dielectric constant versus tempera-ture measurement over a temperature range 266 K–305 K is
correlated with the martensite to austenite phase transition of
lower Ni-Mn-In layer. The transformation from high
FIG. 2. (a) Block diagram of Ni-Mn-In, PZT and PZT/Ni-Mn-In samples grown on Si (100) substrate. (b) Surface morphology of Ni-Mn-In, PZT, and PZT/
Ni-Mn-In samples measured by FE-SEM, (c) cross sectional micrographs of Ni-Mn-In, PZT, and Ni-Mn-In samples.114103-4 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25temperature austenite (cubic) phase to low temperature mar-
tensite phase with orthorhombic structure is accompanied by
in plane lattice parameter “a” contraction. This in plane lat-tice parameter contraction “a” resulted in an expansion in the
corresponding “c” direction. The strain generated in Ni-Mn-
In layer during transformation temperature range is subse-quently transferred to upper ferroelectric PZT layer and
causes a change in its dielectric constant. The dependence of
dielectric constant ( e) on temperature can be measured in
terms of temperature coefficient of capacitance (TCC),
which is defined as
TCC¼
De
er20/C14CðÞ DT; (2)
where Deis the change in dielectric constant ( e) with respect
to dielectric constant at 20/C14C and DT is the change in tem-
perature relative to 20/C14C. A smaller value ofTCC/C244.96/C210/C04C/C01calculated in the temperature range
from 20/C14Ct o9 0/C14C at 1 MHz suggested the better tempera-
ture stability of PZT/Ni-Mn-In heterostructure. The lowvalue of TCC could be due to broadened eversus T peaks as
a result of diffuse transition.
23The resistance versus temper-
ature measurement was done for Ni-Mn-In layer depositedon Si (100) substrate to confirm its martensite and austenite
temperature range. Determined by cooling and heating R-T
curves, as shown in inset of Fig. 3(b), the austenite start (A
s),
austenite finish (A f), martensite start (M s), and martensite
finish (M f) temperatures of Ni-Mn-In were 290 K, 311 K,
291 K, and 273 K respectively. The structural transformationtemperature range of Ni-Mn-In as observed from R-T curve
is in accordance with dielectric hump region, which
appeared in e-T graphs.
The dc electric field dependent dielectric constant of
heterostructures was studied at 1 MHz in martensite tempera-
ture range ( <270 K), austenite temperature range ( >315 K),
and in transformation temperature coarse (270 K <T
<315 K) as shown in Fig. 4(a). A butterfly hysteresis was
observed in e-E curves, which is attributed to ferroelectric
polarization process and indicated the occurrence of polar
nano regions (PNRs).
24,25The tunability n r(E) defined as
field dependent dielectric constant, polarization P(E), anddielectric constant ( e) at an applied electric field E are related
to each other by following relation:
n
rEðÞ¼1/C0e0ðÞ
eEðÞ¼3e0ðÞe0bP2EðÞ
1þ3e0ðÞe0bP2EðÞ
¼1
1
3e0ðÞe0bP2EðÞþ1; (3)
where e0is the permittivity in vacuum and bis the landau
coefficient. The tunability at 330 K, 290 K, and 250 K were
found to be 40.6%, 42%, and 38.6%, respectively. The little
voltage shift in e-E graphs confirms the formation of sharp
interface with low density of charge traps between PZT and
Ni-Mn-In.9Fig.4(b)shows the ferroelectric hysteresis loops
of PZT/Ni-Mn-In heterostructure at different temperatures.A standard bipolar triangular waveform having magnitude
600 kV/cm was applied to measure the P-E loops. The satu-
ration polarization (P
sat) of heterostructure at 250 K, 290 K,
and 330 K was found to be 51.88 lC/cm2, 55.62 lC/cm2, and
45.56 lC/cm2. A small shift in P-E loops along X-axis
(Ecþ6¼Ec-) in PZT/Ni-Mn-In heterostructure can be attrib-
uted to factors like defects, different work function of top
and bottom electrodes, etc.26,27The variation in tunability
(nr) and polarization occurs due to temperature driven struc-
tural change, which induces strain in Ni-Mn-In layer, this
strain is then subsequently transferred to upper PZT layer.
The temperature dependent strain associated with Ni-Mn-Inlayer was ascribed to unit cell volume contraction. The mar-
tensite phase having orthorhombic structure of Ni-Mn-In has
large unit cell volume as compared to austenite phase unitcell volume. The martensite to austenite transformation of
Ni-Mn-In layer occurs over a large temperature range
because the stored elastic strain energy contribution thatoccurs when Ni-Mn-In undergoes shape change requires an
FIG. 3. (a) Variation of dielectric constant ( e) and dielectric loss (tan d)a sa
function of frequency at 500 mV magnitude of applied oscillating electric
field. Inset 3(a) Procedure for measuring the ferroelectric properties of PZT/
Ni-Mn-In heterostructure. (b) Dielectric constant ( e) variation as a function
of temperature (T) at 1 MHz frequency and 300 mV magnitude of an appliedoscillating electric field. Inset 3(b) Resistance vs temperature variation of
Ni-Mn-In film deposited on Si (100) substrate.114103-5 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25extra driving force. Thus, their occurs a co-existence of mar-
tensite and austenite phases in the transformation tempera-
ture region. This co-existence produces a large strain in Ni-
Mn-In layer, which is transferred to upper PZT film andcauses a increase in tunability (n
r), saturation polarization
(Psat), and remnant polarization (2P r). The different parame-
ters calculated from P-E loops and e-E curves have been
summarized in Table II.
I-V curves were measured to clarify the conduction
mechanism in PZT/Ni-Mn-In heterostructure. The leakagecurrent data were recorded for negative and positive bias of
the applied voltages. The symmetric curves for both the
polarities of voltage suggest that the contacts were ohmicand essentially bulk limited conduction was present in heter-
ostructure.
28The current density measured at room tempera-
ture and at 20 kV/cm was /C2410/C03A/cm2. Fig. 5shows the
semi logarithmic plots of leakage current density as a func-
tion of electric field. To analyze the presence of thermally
activated process, I-V curves were taken at different temper-atures. The invariance of I-V plots with temperature rules
out the possibility of schottky emission and poole frenkel
emission. The linear curves in log (J) vs log (E) plots,as shown in inset of Fig. 5, indicate the power law relation
J/E
nsuggesting the presence of either space charge lim-
ited conduction or ohmic conduction in the heterostructure.A slope “s” around 1 as calculated from log (J) vs log (E)curves revealed that thin film heterostructure follow more or
less ohmic conduction. The linear plots between log (J) and
log (E) regardless of measurement temperature indicate that
a PZT thin film contains discrete traps, which are embeddedin the background of continuously distributed traps.
29In
ohmic conduction, well adhered metal electrodes provide a
finite supply of charge carriers by forming an ohmic contactswith the ferroelectric thin film. The current density in ohmic
conduction is given by
J¼nelE; (4)
where lis the carrier charge mobility, e is the electronic
charge, n is the charge carrier density, and E is the applied
electric field. At low electric field, the total density of
injected electrons (n) is replaced by thermal equilibriumelectron density (n
o).30
The magnetic transition temperature (T C) and structural
transition temperatures (T M) of PZT/Ni-Mn-In heterostruc-
ture deposited on 0.5 /C20.5 cm2substrate were determined
from the thermo-magnetic measurements (M-T) in both field
cooled cooling (FCC) and field cooled warming (FCW) con-ditions at a low magnetic field strength of 0.1 Tesla, using
cryo free VSM with temperature range 10 K–300 K. Fig. 6
shows the magnetization versus temperature (M-T) curves ofPZT/Ni-Mn-In heterostructure in the temperature range
10 K-300 K. The magnetization data have been corrected toFIG. 4. (a) Electric field dependent dielectric constant ( e) of PZT/Ni-Mn-In heterostructure at different temperatures. (b) P-E loops of PZT/Ni-Mn-In hetero-
structure in 6600 kV/cm electric field range at different temperatures.
TABLE II. Different parameters calculated from ferroelectric and magnetic measurements of PZT/Ni-Mn-In heterostructure.
Ferroelectric properties Magnetic properties
Temp Tunability P sat 2Pr 2Ec Temp M sat 2Mr 2Mc
(K) (%) ( lC/cm2)( lC/cm2) (kV/cm) (K) (emu/cc) (emu/cc) (Tesla)
250 40.6 51.88 16.76 113.99 10 153.82 48.32 0.069
290 42 55.62 17.68 95.79 100 143.92 44.17 0.050330 39.6 45.46 17.65 116.58 250 131.87 29.84 0.041
285 135.12 32.44 0.046
300 123.11 25.62 0.026114103-6 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25account for background signal arises from diamagnetic con-
tribution of the substrate using the following equation:
Mf ilmðHÞ¼MtotalðHÞ/C0vsubstrate :H; (5)
where vsubstrate is the susceptibility of the substrate, Mtotalis
the total magnetization arise from film and substrate, and H
is the applied magnetic field parallel to the film surface. Thesusceptibility value for Si (100) substrate comes out to be
/C05.736 /C210
/C08. The observed results reveal that below
300 K, with decrease in temperature, the magnetization firstrises sharply to a maximum value and then falls abruptly at
martensitic start temperature (M
s) and reaches minimum at
martensite finish temperature (M f). The similar trend wasobserved for FCW curve. On further cooling below
Martensite finish temperature (M f), the PZT/Ni-Mn-In heter-
ostructure shows normal ferromagnetic behavior. The similartrend in magnetization versus temperature curves in Ni-Mn-
In based heusler alloys were also reported by Krenke et al. ,
Bhobe et al. , Das et al., and Alarcos et al.
18,31–33The varia-
tions in spontaneous magnetization within the temperature
interval 272 K–298 K could be due to the weakening of the
exchange interactions as a consequence of abrupt change inMn-Mn interatomic distance.
34The decrease in magnetiza-
tion can be attributed to formation of variants of new crystal-
lographic phase, which temporarily disturbs the localferromagnetic orientation. The formation of small hysteresis
between FCC and FCW curves in the temperature range
272 K–298 K (Inset Fig. 6) indicates that PZT/Ni-Mn-In het-
erostructure undergoes first order structural transformation
from martensite phase to austenite phase. The thermal
hysteresis ( DT) between FCC and FCW curves can be
defined as
DT¼ðA
sþAfÞ=2–ðMsþMfÞ=2; (6)
where AsandAfare the austenite start and austenite finish
temperatures, and Msand Mfare the martensite start and
martensite finish temperatures of PZT/Ni-Mn-In thin filmheterostructure. The thermal hysteresis between FCC and
FCW curves calculated during phase transformation is 8 K.
The values of A
s,Af,M s, and Mfobserved from M-T curves
were 272 K, 298 K, 285 K, and 269 K, respectively. The
magnetic transition temperature T cwas not observed in PZT/
Ni-Mn-In heterostructure in the measured temperature rangedue to no significant decrease in magnetic moment. The
higher curie temperature of PZT/Ni-Mn-In heterostructure
indicates that the heterostructure is ferromagnetic at roomtemperature. To further investigate the magnetic properties
of PZT/Ni-Mn-In, heterostructure isothermal hysteresis
loops (M-H) were measured at different temperatures. Themeasurements were carried out by cooling the sample from
300 K down to desired temperature of interest and then vary-
ing the magnetic field. Fig. 7shows the well saturated M-H
loops of PZT/Ni-Mn-In thin film heterostructure measured in
61 tesla field at 10 K, 100 K, 250 K, 285 K, and 300 K. A
saturation magnetization of /C24123 emu/cm
3at 300 K again
authenticates the room temperature ferromagnetic nature of
PZT/Ni-Mn-In heterostructure. The M-H loops of thin film
heterostructure are in full agreement with thermo-magneticmeasurements recorded in the temperature range
10 K–300 K. The values of saturation magnetization ( M
sat),
retentivity (2 Mr), and coercive field (2 Ec) at different tem-
peratures have been summarized in Table II. The M-H loops
recorded below 250 K shows the typical ferromagnetic na-
ture. Thus, the decrease in the values of 2M rand 2E cwith
increasing temperature till 250 K is attributed to the fact that
increase in the temperature give rise to thermal motion or en-
tropy that competes with the ferromagnetic tendency of thedipoles to align in the direction of applied magnetic field.
Thus, a maximum value of saturation magnetization is
achievable at lowest temperature. The sudden increase in thevalues of saturation magnetization ( M
sat), retentivity (2 Mr),FIG. 6. Thermo-magnetic curves of PZT/Ni-Mn-In thin film heterostructure
obtained with a magnetic field of 0.1 Tesla. Inset: First order structural phase
transformation of PZT/Ni-Mn-In heterostructure.FIG. 5. (a) Semi logarithmic plots of current density (J) as a function ofapplied electric field at different temperatures, Inset: log (J) vs log (E) plots
of PZT/ Ni-Mn-In heterostructure at different temperatures.114103-7 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25FIG. 7. M-H loops of PZT/Ni-Mn-In heterostructure measured at different temperatures.114103-8 Singh, Singh, and Kaur J. Appl. Phys. 116, 114103 (2014)
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128.193.164.203 On: Sat, 20 Dec 2014 23:11:25and coercive field (2 Ec) was observed at Martensitic phase
transformation temperature (M S/C24285 K), which is in ac-
cordance with M-T curves in this region. As temperatureincreases above 285 K, the twin variants that exists in the
transformation temperature regime, gains sufficient energy
and thus less driving force is required for phase transforma-tion from martensite to austenite phase which resulted in
decrease in 2E
cand 2M r.19
IV. CONCLUSION
In conclusion, to integrate the functions of FSMAs and
ferroelectricity, a multiferroic PZT/Ni-Mn-In heterostruc-
ture was fabricated on Si (100) substrate using dc/rf magne-tron sputtering. The cross sectional FE-SEM micrograph
shows a sharp and abrupt interface with no inter diffusion
layer. A distinctive hump between 266 K–305 K revealed
the presence of mechanical coupling in PZT and Ni-Mn-In
layer of PZT/Ni-Mn-In heterostructure. The temperaturedependent ferroelectric and dielectric properties were
attributed to temperature driven structural changes associ-
ated with Ni-Mn-In layer, which induces strain on upperPZT layer. The maximum value of tunability (42%) and sat-
uration polarization (55.62 lC/cm
2) was observed in the
martensite to austenite transformation temperature regionof Ni-Mn-In. A leakage current density of /C2410
/C03A/cm2
was observed at room temperature and at 620 kV/cm
applied electric field. The linear plots between log (J) andlog (E) with slope near to 1 showed the presence of ohmic
conduction in heterostructu re. A well saturated M-H loops
at 300 K indicated that the heterostructure is ferromag-netic at room temperature. The room temperature multi-
ferroic nature of the heterostr ucture was revealed from the
co-existence of ferroelectric and ferromagnetic properties
and the coupling between two ferroic orders was con-
firmed from the distinctive hump appears in e-T curves.
The findings of this study shows that such a room tempera-ture multiferroic heterostru ctures with reduced thickness
can be implemented as multiferroic tunnel junctions (FM/
FE/FM) in future magnetoelectric random access memory.
ACKNOWLEDGMENTS
The financial support provided by the Defence Research
and Development Organization (DRDO), India under ER &
IPR Project with reference no. EPIR/ER/1100406/M/01/
1439 is highly acknowledge. The author Kirandeep Singh isthankful to Ministry of Human Resource and Development
(MHRD), India for award of Senior Research Fellowship.
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1.4894527.pdf | Note: Differential amplified high-resolution tilt angle measurement system
Shijie Zhao, Yan Li, Enyao Zhang, Pei Huang, and Haoyun Wei
Citation: Review of Scientific Instruments 85, 096104 (2014); doi: 10.1063/1.4894527
View online: http://dx.doi.org/10.1063/1.4894527
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/9?ver=pdfcov
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Note: Differential amplified high-resolution tilt angle measurement system
Shijie Zhao, Y an Li, Enyao Zhang, Pei Huang, and Haoyun Weia)
The State Key Lab of Precision Measurement Technology and Instruments, Department of Precision Instrument,
Tsinghua University, Beijing 100084, China
(Received 22 July 2014; accepted 22 August 2014; published online 3 September 2014)
A high-resolution tilt angle measurement system is presented in this paper. In this system, the mea-
surement signal is amplified by two steps: (1) amplified by operational amplifier and (2) differential
amplified by two MEMS-based inclinometers. The novel application not only amplifies the signal but,
more importantly, substantially reduces the electrical interference and common-mode noise amongthe same circuit design. Thus, both the extremely high resolution and great long-term stability are
achieved in this system. Calibrated by an autocollimator, the system shows a resolution of 2 arc sec.
The accuracy is better than ±1.5 arc sec. The zero-drift error is below ±1a r cs e ca n d ±2a r cs e ci nt h e
short and long term, respectively. © 2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4894527 ]
Inclination measurement plays an important role in mod-
ern manufacturing.
1For decades, various systems have been
developed for angle measurement such as autocollimators,2–4
goniometer,5–8and differential interferometers.9Their high-
resolution and accuracy have widely contributed to scien-
tific researches and industrial measurements. However, due
to their complex structure and complicated operation, thesesystems are usually expensive and time consuming. Recently,
various micro-electro-mechanical systems (MEMS) sensors
have been developed thanks to the rapid evolving in the mi-croelectronic fabrication techniques and micromachining pro-
cesses. A MEMS-based tilt sensor can be considered as a
static accelerometer, which can be used to measure the in-clination of an object by responding to the directional vari-
ation of the gravitational force. Inclinometers have been one
of the most extensively used sensors in the measurement ap-
plication such as electronics, automotive, and even inertial
navigation systems for good stability over time and excellentresolution.
10–14State-of-the-art devices can reach resolutions
approximately 0.001◦.15However, the noise level is the pri-
mary influence factor to limit the measurement resolution andprecision.
In this paper, a differential amplified tilt angle mea-
surement system was developed. Achieved by two MEMSinclinometers, it not only further amplified the signal from
operational amplifier but also greatly reduced the noise from
electrical interference and suppressed the common-modenoise among the same circuit. The structures of the tilt mea-
surement system were elaborated and a series of tilt measure-
ment experiments including calibration and comparison wereconducted. The reliability and feasibility of this system have
been verified.
The SCA103T-D04 chip is a kind of MEMS-based single
axis inclinometers. It has been considered very suitable for
precision measurement.
16To obtain the tilt measurement re-
sults from the SCA103T-D04 chip, there are two methods. On
the one hand, communication can be carried out by any mi-
cro controller that uses Serial Peripheral Interface (SPI) bus.
a)Author to whom correspondence should be addressed. Electronic mail:
luckiwei@mail.tsinghua.edu.cnHowever, in this case the received data are 11 bits. Thus, the
resolution is only about 0.009◦, which cannot meet the re-
quirement of high resolution tilt angle measurement. On the
other hand, two analog inclination signals can be obtainedfrom the chip, which can be differentiated externally by use
of a differential amplifier. Using an A/D converter, the analog
inclination signal can be converted into a digital signal. The-oretically, the output analog voltage value can be amplified as
possible as you can. However, there are some disadvantages
in this method. At first, the tilt angle result is highly affectedby the stability of the energy resource. Second, the result is
also affected by the temperature drift of the amplifiers and
electrical interference in the external circuit.
In our experiments, the inclinometer (SCA103T-D04)
has been proved that it can operate properly as the chip is
upside down. The chip is a surface mount sensor with 12
pins. The setup of the tilt angle measurement system is shown
in Fig. 1. Two inclinometers are surface mounted symmetri-
cally on both sides of a circuit board with a mutually opposite
sensing direction and inclination signals. The output inclina-
tion signals are differentiated externally, either by a differen-tial amplifier or a microcontroller to get a double tilt anger
value, which doubles the signal amplitude. The differential
measurement principle removes the most of common modemeasurement errors from the similar circuits design on both
inclinometers, which gives efficient noise reduction and im-
proves the long-term stability. Thus, the accuracy of the sys-tem is enhanced.
In order to stabilize the output voltage of the inclinome-
ter, a single +5 V supply system with high accuracy and low
noise is developed. The supply system is shown in Figure 2.
Batteries (12 V) are utilized as the power provider, whose rip-
ple noise can be omitted. Two micro-power voltage references
(2.5 V) and a resistant are connected to the battery-power in
series. Thus, the input voltage of the inclinometers is stabi-lized at 5 V . Three amplifiers are used in our system. Note
that the accuracy and stability of these amplifiers affect the
stability of the final tilt angle value directly.
The INA114 is a low cost, general purpose amplifier
offering excellent accuracy. Meanwhile, it operates at very
low offset voltage (50 μV), drift (0.25 μV/
◦C), and high
0034-6748/2014/85(9)/096104/3/$30.00 © 2014 AIP Publishing LLC 85, 096104-1
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132.204.37.217 On: Wed, 10 Dec 2014 19:06:00096104-2 Zhao et al. Rev. Sci. Instrum. 85, 096104 (2014)
FIG. 1. Setup for the tilt angle measurement system. Inclinometer A and B
are surface mounted symmetrically on both sides of a circuit board with a mu-tually opposite sensing direction. The output signals have the same numerical
value as the inclination, but the different sign.
common-mode rejection. The measured signal of the incli-
nometer is amplified by two steps: (1) amplified by oper-ational amplifier respectively; (2) differential amplified by
the third amplifier. After that, the tilt angle can be obtained
from a data acquisition board (DAQ) which captures the finalamplified signal.
In order to verify the measurement performance of our
tile angle measurement system, several experiments such asthe calibration, the long-term stability, the resolution compari-
son, and the response time of the tilt angle are carried out. The
experimental setup for the calibration of the tilt angle is shownin Fig. 3. Our proposed system and a reflector is mounted on
a high-precision nanopositioning stage (P-562.6CD), which
has a 6-degree of freedom used as a motion platform. The
recommended resolution is 0.02 arc sec. To compare the tile
angles in real-time, an autocollimator ELCOMAT 3000(Möller-Wedel) serves as an angle sensor, whose measure-
ment range is 2000 arc sec and the resolution is 0.05 arc sec,
and the accuracy is ±0.25 arc sec over total range.
The analog voltage ramp of the tilt angle measurement
system is converted to 16-bit digital values via a data acquisi-
FIG. 2. (a) Schematic of the tilt angle measurement system. (b) Photograph
of the system.
FIG. 3. Setup for the tilt angle calibration.
tion board from National Instruments (USB-6211). The digi-
tal signals and the angle values of the autocollimator are trans-
mitted to the computer simultaneously. Fig. 4shows a com-
parison of the tilt angle results obtained by our system andthe autocollimator. The stage moves with a range of 2000 arc
sec. The digital signals are linear fitting by the least squares
method with a slope of 198.5 arc sec/V . The residual error iswithin ±1 arc sec.
After the calibration experiments, the long-term stabil-
ity of the tilt angle measurement system is studied, wherethe evolution of the zero point drifts is investigated. The sys-
tem operates under the condition of room temperature of
20±2
◦C. The evolution of the zero point drift is logged
at a total duration of 32 h. The result is presented in Fig. 5,
which shows that the peak-to-peak value is 4.4 arc sec and
the triple standard deviation value is 2.1 arc sec (3 σ)f o rt o -
tal data. However, in 10 min duration experiment, the peak-
to-peak value is 1.9 arc sec and the triple standard deviationvalue is 1 arc sec (3 σ). As shown in Fig. 5, the oscillation pe-
riod of the tilt angle is 24 h. Therefore, the temperature drift
is the main influence caused the difference between the long-term stability and short-term stability.
Comparison experiments are carried out to determine the
resolution of the system. At the initial position of the pro-posed system, the nanopositioning stage is tilted of 0 arc sec.
At the first step, a tilt of 1 arc sec is preformed. Before the
next identical rotation of 1 arc sec angle, the stage stays atthe position for duration of 25 s. The stage is repeatedly tilted
FIG. 4. Calibration results of the tilt angle measurement system. The slope
is 198.5 arc sec/V; the residual error is within ±1 arc sec.
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132.204.37.217 On: Wed, 10 Dec 2014 19:06:00096104-3 Zhao et al. Rev. Sci. Instrum. 85, 096104 (2014)
FIG. 5. Evolution of the zero point drifts with time.
for ten times. In another experiment, the same procedure is
carried out with the tilt angle of 2 arc sec in each step. Fig. 6
shows the position of the stage and the response of the pro-
posed system. Meanwhile, the residual error of tilt angle is
demonstrated. The residual errors are within ±1 arc sec. It
can be concluded that a resolution of 2 arc sec is derived.
The response time of the proposed system is also inves-
tigated. The nanopositioning stage moved after a step of 100arc sec change of tilt at a speed of 200 000 arcsec/s. Fig. 7
FIG. 6. Evolution of the tilt angle over the time for rotation steps. (a) 1 arc
s e cs t e p ;( b )2a r cs e cs t e p .
FIG. 7. Response time of the proposed system.
gives a typical response time constant measurement plot.
Obviously, the value is reached after 300 ms.
In summary, a new tilt angle measurement system with
high-resolution is introduced in this paper. The new system
employs two inclinometers with a differential amplificationway. This new method can reduce the electrical interference
and suppressed the common-mode noise among the same cir-
cuit design. A series of tilt measurement experiments includ-ing calibration and comparison with a collimator are con-
ducted. The results validate the reliability and feasibility of
the proposed system. Calibrated by an autocollimator, the sys-tem shows a resolution of 2 arc sec and the linear operating
range is more than ±3000 arc sec. The accuracy is better than
±1.5 arc sec in the linear operating range, and the zero-drift
error is below ±1 arc sec in the short-term.
The authors would like to thank Dr. Xin Wang and Mr.
Xuejian Wu for their comments and suggestions. We are also
grateful for the support of the National Science and Technol-
ogy Major Project of China, Tsinghua University Initiative
Scientific Research Program, and the State Key Lab of Preci-
sion Measurement Technology and Instruments of TsinghuaUniversity.
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1.4887139.pdf | Investigation of the GaN-on-GaAs interface for vertical power device applications
Janina Möreke, Michael J. Uren, Sergei V. Novikov, C. Thomas Foxon, Shahrzad Hosseini Vajargah, David J.
Wallis, Colin J. Humphreys, Sarah J. Haigh, Abdullah Al-Khalidi, Edward Wasige, Iain Thayne, and Martin Kuball
Citation: Journal of Applied Physics 116, 014502 (2014); doi: 10.1063/1.4887139
View online: http://dx.doi.org/10.1063/1.4887139
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/1?ver=pdfcov
Published by the AIP Publishing
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155.33.16.124 On: Sat, 22 Nov 2014 17:17:13Investigation of the GaN-on-GaAs interface for vertical power device
applications
Janina M €oreke,1,a)Michael J. Uren,1Sergei V. Novikov,2C. Thomas Foxon,2
Shahrzad Hosseini Vajargah,3David J. Wallis,3Colin J. Humphreys,3Sarah J. Haigh,4,5
Abdullah Al-Khalidi,6Edward Wasige,6Iain Thayne,6and Martin Kuball1
1H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
2Department of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
3Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road,
Cambridge CB3 0FS, United Kingdom
4Super STEM Laboratory, STFC Daresbury Campus, Keckwick Lane, Daresbury WA4 4AD, United Kingdom
5School of Materials, University of Manchester, Manchester M13 9PL, United Kingdom
6School of Engineering, University of Glasgow, Rankine Bldg, Oakfield Avenue, Glasgow G12 8LT,
United Kingdom
(Received 25 February 2014; accepted 25 June 2014; published online 3 July 2014)
GaN layers were grown onto (111) GaAs by molecular beam epitaxy. Minimal band offset between
the conduction bands for GaN and GaAs materials has been suggested in the literature raising thepossibility of using GaN-on-GaAs for vertical power device applications. I-V and C-V measurements
of the GaN/GaAs heterostructures however yielded a rectifying junction, even when both sides of the
junction were heavily doped with an n-type dopant. Transmission electron microscopy analysisfurther confirmed the challenge in creating a GaN/GaAs Ohmic interface by showing a large density
of dislocations in the GaN layer and suggesting roughening of the GaN/GaAs interface due to etching
of the GaAs by the nitrogen plasma, diffusion of nitrogen or melting of Ga into the GaAs substrate.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4887139 ]
I. INTRODUCTION
Nitride-based semiconduct or devices, such as Gallium
Nitride (GaN) based transistors, have been the focus of inten-sive research in recent years.
1–3They stand out due to their
wide bandgap, which makes them an excellent candidate for
high power, high voltage, and sw itching applications. Vertical
device geometries are desirable in order to take full advantage
of the high voltage (HV) capability and to avoid the need to
sacrifice a large area for edge termination.4,5Conventional ver-
tical geometries place the drain contact on the substrate, with
the high voltage dropped across a vertically arranged P-N junc-
tion.6However, the lack of an affordable large-area GaN sub-
strate has led to most GaN being grown on heterogeneous
substrates such as Si, SiC, or sapphire,7,8none of which allow
a satisfactory Ohmic substrate contact to be achieved. A keyrequirement for realistic HV a pplications is that growth sub-
strates must be available, which are compatible with process-
ing in semiconductor foundries using wafer sizes /C21150 mm.
Here, we discuss an initial study aimed at assessing the possi-
bility of using GaAs substrates, a standard low-cost material
available in a 150 mm wafer size, as a growth substrate for ver-tical device application.
The theoretical basis for engineering band line ups as
well as semiconductor-semiconductor interfaces in As-basedsystems has been the focus of previous research efforts mainly
through computer simulations.
9–11Despite their vastly differ-
ent bandgaps, GaN and GaAs have been suggested to haveconduction bands of similar energy with respect to thevacuum level.
12GaN-on-GaAs may therefore provide a
potential solution to create the Ohmic conduction path neces-
sary for a vertical power device, therefore potentially enabling
a simple route to vertical GaN electronic devices. However,
growing GaN onto a GaAs substrate does bring challenges. Inparticular, achieving an electrically conducting GaN/GaAs
interface may be difficult as the large lattice mismatch
between GaN and GaAs will introduce a high density ofdefects into the GaN layer.
13Furthermore, while GaN grown
on GaAs has been characterized using optical measurements13
and the electronic properties of GaN/GaAs superlattices have
been evaluated,14an electrical characterization of the GaN/
GaAs interface has not been performed to date. In this work,
we have explored the possibility to create an Ohmic interfacebetween GaN and GaAs for power device applications. We
have performed electrical characterization of the interface as
well as transmission electron microscopy (TEM), scanningTEM (STEM), and energy dispersive X-ray spectroscopy
(EDXS) analysis to investigate the nature of this interface.
II. EXPERIMENTAL DETAILS
A 1.5 lm thick layer of GaN was grown using molecular
beam epitaxy (MBE) at a temperature of /C24660/C14C onto 2 in.
nþ(1–5)/C21018cm/C03(111)B GaAs substrates with a
thickness of approximately 350 lm supplied by Wafer
Technology Ltd. Nitrogen polarity GaN is assumed due to
the choice of GaAs substrate. In contrast, a (111)A GaAs
substrate would have produced Gallium polarity GaN.Growing onto GaAs (111) has been shown in the literature to
produce hexagonal rather than cubic GaN.
15,16Two GaN
layers grown under Ga-rich conditions have been compared,a)Author to whom correspondence should be addressed. Electronic mail:
janina.moereke@bristol.ac.uk
0021-8979/2014/116(1)/014502/6/$30.00 VC2014 AIP Publishing LLC 116, 014502-1JOURNAL OF APPLIED PHYSICS 116, 014502 (2014)
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155.33.16.124 On: Sat, 22 Nov 2014 17:17:13wafer A has no intentional doping in the GaN layer, whereas
wafer B includes an 80 nm layer of ( /C241018cm/C03). Si doped
GaN grown directly onto the GaAs followed by an uninten-tionally doped layer. Deposited onto both the GaN and GaAs
sides of the samples were Ohmic circular transfer length
method (CTLM) structures with a diameter of 200 lm and
varying gap between contacts from 4 lmt o4 8 lmi n4 lm
steps (Fig. 1). The contacts on the GaN were achieved using
a metallization of Ti/Al/Ni/Au and annealed at 800
/C14C for
30 s, while Ni/Au/Ge was used for the contacts on the GaAs
side and annealed at 450/C14C for 5 s.
Lateral current-voltage measurements were performed
using the CTLM structures on the front (GaN) and back
(GaAs) surfaces to check whether Ohmic contacts had been
successfully achieved, and if both the GaN and GaAs layerswere conducting. In both cases, these measurements have
been performed using a Keithley 4200SC system. For vertical
current flow, to remove the need for an isolating etch, whichmight result in edge effects, a grounded guard ring on the top
surface surrounding the sensing Ohmic contact was used to
limit the area of the GaN/GaAs junction, which was beingmeasured (Fig. 2). In this case, the contact on the GaN side
was driven and current measured on the GaAs side using an
approach adapted from previous work on surface leakage cur-rents.
17Guarded capacitance measurements were performed
with the same concept again using the Keithley 4200SCS. In
this case, the alternating current (AC) excitation and biasvoltage were applied on the GaAs side by connecting the ca-
pacitance HI terminal here, while the capacitance LO termi-
nal was connected to the center Ohmic contact on the GaNsurface.
A cross section TEM specimen was prepared from wafer
B by tripod polishing using an Allied Tech
TMmultiprep unit
with polishing scratches and residues being removed through
a final ion milling step using a 691 Precision Ion Polishing
System (PIPSTM). Initial microstructural analysis of the
GaN/GaAs structure was performed using the conventional
diffraction contrast TEM imaging in a Philips CM30 TEM
operated at 300 keV. Higher resolution studies of the inter-face were also carried out using a probe-side aberration-corrected STEM FEI Titan G2 instrument operated at
200 keV. Energy dispersive X-ray compositional mapping of
the interface at high speed and minimal electron dose was
achieved using the Titan’s high brightness electron sourceand Super-X
TMhigh-efficiency silicon drift detector system.
High-angle annular dark-field (HAADF) imaging was per-
formed using a probe convergence semi-angle of 19 mradand an ADF detector semi angle of 54 mrad.
III. RESULTS AND DISCUSSION
Elemental mapping was performed on wafer B with
EDXS in order to gain insight into the microstructure near
the GaN/GaAs interface (Fig. 3). The compositional map
indicates an interfacial roughening of the GaN/GaAs inter-face with GaN-rich areas extending into the GaAs substrate
(Fig. 3(c)). There are several different possible mechanisms,
which could lead to such a result. The active nitrogen plasmaproduced during the growth of GaN is very reactive and
could etch pits into the GaAs substrate before the start of the
GaN growth. Such a nitridation effect on GaAs duringgrowth of GaN has been seen previously.
18,19Alternatively,
the nitrogen could diffuse across the GaAs interface during
growth. A third possibility relies on the fact that at thegrowth temperature used here As is soluble in liquid Ga, so
that any excess Ga melts into the GaAs during the growth of
GaN onto GaAs. It is also unclear whether these areas arecomposed of GaAsN or if they consist of heavily N doped
GaAs or heavily As doped GaN has been found in previous
work on highly mismatched alloys (HMAs) formed at a simi-lar growth temperature.
20The greater intensity for the Ga
X-ray signals in the GaN compared to the GaAs (Fig. 3(e))
stems from the lower absorption cross section of the GaNand compositional analysis as summed EDXS away from the
interface (Fig. 3(b)) suggests a composition consistent with
the bulk materials. Diffraction contrast TEM imaging of wa-fer B (Figures 4(a)and4(b)) reveals that the crystalline GaN
film contains a dislocation density of roughly 4 /C210
12cm/C02,
a typical high density of dislocations for the large lattice mis-match of approximately 20% between GaN and GaAs. The
dark-field (DF) TEM image of the GaN layer in Figure 4(b)
shows that dislocations are not restricted to the region closeto the interface but extend to the surface of the film. The
HAADF-STEM image of the interface in Figure 4(c) also
shows highly distorted regions in the GaN film as the strainproduces strong diffraction contrast as well as the presence
of twin defects identified by the horizontal striations close to
FIG. 1. Schematic of Ohmic contact structure on GaN as well as GaAs side.
FIG. 2. Guarded setup for measuring conduction across interface.014502-2 M €oreke et al. J. Appl. Phys. 116, 014502 (2014)
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155.33.16.124 On: Sat, 22 Nov 2014 17:17:13the left edge of the image. The interfacial roughening of the
GaN/GaAs interface is also depicted in this figure with thered dashed-line showing the nominal surface of the GaAs
substrate.
The Ohmic nature of the contacts to both the GaN and
GaAs is evident for both wafers from electrical measure-
ments. Figure 5(a) presents I-V characteristics for wafer A,
with similar results observed for wafer B. Corresponding re-sistance plots in Figure 5(b)confirm that on the GaN side, the
resistance is dependent on the CTLM gap. From Figure 5(b),
it can also be seen that the sheet resistance increased from thecentre of the wafer towards the edge demonstrated by a
change in slope in the resistance plot. Structures were meas-
ured, which were located in the center, half-radius, and edgeof the wafer. Despite the sheet resistance variation, a good
Ohmic contact was achieved in all regions. Subsequent meas-
urements were performed on the most centrally locatedCTLM structures on the wafers (labeled as structure 1B in
Figure 5). A short transfer length of below 10 lmc a nb e
FIG. 3. (a) HAADF-STEM image of
GaN-on-GaAs (wafer B) near the inter-
face region with the green box high-
lighting the area from which EDXS
maps for (b) N, (c) As, and (d) Ga was
acquired.
FIG. 4. Diffraction contrast TEMimage of the GaN film on GaAs sub-strate (wafer B) (a) bright-field image
of (11–20) zone axis and (b) dark-field
image g ¼0002 as well as the
HAADF-STEM image of the interfa-
cial region of GaN/GaAs with the
nominal position of the interface indi-
cated by the red dashed-line.
FIG. 5. (a) I-V characteristics for circular surface contacts on GaN with
dimensions as illustrated in Figure 1(a)together with (b) the corresponding
resistance plot of k Xagainst CTLM gap for three structures (center, half-
radius, and edge of the wafer).014502-3 M €oreke et al. J. Appl. Phys. 116, 014502 (2014)
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155.33.16.124 On: Sat, 22 Nov 2014 17:17:13estimated from the resistance plot in Figure 5(b), which to-
gether with the Ohmic nature suggests a small contact resist-
ance for the GaN side. On the GaAs side, an Ohmic contactwas also achieved but with no significant dependence of con-
duction on CTLM gap and very low resistances compared to
those associated with current flow vertically. The CTLM gapindependence of the conduction in this measurement indi-
cates that the GaAs contact resistance dominates over the
GaAs bulk resistance. However, as all measured resistancesfor GaAs (about 6 Xbetween all contacts) are about 2 orders
of magnitude lower than the resistances associated with the
GaN layer, an insignificant contact resistance is implied forthe GaAs side. The dependences on top and bottom CTLM
gaps reflect the relative thicknesses of the GaN and GaAs
layers, but also suggest that the transport in the two materialscan be treated independently for these surface measurements.
Guarded measurements for wafer A, shown in Figure 6,
sensing vertical conduction across the GaN/GaAs interfacewith the GaAs side grounded and bias applied at the GaN
side, showed a non-Ohmic rectifying behavior. Very low
currents in the order of 30 lA were observed at a positive
applied voltage of 5 V, while negative voltages of /C05V
resulted in conduction across the interface with around
30 mA. Similar behavior was also observed for wafer B. TheCTLM gap had almost no impact on the I-V characteristic
consistent with the current flowing vertically across the junc-
tion. The fact that the junction conducts only in one polaritysuggests that there is an asymmetrical barrier between the
two layers resulting in the interface effectively conducting
like a diode rather than an Ohmic junction. Estimating the re-sistivity of the GaN/GaAs interface near 0 V resulted in
190X/cm
2, which is well above the typical resistivity of an
Ohmic contact for high power devices of 10/C06Xcm2.21,22
Diode ideality was estimated to be at best 10 meanings that
conventional analysis to extract the barrier height was not
possible. Temperature dependent I-V measurements (notshown here) demonstrating a very weak temperature depend-
ence suggest a tunneling process as the primary mechanism
for conduction across the GaN/GaAs barrier.
Capacitance measurements of wafer A at different fre-
quencies are presented in Figure 7showing C
pin Figure 7(a)
and G p/xin Figure 7(b) as a function of applied bias, i.e.,using a model of capacitance and resistance in parallel (see
inset in Figure 7(b)). Due to high leakage currents in wafer B
capacitance measurements in this sample did not yield any in-
terpretable results. With G p/xbeing smaller than C p,i ti s
clear that C-V profiling measures a capacitance associatedwith a blocking interface rather than an artefact due to leak-
age paths. Applying a model of capacitance and resistance in
series produced results, which were strongly dependent on
frequency and could not easily be interpreted. Using the par-
allel equivalent circuit representation, the observed weak fre-quency dependence and large magnitude of G
p/xin this data
are most likely due to the presence of interface traps with a
range of time constants. Given the rough interface seen inmicrostructural analysis and the high density of dislocations,
a high density of interface traps is highly likely. Furthermore,
G
p/xremains relatively constant in reverse bias, which indi-
cates a wide dispersion of trap time constants.23The reduc-
tion in C pwith increasing frequency is also consistent with
the presence of these traps and, in fact, required due to theKramers-Kronig relationship linking real and imaginary parts
of conduction.
23Parallel conduction appears to be an appro-
priate choice of model for conduction across the interface andany series resistance in the GaN seems to have only a limited
impact. In Figure 7(a), a well-defined slope in the reverse
bias range with some frequency dispersion is observed butwith very little hysteresis. Complex and not easily interpreta-
ble results were observed once the structure started to conduct
in forward bias. C-V profiling using plots of 1/C
p2to extract
doping density, depletion region width, and band offset
between the layers of the junction24has been applied to
As-based systems in the past, but only gave limited informa-tion in this case. The negative slope in reverse bias in Figure
7(a)is consistent with a depletion process and indicates a net
donor-trap density of 1.4 /C210
18cm/C03in the GaN assuming a
uniform single-sided doping profile. Such a depletion process
requires the rectifying barrier, which has been observed in
I-V measurements. Assuming that the voltage is droppedmainly in the GaN, taking the capacitance measurement at
0 V and the relationship of depletion region width and
FIG. 6. I-V characteristics of GaN face CTLM contacts with diameter of
200lm on wafer A when measured across the GaN/GaAs interface with
ground connected to GaAs.
FIG. 7. C-V profiling of the GaN/GaAs interface on wafer A at 100 kHz
(black dotted), 1 MHz (red solid), and 10 MHz (blue short dashed) using the
200lm diameter circular TLM contact with (a) showing capacitance includ-
ing a superimposed corresponding log(I)-V curve (orange dotted-dashed)
showing the onset of conduction across the interface and (b) showing con-
ductance over xas well as an inset of the electrical model of the interface
used here.014502-4 M €oreke et al. J. Appl. Phys. 116, 014502 (2014)
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155.33.16.124 On: Sat, 22 Nov 2014 17:17:13capacitance,25,26a depletion region in the GaN layer of 93 nm
can be estimated. This estimate is based on a simple parallel
plate model of capacitive conduction across the interface,which is clearly not entirely accurate. However, this depletion
region estimate does give an indication of the length scale of
the charge separation in the structure.
The I-V and C-V measurements show that the junction
can basically be represented as a leaky rectifier. Temperature
dependent I-V characteristics indicate, however, that this
model is indeed very simplified as no clear barrier height
could be extracted either from these or C-V measurements.The fact that both GaN and GaAs are n-type suggests that
this rectification is the result of the presence of an asymmet-
ric barrier within the junction, which would most simply beaccounted for by a heterojunction as indicated schematically
in Figure 8. However, the presence of a barrier does not nec-
essarily mean that the conduction bands are mis-aligned.Any evidence for or against alignment is masked by the
effect of this barrier. As shown by STEM results, the rough-
ening of the interface together with the high dislocation den-sity and other crystal defects will result in a complex
potential barrier. Another possibility is that a bandgap varia-
tion of either GaN or GaAs is present at the interface.Previous works, for instance, assessing the effect of N con-
centration in GaAs has seen such a variation in bandgap.
27–29
Similarly increasing As content in GaN also varied the size
of the bandgap.30In addition, a negative polarization charge
associated with the Ga-face of the GaN is expected.31All
these features may in themselves be sufficient to produce theasymmetric barrier, which results in rectification, even if the
expected alignment of the conduction bands of the GaN and
the GaAs is occurring. Therefore, neither a band alignmentnor a band offset can be confirmed here due to the presence
of this potential barrier. GaN-on-GaAs produced leakage
currents of 2 /C210
/C03A/cm2near 0 V, comparable to those
typically observed across a GaN-on-Si structure of the order
of 10/C04to 10/C03A/cm2.32–34While these studies used low re-
sistivity Si, the need for a nucleation layer of AlN betweenGaN and Si generally produces structures with a highly resis-
tive GaN-on-Si structure.IV. CONCLUSION
A GaN/GaAs device structure was grown and fabricated
into devices to test the potential to use this material system
for vertical GaN power devices, benefiting from a potentialalignment of the conduction bands of both materials.
Electrical measurements demonstrated that the as-grown
interface showed a thin interfacial defective layer createdbetween GaN and GaAs, which caused non-Ohmic conduc-
tion across the structure. Several mechanisms have been
proposed for the creation of this thin layer due to the rough-ening of the GaAs surface. N diffusion, N-plasma etching
or melting of Ga into the GaAs as well as the accumulation
of a negative polarization charge at the interface could all
play a role in this process. Vertical conduction through this
interface was observed for n-type GaN and GaAs with arectifying interface. It is clear that dramatically improved
material quality and suppression of the rectification will
need to be addressed for viable vertical device structures tobe realized.
ACKNOWLEDGMENTS
We acknowledge financial support from the Engineering
and Physics Sciences Research Council (EPSRC) under EP/K014471/1 and through access to the SuperSTEM Laboratory.
The FEI Titan G2 was funded through the support of HM
Government (UK) and was associated with the researchcapability of Manchester’s Nucl ear Advanced Manufacturing
Research Centre.
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1.4872491.pdf |
URe 2–A Compressibility Study of Allotropic Phases
B. Shukla*, N. V. Chandra Shekar and P. Ch. Sahu
Condensed Matter Physics Division, Materials Science Group,
Indira Gandhi Centre for Atomic Research, Kalpakkam-603102, India
*E-mail: bshukla@igcar.gov.in
Abstract: URe 2 compound exists in two phases- orthorhombic and hexagonal. The hexagonal phase has been prepared using
arc melting and annealingat 500°C for one week, whereas the orthorhombic phase was achieved by annealing the arc melted
sample at a temperature 150°C for the same period. High pressure x-ray diffraction studies on these two allotropic forms of
URe 2 have been carried out up to ~15GPa using a diamond anvil cell. Normal compression was observed without any kind of
phase transformation; although there is a probability of transformation from the metastable hexagonal to itsstable
orthorhombicphase under pressure.
Keywords: high pressure, URe 2, x-ray diffraction, bulk modulus
PACS: 62.50.+p , 64.30.+t , 64.70.kb
INTRODUCTION
Uranium intermetallics are potential metallic
nuclear fuels and are very interesting from the point of view of dual role of f-electrons in them [1].Uranium-
Rhenium system are likely barrier material in high
temperature nuclear reactors. Rhenium has high
resistance to heat and wear, and the possible compound with uranium is likely to have potential applications in
reactors. Rhenium forms two compounds, URe
2 and
U2Re with uranium. The latter decomposes above
~750°C and the former melts at ~2200°C . W h e n t h e
ratio of atomic diameters of the elements in a binary
compound of the form UX 2 is about 1.2 they tend to
form cubic Laves phases [2]. For U – Re system, this
ratio is 1.16. Therefore its structure is expected to
resemble one of the Laves phases. However, URe 2 has
two allotropic forms. The low temperature form up to
180°C has an orthorhombic structure with space group
Cmcm. Above this temperature, a hexagonal structure
exists with space group P6 3/mmc [2]. Hexagonal
structure is formed by a simple dilation of the unit
cellwithout breaking the atomic bonds of orthorhombic structure at high temperature. These reversible phases of
URe 2 make their high pressure behavior interesting for
investigation.
EXPERIMENT
URe 2orthorhombic phase was prepared by using a
standard arc melting technique. Stoichiometric measure of
U (99.98%) and Re(99.999%) were melted in a tri-arc
furnace in inert atmosphere and the melted button was
flipped 2-3 times to obtain a homogenous compound. The ingot was then vacuum sealed in Ar atmosphere in silica tube and annealed for about a week at temperature of
150
°C. In order to remove any oxide layer, the annealed
ingot was etched in 1:1 mixture of nitric and sulphuric
acid for about 2 minutes. The powdered URe 2 sample was
characterized by x-ray diffraction technique using a high
resolution image plate based diffractometer. It was found
to be in single phase of orthorhombic.Another ingot of URe
2 was prepared in the same aforementioned method.
This time, it was annealed at 500°C and then quenched to
obtain hexagonal phase of URe 2. In situ high pressure X-
Solid State Physics
AIP Conf. Proc. 1591, 62-63 (2014); doi: 10.1063/1.4872491
© 2014 AIP Publishing LLC 978-0-7354-1225-5/$30.00
62
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202.177.173.189 On: Mon, 28 Apr 2014 04:36:43ray diffraction experiments were carried out using a Mao-
Bell type diamond anvil cell (DAC) in the angle
dispersive mode. The sample in the powder form was loaded into a 200 ȝm diameter hole drilled in pre-indented
SS gasket.
For the pressure calibration some particles of silver
wereloaded along with sample URe 2. A mixture of
methanol, ethanol and water in the volume ratio16:3:1was
used as a pressure transmitting medium. Theincident X-ray
beam obtained from a Rigaku ULTRA-X (18kW) rotating
anode X-ray generator was monochromatisedwith graphite
monochromator. An image plate based mar-dtb-345
diffractometer was used.The overall resolution of the
diffractometer system is įd/d~0.001. The Mao-Bell type
DAC was fitted to the diffractometer and the sample to
detector distance was calibrated using a standard specimen
like LaB6. The equation of state of silver was used as a
parameter for pressure calibration.
RESULTS AND DISCUSSION
The high pressure XRD study of URe 2, both orthorhombic
and hexagonal phases were performed upto 14.6GPa and
16.2GPa respectively. The hexagonal phase of URe 2
remainedstablein its parent phase up to the pressure
studied. Although, not an equilibrium structure for URe 2 at
NTP, it could be stable, since it is known that Laves type
structure is the most stable structure found among AB 2 type
intermetallics. The P-V data for the hexagonal phase was
fitted with Murnaghan equation of state (Fig.1) and the bulk
modulus was found to be 280GPa.This compares well
withother isostructural uranium compoundsof transition
metals.
/g3
Figure 2 shows the x-ray diffraction patterns for
orthorhombic phase of URe 2 stacked together up to a
pressure of about 16.2GPa. Although the peaks have
broadened, the important peaks of the parent phase
were retained up to the maximum pressure studied. No
new peaks appeared up the pressure studied. The
experiments are being carried out at higher pressures.
ACKNOWLEDGEMENTS
The authors thank Shri L. M Sundaram for his help in
sample preparation, Shri M. Sekar and Shri N.R. Sanjay
Kumar for valuable suggestions. They thank the IGCAR management for constant support and
encouragement.
REFERENCES
[1] N. V. Chandra Shekar, V. Kathirvel, B. Shukla and P. Ch.
Sahu, Proc. Nat. Acad. Sci. (Section-A) 83 (2012) 163-177.
[2]. B. A. Hatt, ActaCryst. 14, 119 (1961).
Figure 2: High pressure x-ray diffraction pattern of URe 2in
Orthorhombic Phase
Figure 1: The P-V curve for hexagonal C14 type URe 2
fitted with Murnaghan equation of State.
63
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202.177.173.189 On: Mon, 28 Apr 2014 04:36:43AIP
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(AIP).
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1.4868699.pdf | Spintronic switches for ultra low energy global interconnects
Mrigank Sharad and Kaushik Roy
Citation: Journal of Applied Physics 115, 17C737 (2014); doi: 10.1063/1.4868699
View online: http://dx.doi.org/10.1063/1.4868699
View Table of Contents: http://aip.scitation.org/toc/jap/115/17
Published by the American Institute of PhysicsSpintronic switches for ultra low energy global interconnects
Mrigank Sharada)and Kaushik Roy
School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
(Presented 8 November 2013; received 24 September 2013; accepted 19 December 2013; published
online 20 March 2014)
We present ultra-low energy interconnect design using nano-scale spin-torque (ST) switches for
global data-links. Emerging spin-torque phenomena can lead to ultra-low-voltage, high-speed
current-mode magnetic-switches. ST-switches can simultaneously provide large trans-impedancegain by employing magnetic tunnel junctions, to convert current-mode signals into large-swing
voltage levels. Such device-characteristics can be used in the design of energy-efficient current-mode
global interconnects.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4868699 ]
I. INTRODUCTION
With the scaling of CMOS technology, energy-efficiency
and performance of the on-chip global-interconnect degrades.1
As a result, the design of low power and high-speed on-chip
global interconnects can be a m ajor bottleneck for emerging
chip-multi-processors (CMP) that employ extensive inter-
processor and memory to processor communication.1
Technology, circuit, and system level solutions have been
explored to address the design-issues pertaining to global-
interconnects.1,2For instance, the use of current-mode links for
long distance interconnects has been shown to offer reduced
power-consumption and enhanced bandwidth.2But, analog cir-
cuits for current-mode transceivers are more complex thansimple inverters and add significantly to static-power con-
sumption, as well as, area-comp lexity at the I/O interfaces.
In this work, we explore the potential of low-voltage,
magneto-metallic spin-torque (ST) switches for ultra-low
energy and high-performance interconnect design.
3Recently
demonstrated high-speed spin-torque switching phenomenabased on spin-orbital (SO) coupling effects may be condu-
cive to the design of ultra-low voltage, low-current, and
high-speed nano-magnetic switches.
3We present analysis
for device and circuit-level optimization of current-mode
interconnect design using such switches and compare its per-
formance with conventional CMOS interconnects proposedin literature.
II. SPIN TORQUE SWITCHES BASED ON
SO-ASSISTED DOMAIN WALL MOTION
A domain-wall (DW) can be formed in a magnetic
nano-strip connecting two magnetic domains with oppositespin
4–7(Fig. 1(a)). DW can be moved along such a nano-
strip under the influence of spin-torque resulting from
current-flow along the strip.4Experiments have shown the
possibility of current-induced high-speed DW motion in
magnetic nano-strips with perpendicular magnetic anisotropy
(PMA), with relatively low-current density of few MA/cm2.4
Recently, application of SO coupling through Rashba Effect(RE)5or Spin hall Effect (SHE)5,6induced by an adjacent
metal layer (with structural inversion asymmetry6) has been
found to significantly enhance DW speed for a given
current-density (Fig. 1(b)). For Neel-type DW, SHE induced
from an adjacent metal-layer results in an effective field-like
effect (H SHE),6that can be expressed as, H SHE¼K(r/C2m).
Here, mdenotes the magnetization of spin-domains. ris a
current-dependent vector defined as r¼j/C2z, where, jis the
current vector and zis the direction perpendicular to the
magnetization-plane. Kis a quantity dependent upon mate-
rial parameters of the magnet and is proportional to the
effective Spin-Hall angle, /H.6For a Neel-type DW, the
magnetization in the region of the DW lies along the length
of the magnetic nano-strip. For this configuration, the effec-
tive H SHEacting on the domain wall region can be visualized
to be perpendicular to the plane of the magnet. The
HSHE assists the non-adiabatic spin-torque acting on the
DW-region. For a hHof 0.2, micromagnetic simulations
showed an increase of /C245/C2in the DW-velocity for a given
current density, due to the H SHEterm (Fig. 1(b)). This effect
can be used to achieve faster switching for a given current.
An alternate mechanism for high-speed DW-motion has
been ascribed to spin-accumulation due to Rashba-Effect. The
effective field-like ( HRE) term due to REacting on the mag-
netic nano-strip shown in Fig. 1(a)can be expressed as KRr,
where KRis a scalar quantity proportional to the Rashba
parameter6and material parameters of the magnets. ris the
current-dependent vector, as defined earlier. For a magnetic
nano-strip with PMA configuration, the filed-like term HREcan
be visualized to be always orthogonal to the easy-axis (whichis in the z-direction in Fig. 1(a)). This essentially lowers the
energy-barrier for transition between up-spin and down-spin
and, hence, assists the spin-torque induced DW-motion alongthe nano-strip. RE-assisted ST-based DW motion can achieve
up to an order of magnitude faster switching-speed
6and can
hence be suitable for the design of high-speed spin-torqueswitches for interconnect applications.
A. High-speed unipolar domain-wall-switch
SHE-assisted DW-motion can be employed to design
high-speed, magneto-metallic current-mode unipolar domain-
wall switches (UDWS), as shown in Fig. 1(c).7It constitutesa)Author to whom correspondence should be addressed. Electronic mail:
msharad@purdue.edu.
0021-8979/2014/115(17)/17C737/3/$30.00 VC2014 AIP Publishing LLC 115, 17C737-1JOURNAL OF APPLIED PHYSICS 115, 17C737 (2014)
of a ‘free’ magnetic domain d2(with SO coupling), between
two fixed, anti-parallel spin-domains, d1andd3.7The spin-
polarity of d2can be switched parallel to d1by passing elec-
trons from d1tod3along the free-domain and vice-versa. The
spin-state of d2can be detected with the help of a magnetic
tunnel junction (MTJ) formed with a fixed magnetic layer at
its top.7Thus, this device can detect the direction or polarity
of current flow across its free domain. Note that the switching
current-path for the DWS offers a small resistance ( <100X
for dimensions in Fig. 1(e)) and hence allows low-voltage
operation. On the other hand, the high-resistance MTJ port
can effectively provide high-gain binary trans-impedance con-
version for the input-current.
B. High-speed bipolar domain wall switch
A 3-terminal, bipolar domain wall switch (BDWS) is
s h o w ni nF i g . 2(a). Our proposed device consists of two
fixed-domains of opposite magnetization (domain-2 and do-
main-3) that act as input-ports and to polarize the input cur-
rents. The third domain (domain-1) is a free-domain. Thespin-polarity of the current i njected into the free-domain is
the difference between the current inputs I
1and I 2entering
through the two inputs. The free-domain can switch parallelto either of the two fixed input domains depending onwhich of the two inputs currents is larger and hence, this
device acts as a current-comparator. The minimum differ-
ence between the two inputs the BDWS can detect depends
on the critical current density for domain-wall shift in thefree-domain. A difference of few micro-amperes may be
detected using a 15 /C22n m
2domain cross-section, with
a critical current density of the order of 106A/cm2.
Micro-magnetic simulation results for two inputs of 5 lA
and 10 lA are given in Fig. 2(c).REcan be applied to the
free-layer for achieving enhanced DW-motion and hencehigher switching-speed in the free-domain. The state of
free-domain (domain-3) is read through the MTJ formed at
its top.
FIG. 1. (a) Domain wall magnet with
S-O coupling, (b) domain-wall veloc-ity vs. current density, with and with-
out SHE, (c) UDWS with spin-orbital
coupling, (d) transient micromagnetic
plots for DWS with 10 lA input cur-
rent, (e) device parameters for DWS.
FIG. 2. (a) BDWS based on domain-wall-switching, (b) top-view of the de-
vice, (c) micromagnetic simulation plots for the BDWS at three-time steps.
FIG. 3. (a) Interconnect design using UDWS, (b) transient simulation plots
for DWS-based interconnect at 2Gbps signaling-speed, (c) circuit for
on-chip and inter-chip interconnect using BDWS.17C737-2 M. Sharad and K. Roy J. Appl. Phys. 115, 17C737 (2014)III. INTERCONNECT DESIGN USING HIGH-SPEED
SPIN-TORQUE SWITCHES
Owing to its low-resistance, current-mode switching
channel, the DWS can act as an ideal current-mode receiver
and can simultaneously facilitate low-voltage ( /C2450 mV)
biasing of the entire transceiver-link,3as shown in Fig. 3(a).
On the transmitter-side linear region transistors biased at a
source potential of þ//C0DV, relative to the UDWS are used
for supplying the data dependent current. The use of small
DV(/C2450 mV) achieves low static power dissipation per-bit.
At the receiver-end, the MTJ associated with the UDWS
allows conversion of the spin-mode information into binary
voltage-levels through a resistive voltage-divider formed
with a reference MTJ. The ratio of parallel and anti-parallelspin-states of an MTJ is defined in terms of tunnel magneto-
resistance ratio (TMR).
3AT M Ro f /C24200% (corresponding
to resistance ratio of /C243) can provide a voltage swing close
to VDD/3 at the voltage divider output (where VDD is the
supply voltage), that can be sensed by a minimum-size
CMOS inverter (Fig. 3(a)). Thus, the UDWS can act as a
high-gain, ultra-low power, and compact trans-impedance
amplifier (TIA) that can facilitate the design of energy-
efficient current-mode global interconnects.2Simulation-
waveforms for MTJ-based transimpedance conversion are
shown in Fig. 3(b).
Fig. 3(c) depicts the circuit for a current-mode data
interconnect employing a BDWS. At the transmitter end, a
linear region PMOS transistor M1is driven by a voltage-
mode data-signal. Its source terminal is connected to aDC-voltage VþDV, where Vis 0.5 V and DVcan be less than
/C2450 mV. On the receiver side, the BDWS is biased at a volt-
ageV, as shown in the figure. A bias transistor, M2, on the
receiver-end injects a constant DC current (with half the am-
plitude of the input signal) into one of the two inputs of theDWS, which gets subtracted from the data-signal entering
into the other input. This results in data-dependent flipping
of the DWS free-domain. The received data can be detectedusing a high-resistance voltage divider formed between the
SWS-MTJ and a reference-MTJ, as shown in Fig. 3(c). Note
that the BDWS needs only one extra voltage-level for inter-connect operation, whereas the UDWS needs two.
IV. PERFORMANCE
We compare the proposed spin-based interconnect
design with three low-power global-interconnect techniquesbased on CMOS, namely, (1) low-swing, dual-supply link
8
(uses two different voltage levels separated by DVas shown
in Fig. 4(a)), (2) capacitively driven low-swing link,8and (3)
current-mode link.9Fig.4(a)shows that for reducing DVin a
dual-supply link, sense-amplifier and driver power increases
steeply. Similar trends are obtained for the other two cases.The CMOS current-mode transceiver needs a large supply
voltage for trans-impedance amplification of current-mode
signal, which limits the power savings.
8Moreover, analog
transceiver-circuits in these low-swing CMOS links are
significantly complex which make pipelining prohibitive.Spin-torque based compact TIA, on the other hand, can facil-
itate repetition of transceiver units for high-performance
data-buses. Fig. 4(b) shows the figure of merit (FOM,
defined as energy/bit/mm of Lch) of the proposed design with
the aforementioned CMOS techniques, showing close to two
order of magnitude reduction in energy.
Further experimental progress may achieve enhanced
DW-velocity in the range of /C241000 m/s,5which can lead to
powerful spintronic switches suitable for /C2410Gbps on-chip
transmission links for future high-performance processors.10
Experimentally calibrated physics-based simulation
framework for domain wall magnets presented in Ref. 11has
been used in this work. These models essentially involveself-consistent solutions for spin-diffusion transport and
magnet-dynamics in magneto-metallic devices constituting
magnet, metal, and magnet-metal interfaces.
11For circuit
simulations, the equivalent SPICE-circuit model for mag-
netic domains presented in Ref. 12were employed.
ACKNOWLEDGMENTS
This research was funded in part by NSF, SRC, DARPA,
MARCO, and StarNet.
1J. D. Owens et al.,IEEE Micro 27(5), 96–108 (2007).
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FIG. 4. (a) Simulation based determination of energy-optimal DVfor dual-
supply, low swing interconnect, showing increase in sense-amplifier energy
limits the lowering of DV(Lch¼5 mm). (b) Simulation based estimates for
signaling energy of different low swing CMOS interconnects (3Gbps) and
their comparison with proposed scheme (using UDWS), showing more than
100/C2improvement in energy/bit/mm.17C737-3 M. Sharad and K. Roy J. Appl. Phys. 115, 17C737 (2014) |
1.4896850.pdf | Assessment of primary energy conversions of oscillating
water columns. I. Hydrodynamic analysis
Wanan Sheng, Raymond Alcorn, and Anthony Lewis
Beaufort Research-Hydraulics and Maritime Research Centre, University College Cork,
Cork, Ireland
(Received 14 May 2014; accepted 19 September 2014; published online 29 September 2014)
This is an investigation on the development of a numerical assessment method for
the hydrodynamic performance of an oscillating water column (OWC) wave
energy converter. In the research work, a systematic study has been carried out on
how the hydrodynamic problem can be solved and represented reliably, focusingon the phenomena of the interactions of the wave-structure and the wave-internal
water surface. These phenomena are extensively examined numerically to show
how the hydrodynamic parameters can be reliably obtained and used for the OWCperformance assessment. In studying the dynamic system, a two-body system is
used for the OWC wave energy converter. The first body is the device itself, and
the second body is an imaginary “piston,” which replaces part of the water at theinternal water surface in the water column. One advantage of the two-body system
for an OWC wave energy converter is its physical representations, and therefore,
the relevant mathematical expressions and the numerical simulation can bestraightforward. That is, the main hydrodynamic parameters can be assessed using
the boundary element method of the potential flow in frequency domain, and the
relevant parameters are transformed directly from frequency domain to timedomain for the two-body system. However, as it is shown in the research, an
appropriate representation of the “imaginary” piston is very important, especially
when the relevant parameters have to be transformed from frequency-domain totime domain for a further analysis. The examples given in the research have shown
that the correct parameters transformed from frequency domain to time domain
can be a vital factor for a successful numerical simulation.
VC2014
AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4896850 ]
I. INTRODUCTION
Oscillating water column (OWC) wave energy converters have been often regarded as the
first generation of wave energy converters and maybe the most studied wave energy devices.
The early success of oscillating water column wave energy converters saw that hundreds of
small scale OWCs have been deployed to power the navigation buoys in remote areas (seeFalcao
1and Chozas2). The development has been since then advanced to large OWC wave
energy plants and now some practical OWC plants have been built and actually generated elec-
tricity to the grid. It is reported that the LIMPET OWC plant has generated electricity to thegrid for more than 60 000 h in a period of more than 10 years (Heath
3). A recent development
is the Mutriku OWC wave energy plant in Spain4—a multi-OWC wave energy plant with a
rated power of 296 kW, consisting of 16 sets of “Wells turbines þelectrical generator”
(18.5 kW each), is estimated a electricity generation of 600 MW h so far. [EVE, Mutriku OWC
Plant, http://www.fp7-marinet.eu/EVE-mutriku-owc-plant.html (accessed on 10/05/2014).]
OWC wave energy converters are one of the most adaptive concepts: they can be built on
shoreline or breakwaters in a bottom-fixed fashion (LIMPET, PICO, and Mutriku OWC plants),
or in near-shore in a form of either bottom-fixed or floating device or offshore in a form of
floating devices. Its adaptivity may be only matched by the overtopping wave energy
1941-7012/2014/6(5)/053113/24/$30.00 VC2014 AIP Publishing LLC 6, 053113-1JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 6, 053113 (2014)
converters, for example, the bottom-fixed Tapchan [Tapered Channel Wave Energy, http://taper-
edchannelwaveenergy.weebly.com/how-does-it-work.html (accessed on 10/05/2014)] and the
floating WaveDragon [Wave Dragon, http://www.wavedragon.net/index.php?option ¼com_
frontpage&Itemid ¼1(accessed on 10/05/2014)]. These types of the wave energy converters
have a particular advantage over many other types of wave energy converters in the develop-
ment stages: their pioneer wave energy plants can be simply built on shoreline. One advantageof the shoreline wave energy plants is that the problems with the wave-structure interaction
(partially), cable connections, and access to the plant are not present (it is also noted that moor-
ing system is not applied in this case), so that in their development stages, the focus can bemore on the wave energy conversion and power take-off (PTO) (air turbine and control system
and strategies). The experience accumulated and lessons learnt from these developments can be
then easily transplanted to the floating OWC wave energy converters, in which the focus canbe paid on the interaction of wave-structure, mooring system, and cabling connection since the
issues with PTO and control system have been addressed in those pioneer plants.
The second advantage of the OWC wave energy converters is their unique feature in power
conversion. In the OWC wave energy converters, the air flow is normally accelerated from the
very slow airflow in the chamber (driven by the internal water surface (IWS)) to a high-speed
airflow through the power take-off system by 50–150 times if the PTO air passage area ratio istaken 1:50–1:150 to the water column sectional area. This much accelerated air can drive the
air turbine to rotate in a high speed, typically a few hundreds RPM for the impulse turbines
and more than a thousand RPM for the Wells turbines (see O’Sullivan and Lewis
5). The high-
rotational speed of the air turbine PTO allows a direct connection to the generator, and thus
the bulky gearbox may not be necessary, and more importantly, for a certain power take-off,
the high rotational speed can also mean a small force or torque acting on the PTO system,which in turn ensures a high reliability in power take-off systems.
To understand and improve wave energy conversion by the OWC devices, numerical methods
have been developed. Earlier theoretical wo rk on the hydrodynamic performance of OWCs has
shown that OWC devices could have a high primary wave energy conversion efficiency if the opti-
mized damping can be attained (Sarmento and Falcao,
6Evans,7and Evans and Porter8)f o rt h o s e
fixed or simple OWC devices. For the more complic ated and practical OWC devices, the boundary
element method (BEM) (and the relevant commercial software, such as WAMIT [WAMIT, User
Manual, www.wamit.com/manual.htm (accessed on: 10/05/2014)], ANSYS AQWA [AQWA User
Manual, www.mecheng.osu.edu/documentation/Fluent14.5/145/wb_aqwa.pdf ( a c c e s s e do n1 0 / 0 5 /
2014)], etc.) can be readily available for any com plexity of the geometries. Regarding the full
scale device, there may be air compressibility problems. Due to the non linearity and the non-
Froude similarity nature (see Weber9and Sheng et al.10), the air compressibility in the air chamber
may not be evident or present in the small scaled models because the scaled models have normally
small scaled air volumes and pressures in the air chamber. Sarmento et al.11have proposed a line-
arized formula for the flowrate through the power take-off system, based on an assumption of anisentropic flow. Sheng et al.
12have recently formulated a full thermodynamic equation for the air
flow in the chamber by invoking the simple PTO relation of the chamber pressure-flowrate which,
though simple, has included all the effects of the flow through the air turbin e, hence, the detailed
complicated air flow through the turbine can be av oided (note: for improving the performance of
the air turbine, the detailed air flow through the t urbine is still very important if the turbine per-
formance is examined). More recently, Sheng et al.13have also coupled the hydrodynamics and
the thermodynamics for a bottom-fixed generic O WC device and have predicted the internal water
surface and chamber pressure very well when compared to the experimental data.
So far, though successful to some extent, a reliable numerical simulation for the perform-
ance of the OWC wave energy converters is not available yet. Hence, the development of
OWC wave energy converters frequently relies on the experiments in laboratories. Essentially,
physical models include all the effects if the scaling is well prepared. For instance, the modelshould be large enough to ensure the scaling correct in which the Reynolds number would be
large enough to minimise the Reynolds effect (see Sheng et al.
10). In physical model tests, the
scaled OWC models mean smaller air chambers and smaller chamber pressure responses, and053113-2 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)therefore, the air compressibility (i.e., the “spring-like effect”) cannot be scaled and present.
Nonetheless, experiments could provide valuable assessments to the performance of the OWC
devices if the model tests are well conducted. For example, experimental studies on the
bottom-fixed or floating OWCs have shown that the wave energy conversion efficiency of an
OWC device very much depends on the damping coefficients of the flow passing through the
power take-off system, as well as the size and length of the water column (water column sec-tional area and length). Toyota et al.
14have shown that both the size of the air chamber and
the length of the horizontal duct length of a Backward Bent Duct Buoy (BBDB) device have
significant effects on the primary power conversion of the OWC wave energy converters. Imaiet al.
15have studied the influence of the horizontal duct length to the wave energy capture
capacity in a BBDB device and shown that a longer horizontal duct has increased the maximum
IWS response to a longer resonance period. As a result of this, a longer horizontal duct may bedesirable for tuning the BBDB to the wave states of longer wave periods. Morris-Thomas
et al.
16have experimentally studied the hydrodynamic efficiency on fixed OWCs with different
front shapes. From the comparison, it can be seen that the front shapes have some but limitedinfluence on the wave energy conversion efficiencies of the fixed OWC. For the four different
front shapes, the wave energy capture efficiencies are overall similar, and the maximum wave
energy conversion efficiency is about 70%, but no reason has been given why the maximumwave energy conversion efficiency is only about 70%.
Generally, reliable numerical assessments have not been well established for OWC wave
energy converters though this type of wave energy converter has been widely studied and mayhave a longest history when compared to other types of wave energy converters. In this
research, the focus is on the development of a numerical assessment method for the hydrody-
namic performance of OWC wave energy converters, and the details on how to reliably assessthe hydrodynamic performance, which is a prerequisite condition in the overall performance
assessment for an oscillating water column wave energy converter, are presented and discussed.
Examples have shown that special care must be taken if a reliable hydrodynamic model isdeemed to be developed for the OWC wave energy converter.
II. METHODOLOGY
A. Frequency domain analysis
Potential theory has been well-developed in the last century and now widely used in marine
and offshore applications, and more recently applied in wave energy conversions, including the
oscillating water column devices.
For some specific OWC devices, such as two-dimensional OWC devices, or some three-
dimensional OWCs with simple structures, analytical solutions are possible (Evans and Porter,8
Martins-rivas and Mei,17and Mavrakos and Konispoliatis18), but more popular approaches are
the numerical analysis using the commercial codes based on the boundary element method,such as WAMIT and ANSYS AQWA. These commercial codes are readily available for any
geometry of interest.
Based on the assumption of the potential flow, the velocity potential of the flow around the
floating structure satisfies the Laplace equation,
r
2u¼0; (1)
where uis the frequency-domain velocity potential of the flow around the floating structure
(the corresponding time-dependent velocity potential should read U¼ueixtsince the dynamic
system is assumed to be linear in the hydrodynamic study).
An earth-fixed coordinate system is defined for the potential flow problem. The coordinate
is fixed in such a way that the x-yplane is on the calm water surface and z-axis positive up ver-
tically. In the coordinate, the free surface conditions can be expressed in the frequency domain
(see Lee and Nielsen19), as053113-3 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)@u
@z/C0x2
gu¼0; on S f ðÞ
/C0ix
qgp0; on S i ðÞ ;8
<
:(2)
where xis the wave frequency, qis the density of water, gis the acceleration of gravity, p0is
the pressure amplitude acting on the internal free surface, Siis the internal free surface in the
water column, and Sfis the free surface but excludes the internal free surface.
It must be noted that the pressure amplitude acting on the internal free surface is an
unknown, which must be solved when a power take-off system is applied.
Hydrodynamically, the water surface in an OWC can be regarded as a moonpool, which
has been found applications in the operations of offshore platforms and studied in theoretical
and numerical approaches (see Refs. 20–23). The difference between a moonpool and an oscil-
lating water column is that the application of the power take-off system in the OWC waveenergy converters will apply a reciprocating pressure (the alternative positive and negative
chamber pressure, and they may be nonlinear if the nonlinear PTO is applied) on the internal
water surface, which would make the problem more complicated.
To solve the linear hydrodynamic problems in the OWC wave energy devices, different
approaches have been developed and used. The popular approaches include the massless piston
model
19,24and the pressure distribution model.7In the former approach, the internal free sur-
face is assumed to behave as a massless rigid piston (a zero-thickness structure), and the target
solution is the motion of the internal water surface. The internal water surface motion is then
coupled with the PTO so that the chamber pressure can be solved. A slightly different versionof the massless piston model is a two-body system for the OWCs, in which the first rigid body
is the device itself and the second rigid body is an imaginary thin piston at the internal free sur-
face to replace part of the water body in the water column. Hydrodynamically, the two-bodiesare strongly coupled (see Refs. 13,25, and 26). By applying a power take-off system, the rela-
tive motion between the two-body could produce a reciprocating pressure in the air chamber. In
the latter approach, the internal free-surface condition is represented in terms of the dynamicair pressure in the chamber (see Refs. 27and28) and in the numerical simulation, a reciprocity
relation must be employed as shown by Falnes
29so that the conventional BEM can be used.
However, it must be pointed out that this method may be only applicable for the cases of linearPTOs. Tank test and field test data have shown the nonlinear chamber pressure (with both wave
frequency and high frequency components in regular waves) even though the internal water sur-
face motion can be reasonably linear when a nonlinear PTO is applied for wave energyconversion.
Relatively, the physical meaning of the first approach is more obvious, and its implementa-
tion in the numerical assessment is more straightforward. Hence in this research, this approachis applied and studied.
To represent the dynamic system better, a convention for a two-body system is used: The
motion modes of the first body are given by x
i(i¼1, 2,…, 6), corresponding to the first rigid
body motions of surge, sway, heave, roll, pitch, and yaw, respectively, and the motion modes
of the second body are given as xi(i¼7, 8,…, 12), which corresponds to the 6 degrees of free-
dom motion of the second body, i.e., surge, sway, heave, roll, pitch, and yaw. To simplify the
analysis in the oscillating water column wave energy conversion, only the heave motions of the
two bodies are considered for power conversion, because for power conversion in the OWC,the other motion modes may not be useful in contributing to generate power in this particular
case, and because it is generally acceptable when the motions are not too severe, the heave
motions may not be coupled with other types of motions (the generic OWC considered in theresearch has an axi-symmetrical structure).
The heave motions of the two bodies in frequency domain can be written as
f/C0x
2½m33þa33ðxÞ/C138 þixb33ðxÞþc33gf3þf /C0 x2a39ðxÞþixb39ðxÞþc39gf9¼f3ðxÞ;
f/C0x2a93ðxÞþixb93ðxÞþc93gf3þf /C0 x2½m99þa99ðxÞ/C138 þixb99ðxÞþc99gf9¼f9ðxÞ;(
(3)053113-4 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)where m33andm99are the masses of the first and the second bodies; a33(x),a39(x),a93(x),
and a99(x) are the frequency-dependent added masses for the heave motion for the first and
second bodies and their interactions at the infinite frequency; c33,c99andc93,c39are the restor-
ing force coefficients and their interactions (hydrostatic coefficients); b33,b99andb93,b39are
the hydrodynamic damping coefficients for heave motions and their interactions; f3andf9are
the excitations for the first and second bodies, and f3andf9are the complex heave motion am-
plitude of the two bodies, respectively.
Solving Eq. (3), the relative heave motion (complex) between the two bodies termed as the
IWS can be calculated as
fr¼f9/C0f3: (4)
Here, f3andf9are the complex heave motion amplitudes for both bodies.
Accordingly, the amplitude responses of the device heave motion, X3, the piston heave
motion, X9, and the internal water surface motion, Xr, are given as follows:
X3¼jf3j
A
X9¼jf9j
A
Xr¼jfrj
A;8
>>>>>>><
>>>>>>>:(5)
or
X
3¼2jf3j
H
X9¼2jf9j
H
Xr¼2jfrj
H;8
>>>>>>><
>>>>>>>:(6)
where AandHare the amplitude and height of the incoming wave, respectively, and j*jmeans
the modulus of the complex response.
B. Time domain analysis
For OWC wave energy converters, the whole dynamics may very likely be nonlinear if an
air turbine PTO take-off system is included, for example, a linear Wells turbine. When a full
scale OWC device is considered, the air chamber and the pressure can be large enough, so thatthe air compressibility in the air chamber can be obvious (see Falcao and Justino
30), which is
essentially nonlinear. If mooring system is included, the nonlinearity will be more obvious
when the large motions of the device are induced. For a nonlinear dynamic system, frequency-domain analysis is no longer suitable; hence a time domain analysis must be employed.
In the time-domain analysis in the research work, the Cummins-Ogilvie hybrid frequency-
time domain analysis is used, in which the hydrodynamic parameters can be first analysed infrequency domain, and then the Cummins time-domain equation is established using the
Ogilvie’s relation (Cummins
31and Ogilvie32). This hybrid frequency-time domain approach has
been a popular choice in the development of wave energy conversions.27,33–36The nonlinear
effects from PTO or any other sources can be fully implemented in the time-domain analysis.
1. Time domain equations
To simplify the problem in the oscillating water column wave energy conversion, we
assume only the heave motions of the two bodies are useful for power conversion. The053113-5 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)assumption may be acceptable when the motions are not too severe, and the heave motion may
not be coupled with other types of motions, especially for the cylinder-type structures.
The heave motion of the two bodies can be written in time-domain as
½m33þA33ð1Þ/C138 €x3ðtÞþðt
0K33ðt/C0sÞ_x3ðsÞdsþC33x3ðtÞþA39ð1Þ €x9ðtÞ
þðt
0K39ðt/C0sÞ_x9ðsÞdsþC39x9ðtÞ¼F3ðtÞ; (7)
A93ð1Þ €x3ðtÞþðt
0K93ðt/C0sÞ_x3ðsÞdsþC93x3ðtÞþ½m99þA99ð1Þ/C138 €x9ðtÞ
þðt
0K99ðt/C0sÞ_x9ðsÞdsþC99x9ðtÞ¼F9ðtÞ; (8)
where m33andm99are the masses of the first and the second bodies; A33(1),A39(1),A93(1),
andA99(1) are the added masses for the heave motion for the first and second bodies and their
interactions at the infinite frequency; C33,C99andC93,C39are the restoring force coefficients
and their interactions; K33,K99andK93,K39are the impulse functions for heave motions and
their interactions; F3andF9are the excitations for the first and second bodies.
The impulse functions can be obtained if the frequency-domain added mass or damping
coefficients have been assessed via the transform as
KijtðÞ¼2
pð1
0bijxðÞcosxtdx; (9)
or
KijtðÞ¼2
pð1
0xaijxðÞ/C0aij1ðÞ/C2/C3sinxtdx; (10)
where aijandbijare the added mass and damping coefficients in frequency domain, aij(1)i s
the added mass at the infinite frequency, which is a frequency-independent value.
2. IWS motion in time domain
The internal water surface in the water column is the parameter for creating a reciprocating
chamber pressure in the air chamber, thus the pneumatic power which can be used for powerconversion. The internal water surface motion is given by the relative heave motions of the two
bodies as
x
rðtÞ¼x9ðtÞ/C0x3ðtÞ: (11)
III. PISTON REPRESENTATION
To illustrate the problem more clearly, a cylindrical OWC wave energy converter is consid-
ered here. This is a generic OWC wave energy converter which has been widely tested and
studied in HMRC wave basin (see Sheng et al.37). A photo of the device is shown in Figure 1.
The OWC device has a schematic drawing of the vertical section shown in Figure 2. The
whole column of the device (the water and air columns) has a diameter of 0.23 m, and an over-
all length of 0.3 m, of which 0.15 m is emerged in water (i.e., a draft of 0.15 m). The device
has a float of 0.04 m thick and 0.2 m high surround the entire column providing the buoyancy
and stability for the device and 0.10 m submerged in water. A circular plate is fixed on the top053113-6 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)of the air column, with an orifice in middle to model a nonlinear PTO take-off (that is, a non-
linear air turbine PTO). The overall weight of the device is 3.39 kg. The device was also bal-
lasted for a good stability to float rightly in the waves.
As shown in Figure 2, a piston is used to represent part of the water body in the water col-
umn (in the figure half of the length of the water body in the device column), whose motion can
be equivalent to the uniform motion of the water body in the water column. For wave energy
conversion, the up-and-down motions of the piston relative to the column structure can generatea pressurised and de-pressurised air in the air chamber which could exhale or inhale air through
the air turbine and to drive it to rotate, so to generate electricity if it is connected to a generator.
A. Natural period of the piston motion
As shown by Evans and Porter,8the interior free surface has a natural period, T0, if the
length of the cylinder is much larger than its diameter (actually this condition is not well satis-
fied in this case, but for a comparison, the formula is used) as
FIG. 1. A generic cylinder OWC wave energy converter.
FIG. 2. Water column in water and the corresponding piston (the length of the piston is same as the full length of the water
column).053113-7 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)T0¼2pffiffiffiffi
D
gs
¼0:777s; (12)
where D(¼0.15 m) is the draft of the water depth or the length of the water column and gthe
gravity acceleration. This formula corresponds to the natural period of a cylinder of a draft D
in water without a correction from the added mass.
If the imaginary piston is considered as an isolated cylinder, its added mass for the heave
motion has been given according to McCormick (Ref. 38, p. 48) when the draft Dis far larger
than its diameter (again, this condition is not fully satisfied. But unlike the previous case, the
added mass has been included. And for comparison, the formula is again used here) as follows:
a33¼2:664qR3; (13)
where Ris the radius of the cylinder.
The corresponding natural period of the heave motion would be
T0¼2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Dþ0:848R
gs
¼0:998s: (14)
For a large water column or a moonpool, its natural period of the water surface motion has
been studied by Veer and Thorlen,23and they gave a formula for the calculation of the natural
period of the internal water surface motion as
T0¼2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Dþ0:41/C3S1=2
0
gs
¼0:970s; (15)
where S0is the sectional area of the moonpool/water column.
A more appropriate approach in obtaining the internal water surface motion, and thus its rele-
vant natural period is employing the conventional BEM (in this case, WAMIT). In the BEM code,
the interaction between the water body and the flo ating structure is fully accounted. Hence, the
natural period of the internal water surface wo uld be more accurately calculated via the BEM.
All the natural periods using different formulas, including the one obtained from WAMIT
simulation are listed in Table I. One can see that those semi-empirical and numerical methods
give quite similar estimations to the natural period of the internal water surface motion if an
appropriate added mass can be included.
In this study, WAMIT has also been used to study the behaviour of the device and the inter-
nal water surface. In the simulation, the two-body system has been used. Figure 3shows that the
device and the piston have different natural periods (two spikes in the responses in Figure 3), that
is, the imaginary piston has a natural period of 0.935 s, which is close to the results fromEqs. (14) and(15), but larger than that given by Eq. (12), whilst the heave motion of the device
has a natural period of 0.740 s.
From Figure 3, it can be also seen that both heave motion responses of the device and the
piston are modified due to their interaction. For the heave response of the device, there is a
TABLE I. Natural periods of the internal water surface.
Method Natural period of internal water surface, T0 Reference
Evans et al. 0.777 s 8
McCormick 0.998 s 38
Veer et al. 0.970 s 23
WAMIT 0.935 s …053113-8 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)small response when the wave period is at the natural period of the piston heave motion; while
for the piston response, due to the heave motion of the device, the response is modified signifi-cantly when the wave period is at the natural period of the heave motion of the device. As a
result of the relative heave motion between the cylinder and the piston, the IWS motion ( Xr)
has two peaks which correspond to the natural periods of the device and the piston heavemotion, respectively. All three responses have large peak values (more than 5.0). This is mainly
because in WAMIT, only hydrodynamic damping is considered, while the other types of the
damping, for instance, the viscous damping, are ignored in the analysis.
B. Piston length and motion responses
As it is well known that, in many cases in studying an OWC wave energy converter, the
water column of an OWC device has been represented by a thin piston or a zero thickness
structure.25,26The zero thickness structure is replaced the internal free surface (see Figure 4). It
has been shown theoretically by Falcao et al.25(also Evan et al.24) that the added mass for the
thin rigid-body is the entire entrained-water by the water column plus some additional added-
mass. This interesting result can be taken that the mass of the thin piston plus the entrainedwater (i.e., the major part of the corresponding added-mass) may be possibly equivalent to that
FIG. 3. Responses of the heave motions of the float and the piston and their relative motion (X3-heave response of the
device; X9-heave response of the piston; Xr-the relative response of the internal water surface).
FIG. 4. A very thin piston on the internal free surface (L is small or zero).053113-9 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)of a full piston. An extreme case of the thin piston is the zero thickness structure (i.e., a mass-
less piston), which has been also studied by Lee et al.19,39via a method called “generalised
modes,” and the generalised modes for the internal water surface motion can be simply speci-
fied as the additional motion modes in the boundary element codes, so that a significant modifi-
cation to the code is not necessary. As can be seen in many practical cases, the thin/massless
pistons or the full pistons are both popular in studying the performance of an OWC device.Therefore, there may be a question, what will happen if a certain length of the piston is consid-
ered, as shown in Figure 5.
In the above OWC device, a longest piston length could be the full length of the water
column of 0.15 m (i.e., L¼0.15 m, where Lis the actual length of the piston), and the shortest
piston length is zero in the massless piston (Figure 4). In-between, the length of the piston
could be any length between 0.0 m and 0.15 m (Figure 5). In Figure 6, a comparison of the in-
ternal water surface responses for different piston lengths is shown (the lengths “ L¼0.001 m,”
“L¼0.01 m,” etc., indicating the lengths of the pistons). It can be seen that the IWS responses
are very similar when the wave period is larger than 0.5 s for all five piston lengths (Figure 6).
However, the values at the second peaks may be slightly different for the different lengths of
the pistons, especially for the full length of the piston ( L¼0.15 m). And in all these responses,
there are two obvious resonances: the first resonance of a shorter period corresponds to thedevice heave motion resonance and the second resonance corresponds to the natural period of
the pistons. From the comparison, it can also be seen that in the region of very short periods,
the IWS responses can be very different for short pistons (see Figure 7): these response spikes
may correspond to their inherent natural periods of the “pistons” when they are not isolated
without the interaction from the water column structures. The shorter the piston, the shorter the
natural period is (can be deduced from Eqs. (12),(14),o r(15)). In the frequency domain analy-
sis, the relative internal water surface motion responses are dominated by the heave responses
of the two bodies. The small spikes of the motion responses in very short waves are often
beyond any interest (not power extraction from that!).
It must be noted that in the IWS responses in Figures 6and7, they are only damped via
their inherent hydrodynamic damping coefficients. Hence, the responses are relatively high at
the corresponding resonance periods.
C. Piston length and added mass
When a time domain analysis is needed for the dynamics of the wave energy converter, the
relevant hydrodynamic parameters can be obtained by a transform from frequency domain to
time domain, based on the Cummins time domain equation31and the Ogilvie relation.32This
FIG. 5. An illustration of a thick piston for representing the internal free surface.053113-10 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)method has been often named as hybrid frequency-time domain method36and very popular in
the applications in wave energy conversion thanks to its low computation burden and its
straightforward physical meaning. One important aspect in such an application is the assessmentof the added mass at the infinite frequency, because this special added mass and the device
mass itself can form the overall mass in the dynamic system in the time domain system, which
in turn very much decides the dynamic responses of the system, especially the resonanceresponse. Hence, its correctness is of vital importance in such a dynamic system.
Table IIshows the masses and the added-masses at infinite frequency for the pistons and
the device from the simulations using WAMIT. For the massless piston (its length D¼0.0 m),
the “generalised modes” have been used, which represents the IWS motion (named as the
mode 7), while for the cases of certain lengths of pistons, two-body system is used in WAMIT
simulations.
From the table, the added masses for the device heave motion at the infinite frequency are
very close except the one in the massless case, which is obviously “wrong” (a very large nega-
tive added mass!). And the added mass for the “generalised mode” is also wrong (even a largernegative added mass). For the cases of certain lengths of the pistons, the overall mass for the pis-
ton can be different, and their correctness will be examined later in this research. However, one
can see that when the piston length is larger than 0.05 m, the overall mass (given by the massand added mass together) is very similar, though the piston mass itself can be very different
(2.08 kg for the piston length 0.05 m and 6.23 kg for the piston length of 0.15 m), see Figure 8.FIG. 6. IWS response predictions with a 2-body system.
FIG. 7. IWS response predictions (zoom for the responses in short periods).053113-11 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)Figure 9shows a comparison of the added mass for four different lengths of the pistons.
From the figure, it can be seen that for the cases of small lengths of the piston, its added mass
can be a large positive or negative value at certain short periods. These very spiky added
masses (both large positive and negative) happen at the different periods for the differentlengths of the pistons ( T¼0.76 s for L¼0.15 m, T¼0.445 s for L¼0.05 m, and so on), the cor-
responding periods should be very close to the piston natural periods in the absence of the
interaction between the piston and the device. Figure 10shows a comparison for long
(L¼0.10 m and L¼0.15 m). For the cases of piston lengths of 0.10 m and 0.15 m, the added
mass may still be spiky at very short waves, where the negative and positive added masses can
be seen clearly, but not as severe as those of shorter pistons.
The added mass in high frequencies (very short waves) are difficult to calculate, though in
WAMIT, it is possible to specify a simulation so that the added mass at infinite frequency can
be calculated. However, in many practical cases, we may assume that the added mass at a fre-quency large enough can be taken as the added mass at infinite frequency. Then a question
may arise: how large of the frequency is enough?
Figure 11shows the added mass calculations in very short waves of wave periods from
0.005 s to 0.25 s, which correspond to high frequencies 25.1 rad/s and 1256 rad/s, respectively,
for the pistons with different lengths. It can be seen that the added mass for L¼0.15 m and
L¼0.05 m are very steady in most of the periods, but not in the very short wave periods. For
the case of L¼0.001 m, the added mass tends to be steady, but it is very close to zero.
Obviously, it is not correct, and the issue will be further discussed later in this research. For the
case of the piston L¼0.01 m, it is varying very much at all high frequencies.
To calculate the internal water surface motion correctly, the correct calculations of the rele-
vant parameters for the time domain equations (7)and(8)are very important. Among them, the
calculation of the added mass at the infinite frequency is extremely important. Due to the limi-tation of the panels in the numerical simulation, the calculation of the added mass at infinite
frequency is not reliable as other conventional hydrodynamic parameters, which may causeTABLE II. Piston mass and its added mass.
Piston L(m) 0 0.001 0.005 0.01 0.02 0.05 0.1 0.15
M33 3.39 3.39 3.39 3.39 3.39 3.39 3.39 3.39
A33 /C043.44 1.43 1.44 1.44 1.45 1.45 1.45 1.46
A77(1) /C070.10 … … … … … … …
M99 … 0.04 0.21 0.42 0.83 2.08 4.15 6.23
A99(1) … 4.35 5.77 6.30 6.66 6.43 4.66 2.93
M99þA99(1) … 4.39 5.98 6.72 7.49 8.51 8.81 9.16
FIG. 8. Masses and the added masses of the pistons in different lengths.053113-12 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)FIG. 9. Added mass predictions for the pistons with different lengths.
FIG. 10. Added mass predictions for the pistons (L ¼0.10 m and L ¼0.15 m).
FIG. 11. Added mass in high frequency waves (very short waves).053113-13 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)serious problems in the time-domain analysis, because the dynamic responses are fully related
to the overall mass in the dynamic system. This becomes more obvious when the piston is cho-
sen as a massless (i.e., a zero-length piston) or a very thin piston, the added mass at the infinite
frequency may be wrongly calculated (the huge spiky added mass for very short waves, see
Figure 11). The reason for this may be due to the zero or very short length of the piston for
which the corresponding natural period of the piston itself may be extremely small.
Relatively, the added mass at the infinite frequency is more reliable and may be easier to
obtain when the piston is long.
The utilisation of the different pistons in the numerical simulation of the OWC wave
energy converters may have some practical benefits and considerations. As it is shown that for
a full-length of a piston, it seems beneficial because more reliable and stable added mass can
be relatively easy to attain. However, a full length piston in an OWC device is only possiblewhen the OWC has a uniform water column. Unfortunately, this is not the case in many engi-
neering applications. A good example is the BBDB OWC device.
14,40,41Their bent duct of the
BBDB device does not allow a full length of a piston to be implemented if a two-body systemis used. Hence, it is an advantage to choose an appropriate length of the piston for representing
the internal water surface in this regard.
In some practical applications, people have to make a decision how large of the frequency
is enough when its added mass can be taken as the added mass at infinite frequency. Table III
shows the added mass at different frequencies for the pistons with different lengths. When the
massless piston is used, the added mass at infinite frequency is a large negative value, which isobviously incorrect. For short lengths of the pistons, its added mass will be very varying
regarding to the frequencies. In this particular example, when the piston length is longer than
0.05 m, the added mass tends to be steady regardless of the frequencies (also see Figure 12).
However, it must be noted that even for the longest piston ( L¼0.15 m), its added mass at very
high frequency can be unsteady significantly (see Figure 11). Hence, it can be very tricky when
the added mass is decided if the real added mass at infinite frequency is not available. In addi-tion, for the case of massless piston, or the very short piston ( L<0.05 m), the added mass at in-
finite frequency is not well predicted. This may cause a large variation when the added mass at
infinite frequency is calculated when compared to other cases in Table III.
D. Piston length and hydrodynamic damping coefficient
For the pistons with different lengths, the damping coefficients are all very close, especially
when the wave periods are long, for instance, larger than 0.5 s (see Figures 13(a) and13(b) ),
and for very short pistons, the vibrant damping coefficients can be seen in very short waves
when its period is less than 0.25 s. In this vibrant coefficients, negative damping coefficientscan be also seen. It is believed that the negative damping coefficients may be caused by the
inappropriate panel sizes for those very short waves. If the pistons are longer, the vibrant damp-
ing coefficients are less severe. However, it can be seen that corresponding to the inherent natu-ral periods, the damping coefficients exhibit large changes (see Figure 13(b) ).
TABLE III. Added mass (in kg) at different frequencies.
L(m) x¼10 rad/s x¼20 rad/s x¼40 rad/s x¼80 rad/s x¼1
0 8.869 6.833 23.177 0.043 /C070.10
0.001 8.918 12.369 /C00.713 0.282 4.348
0.005 8.751 10.915 0.437 /C00.995 5.771
0.01 8.551 11.345 3.784 7.272 6.304
0.02 8.158 22.029 6.074 6.559 6.663
0.05 6.907 6.055 6.373 6.418 6.4290.1 2.967 4.608 4.650 4.662 4.662
0.15 2.746 2.903 2.927 2.933 2.934053113-14 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)E. Piston length and impulse function
Figure 14shows the comparison of the impulse functions for the heave motions of the pis-
tons of different lengths. It can be seen that impulse functions are very similar, regardless of
the piston lengths. One can notice that for the piston of length 0.10 m, some high frequency
oscillations can be seen for a long time, which is corresponding to large spike at its inherentnatural period. It will be seen later in the research that the small oscillations in the impulse
function for L¼0.10 m will not cause any problem in the time-domain simulation, because this
frequency of the impulse function oscillation is very different from that of the natural frequencyof the dynamic system, and its influence to the motion responses is very small.
In the calculation of the impulse functions, the spiky damping coefficients must be taken
carefully, otherwise it can create a very vibrant oscillation in the impulse functions. To getgood impulse functions shown in Figure 14, the hydrodynamic damping coefficients are
actually those shown in Figure 15, in which the very spiky damping coefficients in high fre-
quencies should not be included in the calculation.
F. Piston length and excitation
Figure 16shows a comparison of the excitation given in the WAMIT simulations. It can
be seen that when the wave periods is longer than 1.0 s, the excitations for the different pistons
FIG. 12. Added mass at different frequencies for different “pistons” (compared to the added mass “black dots” at infinite
frequency).
FIG. 13. Damping coefficients for the pistons of different lengths.053113-15 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)FIG. 14. Impulse functions for the pistons of different lengths.
FIG. 15. Damping coefficients for the piston of different lengths.
FIG. 16. Excitations on the pistons of difference lengths.053113-16 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)are almost identical. However, for very short wave periods, the excitation can be very spiky
(see both Figures 16and17). The maximum values can be much larger than the excitation in
the longer waves. The reason for this may be the interaction between the float and the piston,
and it may be also caused due to the panel limitation for the calculation in very short waves
(see the following comments on this issue). However, the very large spiky excitations do not
create same spiky motion responses (see Figures 3and6). The reason why the very spiky exci-
tations do not generate large responses is that the corresponding periods are much shorter than
the natural periods of the pistons in the dynamic system.
1. Comments on the piston representation
Some additional comments are given as follows:
First of all, in the boundary element method employed in this study, the generation of the
appropriate panels must be considered carefully. For a good simulation, as a rule of thumb, the
largest length of the panels in the simulation must be smaller than 1/7 of the wave length.42
Meanwhile, a good practice in the panel generation is to avoid any rapid change in the sizes of
the adjacent panels. Ideally, the adjacent panels would have a similar size (WAMIT manual).
In this regard, the simulation at the infinite frequency or very high frequencies may be not sat-
isfactory, since the panels satisfying the conditions are impossible. However, this does notmean the calculation of the added mass at infinite frequency can not be conducted. Examples
have shown that the reliable results for the added mass at infinite frequency may be obtained,
but care must be taken for those very short pistons as shown in the example.
The second comment will be on the natural periods of the pistons. If there is no interaction
between the piston and the device itself, a thin piston would have a short natural period in
heave according to Eqs. (12),(14),o r(15) (note: in the calculation, Lshould be taken as the
actual length of the piston, rather than the length of the water column). In this regard, it can be
deduced that the heave resonance period will be longer for a longer piston. Then why all the
pistons mentioned above have same natural periods, regardless of the piston lengths?
Indeed, the thin piston has a short natural period in heave, which can be given by Eqs.
(12),(14),o r (15), and this will become evident when we look at the effect of the piston
lengths later in the research. However, due to the interaction between the float body and theimaginary pistons, in the dynamic system, the mass and added mass must be considered to-
gether, as shown in Table II. Meanwhile, it can be also understood when a very thin piston is
considered, it will perform as a “wave rider,” which only follows the motion of the water bodyin the water column in waves. Hence in this regard, the motion of the water body (i.e., the full
piston) decides the motion of the piston. This may explain why different pistons experience
same responses.
FIG. 17. Excitations on the pistons of difference lengths (zoom).053113-17 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)IV. RESULTS AND ANALYSIS
For studying the time domain analysis, irregular waves of a significant wave height
Hs¼0.1 m and a mean period of T01¼1.0 s are chosen due to its closeness to the resonance
periods of the piston motion ( T0¼0.934 s).
In the irregular waves, the effects of the infinite frequency added mass to the motions are
examined here. An important factor in the time domain analysis is the assessment of the addedmass at infinite frequency. From the time domain equations (7)and(8), the natural frequency
of the dynamic system will be very much decided by the restoring coefficient and the total
mass (structure or piston mass plus their added mass at infinite frequency). Hence, the reliablecomputation of the added mass at infinite frequency is of vital importance.
As shown in Ref. 43, the time domain result can be checked when it is compared to the
transferred result from the frequency domain response, because the later analysis has onlyrelated to the parameters at the relevant wave frequencies, rather than the problems in assessing
the infinite frequency added mass.
A. Criteria of accuracy
Following Sheng and Lewis,44two values are used to assess the goodness of the time-
domain simulation. The first value is the commonly used correlation coefficient (“ R”), which is
a good indicator of the two time-series in phase comparison, but not in the relative amplitudes.
For instance, when two time series are fully in phase regardless of their very different ampli-
tudes, the correlation between them would be a unit.
The correlation coefficient is calculated as
R¼PN
i¼1xi/C0/C22x ðÞ yi/C0/C22y ðÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PN
i¼1xi/C0/C22x ðÞ2PN
i¼1yi/C0/C22y ðÞ2s : (16)
The second value is the relative square root error (“ RRE”), which can be used for distin-
guishing the actual difference between the two time series. This relative square root error is
employed because it removes the effects of the absolute amplitude in the target time series. The
RRE can be calculated as
RRE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PN
i¼1yi/C0xi ðÞ2
PN
i¼1yi/C0/C22y ðÞ2vuuuuuut: (17)
B. Bottom-fixed OWC
In the first case, the time domain analyses have been conducted for the OWC device in a
fixed manner, hence there is no motion for the device, but the piston heave motion (i.e., the in-ternal water surface in this case) can be calculated without a consideration of the device heave
motion. Figures 18–22show the comparisons between the time domain analysis and the fre-
quency domain analysis for the different length pistons. It can be seen when the piston is very
short, the time domain simulation shows significant differences to the result from the frequency
domain analysis (see Figures 18and19). The main reason for the difference is the added mass
at infinite frequency, as it can be seen in Figure 8, for the very short piston, the added mass at
infinite frequency is well underpredicted, hence the corresponding dynamic system for a very
short piston would have a higher natural frequency than it should be, so in the specific irregular053113-18 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)FIG. 18. Heave motion of the piston (piston length L ¼0.001 m).
FIG. 19. Heave motion of the piston (piston length L ¼0.01 m).
FIG. 20. Heave motion of the piston (piston length L ¼0.05 m).
FIG. 21. Heave motion of the piston (piston length L ¼0.10 m).053113-19 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)wave, the heave motion of the piston is far away from the resonance with the wave, that is
why the amplitude of the piston heave motion is much smaller than it should be (note: the
damping and the excitation for all pistons are very similar from Figures 16and14).
When the piston is getting longer, better time domain result can be seen, because their cal-
culated overall mass is getting closer to the actual one, and thus the dynamic system would
have a closer natural frequency to the actual one. For the lengths L¼0.10 m and L¼0.15 m,
the time-domain result is almost identical to that from the frequency domain (Figures 21and
22). Table IVshows the accuracy of the time domain analysis. It can be seen that in the cases
of the very short pistons, the accuracy of the time domain analysis is very low. The correlationcoefficient is getting larger when the piston is getting longer, while the RRE is getting smaller,
which indicates the closeness of the two time series. For the cases of L¼0.10 m and
L¼0.15 m, the correlation coefficients are close to unit, which means that the two time series
are very much in phase, while the corresponding small RRE means a small difference between
the two time series.
C. Floating OWC
Similar to the cases of the bottom-fixed OWC, the time domain analyses have been carried
out for the floating OWC device, in which the OWC device itself and the imaginary piston can
both move un-restrainedly. Figures 23–26show the comparisons between the time domain and
the frequency domain analyses when the pistons of different lengths are used. Again, it can beseen that when the piston is very short, the time domain simulation shows significant difference
to that from the frequency domain analysis (see Figure 23). When the piston is getting longer,
better time domain analysis result can be seen. Again, for the lengths L¼0.10 m and
L¼0.15 m, the time-domain result is same as that from the frequency domain (Figures 25and
26). Table Vshows the accuracy analysis of the time domain simulations, which is very similar
to Table IV, and hence same conclusions can also be drawn.
It must be pointed out that the prediction of the heave motion of structure is better repro-
duced than that of the heave motion of piston, especially when the piston is short. The reason
for this is the added mass at infinite frequency for the device heave motion is very much reli-able regardless of the piston lengths (see Table II). However, it must be also noted that the
heave motions of the two bodies are coupled together (from Eqs. (7)and(8)), the inaccurate
prediction of the piston heave motion would have eventually affected the heave motion of thedevice. That is why we can see some differences of the heave motion between the time domain
FIG. 22. Heave motion of the piston (piston length L ¼0.15 m).
TABLE IV. Accuracy analysis of the time domain simulations.
L¼0.001 m L¼0.01 m L¼0.05 m L¼0.10 m L¼0.15 m
R 0.395 0.328 0.870 0.974 0.999
RRE 0.925 0.967 0.494 0.226 0.047053113-20 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)and the frequency domain analyses for the very short piston (see Figure 23), though the corre-
sponding added mass at the infinite frequency is well calculated (also see Table II).
V. CONCLUSIONS
In hydrodynamic study of OWC wave energy converters, different methods have been
developed in frequency domain if a linear dynamic system is assumed. However, for a fullscale OWC or the practical OWC plant, its dynamics may be nonlinear due to the factors of
the nonlinear air compressibility and maybe of a nonlinear air turbine (PTO). Hence, for such a
dynamic system, time-domain analysis must be conducted. In this research, we focus on a two-FIG. 23. Heave motions of the floating structure and the piston (piston length L ¼0.01 m).
FIG. 24. Heave motions of the floating structure and the piston (piston length L ¼0.05 m).053113-21 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)FIG. 25. Heave motions of the floating structure and the piston (piston length L ¼0.10 m).
FIG. 26. Heave motions of the floating structure and the piston (piston length L ¼0.15 m).
TABLE V. Accuracy analysis of the time domain simulations.
L¼0.001 m L¼0.01 m L¼0.05 m L¼0.10 m L¼0.15 m
R 0.423 0.401 0.908 0.981 0.999
RRE 0.914 0.929 0.419 0.194 0.060053113-22 Sheng, Alcorn, and Lewis J. Renewable Sustainable Energy 6, 053113 (2014)body system to represent the device itself and the imaginary piston for the OWC wave energy
converter for their hydrodynamics. The main reason for such a consideration is that the two-
body system has a very clear physical meaning and the study and implementation of the two-
body system are very straightforward.
In implementing the time-domain analysis, the Cummins-Ogilvie’s equation is used, in
which the hydrodynamic parameters are transformed from the parameters in the frequency-domain analysis to time domain, such as the added mass at infinite frequency and the impulse
functions. In the research work, we examine how reliable we can conduct a time domain analy-
sis for the hydrodynamic performance of an OWC wave energy converter.
From the results and the analyses, following conclusions can be drawn:
(i) The length of the imaginary piston for the water body in the water column has little influ-
ence on the responses of the motions for the frequency range of interest.
(ii) In very short waves (high frequency waves), there will be vibrant responses in added mass,
damping coefficients, and the excitation, though these spiky responses have no significant
effect on the overall responses of motions in frequency domain analysis, but they tend tocause problems when we choose the added mass at infinite frequency or at a very large fre-
quency, or the calculation of the impulse function. As a result of these difficulties, the time
domain solution based on these parameters may not be appropriate.
(iii) The examples show that a favourable length of the piston must be chosen so that reliable
time-domain analysis can be obtained.
ACKNOWLEDGMENTS
This material is based upon works supported by the Science Foundation Ireland (SFI) under the
Charles Parsons Award at Beaufort Research-Hydraulics and Maritime Research Centre (HMRC),University College Cork, Ireland. Statistics and data were correct at the time of writing the article;
however, the authors wish to disclaim any responsibility for any inaccuracies that may arise.
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1.4896751.pdf | Heat transfer and material flow during laser assisted multi-layer additive manufacturing
V. Manvatkar, A. De, and T. DebRoy
Citation: Journal of Applied Physics 116, 124905 (2014); doi: 10.1063/1.4896751
View online: http://dx.doi.org/10.1063/1.4896751
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/12?ver=pdfcov
Published by the AIP Publishing
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42Heat transfer and material flow during laser assisted multi-layer additive
manufacturing
V . Manvatkar, A. De, and T. DebRoy
Department of Materials Science and Engineering, The Pennsylvania State University, University Park,
Pennsylvania 16802, USA
(Received 15 August 2014; accepted 18 September 2014; published online 29 September 2014)
A three-dimensional, transient, heat transfer, and fluid flow model is developed for the laser
assisted multilayer additive manufacturing process with coaxially fed austenitic stainless steel pow-
der. Heat transfer between the laser beam and the powder particles is considered both during theirflight between the nozzle and the growth surface and after they deposit on the surface. The geome-
try of the build layer obtained from independent experiments is compared with that obtained from
the model. The spatial variation of melt geometry, cooling rate, and peak temperatures is examinedin various layers. The computed cooling rates and solidification parameters are used to estimate the
cell spacings and hardness in various layers of the structure. Good agreement is achieved between
the computed geometry, cell spacings, and hardness with the corresponding independent experi-mental results.
VC2014 AIP Publishing LLC .[http://dx.doi.org/10.1063/1.4896751 ]
I. INTRODUCTION
Laser assisted additive manufacturing is a potentially
attractive process for the manufacture of near net shape parts
from a stream of alloy powder in aerospace, automotive, medi-cal, and other industries.
1However, the process requires care-
ful control of laser power, power density, scanning speed,
powder feed rate, size distribu tion, and other variables in order
to achieve an acceptable quality of the parts.2–4Furthermore,
the scale and morphology of the solidification structure, micro-
structure, mechanical properties, and defects also are affectedby the process variables.
5Selection of variables by trial and
error is time consuming and expensive and limits wider indus-
trial usage of the additive manufacturing process. What is nec-
essary and not currently available is a reliable, well-tested,
phenomenological process mod el that can serve as a basis for
the selection of important proces s variables to produce defect
free, structurally sound, and reliable parts made by the additive
manufacturing process based on scientific principles.
Many simultaneously occurring physical processes6–8
affect the structure and properties of the parts in the laser
assisted additive manufacturing process. A stream of pow-der interacts with the laser beam prior to their deposition
on the substrate. The deposited particles rapidly form a
molten pool on the surface of the growing layer and thesolidification of the molten region forms the structure
when the laser beam moves forward.
9A significant spatial
gradient of temperature drives a strong convective flow ofliquid metal due to Marangoni effect and facilitates con-
vective heat transfer within the molten pool.
6–8,10The sol-
idified material undergoes multiple heating and coolingcycles as layers of new alloys are deposited on the previ-
ously deposited layers.
11–14These thermal cycles affect the
evolution of microstructure and mechanical properties ofthe deposited layers.
15–17An understanding of the details
of heat transfer, liquid metal flow, cooling rates, and other
solidification parameters is essential for the control ofmicrostructure and properties of the deposited layer based
on scientific principles.
Numerical models of heat and mass transfer and fluid flow
have provided unique insight into the complex laser welding
processes. However, these models cannot be used for under-
standing the additive manufacturing process because there areseveral important differences between the two processes.
Interaction of the powder with the laser beam, progressive
build-up of the layers, multiple thermal cycles at any specificlocation as new layers are added on the previously deposited
layers, transient changes in the geometry of the part are some
of the differences that preclude the use of existing models ofwelding to understand the additive manufacturing process.
Here, we report the development of a comprehensive,
three-dimensional, transient, heat transfer, and fluid flowmodel for the laser assisted additive manufacturing of parts
from a stream of alloy powders. The model solves the equa-
tions of conservation of mass, momentum, and energy withappropriate boundary conditions and temperature dependent
properties of materials in different regions of the system. The
interaction between the laser beam and the powder particlesduring their flight and subsequently when they are added to
the build surface is considered in the calculations. The outputs
from the model are the temperature and velocity fields, cool-ing rates, and solidification parameters. The model is validated
by comparing several experimentally determined parameters
with the corresponding theoretically calculated results. Forexample, the geometry of the deposited structure is compared
with that computed from the model for the deposition of a
multi-layered structure of an austenitic stainless steel.Furthermore, the experimentally determined scale of the solid-
ification structure and hardness data are compared with the
corresponding theoretically determined values from the mod-eling results. After validation, the model is used to investigate
the spatial variations of peak temperatures, cooling rates, and
solidification parameters during build-up of a multilayer aus-tenitic stainless steel structure.
0021-8979/2014/116(12)/124905/8/$30.00 VC2014 AIP Publishing LLC 116, 124905-1JOURNAL OF APPLIED PHYSICS 116, 124905 (2014)
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42II. PROGRESS MADE IN PREVIOUS RESEARCH
Several useful previous works serve as a foundation for
the work reported in this paper. For example, the work by
Grujicic et al.18shows the importance of laser-material inter-
action during flight of the particles between the nozzle and the
growth surface. He and Mazumder6estimated temperature
rise of the powders during laser-powder interaction using heatbalance. After the particles impinge on the depositing layer,
their absorption of the laser beam is affected by the particle
size, the depth of the particle layer, and their chemical compo-sition.
9The addition of powder particles during deposition
results in the transient growth of the depositing layer along
both the scanning and vertical directions. Previous research
has shown that the addition of mass could be simulated by
progressive activation of elements in the computational do-main. Similarly, the addition of heat both due to the impinging
preheated powder particles and the direct absorption of the
laser beam by the growing layer could be represented by anappropriate Gaussian energy density distribution over a sur-
face or volume or both.
6,7,12–14,17,19,20
Transient temperature fields, residual stresses, and dis-
tortions have been the focus of most of the previous model-
ing works, including those by Neela and De,12Manvatkar
et al.13and Wang and Felicelli.14They used commercial fi-
nite element software for the analysis of heat conduction and
stresses to examine the role of various variables. These cal-
culations do not consider convective heat transfer in the liq-uid region which is often the main mechanism of heat
transfer. Consequently, the computed peak temperatures and
temperature gradients are significantly overestimated, sincethe mixing of the hot and cold fluids is not considered.
Cooling rate which is the product of temperature gradient
and the scanning velocity is also significantly overestimated.
Comprehensive calculations of transient heat transfer
and fluid flow during additive manufacturing are just begin-
ning. The initial two-dimensional calculations
21,22of heat
transfer and fluid flow were followed by adaptation of tran-
sient, three-dimensional models of laser cladding,6,7,19,20and
welding23to additive manufacturing. Tracking of the free
surface was also simulated by the level set method6,7,19,20,22
which is computationally highly intensive. Furthermore, the
quality of the calculations remains to be tested by compari-son with any transient experimental tracking of the topology
of the free surface.
In summary, the previous studies have established the
benefits of numerical simulation of heat transfer and fluid
flow during additive manufacturing and demonstrated the
need to develop transient three dimensional models incorpo-rating additions of heat and mass in a manner that is compu-
tationally tractable. At the same time, the calculations have
to be verified by comparison with measurements of build ge-ometry and metallurgical parameters.
III. HEAT TRANSFER AND FLUID FLOW MODEL
The model calculates transient, three-dimensional, tem-
perature, and velocity fields from process variables, such asthe laser power, power density distribution, scanning speed,
and powder feeding variables, such as the chemicalcomposition, particle size, feed rate, and velocity of the pow-
der particles. The physical processes considered in the calcu-
lations are described below.
A. Assumptions
Several simplifying assumptions are made to make the
complex, three-dimensional, transient calculations tractable.
The densities of the solid and liquid metals are assumed to
be constant. The surface of the growing layer is assumed tobe flat. The loss of alloying elements due to vaporization and
its effects on both the heat loss and composition change are
not considered in the calculations.
B. Particle/laser beam interaction
After emerging from the powder feeding nozzle, the par-
ticles are heated during flight prior to their transfer to the
depositing surface. The heat absorbed by the particles during
flight depends on the residence time of the particles, particlesize, gas velocity, material properties, and laser power den-
sity. The following approximate heat balance is conducted to
estimate the temperature rise of the particles during theirflight assuming that the particles are spherical in shape
DT¼
gm/C2gs/C2P
pr2
b/C22pr2
p/C16/C17
s
4=3/C2p/C2r3
p/C0/C1/C2Cp/C2qp; (1)
where DT is the average in-flight temperature rise of the
powder particles, P is the laser power, r band r pare the laser
beam radius and the average radius of the particles, respec-
tively, C Pis the specific heat, gmis an interference factor to
account for shielding of some particles from the laser beamby other particles, g
sis the fraction of available laser power
absorbed by the solid particles, sis the time of flight which
depends on the velocity of particles and the distance betweenthe nozzle and the depositing surface, i.e., the length of
flight, and q
Pis the density of the particles. The upper hemi-
sphere of the spherical particle surface is directly exposed tothe laser beam. As a result, the absorption of the laser beam
occurs on half of the total surface area (2 pr
2
P) which appears
in the numerator of Eq. (1). After the particles are deposited
on the depositing surface they continue to absorb laser beam
energy efficiently. The rate of absorption of laser beam
energy by the powder bed is calculated based on previouswork on the absorption of laser beam energy by the powder
bed.
9The amount of laser power absorbed by the depositing
surface, P s, is given by
Ps¼gl/C2ð1/C0gpÞ/C2P; (2)
where gpis the fraction of the laser power absorbed by the
powder in-flight and glis the fraction of available laser
power absorbed by the growing layer. Its value is high when
the powder is still solid, but a short time (a few milliseconds)after the heated particles arrive on the growing layer, they
melt and then the liquid surface absorbs energy by Fresnel
absorption.
13So, the value of glis high initially when the liq-
uid layer is forming but reduces once the surface melts.
When the material is in powder form, the laser beam124905-2 Manvatkar, De, and DebRoy J. Appl. Phys. 116, 124905 (2014)
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42undergoes multiple reflections within the powder layers. As
a result, the coefficient of laser beam absorption by the pow-der bed is higher than the absorption coefficient of the liquid.
The energy absorbed by the powder and the growing
layer is used as a source term in the energy conservationequation as follows:
S
i¼Pd
pr2
btgpþgl1/C0gp/C0/C1/C2/C3exp/C0dr2
r2
b !
; (3)
gpis fraction of laser energy absorbed by the powder during
flight, P is laser power, d is laser energy distribution factor, t
is layer thickness, and r is radial distance from laser beamaxis. The layer thickness, t, is determined experimentally.
The two terms within the square bracket represent the frac-
tion of laser energy transferred to the particles during theirflight through the beam and the irradiation of beam on the
depositing surface, respectively. The exponential term
accounts for the Gaussian distribution of laser energy as afunction of distance from the axis of the beam.C. Governing equations
The model solves the conservation equations for mass,
momentum, and energy in transient three-dimensional form.
These equations are available in standard text books24and in
many of our previous publications25,26and are not repeated
here. The specific discretization scheme and the solution
methodology for transient three dimensional form are also
discussed in details in the literature.24,26Only the special fea-
tures of the calculations are discussed here. The process pa-
rameters and material properties used for numerical
calculations are presented in Tables IandII, respectively.
D. Computational domain and the boundary
conditions
The transient heat transfer and fluid flow calculations
are performed for a rectangular solution domain representing
the substrate, deposited layers, and the surrounding gas
shown in Fig. 1. In order to expedite calculations, advantage
is taken of the geometrical symmetry of the deposited layers
along the mid-width longitudinal plane and calculations are
done only in one half of each layer. The deposition is simu-lated through discrete time steps. At the beginning of the
simulation, all the cells above the substrate are assigned
properties of an inert gas and the initial temperature of thedomain is taken as the room temperature (298 K). The mov-
ing heat source is simulated by progressively shifting of the
laser beam axis by a very short predetermined distance, X
s,
in the direction of deposition equal to a small fraction of the
laser beam diameter. The corresponding time step, Dt, is cal-
culated from the scanning velocity, v
Dt¼Xs=v: (4)
During each shift, the properties of the computational cells
representing the volume of the deposited material are
changed from the properties of the gas to that of the deposit
material. At the end of each layer, an idle time is provided toallow the laser beam to move to the initial location prior toTABLE I. Data used for numerical simulations. The laser material interac-
tion length is the distance between the point, where material powders areintroduced into the laser beam and the top surface of the layer being
deposited.
Process parameter Value
Substrate size (mm /C2mm/C2mm) 10 /C23.1/C24
Deposited layer size 4 /C20.72/C20.38
Laser power (W) 210Laser scanning speed (mm s
/C01) 12.7
Laser beam diameter (mm) 0.9Idle time (s) 0.03Laser distribution factor 3Material flow rate (g min
/C01)2 5
Material powder size ( lm) 175
Laser material interaction length (mm) 2
Particle velocity (mm s/C01) 2.4
Carrier gas flow rate (l min/C01)4
TABLE II. Material properties used for numerical simulations. The absorption coefficient values in the table are for 1.06 lm wavelength laser beam.
Material properties Values References
Properties of SS316
Density (kg mm/C03) 7800 27
Solidus temperature (K) 1693 27
Liquidus temperature (K) 1733 27
Thermal conductivity (W m/C01K/C01) 11.82 þ0.0106 T 27
Specific heat (J kg/C01K/C01) 330.9 þ0.563 T /C04.015 /C210/C04T2þ9.465 /C210/C08T327
Latent heat of fusion (J kg/C01) 2.67 /C210527
Coefficient of thermal expansion (K/C01) 1.9 /C210/C0527
Viscosity of liquid alloy (kg m/C01s/C01) 6.7 /C210/C0327
Temperature coefficient of surface tension (N m/C01K/C01) /C00.4/C210/C0329
Absorption coefficient in solid/liquid ( gs,gl) 0.3 9
Absorption coefficient in powder bed ( gP) 0.7 9
Interference factor ( gm) 1.0 …
Properties of argonDensity (kg mm
/C03) 0.974 28
Specific heat (J kg/C01K/C01) 520 28
Thermal conductivity (W m/C01K/C01) 26.41 /C210/C0328124905-3 Manvatkar, De, and DebRoy J. Appl. Phys. 116, 124905 (2014)
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42the deposition of the next layer. The idle time is the time gap
necessary for the laser beam to travel between the end of onelayer and the beginning of the next upper layer. The laser
beam is switched off and no material is deposited during this
time. The aforementioned procedure is repeated till the depo-sition of all the layers.
The variation of all variables across the mid-section lon-
gitudinal symmetry plane is set to zero. In the remainingsurfaces, heat loss by radiation and convection is applied as
boundary conditions for the solution of the enthalpy equa-
tion. For the solution of the momentum equations, the longi-tudinal and transverse velocities at the melt pool surface
boundary were related to the corresponding velocities in
locations just below the surface through Marangoni bound-ary conditions.
25
E. Grid spacing, time steps and convergence of the
solution
Spatially non-uniform grids, with finer grid spacing near
the axis of the laser beam were used for efficient calculation
of variables. A computational domain, 10 mm in length,
3.1 mm wide, and 5.5 mm in height, was considered and di-vided into 160 /C229/C237 or 171 680 grid points. The dura-
tion of the time step is decided using Eq. (4).
The governing equations were discretized by following
a control volume method.
24The velocity components and
the scalar variables were stored at different locations to
enhance the convergence and stability of the computationalscheme. At each time step, the three components of veloc-
ities and the enthalpy were iterated following a sequence
known as the SIMPLE algorithm.
24The implicit computa-
tional scheme adapted is unconditionally stable. The discre-
tized linear equations were solved using a Gaussian
elimination technique known as the tri-diagonal matrix algo-rithm.
24At any given time step, the iterations were termi-
nated when two convergence criteria were satisfied. The
magnitudes of the residuals of enthalpy and the three compo-nents of velocities, and the overall heat balance were
checked after every iteration. The largest imbalance of anyvariable on the two sides of a discretization equation for all
interior grid points had to be less than 0.1%. In addition, the
overall heat balance criterion required that the sum of thetotal heat loss from the domain and the heat accumulation
had to be almost equal to the heat input into the calculation
domain. Their difference had to be less than 0.5% of the heatinput for this convergence criterion to be satisfied. The crite-
ria were selected so that the final results were not adversely
affected while maintaining computational speed. Typically atotal of 26 000 iterations were necessary per layer and a total
of 13.5 billion linear equations were solved cumulatively for
all time steps for a three layer structure.
F. Cell spacing and hardness calculations
Cooling rate in the solidification temperature range
(1733 K–1693 K) is calculated from the computed tempera-ture at several locations for every layer. The layer wise varia-
tion of the secondary dendrite arm spacing is calculated
considering the average cooling rate in every layer using thefollowing expression:
13,30
k2¼AðCRÞ/C0n; (5)
where k2is secondary dendritic arm spacing (SDAS) in lm,
CR is cooling rate in K/s, and A and n are material specific
constants having values of 80 and 0.33, respectively. SDASis the smallest dimension in a typical columnar dendritic
microstructure. Experimental observations revealed very fine
cellular microstructure in the range of 3–10 lm, in such layer
wise deposited structure.
13,30Manvatkar et al.13showed that
Eq.(5)fits well for predicting cell spacing in very fine cellu-
lar structure. Further layer wise yield strength is estimatedusing a Hall-Petch like relationship presented in Eq. (6)and
replacing the grain size by cell spacings as suggested by
Manvatkar et al.
13
ry¼r0þkyðdgÞ/C00:5; (6)
where ryis yield strength, r0is lattice resistance, kyis grain
boundary resistance, and dgis grain size replaced by cell
spacing. The values of r0andkyused for calculations are
150 MPa and 575 MPa ( lm)0.5. The layer wise hardness (H V)
from yield strength ( ry) is estimated as
Hv¼3ryð0:1Þ2/C0m; (7)
where H Vis in kg mm/C02and m is Mayer exponent with
value 2.25 for steels.13,31–34
IV. RESULTS AND DISCUSSION
Figure 2shows the computed melt pool geometry in the
first, second, and third layers deposited for the experimental
conditions presented in Table I. Each color band in the pro-
file represents a temperature range shown in the legend. Thegreen colored regions in all the figures indicate that the de-
posited material reached solidus temperature of the SS316
alloy (1693 K). The vectors show the computed velocityfields in the molten region. A reference vector is shown by
an arrow and a comparison of the length of this arrow with
FIG. 1. A schematic representation of the solution domain.124905-4 Manvatkar, De, and DebRoy J. Appl. Phys. 116, 124905 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
132.238.2.115 On: Mon, 06 Oct 2014 04:44:42the vectors shown in the plots reveals the magnitudes of the
computed velocities. The velocities are larger at the surface
than in the interior because the motion of the liquid metal inthe molten region originates at the surface owing to the
Marangoni convection. The Marangoni stress results from
the spatial gradient of surface tension because of the temper-ature variation. The computed surface velocities are some-
what higher than 500 mm/s which is comparable with what
is reported for laser welding. At these velocities, the com-puted Pe for heat transfer which represents the ratio of heat
transported by convection to that by conduction is much
higher than 1 indicating convective heat transfer to be themain mechanism of heat transfer. Consequently, many of the
conclusions made by heat conduction calculations need to be
revised.
The transverse sections of the computed melt pool pro-
files in the first three layers are shown in Fig. 3to examine
the geometry of the build. This figure also shows a compari-son between the numerically simulated and the correspond-
ing experimentally observed transverse sections for the three
layer structure. The good agreement between the two geome-tries indicates that the model is capable of predicting the cor-
rect geometry of the build layers.
Figure 4shows the computed thermal cycles at three
monitoring locations, each at mid-length and mid-height
within the first, second, and third layers. Each thermal cycleshows the expected recurrent spikes. The first spike in the
thermal cycle for a particular layer shows the peak tempera-
ture corresponding to the laser beam positioned above themonitoring location. The subsequent peaks correspond to the
positioning of laser above the monitoring location in subse-
quent passes of the laser as the upper layers are deposited.Thus, the thermal cycles are indicative of the progress of
FIG. 2. Evolution of the melt pool geometry in the first three layers. (a)–(c) show the progression of deposition in the first layer, (d)–(f) show changes in the
melt pool geometry in the second layer, and (g)–(i) show the same in the third layer.
FIG. 3. Comparison of the experimental13and theoretical transverse section
of the three layer structure.124905-5 Manvatkar, De, and DebRoy J. Appl. Phys. 116, 124905 (2014)
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42deposition during the process. The peak temperatures experi-
enced by the first, second, and the third layers are 1946 K,
1998 K and 2035 K, respectively. The rise in the peak tem-
perature from the first layer to the second layer is 52 K.However, this rise is reduced to 37 K from the second to the
third layer. The first layer can efficiently transfer heat into
the substrate because the substrate is cold initially and closeto the deposited layer. Thus, the substrate can effectively act
as an efficient heat sink. During the deposition of the subse-
quent top layers, the peak temperature rises as the distancebetween the substrate and the build layer increases and the
new layers are deposited on the previously deposited hot
layers. However, the increase slows down with the progres-sive deposition of subsequent layers, since the heat loss also
increases with higher temperatures in the deposited layers.
The computed peak temperatures in various layers are
plotted in Fig. 5. The increase in peak temperate in the upper
layers owing to the progressively diminished heat extraction
by the substrate is clearly observed in the figure. The com-puted peak temperatures are also compared with those
obtained from an independent heat conduction calculations
13
in the figure. As expected, the rise in the peak temperature is
more pronounced in the conduction model because the heattransfer by convection is ignored and the diminished heat
transfer rate leads to rapid increase in temperature.
Fig. 6shows that the computed cooling rates diminish
from 6548 K/s in the first layer to 4245 K/s in the second
layer and further to 2779 K/s in the third layer. The averagecooling rates independently estimated using a heat conduc-
tion model were approximately 12 000 K/s and 6000 K/s in
the first and third layers, respectively. These values are unre-alistically high because mixing of the hot and the cold
liquids that reduce the temperature gradients in the melt pool
is ignored in the heat conduction calculations. Since thecooling rate is the product of temperature gradient and the
scanning velocity, the cooling rate decreases when the tem-
perature gradient is reduced owing to mixing.
The ratio of the temperature gradient G and the solidifi-
cation growth rate R affects the solidification morphology.
The constitutional supercooling criterion for plane front sol-idification is given by the following:
G=R/C21DT
E=DL; (8)
FIG. 4. Thermal cycles at three monitoring locations in the first three layers.
FIG. 5. Comparison of the computed peak temperatures at three monitoring
locations within the three layers with those independently reported using a
heat conduction model.13
FIG. 6. Variation of cooling rate at three monitoring locations in the threelayers. The results of the heat conduction calculations are from the
literature.
13
FIG. 7. Variation of the computed values of the solidification parameter
G/R, where G is the growth velocity and R is the temperature gradient.124905-6 Manvatkar, De, and DebRoy J. Appl. Phys. 116, 124905 (2014)
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42where DTEis the equilibrium solidification temperature
range and D Lis the solute diffusion coefficient. For a given
alloy, G/R defines the stability of the solidification front.
Figure 7shows that the computed value of G/R decreases
along the build height since the temperature gradient reducesin the upper layers because of heat buildup. The computed
value of G/R decreases from 49.5 (K s)/mm
2in the first layer
to 18.6 (K s)/mm2in the third layer. The value of DTEfor
the stainless steel is 40 K and D Lfor Cr diffusivity in liquid
steel is about 5 /C210/C03mm2/s. The resulting DTE/D Lof
8/C2104(K s)/mm2is much higher than the computed values
of G/R in all the layers. Thus, a plane solidification front is
unstable and the variation of G/R shows that solidification
will occur with progressively lower stability of plane front inthe upper layers. The solidification structure will be either
cellular or dendritic.
Figure 8shows the computed variation of the average
cell spacing in different layers. The cell spacing increases
towards the upper layers from 4.5 lm in the first layer to
6lm in the third layer due to the reduction in the cooling
rate at the solidification front. The cell spacings computedusing the cooling rates obtained from the conduction based
models are much lower than the experimentally observed
values
13and varied from 3.5 lmt o4 . 5 lm from the first to
the third layer. Thus, the convective heat transfer calcula-
tions provide much more realistic cell spacings than the heat
conduction model.
Figure 9shows the decrease in the computed hardness
value towards the top layer owing to an increase in the cell
spacing. The computed hardness decreases from 230 MPa inthe first layer to 209 MPa in the third layer. These values are
lower than the values computed from an independent investi-
gation using a heat conduction model
13and agree much
more closely with the independent experimental results.13
V. CONCLUSIONS
A three-dimensional, transient, heat transfer, and fluid
flow model is developed and tested for the laser assisted dep-
osition of a multilayer structure from coaxially fed austeniticstainless steel powder. The layer wise evolution of tempera-
ture and velocity fields and melt pool geometry is examined
for a three layered structure.
The computed melt pool geometry agreed well with the
corresponding independent experimentally measured results.
Both the computed results and the experimentally deter-mined built geometry showed a slight increase in the melt
pool size towards the upper layers.
The computed cooling rates decreased progressively
with the addition of new layers. The cooling rates decreased
from about 6550 K/s in the first layer to about 2780 K/s in
the third layer. These results are in agreement with the inde-pendently observed changes in the solidification structure.
Both the independently observed coarsening of the cell struc-
ture and the consequent decrease in the hardness of the de-posited material in the upper layers agree well with the
computed variation of cooling rates in different layers.
The computed cell spacings from the computed cooling
rates and empirical equations available in the literature were
in the range of 4–6 lm. These values agreed well with inde-
pendent experimentally determined results. The hardnessvalues computed using the computed cooling rates agreed
fairly well with the independent experimentally determined
results.
The results show that ignoring convection in the liquid
pool results in unrealistically high cooling rates and the use
of heat transfer and fluid flow model provides much morereliable results of cooling rates, cell spacings, and hardness
than those obtained using a heat conduction model.
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132.238.2.115 On: Mon, 06 Oct 2014 04:44:42 |
1.102407.pdf | Critical current enhancement in fieldoriented YBa2Cu3O7−δ
K. Chen, B. Maheswaran, Y. P. Liu, B. C. Giessen, C. Chan, and R. S. Markiewicz
Citation: Applied Physics Letters 55, 289 (1989); doi: 10.1063/1.102407
View online: http://dx.doi.org/10.1063/1.102407
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/55/3?ver=pdfcov
Published by the AIP Publishing
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Fluxcreeplimited critical currents in YBa2Cu3O7−δ ceramics
Appl. Phys. Lett. 55, 1135 (1989); 10.1063/1.102459
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128.235.251.160 On: Fri, 19 Dec 2014 02:30:43Critical current enhancement in field~oriented YBa2 Cus 07 _ S
K. Chen,a),d) B. Maheswaran,a),d) Y. P. LiU,b) B, C. Giessen,C),rJ) C. Chan,b)
and R. S. Markiewicza),d)
Northeastern University, Boston. lvlassachusetts 02115
(Received 2 March 1989; accepted for publication 15 May 1989)
The crystalline anisotropy of YBa2 Cu) °7 .. (i is found to have a significant effect in degrading
critical current Je" Pressed polycrystalline pellets offield-oriented grains have signiilcantly
higher Jc values ( > 5 times larger) than unoriented samples of the same materiaL Effects of
annealing and metal doping are also discussed.
The recent discovery of high-temperature oxide super
conductors, I including a number of materials which super
conduct above liquid-nitrogen temperature,l-5 has stimulat
ed considerable interest and activity. A limitation to
applications of these materials is the low critical current den
sity J, measured in bulk poly crystalline samples. It has been
shown that these low Je values are not intrinsic, but are due
to poor intergrain coupling. Here we report a new technique
to increase transport Jc by aligning single-crystal grains in a
magnetic field and then pressing and sintering into a dense
pellet. The transport Jc in the a-b plane of these magnetical
ly-oriented samples can exceed 1350 A/em2, more than five
times higher than we find in similar unoriented samples.
Farrell et al. (, showed that a crystalline grain of
YBa2Cu\07 h (YBCO) can be aligned in an intense mag
netic field such that the direction having the greatest mag
netic susceptibility lies along the field. For YBCO, this direc
tion is along the c axis. In the present experiments, this
technique is used to make dense, pressed pellets. YBCO sam
ples were annealed at 990°C in air ( or flowing O2 ) for one or
two days to obtain single crystal grain size:::::; 10 p.m, as
determined by optical microscopy. Then the samples were
ground to a fine powder, either in chloroform suspension or
using a ball mill, such that the average grain size is less than
10 pm. These powders were then mixed with 2% by volume
of a surfactant (Triton or ordinary soap), dissolved in an
equal volume of chloroform, stirred in an ultrasonic vibrator
for 30 min,7 and then poured into a heat-treated eu-Be die.
The die was then placed in a magnetic field of 5 T or higher,
where the solution was left to evaporate ( ~ 2 h).
The dry mixture (powder and surfactant) was then
pressed into a peBet using a pressure ~ 5 kbar. The pellets
were first sintered at 300°C for 1 h to evaporate the surfac
tant, then annealed at 950 "C for two days,
The degree of orientation was determined from x-ray
reflection spectra. The reflectivity is from the broad face of
the sample, perpendicular to the c axis in an oriented sample,
so that in a perfectly aligned sample only (OOI)-refiections
would contribute to x-ray reflection. Orientation is mea
sured by the relative intensity r of a forbidden (non-OOl)
", Department of Physics.
h) Department of Electrical Engineering.
,) Department of Chemistry.
d) Barnett Institute. reflection, compared to an unoriented sample. We defineS
the orientation factor P by
p= (1-nXlOO%. (1)
In Ref. 9, we show how P can be related to average mosaic
spread of the c axis. For instance, P = 98% corresponds to a
spread of ~ 10° in the average c-axis orientation.
After annealing, the samples were cut into rectangular
bars with cross-sectional area -1 mm2• Silver paint contacts
were painted on the top surface of the sample. Then the sam
ple was sintered at 900 °C for 1-2 h in flowing oxygen. Pre
liminary microscopic studies;o indicate that during this heat
treatment, the silver essentially fills the surface pores of
granular YBCO, and improves the contact between grains,
hence reducing the contact resistance. The contact resistiv
ity was -10 5_10 -6 n cm2 at liquid-nitrogen temperature
(77 K). Leads were attached to the annealed silver contacts
using indium or tin. A four-terminal method was used to
determine the transport critical current density. The dis
tance between the two voltage probes was ~ 1.3 mm. The
resistive transition is sharp (Fig. 1), and we define the nomi
nal Jc to be that current at which a 1 pV signal appears
across the voltage leads. All J, values were measured at liq
uid N2 temperature, 77 K.
Measured values of transport Je are shown in Fig. 2,
both for (a) field-aligned and (b) unaligned samples. We
I(A)
FIG, 1. [-Veurve ofa field-aligned, pressed, sintcrcd YEa, CUi) 07 ,\ pellet
with cross-sectional area 0.4;( 2.26 mm', J, ~640 A/em'.
289 Appl. Phys. Lett. 55 (3), 17 July 1989 0003-6951 i89/290289-03$Ol .00 (C) 1989 American Institute of Physics 289
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128.235.251.160 On: Fri, 19 Dec 2014 02:30:43find considerable spread in Je values from samples prepared
at different times, but by preparing a batch of samples at the
same time, under identical circumstances, we are able to dis
cern consistent trends. Thus Fig. 2(b) shows Je vaJues of
three batches of YBa2Cu}Z, 07,;, "'doped" with excess
Z = Cu or Ag (this metal most probably occurs intergranu
larly, as a second phase). In each case, J,. maximizes at a
finite dopant concentration, x = 0.05 for Ag, 0.1 for Cu.
Note that the excess Cu nearly doubles Je. The trends show
up clearly even though the undoped Je varies from 25 to 140
A/cm! in different batches. The above data are for samples
annealed for four days at 950°C. For longer anneals, the Jc
of all samples varied in a random fashion between 150 and
250 A/cm2•
In all cases studied, the field-oriented samples display
considerably higher Jc values, from 440 to 1370 A/cm2•
These Jc values are found to depend strongly on the duration
of the 950°C sintering step. In the examples shown in Fig.
2(a) (arrows), the shorter sintering time is four days, the
longer five to six days (see caption), and Jc can increase by
> 30%. On the other hand, even longer sintering is found to
be deleterious for J( .. Thus, the sample which showed J, of
1130 A/cm2 (four day anneal) and 1190 A/cm2 (six days)
fell to 400 A/cm2 (eight days) and 150 A/cm2 (ten days).
This result is typical of all samples. In contrast, the unorient
ed samples had only low Jc values for anneals of up to ten
days.
The critical current values are also sensitive to grain
size, which was varied by ball milling the samples for differ
ent lengths of time. Typical results are shown in Fig. 3. By
electron microscope examination, it was found that the 15
min ball milling corresponded to an average grain size < 10
pm, 30 min to a size <5 pm.
1500
)( (0)
x 0
t 1 x
1000 xo
Ii xo
r J
__ x _________________ ~
----___ 0------'-, (b) J
u"'~_--~B----~ (l .... 0 .... ,
<> - ----0-0----0 '0_
~j~I~J.....ll, J ,I . 500 -
0.1 0.2 0.3
X (Ag, eu)
FIG. 2. Transport critical current density in YBa, CUi (Z, )0, ".
(a) Field-aligned pellets. Arrows indicate the effect of sintering for two
more day, (x ~ 0) or one more day (Z ~ Cu. x 0.1). (b) Unorientcd
pellets. Dashed line connects samples from a given batch. (0), (0),
z = Cu, (u) Z = Ag. In the low J, batch (0) 39's purity CuO was used as a
starting material. while the other batches used 5 'l's CuD.
290 Appl. Phys. Lett., Vol. 55, No.3, 17 July 1989 1500r" ' ('a; ']
"
25: _'~~~~..L....>~...LI~'~~~l~~
o 1::['
67 r
S6 Fe
e5 t.. J_L--J o I '
10 20
T(mlns) 30 40
·FIG. 3. Ball mill time dependence of (a) transport critical current density
J, : and (b) orientation factor P, for YB, CUi . ,07 "with Xcc () ( X ) or
X= 0.1 (e).
Preliminary measurements suggest that J, also de
creases with time. Thus, the sample of Fig. 1 is the same as
the x = 0.1 Cu sample of Fig. 2, showing the Jc has de
creased by ~40% after two months' storage.
The annealing results are very reminiscent of the work
of Alford et ai, II They found that long-term annealing of
extruded (but not field oriented) YBCO samples promoted
grain growth and densification. Annealing also enhanced Jc,
up to values of ~ 900 A/cm2 at a critical densifieation of
~90%, but Jc was found to decrease precipitously with
further densification. Presumably, 11 oxygen diffuses in
YBCO mainly along intergranular pores. Above the critical
densification, the pores are scaled off' and the center of the
sample is left oxygen deficient, thus accounting for the low
Je values. Interestingly, we find that the orientation factor P
is also significantly enhanced by annealing, typically from
-90% in the pressed, unsintered sample to > 98% in well
annealed samples. This enhancement of P continues even
when J,. begins to decrease.
The peak in Je versus particle size (milling time) in Fig.
3 can be understood as due to two effects. Tfthe particles are
too large, they are not single crystalline, so both P and.i, arc
low [Note that Pmonotonically increases with milling time,
Fig. 3 (b) 1. On the other hand, Jc decreases if the particles
are too small, probably due to weakened superconductivity
at the particle surface (source of intergranular Josephson
coupling).
Ekin 12 has suggested that anisotropy should be the sec
ond most important factor limiting Jr" next in importance to
the weak, Josephson-like intergranular coupling. We have
demonstrated that anisotropy does indeed play an important
role in Je reduction. Even in the oriented samples, links
between grains remain weak. This can be seen from the
strong Held dependence of Jc' which we will report in a sepa
rate publication. This result is consistent with that of Dimos
Chen etal. 290
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128.235.251.160 On: Fri, 19 Dec 2014 02:30:43et al.]J who found that in-plane grain misalignment causes
large lc reductions.
K. Chen, B. Maheswaran, R. S. Markiewicz, and B. C.
Giessen acknowledge support by E.!. DuPont de Nemours
Co., Inc. This is pUblication 373 of the Barnett Institute.
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............................. ' ..... " ....... r····· .. ···.'.·.·.·.·.·.·.·.·.·.·.v.·.·.·.·.·.'.· .• ; •.•.•.•. -; ...........•.....•.•.•.•... :.:.~ .•.•. : ....... -........•.. ~.-................. -............. . 'P. Maldar, K. Chen, ll. Maheswaran, A. Roig-Janicki, N. R. Jaggi, R. S.
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1.100632.pdf | High T c screenprinted YBa2Cu3O7−x films: Effect of the substrate material
Narottam P. Bansal, Rainee N. Simons, and D. E. Farrell
Citation: Applied Physics Letters 53, 603 (1988); doi: 10.1063/1.100632
View online: http://dx.doi.org/10.1063/1.100632
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/53/7?ver=pdfcov
Published by the AIP Publishing
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AIP Conf. Proc. 182, 8 (1989); 10.1063/1.37942
High T c superconductivity in YBaCuO screenprinted films
Appl. Phys. Lett. 53, 1110 (1988); 10.1063/1.100658
Preparation of superconducting YBaCuO thick films with preferred caxis orientation by a screenprinting method
Appl. Phys. Lett. 53, 606 (1988); 10.1063/1.100633
High T c YBa2Cu3O7−x thin films on Si substrates by dc magnetron sputtering from a stoichiometric oxide target
Appl. Phys. Lett. 52, 2263 (1988); 10.1063/1.99771
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142.157.129.8 On: Sat, 13 Dec 2014 17:59:32High Tc screen"printed YBs2CU307 ~X fUms: Effect of the substrate material
Narottam P. Bansal and Rainee N. Simons
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
D. E Farrell
Physics Department, Case Western Reserve University, Cleveland, Ohio 44106
(Received 25 Apri11988; accepted for publication 15 June 1988)
Thick films of YBa2Cu:>07 __ x have been deposited on highly polished alumina, magnesia
spinel, nickel aluminum titanate (Ni-Al~Ti), and barium tetratitanate (Ba-Ti) substrates by
the screen printing technique. They were baked at 1000 ·C for 15 min, oxygen annealed at a
lower temperature, and characterized by electrical resistivity measurements, x~ray diffraction,
and optical and scanning electron microscopy. Properties of the films were found to be highly
sensitive to the choice of the substrate material. The film on Ba-Ti turned green after firing,
due to a reaction with the substrate and were insulating, A film on Ni-Al-Ti had a Tc (onset)
-95 I( and lost 90% of its resistance by -75 K.. However, even at 4 K it was not funy
superconducting, possibly due to a reaction between the film and the substrate and
interdiffusion of the reaction products. The film on alumina had Tc (onset) -96 K, Tc (zero)
-66 K, and f1 Tc (10-90%) -10K. Our best film was obtained on spinel and had Tc (onset)
~ 94 K, zero resistance at 81 1(, and a transition wi.dth (10-90%) of -7 K.
High Tc superconducting films may be useful for a var~
iety of microelectronic and microwave applications and a
number of techniques have been employed 1,2 for their depo
sition. Screen printing is a relatively simple method which
has been explored by us3 and by other workers.",5 It may be
particularly useful for the direct printing of microwave and
electronic circuits. We have recently reported3 the optimjz~
ation of post-printing firing and annealing conditions for
screen-printed Y-Ba-Cu-O films on alumina.
In this letter, we report on the strong influence of the
substrate material on the characteristics of the screen-print
ed YBa2Cu307 _ x films. Thick films (30--60 ,um) on various
substrates commonly used in microelectronics and micro
wave integrated circuits have been characterized by x-ray
diffraction (XRD), optical and scanning electron micros~
copy (SEM), and resistivity measurements.
YBa2Cu307 _~ x powder was prepared from Y 203 (Mo-
1ycorp 99.99%), BaC03 (ALFA technical grade), and CuO
(ALFA ACS grade) powders by the solid-state reaction
method folIowing a procedure essentially the same as de
scribed previously. 6 Fine YBa2Cu307 ~ x powder was mixed
thoroughly with an appropriate amount of organic vehicle to
form a paste. This was printed on several flat ceramic sub
strates through a stainless-steel screen. The substrate materi
als used were high-purity alumina (superstrate 996 from Materials Research Corporation), spinel (S-145), barium
tetratitanate (Ba~Ti, types D8512 and D-38), and nickel
aluminum titanate (Ni-AI-Ti, type D~30) all supplied by
Transtech, Inc. The films were oven dried at 300-350·C for
1.5-2 h. They were then heated at 5 ·C/min to 1000 ·C, held
for 15 min, cooled at 3 ·C/min to 450 ·C, annealed for 3 h,
and then finally slow cooled to ambient temperature. The
complete sintering and annealing cycle was carried out in
flowing oxygen. The film thickness was -30-60 ,urn as de
termined using a surface profile measuring system (Dektak
UD, Sloan Technology Corporation).
The phases present in the baked films were identified
from XRD patterns which were recorded using a Phillips
ADP-3600 automated diffractometer equipped with a crys
tal monochromator employing Cu Ka radiation. The film
morphology was observed in an optical microscope and a
SEM. Resistivity and its temperature dependence were mea
sured in the standard four-probe configuration down to 4.2
K. Silver paint was used to attach the leads.
We recently reported3 that the optimum firing condi
tions for YBa2Cu307 x screen-printed films on alumina
substrates are 15 min at 1000·C in oxygen. The films on
various substrates in the present study were, therefore, fired
under these conditions. The physical appearance, resistive
transition temperatures Tc, the transition width (10-90%)
TABLE I. Properties ofYBa2Cu307 ~ x films screen printed on various substrates, baked for 15 min at 1000 'C, and oxygen annealed at 450 'C for 3 h.
Film
No. Substrate
5 AlzO,
MG-l Spine!
NAT-I Ni~AI-Tia
D38-1 Ba-Ttb
D8512-1 Ba-Tib
• Nickel aluminum titanate,
b Barium tetratitanate, cnset
96
94
95
603 Appl. Phys. Lett 53 (7), 1 5 August 1988 T,(K)
midpoint completion
89 66
87 81
88
Insulator
Insulator
0003-6951/88/330603-03$01.00 6.1:(K)
(10-90%) Color Adhesion
10 Black Excellent
7 Black Excellent
18 Black with Excellent
greenish
tinge
Green Excellent
Green Excellent
@ 1988 American Institute of Physics 603
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142.157.129.8 On: Sat, 13 Dec 2014 17:59:32!l, Te, etc. for various films are given in Table 1. All films had
excellent adhesion with the substrate. The film on Ba-Ti had
turned green after sintering due to a chemical reaction with
the substrate. This was insulating at room temperature and
no further resistivity measurements were carried out on this
film. Those on Al203 and spinel were black and that on Ni
Al-Ti had a light greenish tinge. Figure 1 shows the tempera
ture dependence of a normalized resistivity for films on three
different substrates fired under identical conditions. Film
No.5 on alumina had Tc (onset) = 96 K, Tc (comple
tion) = 66 K, and .6. Tc (10-90%) = 10 K. The large transi
tion width may be due to the interdijfusion of aluminum as
reported by other researchers.7 Alumina is reported8 to have
a limited solubility in YBa2Cu307 but chemically decom
poses it. The Tc of the unreacted YBa2Cu307 phase is not
affected but the transition width becomes large due to the
presence of the decomposition products as impurities. The
film NAT-l on Ni-AI-Ti showed semiconducting behavior
from room temperature to Tc (onset) -95 K and lost 90%
of its resistance by ~ 75 K. However, it did not become fully
§uperconducting even at 4.2 K. It also showed a -20% in
crease in resistance on thermal cycling. A long tail in the
resistivity versus temperature curve suggests the presence of
severe inhomogeneities. An insulating second phase materi
al in the grain boundaries and/or chemi.cal reactions at the
interface are possible sources7 of such inhomogeneity. To
observe the film-substrate interface a part of the NAT -1 film
was mechanically scratched off. In the optical microscope
the interface layer was observed to be green and the film
surface also contained green particles. These observations
strongly suggest that a chemical reaction occurred at the
interface with the subsequent interdiffusion of the reaction
products. The resistance ofthe film MG-l on the spinel sub
strate remains almost unchanged between room tempera
ture and the Tc (onset) -94 K where a sharp drop in resis
tivity occurs and the film becomes fuUy superconducting at
81 K with t1 Tc (10-90%) of -7 K. The high Tc and rela
tively sman resistive transition width of this film may sug
gest very small or no interdiffusion of magnesium and a neg-
604 Appl. Phys. Lett, Vol. 53. No." 15 August 1986 H5
~-1
O.b
0."
0.1
-.+o--~ ';0 -<>,k----;;25~lo-_c;:;.'oo
TO!?[RA1URL K
FIG. l. Temperature dependence of electrical resistivity of screen-printed
YBa2CIl,07_x films on various substrates fired for 15 min at lOOO·C in
oxygen: (X) A1203; (0) spinel; (D) Ni-Al titanate.
ligible reaction at the film-substrate interface. According to
Yan et aI.8 Mg substitutes at the copper sites in the
YBaZCu307 structure and significantly decreases its Tc
When YBaZCu307 was doped with 2 mol % ofMgO in place
of CuO, its T" reduced from 91 to 65 K. Naito et al.7 ob
served Tc (onset) values as low as 68 K for the Y-Ba-Cu-O
films on MgO substrates prepared by electron beam codepo
sition. A possible reason for this low Tc was suggested to be a
large amount of interdiffusion of magnesium from the sub
strate into the film. This is puzzling in view of the fact that
they employed processing temperatures (-850 ·C) that
were lower than those in the present study.
The films on various substrates were smooth as shown
in the optical micrographs in Fig. 2. The NAT -1 film was not
homogeneous; it contained some green particles and the
film-substrate interface was observed to be green. SEM mi
crographs of some of the films on various substrates are pre
sented in Fig. 3.
In Fig. 4, the XRD patterns of films on various sub
strates fired at 1000 °C for 15 min are compared with those
for a bulk YBa2Cu30, <> x powder sample. All the diffraction
FlO. 2. Optical micrographs of
YBa,CU,07 _ x films screen printed on (a)
Alz03, (b) spinel, (c) Ni-AI titanate, and
(d) barium tetratitanate substrates and
baked at l000·C for 15 min in oxygen.
Bansal, Simons, and Farrell 604
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142.157.129.8 On: Sat, 13 Dec 2014 17:59:32FIG. 3. Scanning electron micrographs of high-temperature superconduct
ing YBa2Cu,07_x films screen printed on (a) AltO" (b) spinel, and (c)
Ni-Al titanate substrates and sintered for 15 min at 1000·C in oxygen,
lines of the perovskite superconducting phase are present in
the films. The most prominent lines for Y 2BaCuOs at
d = 2.989, 2.923, 2.824 A and for BaCu02 at d = 3.045 and
2.964 A are also present in some of the films. However, the
intensities of these peaks, labeled as Yand B, are very weak.
These results indicate that the films prepared in the present
study consist of the perovskite superconducting phase along
with very small concentrations of impurities. The XRD of
the green film on Ba-Ti substrate showed the presence of no
perovskite phase at alt
Koinuma et 01.4 prepared superconducting films of
Yb-Ba-Cu-O on yttria-stabilized zirconia (YSZ) substrates
by screen printing and firing them in air at 900 ·C. No infor
mation about the film adhesion to the substrate was reported
but their attempts to fabricate similarly fired superconduct
ing films on quartz, alumina, or La2Cu04 substrates were
not successful. Budhani et al.5 deposited superconducting
films of Y -Ba~Cu-O on alumina and sapphire substrates by
605 Appl. Phys. Lett .• Vol. 53. No.7. 15 August 1988
••••••••• ••• • ••••••••• <;· ••• ~.·;-7.V.·.~.·.·.~.;.:.:.;.:.:.:.:,:.:.:.:.~.:.:.:.:-:.:.;.:.;.~.:.:.:.;.:.;-:o;.,.: •.•. -•. : .•••...•.• ,' .• ,.,.,',. B"f1AClJu2
Y -"2BACUo5 l I
I I I I . (a)
~---L~l~·~l_!. ___ -.-.~ L.~)~·,,,,.
, ~ I " b) I h. I '~ " . r----'-I' .. ''''J-L .. .J ....... ~l.,.."..,...j\......-.-.... I'
~ " I (e) I
Y. B~\~; ~~ /'\ } ,
~l~ ,~ '-"---' c....--"'J
Ii t (d)
. ___ ~~~...., __ "'_/"}"'_J.~I/ __ f'(:::::'\ __ ~::=:"::'
10 211 .$8 ~2 Gf) !ro
2 G. Df!>
FIG. 4. X-ray diffraction spectra of (a) bulk powder, and screen-printed
YBa2Cu,07 -x films on (b) Al,03' (c) spinel, and (d) Ni-Al titanate sub
strates fired at 1000 'C for 15 min in oxygen. The unlabeled peaks corre
spond to the perovskite superconducting phase.
screen printing and sintedng at 1000 °C for 30 min in flowing
oxygen. This resulted in phase separation and the presence of
BaCu0 2 and Y 2CU20S in addition to YBa2Cu307 ,,' By
contrast, the films synthesized in the present study were es
senti.ally single phase perovskite YBaZCu307 _ x'
A number of materials are being studied as interfacial
barrier coatings to prevent the reaction between the sub
strate and the superconducting film. The results of these in
vestigations will be reported in the future.
In conclusion, it has been shown that essentially single
phase high Tc superconducting films can be synthesized us
ing a relatively simple screen printing technique. Their prop
erties are highly sensitive to the choice of the substrate mate
rial. Spinel is the best substrate material we have tested, with
zero film resistivity at 81 K and ATe (10-90%) -7 K.
We are pleased to acknowledge technical assistance
from Ron Phillips and Ralph Garlick.
lA. Kapitl.llnik, B. Oh, M. Naito, K. Char, A. D. Kent, N. Missert, E. Hell
man, S. Amason, J. W. P. Hsl.l, M. R. Hahn, P. Rosenthal, R. Barton,
M. R. Beasley, T, H. Geballe, and R. H. Hammond (unpublished).
2M. Hong, J. Kwo, C. H. Chen, R. M. Fleming, S. H. Liou, M. E. Gross,
B. A. Davidson, H. S. Chen, S, Nakahara, and T, Boone (unpublished).
'N. P. Bansal, R. N. Simons, ami D. E. Farrel!, Proc. Am.. Ceram. Soc.
Mtg., Cincinnati, OH, May 1988 (unpublished).
4H. Koinuma, T. Hashimoto, T. Nakamura, K. Kishio, K. Kitazawa, and
K. Fueki, Jpn. J. AppL Phys. 26, L761 (19B7).
'R. C. Budhani, S.-M. H. Tzeng, H. J, Doerr, and R. F. Bumnah, Appl.
Phys. Lett. 51,1277 (1987).
6N. P. Bansal and A. L Sandkuhl, Appl. Phys. Lett. 52, 323 (1988).
7M. Naito, R. H. Hammond, B. On, M. R. Hahn, J. W. P. Hsu, P. Ro
senthal, A. F. Marshall, M. R. Beasley, T.H. Gebalie, and A. Kapitulnik, J.
Mater. Res. 2, 713 (1987).
8M. F. Yan, W. W. Rhodes, and P. K. Gallagher, J. Appl. Phys. 63, 821
{l988}.
Bansal, Simons. and Farrell 605
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142.157.129.8 On: Sat, 13 Dec 2014 17:59:32 |
1.584073.pdf | Contrast enhancement of resist images by surface crosslinkage
H. Hiraoka, W. Hinsberg, N. Clecak, A. Patlach, and K. N. Chiong
Citation: Journal of Vacuum Science & Technology B 6, 2294 (1988); doi: 10.1116/1.584073
View online: http://dx.doi.org/10.1116/1.584073
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/6/6?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 128.59.226.54 On: Wed, 10 Dec 2014 00:16:14Contrast enhancement of resist images by surface cross .. linkage
H. Hiraoka, W. Hinsberg, N. Clecak, and A. Patiach
IBMAlmaden Research Center. San Jose. California 95120-6099
K. N. Chiang
IBM 1: J. Watson Research Center. P. O. Box 218, Yorktown Heights, New York 10598
(Received 3 June 1988; accepted 2 August 1988)
A general method of contrast enhancement which provides control of resist image wall profiles
and is applicable to both positive and negative work.ing resists may be obtained by surface cross
linking. The cross-linking is used in our process to retard dissolution at the resist surface. The
creation of a slower dissolving surface layer affords greater control of wall profiles and enhanced
contrast or sensitivity. One method is to use mid-and deep-UV flood exposure. For a negative
working electron beam resist this method is the same as surface photo absorption for contrast
enhancement. With our experimental resist containing 4,4'-diazido-diphenylsulfide as a
sensitizer, the improvement in its electron beam sensitivity was not substantial. For a positive
working photoresist, the same aromatic bisazide was added to conventional positive working
photoresists composed of a diazo-naphthoquinone-type photosensitizer and novolac resin. A
short-300-nm UV flood exposure fonowed the G-line imagewise exposures. Another method is to
use diffusion-controlled chemical reactions by treating imagewise exposed resist films in a
multifunctional cross-linking agent prior to image development. Using these methods, a higher
contrast and wall profile centrol have been demonstrated with positive working photo and
electron beam resists,
I. INTRODUCTION
Many advances in the field of optical lithography have made
possible the extension of its resolution to the one-half-mi
cron range. Advances have been made in optical systems,
lithographic materials, and processes which use these mate
rials. The use of contrast enhancing layers (CEL) in optical
lithography contributes to the general effort to extend its
capability. I However, because CEL depends on bleaching
for its effect, its use requires an excessive dose of UV light.
Further, its application is limited to positive working photo
lithography.
The surface photo absorption for contrast enhancement
(SPACE) method has been reported for negative working
electron beam resists, specifically RD2000N.2 With a deep
UV flood exposure of ~ 10 mJ/cm2, in addition to
imagewise electron beam exposures, an enhancement of con
trast and resolution ofRD2000N resist is obtained. Further
more, a sensitivity increase by a factor of 4 is reported in a
negative working electron beam resist.2
Several other methods have been reported for increasing
the resolution and contrast of photo resists such as the built
on-mask (BOM)/,4 built-in-mask (BIM),5 and portable
conformable mask (PCM) techniques.6 Related to contrast
enhancement, wall profile control of resist images has been
demonstrated using a profile modification technique (Pro
mote),4,7 image reversal (ImRe),8 orchlorobenzene soak
ing.9 However, these techniques are either complicated, or
they are limited to a certain mode of lithography, and are
applicable only for a specific kind of photoresist.
We would like to expand the concept of SPACE to the
more general case, including both positive and negative
working resists. This surface cross-linking process may work
for any kind of microlithography, although the results pre
sented here are limited to positive working photoresists. Sur-face cross-linking is used in our process to retard dissolution
at the resist surface. The creation of a slower dissolving sur
face layer affords greater control of waH profiles and en
hallCed contrast or sensitivity. There are several methods to
achieve surface cross-linking. One approach is to use flood
exposure with low-energy electron and ion beams. The sec
ond method is to perform a mid-and deep-UV flood expo
sure to activate a cross-linking agent like an aromatic bisa
zide which has been added to a conventional photoresist. An
aromatic bisazide like 4,4' -diazido-diphenylsulfide has an
absorption band at 310 nrn and no absorption at the Hg G
line at 436 nm. The third method of surface cross-linking is
to use diffusion controlled, chemical reactions with a func
tional reagent in an inert solvent. In the last case, improved
contrast, wall profile control, and reduced resist thickness
loss can be obtained. For the present purpose such a chemi
cal treatment must be carried out prior to the image develop
ment, which is different from similar image enhancement
processes. 10
Ii. EXPERIMENTAL
A. Resist formulation
For photochemical surface cross-linking, an aromatic bi
sazide was added to a composite photoresist of a diazon
aphthoquinone-type photosensitizer and a cresol-formalde
hyde novolac resin. The requirement for the aromatic
bisazide is that its UV absorption range should be far away
from the Hg G-line (436 nm), wi.th which these photoresists
are imagewisc exposed. Typically, 4,4'-diazido-diphenylsul
fide and 3,3' -diazido-diphenylsulfone meet this require
ment. Other cross-linking agents may also qualify for our
purpose. The results presented here were obtained with 4,4'
diazido-diphenylsulfide added to a concentration of 10
wt. % of total solids. Positive working photoresists like
2294 J. Vae. Sci. Techno!. B 6 (6), Nov/Dec 1988 0734-211X/88/062294-04$01.00 19 1988 American Vacuum Society 2294
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AZl350J, AZ1350J, AZ1450J, and AZ1375 were success
fully tested in our experiments.
B. Imagewise UV exposures
Projection printing using Perkin-Elmer model 500 and
300 aligners, and proximity printing with a Cobalt aligner
were carried out. all yielding equivalent results.
C. MidaUV flood exposure
An array of Rayonet photochemical reactor lamps for
300-nm irradiation was used with exposure times of8 to 14 s.
This lamp bank has an output of 1 rnJ/cm2 with almost 80%
in a range of 300 to 320 nrn and the rest at 254 nm.
D. Scanning electron beam exposures
Electron beam exposures were done in our facility using a
vector-scan electron beam exposure system.
E. Diffusionacontrolled chemical crossalinklng
Prior to image development but after imagewise exposure,
the resist film was dipped into a xylene solution containing
cross-linking agents heated at 60 "C for 2 to 8 min. After this
treatment, thorough rinsing in xylene is necessary.
F.lmage development
A KOH-based developer AZ2401 was diluted four times
by volume in water. The image development was carried out
in a dipping mode. As described later, mid-UV flood-ex
posed resist films required a longer development time than
the unexposed ones by a factor which depended on the
imagewise exposure scan speed and the mid-UV ft.ood expo
sure period. Similarly, chemically surface-treated resist
films took longer image development times than the ones
without the treatment.
III. RESULTS AND DISCUSSION
A. Wall profile control by photochemical surface
cross~linkage
Without a mid-UV flood exposure after imagewise expo
sure, the patterns obtained with the modified resist formula
tion are exactly the same as those obtained with unmodified
resist, as shown in Fig< 1 (a). The characteristic of non inter
ference of these two photoactive compounds (PAC), the
positive working diazonaphthoquinone-type PAC and a
negative working, cross-linking aromatic bisazide. has been
reported in a dual tone resist. 1 1,12
With a short mid-UV flood exposure after imagewise ex
posure but prior to image development, only superficial
cross-linking occurs. The extent of cross-linking depends on
the mid-UV flood exposure period, the concentration of aro
matic bisazide and on its absorption spectrum (thereby on
the structure of the aromatic bisazide), The results present
ed here were obtained with 4,4'-diazido-diphenylsulfidc at a
concentration of 10 wt. % of total solids. As shown in Fig.
l(b), with a short flood exposure (8 mJ/cm2 for 8 s), a
surface cross-linked layer appears with small undercutting.
The image development behavior of UV flood-exposed
J. Vac. Sci. Technol. 13, Vol. 6, No.6, Nov/Dec 1938 2295
FIG. l. SEM photographs of AZ1450J containing an aromatic bisazide
with imagewise exposure using No.4 filter by PE-500; (a) no UV flood
exposure, 8000 scan speed, 120 sin (1:4) AZ2401 developer, (b) 8-s UV
flood exposure, 8000 scan speed, 150 s in the developer, (c) no UV flood
exposure, 6000 scan speed, 90 s in the developer, and (d) 14 s UV flood
exposure, 6000 scan speed, 130 s ill the developer.
AZ1450J film with an added bisazide is shown in Fig. 2, and
the resist film thickness after complete image development
and development times are shown in Table I, using varying
scan speeds ofthe PE-500 aligner. During the development,
the mid-UV flood exposed resist layers show no thickness
loss, while in absence of the flood exposure a small amount of
thickness loss is always observed. This thickness loss is par
ticularly severe with micron-sized images as shown in Fig.
1 (c) in comparison with Fig. 1 (d). However, in electron
beam exposures of a negative-tone resist composed of chlor
inated cresol-formaldehyde novolac resin and 4,4/ -diazido
diphenylsulfide,13 no large sensitivity enhancement was ob
served, although a small, but definite increase due to reduced
Development Time, min.
FIG. 2. Dissolution rates of AZ 14501 exposed by PE-500 aligner with No.
4 filter in ( 1:4) AZ240 1 developer for different scan speeds: (-) without
UV flood exposure, (---) with 8 mJ/cm2• (0, It) 800088 (6, AI.) 600088.
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TABU L AZ 1450J with 4,4' -bisazido-diphenylsulfide ( 10 wt. % of solids) .
Mid-UV Resist
exposure thickness Development
(s) ({lm) (min)
(a) 4000 scan speed (PE-SOO):
0 1.850 3.5
8 1.955 4.7
II 1.955 5.7
(b) 6000 scan speed (PE-500):
0 1.960 3.4
8 1.975 4.2
(c) 8000 scan speed (PE-SOO):
0 1.940 3.8
8 1.980 5.1
resist thickness loss has been noticed, as shown in Fig. 3.
More experiments are necessary to further establish these
factors. Electron beam exposures of a positive working pho
toresist will be reported next.
B. Diffusion-controlled surface cross-linkage
A dual tone photoresist with an added aromatic bisazide
cannot be used in electron beam lithography, because both
bisazide and diazonaphthoquinone photoactive compounds
undergo electron beam induced reactions, which provide op
posing effects to the dissolution characteristic of novolac res
ins. One solution for this nonselective behavior of electron
beams is to use high flood exposure doses onow-energy elec
tron or ion beams after imagewise exposures, so that cross
linking ranges are limited by shallow penetration depths of
keY energetic particles. The high-dose electron or ion beam
exposure for surface cross-linkage is not limited for doped
novolac resin-based photoresists, but it works on nondoped
photo resists as well.
Another method is to use diffusion-controlled chemical
reactions with a multifunctional cross-linking agent dis-
1.0
'" c 'c
'(ij
E
OJ a:
"' '" '" c
-'" .!2 0.5 .r:: l-
t;
'1); .,
a:
'" .~
'" 0; a:
0.0
1.0 10.0 100.0
Dose, 1O-6C/cm2
FIG. 3. Effects of UV flood exposures on the electron beam sensitivity of
chlorinated cresol-formaldehyde novolac resin-4,4' -diazido diphenylsul
fide. (---) 0 flood UV, (-. -) 8 mJ/cm', and (-) 12 mJ/cm2•
J. 'lac. Sci. Techno!. 5, Vol. 6, No.6, Nov/Dec 1988 2296
solved in an inert solvent like xylene. A silicon containing
compound is used in the present study. However, it is not
limited to such a compound, but many others will serve for
the same purpose. The result obtained is shown in Fig. 4.
Diffusion-controlled surface cross-linking is applied with
the retention ofthe resist working mode. It works in positive
tone without image reversal and without a further excessive
dose of UV or electron beam exposure. Figures 4(a) and
4(b) show patterns of resist films from the same wafer,
which are exposed in exactly the same way imagewise, with a
Perkin-Elmer model 300 aligner, after prebaking at 85°C
for 15 min. Figure 4 (a) is the image obtained in (1:4)
AZ2401ldeveloper after 1.0 min development with a thick
ness loss of 0.025 11m from the original thickness of' 2.405
lim. Figure4(b) is the image obtained after a chemical treat
ment at 60 cC, followed by rinsing and 2.5-min development
in ( 1:4) AZ2401 developer with no thickness loss. The con
trast of the images has been improved significantly, as
shown. The resist wall profile control may be possible in this
way. The enhancement of oxygen reactive ion etching and
thermal flow resistances of developed resist images treated in
a similar process has been reported. 10
The diffusion-controlled chemical treatment has been
successfully applied to a positive working electron beam re
sist as shown by undercutting structures of AZ1450J shown
in Fig. 5. Figure 5(a) shows the AZ1450J resist images of25
keY scanning electron beams with a dose of 50 f.1C/cm2. The
images were developed in (1:4) AZ2401 developer for 50 s
with a thickness loss 01'0.08 f.1m from the original thickness
of2.525 f.1m. Figure 5 (b) shows the images developed after a
2.S-min chemical treatment at 60°C of the electron beam
exposed AZ 1450J resist films with a dose of 50 f.1C/cm2• The
image development took longer, 2.5 min, but due to the sur
face cross-linking no thickness loss was observed. Instead,
the undercut wall profile with a clearly defined opening was
obtained. In order to obtain this kind of wall profile in elec
tron beam lithography, a much higher electron exposure
dose is required with such a slow photoresist, 14 indicating a
practical improvement in the positive working electron
beam resist.
FIG. 4. Effect of a diffusion-controlled chemical treatment on positive
working AZ1450J photoimages; (a) no treatment after imagewise expo
sure, followed by development in (1:4) AZ2401 developer for 1.0 min,
and (b) 705 min in a cross-linking agent containing xylene at 60 "C, fol
lowed by rinsing and image development in (1:4) AZ2401 developer for
2.5 min.
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FIG. 5. Effect of a diffusion-controlled chemical treatment on positive
working AZ1450J electron beam images with 50 fJ.C/cm", (a) no treat
ment after scanning c-beam exposure, followed by image development in
(1:4) AZ240i developer for 50 s, and (b) 2.5 min in a cross-linking agcnt
containing xylene at 60 'C, iollowed by rinsing and imagc development in
(1:4) AZ2401 developer for 2.5 min.
IV. CONCLUSION
Surface cross-linkage provides a means to control the wall
profiles of resist images, and to reduce resist thickness loss
J. Vac. Sci. TechnoL e, Vol. 6, No.6, Nov/Dec 1985 2297
during image development. Surface cross-linking by photo
chemical reactions has been applied to positive working pho
toresists. For positive working optical and electron beam
resists, diffusion-controlled chemical reactions using a mul
tifunctional cross-linking agent have been successfully ap
plied,
'P. R. West and B. F. Griffing, Proc. SPIE 394,33 (1983).
20. Suga, E. Aoki, S. Okazaki, F. Murai, H. Shiraishi, and S. Nonogaki, J.
Vac. Sci. Techno!. B 6,366 (1988).
'F. A. Vollenbroek. W, 1'. M. Nijssen, H. 1. J. Kroon, and B. Yilmaz,
Microelectronic Eng. 3, 245 (1985).
"F. A. Vollcnbrock and E. J. Spiertz, Adv. Polymer Sci. 84, 86 (1988).
'F. A, Vollenbrock, W. P. M. Nijsscll, M. J. H, J. Geomini, C. M. 1. Mut
saers, and R. J. Visser, Microc1ectron. Eng. 6,495 (1987).
'fl. J. Lin, Solid State Technol. 26,105 (1983).
7F. A. Vollenbroek, E. 1. Spiertz, and Ii. J. J. Kroon, Polym. Eng, Sci. 23,
925 (1983),
xH. Moritz and G. Paal, D, S. Patent No.4 104070 (1978).
OM. Hatzakis, B. C'anavello, and J. Shaw, Proc. Microcircuit Eng. 439
( 1980).
IOFor example, H. Hiraoka, Proe. SPIE 771,174 (1987).
!ly. Nakamura, S, Yamamoto, T. Kornine, A. Yokota, and H. Nakane,
German Patent. DE3337315Al; Japanese Patents JP57-179325, JPS7-
190544, JP57 -190545.
"w. D. Hinsberg, S. A. MacDonald, L A. Pederson, and C. G. Willson,
Proc. SPIE 920, 2 (1988).
uH. Hiraoka, A. Patlach, K. N. Chiong, D. Seligson, and P. Pianetta, Pmc.
SPIE 920, 128 (1988).
\'M. Hatzakis, J. Vac. Sci. Techno!. 12, 1276 (1975).
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 128.59.226.54 On: Wed, 10 Dec 2014 00:16:14 |
1.575330.pdf | Deep level formation and band bending at metal/CdTe interfaces
J. L. Shaw, R. E. Viturro, L. J. Brillson, D. Kilday, M. Kelly, and G. Margaritondo
Citation: Journal of Vacuum Science & Technology A 6, 1579 (1988); doi: 10.1116/1.575330
View online: http://dx.doi.org/10.1116/1.575330
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Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 155.33.16.124 On: Wed, 26 Nov 2014 17:41:44Deep level formation and band bending at metal/CdTe interfaces
J. L. Shaw, A. E. Viturro, and L. J. Brillson
Xerox Webster Research Center. Webster. New York 14580
D. Kilday, M. Kelly, and G. Margaritondo
University of Wisconsin. Madison. Wisconsin 53706
(Received 4 November 1987; accepted 29 December 1987)
We present depth resolved photoluminescence and soft x-ray photoemission spectra of cleaved
(110) CdTe interfaces with Au and In measured as a function of thermal and laser annealing.
These techniques reveal Fermi-level positions at the processed interfaces which are clustered
around discrete energies, which in tum coincide with the energies of deep levels produced by
interdiffusion and reaction at metal/CdTe interfaces.
I. INTRODUCTION
Metal interfaces with CdTe are of interest both as a prototy
pical example of a II-VI semiconductor interface and as a
key factor in device applications. 1 Metal contacts to CdTe
have been produced with a wide range of barrier heights.2
However, reproducible results for the same metal are often
difficult to achieve. 2 One reason for the poor reproducibility
is the variable quality of CdTe crystals, which may contain
large concentrations of deep and shallow levels due to both
native defects and impurities. Segregation of either Cd or Te
at the interface may produce additional states. For example.
a traditional method of fabricating Ohmic contacts to p
CdTe utilizes the p + layer, presumably created when Cd is
depleted from the surface with etchants.3 The relationship of
the interface electronic structure and chemistry at contacts
to etched surfaces is difficult to determine, however, since it
is complicated by various oxides and other contaminants.4.5
We measured the formation of deep levels at clean metal!
CdTe interfaces with photoluminescence spectroscopy
(PLS), Fermi-level movements at the interface with soft x
ray photoemission spectroscopy (SXPS). and barrier
heights with internal photoemission as a function of metal
coverage and annealing. By using these complementary
techniques, we are able to observe both the phenomenon of
band bending, and the formation of gap states at the inter
face, often cited as a possible cause of band bending.
II. EXPERIMENTAL
We prepared CdTe surfaces by cleaving bars of bulk
grown material in ultrahigh vacuum (UHV) to expose the
(110) face. SXPS measurements were carried out at the Uni
versity of Wisconsin Synchrotron Radiation Center Grass
hopper II beam line with spectral resolution better than 0.15
eV. We measured surface (bulk) sensitive Cd 4d and Te 4d
core level spectra using photon energies of 70 e V (40 e V)
and 100 eV (70 eV), respectively. The specimens used to
make SXPS measurements of Au and In interfaces (Cleve
land Crystals Inc.) had resistivities of 10 and 1000 n cm
respectively. The crystal used for the PL measurement~
(Galtech Inc.) had resistivity> 106 n cm. We reduced the
resistivity of this crystal by annealing it at 800·C in a sealed
high-purity quartz ampule in the presence of Cd metal. 3 Oh
mic In contacts were prepared by heating in a reducing at-mosphere.6 Based on the sample resistivity of 2.3 n cm and
assumingJt = 1000 cm2 IV s at room temperature we calcu
late a net ionized donor concentration of 2.7X 1015 cm-3•
We P!epared a Au/CdTe interface by thermal deposition of
loo-A Au onto a cleaved (110) surface of the Cd-treated
Galtech crystal. We then annealed the interface in UHV'
first at room temperature, then at 300 ·C for 2 min, and final~
ly with a XeCI excimer laser producing 0.1 J!cm2 at 308 nm
in 5-ns pulses at the interface. Internal photoemission spec
tra (IPS) of this interface were measured in situ at 15 K by
contacting the Au covered surfaces with a smooth Au wire
tip. The photocurrent was induced by light from a prism
monochromator illuminated with a quartz-halogen bulb. In
situ 15 K PL spectra were measured using the same mono
chromator and a Ge detector. The response of the detection
system was corrected numerically by comparison of a black
body spectrum with the measured spectrum of the quartz
halogen bulb. Electron-hole pair excitation was provided by
HeNe and HeCd lasers emitting 6328 A (red) and 4416 A
(blue) photons, which have extinction depths in CdTe of
-2000 and 1000 A, respectively (based on theoretical val
ues of the complex dielectric function 7).
Comparison of PL spectra excited with blue versus red
light provided an effective means of distinguishing between
bulk and near-interface recombination centers. The built-in
electric field eliminates diffusion of excited electron-hole
pairs generated within the depletion width. II Thus the rela
tive intensity of luminescence from deep levels located only
near the surface is increased in spectra for which electron
hole pairs are excited close to the surface in comparison with
spectra excited deeper within the depletion layer. Band
bending can also be detected since transitions involving
loosely bound carriers are quenched within the depletion
layer. Transitions from deep levels will occur even in the
presence of an electric field, provided that the capture cross
sections of the states are large enough to keep the states pop
ulated despite the reduced free-carrier concentration.
III. RESULTS
Figure I shows two PL spectra of an aged Au/CdTe inter
face excited with red (bottom) and blue (top) light. Two
features, a peak at 1.57 and a shoulder at 1.0 eV, are present
in the red light excited spectrum only. The states associated
1579 J. Vac. Sci. Technol. A 6 (3), May/Jun 1988 0734-2101/88/031579-05$01.00 © 1988 American Vacuum Society 1579
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>
~
en z
UJ
~
Z
w
U
Z w
U (/) w z
~
::J
...J Au/CdTe
PL 14 K
0.7 0.9 1.1 1.3 1.5 1.7
PHOTON ENERGY(eV)
FIG. 1. 14 K photoluminescence spectra of an aged Au/CdTe interface as
excited with 6328-and 4416-A light.
with these transitions have low capture cross sections and
can be filled only in the neutral region, where a small fraction
of the red light penetrates. (Assuming a donor concentra
tion N D = 2.7 X lOIS cm -3, and a barrier height of 0.6 eV,
the depletion layer will be ~5100 A wide, so that -8% of
the red light will penetrate into the neutral bulk. ) In contrast
to the features at 1.0 and 1.57 eV, excitation with blue light
increases the 1.1-eV peak intensity relative to the peak at 1.4
eV. This feature may therefore be associated with a state
concentrated close to the metal interface.
Figure 2 shows blue light excited PL spectra ofa CdTe
surface just after cleaving, and covered with 100 A of Au
after aging, thermally annealing, and laser anneaJing. We
find that cleaving in vacuum is necessary to produce uniform
and unpinned surfaces. Air-exposed and etched surfaces
produce PL spectra which vary across the surface and have
much lower intensity than the spectrum ofthe UHV cleaved
surface shown. This spectrum shows transitions at 1.57, 1.4,
1.1, and 1.0 eV. The peaks at 1.57 and 1.4 eV are commonly
observed.9 The 1.57-eV peak may be resolved into several
lines corresponding to bound excitation and donor-valence
band transitions. The presence of this peak shows that no
band bending is present at the cleaved surface. The 1.4-eV
peak is made up of several phonon replicas arising from do
nor-acceptor recombination." The broadband near 1 eV is
made up of two peaks at 1.0 and 1.1 eV. Spectra of UHV
cleaved surfaces excited with red and blue light have identi
cal shape.
After measuring initial PL spectra, 100 A of Au was de
posited onto the same surface. No luminescence could be
detected immediately after Au deposition; however, lumi
nescence returned after aging the interface for one day. The
J. Vac. Sci. Techno!. A, Vol. 6, No.3, May/Jun 1988 Au/CdTe
PL 14 K 4416A
annealed
300 C
100 A Au
aced 20hr
0.7 0.9 1.1 1.3 1.S
PHOTON ENERGY(eV) 1580
x200
x200
1.7
FIG. 2. 14 K photoluminescence spectra excited with 4416-A light of a UHV
cleaved (110) surface of Cd treated CdTe (Galtech) and the 100-A
Au/CdTe interface aged 20 h, annealed at 300 'C for 2 min, and laser an
nealed at 0.1 l/cm'.
peak at 1.57 eV is quenched in this spectrum, indicating
band bending. Band bending at this interface was verified
with IPS, which showed the EF position to be 0.7 eV below
the conduction-band miminum (Ec). The peak at 1.0 eV
was also quenched by the electric field. As shown for a simi
lar interface in Fig. 1, the intensity of the peak at 1.1 e V
relative to the peak at 1.4 eV was larger in the blue light
excited spectrum than in the red light excited spectrum, indi
cating that the associated state is concentrated near the sur
face. This result is confirmed by the additional increase in
the relative height of the l.l-eV peak found in the spectrum
measured after thermal annealing.
Laser annealing induced several dramatic changes in the
PL spectrum. The donor-acceptor band formerly peaked at
1.4 eV shifted nearly 50 meV to lower energy. This shift was
reduced by 10 meV in the spectrum excited with red light.
The I.l-e V peak associated with interface states is also shift
ed to lower energy. The relative intensity of the 1.35-and l
eV peaks is also reversed from the previous spectra. Finally,
the high-energy tail of a new emission is found just above
0.73 eV, the cutoff of our Ge detector. Each of these changes
was exaggerated in the spectra excited with blue light com
pared to the red light excited spectra. We were able to ob
serve the peak of a low-energy emission similar to the 0.7-eV
tail promoted by laser annealing in a CdTe specimen doped
with Ga by using an InSb detector. This emission peaked at
0.64 eV.
The SXPS Cd 4d and Te 4d core level spectra of a CdTe
surface measured as a function of Au coverage and subse
quent annealing are shown in Fig. 3. Valence-band spectra of
the cleaved surface indicated an initial E F position just below
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24 26 28 24 26 28
KINETIC ENERGY
FIG. 3. Soft x-ray photoemission Te 4d and Cd 4d core level spectra of a
CdTe( I 10) surface: cleaved. after deposition of the Au coverages indicated.
and after laser annealing at the power levels indicated.
Ee. The Te 4d doublet is well resolved and showed little
chemical shift, either in the bulk or surface sensitive spectra,
thus providing a straightforward reference for Fermi-level
shifts. The Te 4d core level shifts continuously to higher
kinetic energy with Au coverage, showing Fermi-level
>tiii z w
~
H
53 54 55 56 CdTe (110). In
55 56 57 58
KINETIC ENERGY (eV)
J. Vac. ScI. Technol. A, Vol. 6, No.3, May/Jun 1988 59 55 1581
movement toward the valence-band maximum (E v), The
final EF position after 20-A Au deposition was 0.5 ± 0.2 eV
above Ev. The EF position moved 0.4 eV back toward Ee
after aging the interface at room temperature one day.
Changes in SXPS core level intensities reveal that Te outdif
fusion and Cd dissociation accompanied the core level shift
after aging. Laser annealing the surface caused further E F
movement until the Te 4d peak returned to its initial posi
tion. The EF shifts found as the interface was formed and
subsequently annealed are plotted in Fig. 5.
The In 4d, Te 4d, and Cd 4d core level spectra measured as
In was deposited and after laser annealing are shown in Fig.
4. Analysis of the valence-band spectra of the clean surface
showed the E F position to be at midgap, close to the position
expected for a high-resistivity sample without band bending.
The initial O. 5-A In coverage leads immediately to a metallic
In peak plus a small reacted (In-Te) component. Neither
the Cd 4d or Te 4d peaks show any reaction, but both shift
0.3 e V towards lower energy, showing E F movement toward
Ee. Increased In coverage causes no further energy shifts or
shape changes. Strong and complete In bonding does occur
upon laser annealing, as indicated by the large In 4d shift to
higher binding energy. The bonding occurs simultaneously
with EF shifts toward Ee. The EF shift occurs in two stages
with power thresholds at -0.15 and 0.7 J/cm2• This staged
band bending induced by annealing is shown in Fig. 5.
IV. DISCUSSION
Both metal deposition and thermal processing cause pro
nounced changes in CdTe deep level emission and EF posi
tion. The initial E F position at the In/CdTe interface was 0.8
56 57 58 59 FIG. 4. Soft x-ray photoemission In 4d. Te 4d.
and Cd 4d core level spectra of a CdTe( I 10)
surface: cleaved. after deposition of the In
coverages indicated. and after laser annealing
at the power levels indicated.
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o 1.0
CD
0.5
0···· L.~} I
> 0 2 4
~ Q
> In COVERAGE (AI
w , ... w
l.5 "'~'T -II-,-
l.0
0 0
0.5
0 I.-..-.-L
0 2 4
Q
Au COVERAGE (AI o
20 00 0 o
0.2 o
In/p'CdTe
OA 0.6
J/cm2 0.8
l---LASER ANNEALlNG~
--~. ---'----------"\
0 0
0 0 I
36HR
I
0 Au/n-CdTe
20 0.2 0.4 0.6 0.8
J/cm2
FIG. 5. Fermi-level positions relative to the valence-band edge for the Inl
CdTe interface and the Au/CdTe interface as a function of metallization
and laser annealing.
e V above E v' This position is 0.9 e V lower in the gap than
expected from a classical work function model. The low po
sition may be caused by midgap defects present in the bulk
material or the In-Te reaction indicated in the In 4d core
spectrum measured at submonolayer coverage. The E F posi
tion at the clean and still relatively abrupt Au interface is
only 0.5 eV above E v' however this position is unstable, even
at room temperature. The initial EF position is in agreement
with a work function model for barrier height 10.11 and argues
strongly against a metal-induced gap states model. 12 Similar
results have been obtained previously with alloyed Au/Cd/
n-CdTe interfaces I, and occasionally at pure Au interfaces
with cleaved n-CdTe.2 After aging the Au/CdTe interface at
room temperature in UHV, both IPS and SXPS show EF
movement to E v + 0.9 eV, accompanied by Au-Te interdif
fusion. This higher E F position is the one usually reported. 14
Thus, larger Schottky barrier heights than usually found can
be achieved by preventing Au-CdTe interdiffusion. If the
low-energy (0.64-eV) PL peak is due to a transition between
a shallow donor and a deep state, the energy of the deep state
will be -0.7 eV below the conduction-band minimum. The
correlation between the E F position and the energy of this
deep state suggests that the state is stabilizing the EF•
Further E1' movement occurs as both the Au and In/
CdTe interfaces are laser annealed. The EF movements plot
ted in Fig. 5 show that the E F is stabilized at an intermediate
position near 1 eV. Again, this position corresponds to the
energy of a deep level revealed in the PL spectra. We mea
sured surface photovoltage and photocapacitance spectra
which allow us to assign the I.I-e V peak to a transition with
the valence band, showing that the deep level is 1.1 e V above
E v' PL transitions below 1.4 eV apparently located at the
surface region have been reported previously,9,14 however,
J. Vac. Sci. Techno/. A, Vol. 6, No.3, May/Jun 1988 1582
their identity is not clear. We observe the 1.0-and l.l-e V
peaks as well as peaks at 0.9 and 1.2 eV in PL spectra of melt
grown CdTe specimens from several suppliers. The intensi
ty, but not the energy, of these peaks varies dramatically
from crystal to crystal. Hence, we expect that one or more of
these peaks are related to native defects. Since the relative
intensity of the 1.I-e V transition increases at the interface
concurrently with Au diffusion, the associated level may ei
ther be induced directly by diffused Au, or related to a re
duced Te concentration at the interface which occurs as Te
outdiffuses. The latter possibility seems more likely since the
1.1-eV emission was observed before Au deposition.
Laser annealing at high-power densities causes the E1' to
move nearly to Ec-The PL spectra show a corresponding
shift in the position of the 1.4-eV donor-acceptor band, indi
cating a major change in the coupling between these defects
and the lattice, and probably an increase in their concentra
tion. Similar shifts in this peak position have been related to
stoichiometry shifts 15 toward Cd excess, in agreement with
our SXPS data. Excess Cd produces shallow donor states,3
explaining the high final EF position.
The correlation of the Ep position found at both the Au/
CdTe and In/CdTe interfaces with the PLS transition ener
gies is illustrated in Fig, 6. Here the In/CdTe interface EF
positions and the 77 K PL spectrum of a cleaved, air-exposed
surface from the same CdTe crystal are plotted with coinci
dent energy axes for comparison. Plateaus in the EF position
as a function of metallization and processing are approxi
mately coincident with the deep level emission energies. The
correlation is improved when the difference in band gap at
low versus room temperature is considered. The relative in
tensity of the I.I-e V peak in this PL spectrum is very large,
suggesting a role of bulk defects in determining the initial E F
position. A similar correlation can be made with the Fermi
level movements observed at the Au/CdTe interface and the
PL spectrum ofthe corresponding CdTe crystal. The similar
EF stabilization energies found at both interfaces suggests
that the deep states involved are due to native defects or
INTENSITY 1.6,---------------------------;
~
~ 1.2
~ 0.8
w
~ 5
if 04 o
o
o L-____ ..L.----'-_.L-._-----' __ -'--_~_ ..
0.2 0.4 0.6 0.8
LASER ANNEALING (J/cm2) > w
I
"w
FIG. 6. Correlation of the Fermi-level movements as a function of metal
coverage and laser processing from Fig. 5 with the 77 K photoluminescence
spectrum of the air-cleaved surface (plotted on the same energy axis).
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impurity complexes whose energy is nearly independent of
the impurity.
v. CONCLUSIONS
We have measured the chemical reaction and diffusion
which occur at Au and In/CdTe interfaces as well as the
associated Ep changes which occur with metallization and
processing. These results show that the E p position depends
on the degree to which the interface is interdiffused or react
ed. Furthermore, the E p positions correlate with the ener
gies of deep levels present in the bulk material and generated
at the interface. These results demonstrate the possibility of
improved control over the electronic properties of metal!
CdTe interfaces.
ACKNOWLEDGMENTS
Sample CdTe specimens donated by Galtech Inc. and II
VI Inc., assistance from Jim Zesch in orienting and cutting
them, plus partial support by the Army Research Office
J. Vac. Sci. Technol. A, Vol. 6, No.3, May/Jun 1988 1583
(Contract No. DAAL03-86C-0003 ) are gratefully acknowl
edged.
I K. Zanio, Semiconductors and Semimetals (Academic. New York. 1978).
Vol. 13.
21. M. Dharmadasa, W. G. Herrendon·Harker, and R. H. Williams. Appl.
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°v. S. Vavilov, A. A. Gippius, and J. R. Panossian, in II-VI Semiconduct·
ing Compounds, edited by D. G. Thomas (Benjamin, New York, 1967). p.
743.
IOAssuming the CdTe electron affinity is 4.3 eV and work function of Au is
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D. E. Eastman. in Techniques of Metals Research (Interscience, New
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lie. Mailhiot and Duke. Phys. Rev. B 33, 1118 (1985).
"J. Tersoff, Phys. Rev. Lett. 52. 465 (1984).
13T. F. Kuech,J. Appl. Phys. 52. 4874 (1981).
14D. J. Friedman. J. Lindau. and W. E. Spicer (in press).
I'C. B. Norris and K. R. Zanio, 1. Appl. Phys. 53. 6347 (1982).
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1.342389.pdf | Singletarget magnetron sputter deposition of highT c superconducting BiSrCaCuO thin
films
Neelkanth G. Dhere, John P. Goral, Alice R. Mason, Ramesh G. Dhere, and Ronald H. Ono
Citation: Journal of Applied Physics 64, 5259 (1988); doi: 10.1063/1.342389
View online: http://dx.doi.org/10.1063/1.342389
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/64/10?ver=pdfcov
Published by the AIP Publishing
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141.212.109.170 On: Mon, 22 Dec 2014 14:40:29Single .. target magnetron sputter deposition of high", Tc superconducting
Bi .. Sr .. Ca .. Cu .. O thin films
Neelkanth G. Ohare,a) John P. Goral, Alice R Mason, and Ramesh G. Ohere
Solar Energy Research Institute. 1617 Cole Boulevard, Golden, Colorado 80401
Ronald H. Ono
National Bureau a/Standards. 325 Broadway, Boulder, Colorado 80303
(Received 31 May 1988; accepted for publication 8 August 1988)
Single-target RF magnetron sputtering was used to deposit superconducting thin films of Bi
Sr-Ca-Cu-O with a T cO above 80 K. Varying Po, modified the concentrations of Bi, Cu, and 0
in the films by 10%-20%. Higher annealing temperatures, especially with brief melting,
favored the ~ormation oft~e higher Tc phases. Tetragonal phases (6-and 75-K Tc), with
a = 3.8097 A, c = 24.607 A, and Bi2 Sr2 Cu06 composition, and a = 3.812 A, c = 30.66 A, and
Biz Sr 2 _ x Cal + x CUz Os composition, were identified. 70-84 K films contained large
proportions ofa new tetragonal phase, with a = 3.81 A and c = 55.23 A.
Following the discovery 1 of a superconducting material
based on Hi-Sr-Ca-Cu-O, several groups have been working
on the preparation of Hi-based superconducting thin films.
Bi-based superconducting thin films have been deposited by
Adachi et al.,2 using single-target rf planar magnetron sput
tering; by Osofsky et aJ., 3 using flash evaporation of pellets;
and by Kang et at., 4 using multitarget magnetron sputtering.
Several groups have opted for evaporation or sputtering
from multiple sources in efforts to control the composition of
superconducting thin films. Sputtering, it should be noted,
allows a certain latitude in modifying the composition by
varying the process parameters. Fairly complex geometries5
are being employed to avoid negative ion bombardment dur
ing sputter deposition of Y-based superconducting thin
films. It may not, however, be necessary.
Direct deposition from a single source has the advan
tages of simplicity and ease of process development for large
scale production. Among the techniques employed, flash
evaporation suffers from the problem of dispensing fine
powders in high vacuum. Single-target sputtering from a
ring source on directly facing substrates, however, has the
additional advantages of more efficient material utilization
and better plasma isolation.
The crystallographic structure and composition of three
bul.k superconducting phases with transition temperatures
of 6, 75, and 120 K have been determined by Torrance et al.6
and Subramanian et al.7 Michel et al. B have also analyzed a
phase with a transition temperature between 7 and 20 K.
However, information about the effects of composition and
annealing temperatures on the formation of the supercon
ducting phases in thin films is scarce. We report, in this com
munication, on the preparation of Hi-based, high-Tc super
conducting thin films from a single sputter-gun ring target;
on a study of the variation in the composition with different
oxygen partial pressures and substrate locations; and on the
oj Permanent address: Instituto Militar de Engenharia, Rio de Janeiro,
Brazil.
5259 J. Appl. Phys. 64 (10),15 November 1988 effect of annealing temperature on the formation of different
superconducting phases.
Thin films of Bi-Sr-Ca-Cu-O, 2500 A to 3 f1.m thick,
were deposited on unheated MgO and SrTi03 single-crystal,
fused quartz, and alumina substrates, by rfmagnetron sput
tering in a cryopumped sputtering system fabricated by Uni
film. Oxygen partial pressures, po., in the sputtering gas
were varied between 5 X 1O~5 and 3 X 10-3 Torr (7 X 10-3_
0.4 Pa), but the total pressure of argon and oxygen was
maintained at 5x 10-3 Torr (0.7 Pa). The hot-pressed ring
targets, made of an unreacted mixture of oxides (Bil 03 ,
SrO, CaO, and CuO) for a Sloan 8310 sputter gun, were
supplied by Kema. The nominal proportion of the target
chosen was Bi2.2 Sr 2.0 CaO.81 Cu2.0 08, based on information
available in the literature7,9 at the time the target was OT
dered. The thickness of the samples was measured by a profi
lometer. The samples were annealed at temperatures from
810 to 850·C for 5-6 h. Some of the thi.n films were held
above the melting temperature at 862 to 867 ·C for up to 20
min. The composition and crystalline structure of the films
were analyzed by electron probe x-ray microanalysis and a
Ri.gaku rotating anode x-ray diffraction system using CuKa
radiation. The sheet resistance was measured with a four
point probe. Resistance-versus~temperature measurements
were carried out at the National Bureau of Standards. The
resistance of the sample was measured, as a function of tem
perature, in a probe that was slowly lowered into a liquid~
helium dewar. The temperature was monitored by using a
calibrated carbon-glass resistor. The sample resistance was
measured in a four-probe configuration, with an ac excita
tion current of 10 pA. Contacts to the film were made with
smail-area, spring-loaded pins.
The as-deposited thin films were smooth, brownish, ho
mogeneous, transparent, and insulating. Electron probe x
ray microanalysis of the films showed them to be richer in Bi
and poorer in 0 in comparison to the target composition.
Under the target, the thickness varies as a bell-shaped func
tion. Superimposed on this, depending on the targets, there
could be up to a 10% variation in the compositions ofBi and
5259
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141.212.109.170 On: Mon, 22 Dec 2014 14:40:29Cu over a distance of7.5 em. In the present target, the con
centration of Bi increased from the center to the sides, and
that of Cn decreased. Our results are for substrates placed
near the center.
The concentrations of Bi, Cu, and 0 in the films were
found to vary with the variation of Po, in the sputtering gas.
The Sr and Ca contents of the films remained largely unal
tered. Decreases in Po, reduced the incorporation of oxygen
in the films and made them darker. The variation of Po, also
had a more interesting and potentially useful effect. At lower
Po, values, the concentration ofBi in the deposited films was
lower by up to 20%, while that of Cu was higher by -10%,
in comparison to films deposited at high Po, values. Since
oxygen incorporation in the films was significant even at the
lowest values of Po" a reduction in the excess Bi concentra
tion was obtained-by maintaining Po, at 5 X 10-:; Torr
(7 X 10-3 Pa), the lowest oxygen partial pressure employed
in the present study. At this pressure, the composition of the
as-deposited films was typically Bi2.45 Sr2.0 CaO.79 CUL87 °8.45,
The films were annealed in air at temperatures from 810
to 870·Co Films deposited on SrTiO) substrates showed
signs of peeling, while those deposited on alumina and fused
quartz substrates remained insulating. The work with
SrTi03 substrates was not pursued; the following results re
fer to films deposited on MgO substrates. Adachi et ai.2 ob
tained the best results with films that were first melted at a
temperature from 890 to 900·C for 20 min and then an
nealed at 850-865 ·C for 5 h. Greenish, insulating films re
sulted when 2soo-A-thick films were melted at 900·C and
then annealed at 865 ·C for 5 h. Our experiments were there
fore carried out by annealing the films at lower temperatures
and maintaining the annealing time at 5 h. Films annealed at
810 cC showed only a partial superconducting transition
around 70 K (Fig. 1). The films were semiconducting, and
there was a sharp drop in resistance below 20 K. The x-ray
diffraction patterns of these films showed mostly peaks from
the superconducting tetragonal phase I, in which a = 3.8097
A and c = 24.607 A (Fig. 2). This phase, with a composition
ofBil Sf2 Cu06, has been identified as the 6-K phase by Tor
rance et ai.o Increasing the annealing temperature to 825 QC
resulted in a mildly semiconducting film that showed a
W 4
U
Z
~
~
!'! 2
<fl
W a: ........• Annea.(ing Temp. 810" C
"". ....... ,,,
o~"'-........
8654-850" C ............. .t .•. , ... '
~--" .. -,,,_"'N""'·~
O~~-b~~~~~~~~~~~~~~~~
o 20 40 60 80 100 120 14D 160 iSQ 200 220 240 260 280 300
TEMPERATURE (K)
FIG. 1. Resistance-vs-temperature plots of Bi-Sr-Ca-CII-o thin films an
nealed for 5 h at 810,825,865 (20 min), and 850 ·C.
5260 J. Appl. Phys., Vol. 64, No. 10, 15 November 1968 0 " Annealing Temp. 0 ~
N 8 o 11100C a
~ '" ~
to
M
'" N 0 '"' 0 ;; 0
N
~j --== -
~ 825°C
-'" C')
8 :g o --
;?
" a <0 N "f N to 0 ",0 N 0 0 00
0 :: '" 0= -
65 60 55 45 40 35 30 25 20 15 10 5
2f1 (degrees I
FIG, 2. X-ray diffraction patterns of films annealed at 810, 825, 865, and
850 ·Cshowing the formation of phases 1(6 K), II (75 K), and HI (a new
84-K tetragonal phase).
stronger superconducting transition around 70 K and a T cO
of 12 K (Fig. 1). The best results were obtained with 2-to 3-
,urn-thick films that were first melted at 862-867·C for 20
min and then annealed at 850·C for 5 h. The resistance
versus-temperature measurements showed the onset of the
superconducting transition at 88 K, the mid transition point
at 84 K, and T cO at 80.5 K (Fig. 1). There was also an indica
tion of a very weak transition at 120 K. X-ray diffraction
patterns from the films annealed at higher temperatures
showed higher proportions of7S-K tetragonal phase II, with
a = 3.812 A and c = 30.66 A and a proposed composition of
Bi2 Sr 2 _ x Cal ~ x CUz 08•6 Several intense peaks not belong
ing to either of these phases could be indexed with a new
tetragonal phase in which a = 3.81 A and c = 55.23 A .
These peaks are marked in Fig. 2 as phase III. Michel et al.8
have proposed a phase in which a = 26.6 A, b = 5.32 A, and
c = 48.8 A for the composition Bi2 Sr2 Cu, 08" y' with the
transition temperature at 7-20 K. Subramanian et al.7 have
also observed a superlattice on thea axis of the 120~K phase.
The layer structure of the Bi family of superconductors
with its strong tendencies toward twinning and forming su~
perstructures may be permitting the formation of several re
lated phases. The lattice parameters of the new phase III do
not match those of the phase observed by Michel et al.8 The
Dhare eta!. 5260
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141.212.109.170 On: Mon, 22 Dec 2014 14:40:29phase with a transition around 6 K. that formed in the pres
ent study conforms to that proposed by Torrance et al!' As a
result of deviation from the appropriate composition in the
present target, only traces of the 120-K phase seem to have
formed.
In summary, superconducting thin films of Bi-Sr-Ca
Cu-O having a T cO above 80 K have been prepared by using
an rf magnetron sputter gun with a single target. It has been
shown that we have some latitude in adjusting the composi
tion even with a single target. It was also found that higher
annealing temperatures, especially with brief melting, favor
the formation of the higher Tc phases. Two of the phases
have been identified as tetragonal, in which a = 3.8097 A
and c = 24.607 A, the composition is Bi2 Sr 2 Cu06, and T cO
= 6 K; and a = 3.812 A and c = 30.66 A, the composition is
Bi2 Sr 2 __ x Cal t-" CU2 08, and Tc = 75 K. Large proportions
of a newer tetragonal phase in which a = 1.81 A and
c = 55.23 A were found in films showing a strong super con
ducting transition in a range from 75 to 93 K.
This work was supported by the U.S. Department of
Energy under Contract No. DE-AC02-CHl0093. It was
also partially supported through the Brazilian Ministry of
Education. The authors would like to gratefuliy acknowl
edge the late Professor John A. Thornton of the University
of Illinois for detailed discussions on the general approach
followed in this study. The authors would also like to thank
Michael Madden for help with the resistance-versus-tem-perature measurements. The product names have been men
tioned for descriptive purpose and no endorsement is im
plied.
'H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano, Jpn. J. Appl. Phys.
Lett. 27, 2 (1988).
2H. Adachi, Y. Ichikawa, K. Setsune, S. Hatta. K. Hirochi, and K. Wa~a.
lpn. J. AppJ. Phys. 27, L643 (1988).
3M. S. Osofsky, P. Lubitz, M. Z. Harford, A. K. Singh, B. S. Qadri, E. F.
Skeltoll, W. T. Elam, R J. Salllen, Jr., W. L. Lechler, and S. A. Wolf
(unpublished) .
4J. H. Kang, R. T. Kampwirth, K. E. Gray, S. Marsh, and E. A. Huff, Pitys.
Lett. 12SA, 102 (l98B).
'R. L. Sandstrom, W. J. Gallagher, T. R. Dinger, R. H. Koch, R. B.
Laibowitz, A. W. Kleinsasser, R. J. Gambino, B. Bumble, and M. F. Chis
holm (unpublished).
"J. B. Torrance, Y. TokuTa, S. J. Laplaca, T. C. Huang, R. J. Savoy, and A.
L Nazzal, Solid State Commun. 66, 703 (1988).
7M, A. Subramanian, C. e. Torardi, J. C. Calabrese, J. Gopaiakrishnan, K.
1. Morrissey, T. R. Askew, R. B. Flippen, U. Chowdhry, and A. W.
Sleight, Science 239,1015 (1988).
"e. Michel, M. Hervieu, M. M. Borel, A. Grandin, F. Deslandes, J. Pro
vost, and Ii Raveall, Z. Phys. B 68, 421 (1987).
9S. A. Sunshine, T. Siegrist, L F. Schneemeyer, D. W. Murphy, R. J. Cava,
B. Hatlogg, R. B. van Dover, R. M. Fleming, S. H. Glarum, S. Nakahara,
R. Farrow, J. J. Krajewski, S. M. Zahurak, J. V. Waszczak, J. M, Mar
shall, P. Marsh, L. W. Rupp, Jr., and W. F. Peck (unpublished).
Composition dependence of dynamic Youn~)'s modulus and internal friction
in AI2 03 ... 3Y ... Zr02 composites
Teruaki OnD
Department of Physics, Faculty of Engineering, Gi/u University, Yanagida, GI/U 501-11, Japan
Yukio Nurishi and Minoru Hashiba
Department o/Chemistry, Faculty of Engineering, GI/U University, Yanagida, Gifu 50/-11, Japan
(Received 15 June 1988; accepted for publication 3 August 1988)
The specific dynamic Young's modulus E'/p and the internal friction Q-l of A1203 -3Y-Zr02
composites with different 3Y -Zr02 content were investigated. With the increase of 3Y -Zr02
content, the E' / P decreased linearly showing a large inflection point at about 20% and. a small
one at 65%, and the Q-j reached a peak at 17% and a trough at 40%, and increased showing
a shoulder at about 70%0 The specific loss modulus E"/p calculated from E'lp and Q-l
showed the peaks at 17% and 65%. The E " / p peaks corresponded with the E' / p inflection
points in composition. As a result, it was estimated that they were due to the tetragonal to
monoclinic transformation of Zr02 phase, and that the increase of internal friction at above
40% was not due to the crack formation and the zr02 phase transformation, but due to the
flexural deformation caused by shearing force.
Alz 03 -Zr02 composites have become the object of at
tention as ceramics of high toughness. As the interior struc
ture of a material is reflected in its mechanical properties, it
is important in the studies on the mechanical properties of
composites to make clear the variation of interior structure with composition. It has been recognized that stress-induced
phase transformation and microcracks pray an important
role in the toughening of Alz 03 -ZrOz compositeso 14 How
ever, the toughening mechanism of the composites has not
been made clear sufficiently. As the tests with high stress
5261 J. Appl. Phys. 64 (10), 15 November 1988 0021-8979/88/225261-03$02.40 ® 1988 American Institute of Physics 5261
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141.212.109.170 On: Mon, 22 Dec 2014 14:40:29 |
1.1141869.pdf | Efficient generation of multigigawatt rf power by a klystronlike amplifier
M. Friedman, J. Krall, Y. Y. Lau, and V. Serlin
Citation: Rev. Sci. Instrum. 61, 171 (1990); doi: 10.1063/1.1141869
View online: http://dx.doi.org/10.1063/1.1141869
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Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsEfficient generation of multigigawaU rf power by a klystronlike amplifier
M. Friedman, J. Krall, Y. Y. Lau, and V. Serlin
NalJal Research Laboratory, Washington, DC 20375-5000
(Received WJuly 1989; accepted for publication 25 September 1989)
This article addresses the new development of high-power rfklystronlike amplifiers using
modulated intense relativistic electron beams. Development of these amplifiers follows earlier
research in which the interaction between a high-impedance ( 120-n) intense relativistic electron
beam and a low-power rf pulse resulted in the generation of coherent bunches of electrons with
excellent amplitude and phase stabilities. In the present experiment a low-impedance (30-,0,)
large-diameter ( 13.2-cm) annular electron beam of power -8 GW was modulated using an
external rf source (magnetron at 1.3 G Hz) of 0.5 MW power. The interaction of the modulated
electron beam with a structure generated a 3-GW rfpulse that was radiated into the atmosphere.
The self-fields of the intense beam provided significant electrostatic insulation against vacuum
breakdown at the modulating gaps and at the rf extraction gap.
iNTRODUCTION
In this article we describe the construction and operation of
new rf amplifiers which use intense relativistic electron
beams (IREBs). These amplifiers exploit the unique proper
ties of IREBs, specifically the high self-electric fields which
enhance the generation of electron bunches and prevent rf
breakdown at high-voltage gaps.
In 1983, we found that a high level of coherent current
oscillation appeared on IREBs propagating through a drift
region consisting of a smooth metallic tube in which two or
more coaxial cavities were inserted. l The following charac
teristics were observed2 in these early experiments of self
modulation: (1) The frequency of oscillation depended
strongly on the geometry and weakly on the IREB current
and voltage. (2) The frequency of modulation was mono
chromatic. (3) Electron beams of voltage up to 3 MV and
current up to 50 kA were fully modulated with efficiency of
nearly 100%.
A simple theoretical modell-4 showed that the "classi
cal" space-charge waves on tenuous electron beams were
modified by the self-electric field of the beams5 and that
these modified space-charge waves played an important role
in the new bunching mechanism. The theoretical model
agreed with the experimental results. Numerical simulation
confirmed theoretical predictions and extended our under
standing of the mechanism into the nonlinear region. Both
theory and simulation showed that the self-fields of the
IREB and the induced electric fields that originate from
IREB propagation through cavities caused redistribution of
energy and density within the beam in such a way that coher
ent bunches of electrons were formed.
The theory and simulation suggested that the modified
space charge waves could be launched by external rf sources
and used in klystronlike amplifiers. This theoretical predic
tion was verified experimentally in 1986.' Later, a series of
experiments combined with theory and numerical simula
tions showed that4 (1) an IREB could be modulated by a
low-power external rf source with high efficiency; (2) the
amplitude of the current modulation was stable, and the
171 Rev, Sci.lnstrum. 61 (1), January 1990 electron bunches were phase locked to the external rf source;
( 3) the shape of the electron bunches could be tailored by
changes in the geometry; (4) the bunching mechanism for a
fully modulated IREB was unique in its behavior, and using
this mechanism, a long drift region was unnecessary for op
eration (unlike the case of a classical klystron). It is known
that rf power can be extracted from modulated electron
beams. We demonstrated extraction of rf power from modu
lated IREBs with efficiencies of about 40%.
A drawback of rf sources based on this mechanism was
the high impedance (120 n) of the IREB that was used in
the earlier experiments. This drawback makes it difficult to
efficiently match the high-impedance electron beam to the
relatively low impedance of IRES generators (3011). To
achieve an efficient transfer of energy, the impedance of the
IREB generator should be equal to the impedance of the
electron beam, and we note that low IREB impedance can
easily be obtained by increasing the diameter of the annular
electron beam.
In this article, the construction and operation of an rf
amplifier that employs a large-diameter annular IREB is de
scribed. The IREB parameters were the following: diameter
13.2 cm, thickness 0.3 cm, current 16 kA, beam impedance
30 n, total power -8 GW, and beam duration 120 ns. This
electron beam was strongly modulated by an external rf
source at a frequency of 1.328 GHz (Sec. II). About 3
G Watts of rf power was extracted from the modulated IREB
and radiated into the atmosphere (Sec. III). Summary and
conclusions are given in the last section.
I. MODULATION OF A lARGE"DIAMETER HIGH
CURRENTIREB
The physics of externally modulated IREBs was de
tailed in our earlier article.4 Here, we shall give only results
needed to explain the construction and operation of the am
plifier. Specifically, we will discuss three aspects: (a) first
gap-interaction-smaH-signaI analysis; (b) second-gap-in
teraction-large-signal analysis, and (c) electrostatic
insulation of high-voltage gaps,
171
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsA. First~gap~interaction-small-signal analysis
The arrangement is si.milar to our previous work (Fig.
1 ). Here, a voltage pulse of 500 k V and 120 os was applied on
a foiless diode. As a result, the diode emitted and launched
an IREB inside a 14-cm-diam metallic drift tube. The IREB
diameter was 13.2 cm with a thickness of 0.3 cm. The IREB
current was 16 kA. The drift tube was immersed in a quasi
dc magnetic field of 10 kG and was evacuated to a base pres
sure ofless than 10-5 Torr. A gap feeding a cavity was in
serted in the drift tube. This cavity supported many modes
one of which was a hybrid of a coaxial TEM and TM modes
(Fig. 2) with a resonant frequency of 1.328 GHz. The "Q"
facter of the cavity was 1100. An external rf source pumped
power into the cavity for a duration of 1 f-ls.
The electrical parameters of the cavity were calculated
using the SUPERFISH computer code. (, We found that the gap
voltage Vg was about half of the maximum voltage in the
cavity. The electrical parameters of a same geometry cavity
made out of copper were also determined (power dissipation
P, energy stored W, quality factor Q, and gap voltage Vg).
Using these parameters, one can calculate the relation
ship between the input power and Vg for any real cavity of
the same geometry, but of a different Q. It is easy to show
that for two cavities (subscript 0 and 1) of the same geome
try, but of different Q, the following relationship exists:
Vg, = VgO(PJQ,/PoQO)1/2. (1)
Using the SUPERFISH code, we obtained the following values
of electrical parameters for a cavity shown in Fig. 2 made out
of copper: for Qo = 39700 and for Po = 5.25 X 104 W, one
gets VgO = 87 kV. Hence, for the real cavity with similar
geometry, Eq. (1) gives Vg, = 63.2P ]/2. Since power inject
ed into the real cavity was typically P, = 0.5 MW, we found
the gap voltage to be
Vg, = 45 kV. (2)
Sometime after the rfvoltage at the gap reached its max
imum value, a Blumlein transmission line energized the di
ode, resulting in fREB propagation through the gap of the
cavity.
The oscillatory voltage Vgl at the gap partially modula
ted the IREB, generating at point z an rf current II (z) and rf
voltage V, (z):
WINDOW
RF out
'3 GWatts
+-
RADIATOR 3 GW RF AMPLIFIER
AUGUST 1988
FIG. 1. The experimental arrangement.
172 Rev. SCi.lnstrl.lm., Vol. 61, No.1, January 1990 r
7.0"
FIG. 2. Electric field configuration inside the first cavity.
I, (z) = j(M Vg; IZ)sin(kz),
V, (z) = MVg, [cos(kz) -jt sin(kz)], (3)
(4)
where Z, k, and t are quantities that depend on the geometry
and beam parameters,4 and M < 1 is the coupling coefficient
of the gap and its presence is due to finite transit time of
electrons across the gap.7 Note that unlike in a classical klys
tron,I,(z) and V1(z) are partially in phase (see Ref. 3).
Using the experimental parameters and the equations in
Ref. 3, one gets
Z= 16H, k=O.039cm-l, b= -0.35.
The value of M has been inferred from particle simula
tions and analytic studies (Appendix B). We found M =0.6
at 1= 16 kA, and M as low as 0.3 for 1=40 kA. With
M = 0.6, Eq. (2) gives maximum II = L8 kA at a distance
of 40 cm downstream from the gap.
Experimentally, we found that the IREB rf current
reached a maximum at z = 35 cm. At this point, II = 1.75
kA.
Simulations of current modulation from a single gap for
a beam of diameter 3.8 em and current of 5 kA have been
previously presented.4•8 For the present case, these simula
tions were repeated with a beam of radius 12.6 em and 16 kA
current. We obtain a peak value of rl current II = 3.2 kA at
z = 44 cm, using an oscillating voltage of 50 kV at the gap.
(Details of the computer simulations using the CONDOR
code9 are given in the next section. ) The higher amplitude of
rf current obtained in the computer simulation in compari
son with experiment and theory is due in part to minor dif
ferences in parameters, such as the IREB diameter and
thickness and in part to the idealizations ofaxisymmetry and
of a simpler cavity oflength A /4.
B. Second-gap-interaction-Iarge-signal analysis
At z = 35 em downstream of the first gap, a second gap
was inserted in the drift tube (Fig. 1). This gap was feeding a
coaxial cavity of low impedance, Zc = IOn. The length of
the cavity was ~A (/= ciA = 1.328 GHz). In this cavity
four resistive wires (Fig. 3) were placed radially connecting
the inner and outer conductors. The purpose of the wires was
to reduce the Q of the cavity at resonance frequencies lower
than 1328 GHz.
The geometry of the second cavity was chosen such that
(a) the ratio of gap voltage to peak voltage was maximized
Klystron-like amplifier 172
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsand (b) the shunt impedance of the cavity, Rs' was maxi
mized. Using the SUPERFISH6 computer code and experi
menting with various cavities, we found the best cavity ge
ometry that fulfilled the above conditions (Fig. 3). For this
cavity the ratio ofthe gap voltage to the peak voltage was 0.8.
The input impedance of this ~)c cavity was
(5)
When a modulated IREB traversed such a cavity locat
ed at distance L = 1T/2k downstream of the first gap, an in
duced rf voltage appeared on the second gap with a gain
factor GA:
(6)
GA was evaluated and found to be GA = 30.
Using this gain an rf current exceeding the dc current
was obtained. The result indicates that Ii nonlinear treatment
is needed to explain experimental observations.
Experimentally, the IREB current downstream from
the second gap was found (Fig. 4) to have the following time
dependence.
1 = 10 + I, cos(cut) + ....
1\ reached the maximum value of 8.5 kA at a distance 39 cm
from the second gap.
Large changes in the input rf power into the first cavity
affected 11 only marginally. Hence, we assumed that satura
tion of the mechanisms was achieved. But unlike our pre
vious experiment in which 11/10 = 0.8, here 11/10 = 0.5 and
could not be further increased. Since the rf current measure
ments were inferred from measuring the magnetic field asso
ciated with the electron bunches, we investigated whether
this magnetic field differed from the one associated with dc
IREB current. Using linear theory,? we found (Appendix
A)
11(real) =It(measured)X2l(l + U},
where
r (41T[(Y w-Yb)IA]) U =exp- ,
/300 -I lIe) (7)
(8)
I I (real) is the real rf current and II (measured) is the mea
sured rf current, r wand r b are the radii of the drift tube and
the IREB, respectively,/3o = vole, Vo is the speed of the elec
trons in the drift tube, and Ie is the critical current in the drift
tube. Substituting the experimental results, one gets that
v. --.. V,
when
t:I--"0
Z =:: 60 ~ n
2
FIG. 3. Electric field configuration inside the second cavity.
173 Rev. Scl.lnstrum., Vol. 61, No.1, January 1990 .. '0
"' -.....
'C
--l 140 r1S&C ~ FIG. 4. Time derivative of tile IREB cur
rent measured by a I-GHz 7104 oscillo
scope.
1\ (real) = L4XI! (measured) = 12 kA. (9)
Note (1) that Eq. (7) was not solved self-consistently since
we have substituted 1=10 + II (measured) and (2) that
only linear theory was used to derive Eq. (8). But we can
conclude that the measured rf current is probably lower than
the value of the true rf current. Our numerical simulation
using the CONDOR code" also pointed to this conclusion.
In Ref. 4 an extensive theoretical study gave a qualita
tive picture ofthe mechanisms involved in the generation of
a funy modulated IREB. We will not repeat this work here.
However, since the only self-consistent picture was derived
from particle simulation, we decided to present computa
tional results, especially those which can help us later on to
understand the factors which determine the overall effi
ciency.
As in the single-cavity case, simulations of the second
cavity interactions have been previously carried out4•8 for a
beam of diameter 3.8 cm and current 5 kA. In the present
case we demonstrate that the interaction scales to larger ra
dius and present detailed diagnostics of rf energy and power
in the modulated IREB.
The geometry for the two-cavity simulations is given in
Fig. 5 (top). The first cavity was driven by an external rf
source, starting at t = 0 ns. The low Q of the numerical cav-
E
~t~ II u
c:::
I 1
12
« x 8 0 20 40 60 80
Z (em)
~(r~l
-H
:0~'~~'~--~!~~~~-71 20 40 60 80
Z (em)
FIG. 5. The geometry (top) and the rf current modulation (bottom) ob
tained from particle simulation.
Klystron-like amplifier 173
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsity was such that at t = 6 ns, the fundamental TEM mode of
the cavity saturates, producing a gap voltage of40 kYat 1.24
GHz. At this time a 6OO-keV, 16-kA electron beam was in
jected with a current rise time of 5 ns. The simulation contin
ues until t = 20 ns. The impedance of the radial transmission
line, from which the first cavity is driven, is 6.25 n. The
presence Of this transmission line lowers the de energy of the
beam from 600 to 500 ke Vas it crosses the first gap. The gaps
are located at axial positions z = 2.8 and 36.8 cm. The IREB
diameter was 12.6 cm and its thickness was 0.2 cm. The first
gap produced an rf current 11 = 2.6 kA at z = 30 cm down
stream. The modulated current excited the fundamental
TEM mode of the second cavity to produce an oscillating
voltage of 425 kV at the second gap. This voltage caused an
increase in the rf current of the IREB to II = 5.5 kA at a
distance of 2 cm past the second gap. The rf current increases
to 12.8 kA, 34 em beyond the second gap. II vs Z is plotted in
Fig. 5(bottom). Using the particle simulation calculations
with the present experimental parameters, we have verified
results obtained in our previous papers.4
( 1) The bunching mechanism reaches steady state after
a few rf cycles. Phase-space plots, electrostatic potential
plots, and modulated current are identical from rf cycle to rf
cycle.
(2) Transients in IREB current are of no importance,
and electron reflections are not necessary for the bunching
mechanism to work.
(3) During a half of each cycle, the energy of the beam is
decreased at the second gap such that the propagation of the
slow space-charge wave is halted and the electrons are
slowed to a nonlinear limiting velocity. 10
( 4) During the second half of each cycle, the energy of
the particles is increased to a higher level than the injection
value. These particles emerged with a narrow energy spread.
The modulated electron beam was diagnosed in some
detail at a distance of z = 66.8 cm, where the peak modula
tion was observed in the experiment. The total beam energy
(potential plus kinetic) and current are plotted versus time
over two rf cycles, from t = 18.5 to 20 ns (Fig. 6). From this
figure the following additional results are drawn:
I
18.6 19.0 19.4
T (ns) fT1
500 ~
:;0;
ct) <
FIG. 6. Current modulation and energy modulation at z = 66.8 em accord
ing to particle simulation.
174 Rev. Sci.lnstrum., Vol. 61, No.1, January 1990 (5) The particle energy is modulated as E(t) =Eo
+ EJ sin mt, El does not vary from cycle to cycle. The elec
tron energy modulation is partially in phase with the current
modulation. Note however that the bulk of the rfpower is in
phase with the rf current.
(6) The electron energy increase does not reach the full
425-k V amplitude of the voltage that appeared on the second
gap. This is a result of the finite transit time of electrons
across the gap. The gap coupling coefficient M varies with
the IREB current and is between 0.7-0.3.
(7) Significant compression of IREB power has oc
curred in each rf cycle with more than 80% of the power
compressed into less than 30% of the rf cycle.
(8) When the first-gap voltage was increased by 25%,
the current modulation amplitude increased by ~ 3%, indi
cating near saturation of the bunching mechanism.
c. Electrostatic insulation (Refs. 4 and 11)
The output power of a classical klystron is limited by
voltage breakdown across cavity gaps. The factors that influ
ence breakdown are electric field, geometry, frequency of the
rf, material used, vacuum, and cleanliness. These factors are
optimized in high-power rf devices so that the largest voltage
possible can be sustained across a gap. Most of these factors
cannot be optimized in the environment ofIREB generators.
Moreover, in the experiments discussed earlier no special
care was taken to prevent vacuum breakdown. Even then,
we found that voltage of the order of 0.5 MV appeared and
sustained on the gaps without any indication of vacuum
breakdown.
The reasons for such behavior were discussed by uS be
fore. 11 It is rooted in the unique properties ofIREBs, proper
ties that do not exist for tenuous electron beams. We found
that the self-electric field of an annular IREB modifies the
electric field configuration of a high-voltage gap in such a
way that the voltage gradient on a negatively charged elec
trode is reduced and for high IREB current can even reverse
its sign. This effect suppresses emission of secondary elec
trons and eliminates conditions necessary for vacuum break
down. We called this effect electrostatic insulation.
We showed in previous work the importance of electro
static insulation in different experimental settings. Here, the
importance of the effect will be demonstrated via particle
simulation using the CONDORY code.
The geometry for these simulations is the same as in Fig.
S except that the second gap is now sealed. The electron
injected energy was E = 500 keY, and the IREB current was
1= 16 kA, with a current rise time of 5 ns. The voltage
across the (first) gap was controlled by an external voltage
that was applied via a radial transmission line of impedance
of 6.25 n. At time t = 6 ns, the externally applied voltage
across the gap was increased linearly from zero to 400 kV
during a 4-ns period. A second beam of current 1= 1 A and
electron energy of I kV was injected continuously from the
left gap wall at z = 2 cm. This electron beam was used to
probe the behavior of the gap. The simulation was terminat
ed at t = IOns. Figure 7 shows the leakage current crossing
the gap as a function oftime. Initially, the low-current, low
voltage electron beam did not propagate across the gap. At
Klystron-like amplifier 174
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300 I /
-0.4 I
I
I 200 « r < -1.2 I \0
I
I 100 I--i I " (I) -2.0, I < I r-,
... ,,~g I 0
I
-2.8 I
I
............. ~~ j-IOO
-3.6
0 2 4 6 8 10
T (ns)
FIG. 7. Imposed gap voltage ( VK) and the leakage current (1) across the
gap.
time 8.6 ns when the gap voltage was 150 kY, the leakage
current increased instantaneously, indicating short-circuit
ing of the high-voltage gap. It is clear that the hold-off vol
tage is proportional to the electron density at the gap. Theo
retical analysis indicates that as the limiting current is ap
proached electrostatic insulation becomes more effective
and the hold-off voltage increases faster than linearly with
the IREB current (see discussions in Appendixes A and B).
In the next section we shall show that electrostatic insulation
also plays a role in rf power extraction.
We stress that this effect is of critical importance in any
device in which IREBs interact with high-voltage gaps. It is
responsible lor the fault-free operation of the amplifier.
II. rf EXTRACTION FROM MODULATION IREBs
It is well known that rf power can be extracted from a
modulated electron beam. Since the electrons in an IREB are
relativistic, there will be less reduction in particle velocity
(or IREB current) while the electrons are losing energy.
Hence, we can model the modulated IREB as a constant
current source I:
1=10 + 11 cos(wt) + ....
The interaction of this constant-current source with an
rf structure can lead to transfer of power from the electrons
to a load. The structure can be described as an electrical
element with an input impedance of Zin' A voltage V;n will
develop across the electrical element:
V;n = ZinI.
To extract maximum rf power from the IREB, at a fre
quency {t)121T, the following requirements must be fulfilled:
(a) V;n < Vo• otherwise the constant-current source model
for the IREB will not be correct, and the flow of IREB will
be disrupted. (b) Zin must be real at the frequency of the
extracted rf [Zin at this frequency will be denoted as Z ((t) ) ] .
(c) The absolute value of Zin at other frequencies has to be
smaller than Z ((t) ). (d) Zin = 0 at low frequencies of the
order of liT, where Tis the beam duration (in the experi
ment T = 120 ns). In order to transport this power into such
175 Rev. Scl.lnstrum., Vol. 61, No.1, January 1990 a load an additional requirement must be fulfilled: (e) elimi
nation of rf breakdown.
The rf converter shown in Fig. 1 addresses an of the
above requirements and consists of the following parts:
( 1) A high-voltage gap across which the electron
bunches are moving and losing energy. Electrostatic insula
tion is extremely important here since voltage of the order of
0.5 MY will appear across the gap when efficient extraction
of rf power is taking place.
The potential hill at the gap limits the energy which an
IREB, with a current I, can lose. The geometry of the gap
together with the voltage across the gap dictate the maxi
mum current (critical current) that can cross the gap. This
point is discussed in Appendix C.
(2) The gap is connected to an antenna via a coaxial
transmission line. The center conductor is supported by thin
metallic rods which are terminated in!A. cavities. The axial
positions of these rods are the locations of the zero-ampli
tude nodes of standing waves. The total impedance of the
parallel circuits is large and can be considered infinite for the
1.328 GHz component of the rf current. The input imped
ance is lower for higher frequencies and zero for the the low
frequency and the dc components of the current.
(3) At the far end of the inner conductor, an rf "obsta
cle" in a shape of a disk was placed. The axial position and
diameter of the disk could be varied. This part of the conver
tor was modeled using transmission line calculations. Figure
8 shows the model. The gap is represented by a capacitor of
value Co, the obstacle is represented by a capacitor C, the
load is R1, and the transmission line is oflength 1 and imped
ance ZOo Realistic values for the parameters in the model
were found in the following way: Co was calculated from the
shift of the resonance frequency of an ideal 1..1. cavity with a
similar gap geometry:
1 + j2rrfCo = 0, (10)
j Zo tg[ (1T12)( 1110)]
where fo is the resonance frequency of an ideal!"t. cavity, and
fis the resonance frequency of a cavity with a gap of capaci
tance Co. We found that Co = 6 pF.
The value for R 1 was assumed to be equal to ZOo The
Equivalent Circuit for the R F Extraction System
I
Z In = R + jX
FIG. 8. Equivalent circuit of the rf COllvertor.
Klystron-like amplifier 175
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsreason for this was that when the obstacle was removed the
VSWR was close to unity over a wide range of frequencies.
The values of C and I were left as free parameters, optimized
so that the input impedance Zin = R + jX is real at 1.328
GHz with a value between 50 and 100 n. Note that I can
have a series of solutions separated by ~ wavelength. Figure 9
displays one solution for R and X. We found that! had to be
chosen with great accuracy and that the value of R increased
when C was increased.
The model is only qualitative in nature since it does not
take into account the existence of non-TEM modes at var
ious places inside the convertor.
(4) The last part of the convertor was the antenna
which has a conical shape for both the inner and outer parts.
The length of the antenna was a few wavelengths. A lucite
plate 5 em thick acted as a window.
A set of experiments were performed in which I and C
were adjusted so as to get maximum radiated power. With
optimum conditions we observed radiated power (outside
the horn) of 2.7 GW. The IREB parameters were 16 kA
current and 500 kV voltage. (note that the Iucite window
attenuates the rf power by 10% ). The power measurement is
described later in this article.
The ability to extract high-power microwaves depends
critically on the suppression of electron and ion flows across
the coaxial line by the externally imposed axial magnetic
field Bo. The fonowing estimates show that the axial magnet
ic field ~ 10 kG used in the current experiment is sufficient
to provide the required insulation.
Since the rf frequency W is considerably less than the
relativistic electron cyclotron frequency, we may treat the rf
fields as essentially static as far as electronic motions are
concerned. Under this assumption, the relativistic cutoff
condition used in magnetron studies would give the magnet
ic field required for insulation. In a coaxial line of inner radi
us a and outer radius b, the required magnetic field to pro
vide magnetic insulation is given by12
Real and Imaginary Components of the
Input Impedance Z In VS Length
X R
tlO t45.41
E 0 t35.4 .r=
0
-10 + 25.4 ---
-20~ + 15.4
-30j +5.4
90 91
em
FIG. 9. Real and imaginary components of the input impedance Zoo vs
length.
176 Rev. SCi.instrl.lm., Vol. 61, No.1, January 1990 where D= (b 2 -a2)/2a is the equivalent separation, and V
is the voltage across the coaxial line. This equation is relati
vistically correct. Numerically, it reads
E (kG) = 1.07 {(~)(_I_)
C D (cm) 10 n 10 kA
+ 0.098 [C~~) Co ~A) JT12, (11)
where Zo = (60 n) Xln(b fa) is the characteristic imped
ance ofthe coaxial line, and I is the current flowing along it.
If a = 6.8 cm and b = 11.5 em, then D = 6.3 cm and
Zo = 31.53 n. For a maximum current of 10 + II = 30 kA,
for instance, Be = 0.73 kG. The imposed magnetic field is 10
kG, which is about 14 times higher than Be' the value re
quired for magnetic insulation. Thus, magnetic insulation
for electron flow is virtually guaranteed.
For the ions, their Larmor frequencies being much
smaller than the rffrequency, we may not use the static for
mula. We instead solve the equation of motion and place an
upper bound on their displacement across the field line.
The ions satisfy the nonrclativistic force law
dv M, -= e(E + vXBo), dt
where, for simplicity, we ignore the rfmagnetic field in com
parison with the external magnetic field, and E is the radial rf
electric field. We differentiate this equation with respect to t
to obtain
M, d2~ = e (dE + ~XBo). , dt- dt dt
The radial (x) component of this equation gives
d2vx 2 e dEx --2-+ (udVx --dt' dt M,
where we have eliminated dv/dt using the force law, and Wei
is the ion cyclotron frequency. Since dx/dt = Vx the last
equation becomes
d2x e --2 + W~iX = -Ex' dt It!;
For Ex = Eo sin wt, the solution is [x(O) = 0, x(O) = 0]
(e Eo/ Mi ) ( . w. ) x(t)= 2 2 smwt--s1nwc;t ,
Wei -{Il \ Wei
which gives
I ( ) I (eEo/ M; ) xtl< 2 2
IrVci -ell I e Eo
M, Wei I (W -Wei ) I
(12)
For M; = 1840m .. Eo = 10 kG, Wei = 2uXO.0608 GHz,
and (v = 21iX 1.3 X 109 s-l, Eq. (12) gives Ixl <0.78 mm if
Eo < 300 kV /5 cm. Thus, magnetic insulation for the ions is
also assured.
The total radiated power was measured in two ways: ( 1 )
The radiation pattern was measured and the power/cm2 was
obtained. The total radiated power was then calculated by
integration. (2) An external rf source of 50 n impedance
was connected at the gap via a slotted transmission line. The
electrical parameters of the convertor were adjusted to
Klystron-like amplifier 176
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsachieve a VSWR of 1, as measured by the slotted line. This
implied that the convertor acted as a matched load to the
external source. Measuring the input power and the re
sponse of a receiving hom yielded the calibration factor. The
two power measurements agreed to within 10%.
In the power measurements, the receiving horn was con
nected to a 7103 Tektronix I-GHz oscilloscope. All of the
electrical components that were used in measuring the pow
er were calibrated whenever a series of experiments were
performed.
From Fig. 10 one can see that the radiated rf power had
a slow rise time, about 60 ns. The rffill time of the cavity was
r;.::; (2IM)rle' rle = 2Q Iw.
Experimentally, we found Q-80; hence, 1"-60 ns. At
low rf output power the decay time of the power also lasted
60 ns. At high power the decay time was shorter and at a
power of 2. 7 G W this time was 30 ns long. We speculate that
the gap lost its electrostatic insulation due to the drop of the
current at the end of the IREB pulse and rf vacuum break
down occurred.
On a few occasions when the current was terminated
earlier due to flashover in the diode the fall time of the rf
power was shorter, but similar to the fall time of the IREB
current.
Efficiency of the relativistic klystron amplifier of the
sort discussed in this article depends mainly on two quanti
ties: The current modulation and the impedance of the load.
As in the conventional klystron the modulated beam acts as
a current source, the major fraction of which flows through
the load and is converted to useful rfpower. The load imped
ance RL =Zin should be sufficiently low to prevent electron
reflection by the output gap voltage, yielding Vg ~IIRL'
The rf power which may be extracted is then approximately
equal to RL If 12. Power conversion efficiency of 50%
would be obtained on a fully modulated beam (II =10) if we
set the output gap voltage Vg to be about equal to the dc
beam energy (i.e., RL = VgII1= Vollo)'
The above argument is clearly highly simplified. Here,
we address several aspects, some of which are unique to our
high-current klystron, which control the conversion effi
ciencies. Unfortunately, these factors are nonlinear, tran
sient, and local in nature so that a simple analytic scaling of
RF Power vs. Time for Shot no, 1118
3 ,--..-----------------
2
AVERAGE POWER
o o
nanoseconds
FlG_ 10. Measured rfpower vs time.
177 Rev. Sci. Instrum., Vol. 61, No.1, January 1990 the efficiency is unavailable at the moment. However, some
interesting observations emerge from the discussion given
below.
The first obvious question concerns the maximum cur
rent modulation 11 which can be imposed on an intense beam
by an external rf source, Both our numerical simulation and
experimental results indicated that the maximum rf current
II' the fundamental component, is limited to about 12 kA on
a 16-kA dc beam. Increasing the external rf drive would not
increase the current modulation much beyond 12 kA. One
possible explanation for the saturation of the current modu
lation is the M factor. As the modulating voltage increases,
the charge bunching at the gap increases. The nonlinear M
factor decreases, which in turn limits the current modulation
11,
This gap factor M, while restricting the achievable cur
rent modulation, may actually enable the output gap to sus
tain an rf voltage VI at a value substantially larger than Vo
without causing electron reflection. The underlying reason is
simple. Because a low value of M implies a long transit time,
an electron crossing the output gap would not experience the
peak voltage at all times during its passage" The requirement
on the gap voltage to avoid electron reflection is then re
laxed. It becomes
MVg <KE,
where KE is the kinetic energy of an electron entering the
gap. This relation suggests that a higher gap voltage can be
sustained. Since a high gap voltage implies high power effi
ciency, the use of the gap factor 114 to increase the power
efficiency is an interesting possibility. (The energy conver
sion efficiency is not increased by the M factor, however.)
There are other physical factors which could influence
the efficiency: They include the beam's energy modulation
and its phase relation to the current modulation, the kinetic
energy spread within the bunch, the partition between the
kinetic and potential energy as the electrons enter the output
gap, the substantial current modulation in higher harmonics
and their (transient) interaction with the output gap vol
tage, geometrical effects, etc. The interplay of aU of these
quantities determines the condition under which a virtual
cathode would be formed. An accurate assessment of the
relativistic klystron efficiency and its optimization requires
further study.
In Appendix C, we determine the limiting current
which can flow across a gap that is subject to a biased vol
tage. This is an extention of Ref. 13. In Appendix D, we
present conceptual design of a high-power rf converter, from
the coaxial TEM mode to a rectangular TE(H waveguide
mode.
III. DISCUSSION
In this article, the construction and operation of a high
power amplifier were detailed. An intense relativistic elec
tron beam oflow impedance (30 n) and of high power (8
GW) energized the amplifier. The gain of the amplifier was
37 dB and the radiated power was 3 GW. Power efficiency
was 35% and energy efficiency 20%. Unlike in the classical
klystron, a long drift tube was not necessary for beam modu
lation.
Klystron-like amplifIer 177
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsExperimental and numerical results suggest that the
electrostatic insulation that originated from the self-electric
field of the IREB was of critical importance in preventing rf
vacuum breakdown at the high-voltage gaps. These gaps
were used to modulate the IREB and to extract rf power.
Note that electrostatic insulation does not exist in classical
klystron devices. Magnetic insulation was used to prevent
breakdown in the cavities and the transmission line that car
ried the rf output power into the load. Even though the am
plifier was operating at 1.328 GHz, scaling up the frequency
by at least a factor of 3 seems possible. The operation of a
high-power amplifier at a higher frequency of 3.S GHz is
being planned.
Note added proof The modulated IREB reported in this
article was recently used to accelerate electrons with a cur
rent of 200 A (peak)-60 MeV over a distance of 1 m. This
experiment was reported by the authors in Phys. Rev. Lett.
63,2468 (1989).
ACKNOWLEDGMENT
This research is sponsored by the Strategic Defense Ini
tiative Organization, Office of Innovative Science and Tech
nology, and managed by the Harry Diamond Laboratory.
APPENDIX A.: RELA.TIONSHIP BETWEEN Bll) and 11
When the beam current is highly modulated, as in the
present experiment, the dc relationship BIO = polJ21Tr w no
longer holds. How one should interpret the modulated cur
rent II from the measured value of the magnetic field Blo
requires careful consideration, and this is the subject of dis
cussion in this Appendix.
Consider a thin annular electron beam of radius rb car
rying an axial current
(AI)
where II' w, and k are constants. This annular electron sheet
gives rise to a value of B iO at r = r w' the wall radius of the
drift tube. From Maxwell's equations, it may readily be
shown that 11 and Hw = Ble/Ilo are related by
II = HIIJ217rw [Jo(pr w )/JO(prb ) ], (A2)
where
p2 = (i)2/c2 _ k 2, (A3)
and Jo is the Bessel function of order zero.
Before we proceed further, we note that in the dc limit,
w->O, k->O, andp ..... O, (A2) gives
II (de) = Hw217ru" (A4)
which is a well-known relation. This relationship ha..<; fre
quently been used to infer the beam current from B-dot loop
measurements.
In the present experiment, the beam current II is a su
perposition of the fast and slow space-charge waves.5 Since
we are considering the relationship between II and RiO
through Maxwell's equations (which are linear), we may
separately consider the fast wave component and the slow
wave component. For the present geometry, (i) and k in Eq.
(A 1) are governed by the dispersion relation5
«(U-kvo)2=a(k2c2-o/). (AS)
Here, a = IoIUsY0/3o), Is = 8.53 kA/ln(rw/rb)' and Uo is
178 Rev. ScL Instrum., Vol. 61, No.1, January 1990 the electron speed in the drift tube. Equation (AS) gives
k = w(1 + a) (A6)
J,s vo( 1 ± all) ,
where
ap= (a2+alra)1/2/fJo, !3o=.volc, ro=.(l-/36)-1/2,
Here, and in what follows, we shan use the subscripts! and s
to denote the fast-and slow-wave components, respectively.
Let us denote
Jo(prw) lo(rrw)
E=' (A7)
JO(prb) 10C rrb)
where r2=. -p2, and 10 is the modified Bessel function of
order zero. Referring to Eq. (A2), we see that if E> 1, the
true value of II would be greater, by a factor of E, than the
value inferred from BIB under the assumption of the dc rela
tionship (A4). Of interest are the values EJ,s corresponding
to the fast and slow waves. Useful expressions may be ob
tained in the low-current limit (a--O) and in the high-cur
rent limit, as the limiting current is approached.
In the limit of very weak current, a--O, both kf and k,.
approach
ks =kf=o)/u O
by Eq. (AS). Thus,
which, together with (A7), we have
Es =cj'""ex p[ 217 (_1_) (rw -rb)] •
A !3oro (AS)
(AW)
In obtaining (A 10), we have used the asymptotic expression
for IoCrrw)' For A=23 cm, rw-rb=O.4 cm, and
/3oro= 1.8, the enhancement factor Ef' £s is approximately
equal to 1.063. Thus, for very low dc current, one may use
the dc relationship, the error being of the order of 6%. This is
in good agreement with our simulations.
When the limiting current is approached, a--/3 6. In
this limit, ap--1 and kr-> (u (1 + /3 ~ ) /2uo by (A6). Then
rr-> (O)lc) (1 -/36 )/2(30 = 1T/(Ara/3 o), and
Ef=exp(-_l7- (rw -rb)) •
Ara!3o (All)
In our experiment, £1"===_1 to within 2%. Thus, the fast-wave
component of the current modulation would give rise to BIB
with magnitude very close to the dc case.
The above conclusion is no longer true for the slow
wave component of the current modulation when the limit
ing current 1< is approached. Let us denote
(AI2)
a quantity close to unity as a approaches the critical value
ac =/3~. It can be shown that, as IoIIc-+1,
a = /3 ~ -(1 -IoIIc )/3~, and
(1+f3~)( 10) 1 -ap. = 2 1 - Ie . (AI3)
We next use this expression in (A6) to find k" which is then
used to obtain r s' After some manipulation, we find
Klystron-like amplifier 178
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whence
( 411" (Yw -r b ) ) €s=exp - ,
A (l -101 Ie )flo CAt5)
which gives a large value asIa-Ie. Thus, the presence ofthe
slow-wave component may lead to an underestimation of the
current modulation (when the limiting current is ap
proached), if one applies the dc relationship (A4) to the
measured value of B HJ'
One might be tempted to use I, the instantaneous cur
rent, in place of 10 in Eq. (A15) when the beam is highly
modulated. In the present experiment, we take Yb = 6.3 cm,
Yw = 6.8 em (cf. Fig. 1), f30=O.8, A = 23 em, I lIe = 0.6,
then IEf""" 1 and €, =2.4. If we further assume that the fast
and slow-wave components of the currents modulation are
about equal, then
II =Hl()2TrY w2€f€.J(lEf + IEs) =Hlf!2trY tv X 1.4. (A16)
Thus, the use of (A4) may underestimate the modulated
current by as much as 40%-a point suggested by our exper
iment and consistent with our simulations.
APPENDIX B: TRANSIT TIME EFFECTS IN GAP
Transit time effects, which are quite important for
IREBS, are now considered. These effects are well-known
for the case of a tenuous beam. Here, we extend the classical
analysis for an IREB. The estimates given here show that the
space-charge effects are significant if the beam current is a
sizable fraction of the limiting current.
For our geometry of an annular beam, the transit time
effect can be analyzed by solving the equation4,J()
(8 a)2 0-0(2a2 a2) at + v az s = r c 8z2 -at 2 S
eE (z) . + -g-3-sm wt.
mor (Bl)
In this equation, S is the (nonlinear) displacement of an
electron at position z at time t and 0-0 = Io/(lsf3o)' The last
term in the right-hand side of this equation represents the
modulating electric field Eg (z), which is assumed to be a
nonzero constant for 0 < z < D and zero elsewhere. The clas
sical transit time effect is deduced from (B1) if we set au"'" 0,
A linearized study ofEq. (B 1) shows that the electrons,
as they cross the gap, experience an equivalent electric field
which is reduced by a factor
(B2)
where Me = jsin(wD 12vo)/(wD 12vo) I is the well-known
transit time factor for a weak beam and <P = a,u8wD luo'
Here, a = 10/(1,"10(30), ap = (a2 + alr1yI21/30, and
8 = f3 ~ I (f3 6 -a).
For D = 2 em, w = 2trX 1.3 GHz, Vo = D.Se, alf3 ~
= O.S (beam current is 50% of the limiting current), then
Me "",0.97 and I cos <PI = 0.733. For D = 3 cm and the re-
119 Rev. Scl.lnstrum., Vol. 61, No.1, January 1990 maining parameters unchanged, Me "",0.96 and
Icos <1>1 = 0.434. There is a substantial reduction in the effec
tive gap voltage which the beam experiences due to space
charge effects, Thus, in the energy distributions of the elec
trons (cf. Fig. 6), the peak energy is not necessarily equal to
the sum of the peak gap voltage and the peak kinetic energy.
The transit time effects allow a higher voltage to be sustained
at the output gap without causing the beam electrons to be
reflected.
APPENDIX C: LIMITING CURRENT ACROSS A GAP
WITH A BIASED VOLTAGE
The modulated IREB converts its kinetic energy to rf
energy when the electrons are retarded by the decelerating
voltage across the gap of the extraction section. One limit on
the extraction efficiency is governed by the maximum re
tarding voltge which the gap can substain without the forma
tion of a virtual cathode. Equivalently, we may ask; given a
biased gap voltage, what is the maximum current which can
be transmitted without forming a virtual cathode? In this
Appendix, we examine this question via the use of the simple
parallel-plate model. The extension to the actual experimen
tal setup will be given toward the end of this Appendix.
Consider an ideal gap consisting oftwo parallel plates of
areaAo, separated by a distanceD. The left plateK (Fig. 11)
is grounded and right plate A is held at a voltage VI cos wt.
We assume that the transit times of the electrons are so small
compared with the rf period 2trlw that we may consider
w=O. Thus, when transversing the gap, the electrons essen
tially see only a static field.13-15 Only one-dimensional mo
tion is considered,
Let Jbe the current density of the electron impinging on
plate K. Letf3i =v,lc, Yi = (1 -P ;)-112 be the normalized
velocity and the normalized energy of the electrons when
they enter plate K, and f3f = v;i c and Yf be the corresponding
values when the electrons exit plate A. Since we are now
dealing with a static problem, conservation of energy gives
leiV, Yf= Yi +--, (Cl) moc2
and conservation of charge gives
z=o Z" I
--~) K
x=o
FIG. 11. A simplified model for beam-gap interaction.
Klystron-like amplifier 179
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsJ = lelnv = I lAo = const, (C2)
everywhere, where n and v are the number density and veloc
ity of the electrons. Let E be the electric field. We need to
solve the force law and the Poisson equation:
a f3 -(rfJ) = az -~, (C3)
a~ ] (C4) -= --az f3
Here, we have introduced the dimensionless quantities:
z=.xID, ~ =. lelED Imoc2, and]= lelD 2J ImocEo (> 0).
We differentiate (C3) with respect to z and use (C4) to
yield
a (a )- f3 -f3 -(rf3) = J = canst. az az
We now introduce a time variable S, defined by
a a
/3 az = as .
In terms of S, the solution to (C5) reads
r/3 = 152/2 + CIS + rili'
where 5 is related to z by
z = f-/3(s')ds' (C5)
(C6)
(C7)
(C8)
and C I is a constant to be determined. In writing (C7), we
have used the boundary condition at plate K: r/3 = rif3i
when 5 = Z = O. The constant c 1 is related to the normalized
transit time Sf:
rilf = J n/2 + CISf +rJl;. (C9)
It can be shown 16 that the total amount of charge Q within
the plates is proportional to Sf:
Q = -CIS> X (511 keV) , (ClO)
where C is this capacitance of the gap, which in this case is
simply AoEoID. Note that Sf is determined from [cf. Eq.
(C8) J
I = LSI /3(5') ds'.
It can be shown that, with
A='Sr/J,
Equation (C 11) may be rewritten as
ff = Ail dTj I PI(Tj) ,
o ,,1 +P1(Tj)
where (CII)
(CI2)
(C13)
P1(Tj) = [A2(Tj2 -Tj)/2 + rif3i + Tj(rl3r -rilj) ]2.
(C14)
Equation (C 13) determines the limiting current as function
of the biased gap voltage as follows. Suppose that we specify
ri and rf (i.e., initial beam energy and gap voltage), the
right-hand side of (Cl3), denoted by F(A), is a function of
A. The critical value of ff is then given by the stationary
values of F, and the critical amount of charge within the
plates [i.e., Sf; see Eq. (ClO)] is determined from (Cl2)
using those values of A which yield stationary values of F.
180 Rev. SCi.lnstrum., Vol. 61, No.1, January 1990 In general, there are two critical currentsJ"j andIc2 for
given values of ri and rf' The one with lower value, Ie! , is
given by
(Jd ) 1/2 = {i [f (~rif3 i) + f (~rff3 f)],
where
fez) = f dtt2j~1 +? (CI5)
(C16)
The properties off (z) are described in considerable detail in
Ref. 14 (see also Refs. 13 and 15). Physically, Icl is the
minimum value ofJ which is required to retard some elec
tron to zero velocity somewhere within the diode, at given
values ofrl' rfC rf > 1). The other criticalcurrent,l c2, is the
maximum amount of current which can be transmitted, at
given values of ri and rf' At the moment, we have not found
an analytic solution for IC2 even though it is the more rel
evant quantity. Shown in Fig. 12 are the values ofJc! ,JC2 as a
function of the gap voltage Vg = VI when ri = 2, Also
shown in Fig. 12 is Sf corresponding to Jc2'
Finally, we comment on the extension of our analysis
and the use of Fig. 12 for other realistic geometries. The
crucial quantity is the current scale Is, which enters in the
definition of the normalized current J.. In general; we write
1= Ills,
where
Is = C(moc2je)IT, eC17)
(CI8)
and C is proposed to be the capacitance (in vacuo), and Tis
the time required for light to traverse the system. In the
parallel plate system, C = AoEol D and T = Die, and the
normalized current] in (C5) is consistent with the one in
troduced in Eq. (C17). It is ofinterest to note that the cur
rent scale Is introduced in Eq. (CI8) is also adequate to
describe an entirely different system-that of a thin annular
beam of radius rb drifting in a circular waveguide of radius
rw and length L. In this geometry, C = 21TEaL !lnCr wlrb )
6 3
4 2
2
-400 -200 o 200 400
Vg (keV)
FIG. 12. The normalized limiting current fel, and fe2, and the normalized
transit time Sf corresponding to Ja.
Klystron-like amplifier 180
Downloaded 17 Jul 2013 to 131.170.6.51. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissionsand T= L /C. Equation (CI8) then yields Is = 8.53
(kA)/ln(ru/rb), the current scale which enters repeatedly
in our studies of this system. Finally, for the present extrac
tion experiment, C is capacitance at the extraction gap and
T= Die whereDis the gap length. For C=Co = 6 pF (cf.
Fig. 8) andD = 2 em, Is = 46 kA from Eq. (CIS). IfYi = 2
and Yr = 1, Fig. 12 gives:r C2 =:rcl =0.55 andIc =IsJc2 =25
kA. Note that this value of 25 kA is very close to the peak
current observed in the experiment.
APPENDIX D: A HIGH~POWER MODE CONVERTOR
Many applications (e.g., rf accelerators) demand a high
power of rf in a TEol rectangular mode. In this article, we
demonstrated successful mode conversion from a TEM
coaxial to TMo, cylindrical high-power rf pulse. The conver
sion took place inside an applied magnetic field which eli
minated conditions that could lead to breakdown. Mode
conversion from a TEM coaxial to TEo! rectangular can be
achieved in a similar fashion. The mode transition can take
place in a way that will ensure that the rf electric field will be
perpendicular to the axial magnetic field. In Fig. 13 such a
mode convertor is shown. The changes in the radial geome~
try take place over long distances ensuring "adiabatic" coo
version.
In this convertor a number of "fins" are emerging
graduaHy from the center conductor of a coaxial line. The
radial dimension of the fins increases along the axial posi
tion. At a point downstream the fins connect the inner and
outer conductors of the coaxial line dividing the cross-sec
tional area into equal parts. These areas are slowly trans
formed into a cross section of a rectangular waveguide. The
end result is a mode convertor embedded inside an axial
magnetic field. One end of the convertor looks like a coaxial
line, and the other end looks like rectangular waveguides
running parallel to each other and to the loads. The number
of rectangular waveguides is large for a large diameter coax-
181 Rev. Sci.lnstrum., Vet 61, No.1, January 1990 HIGH POWER MODE CONVERTER
FOR THE RELATIVISTIC
KLYSTRON AMPLIFIER
/ EXTERNAL MAGNETIC FtEi....D COIL
ILZ 7 ,.=:7!=r~~=
COAXIAL
LINE --------~
@, ~' 88' --. ~ "
. ~ " ,", , ' .' ' "
FIG, 13. High-power mode convertor. mmm
ffiJJTII1
RECTANGULAR
ialline so that the rf power/waveguide is below the break
down level.
1M. Friedman, V. Serlin, A. Drobot, and L. Seftor, Phys, Rev. Lett 50,
1922 (1983).
2M. Friedman, V. Serlin, A, Drobot, and L. Seftor, J. Appl, Phys. 56, 2459
(1984).
3M. Friedman and V. Serlin, Phys. Rev. Lett. 55, 2860 (1985).
4M, Friedman, J. Krall, Y. Y. Lau, and V. Serlin, J. Appl. Phys. 64, 3353
(1988).
SR. 1. Briggs, Phys. Fluids 19, 1257 (1976).
oK. H. Halbach and R. F. Holsinger, Lawrence Berkely Lab. Report No.
LBL-5040 (1976).
7y. Y Lau, J. Krall, M. Friedman, and Y. Serlin, Proc. Soc. Photo-Optical
lnstrum. Eng. 1061,48 (1989).
8J. Krall and Y. Y Lau, App!. Phys. Lett. 52,431 (1988).
9CONDOR is an extension of the MASK code developed by A. Palevskyand
A. Drobot, in Proceedings of the 9th Conference on Numerical Simulation
of Plasmas, Northwestern University, Evanston, IL, 1980 (unpublished).
lOY. Y. Lau, J. Krall, M. Friedman, and V. Serlin, IEEE Trans. Plasma Sci,
PS-16, 249 (1988).
liM, Friedman and V. Serlin, IEEE Trans. Electr. Insul. EI-23, 51 (1988).
12See, e.g., R. B. Miller, An Introduction to the Physics of Intense Charge
Particles Beams (Plenum, New York, 19B2), p. 21 i.
By. S. Voronin, Yu T, Zozulya, and A N. Lebedev, Sov. Phys. Tech. Phys.
17,432 (1972).
14y. Y, Lau, J. Appl. Phys. 61,36 (1987).
ISH. Jory and A, Trivelpiece, J. AppL Phys. 40, 3924 (1969).
16M. Friedman and V. Serlin, J. Appl. Phys. 58, 1460 (1985).
Klystron-like amplifier 181
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1.584122.pdf | Microstructures for particle beam control
G. W. Jones, S. K. Jones, M. Walters, and B. Dudley
Citation: Journal of Vacuum Science & Technology B 6, 2023 (1988); doi: 10.1116/1.584122
View online: http://dx.doi.org/10.1116/1.584122
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Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Mon, 24 Nov 2014 02:57:07Microstructures for particle beam control
G. W. Jones, S. K, Jones, M. Walters, and B. Dudley
Microelectronics Center of North Carolina, Research Triangle Park, North Carolina 27709
(Received 21 June 1988; accepted 24 August 1988)
Submicron lithography presents significant challenges to the fabrication of high-density complex
devices. Resolution, speed, critical dimension precision, variable design sets, and registration
generally are conflicting goals for a lithography system. In this paper, we will present a new
concept in electron or ion beam lithography with the potential to write far submicrometer
patterns at speeds well beyond those of single beam systems currently available. This structure
serves as a combined multiple aperture and beam deflection structure in a high-speed multibeam
raster scan writing system. The principle device structure to be discussed consists of an array of
apertures micromachined into a portion of a silicon substrate with electrostatic deflection lines
connected to each aperture. This structure is a key part of a lithography system with targeted 0.1-
,urn-pixel resolution. Apertures of 0.08 ,um diameter with 10% dimensional control have been
fabricated along with multiple multi pole lenses using various microfabrication techniques. The
paper will focus on the fabrication of these novel structures and will discuss potential system
applications.
I. INTRODUCTION
Fabrication of next-generation high-density complex de
vices with requirements for far submicron critical dimension
patterning presents significant challenges for lithographic
technologies as they exist today. Resolution, speed, critical
dimension precision, variable design sets, and registration
generally are conflicting goals for a lithography system. A
new system concept for electron or ion beam lithography has
been developed with the potential capability to write at high
gigahertz data rates and produce submicron features. This
new method is achievable due to novel control structures
made possible by microfabrication techniques. These new
structures consist of arrays of apertures which shape an in
coming broad beam into individual beams and allow simul
taneous deflection of individual beams along with common
focusing for the aggregate of beams. The control structures
fabricated demonstrate the potential power of such an ap
proach and the feasibility of construction. An array of such
beam aperture, deflector, and optional lens combinations
has been designated with the name lithography wand 1 as it
generates a linear wave of patterns as its beam array is
scanned across a prepared surface,
The use of the wand concept has considerable impact on
an overall system design and methodology, as will. be dis
cussed in more detail subsequently. The sections to follow
will provide an example of a wand-type system implementa
tion utilizing some novel concepts such as combining por
tions of system control circuitry into a wand deflector and
aperture array. Microfabrication techniques utilizing a tri
layer resist structure are used to construct a sub-tenth-mi
cron wand aperture and a multipole wand lens.
II. SYSTEM CONCEPTS
The use of an array of beams all prealigned to each other
with individually deflectable beams offers the potential of
significantly enhanced data rates using conventional com
puter systems and rapid alignment capability. While a num
ber of system variations exist, such as attaching on or com-bining a charged particle source into the wand, this example
system provides a reasonable review of wand design con
cepts. The potential benefits of beam lithography have been
known for some time as several papers have been written
addressing alternate approaches?-4 The concept presented
herein, especially the lens/deflector combination, offers a
great amount of potential flexibility and benefit.
The wand controller is the heart of this type of system,
defining the beams and selecting which beams are deflected
on and off'. In the particular example shown in Fig. I, an
incombing collimated beam is broken up by the aperture
portion of the wand into a number of individual beams
which are arranged linearly. The exiting beams are deflected
into a gutter aperture to be turned off, or left undefiected to
expose the substrate. The edges of the pattern to be printed
are correlated with the ends of the beam array and the deflec
tion voltages required to position the beams on the target
alignment patterns. The target x, y, and e electrostatic de
flectors can be iteratively modified until the designed align
ment of the wand array to the target pattern is obtained.
Mechanical alignment and scanning is also possible using
this system configuration. The x and y deflection voltages
necessary for an aligned scan of the target are calculated
following test scans of the alignment structures, then single
or multiple beams may be scanned over alignment structures
to obtain verification of proper alignment prior to patterning
the target. Once the beams at each end of the beam array are
properly positioned relative to the target pattern, the re
mainder of the array is also aligned, thereby providing signfi
cant potential alignment accuracy and speed for patterns
produced on wand machines of similar design. A stepping
stage is shown for stepping between target sites in Fig. 2. The
requirement to stitch would depend upon chip size, wand
array length, and the practical x scan distance for the partic
ular wand system.
Figure 2 also shows a complete wand column looking
broadside at the beam array. The source end of the column
consists of an array of field emission sources of a line-shaped
source which is highly collimated. Apertures for accelera
tion control and deflectors for source to wand array align-
2023 J. Vac. Sci. Techno!. B 6 (6), Nov/Dec 1988 0734-211X/88!062023-05$01.00 @ 1988 American Vacuum Society 2023
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Mon, 24 Nov 2014 02:57:072024 Jones et sl.: Microstructures for particle beam control
ment and energy separation are also shown between the
charged particle source and the wand array.
While conventional electrostatic or magnetic deflection is
possible, deflection can also be performed utilizing oxidized
silicon substrates with an etched beam line and thin-film
conductors for electrostatic deflectors. Pairs of silicon sub
strates may be separately formed and sandwiched together
using recently reported bonding techniques.5•6 This new
technique provides a method of precisely fabricating com
plex deflector designs with high electric fields at moderate
operating voltages.
The silicon substrate used in the fabrication process may
contain additional control circuitry. A simple block layout
showing controls built on a wand array chip with 3-pm n
type metal-oxide semiconductor 5 V technology and its re
lated off chip systems for a 40% beam array is shown in Fig.
3. The aperture block previously shown in Fig. 1 shows a
diagram of a simple wand structure cross section showing a
restricted aperture formed by oxidation such as the one to be
discussed in the section to foHow. Figure 4 gives a cross sec
tion of a wand aperture containing a five-pole lens for use
with a remote source and Fig. 5 is a cross section of a wand
with a combined field emission electron source and lens.
While Figs. 4 and 5 show insulator walls in the beam line
J. Vac. Sci. Technol. S, Vol. 6, No.6, Nov/Dec 1988 2024
FIG. 1. Diagram of lithography wand con
troller.
which might be prone to charging, it is possible to etch back
the walls of these structures using common oxide etches to
recess the insulators away from the beam line. Charging ef
fects that might occur due to scattered particles will reach an
equilibrium and can be compensated for using the lens sys
tems after a short period of lens operation.
III. FABRICATION OF WAND CONTROLLER
The fabrication of the wand controller shown in Fig.
begins with the selection of a lightly doped 100 p-type sub
strate such as used for silicon very large scale integrated
manufacturing, but with both sides polished. The substrate
is oxidized to form Si02, the oxide on the frontside of the
substrate is chemically removed, and the wafer is subjected
to a boron deposition and drive-in process using boron ni
tride furnace process in the region which will become the
wand aperture array. The substrate is stripped of oxide, then
reoxidized. The backside of the wafer is then patterned with
slots to open the length of the array. Following reactive ion
etch and resist removal, a silicon etch through the wafer is
performed. An angle of 55° between the < 100) and < 111)
silicon planes was repeatably obtained, using a mixture of
ethylenediamine, water, pyrocatechol, and pyrazine in an
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Mon, 24 Nov 2014 02:57:072025 Jones et sl.: Microstructures for particle beam control
~~::",<";:J- Electron or Ion Source
I
=-~:.-=--_-,- ~-Aperture1 1 01 ,~ ... ~~"~,
-Optional prepositionmQ deflectors
x,y,a of charge ribbon mounted
in x,y, 6 mechanical support
< I
Incoming charge ribbon -I t§ I I :l-Support block Cooled back plate ~ •• :_' ~ WAND array
Spacer " ,_~ I Getterlng aperture -lii"m LI
'i,:::,;,:lli:::~
, ','!',',: 'i!!, "', -x,V,e positioning deflectors
': .. and x scan deflector mounted
II: I In x,y,a mechanical support ~
,i:ii,!:'I:!li!I;
-ii'~:-'
Array of beams -'ill ::,,1':.: I
~ :Iiii:f'" tt ~:~e:;~~~dafY electrons}
iii: " / Substrate to be patterned
C-=~~---<-<--=<j5tepPI"gtable
FIG, 2, Illustration of wand column viewed broadside at beam array.
apparatus similar to that presented by Reisman et ai.7 This
process produces a 1.3-flm silicon membrane capped with
0.25-,um silicon dioxide. This etching process was also used
by Bassous to produce arrays of ink jet nozzles in silicon
substrates.8 A highly doped boron layer may also be deposit
ed epitaxially.
~mor\l
Cache 1
pata In
641iMs
32bits lor.g
T
Contr.l Control
System
-CentraIO"t ..
Bas.
-Projoct D.1a
Base
-Human Int.rfac.
-Electrode
P.'W~r
-Conkols &
Supplies
T I II
II 5V lO!lic
Gmd
0-15 Deflection Supply
Clock/Timing I/o's
I.D8te In Shift Clock
2.Expo3ure I ntefv81 Clock
3.Dete ClJcle Clocl:
4.EC 1/0's (2x4)
5.Serial Data Out (test)
6.Deta Acu 1/0's
J. Vac. Sci. Techno!. e, Vol. 6, No.6, Nov/Dec 1988 ~o"us
Amp.1It
DAC 2025
-51°2
-S102
-5;°2
'<.Lo ...... :....:...:...:..<:..4.J....:;..<...J- W
FIG. 4. Cross section of wand aperture with five-pole lens.
The next portion of the process involves preparing the
wafer frontside with a modified trilayer resist structure9 con
sisting of planarization layer of polyester (Futurrex 1500D)
(Ref. 10), an intermediate layer of evaporated silicon, and
an imaging layer of Shipley S2400-17. II The imaging layer
was exposed on a Perkin-Elmer MEBES III at 10 keY and
30 flC/cm2 to produce a linear array of apertures measuring
0.4 j-tm in size on a I-flm pitch. Following resist develop
ment, the patterns were transferred via reactive ion etching
through the intermediate and planarization layers of the tri
layer structure.
The substrate was etched using an Applied Materials
AME 8110 for the silicon dioxide film and an AME 8120 for
the silicon trenches using a helium trench etch. Following
resist removal and cleaning, the trenches were oxidized at
high temperature until apertures of the desired size were
obtained.
Top-down and cross-sectional view micrographs of a
O.08-j-tm wand aperture are shown in Figs. 6(a) and 6(b).
The square profile is obtained due to preferential oxidation
in the (111) direction. The wand aperture shown has under
gone nearly complete conversion of silicon to silicon dioxide.
The use of upper and lower capping layers of silicon nitride
Daia In
641in~s
.. 32bits long
WAND $ubsilstems I
I R~ster Scan
system
2.Scan corr.ciion
3.Prealignment
4.Alignmont
S,lmag. M@ilitor
6.Y .. cwm ~st.m
status
7.'rIofe .. handling
e ,stag" conti' .. 1
9 .S ....... c~ control
I FIG. 3. Layout of wand controls.
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W (x deflected scan)
Polyimide
f'L'CLL.L:L.t:LL:LL.~+<..<..4.LL,'-<-LLL-'4 W (y scan)
1-.................... """ .......... _-"'--t N+ poly Poi" 5
J==;=;;,:'t====:=tW poly Pole 3 N+ poly Pole 2
,.. N+ poly Pole I
Restricted apertures (Ni) /' i""'==="'-t TISi2 extraction
Polyimide
~--------~~~~------~
Tungsten clad silicon emitter/'
Silicon substrate N+
Stress control '-__________________ ---' conductive backlayers
FIG. 5. Cross section of wand with combined field emission electron source
and lens.
and a thicker silicon membrane would normally be desired
to provide a more vertical trench and the capability ofform
ing smaller capillaries. The size distribution of these wand
apertures is shown in Fig. 7, with 10% (2a) dimensional
control. While hundredth micrometer dimensional control
(al
fbI
FIG. 6. SEM micrographs ofO.OR-,um wand aperture viewed Ca) top-down
and (b) cross section.
J. Vac. Sci. Technol. S, Vol. 6, No.6, NovlDec 1988 .. u <:
~
:>
<> u
0
<5
~ 30
25
20
o~----------~~ o. 0.02 0.04 c::J Up/Down Measurement
_ Left/Right Measurement
UD III.,," ... 084 +1-.006
LR lIIea" " .078 +/-.006
0.16 0.18
Diameter (microns)
FIG. 7. Histogram of size distribution of wand apertures. 2026
of 0.1 O-pm structures is impressive and may be acceptable
for non focused shaped beam applications such as this,
further improvement in two areas is desired. First, measure
ment of such structures is difficult and is believed to contrib
ute substantial error as is demonstrated by the Hitachi S6000
up/down and left/right measurements shown in Fig. 7. The
bias reversed when the sample was rotated 90°. Second,
further refinement of the electron beam (e-beam) process
and possible use of e-beam direct write system with better
dose control at sub-half-micrometer spot sizes and/or
smaller spot size capability is anticipated.
A target mean aperture diameter may be obtained by re
peating oxidations to obtain a specific size opening. Aper
tues as small as 350 A have been fabricated with the above
technique. Series of these apertures have been placed in a
scanning electron micrograph (SEM) column and used to
define beams. Patterns printed with short aperture to target
distances demonstrated patterns of slightly less than aper
ture size. Figure 8 demonstrates resist structures of sub-half
micron features which were printed in O.23-pm film thick
ness of Shipley SAL601 (Ref. 11) negative electron beam
photoresist using the wand apertures with -5 pC/cm2 dose
of 2-keV electrons in a proximity mode.
FIG. 8. SEM micrograph ofseries 0["0.10-, 0.20-, and 0.25-,urn resist struc
tures electron beam exposed in O.23-,um Shipley SAL601 using wand aper
tures.
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.102.42.98 On: Mon, 24 Nov 2014 02:57:072027 Jones et al.: Microstructures for particle beam control
A thick resist (3.5 ,um) lift-off stencil is patterned using
image reversal processing12 for the metal deflector level. A
conductor such as aluminum is then deposited and the unde
sired metal lifted-off in an acetone bath leaving the conduc
tive lines with a narrow gap in the proximity of the aperture.
The use of deflectors on these apertures has not yet been
evaluated due to the configuration of the current test col
umn.
IV. FABRICATION OF WAND LENS
An alternate structure which is of interest is a wand array
with built-in lenses to obtain focusing ability. The lens arrays
potentially offer substantial improvement and flexibility
over the nonlens arrays as they should allow individual spot
size control, longer working distances for a given source to
wand column length, and greater writing speed for the tar
geted O.l-,um final beam spot size/4K aperture wand array
design due to higher overall beam currents resulting from
increased total aperture area for a given array length at a
given beam power level incident on the wand. (Wand array
heating limits acceptable beam power levels incident on a
wand array for a given mounting and, thereby, acts as a key
writing speed limit along with data rate for a particular
wand/wand mounting design). The larger diameter aper
tures and a thick refractory metal or silicide layer on the side
of the wand array incident to the particle beam should be
more stable and reliable than the oxidized restrict or arrays.
A diagram of a five-pole lens is given in Fig. 4, and a cross
section micrograph of an etched stacked lens structure is
shown in Fig. 9. In the example diagram, a high-concentra
tion boron etch stop is not required; etch stop on Si02 is used.
To etch through this thicker structure, a thicker polyester
planarization layer may be used (-5 ,um) during formation
of the trilayer structure. The conductor layer for the deflec
tors may be placed on the substrate prior to the etch to allow
self-alignment of the deflectors to the apertures to minimize
the required deflection voltages during operation. Alternat
ing layers of n+ silicon and Si02 are reactively ion etched
using processes previously discussed to produce the lens
structure for this example. Restrictions of aperture size may
be obtained using electrolytic plating techniques or selective
FIG. 9. Cross-section SEM micrograph of etched stacked lens structure.
J. Vac. Sci. Technol. e, Vol. 6, No.6, Nov/Dec 1988 2027
chemical vapor deposition if desired. Target size for such
lens diameters is in the l-,um range although only 2.0 and
2.8-JLm lenses have been fabricated to date with vertical
walls. At this time we have demonstrated the concept and
fabrication of such lens stacks; however, no testing of such
lenses have been performed. The use of such lenses could
eventually allow fabrication of an entire writing column on a
chip as shown in Fig. 5.
V. CONCLUSIONS
Structures have been fabricated with the potential to pro
vide multiple particle beam control for various applications
including lithography which have the potential of gigahertz
tenth micrometer pixel rates. Construction of version of
these structures with very small O.OB-,um apertures and with
aperture/Einzellens combinations has been demonstrated.
Far-submicron « 0.10 ,um) resist structures have been
printed using wand apertures fabricated by oxidizing silicon
orifices.
While considerable investigation and development is still
required, this new technology presents a potential method
for reasonable throughput, direct-write patterning of 100
nm and below semiconductor circuit structures.
ACKNOWLEDGMENTS
The authors express their gratitude to the staff of the fabri
cation facility of the Microelectronics Center of North Caro
lina, and especially to Y. Ho for trilayer structure etching
and J. Standish for photomask fabrication. Appreciation is
expressed to C. Peters and to the staff of the General Elec
tronic Microelectronics Center, Research Triangle Park,
NC, for electron beam exposures and to the Linear Device
group of General Electric for boron nitride processing sup
port. Appreciation is expressed to A. Reisman and C. Os
burn for technical discussions and support of this program.
'G. Jones and S. Joncs, patent pending to Microelectronics Center of North
Carolina.
'H. Pfeiffer, IEEE Trans. Electron. Devices 26, 4 (1979).
\T. Newman, R. Pease, and W. DeVoro, J. Vac. Sci. Techno!. B 1, 999
( 1983).
4B. Roelofs, J. LePoolc, J. Barth, and C. deGruyter, Microcircuit Engineer
ing. 1983, edited by H. Ahmed, J. Cleaver. and G. Jones (Academic!
Harcourt Brace Jovanovich, New York, 1984), p. 224.
'R. Black, S. Arthur, R. Gilmore, N. Lewis, E. Hall. and R. LiIlquist. J.
App!. Phy,. 63, 2773 (1988).
"J. Lasky, App\. Phys. Lett. 48, 78 (1986).
71\. Reisman, M. Bcrkenblit, S. Chan, F. Kaufman, and D. Green, J.Elec
trochem. Soc. 126(8), 1406 (1979).
"E. Bassous, H. Taub, and L Kuhn, App!. Phys. Lett. 31,136 (1977).
oS. Jones, R. Chapman, Y. :Bo, and S. Bobbio, in Proceedings of Interface
'86 Microelectronics Seminar (Eastman Kodak Company, Rochester,
NY, 1987), Kodak Publication No. G-155.
'''Available from Futurrex, 44·50 Clinton St., Newton, NJ 07860.
"Available from Shipley Company, 2300 Washington St., Newton, MA
02162.
"S. Jones, R. Chapman, and E. Pavelchek, in Proceedings afthe First Inter
national.Symposium on ULSI Science and Technology (Electrochemical
Society, New York, 1987).
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1.99827.pdf | Lowtemperature (250°C) selective epitaxy of GaAs films and pn junction by laser
assisted metalorganic chemical vapor deposition
N. H. Karam, H. Liu, I. Yoshida, and S. M. Bedair
Citation: Applied Physics Letters 53, 767 (1988); doi: 10.1063/1.99827
View online: http://dx.doi.org/10.1063/1.99827
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/53/9?ver=pdfcov
Published by the AIP Publishing
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Lowtemperature (600–650°C) silicon epitaxy by excimer laserassisted chemical vapor deposition
J. Appl. Phys. 65, 4268 (1989); 10.1063/1.343311
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J. Appl. Phys. 58, 979 (1985); 10.1063/1.336144
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128.193.164.203 On: Sat, 20 Dec 2014 18:04:19Low~temperature (250 °C) se~ective epitaxy of GaAs fUms and p""n junction by
~aser .. assisted metalorganic chemical vapor deposition
N. H. Karam,a) H. Liu, I. Yoshida, and S. M. Bedaif
Electrical and Computer Engineering Department, North Carolina State University. Raleigh,
North Carolina 27695-7911
(Received 3 March 1988; accepted for publication 22 June 1988)
Low-temperature seiective epitaxial growth of device quality GaAs has been achieved by laser
assisted chemical vapor deposition (LCVD). GaAs substrates thermally biased to
temperatures in the range 250--500 °C were irradiated by an Ar ion laser to induce localized
deposition of GaAs. Carefully selected growth conditions resulted in growth rates as low as a
monolayer per second at 250°C. This is the lowest substrate temperature for epitaxial GaAs
with optical and structural quality comparable to those achieved in conventionally
metalorganic chemical vapor deposition grown GaAs. Also reported is the first p-n junction by
LCVD technique using zinc as the p-type dopant. This new low-temperature selective
deposition process can lead to maskless fabrication of muhicomponent devices on the same
wafer.
Low-temperature deposition of epitaxial films is of great
interest to the development of many semiconductor technol
ogies. This is because it would lead to improvement in the
abruptness of doping profiles, as well as a reduction in the
outdiffusion of impurities from the substrate and in the intcr
diffusion at heterojunction interfaces. These advantages
meet some of the current trends for reducing device dimen
sions. Several approaches have been proposed to reduce the
growth temperature using both molecular beam epitaxy
(MBE) and metalorganic chemical vapor deposition
(MOCVD) techniques. They include plasma-assisted
growth, migration-enhanced epitaxy, and precracking of
reactant species. The quality of the deposited films is usuaHy
inferior to that deposited at h;gher growth temperatures
(i.e., 500-600 °C). These low-temperature-deposited films
were found to be heavily compensated and in some cases
exhibited high resistivity with poor optical properties. 1,2
Laser-assisted chemical vapor deposition (LCV D) of
HI-V compounds previously reported-,-8 is a potential means
for low substrate temperature deposition processes. The in
teraction of the laser beam can result in localized heating and
photocatalytic deposition of the reacting species at the sub
strate surface. Laser-assisted deposition also allows epitaxial
growth sdectivcly in the area irradiated by the laser beam.
Thus device structures can be selectively deposited on sub
strates thermally biased to fairly low temperatures, This will
allow the selective addition of particular devices (e.g.,
sources and detectors) on substrates that already have digi
tal or analog circuits. This can be achieved without any deg
radation of performance of these circuits as long as they are
not exposed to temperatures higher than a few hundred de
grees. We report for the first time the laser-assisted epitaxy
of GaAs films on a substrate that is thermally biased to tem
peratures as low as 250°C. To the best of our knowledge this
is the lowest substrate temperature used to deposit device
quality GaAs using MOCVD or MBE techniques. We also
report on the first maskless selective deposition of GaAs p-n
junctions using this LCVD technique.
The experimental setup is a vertical MOCVD system
.) Currently with Spin: Corporation. Patriots Park, Bedford, MA lH 730, operated at atmospheric pressure that was modified to serve
the LCVD experiment. 3,5 The substrates were biased induc
tively to uniform temperatures in the range of 250--500 ·C.
TrimethylgaHium (TMG), AsH, 00% inHz), anddimeth
ylzinc (DMZ) or diethylzinc (DEZ) were the sources used
for Ga, As, and p-type dopant, respectively. GaAs was de
posited using the multiple scanning approach,4 An Ar ion
laser was scanned relative to a thermally biased substrate
while simultaneously exposed to TMG and AsH, in a H2
carrier gas. Deposition parameters including the TMG mole
fraction, substrate thermal bias, laser power density. and
scanning speed were adjusted to deposit about one to two
monolayers of GaAs per laser scan. The desired GaAs film
thickness could be achieved by multiple laser beam scanning
at speeds in the range 100-200I1m/s, Lines about 0.3 em
long and 200-500 pm wide were deposited, and the thickness
profiles were measured by a microstylus. The thickness of
the deposited lines, measured normal to the scanning direc
tion, peaked at the center and decreased gradually to about
zero value at the peripheries. Experiments performed on
substrates heated to temperatures lower than 250°C were
not successful because of the instability of the rf generator.
We found that in order to achieve a meaningful growth rate,
the laser power had to increase as the substrate bias tempera
ture decreased. This would allow higher local temperature of
the irradiated area and also higher photon density to en
hance the photocatalytic reaction process. The maximum
surface temperature rise .:.1 T at the center of the laser spot
cakuated from the Lax model is about 50°C for a laser pow
er of 2.5 Wand 620 lim spot size. For a substrate bias of
250°C, the peak surface temperature at the center of the
laser spot is estimated to be about 300 0C. This surface tem
perature rise due to the laser heating decreases very rapidly
in a nearly Gaussian fashion away from the spot center. Lo
calized strain induced by such a temperature rise is elastical
ly accommodated and hence results in no lattice distortion. 10
This very low surface temperature is not high enough to
initiate the growth ofGaAs from TMG and AsH 3 in conven
tional MOCVD which relies only on the pyrolytic process.
The substrate surface temperature is not hot enough to result
in the complete thermal cracking ofthe TMG or AsH] mole-
767 AppL Phys. Lett 53 (9), 29 August 1988 0003-6951/88/350767-03$01.00 @ 1988 American Institute of Physics 767
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128.193.164.203 On: Sat, 20 Dec 2014 18:04:191.2. I (a) I i.0
~ 1 0.8
::5
oj
~ 0.6
·in
~I t:
OJ 5 0.4
C.2
0.0 -L.-. . I J
u.7G o.Be 0.114 0.8R (l.S?
wavelength ()J.m)
1.2 !
f(OJ 1.0
~ -; 0.8
oJ )\ ~ 06 ~
<Ii
'" oJ III s ,,[
0.0 ! ,
0.76 0.80 0.84 0.38 0.92
wavelength (}.lm)
1.2
(c)
1.0
0.8
:::l
~
.~ C.G
Vi r::
I OJ)
:5 0.4
I
::l.~: )
o.aL-
0.76 a so O.8.tf 0.88 0.92
wavelength (!J.m)
FIG. 1. Photolumint'scencc spectra at 77 K for conventional LCVD sam
ples on GaAs at (a) 500 'C. (b) 4(X)"C, and (c) 250 'C.
culcs. On the other hand, the photon energy of the Ar+ laser
(2.3 eV) is not sufficiently high to break thc Ga--C bond
and free Ga atoms. Thus it is possible that photocatalytic
decomposition of the reactants on a relatively warm GaAs
substrate surface is responsible for this laser-activated depo
sition process. II
The optical quality ofthe laser-deposited GaAs lines has
been investigated by low-temperature photoluminescence
(PL). Figure 1 shows PL dat~ for laser-assisted deposition
of GaAs films on substrates thermally biased to (a) 500, (b)
400, and (c) 250°C, respectively. By adjusting the laser
power density, films with the same opticai quality, full width
at half-maximum (FWHM-17 meV), are obtained on sub
strates thermaily biased to 400 or 250 °C which are selective
ly deposited at nearly the same growth rate ( -3-4 A/scan) .
The PL intensity ofthe LCVD films is comparable with con
ventionally deposited MOCVD films. The optical quality of
these deposited films deteriorates with an increase in the la
ser power density. This may be a result of the thermal stress
and the accompanying localized lattice distortion associated
768 Appl. Phys. Lett., Vol. 53. No.9, 29 August 1988 200
<1; 1 tl 0 ~ ~
~ ....
I: 0 III .. '-
::J "1 00 <:.l
HG. 2. J-V characteristics uf p-n junction selectively deposited by LCVn
on GaAs at 300 0c.
with high laser powcr density. On the other hand, Fig. 1 (a)
shows a broad PL spectrum (FWHM~60 meV) that corre
sponds to a growth rate (OR) ~63 A/searl. This broadening
may be due to defect-related transitions as a result of the high
OR and the inefficient separation of the reaction products
from reaction site. Structural properties of GaAs deposited
by LCVD technique have been studied by x-ray diffraction
topography technique, I() and results were found to be consis
tent with those ohserved for the optical properties.
The LCVD technique has also been utilized to selective
ly deposit p-type GaAs films on Si-doped GaAs substrates
(n = 10 I N / cm1). Initially, D EZn was used as the source for
Zn; however, experiments conducted at 400 and 300 cC were
unsuccessful as a result ofthe high eflkiency ofthe Ar -t laser
in cracking DEZn. This resulted in Zn deposition all over the
substrate, even in the nonirradiated areas, as weil as window
fogging of the reactor. Less severe problems were encoul1-
ten.~d with DMZn where a junction was fabricated at a sub
strate bias temperature -300°C and laser power of 3 w.
The p-n junction (100 X ZOO ,um2) was fabricated by stan
dard photolythoyrophic techniques. Metallization was done
using Au-Cr-Au for the LCVD p-type film, while indium
was used for back contacts on the n-type substrate. Figure 2
shows the current-voltage (1-V) characteristic of this selec
tively deposited P-I! junction. The diode showed a soft break
down which may be due to the high doping levels on both
sides of the junction. The carrier concentration in the
LCVD-grown film is estimat.ed in the high lOls/cm' range
from HaH measurement. Currently, experiments are under
way to control the p-type dopant levels. It is hopeful that
other p-type dopant sources, such as hiscyciopentadienyl
magnesium, can alleviate current difficulties.
In conclusion, LCVD technique has been successfully
demonstrated as a powerful tool !()r low-temperature
(250°C) selective expitaxy of device quality GaAs. Photolu
minescence results show that the optical property of the de
posited fllms are comparable with those grown by conven
tional MOCVD and MBE techniques. To the best of our
knowledge this is the lowest bias temperature reported for
device quality GaAs growth. Furthermore, we have demon
strated the potential of the LCVD technique in producing
the first direct writing of a p-n junction selectively grown at
300 "C.
This work is supported by the National Science Founda
tion (DMR 8303914-95).
Karam eta!. 768
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128.193.164.203 On: Sat, 20 Dec 2014 18:04:19'F. W. Smith, A. R. Calawa, Chang-Lee Chen, M. J. Manfra, and L. l.
Mahoney, IEEE Electron Device Let!. 9. 77 (1988).
'G. Metze and A. R. Calawa, Appl. Phys. Lett. 42, 818 (1983).
.lS. M. Bedair, 1. K. Whisnant, N. H. Karam. M. A. Tischler. and T. Kat
suyama, App!. Phys. Lett. 43, J 74 (1986).
'N. H. Karam, N. A. EI-Masry, and S. M. Bedair, Appl. Phys. Lelt. 49, R80
(1986).
5S. M. Bedair, J. K. Whi~nant, N. H. Karam, D. Grims, N. A. EI-Masry.
and H. H. Stadelmaycr, J. Crys!. Growth 77, 229 (1986).
"N. H. Karam. S. M. Bedair, N. A. El-Masry, and D. Griffis, Mater. Res.
Soc. Symp. Proc. 75, 241 (1987).
769 Appl. Phys. Lett., Vol. 53, No.9, 29 August 1988 7N. H. Karam, H. Liu, 1. 'Yoshida, 1'. Katsuyama, N. EI-Masry, B. laing,
A. S. M. Saleh, G. Rozgonyi, and S. M. Bedair, Mater. Res. Soc. Symp.
Proc. 101, 285 (198R).
'N. H. Karam, H. Liu, 1. Yoshida, and S. M. Bedair, App!. Phys. Lett. 52 .
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OM. Lax, J. AppL Phys. 48, 3919 (1977).
I"N. H. K:1ram, H. Liu, r. Yoshida, B. L Jiang, and S. M. Bedair, in Pro
ceedings of the 4th International Conference on Metalorganic Vapor
Phase Epitaxy, Hakone, Japan, Ing.
'Iy. Aoyogi, S. Masuda, S. Namba, and A. Doi, App!. Phys. Lett. "-7, 95
(1985).
Karam eta/. 769
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128.193.164.203 On: Sat, 20 Dec 2014 18:04:19 |
1.458561.pdf | Ultraviolet photoemission study of oligothiophenes: πband evolution and
geometries
H. Fujimoto, U. Nagashima, H. Inokuchi, K. Seki, Y. Cao, H. Nakahara, J. Nakayama, M. Hoshino, and K.
Fukuda
Citation: The Journal of Chemical Physics 92, 4077 (1990); doi: 10.1063/1.458561
View online: http://dx.doi.org/10.1063/1.458561
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/92/7?ver=pdfcov
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138.251.14.35 On: Sat, 20 Dec 2014 18:15:07Ultraviolet photoemission study of oligothiophenes: 1r-band evolution
and geometries
H. Fujimoto,a) U. Nagashima, and H. Inokuchi
Institute for Molecular Science (IMS). Myodaiji, Okazaki 444. Japan
K. Seki
Department of Materials Science. Faculty of Science. Hiroshima University. Hiroshima 730. Japan
Y. Cao
Institute of Chemistry. Academia Sinica. Beijing. China
H. Nakahara, J. Nakayama, M. Hoshino, and K. Fukuda
Department of Chemistry. Faculty of Science. Saitama University. Urawa 338. Japan
(Received 30 October 1989; accepted 7 December 1989)
Ultraviolet photoelectron spectroscopy (UPS) has been applied to the investigation of the
electronic structure of oligothiophenes with 4-8 thiophene rings. In a series of a-linked
oligomers (an with n being the number of rings), a systematic evolution of the 1T band is
observed. Several peaks which correspond to the 1T band are observed in the region of 0.7-3 e V
below the Fermi level (EF), and the bandwidth becomes broader with increasing n. The
nonbonding 1Tband is observed at 3.5 eV below EF and its energy is almost independent of the
number of thiophene units. UPS spectra of a7 and a8 are fairly similar to the spectra of
poly thiophene, showing that these oligomers are good model compounds of the polymer. The
ionization threshold energy of a7 and poly thiophene was observed to be 5.3 eV. The effect of
irregularity on the 1T-electron system was also studied by using oligomers which contain a (3
iinkage or a vinylene group at the middle of the molecule. The UPS spectra showed that the (3
linkages significantly affect the electronic structure of poly thiophene, while the vinylene group
does not. In order to analyze the UPS spectra and to investigate the electronic structures of
oligomers, the orbital energies and the geometries of these oligomers are calculated by the
semiempirical MNDO-SCF-MO (modified neglect of diatomic overlap self-consistent-field
molecular orbital) method. Theoretically simulated spectra of these oligothiophenes derived
from the obtained orbital energies by Gaussian broadening are compared with the observed
ones. The agreement between the observed and calculated spectra is very good, particularly in
the 1T region. It is shown from the optimized geometry that (I) an's have planar structure and
1T electrons are delocalized, (2) the oligomer with (3 linkages has non planar structure leading
to limited delocalization of 1T electrons, and (3) the oligomers with a vinylene group are almost
planar and the disturbance by the vinylene group on the delocalization is small.
I. INTRODUCTION
Conducting organic polymers are the subject of a major
research activity initiated from the discovery that a large
number of organic polymers can be doped with either elec
tron acceptors or electron donors to yield highly conducting
complexes. 1 Among these, polyheterocycles have attracted
much attention because of a non degenerate ground state and
a possibility of nonlinear excitations such as polarons and
bipolarons.2-18 This property is of great interest in view of applications such
as electrochromic displays,47 electro-optic devices (color
switching and memory),48.49 protection of semiconductors
against photocorrosion,50 and energy storage. 51 Further
more, poly thiophene has various interesting properties: ease
of chemical modifications,21-23.25.30-42.52-56 high conductiv-
In the field of conducting polymers with the nondegen
erate ground state, poly thiophene and its derivatives have
been synthesized by many methods such as a Grignard cou
pling reaction,19-23 a one-step chemical polymerization,24.25
and an electrochemical method.26-42 These polymers show
good stability towards atmospheric exposure32.43-45 and
thermal treatment36.46 in both doped and undoped states.
.) Present address: Department of Environmental Science, The Graduate
School of Science and Technology, Kumamoto University, Kurokami,
Kumamoto 860, Japan. ity of 190 S/cm,35 existence of a rather narrow optical band
gap of about 2 eV,20.30.35.51.57-59 the possibility of a highly
crystalline state,20.6O and solubility achieved by appropriate
substitution at the (3 position of the thiophene
ring.22.23.4O.61.62
It is evident from 13C nuclear magnetic reson
ance,46.63-65 infrared vibrational,35,36.44.46.65-69 and Raman
spectroscopic studies68 that poly thiophene chains are pri
marily composed of a-a' linkages of the monomer rings, that
is, poly (2,5-thienylene). However, the existence of partial a
(3' linkages «(3 linkages) has also been suspected.67,68 The (3
linkages are expected to prohibit the delocalization of 1T elec
trons on the analogy of the calculations for poly(m
phenylene) and poly(p-phenylene),'o,71 and optical stud
ies21 showed that the 1T-1T* transition energy of poly(2,4-
thienylene) and the resistivity of its doped form are actually
J. Chern. Phys. 92 (7), 1 April 1990 0021-9606/901074077 -16$03.00 ® 1990 American Institute of Physics 4077
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larger than those of neat and doped poly (2,5-thienylene).
Furthermore, poly(3-methylthiophene), which is free from
/3 linkages, shows a high conductivity as compared with po
lythiophene.31,35
In a detailed study of these polymers, however, a major
problem is caused by the difficulty in controlling their chem
ical forms. For chemically synthesized polymers a distribu
tion of the molecular weights is inevitable, and for electro
chemically obtained polymers the presence of /3 linkages and
cross linkings can not be excluded. In both cases, their amor
phous nature and insolubility make characterization and pu
rification difficult. This problem can be avoided by using
oligomers as model compounds. Moreover, we can study
( 1) the evolution of the electronic structure of a polymer
chain by using regular oligomers with various chain length,
and (2) the effect of defects such as /3 linkages by using
oligomers with such defects and compare them with regular
oligomers.
In this paper, we will report a combined experimental
and theoretical study on the electronic structures of oligo
thiophenes containing 4-8 thiophene rings. The systematic
evolution of the 1T band with increasing ring numbers and the
effect of the irregularity (a/3 linkage and a vinylene substitu
tion) on the 1T-electron systems are studied by the ultraviolet
photoelectron spectroscopy (UPS). The electronic and geo
metric structures of these oligomers are calculated by the
modified neglect of diatomic overlap self-consistent-field
molecular orbital (MNDO~SCF-MO) method, and the re
sults are discussed in comparison with the UPS results.
II. EXPERIMENTAL
The angle resolved UPS (ARUPS) system used in this
work was constructed at the UVSOR Facility of IMS.
Syachrotron radiation is monochromatized by the previous-
'. ~';5' ,2":5",2"'-quartllrthloph_
2,2':5' ,2":5" ,2 ... :5 .. ·,2 .... -qulnquettt~
2,2·:5·.2 .. :5 .. ,2 ... :5· ... 2 .. ··:5 .... ,2 ..... -sexHhlophen.
2,2·:5·,2 .. :5 .. ,2 ... :5· .. ,2· .. ·:5·~ .. ,2 .... ·:5 .... ·,2 ...... ....,tlthlophene ly reported plane-grating monochromator supplying radi
ation in the energy range of 2-150 e V. 72 The photoelectron
spectrometer consists of a sample preparation chamber, a
measurement chamber, and a sample transfer system.73
All oligothiophenes used in this study are shown in Figs.
1 and 2, along with the structural formulae, the IUPAC
name, the melting points, and the wavelength of the absorp
tion maxima in chloroform solutions.74 These compounds
were synthesized as reported74-76 and purified by recrystalli
zation from hexane or chlorobenzene, except for a7 and a8
purified by sublimation. Thin films of 30-50 nm thickness of
these compounds were prepared on a polished molybdenum
substrate by in situ vacuum evaporation in the preparation
chamber (base pressure 10-7 Pal, and subsequently trans
ferred to the measurement chamber (base pressure 10 -8 Pa)
of the UPS system in vacuum. The infrared absorption spec
tra and the x-ray diffraction pattern showed that these oli
gomers do not decompose on evaporation and that the de
posited thin films are polycrystalline.
Photoelectron spectra were measured for electrons
emitted normal to the sample surface with an incident angle
60· of the light beam. A hemispherical electron-energy ana
lyzer of 25 mm mean radius was used in the measurement
chamber. The Fermi energy (EF) of the UPS system was
determined by using the Fermi edge of gold films evaporated
in situ. The total resolution was found to be constant (about
0.2 e V) in the photon energy region of20 e V <hv< 100 e V, by
measuring the Fermi edge of gold at the electron pass energy
of6 eV.
All theoretical calculations were carried out on a
HIT AC S-81 0/ 1 0 and a HIT AC M-680H computers at the
Computer Center of IMS. The MOPAC program developed
by Stewart 77 was slightly modified to handle the large mo
lecular systems and was used for the MNDO-SCF-MO cal
culations.
m.p. I ·C A. max I nm
(CHel3 80In.)
213 -214 390
252 -254 416
326 -328 438
300 440 FIG. 1. a-linked oligothiophenes used in
this work. Their UV and visible absorp
tion maxima in chloroform solutions and
melting points (Ref. 74) are also given.
2,.2':5'12":5" ,2'" :5''',2'''' :5"",2"''':5''''' ,21t1'" :5'111" ,21tJlttl ooOCtIthlophene 364
J. Chern. Phys .• Vol. 92. No.7. 1 April 1990
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m.p. I °C A. max I nm
(CHeI3 soln.)
370 2,2' :5' ,2":5" ,3'":4''' ,2"":5"" ,2'"'':5''''' ,2"''''-septlthlophene 203
(E)-bls(2,2'-blthlophene-5-yl)ethylene 214 -215 423 FIG. 2. Oligothiophenes with ir
regularity. Their UV and visible
absorption maxima in chloroform
solutions and melting points (Ref.
74) are also given.
(E)-bis(2,2' :5' ,2"-terthiophene-5-yl)ethylene 282 -283 460
III. RESULTS AND DISCUSSION
This section will be divided into four parts: the opti
mized geometry by the MNDO-SCF-MO method, the sys
tematic evolution of the 1T bands, the effect of the irregularity
on the 1T-electron system, and the photon energy dependence
of the UPS spectra. In last three parts, the electronic struc
tures obtained by UPS measurements are discussed in com
parison with the results of MO calculations.
A. MNDO-SCF-MO calculation and molecular
geometries
In order to investigate the electronic structures of oli
gothiophenes, we have carried out the semiempirical
MNDO-SCF-MO calculations. The detailed calculation
method and results on several oligothiophenes were reported
in our previous paper,78 so we will only summarize the re
sults obtained by the calculations.
The reliability of the calculation method was carefully
inspected by a comparison with the observed molecular ge
ometry and UPS spectra of thiophene and 2,2' -bithiophene
(a2) and with the results by the ab initio calculations at the
minimal Slater-type three Gaussian orbital (STO-3G) level.
According to the Koopmans' theorem, ionization energies
are obtained as the negative of orbital energies. It should be
noted that the results obtained by the MNDO-SCF-MO
method is more reliable than the STO-3G ab initio results in
the case of thiophene and a2• Therefore, we expect that the
MNDO molecular geometry and the ionization energies are
reliable even for the large oligothiophenes.
Figures 3-8 show the optimized molecular geometries
of a2 -as with the values of the bond lengths and angles. It is
noteworthy that in this series of an' a twofold symmetry axis
automatically appears at the center of the molecule without
any symmetry restrictions in the MNDO-SCF-MO calcula
tion. The compounds with odd n have C2v symmetry and the even-numbered oligomers show C2h symmetry. The left and
right halves of Figs. 3 and 4 show the values of the bond
lengths and angles, respectively. Figures 5-8 show only half
of the molecules, in which the leftmost and rightmost rings
are the end and middle rings ofthe molecule, respectively.
The most stable conformations of an are such that the
molecule is coplanar with sulfur atoms on adjacent rings
pointing in the opposite direction. The stabilization of such a
structure can be ascribed to (1) the delocalization of 1T elec
trons and (2) the hydrogen-bond-like effect or the Coulomb
interaction between a sulfur (S) atom and hydrogen (H)
atoms on /3 carbons (Cp) in the neighboring rings. This
structure with alternating sulfurs has also been confirmed by
x-ray diffraction data on a2,79 infrared (lR) spectra of
a2 -a4 and a6, 80 and calculations on a2 .81 The geometries
of the terminal rings are the same as that of a2• The rings
other than these terminal ones have almost identical struc
ture, with local C2v symmetry in each thiophene ring. It
should be stressed that the bond length between the two a
BOND LENGTH I A
FIG. 3. Optimized molecular geometry of 2,2'.bithiophene (a, ) by the
MNDO-SCF-MO method. The left and right halves show the bond lengths
and angles, respectively.
J. Chern. Phys., Vol. 92, No.7, 1 April 1990
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BOND LENGTH I .l BOND ANGLE I "or ..
carbons on two adjacent rings (Ca and C~) in an are almost
constant around 1.444 A, which is nearly equal to that of a2'
and the inner part of the oligothiophenes are quite similar
with the central part of a2 (part A in Fig. 3), as pointed out
by Bredas et al.82-85 These facts clearly show that the end
effects are localized on the terminal rings.
In Fig. 9, the MNDO-SCF-MO optimized molecular
geometry of a)Pa 3 is shown. This molecule again has C2
symmetry without restrictions. Hence, only half ofthe mole
cule is shown and the p-linked thiophene ring is drawn on
the right end. For easier understanding, the optimized geom
etry is also depicted three dimensionally in Fig. 10.
SOND LENGTH 11
SOND ANGLE I degree FIG. 4. Optimized molecular geo
metries of a, and a. obtained by
the MNDO-SCF-MO method. In
left and right halves, the bond
length and the bond angle are
shown, respectively.
As shown in Figs. 9 and 10, this molecule consists of a p.
linked thiophene ring (P ring) and two planar terthiophene
parts perpendicular to the P ring. This structure is caused by
the steric repulsion between the two thiophene rings con·
nected to the P ring. Moreover, the repulsion of the 11' elec
trons on the planar terthiophene parts makes the C~ -Cp -Cp
angle of the P ring larger than the H-C,8 -C,8 angle in a2•
Consequently, the aromatic nature of thiophene is weakened
in the region of the P linkage. The two terthiophene parts
have almost similar structure with a 3 with small differences
arising from the difference in the end groups of a hydrogen
atom and a P ring. These facts imply that the P linkages
FIG. 5. Optimized molecular geometry of a,
obtained by the MNDO-SCF-MO method.
Only the left half of the molecule is shown be
cause of the molecular symmetry (see text).
J. Chem. Phys., Vol. 92, No.7, 1 April 1990
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Cl6
BOND LENGTH I 1
obstruct the delocalization of 1T electrons by shortening the
extended 1T system. In other words, the f3 linkages work as
strong irregularity on the 1T-electron system of polythio
phene.
In contrast with the {3 linkage, vinylene-containing oli
gothiophenes show almost planar optimized structures as
shown in Figs. 11 and 12, suggesting that the vinylene group
does not disturb the 1T-electron delocalization in thiophene
based compounds. This weak effect as irregularity of the
vinylene group on the 1T-electron system is also confirmed
from the similarity between the geometries of the thiophene
rings tied to the vinylene group and the central ring of a7•
BONO LENGTH I l
BOND ANGLE I degr •• FIG. 6. Optimized molecular geometry of a.
obtained by the MNDO·SCF·MO method.
Only the left half of the molecule is shown be·
cause of the molecular symmetry (see text).
Moreover, inversion symmetry (C;) exists in the center of
a2 Va2 and a3 Va3, and the planes of two a-linked parts are
parallel to each other.
The small nonplanarity in a2 Va2 and a3 Va3 is caused
by the nuclear repulsion between the hydrogen atoms of the
vinylene group and those at the C{3 positions of the neighbor
ing rings. The irregularity appearing as the angle formed by
Ca and the vinylene carbons (Ca -Cui -Cu2 ) is slightly larger
in a2 Va2 than in a3 Va3 as a result of delicate balance be
tween the stabilization of the 1T system and the repulsion of
hydrogen atoms.
For the comparison with the UPS results, the orbital
FIG. 7. Optimized molecular geom
etry of a, obtained by the MNDO·
SCF~MO method. Only the left half
of the molecule is shown because of
the molecular symmetry (see text).
J. Chern. Phys., Vol. 92, No.7, 1 April 1990 •
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80NO LENGTH I .l
energies (€) of these oligomers calculated by the MNDO
SCF-MO method are used. The values of € relative to the
vacuum level are shown in Fig. 13 for the series of an' Thio
phene has two 1T levels with 1a2 and 3b, symmetry in the low
binding energy (Eb) region.86•8? The 1a2levelhasnocontri
bution from as 3pz orbital and only consists of C 2pz orbi
tals ofCa and C{3' In contrast to tl,tis, the 3b, level consists of
the S 3pz orbital and the C 2pz orbitals on C{3' with no con-
BOND LENGTH I .I. FIG. 8. Optimized molecular geom
etry of a. obtained by the MNDO
SCF-MO method. Only the left half
of the molecule is shown because of
the molecular symmetry (see text).
tribution from the C 2pz orbitals of Ca'
In the oligomers, the 1a2 levels split into a wide 1T band,
and the 3b, levels make a dense non bonding 1T band. Ac
cordingly, the highest occupied valence band has no contri
bution from the sulfur atoms, as suggested by calcula
tions82•88 and electron spin resonance data.89 Thus, the
systematic 1T-band formation is expected to be observed
clearly in the lower Eb region.
II
.~ 3 FIG. 9. Optimized molecu
lar geometry of a,{3a, ob
tained by the MNDO-SCF
MO method. Only the left
half of the molecule is
shown because of the mo
lecular symmetry (see
text).
J. Chern. Phys., Vol. 92, No.7, 1 April 1990
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J. Chern. Phys., Vol. 92, No.7, 1 April 1990 4083
FIG. 10. Illustration of the
optimized geometry of
a.,/3a) .
FIG. 11. Optimized molecular geometry of
a2 Va2 obtained by the MNDO-SCF-MO
method. The left half of the molecule is
shown because of the molecular symmetry
(see text).
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BONO _ENGTH I l
II I , , I , , ,
II I I I II I I
I I 1111 III I I I
I I II 11111 III III I II I
II I II III I I I 111111111 III 1111
I I I II II I I I I III 1111111 I II I I I
II I I II 1111 II I I II 111111111111. I I III I I I
III I I II 1111 II I I I II 1111111111 I I III I I II
III I I I II 11111 II I I I III 11111111 II 'I' I I II
• • • I • I , I • 25 20 15 10
-£ I eV
FIG. 13. Orbital energies of an' The vacuum level is taken as the origin of the energy scale.
J. Chern. Phys., Vol. 92, No. 7,1 April 1990 ,
• FIG. 12. Optimized molecular geometry
of a, Va, obtained by the MNDO-SCF
MO method. The left half of the molecule
is shown because of the molecular symme
try (see text) .
, I . ,
n=l
n=2
n=3
n=4
a.n
n= 5
n=6
n= 7
n=8
~ ,
5 0
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We note that the calculated energy of the highest occu
pied molecular orbital (HOMO), which corresponds to the
ionization threshold, is lowered with increasing n and the
change is saturated at around n = 6. Thus, it is expected that
the electronic structures of oligomers beyond n = 6 can be
regarded to be almost the same as that of the polymer.
B. Evolution of the 11' band and electronic structure of
the polymer
The UPS spectra of the oligomers are shown in Figs. 14-
17 as solid lines. Hereafter, the values of Eb are scaled
against E F' In order to complete the series of an' UPS spec
tra of solid thiophene (al ), a2, and 2,2':5',2" -terthiophene
(a3) reported by Tourillon and Jugnet90 are also shown in
Figs. 14 and 15. The broken curves show the simulated UPS
spectra derived from the MNDO orbital energies shown as
the vertical lines.
The simulated spectra were obtained by broadening the
delta function located at each orbital energy with a Gaussian
function without correction for cross-section effects. The
value of the Gaussian width is chosen to be 0.6 eV in order to
Ii
I I
I I I ~ 1\ I
I I l\ ,
I \ I \ " -/ II \ ____ J I ''-___ " I II
" I,
I , -
I , " I ,I \ , \"
I ' hv =40.8eV
a1(thiopene)
hv =40.8eV
_... '\ .. ft I " /"'\,'\/\/\/\/ "I ll\ 'I I" I .' 1 '.' 1 \~I 1 ,., 1111 III I '. __ ~, I I \/ I ,_
15 10 5
FIG. 14. Observed and simulated UPS spectra of thiophene (upper) and
2,2'-bithiophene (lower). The observed UPS spectra are those reported by
Tourillon and Jugnet (Ref. 90). The solid and broken curves show the ob
served and simulated UPS spectra, respectively. The vertical lines indicate
the orbital energies. The Fermi level (E F) is taken as the origin of the energy
scale. The simulated spectra and the ionization energies are sifted down by
5.3 eV in a, and 6.0 eV in a2 to get a better fit to the observed UPS spectra
(see text). hv =40.8 eV
" I, : '",,"\.,
I \ \ I ,
,.. r. ", \ ,-, I \ : \ ,. '\ "\ : \,~ \ ,.
I \ I \ , , 1\ " t " ,I, ,"
/11'·'11 '.' I \J I'~'I '-,'1 11111111111 ' __ /1 II 1-'1 '.
hv =45 eV
15 10 5
FIG. 15. Observed and simulated UPS spectra of a, (upper) and a. (low
er). The spectrum of a, is that reported by Tourillon and Jugnet (Ref. 90).
The solid and broken curves show the observed and simulated spectra, re
spectively. The vertical lines indicate the orbital energies. The Fermi level
(E F) is taken as the origin of the energy scale. The simulated spectra and the
ionization energies are shifted down by 6.0 eV in a3 and 6.5 eV in a. to get a
better fit to the observed UPS spectra (see text).
take account of the resolution of the UPS system and the
solid-state effects91 such as site-dependent polarization ef
fects and disorders. To get a better fit between the observed
and simulated UPS spectra, the simulated spectra are shifted
down by about 6.5 e V, except for those of a I , a2, and a 3,
which are shifted by 5.3, 6.0, and 6.0 eV, respectively. This
shift arises from the work function and the polarization ener
gy.91.92
The correspondence between the observed and simulat
ed spectra is good, especially in the binding energy region of
o eV <,Eb <, 10 eV. It should be noticed that the simple simu
lation can reproduce the observed UPS spectra in the 17'-band
regions, and this fact shows that the Koopmans' theorem
holds in this energy region of these thiophene-based com
pounds. The good correspondence also confirms that the
MNDO-SCF-MO method is reliable in the thiophene-based
large molecules.
From this good agreement between the observed and
simulated spectra and by analogy of the assignments for po
lythiophene,7o,71 the bands observed at 1 eV <,Eb <,5 eV and 8
e V regions are ascribed to the 17' and (7 bands, respectively. In
J. Chern. Phys., Vol. 92, No.7, 1 April 1990
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''''', .. I ,
: "'..1\
~ I \
" I \
I \ I \
/'\. /\ I \.... ..,./ \
I -'''' \ I \ I \ _ I \ 1_'
" I I I II ,./ II \,'1 I ~'I'-'II 111111111 \,11
15 10 5 hv =45 eV
FIG. 16. Observed and simulated UPS spectra of a, (upper) and a. (low
er). The solid and broken curves show the observed and simulated spectra,
respectively. The vertical lines indicate the orbital energies. The Fermi level
(E F) is taken as the origin of the energy scale. The simulated spectra and the
ionization energies are shifted down by 6.5 eV to get a better fit to the ob
served UPS spectra (see text) .
the low Eb side of the 1T region, several peaks are observed
depending on the number of repeating units, n. The spectra
of this region lose fine features with increasing n and become
almost independent of n beyond n = 6. Moreover, an intense
band is observed at Eb = 3.S eV and its location is almost
independent of n. These facts show that the structures in the
low Eb side of the 1T band arise from the strong interaction
between the repeating units, and that the intense band at 3.S
e V consists of the noninteracting orbitals in the repeating
units.
Therefore, we can assign the structures in the low Eb
side of the 1T-band region and the intense band at 3.5 eV in
the observed spectra to the anti-bonding and non bonding 1T
bands, respectively. The anti-bonding 1T band grows with n
in the low E b side of the 1T bands overlapping with the intense
nonbonding1Tband located atEb = 3.S eV. The high-energy
bonding wing of the widely dispersive 1T band is merged into
the tail of the 0' bands.
In Fig. 18, the 1T-band regions of these oligomers are
summarized along with the simulated results and compared
to the data of x-ray polymerized thiophene'! and poly(3-
methylthiophene).90,93 The band formation in thiophene
based polymers is clearly demonstrated in Figs. 13-16. The
spectra of a, and as are similar to those of polythio-IN =45eV
a,7
'-"' ... ,
: \l\
~ : \ ,\ \ " ' \ 1, I, ". " ,.., ,,' \
I ' ...... ' \ I \ '''...,' \ #' '" ." ... ,
/11111 ft '/1111 \/11 1"f'llI .1.1 .. 1 '.-'111111 i 11',_
',,-. , I
I' \,/,
" : \ : I , I hv =45 eV
t\ , ' I ,I \ / ' ..... _ ... '\ I \ '''''' ...... ,,/'" \ , .. / \._ .... -\
,'1111110' .. '111 './III-n III 1111,. 'V111111111\_
15 10
FIG. 17. Observed and simulated UPS spectra of a, (upper) and ag (low
er). The solid and broken curves show the observed and simulated spectra,
respectively. The vertical lines indicate the orbital energies. The Fermi level
(E F) is taken as the origin of the energy scale. The simulated spectra and the
ionization energies are shifted down by 6.5 eV to get a better fit to the ob
served UPS spectra (see text).
phene,o.'1 showing that these oligomers are good model
compounds of poly thiophene. Moreover, these two oli
gomers show even sharper features than the x-ray polymer
ized'! or electrochemically prepared'o polymers, which
may contain a fraction of the short conjugation length pro
vided by {3 linkages and cross links and may have not such
clean surfaces. Correspondingly, poly(3-methylthio
phene),9o.93.94 where the {3 position (3-position) is blocked,
shows sharp features.
Finally, we discuss the ionization threshold energies and
the bandwidths of polymers and long oligomers. The ioniza
tion threshold energy, or the energy difference between the
vacuum level and the HOMO, was measured for a7 and
electrochemically polymerized poly thiophene on other UPS
apparatuses with retarding-field-type energy analyzers, us
ing a monochromatized hydrogen discharge lamp and rare
gas emission lines. The same value of S.3 eV was observed for
a795 and poly thiophene. 96 The same values of ionization
thresholds of the oligomer and poly thiophene again confirm
that these long oligomers are good model compounds of the
polymer. The values ofS.3 eV are smaller than those of poly
(p-phenylene) (S.6S eV),97 poly (p-phenylene sulfide) (6.0
eV),98 and poly(p-phenylene vinylene) (S.S eV),97 and
close to that of trans-polyacetylene (5.24 eV).99 This trend
J. Chern. Phys .• Vol. 92, No.7, 1 April 1990
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138.251.14.35 On: Sat, 20 Dec 2014 18:15:07Fujimoto et al.: Ultraviolet study of oligothiophenes 4087
UPS
RED
OX
PMeT
PT CALC
(MNDO)
12 10 8 6
-deY
FIG. 18. Observed (left) and simulated (right) UPS spectra in the 17 region
with extended scale for oligothiophenes used in this work. The origins of the
energy scale of observed and simulated UPS spectra are taken as the Fermi
level (EF) and the vacuum level, respectively. For a comparison, the ob
served UPS spectra of neat poly thiophene (PT) (Ref. 7 I ), reduced (solid
line) and oxidized (broken line) poly(3-methylthiophene) (PMeT) (Refs.
90 and 93) are also shown.
agrees with that in the easiness of acceptor doping: polythio
phene and trans-polyacetylene can be doped with weak ac
ceptors like iodine, while phenylene-based polymers can be
doped with only strong acceptors such as arsenic pentafiuor
ide (AsFs)'
The half bandwidth of the anti-bonding 1T band can be
estimated to be about 1.4-1.5 e V, from the energy difference of2.0 eV between the peaks at 1.5 and 3.5 eV, taking account
of the splitting (0.5-O.6eV) 100,101 of the ta2 and3b2 1Torbi
tals in thiophene, This value is comparable to those of phen
ylene-based polymers (1.4-2,0 eV),96-98 but smaller than
that of trans-polyacetylene (2.5-3 eV) .96
C. Effect of irregularity on the 1T-electron systems
The {3 linkages have been predicted to prohibit the delo
calization of 1T electrons on the analogy of the calculated 1T
bandwidth of poly (m-phenylene) and poly (p-phenyl
ene).70.71 Actually, an optical study21 has shown that
poly(2,4-thienylene), in which half of the inter-thiophene
bonds is {3 linked, has a shorter maximum wavelength of the
1T .... 1T* transition (280 nm) than that of regularly a-linked
poly(2,5-thienylene) (4IOnm), and that the conductivity of
iodine-doped poly(2,4-thienylene) (10-10 S/cm) is lower
than that ofpoly(2,5-thienylene) (10-2 S/cm). Moreover,
poly(3-methylthiophene),9o.93,94 which is free from {3 link
ages, shows sharper UPS features than polythiophene.7o,71
These effects of irregularities on the electronic structure are
revealed explicitly in the UPS spectra of oligothiophenes list
ed in Fig. 2.
The UPS spectra of a3{3a3, a2 Va2, and a3 VaJ are
shown in Figs. 19 and 20. The solid curves show the valence
band spectra and the broken ones are the simulated spectra
by using a Gaussian function with a width of 0.6 eV. The
vertical lines show the orbital energies. The simulated spec
tra and the orbital energies are shifted down by 6.5 eV to
obtain a better fit.
The UPS spectrum of a3{3a 3 is significantly different
from that of a7, although they contain the same number of
thiophene rings. Four peaks shown by arrows are observed
at Eb = 1.5,3.0,3.9,4.8 eV in the 1T region, and the 1T-band
structure is not as clear as those of a7 •
The MNDO-SCF-MO calculations show that a3{3a 3
consists of two planar terthiophene (a3) parts and a{3 ring,
with the a3 and {3 parts being perpendicular to each other.
As a result, the 1T conjugation is broken at the {3 linkages.
Correspondingly, the calculated 1T bands of a3{3a 3 can be
reproduced by adding those of two trimers and a monomer
(a3 + a3 + a1) rather than a tetramer and a trimer
(a4 + a3), as shown in Fig. 21. The broken and vertical
lines show the simulated spectra and the orbital energies,
respectively. On the other hand, the a bands in theEb region
from 13 to 19 eV of a3{3a 3 are better simulated by a4 + a3
than by a3 + aJ + a1 and are similar but slightly different
from those of a7, because the a skeleton of a J{3a 3 is contin
uous at the position of {3 linkages as compared with aJ and
the continuity is not identical with a7 • These facts imply that
a drastic effect of irregularity appears both on the 1T-and a
electron systems of poly thiophene by the introduction of {3
linkages.
On the other hand, the observed UPS spectra of a2 Va2
and a3 Va3 are similar to those of as and a7, respectively. In
particular, the correspondence of the 1T-band shapes is very
good. The 1T bands of the simulated UPS spectra of these
vinylene-containing oligomers are also identical to those of
corresponding an's. This fact reveals that the1T system of
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138.251.14.35 On: Sat, 20 Dec 2014 18:15:074088 Fujimoto et s/.: Ultraviolet study of oligothiophenes
" , , , ,.. "
, w .... , " , \ ' , , , ' , .. I,' , hv =45 eV
FIG. 19. Observed and simulated UPS spectra
of a3f3a.,. The solid and broken curves show the
observed and simulated spectra, respectively.
The vertical lines indicate the orbital energies.
The Fermi level (EF) is taken as the origin of
the energy scale. The simulated spectra and the
ionization energies are shifted down by 6.5 e V to
get a better fit to the observed UPS spectra (see
text).
1\ 1,,' \ l\ I \ I
I '.-.. ''', I \ ,... ',' \" /1111(11'-'. ~..,/il'j"'i"'IIIII.lftlllll\ .. /1 III' .. 'I\'
15 10 5
hv =45eV
,'\ /' '" ' , ~ \
I \ , ,
I ,
r... Ito ,.. " , \', '\ I, , ' I '/ ",--" '-'\ " ..... ., I "II' \ , ....
',,1 I ~ II ~ I " I ,./ I "I I /I" 1111 111111 './1 "I I I ~I I \
r, , ..... .,"\
, I • , \ " , , "
" ,': ' 1 , , f \ ," ,1,
l"'~\. ,"', I \. t".,,, " .. .,1 ' ....... /., )1 I~'II~/III\'/I 11'~I""J11111111 \~'I 111111 11\_
15 10 5
FIG. 20. Observed and simulated UPS spectra of a2 Va2 (upper) and
a3 Va3 (lower). The solid and broken curves show the observed and simu
lated spectra, respectively. The vertical lines indicate the orbital energies.
The Fermi level (E F) is taken as the origin of the energy scale. The simulat
ed spectra and the ionization energies are shifted down by 6.5 eV to get a
better fit to the observed UPS spectra (see text). vinylene between the a parts does not strongly affect the 1T
band structures of the host chain. The theoretical results
show that the molecular geometries of these oligomers are
almost planar and that the 1T electrons can delocalize over
the whole molecule.
In contrast with the 1T bands, the u-band shapes of vi ny
lene-containing oligomers are different from those of the
corresponding a", because the skeleton of the main chain is
deformed by the introduction of the vinylene group. This
discrepancy is more prominent in a2 Va2 than in a3 Va).
This fact confirms that the electronic and geometric struc
tures of these vinylene-containing oligomers are settled by
the balance of the 1T-electron stabilization and the nuclear
repulsion of hydrogen atoms as discussed in the previous
section. That is, the 1T electrons tend to delocalize over the
whole molecule to stabilize the total energy and the nuclear
repulsion between hydrogen atoms on Cp and on vinylene
distorts the molecular geometry.
As shown in the lower side of Fig. 18, the ionization
onset of a)f3a 3 relative to EF is about 0.3 eV higher than that
of a7, while those of the vinyl ene-containing oligomers are
almost the same as those of the corresponding a". In the
MNDO-SCF-MO calculations, the energy difference of
HOMO between a7 and a3f3a 3 is also 0.26 eV, while the
HOMO of a3 Va3 is 0.06 eV higher than that of a7, which
cannot be distinguished within the experimental resolution.
These results of ionization onset suggest that the carrier gen
eration will be suppressed by the introduction of f3 linkages.
These UPS results correspond well with the trend in the
observed 1T-+1T* transition energies. The value of a3f3a 3
(3.35 eV) is significantly higher than that of a7 (2.82 eV),
and those ofthe vinylene-containing oligomers (2.93 eV for
a2 Va2, 2.70 eV for a3 Va3 ) are almost the same as the corre-
J. Chern. Phys., Vol. 92, No.7, 1 April 1990
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138.251.14.35 On: Sat, 20 Dec 2014 18:15:07Fujimoto tit at; Ultraviolet study of oligothiophenes 4089
I I I
{'~ ...
/ ' ....
I \ (\
/\ " I \ "
I'~\ / \ / \ I~""~-' / .... j \ ;,J \""
~ " '''' ... / ,; ,-., ... ' '-, I I HI I II I I 1111111111111 I II I
/\ ...... "-, ,\ / \ I \
,.. I \ / \
" /- I \ I \ I \ J ',-\ / \ , .... __ .... ,,-'J \,'" \ '"
,; 1111 In ' .... II -;\1 II-i II 11111111 '~./II 1I111'~"'11 '-
I I I
25 20 15 10
-£ I eV
sponding an as shown in Fig. 2. In addition, the reported
1T --1T* excitation energy of poly (2,4-thienylene) and the re
sistivity of the doped one are higher than those of neat and
doped poly (2,5-thienylene).21
We note that the effect of {3 linkages consists of two
factors according to our calculations. One is the character of
uppermost 1T orbitals, as pointed out from the analogy to
poly(m-phenylene). Neither of the high-lying 1T orbitals,
whose atomic orbital coefficients are depicted in the inset of
Fig. 18, has large coefficients at both 2 and 4 positions. This
results in ineffective transfer of 1T-electron interaction. An
other, more important factor in the present case, is the non
planarity of the molecule caused by steric hindrance, which
completely breaks the 1T conjugation. The present results
demonstrate the importance of the geometrical factor in the
study of electronic structure.
O. Photon energy dependence of UPS spectra
All oligothiophenes used in this study show rather simi
lar photon energy dependence of the UPS spectra. Figure 22
shows the typical photon energy dependence of the valence
band spectra for as normalized at the high-intensity (T band
of 8 eV in the photon energy region of20 eV..;;;Eb<80 eV.
The peak at Eb = 3.5 eV (A) and the lower Eb side of
the band at around 8 eV (B) are intensified with increasing
hv compared to the (T band at 8 eV. A shoulder grows at
around Eb = 12.5 eV from hv = 25 eV and increases its in
tensity with hv. Moreover, new peaks are observed at
Eb = 16 eV from hv = 30 eV and at Eb = 20 eV from
hv = 45 eV, and these peaks are intensified with increasing
hv.
These observations can be qualitatively explained by the I
5
35 o
30 FIG. 21. Simulated UPS spectra (broken
curves) and the orbital energies (vertical lines)
for al{3a 3 and two models for this oligomer.
The vacuum level is taken as the origin of the
energy scale. a3 + al + a, shows the addition
of the results on two trimers and a monomer cal
culated by the MNDO-SCF-MO method, and
a. + al indicates that of a tetramer and a
trimer.
FIG. 22. Photon energy (hv) dependence of the UPS spectra for a •. The
Fermi level (E, .. ) is taken as the origin of the energy scale.
J. Chem. Phys., Vol. 92, No.7, 1 April 1990
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hv dependence of the photoionization cross section.
The MNDO-SCF-MO calculation shows that (1) the
nonbonding 1T' band A contains the contribution from the
S 3p. orbitals, (2) the peaks at 7 and 8 eV in the simulated
UPS spectrum shown in Fig. 16 mainly consist of the C 2p
orbitals, and (3) the peak B at around 6 e V has a contribu
tion from the S 3p orbitals. On the other hand, C 2s, S 3p,
and S 3s atomic orbitals contribute to the molecular orbitals
in the regions of Eb = 12.5-16 eV (C, D), and the main
contribution at around Eb = 20 eV (E) is from the S 3s.
In the observed region of 20 eV <hv<80 eV, the atomic
subshell photoionization cross section decreases gradually
and rapidly in the C 2s and C 2p orbitals, and the value of
C 2p is larger than that ofC 2s below hv = 55 eV, at which
the ionization cross section is reversed,102 as shown in Fig.
23. The cross section ofS 3p gently decreases until hv = 35
eV and increases with a maximum at around hv = 60 eV
accompanied by a gradual decrease, and that ofS 3s orbitals
also shows a peak at hv = 45 e V following a gradual decrease
(see Fig. 23).102 As a result, the bands which have the C 2s,
S 3s, and S 3p characters are intensified as compared to the
bands of the C 2p characters with increasing hv in the ob
served hv region.
-I
I ,
I ,
I ,
hv I eV
FIG. 23. Atomic subshell photoionization cross sections of carbon (solid
lines) and sulfur (broken lines) reported by Yeh and Lindau (Ref. 102). IV. CONCLUSION
The UPS technique has been applied to the investigation
of the electronic structures of oligothiophenes with 4-8 thio
phene rings. The effect of irregularity on the 1T'-electron sys
tem of poly thiophene has also been studied by using the oli
gomers with "impurities" such as {3 linkages or a vinylene
group. The observed UPS spectra have been discussed with
the optimized molecular geometries and the molecular orbi
tal calculations of these oligomers by the semiempirical
MNDO-SCF-MO method. The reliability of this method
was carefully inspected by a comparison with the observed
molecular geometries and UPS spectra of thiophene and
2,2' -bithiophene, and it is shown that the MNDO method is
superior to the ab initio calculations with a small basis set.
The series of a-linked oligothiophenes, an (n = 4-8)
shows a typical 1T'-band evolution: (1) the la2 molecular
orbital of thiophene, which has contributions from 2pz orbi
tals of a carbons, is split into the same number of levels as
that of the interacting rings and to form a wide 1T' band in
poly thiophene, (2) on the other hand, the 3b, molecular
orbital of thiophene, which has no contribution from 2pz
orbitals of a carbons, forms a dense nonbonding 1T' band with
little dispersion, and (3) the observed UPS spectra of oli
gomers beyond n = 6 are almost the same as that of poly
thiophene, showing that these oligomers are indistinguish
able with poly thiophene from the viewpoint of the electronic
structure. These results are confirmed by the MNDO-SCF
MOcalculations. The optimized geometries of an are
planar, making the 1T electrons delocalize over the whole
molecule. The simulated UPS spectra of an using the calcu
lated orbital energies are in good agreement with the ob
served spectra, showing that the MNDO-SCF-MO method
is also reliable for the thiophene-based large molecules and
that Koopmans' theorem holds in the thiophene-based com
pounds.
The oligomer with {3 linkages, a3{3a 3' shows quite dif
ferent UPS spectra from those of an'S: four peaks are ob
served in the 1T'-band region and some difference is also ob
served in the (T bands. Moreover, the ionization threshold of
a3{3a 3 is about 0.3 eV larger than that of a7• The MNDO
SCF-MO calculation shows that the two planar a3 parts in
a3{3a 3 are perpendicular to the central {3 ring, resulting in a
limited delocalization of 1T electrons. The 1T' bands in the sim
ulated UPS spectrum of a3{3a 3 are well reproduced by add
ing those of two trimers and a monomer. Thus, the control of
polymerization is important for achieving good conductivity
by reducing miss-bondings such as {3 linkages. On the other
hand, the introduction of a vinylene group in a2 Va2 and
a3 Va3 does not strongly affect the 1T-band structure of
the host chain. The optimized molecular geometries of the
vinylene-containing oligomers are almost planar and the 1T
electrons can delocalize over the whole molecule.
Thus, in this study, we have demonstrated the advan
tage of using purified oligomers for studying the electronic
structures of polymers. Furthermore, we have shown that
oligomers with seven or eight repeating units can be already
regarded as polymers from the viewpoint of the electronic
structure.
All oligomers used in this study show similar photon
J. Chem. Phys., Vol. 92, No.7, 1 April 1990
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138.251.14.35 On: Sat, 20 Dec 2014 18:15:07Fujimoto 9t al.: Ultraviolet study of oligothiophenes 4091
energy dependence: the nonbonding 1T band and the low
binding-energy side of the first uband are intensified relative
to the first u band, and the several new u peaks appear with
increasing photon energy. These changes can be explained
by the photon energy dependence of the ionization cross sec
tion: the bands with the contributions from S 3p, S 3s, and
C 2s orbitals are intensified with increasing photon energy
compared with the bands derived from C 2p orbitals.
ACKNOWLEDGMENTS
We thank Professor M. Watanabe, Professor T. Ka
suga, Dr. H. Yonehara, Dr. A. Hiraya, Dr. K. Fukui, Mr. K.
Sakai, T. Kinoshita, O. Matsudo, M. Hasumoto, E. Naka
mura, and J. Yamazaki of the UVSOR Facility ofIMS for
the continuous and efficient support. We are also grateful to
S. Asada and T. Sugano for taking some part in the UPS
measurements. One of us (HF) acknowledges support from
a Grant-in-Aid for Scientific Research (No. 61790148)
from the Ministry of Education, Science and Culture of J a
pan, and is grateful to the Japan Society for the Promotion of
Science and to the Toyoda Physical and Chemical Research
Institute for the postdoctoral fellowship.
This work was partly supported by the Grants-in-Aid
for Scientific Research on Priority Areas of "Dynamic Inter
actions and Electronic Processes of Macromolecular Com
plexes" (No. 01612003) and "New Functionality Materi
als" (No. 63604514) from the Ministry of Education,
Science and Culture, Japan, and also by the Joint Studies
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1.584743.pdf | Si/Ge x Si1−x /Si resonant tunneling diode doped by thermal boron source
S. S. Rhee, R. P. G. Karunasiri, C. H. Chern, J. S. Park, and K. L. Wang
Citation: Journal of Vacuum Science & Technology B 7, 327 (1989); doi: 10.1116/1.584743
View online: http://dx.doi.org/10.1116/1.584743
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/7/2?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 137.207.120.173 On: Tue, 25 Nov 2014 03:17:46Si/GexSi1_x lSi resonant tunneling diode doped by thermal boron source
s. S. Rhee, R. P. G. Karunasiri, C. H. Chern, J. S. Park, and K. L. Wang
Device Research Laboratory, Electrical Engineering Department,
UniversityojCaltfornia, LosAngele5; California 90024
(Received 22 September 1988; accepted 22 September 1988)
A study of resonant tunneling of holes in a Si/GexSil x/Si double barrier structure doped by a
thermal boron doping source is presented. The source consists of a pyrolytic boron nitride
crucible and uses filament heating. Sharp and constant doping levels between 1 X 1017 and 4 X 1019
cm-3 are obtained with a maximum K-cell temperature of ~ 1560 "C. The double barrier
tunneling devices realized by this source shows 2.1/1 peak-to-valley ratio at 4.2 K in current
voltage characteristics. Magnetotunneling measurements confirm that both the light and heavy
holes participate in the resonant tunneling.
Recently, strained layer GeSi heterostructures have attract
ed considerable attention due to possible Si-based quantum
well and superlattice device application. 1-3 The devices en
gineered using the valence band of the GeSi system have
advantages both due to the large band offset as well as the
small light-hole mass. However, realization of such devices
in this system has been hampered mainly due to difficulties
of achieving desired doping concentrations with sharp pro
files. In Si molecular-beam epitaxy (Si MBE) Ga and Bare
normally used as p-type dopants. Ga which has a relatively
higher vapor pressure than B has a serious problem in con
trolling the doping profile. The difficulties come from the
long residence time at low substrate temperature (T,) as
wen as the low sticking coefficient at high T,. 4 For a typical
GeSi growth temperature which is lower than 550 ·C, this
results in serious smearing of the doping profiles. Also, the
higher ionization energy ofGa further imposes limitation on
the achievable carrier concentrations.
It has been reported that B has a very short residence time,
no surface segregation5,6,7 and unity sticking coefficient.
However, B has a low vapor pressures and high tempera
tures (1300-2000 DC) are n~eded to obtain an appreciable
doping concentration.5,7.9 In order to obtain high boron
source temperatures, Kubiak et al.s employed a direct heat
ing method by passing electric current through conductive
crucibles such as graphite or refractory metals. Recently,
Andrieu et al.9 reported a technique combining electron
bombardment and radiative heating in boron doping. How
ever, these methods have several drawbacks arising from the
complicated cell structures necessary to obtain such high
temperatures. Several groups have also experimented with
boron compounds such as B203 (Refs. 6,10,11) and HB02
(Ref. 12) in lieu of pure boron for producing boron at lower
K-cell temperatures. Even though the sticking coefficient
seems to be independent of the growth temperature in the
case of B203, the incorporation of oxygen into the epitaxial
film at low growth temperature and surface segregation of B
due to chemical reaction have been observed. 13ln this paper,
we present characteristics of doping profiles achieved by a
conventional K-ceU designed specifically for moderately
high-temperature operation and the results of resonant tun
neling ofSi/GeSi/Si double barrier diodes doped using such
a source. In the experiment, samples were grown in a Si MBE
chamber with a base pressure of7 X 10-11 Torr. The samples
were chemically cleaned by the Shiraki method4 and the pro
tective oxide was removed in situ by heating the substrate at
950 "C for -10 min. The performance of the boron source
was characterized for both Si and GeSi epitaxial films grown
at different cell temperatures. The doping profile and the
concentration were obtained from spreading resistance
(SR) and secondary ion mass spectrometry (SIMS) mea
surements.
First we estimated the temperature range for the neces
sary boron fluxes to obtain the required doping concentra
tions using the equation 15
1= Ll18X 1022PA /12.JA{f-
where I is the flux at the sample surface in molecules/cm2 s,
P is the partial pressure in Torr, A is the area of the source
opening, l is the distance between the source and the sample,
Mis the molecular weight and Tis the temperature of the cell
1020
15ElOoC
(1b 15000C
1019
6 b !~ ,.." & b 0 ("')
! i I I \ 'f\~ E t)
1018 ...., .
0
j \'=~ j I t \ c a
u 1017
~ 1\ 1 ~ OJ c
J \111 ~ l a. a
0
1016 ~ ~l ~~ tIl
16 00
10 0 1 2 3
Depth (microns)
FIG. 1. Spreading resistance measurement of a B doped Si MBE film. Differ
ent B doping cell temperatures are shown. Si flux used was 160 Aim.
327 J. Vac, Sci. Techno!. B 7 (2), Mar/Apr 1989 0734-211X/89/020327-05S01.00 @ 1989 American Vacuum Society 327
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 137.207.120.173 On: Tue, 25 Nov 2014 03:17:46328 Rhee et al.: Si/GexSi,_x/Si resonant tunneling diode 328
1013~~~ ________________________________ -.
......
1012 0 m
(I)
(\J
E 10" 0
"-(I)
E 0 +I a 1010
"-'
x • • Exper i mental
Theoret i cal
FIG. 2. Experimental and theoretical flux
rates as a function of temperature of the
thermal boron source.
:J •
!l. 109
ill
loB
0.50 0.55 0.60
1000/TCK)
in Kelvin. For the system we used, A = 0.73 cm2 and 1= 15
cm. the vapor pressure of B was obtained from Ref. 8.
Figure 1 shows SR measurement data of a boron doped Si
film grown at 700 ·C substrate temperature and the growth
rate was maintained at 160 A/min throughout the growth.
The boron cell temperature was varied from 1300--1560·C
and the power rating of the cell is 280 W at -1560·C. The
SR data exhibits a well-controlled doping profile in the range
of 1 X 1017 to 4 X 1019 cm 3. Doping concentration changes
more than one decade per 1000 A as seen in the SR data. It is
noted that the boron cell temperature of only 1400·C is
needed to obtain the 1018 cm -3 doping level for a reasonable
growth rate of 2-3 A/s. The background doping level is
~ 1 X 1016 em --3. Figure 2 shows the experimentally ob
served doping concentrations as a function of temperature
compared with the data calculated from the above equation
and good agreement is seen. The actual abruptness of the
doping profile should be better than that shown in Fig. 1 due
to the inherent limitations of the SR measurement.
In order to obtain a better estimate for the abruptness of
the doping profile, different samples were grown for the
SIMS measurement. The structure consists of four periods
of intrinsic Si and boron doped Si layers. The growth rate of
Si was 48 A/min and substrate temperature was kept at
530 ·C. The boron cell temperature of 1325 ·C was used to
dope the p-Si layers. Thicknesses for each layer of a period
were 100, 250, 500, and 1000 A, beginning from the surface.
The SIMS data in Fig. 3 show an abruptness of ~ one dec
ade/200 A. However, the slope of the doping profile should
be even better considering smearing effects from the ion mix
ing and incomplete coverage of primary ions over the sur
face. Considering these effects together with the background
signal in the SIMS system, the actual doping profile should
have an abruptness better than the SIMS data as shown in
Fig. 3. A high doping concentration of ~ 5 X 1017 em -,3 in
J. Vac. Sci. Technol. B, Vol. 7, No.2, Mar/Apr 1989 0.65 0.70
undoped layers seems to be mainly from the background of
the SIMS system.
To investigate the performance of devices using the above
boron source, we have fabricated a SilGeO.4 Sio.6/Si double
barrier tunneling structure on a low resistivity (0.01 n cm)
SiC 100) wafer. Ge was evaporated from a conventional
Knudsen cell. The growth temperature was 530·C. The Si
and Ge deposition rates were 45 and 30 A/min, respectively.
The structure of the sample consists of a double barrier
structure sandwiched between a 7ooo-A Ge0.4SiO.6 buffer
......
(")
I
E ()
"-' .
U
C o U
[J)
C
g-
O
ill
1 d 7~_T---:~_'!:-_-';-----::! a 1 2 3 4 5
Depth ( x 100nm )
FIG. 3. SIMS doping' profile of a Si film doped using the thermal boron
source at 1325 °C. Sharpness of the profile is better than a decade/200 A. Si
flux was 48 A/min.
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 137.207.120.173 On: Tue, 25 Nov 2014 03:17:46329 Rhee et 81.: SilGexSi'_xlSi resonant tunneling diode
FIG. 4. TEM picture of the double barrier resonant tunneling structure. It
shows 43-A well and two 50-A Si barriers. All the layers are Ge04 Sio6
except Si barriers.
and a cap layers. Both layers were doped to 5 X 1018 cm-3•
The double barrier structure was composed of an undoped
43-A. GeOA SiO.6 quantum well between 50-A Si barriers.
Outside the two Si barriers, two ISO-A GeO.4 Sio.6 layers were
undoped to prevent the diffusion of dopants into the active
region. In the structure, only the Si barriers are strained and
all the GeM SiO.6 layers are unstrained. Figure 4 shows a
transmission electron microscopy (TEM) image of the dou
ble barrier structure used in the experiment and the thick
ness obtained from TEM is in good agreement with the
thickness that is estimated from the flux rates. We have also
used x-ray diffraction to determine the lattice constant of the
substrate (aSi), and the relaxed buffer and contact }ayers
(aoes;)' The measurement yields aSi = 5.4236 A and
aOeSi = 5.5213 A along the growth direction for the Si sub
strate and unstrained GeSi layers, respectively. We have cal
culated the percentage of the lattice mismatch E
= (aGeSi -aSi )/aSi to be 1.8%. for a completely relaxed
GeOA SiO.6 layer, we have E = 1.6% using the lattice con
stants of Si and Ge. 16 This indicates that the buffer and con
tact layers are not completely relaxed and a small amount of
residual strain remains even though the film thickness is well
above the critical thickness.
Figure 5 shows splitting of the light-and heavy-hole bands
together with the valence-band offset for strained films on a
~-.--------- .. ~--
200
Ge Content
FIG. 5. Heavy-(HR), and light-hole(LH) band-edge .plitting and the va
lence-band offset (I:.E,,) for strained GC,Si, _ , film grown on Gen.-Sioo
buffer layer.
J. Vac. Sci. Techno!. B, Vol. 7, No.2, Mar/Apr 1939 329
FiG. 6. Band diagram (lfthe resonant tunneling structure used in the experi
ment. The heavy-alld light-hole band edges are degenerated in unstrained
Gen.4Si,," layers.
completely relaxed GeO.4 SiO.6 buffer layer. The valence-band
offset was obtained from the self-consistent ab initio pseudo
potential results of Van de Walle et al.17 The light-and
heavy-hole band splitting due to strain was obtained using an
empirical deformation potential theory.r8,19 In order to cal
culate the bound state energies in the quantum well for the
light and heavy holes, the envelop function approximation
using different masses for the well and barriers was used. The
effective masses of the light and heavy holes were estimated
using a linear interpolation of (001) masses of the warped
bulk Si and Ge valence band and the calculated masses for a
relaxed GeOA SiC.6 layer are 0.08 me and 0.26 me respective
ly. Figure 6 shows the band diagram of the double barrier
structure. For the heavy hole, there are two bound states in
the quantum wen at energies EhhO = 43 me V and E hhl = 167
me V and for the light hole only the ground state at E IhO = 61
me V is obtained. Tunneling diodes were fabricated by a con
ventional lift-off technique and electrical measurement data
were obtained for 50-pm diam diodes. The I-V characteris
tics of the diode at 4.2 K, 77 K and room temperature are
shown in Fig. 7. Inset of the Fig. 7 shows the 77-K measure
ment for higher bias. At 77 K there are two resonant peaks at
270 and 900 m V due to the light-hole ground state (E IhO )
and the heavy-hole first excited state (Ehh1 ), respectively,
Another resonance fea.ture is observed from the d 2 [ I d V 2
data at 170 m V (see Fig. 8) and is believed to be due to the
heavy hole ground state (EhhO)' As seen in Fig. 5 the light
and heavy-hole hands are degenerated in GeUA SiO.6 layers
and light-hole tunneling current is dominant due to the
smaller mass and lower barrier.
In order to identify whether the resonant tunneling is due
to light or heavy holes, we have carried out magnetotunnel
ing experiments with a magnetic field applied parallel to the
. h' I . t' 20 t1 k interfaces. Accordmg to a t eoreilca estlma lOn Ie pea
shift is proportional to B 2 and the gradient of the peak shift
vs B 2 is inversely proportional to the effective mass. Figure 9
shows the peak shift vs B 2 for the two peaks at 170 and 270
mY. The ratio of the slopes of two lines gives mhh/mth = 3.9
as compared with the theroetically estimated value of 3.3.
This indicates that the peak at 170 m V is due to the heavy
hole and the one at 270 m V comes from the light hole. The
effect of the series resistance of the device on the peak voltage
shift may be small since the peak resonant tunneling current
remains the same as the magnetic field is changed? The for-
•.• -••• -.-••••••.••• , ••••••• ;r. ••••• ,' ••••••••.•.•••••.••• , •••• ' ••. ' .••• :-; •.••••.• > ••••• -.~.-...".~.;.; ••• , ................ :.:.:.:.:.:.:;;:-.:.:.;.:.;.;.:.:.: .......... ";< ............ " ................... -•••••••
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 137.207.120.173 On: Tue, 25 Nov 2014 03:17:46330 Rhee etal.: Si/GexSi,_JSi resonant tunneling diode
I
I
6 I
I
I
I
300 K' ,
4 I
I r-. I a: ,
I
E I
I
'-' I
2 , , , l-I
Z , , , W , ,
0:: 0 ,
0::
:::J U
u -2
0
-4 ....
-6
-600 -400 -200 0 200
DC VOLTAGE CmV)
mation of Landau levels in the emitter region may be ignored
due to ionized impurity scattering of carriers. 20
In conclusion, we have demonstrated the use of a conven
tional K-ce11 for pure boron doping in Si MBE and sharp
doping profiles with concentrations needed for device appli
cations are obtained. A resonant tunneling structure was 77 K
400 600 330
FIG. 7. 1-V characteristic.~ of a SO-p:m diam
etcr resonant tunneling diode at 4.2 K, 77 K,
and room tcmperature. Inset shows the [-V
and conductance measurement of an addi
tional peak tor high bias at 77 K.
fabricated using the boron source and both light-and heavy
hole tunnelings were observed. The dominant types of tun
neling carriers corresponding to the different peaks were
identified using the voltage shift of the resonant tunneling
current peaks in the presence of a strong magnetic field ap
plied parallel to the interfaces.
2OOr-----------------------------------------~~
C
:::J
:J)
L a
L
o+J
..0
L a:: 100
o
. " '>~.,: .!
'-'
l\I > 1J -100 -10
"-1-1
l\I
1J
-200~----~~----~----~------~--~--~----~-ro
-600 -400 -200 0 200 400 600
DC VOLTAGE CmV)
J. Vac. Sci. Techno!. B, Vol. 7, No.2, Mar/Apr 1989 FIG. 8. Second derivative of l( V) at
4.2 K and room temperature showing
the tunneling due to the heavy-hole
ground state .
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o > Rhee et {II.: Si/GexSI,_xlSi resonant tunneling diode
25
20
15
to
5 331
FIG. 9. Peak voltage shift vs B 2 for the
peaks at 270 mV (dashed curve) and
at 170 mV (solid curve) for the mag
netic field parallel to the interfaces.
o ~ ~ 00 00 100
82 CTes I 02)
ACKNOWLEDGMENTS
The authors would like to acknowledge the support of
SRC, ONR, and ARO.
IS. S. Rhce, J. S. Park, R. P. G. Karunasiri, Q. Ye, and K. L. Wang, App!.
Phys. Lett. 53, 204 (1988).
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LeU. 52, 1809 (1988).
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1.38450.pdf | Electrode surface rf harmonics generated by the nonlinear
sheath in a coaxial capacitive rf discharge
Stephen E. Savas
Citation: AIP Conference Proceedings 190, 470 (1989); doi: 10.1063/1.38450
View online: https://doi.org/10.1063/1.38450
View Table of Contents: http://aip.scitation.org/toc/apc/190/1
Published by the American Institute of Physics
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Journal of Applied Physics 79, 3445 (1996); 10.1063/1.361392470
~T~DE SURFACE rf HARMONICS
BY THE NONLINEAR SHEATH IN A COAXIAL
CAPACITIVE rf DIS(~ARGE
Stephen E. Savas
Applied Materials, Santa Clara, CA 95054
ABSTRACT
rf harmonics of the 13.56 MHz excitation signal have been
measured on the electrode surface in a large coaxial capacitive
disc~e. Tnese are ~n to have flc~[t 10% of the ~tal
amplitude for the second harmonic to between 1% and 4% for the
third and fourth harmonics. There is evidence that these modes
propagate as T~4 surface waves (Gould-Trivelpiece modes)along
the length of the electrode. The Telegrapher's equations can be
written for the system with non-constant shunt capacitance and
admittance. The resulting nonlinear equation for the sheath
voltage is solved for the harmonics to yield approximate
agreement with their observed magnitudes.
INTRODUCTION
Measurements have shown the presence of rf harmonics (up to
10th) on the power input lead to the elective in capacitive rf
plasmas used for semiconductor processing ~-~. These harmonics
only appear when the plasma is turned on. In small parallel plate
systems used for etching it has been impractical to determine the
source of the harmonics. In our system, however, the large - 65
cm tall, 32 cm wide - hexagonal electrode is coaxial with a 72 cm
diam. cylindrical metal vacuum vessel, (see Fig.l) this permits
good access for our capacitive, high i~nce probes ~ to touch
the electrode surface. These probes (see Fig. 2) allow the
amplitudes of the fundamental
three points on the electrode
along its length.
SELL JAR
| HEXODE fl~ ELECTRODE
FEEDTHROUGH ~~ "~\
50Q COAXIAL WAFER CABLE TO
OSCILLOSCOPJ
SHIELDED ~~ ~
PROBE ~ ANODE
SENSOR
TIP rf POWERED
ELECTRODE and harmonics to be measured at
surface, nearly equally spaced
SUPPORT AND SPRING SOLID FOR TIP COPPER-SHIELDED (STAINLESS STEEL) 50=3 COAXIAL \ CABLE \ \ RECTANGULAR
' CAPACITIVE TRANSM TTER \ s~AL~ TTIP
AND SENSOR "~ ~ NLESS I ~ STEEL)
/ INSULATION \ QUARTZ
OUTER SHIELD \ PROSE (STAINLESS \ BODY STEEL) \
O-RiNG SEAL
Fig. i. Cylindrical Plasma
Chamber. Fig.2. Shielded Capacitive
Probes.
© 1989 American Institute of Physics
471
~~AL RESULTS
The results of these ~ are shown in Figure 3 for
plasma with and wi~ a large capacity termination. Tney show
consistent patterns in the maxima and minima of the am~plitude of
each mode as determired with an rf spectrum analyzer. The second
harmonic is always about an order of magnitude smaller than the
fundamental, while the third and fotLvth harmonics are several
times smaller than the second. The magnitude of the variation of
the amplitudes along the electrode's length increa_~es with
increasing frequency. Tne fourth harmonic seems to have its
maximum at the top of the electrode and a minimum, which is
sev~ times smaller, between the middle and bottc~ points. This
oontrasts with the fundamental which decreases by about 10% frc~
the electrode top to its bottam. This is what one would expect if
the wavelengths of the modes are in nearly the same proportion,
but about three times smaller than their free space values.
Finally, it is notable that while the fundamental and fourth
harmonic have their maximum amplitudes at the top of the
electrode, the second and third harmonics' peak magnitudes are at
the bottnm of the electrode where the rf power is fed in.
o-
•
matchi.ng network
• 1;- :
0 30 6~0
DISTANCE F1ROM
HEXODE Bo'rroM ('cm)
Fig.3. Spatial dependence of Fig.4. Electrode-plasma
amplitudes of Fundamental equivalent circuit, trans-
and harmonics, mission line model.
CIRCUIT ANALOG OF THE ~7;L~IR3DE SURFACE MODES
In order to understand the structure of the modes' amplitudes
and the generation of the harmonics we could model the system ~s
a coaxial transmission line or an antenna ~ in plasma ~.
Tne surfaoe modes are TEM in which the radial electric field is
essentially confined to the sheath with a thickness d while the
azimuthal magnetic field penetrates well into the glow region
with a resistive skin depth, . These are Gould-Trivelpiece
modes 6 with phase velocities less than c by a factor of I
d in these plasmas is about 1.5 cm and varies from about i0
to 15 cm.
472
Using the transmission line analogy (c~_ Fig.4 for the
circuit) the ~mpe~ance along the electrode is assumed to be a
pure ccr~tant ~, while the p~y capacitive
shunt impedan~ (acres the sheath) is modeled as voltage
dependent. The modified Tel~'s equations can be written,
and then combined to yield a non-linear PDE for the sheath
voltage, V I. ~he modified Teleg~'s equatior~ are:
(i) ~V, ~ L - ~.R
(2) ~z _- _ ~v,~ .cCv,) - ~ ~×p(~ v,/~.T~)
~here the sheath voltage, V 1 is found from:
(3) V, - V- ~_!, p. ~×
we denote electrode voltage as V, the current as I, electrode
inductance per unit length as L, shunt capacitance per unit
length across the sheath as C and glow resistance per unit length
as R. T e is the electron temperature and Je the electron
flux, (i/4)neV e where n~ is the density and V e the
therma! speed.-~e equation which results for Vl, is:
'" :
In o _r~e__r to solve equation (4) the sheath voltage is
to be a linear combination of the fundamental and ~cs, each
with cum~ prupagating in both directicr~ on the electrode.
i'l
the ooeffici~ of each mode are zelat_J~ by the
reflection ooeffiei~ whic~ are caloala~ £L~. the
of the termination at the tup of the electrode, Zl, and the
~~i~ic ~ of ~ el~l~ ~, z~.
reascnablwhere X~e is the position of the end of the electrode. ~ds is
since the ncn-lir~gr coupling terms on the right of
equation (4) are negligible for much of the rf cycle since
c(v I) is My w~my ~ on v 1 ~v lis~sthan 10k~e/e. ~e admittance, whic~ is prqsorti6nal to the
exp(eVl/M~e) , is essentially zero unless eV1./~.@ is more
than -5. ~hen eVl/M~ e is greater than -lu rne r~gn~ hand side
of equation (4) 5ec~es non-negligible. In order to calculate
473
this we have assumed a specific form for C(VI):
(7) d_..(v,) = V,-C,+(,,
where s is om~tant of order 10 whi~ yields a maxi~m of CC~I)
about an order of magnitude greater than C o . using this form
for C equation (4) is first solved for the ~ ~c by
using only the fu~m~ntal for V 1 (t) in the terms on the right
hand side. ~hese terms, incl, e~ng aIl terms with first power time
or space derivatives of V 1 contribute to the power flow to the
harmonic when the sheath vol£age is small. ~he right hand side of
equation (4) thus reduces to:
(8) LCo ~v,~ _ L ¢, ~w,~. _ ~,j~ ' ~p~v,l~%) _ R { Co ~v' +
~he resulting magnitudes for second, third and fourth
harmm~cs in the solution of equation (4) are of the correct
magni~e_ for physically reasonable values of s (i.e. about 5),
but the spatial variations of the ~ based cn the reflection
ooefficients in equation (6) are not as c~rved. A numerical
treatment of equation (4) will be necessary, ~ believe, to
a~_ng~/nt for spatial profiles but we are encouraged that the basic
model incorporates the essential physics of the phenumencn.
1. W. G. M. van den Hoek, C. A. M. DeVries andM. G. J.
Heijman, J.V.S.T., BS, 647 (1987).
2. K. R. Stalder, private cummunication.
3. S. E. Savas and R. W. Plavidal, J.V.S.T. A6, 1775 (1988).
4. S. E. Savas and K. G. Donchoe, submitted to Review of
Scientific Instruments.
5. S-H. Lin and K. K. Mei, , ~:~:~: Trans. on Antennas and ~.
Vol AP-18, 672 (1970).
6. A.W.Trivelpiece and R.W.Gould, J.Appl.Phys, 3__0, 1784 (1959).
|
1.100047.pdf | Identification of residual donors in highpurity undoped ptype epitaxial GaAs by
magnetophotoluminescence
S. S. Bose, M. H. Kim, and G. E. Stillman
Citation: Applied Physics Letters 53, 980 (1988); doi: 10.1063/1.100047
View online: http://dx.doi.org/10.1063/1.100047
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Published by the AIP Publishing
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129.120.242.61 On: Sat, 22 Nov 2014 15:37:59identification of residual donors in high~purity undopedp~type epitaxial GaAs
by magneto photoluminescence
s. S. Bose, M. H. Kim, and G. E. Stillman
Center for Compound Semiconductor Microelectronics, Coordinated Science Laboratory and Materials
Research Laboratory, University of /Jlinois at Urbana-Champaign, Urbana. Illinois 6180]
(Received 21 April 1988; accepted for pUblication 5 July 1988)
The residual donor species, Si, S, and Ge, have been identified in high-purity un doped p-type
epitaxial GaAs grown by metalorganic chemical vapor deposition and arsenic trichloride vapor
phase techniques using the magnetic splittings of "two-electron" replicas of donor bound
exciton transitions at low temperature (-1.8 K) and at a high magnetic field (9.0 T). This
technique permits identification of donors in certain high-purity p-type GaAs samples in which
donor species cannot be identified by photothermal ionization spectroscopy or any other
technique.
Low-temperature magnetophotoluminescence (MPL)
is a very sensitive optical technique that can be used to iden
tify both donor and acceptor impurities in narrow gap semi
conductors such as GaAs and InF. Low-temperature photo
luminescence is widely used to identify acceptor impurities
in hoth n-and p-type GaAs. However, this technique cannot
generally be used to identify donor impurities in GaAs since
donors have nearly the same binding energies. The use of a
high magnetic held in low-temperature photoluminescence
has been found to be very helpful to discriminate between
different donor species in InP!,2 where "two-electron" repli
cas of donor hound exciton transitions have been used to
identify donor impurities from their splittings in a high mag
netic field. This technique has been successfully used to iden
tify donors in GaAs.3 7 A unique feature of this technique is
that in addition to the identification of donors in n-type ma
terial it can also be used to identify donors in p-type and
high-resistivity GaAs. In contrast, photothermal ionization
spectroscopy, while perhaps more sensitive than MPL, is
only useful for the identification of majority impurities.8
Very recently Watkins et af. <) have identified residual donors
in undoped n-type GaAs grown by metal organic chemical
vapor deposition at zero magnetic field. This technique has,
however, very limited application in identifying donors in /1-
type GaAs. Reynolds et al.4 have previously identified Si, S,
and Gc donors in p-type GaAs by photoluminescence mea
surements using a low magnetic field (3,6 T). However, the
use of a high magnetic field has been shown by Dean et aI.2 to
permit more reliable identification of donors in n-type InP.
A magnetic field of strength >5.0 T permits clear identifica
tion of donors in high-purity n-type GaAs.lo The technique
of high-field magnetophotoluminescence can also be used to
identify donors in p-type GaAs sampies in which the donor
bound exciton emission under weak excitation and at low
temperature has sufficient intensity. This is the case for p
type high-purity GaAs samples which have fairly high com
pensation. If the donor bound exciton peaks are weak, their
two-electron replicas may not be detectable and in this case
donor identification is very difficult or impossible through
two-electron transitions. Thus this technique has limited ap
plication in identifying donors in p-type GaAs, but in those high-purity p-type GaAs samples that are suitable, it permits
identification of donor species that is not possible by any
other technique.
In this letter we present results of magnetophotolu
minescence (MPL) measurements at a high magnetic field
(9,0 T) with resonant excitation which dearly identify the
residual donors in high-purity p-type epitaxial GaAs grown
by metalorganic chemical vapor deposition (MOCVD) and
arsenic trichloride vapor phase epitaxy (AsCI3 VPE) tech
niques. The resonant excitation was achieved using a tunable
dye laser which is pumped by an argon ion laser. The experi
mental conditions used for the MPL measurements arc de
scribed elsewhere.6 The results of 300 K Hall effect measure
ments on these p-type samples are given in Fig. 2. The sharp
exciton peaks in the MPL spectra confirm the high purity of
the layers. Three different donor species, Si, S, and Ge, have
been identified in these layers from well-resolved two-elec
tron replicas of donor bound exciton transitions in MPL
spectra.
Figure 1 shows a typical MPL spectrum of exciton re
combination in high-purity p-type epitaxial GaAs (sample
B) grown by MOCVD. The spectrum was recorded at ~ 1.8
K in a magnetic field of9.0 T, The output from a tunable dye
laser was tuned close to the band gap of GaAs to optically
excite the sample. The lines labeled (Du,X) Is are the princi
pal lines of donor bound exciton transitions in which the
initial state is the ground state or an excited state of the
(D () ,X) complex, and the final state is the ground state of the
donor. The peaks at lower energy, labeled (Ao,X) IS' are the
principal lines of the carbon acceptor bound exciton transi
tions. The dominance of the acceptor bound exciton transi
tions in this spectrum is typical of p-type GaAs samples. The
peaks between (Do,X)!s and (Au,X) 15 arise frem the ionized
donor bound exciton transitions and free hole-io-neutral do
nor transitions. The peaks in the lowest energy region are the
two-electron transitions which differ in energy from the
principal lines of donor bound exciton transitions by the en
ergy (above the donor ground state) of the final state efthe
transition in which the donor is left in its first excited state.
These transitions are described in more detail elsewhere.6
Two groups of peaks labeled (0' and f3 in the two-electron
980 Apo!. Phys. Lett. 53 (11). 12 September 1988 0003-6951 188i370980-03$OI ,00 @ 1988 American Institute of Physics 980
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129.120.242.61 On: Sat, 22 Nov 2014 15:37:59Sample 8: MOCVD GoAs
H=9.0T
T~l 8K
1.510 1.512 1.51'1 15[6
Energy leV) 1.5[8
FIG. L Low-temperature (~1.8 K) magnetophotoluminesccnce (MPL)
spectrum of exciton recombination in high-purity p-type MOCVD GaAs at
a m<lgnetic field of 9.0 T. The peaks due to free-exciton recombination la
beled FE and the principallincs of donor bound exciton transitiolls lie 011
the high-energy side ofthe figure. To lower energy lie the strongest peaks of
acceptor bound exciton transitions. To energies lower than 1.5] 5 eV lie the
"two-electron" replicas of the donor bound exciton transitions which leave
donors in the 2[1 _ 1 and 2pn terminal donor magnetic suhstates. The peaks
labeled fJ and E' arc the two-electron replicas of the principal lines band e'
(which lies between d and e, and is not observed), respectively.
transition to the 2p _. l donor magnetic substate are the two
electron replicas of the principal lines e' (which lies between
d and e, and is not observed) and b, respectively. The differ
ences i.n energy between the principal lines and the corre
sponding satellites give the ls-2p _ I donor energies. The
peak labeled {J in the two-electron transition to the 2p 0 do
nor magnetic substate is also a two-electron replica of the
principal line labeled b. The assignment oflines is based on
correlation of photothermal ionization measurements on the
n-type GaAs samples and the results of resonant excitation
MPL measurements.6 Detailed analysis of MPL spectra ob
tained with resonant excitation of different principal lines
has been found to be essential for the assignment of the two
electron replicas. This point will be discussed in more detail
in a separate report. 10
The well-resolved "two-electron" satellite peaks are ob
tained by resonant excitation of one of the strong principal
lines of donor bound exciton transitions (Fig. 1). The spec
tra in Fig. 2 are the spectra of two-electron transitions re
corded with the resonant excitation of the principal line c.
Donors can be identified from any of the three two-electron
satellite groups labeled {3 and {;' in Fig. 2. The ratios of the
peak heights for different donor species in each group reflect
the relative abundance of different donor species in the sam
ple. Si is identified as the dominant donor species in aU three
samples. The Is-2p _ I energy of the Si donor at a magnetic
field of 9.0 T is measured to be 4.63 meV. In some samples
this peak was shifted as much as ± 0.0124 meV. The S do
nor is also identified in aU three samples at very low concen
trations. The energy separation of the peaks due to different
donors in the two-electron satellites labeled 2p __ I and 2po
gives the difference in central cell shifts between the 1s
(ground) states of the donors. The difference in central ceH
shifts between 5i and S donors measured from the spectra is
0.11 ± 0.01 meV at a magnetic field of 9.0 T. All of these
values agree extremely wen with the values obtained pre-
981 Appl. Phys. Lett., Vol. 53, No.1 i , 12 September 1988 ..--'...----->-~.--:---'~___,__-'-____r---,~-,
I "Two Electron" Satellites, I. I
(O".XI2P ,(S"
. ·1,0 !
I ~ ~ {~ ~ Sample A 1:'1',2" :
MOCVO GoAs.
I ~}:'c ~~~J(~~'2 'J 0,
j c!(:.
l'_:~J~':~\':;'S~' ___ '. __
T
I
I
;1 ~).no-3 :),:»( 1,)Llcn '
r~(J,
';orrnl:e C
A~Clj VPE GoA~
\ : ,~f) }( lC:; 1 j f.!' \ ~
r'3(>0· 177("1'2;,/ ')
FIG. 2 'Two-dectron" satellite spectra for three high-purity GaAs samples
grown by MOCVD and AsCI, VPE, recorded at -, 1.8 K and a magnetic
field of9.0 T. The peaks labeled a', {3, and £' are the two-electron replicas of
the principal lines a', h, and e'. respectively. Si, S, and Ge donors are identi
fied ill samples A and B whereas only Si and S donors are identified in sam
ple C.
viously.6 The third donor, Ge, is also detected at very low
concentrations in samples A and B. The peak labeled a' (5i)
(which is a two~electron replica of the principal line labeled
a' due to Si donors) is detected ill aU three spectra in Fig. 2.
This peak, a' (Si), in the top two spectra in Fig. 2 also con
tains a component which is a two-electron replica of the
prindpalline b due to Ge donors. The peak intensity of thai
component is, however, extremely low since the peak heights
for different donors in each "two~electron" satellite group
(€', {3, a') should be the same.
The differences in central cell shifts between Si, S, and
Ge donors as measured from the spectra in Fig. 2 for samples
A and B agree well with those measured from the spectrum
in Fig. 3 for a high-purity n-type AsH] VPE GaAs sample
D. This sample has 77 K carrier concentration 1177
= 2A X 1014 em'· 3 and 77 K mobility /177 = 100 000 cm2j
V s. The same donors (Si, S, and Ge) have been previously
identified in this sample (VPE G-I1O) by photothermal ion
ization spectroscopy. I I The difference in central cell shifts
between Si and Ge donors as measured from MPL spectra is
~O.29 ± 0.01 meV at a magnetic field of9.0 T. A new set of
peaks labeled P and P' appears between (;' (S) and (;' (Ge)
peaks and between/3(S) and a' (Si) peaks respectively in the
spectra in Fig. 2. Those peaks may arise from an unknown
donor with a chemical shift of 0.25 meV relative to the Si
donors. Although these peaks are present in all three spectra,
80se, Kim, and Stillman 981
... '.'; ..•..... ~ .•.•... _._ .. -:.;.; ......................... 7 .. :.;.;.-:.;.; ..... ; ........... ' .•. r •• / •• ~.:.:.:.:.:.;.,.;.; •••• <;':.;;~<.:.:.:.:.:.:.-:.:.; •.• ; ••••.• ' •• ?~ ... :<.:.:.:.;.:.:-;.,.: .••.••• ?~.~<.: ...... ;.:.:.7..: •••.•.•.•. ' .•.•• w •••••••••••• -•••••••••••• , ••••••••• ,. ••• -.-.~-: ••• ' ••••• r ••••• ' ............. :.;.;.;.:-:.;.; ••• ; ............... •• ' ••••••• -.: •• ,-.: •••• ".' ••• -;'7'".,'"~,:;.-.-.~ • .-.--.-•• ~_."-. ••••••• ~ ••• , •• -••• -•••••••. <;, •••••• _._ ••• _ •••• _ •• , .................... _._-:.; •• ', •••••• , ................... ~ ........... , ••••••••• , •• _._._-:.~ ••••• .' ••••• ";'.".V.'.'
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129.120.242.61 On: Sat, 22 Nov 2014 15:37:59.~
H "Two Eleciron" Satellites: (Do,X)2
Ho9.0T, T-1.8K P-1,c
I
(3IS) IDa X) ,'IS) I' I • 2p. II r.-- r---~-·I;-·-I
I (~(S) I'/(Si)
If 1 miil-hl! '
IIII SompleD:C-110 Illjlll I
AsH] --VPE GaAs ' I
.8IGe)1 \' "(G3)-I~Uv 1\ I'
IV \" ,8:Gel
"l I ~.
I I ~V\. Iv i' ,~ ""-J \ J
~_ .. /J I ,,~.- I
l.:'1()O 1.'):10 I ~l2~) ~.5L~O 1.:)1'10
Energ, leV)
I'IG.~" "Two-electron" satellite spectra for a high-purity Il-type AsH, VPE
GaAs s~llnple, sample D (VPE 0-110). Si, S, and Ge donors are identified
in this sample. The results agree with the identification of donor sPecies in
the same sample hy photothermal ionization spectroscopy presemed in Ref.
11. The principal lines and the two-electron satellites lie at slightly higher
energy in this sample compared to samples A -C.
they are very weak and do not contribute significantly to th(!
total donor concentration.
The residual donor species in the p-type MOCVD GaAs
samples which were grown with a triethylgallium source are
consistent with the residual donor species identified by pho
tothermal ionization spectroscopy in n-type samples which
were also grown in the same reactor using the same source
materials under different growth conditions. In all these
MOCVD GaAs samples (both n andp type), Si is found to
be the dominant donor with a lower concentration of Gc
donors in n-type samples and only trace levels ofGe donors
in p-type samples. The residual donor species that is most
frequcntly dominant in MOCVD GaAs grown using tri
methylgaUium is Ge. On the other hand, no systematic stud
ies on identification of donor and acceptor impurity species
in MOCVD GaAs grown using tri<::thylgaHium have yet
been made. Low-temperature photoluminescence measure
ments of donor-acceptor pair and band-acceptor bands have
also been made on these MOCVD samples to identify the
residual acceptor impurities. The results show that C is the
dominant acceptor species with a much lower concentration
of Zn acceptors. Gc acceptors have only been observed (at
trace level) in one n-type sample which has a large concen
tration. of Ge donors present in addition to the dominant
residual Si donors. On the other hand, Si acceptors are not
detected in any of these samples. These results demonstrate
982 Appl. Phys. Lett., Vol. 53, No. 11,12 September 1988 the extraction of information about the donor incorporation
in p-lype GaAs samples from magnetophotoluminescence
measurements.
In summary, Si, S, and Ge have been identified as resid
ual donors in high-purity unctoped p~type epitaxial GaAs by
magnetophotoluminescence measurements. The technique
of magnetophotoluminescence has been demonstrated to
permit clear identification of donor species in selected high
purity p-type GaAs samples in which the donor species can
not be identified by photothermal ionization spectroscopy or
any other technique.
We would like to thank T. H. Miers of Ball Aerospace
and p, E. Norris of GTE (now at EMCORE) for providing
some of the samples used in this research. We also thank
B. Lee for making his results on photothermal ionization
measurements for the n-type MOCVD samples available to
us, and B. L. Payne and R, MacFarlane for assistance in the
preparation of the manuscript. This research has been sup
ported by the Joint Services Electronics Program under con
tract N00014-84-C-0149 and the National Science Founda
tion under grant NSF CDR 85-22666. The initial work on
residual impurities in GaAs at the University of Illinois at
Urbana-Champaign was supported by the Defense Ad
vanced Research Projects Agency under contract NOOO 14-
83-K-0137 and the Air Force Office of Scientific Research
under contract 83-0030.
'P. J. Dean and M. S. Skolnick. 1. Apr!. Phys. 54, 340 (1983).
"P. 1. Dean, M. S. Skolnick, and L. L. Taylor, J. AppL Phys. 55, 957
(1984 )
lD. C. Reynolds, K. K. Bajaj, C. W. Litton, ,md E. B. Smith, Phys. Rev. B
28,3300 (1983).
'D. C. Reynolds, P. C. Colter, C. W. Litton, andE. B. Smith, I. Appl. Phys.
55,1610 (l984).
:'T. D. Harris and M. S. Skolnick, in Defects in Semiconductors, edited by
H. J. von Bardeleben, Materials Science Forum (Trans. Tech. Publica
tiano, Swijzcrlaml, 1(86), Vol. 10-!2, p. 1219.
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937 (1987).
11'0 D. Harris, M. S. Skolnick, J. M. Parsey, Jr., and R. Bhat, App!. Phys.
Lett. 52, 389 (l988).
"G. E. Stillman, C. M. Wolfe, and J. O. Dimmock, in Semiconductors and
,<,'emimelals, edited by R. K. Willardson and Ao C. Beer (Academic, New
York, 1977), Vol. 12, p. 169.
"~So P. Watkins, G. Haacke, and H. Burkhard, AppJ. Phys. I.ett. 52, 401
( I9ilS).
lOS. S. Bose and G. E. Stillman (unpublished).
"B. J. Skromme, S. S. Bose, B. I,ce, T. S. Low, T. R. Lepkowski, R. Y.
DeJule, G. E. Stillman, and 1. C. M. Hwang, 1. App!. Phys. 58, 4685
( 1985).
Bose, Kim, and Stillman 982
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129.120.242.61 On: Sat, 22 Nov 2014 15:37:59 |
1.344231.pdf | Texture and textural evolution in explosively formed jets
Sheila K. Schiferl
Citation: Journal of Applied Physics 66, 2637 (1989); doi: 10.1063/1.344231
View online: http://dx.doi.org/10.1063/1.344231
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30Texture and textural evolution in explosively formed jets
Sheila K. Schiferl
Los Alamos National Laboratory, Los Alamos. New Mexico 87545
(Received 30 January 1989; accepted for publication 16 May 1989)
The potential effects of crystallographic texture (preferred grain orientation) on the behavior
of metallic shaped-charge jets are examined. There is some experimental evidence that strong
initial liner textures can be beneficial to overall performance; in this paper we investigate the
mode of action of such textures. A crystallographic-texture code was used to calculate the
changes in preferred orientation, and the corresponding changes in yield anisotropies, for
deformation paths typical of early jet formation. Simulations were performed for two different
initial textures, and for two different regions in a hemispherical titanium liner. It was found
that the initial texture and its corresponding pattern of anisotropy do not persist beyond the
earliest stages of liner collapse; the state of the material in a well-formed solid jet reflects the
most recent deformation, not the initial texture. Any initial texture effect on subsequent jet
behavior would be exerted indirectly, e.g., through changes in flow patterns induced during the
first few microseconds of defomlation. During this time, the evolution of texture and the
corresponding anisotropies were found to be significantly different, not only for different initial
textures, but also for different regions of the liner. This is due to the variation in deformation
paths, and, in our model for titanium, to differences in the relative importance of slip and
twinning.
I. INTRODUCTION
High-speed metallic jets from shaped-charge liners have
been a system of interest for a number of years. The basic
theory of jet formation was given by Birkhoff et al,l and
expanded by Pugh, Eichelberger, and Rostoker.2 More re
cent treatments of jet behavior3-h focus on predictions of
breakup in solid jets with regard to plastic instabilities and
perturbation growth in stretching rods.
We take a different approach here. In this study, we
investigate a largely unexplored liner material property, the
crystallographic texture, and the possible beneflcial role of
texture in solid jet behavior, including breakup. Before dis
cussing calculations of texture effects in jets, it is useful to
give some definitions, and to relate textures to mechanical
properties,
Crystallographic texture refers to preferred orientation
of the single-crystal grains in a poly crystalline soHd. A sche
matic of textured versus randomly oriented material is
shown in Fig. 1. The irregular "puzzle pieces" represent in
dividual grains (while each grain is a single crystal, a typical
grain does not have a regular shape). The heavy lines are
grain boundaries, and all of the parallel lines represent a
specific crystallographic direction-the body diagonal for
cubic crystals, for example. The distribution of orientations
in a polycrystalline sample is commonly determined by x-ray
(or neutron) diffraction. The result is a pole figure, a stereo
graphic projection showing the density of a certain crystallo
graphic direction as a function of orientation. 7
The oriented material will tend to be anisotropic, since
single crystals are typically anisotropic. The bulk anisotro
pies due to texture can be quite large: ratios of yield anisotro
py (zirconium), 8 elastic anisotropy (copper), 9 and fracture
toughness anisotropy (titanium alloys) 10 can be > 2: 1.
Strain anisotropy produces even larger ratios. For metal
sheet, the plastic strain ratio R, or Lankford coefficient, II is
defined as where ew is the width strain and e, the thickness strain in a
tensile test. For isotropic materials. R = 1. For some metals
with hexagonal-dose-packed (hcp) crystal structures (zir
conium, titanium), R values of 3-7 for textured material are
common. 12 Such large strain anisotropies indicate high resis
tance to thinning; this property can be very desirable for
deep-drawing applications.
A strong preferred orientation is typically the result of
large deformation (50% to several 100% equivalent plastic
strain); random material can become textured, and textured
material evolve to new preferred orientations, under large
deformations. Other texturing processes include crystal
growth and recrystallization. While all ofthese processes are
typically involved in liner fabrication, only deformation tex
turing is likely to be a major mechanism for changes in pre
ferred orientation during liner collapse and jetting. Jet defor
mations are very large (several 100% equivalent plastic
strain during liner coUapse alone), and the time between
explosive initiation and jet breakup (much less than a milli
second) is too short for appreciable crystal growth. It is im
portant to note that the patterns of deformation textures
ISOTROPIC TEXTURED
FIG. I. Schematic of isotropic (random) and preferred textures.
2637 J. AppL Phys. 66 (6), 15 September 1989 002, -8979/89/1 82637-14$02.40 (,,) 1989 American Institute of Physics 2637
• " •• -.-.".-••••••••• -.-. -.-.-•••••••••• " •••• ~..... • •••••••••••••••••••••• :.:.:.;.;.:.;.;.;.;-:.; ••• ; •••••••••••••••••••• ' ••••••••• :.:.:.:.:.;.:.:.:.:.;.;.;.;.; •••••••••••••••••• :.:-:.;.:.:.:.:.:.:':.:.:.:.:.:.:.;.:.:,:.:.:.:.: •••••••• : •••• -: ••••••• : ••••• :.:.:.~.:.~.:.:.~.:.:.:.:.:.:.;.;.;.:.;.:.:.; ••• ;.-• .-•••• , •••••• ' ••• ~.:.~ ••• -:-.:.:.:.:,;;;:.:.:.:,:.~.-.- ••• '"';'.' ' •••• , •••••••••• '.'... • •••••••• ~.:-:.:.:.:.:.~.:.;.;.;.;"............ •• • ••••••••• _._ •.•••••••.•.•.•.• ., ,.' •.••••••••• n •• , • r ••
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30depend on both the crystal structure (cubic crystals, such as
copper, give different preferred orientations than hexagonal
crystals) and the deformation path (compression and ten
sion textures are different).
These properties of oriented material suggest several
possibilities for the role of texture injet formation and break
up: altered flow patterns (from strain anisotropy), altered
local heating patterns and corresponding instabilities, aniso
tropic strength and damage distribution in well-formed jets,
etc. This also suggests that a penetrator design optimized for
one material may perform poorly when adapted for a materi
al with a different crystal structure.
We might be able to control some of these effects if ini
tialliner texture had a large enough influence on subsequent
jet behavior, since liner fabrication could then be designed to
exploit texture properties. Other aspects of liner metallurgy
are known to influence jet behavior; grain size, in particular,
is an important factor in jet breakup and penetration. 13
There is some evidence that initial texture can be significant
for jet breakup. First, in spin-compensated copper conical
liners, 14 the fabrication results in a particular texture. If this
particular texture is not present, the spinning jet flies apart.
Second, for aluminum conical liners, 15 a preferred orienta
tion of cube body diagonals along the cone axis results in
considerably later breakup times than an orthogonal orien
tation of the same material.
The effects of texture in these t\vo cases arc most likely a
Fesult of anisotropic mechanical properties. However, the
details of how initial texture affects subsequent jet behavior
are not clear, particularly since the texture will change as the
liner deforms. We can use texture calculations to investigate
the mode of action of initial texture to sec if it might be
significant for jet behavior and if so, how. In the absence of a
texturing model for ajet simulation code, we set up a simpler
test. We start with two different liner textures-one random
and one with a strong preferred orientation and strong ani
sotropy-and calculate texture changes (and the corre
sponding yield-surface changes) for conditions typical of
early jet formation.
In the present work, we simulate the conditions during
collapse of a thin hemispherical titanium liner: we choose
titanium for strong yield anisotropy, and a hemispherical
shell for smoother deformation paths than a conical shell.
The results of our calculations indicate that during early
deformation, the rate of texture change and the resulting
textures depend strongly on the deformation path and hence
on the particular region of the liner. However, any direct
effects ofinitial texture are limited to very early times in liner
collapse; the orientation patterns, and associated mechani
cal anisotropies characteristic of even very strong initial tex
tures, do not persist for more than a few microseconds. The
material texture in the well-formed jet will reflect the most
recent deformation, not the initial conditions. The effect of
initial texture on such a jet would be, of necessity, indirect,
through changes in the velocity distribution, for example.
II. BACKGROUND: TEXTURE CALCULATIONS
The methods for texture calculations have been de
scribed in detail elsewhereI6•J7; we give a brief outline here.
2638 J. AppJ. Phys., Vol. 66, No.6, 15 September 1989 Texture calculations are based on simulation of the
dominant physical mechanisms of plastic deformation un-.
derlying deformation-texture evolution. These mechanisms
are reasonably well understood for a variety of conditions,
including shocks and high temperatures. We consider plas
tic deformation of a polycrystalline material to be a result of
shear in each crystal, according to two basic mechanisms:
crystallographic slip and twinning. For jet conditions, we
ignore grain-boundary sliding. In slip, the "stack" of crystal
planes shear in a particular direction. Several characteristics
of slip should be noted 11\: slip involves the whole crystal, but
is discontinuous; the shear associated with slip only occurs
on certain crystal planes, both forward or backward along
certain crystal directions. Also, slip tends to rotate the crys
tal lattice. In deformation twinning, a band of the crystal
shears along a certain plane in a certain direction, and the
shear is accompanied by a slight shuffle in atom positions.
Twinning differs from slip in a number of ways. 19.20 First,
twinning does not generally involve the whole crystal; the
twinning shear is fixed and depends on the crystal structure,
while the volume fraction twinned can vary. Also, twinning
is unidirectional; the twinning shear has a fixed sign, as well
as a fixed magnitude. The twinned material is effectively
rotated relative to the untwinned matrix. This rotation can
be very large: the c axis (the "hard" direction) rotates by
::.::; 85" for one kind of hcp crystal twin system. This is not a
physical rotation, but the shear plus the shuffle in atomic
positions is crystallographicaUy indistinguishable from a ro
tation.
We consider the activation of any slip or twinning sys
tem (where a system consists of a slip, or twinning, plane
plus a direction) to require a certain critical-resolved-shear
stress (CRSS). The particular slip, or slip and twinning, sys
tems that can exist depend on the crystal structure. The rela
tive difficulty of operation of different kinds of systems, and
hence the relative CRSSs depend on the particular material
and the conditions, as well as on the basic crystal structure.
Physically speaking, a CRSS criterion is an oversimplifica
tion for single-crystal behavior, particularly for certain
kinds oftwinning, but it is a very useful device to indicate the
relative importance of different systems in deformation of
poly crystalline materials.21
There are two basic numerical schemes used to simulate
texture evolution (and to calculate the associated yield sur
faces): the Bishop-Hill and the Taylor algorithms. These are
mathematically equivalent; we use a version of the latter
method. In both methods, we consider a polycrystalline
sample, with n single-crystal grains, and with N specified
deformation systems for each grain. We assume homoge
neous deformation; the distortion field for the sample and
the single crystal distortion are considered identical. This
assures compatibility but not stress equilibrium; the conse
quences of this simplification will be discussed below. We
further assume that elastic strains can be neglected com
pared to plastic ones,
We store information on each slip and twinning system
(the plane and direction in the crystal frame of reference,
plus the CRSS). We also store the current set of grain orien
tations (three Euler angles for each grain). Each cycle of the
Sheila K. Schiferl 2638
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30simulation results in a new set of orientations. The cycle
consists of several steps.
We first apply the current deviatoric distortion tensor U
(displacement gradient tensor) to each crystal:
E= TUT'. (1)
Equation (1) transforms the distortion tensor to the crystal
frame of reference. U is not necessarily symmetric.
N
Eij = Hij + 2: rfnfyO· (2)
D--l
Equation (2) divides the tensor into rotation, .0, and strain
terms. ,.pis the ith component of the shear direction, nfis the
jth component of the normal to the slip (or twin) plane, and
yO is the (unknown) shear on system D.
1 N EW1=-I (rfnf+!fnp))/Y. (3)
2 D~ 1
Equation (3) takes the symmetric part of E to solve for the
shears yD. This equation represents five equations in N un
knowns, since there are only five independent terms in the
symmetric deviatoric strai.n tensor-three off-diagonal
terms and two diagonal terms-and N possible systems. If W
is the internal plastic work, the equations can be solved, sub
ject to the constraint,
N
'" DAJJ minimize W = £.t 7 r , (4)
D=l
via the simplex algorithm, a standard linear-programming
method.22 The solution identifies the particular systems D
operating in a particular grain, and the amount of shear yO
on each system. There will be, at most, five systems with
nonzero yD.
This mathematical treatment gives an upper bound to
the limiting yield behavior of a polycrystal. It can be shown
that solving the linear-programming problem is mathemat
icaHy equivalent to using the maximum-external-work prin
ciple, and that strain normality (the orthogonality rule)
holds.
After Eq. (3) is solved, Eq. (5) gives the grain rotation.
Note that the rotation has two parts: the antisymmetric por
tion of the distortion tensor (a standard continuum rota
tion) , and a second term depending on the texture. When aU
of the grains have been rotated, we consider additional reor
ientations due to twinning.
Twinning poses special calculational problems, since
continued twinning produces an unworkable number of ex
tra orientations after only a few deformation steps. The stan
dard treatment is to assign either the twinned or the
non twinned orientation to a crystal based on the volume
fraction twinned, according to a Monte Carlo technique. 23
After all of the twinned crystals have been reoriented, the
next distortion tensor can be applied to the new texture, etc.
The deviatoric yield surface associated with a given tex
ture can be calculated using most of the same techniques as
texture evolution. The method is described by Bassani24 and
by Tome and Kocks.25 For this kind of calculation, it is COll-
2639 J. AppJ. Phys., Vol. 66, No.6, 15 September 1989 which the three deviatoric diagonal components are at 1200
to each other. We take a set of equally spaced strain "direc
tions" in the 1'1' plane. For each strain, the Taylor-simplex
solution of five shears is found, and the equivalent work {W}
[Eq. (4) ] calculated. For each strain direction, we construct
a tangent to the strain direction at the distance { W} from the
center, where the brackets indicate an average over aU
grains. The yield surface is the inner envelope of these tan
gents.
This theory has been found to give reasonable descrip
tions of texture evolution for a number of materials, and for a
range of deformation modes characteristic of both metal
forming and geological processes. 16 The measured and cal.
culated pole figures for major components tend to look very
similar, and the positions of the orientation maxima tend to
agree to within a few degrees. The main discrepancies in
volve the intensity distribution of minor components, and
the sharpness of the textures (calculated textures are gener
ally sharper than experimental ones). For purposes of a bet
ter understanding of textures and the associated mechanical
anisotropies in jets, this theory should be quite adequate.
III. PROCEDURE
OUf method to examine the consequences of two differ
ent initial liner textures for subsequent jet behavior consists
of two connected simulations. We first use a Lagrangian fi
nite-difference code to simuiate the collapse of a hemispheri
cal titanium liner. The jet design is shown in Fig. 2, From the
simulation results, we can construct a deformation history
a time series of deviatoric distortion tensors-for any piece
of the liner. We then "sample" the chosen liner element with
the texture code: we set up an initial texture as a set of grain
I ' O",TONATOR
PBX 9404
........ ~_~_ ,~~~-- EXPLOSIVE
i6cm
I
I
I 4.3:mm /~tTITANIUM
1 , tJ i r--_._-- Scm --_ .. _--I
~-~--. ----.. ~o em ----_. __ .-1
FIG. 2. Schematic. ofhernispherical titanium shaped charge.
Sheila K. Schiferl 2639
•••••••••• -•• ; •• ; ••••••••••• '.' ••••••••••••••• -•••• > ••• ·.·.·.'.·.·.:.:.:.:;;:O:.;.:O:.;.; •• ·;·.·.·.·l.;.>:.:.:.: .:.;.;.; •.•.•••. 0;0; ••• .' •••••• [ ••• -••••• ; •••••••••••••••••••••• :.:.:.;.; •••••••• <; •••••• " •••• -••••• -.:.; •••••• ; •• ·.·~v.·.·,·.·.·.-.,···,_·.· ... ·.·.·.· ..... ·.
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30orientations, and apply each distortion tensor in turn to all of
the grains. This gives a set of changing textures, plus their
associated yield surfaces.
In general, both jet deformation and texture evolution
are three-dimensional (3D) problems. To simplify our cal
culations, we constrain the deformation to be symmetrical
about the jet axis; this is a reasonable approximation to the
behavior of many real jets. This axisymmetry is also compa
tible with texture and texture development if the initial tex
ture is at least axisymmetric. Experimentally, textures
evolve under deformation to match the symmetry of the
principal strains.26 If the initial texture has symmetry equal
to or higher than axisymmetric, and the principal strains are
axisymmetric, the evolving texture will be axisymmetric.
These symmetry relations for textures also apply to the
modified Taylor calculations described in the previous sec
tion. To maintain compatibility of deformation symmetry
and texture symmetry, the two different initial liner textures
used in these simulations are both symmetric about the jet
axis. This axisymmetry enables us to use a two-dimensional
(2D) Lagrangian code, rather than a 3D code, to calculate
the distortion tensors for the texture calculations. We de
scribe the Lagrangian code and the details of the texture
calculations below.
Liner collapse was simulated with TEW A, an explicit 2D
finite-difference Lagrangian code incorporating high-explo
sive burn. This code has been used extensively at Los Alamos
for modeling jets and other penetrators. The liner equation
of state was obtained from a fit to Hugoniot data. The consti
tutive behavior was approximated by a high-strain-rate iso
tropic model,27 using an initial yield strength of 1.4 kbar,
which would be characteristic of a soft annealed liner sheet.
The initial Lagrangian mesh (one quadrant) for the lin
er is shown in Fig. 3; the simulation is symmetric about the
jet axis. The two liner elements we wish to sample are shown
in Fig. 3 as shaded cells. The centers of the cells are located at
() = 3° and e = 52° , where () is the angle between the jet axis
and the line connecting the liner center of curvature with the
cell center. We calculate the deviatoric distortion tensors for
4.3mm
FIG. 3. Initial Lagrangian mesh geometry for the hemispherical liner. The
deformation and texture development of the two shaded cells (at e = 3" and
52°) are analyzed in detail ill the text.
2640 J. Appl. Phys .• Vol. 66, No.6, 15 September 1989 a liner element by using successive positions of the corners of
its corresponding Lagrangian cell, plus the cell compression.
The tensors were calculated at simulation intervals of 0.25
ps. For the first microseconds ofliner collapse, this sampling
time step produces equivalent von Mises strains of < 10%.
To preserve material integrity, only scheduled, minimal re
zoning was applied; either cells were combined, or celis were
split in half. After cells were combined the respective corners
were obtained by linear interpolation.
The input deformation path required to calculate tex
ture evolution is the set of deviatoric distortion tensors from
the Lagrangian code calculation. The actual tensor compo
nents for texture calculations need to be small; we require the
equivalent von Mises strain of any deformation step to be
< 2.5%, and divide each input tensor into two or more equal
steps if necessary,
Texture evolution calculations were performed for a
sample of 3000 grains, using the Taylor-simplex algorithm
described previously. Twinning was treated as pseudo-slip,
and a Monte Carlo method was used to assign twinned and
nontwinned orientations. This texture-evolution program is
optimized to run on a CRA Y-XMP. For 24 slip systems and
12 twinning systems, approximately 1350 new orientations
can be calculated per second of CPU time.
This texture code allows for different critical-resolved
shear stresses (CRSSs) for different kinds of slip and twin
ning systems. There are several crystallographically equiva
lent systems for each kind of system; to avoid redundant
solutions to the Taylor equations, we treat the CRSS for each
set of equivalent systems as a narrow Gaussian distribution28
(x = Tc,O" = O.OOl1"e ). The distribution is recalculated for
each grain, and at every deformation step.
Yield-surface calculations were performed using the
same Taylor-simplex algorithm, but without any crystal
reorientation. A deviatoric 1r-plane yield surface was calcu
lated, using the tangent construction described in Sec. II, for
24 equally spaced strain directions.
For both texture evolution and yield surface calcula
tions, we use single-crystal properties of pure titanium at
moderately high temperatures (;::::0 to several 100 °C) and
very high strain rates (> 105 s-I ). The dominant form at
ordinary temperatures and pressures is a-titanium, with an
hcp crystal structure and cia = 1.59. For the purposes of
this study, we assume there are no phase transitions. The slip
and twin systems characteristic of a-titanium at various
temperatures, plus CRSSs for these systems, have been sum
marized by Conrad.21
The changes in dominant systems and relative CRSSs
for shock and high-strain-rate conditions for a number of
metals, including hcp structures, are discussed by Meyers
and Murr29 and Murr. ~o They report that the general effect
of high strain rates is to shift the dominant systems from
higher-to lower-temperature modes.
Twinning, in general, is promoted at high strain rate and
shock conditions, or low temperatures. Hence, we model the
system activity at moderate temperatures, and favor twin
ning over the high-temperature (or low-purity titanium)
slip systems.
Our active systems, and the CRSS for each kind of sys-
Sheila K. Schiferl 2640
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30TABLE 1. Active deformation modes and critical-resolved-shear stresses
for a-titanium.
No. of
Designation Plane Direction eRSS" cquivalerlt systems
Prism slip ( lOTO) (1120) 1 6
Pyramidal slip (lOT l) (1120) 2 12
Basal slip (0001) ( H2O) 3 6
Tensile twin ( 1012) <Tall) 2.5 6
Compressive twin (1122) < 1123) 3.75 (,
"Normalized to the eRSS for prism slip.
tern, are given in Table 1. The first three systems listed are
generally agreed to be the easy slip systems, in order of in
creasing difficulty, for a wide range of conditions. None of
these systems accommodates deformations in the c-axis di-
c
c
(10Ti)
c
FIG. 4. Easiest slip systems in a-titanium. Slip is in one of the Ii directions,
(lllO}, for all three systems.
2641 J. Appl. Phys., Vol. 66, No.5, 15 September 1989 St FIG. 5. Deviatoric ('fr
plane) yield locus for Ii sin
gle crystal of a-titanium,
with critical-resolved-shear
stresses as given in Table 1.
The c axis is in the [! 1 di
rection.
reetion (see Fig. 4). The two principal modes of c-axis defor
mation, for low and moderate temperatures, and hence for
high strain rates, are the twinning systems listed in Table I.
Only tensile twinning will accommodate c-axis tension, and
only compressive twinning will accommodate c-axis com
pression.
The deviatoric yield surface for our model of a single
crystal of pure a-titanium, oriented with its c axis in the [1 J
direction, is shown in Fig. 5, The sharp corners on the yield
surface are characteristic of a single crystal, and are conse
quences of the discontinuous nature of yield in slip and twin
ning. The c-axis direction is, experimentally, much "harder"
than other directions. The unequal yields in the SI and -SI
directions are due to the unidirectional nature of twinning.
We use two initial textures of liner sheet for these simu
lations: one texture contains a very strong preferred orienta
tion and strong anisotropies, the other texture is random,
and essentially isotropic. We then map these textures onto
hemispherical1iners.
The strong texture is modeled from the general features
of cross-roned titanium sheet.31 Larson and Zarkades!()
show a variety of pole figures for very strong titanium and
titanium-aHoy sheet textures, and report strain anisotropy
(R) values of 9 and higher for some of these textures. For a
jet liner, we consider the main features of this texture: a
strong tendency of the (0002) poles (c axes) to be clustered
around the compression direction, and in-plane isotropy, the
absence of any preferred orientation direction in the plane of
the sheet.
We idealize the compression texture by clustering the
(0002) poles symmetrically around the normal direction of
the sheet; the pole angles from the sheet normal are assigned
from a Gaussian distribution with the standard deviation
(7 = 18°, The (0002) pole figure for this texture is shown in
Fig. 6. The projection plane is parallel to the sheet.
This texture gives an anisotropy ratio Z IX ;::::2.2.5,
where Z is the compressive yield normal to the sheet, and X
is the average compressive yield in the plane of the sheet.
From a HilI quadratic anisotropic yield model for metal
sheet!! with in-plane yield isotropy, we obtain
Z IX = J(T+ RfFi
and R:::::: 9 for the strong liner texture. The deviatoric yield
surfaces for the strong and the randomly textured liner
sheets are shown in Fig. 7<
Sheila K. Schiferl 2641
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30FIG. 6. Theoretical (0002) pole figure for the strongly-textured titanium
sheet. Intensities are given in multiples of a random distribution (rurd);
contours are 7.14 •...• 63 mrd. Stereographic projection; projection plane is
parallel to the plane of the sheet.
To make a textured hemispherical liner, for simplicity
we map the entire sheet texture separately onto each element
of the liner shell. In this mapping, a liner element whose
center is at the angle e (see Fig. 3) contains all of the grain
orientations in the sheet texture, but with each orientation
rotated bye. (This deep-drawing texture is not strictly cor
rect for e near 90"; we take the largest angle for texture calcu
lations to be e = 52°.) With this construction, a sheet texture
with in-plane isotropy gives a liner texture symmetric about
the jet axis.
Deviatoric rr-plane yield surfaces for elements in the col
lapsing liner were constructed with respect to the axes of
principal strain, Under our conditions, the laboratory co
ordinates (where the [ 1 J direction is parallel to the jet axis)
are in general not the principal axes of deformation. In addi
tion, we cannot consistently define a set of preferred material
coordinates, since jet deformations typically involve consid-
I
!
I
\ I
/
\ / /~
/" " " RANDOM '\ ..... _---
/" \
\
\
I
I
I
I
I
/
EXTURED
FIG. 7. Deviat.oric yield loci for the two different titanium sheet textures
used in this work. The sheet normal is in the [I J direction.
2642 J. Appl. Phys., Vol. 66, No.6, 15 September ,989 o 1 em
FIG. 8. Lagrangian mesh for the deforming liner. All times in microseconds
after explosive initiation. The shaded regions correspond to the 0 = 3' and
52' cells.
erable shear coupling. Instead, we first calculate the texture
of a liner element at a particular time. The deviatoric yield
surface is then constructed in the system of principal strain
for the succeeding time step.
IV. RESULTS AND DISCUSSION
Our results for textures and yield anisotropies, for two
different liner elements and two different initial textures,
during liner collapse in a titanium jet, are shown in Figs. 8-
16. We will divide our analysis into three parts: (1) deforma~
tion-path details; (2) texture evolution; and (3) yield sur
face evolution.
A. Deformation~path details
Figure 8 shows the Lagrangian mesh for the deforming
metal liner. All times are in microseconds after explosive
ini tiation, and the direction of jetting is toward the bottom of
the page. The two cells to be studied-at (J = 3° and 52° from
the axis-are shaded. The cumulative deviatoric strain com
ponents for these cells are shown in Figs. 9 and 10, where the
[ 1] component represents the jet axis direction.
For the axial (e = 3°) cell, the shock arrives at ::::: 13.75
f.ls. The initial deformation is a compression, approximately
along the jet axis (note the flattening of the center of the liner
shell in Fig. 8). This compression ends at::::: 14.5 f.ts (;:::,7%
Sheila K. Schiferl 2642
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30Z 2.5
1
2.0 (-
1.5 _j
<: 1.0 - J
~ 0.5 - J
go: r-_-~-""",,~,.~,~:::.~.:=:=:.~:~.-.-:~:_._._.-j
••••• 622 I
-1.0 - ......................
-j.5 '-------L.---_.L.... ___ -.L ___ -.J
10 15 20
TIME (IlS) 25 30
FI~. 9. Strain path for the () = 3' celL The eij refer to cumulative deviatoric
stram components; the jet axis is in the [ 1) direction.
von Mises strain) and is followed by tension along the jet
axis.
For the (J = 52° cell, the shock arrives at ;:::: 15.75 flS.
There are no clear-cut regimes of deformation for this cell,
but rather a complex history of large shears and rotations.
B. Texture evolution
Figures 11 and 12 show the results for evolution oftex
ture during the early stages of liner collapse for the {} = 3°
cell. Figure 11 corresponds to results from a strong initial
texture; Fig. 12 is for random initial texture. Figures 13 and
14 give corresponding texture evolution for the () = 52° celL
All of these diagrams are (0002) pole figures; the density
contours indicate the directions of c ("hard") axes. This is
generally the most useful kind of pole figure for indications
of material anisotropy in hcp crystals. The projection plane
for the pole figures is perpendicular to the jet axis. We will
also refer to system activity-the relative importance of a
particular kind of system or systems-in discussing texture
evolution.
2.5 r-----,----- ,--------,
2.0 -
1.5 -
~ 1.0 - ~'-':'~~'-'-l' ~ /-"
f- ,$F----(f) 0.5 ",'
.... ~ W ./
~ 0 f----- ...... .:;:;;;,........... .............. -
f- •........ ~:: . .J
-0.5 - I
-;.0 --1
_1.5'--___ -'--____ ... 1 ----"------'
10 15 20 25 30
TIME (115)
FIG. 10. Strain path for the e = 52' cell. The eij refer to cumulative devia·
toric strain components; the jet axis is in the ( I J direction.
2643 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 We consider first the texture evolution of the (:) = 3° cell,
which exhibits simple modes of defomlation: a compressive
shock, followed by uniaxial tension, along the shock direc
tion. For the strong initial textu.re, the dominant system dur
ing the compressive phase is compressive twinning. The pole
figure at 14.5 f.ls [Fig. 11 (b) J illustrates the activity of the
dominant system: the original duster of poles near the axis
has thinned out, and there is now a ring of poles centered at
about 64° <the c·axis rotation angle for compressive twin
ning ) from the axis. As compression proceeds, prismatic
slip gradually increases in importance. The newly twinned
grains are now better oriented to slip for subsequent axial
deformation.
After 14.5 fls the axial cell goes into tension. The domi
nant system immediately after 14.5 J1S is tensile twinning,
but slip and compressive twinning graduaUy increase in im
portance.
By 15 f,iS, after a total von Mises strain of ;::::;22%, the
original concentration of poles is essentially gone and a sta
ble (but weaker) texture is deVeloping.
The axial ceH with random starting texture foHows an
initially different evolution. The dominant systems during
compression are the slip systems; twinning accommodates
less than 30% of the shear with tensile twinning fa vored (the
CRSS for tensile twinning is lower). The tensile twin reor
ientation (85°) brings grains with c axes originally perpen
dicular to the jet axis to new orientations, with axes almost
parallel to the jet axis. At 14.5 J1S, the material exhibits a
weak compression texture. After 18 f,iS, the pole figures re
sulting from both random and strong initial textures are es
sentially identical.
The () = 52° cell presents a different picture. As dis
cussed above, there are no well-defined stages of deforma
tion, and no wen-defined deformation modes. The strain
components change with time and the cell also rotates
(which rotates the existing texture).
For the strong initial texture, this deformation history is
reflected in the system activity; the dominant systems
change repeatedly, but with slip accommodating the bulk of
the deformation (66%-70%). The preferred orientations
dissolve much more slowly than in the (:) = 3° cell; at t = 18
f.ls ( ::::;45% von Mises strain) the original maximum for the
() = 52° cel] is still significant, while the original maximum in
the e = 3° cell has essentially disappeared by ;::::;22% von
Mises strain. The t = 30 J1.s pole figure for the e = 52° cell
resembles the stable texture of the () = 3' cell, but the texture
of the former cell is not axially symmetric, and is still chang
ing.
For the random starting texture, the initial system activ
ity and texture evoluti.on somewhat resemble that of the ran
domly textured (J = 3° cell, but occur at larger strains in the
() = 52° cell. This resemblance may be fortuitous; after 16.75
f-ls, the system activity and the orientation pattern resemble
that of the strongly textured () = 52° cell, but without the
persisting maximum at 8;::::52°.
The differences between texture evolution in the e = 52°
cell and in the (:) = 3° cell are related to the differences in
deformation paths and to the relative importance of slip and
twinning for accommodating deformation. The {} = 3° cell
Sheila K. Schiferl 2643
.••• , ., .... '.-••• :.~.:.~ •..••• :.~.:.:.:.:'.:.:o:.;.;.; •• :.~.;.:.:;:.:.:.:.;.;.- •••••••••• ;-:;:.;.;.:.: •.•. ' .•. ' •••••.• :.:·;·;·.v.·.·.·.·.·.;.:.;.:.: •.•.•. • .•••••• ·.'.·.·.;.: •.•...•.• ~ •.• ; .-.",-••• F' ............. -••••••••••••••••• -.-.-.-••••••• " •••••••• ".-•••••••••• __ •
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30a) initial texture
b) time'" 14.50 fi-s
von Mises strain = 0.07
c) time 0= 14.69 p.s
von Mises strain = 0.14
deformation is driven heavily by twinning. Twinning, with
its large orientation changes, effectively destroys the strong
initial texture within a rather small amount of deformation.
For the () = 52° cell, twinning is important but slip is
also effective in accomplishing much of the deformation. For
the strong initial texture, most of the eady deformation can
be accommodated by slip, with its gradual orientation
changes, and remnants of the original texture persist after
rather large strains (:::::45%).
2644 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 d) time = 15.00 J-Ls
von Mises strain = 0.22
0) time co 30.00 J-LS
von Mises slrain = 2.66
FIG. 11. (0002) pole figures for the e = 3" cell, strong initial texture. Con
tours are 7, 14, ... ,56 mrd for (a); 1,2, ... ,22 mrd for (b)-(e). Projection plane
is normal to the jet axis.
C. Yield~surface evolution
Among the mechanical effects of texture evolution dur
ing liner collapse are changes in the amount of yield anisot
ropy and in the directionality of yielding. Figures 15 and 16
show the results for evolution of yield anisotropy during the
early stages of liner collapse for strong initial texture, for
() = 3° and 52° cells, respectively. Both sets of figures repre
sent 1T-plane deviatoric yield surfaces; the units for flow
Sheila K. Schifer! 2644
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30a) initial texture c) time = 15.00 J.LS
von Mises strain = 0.22
b) time'" 14.50 J.Ls d) time"" 30.00 J.LS
von Mises strain = 0.07 von MiSes strain = 2.66
FiG. 12. (0002) pole figures for the 8,.= 3" cdl, random initial texture. Contours are 1,2,3 mrd. Pole intensities for the initial texture vary from 0 to 2.2 mrd,
with no particular pattern.
stress are the same as in Fig. 7. The axes of a yield surface for
a particular time correspond to the system of principal strain
at that time. We will discuss, but not show, the evolution of
yield anisotropy for random initial texture. The latter anisot
ropies are not large, and are difficult to discern in yield
surface diagrams.
We consider first the evolution of yield anisotropy in the
e = 3" cell. For this ceH, the shear coupling is negligible, and
the principal axes of strain are nearly identical to the labora
tory coordinates, where the r 1 ] direction is paraUe1 to the jet
axis. For the strong initial texture, the yield evolution fol
lows a fairly simple form: the jet axis direction starts out
"hard" and the radial direction "soft"; as the texture
evolves, this relation reverses. However, the radial yield will
never become as hard as the axial yield can be, since the c
axes in the new texture will be distributed around 360', not
clustered around one direction. The yield surfaces in Fig. 15
reflect this pattern. The initial texture produces a yield ani
sotropy ofsma,/Smin ;:::::;2.5; the hard direction is -j\ (com
pression along the jet axis)) and the softest direction corre
sponds to biaxial stress: 52 = -53 . The radial directions are
very soft: 5max /52 :::::: 2.2. Also, the compressive and tensile
yield strengths in the axial direction are not equal: S,'/5,
2645 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 :::::: 1.33. For this texture, most grains cannot yield in com
pression or tension without twinning, and the stresses re
quired to activate compressive and tensile twins are differ
ent.
By 14.5 ps, at the end of the compressive shock, a signifi
cant fraction of the grains have twinned, thus reorienting
many of the crystals so they can accommodate compression
and tension along the jet axis largely or entirely by slip,
which tends to be easier than twinning. The anisotropy ratio
has been reduced to 1.5, and sc/s,:::::: 1.12.
By 14.7 !ls, after 7% compression followed by 7% ten
sion, the anisotropy is weaker stilL The anisotropy ratio has
fallen to L 14, but retains the pattern of the initial yield ani
sotropy. Compressive yield is still greater than tensile yield.
After another 8% tensile strain (22% von Mises
strain), at 15 ps, the original pattern of yield anisotropy is
lost, and the anisotropy ratio is < 3%; the yield (but not the
texture) is now approximately isotropic. After 15 ps, a weak
tensile texture evolves. At 30 ps, this texture gives a weak
anisotropy of ;:::::;6%; the strong direction is radial compres
sion, the weak is axial compression.
For a random initial texture, the yield surface for the e = 3° cell evolves to a weak anisotropy of :::::; 5% at 14.5 j..ls,
Sheila K. Schiferl 2645
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30I
(@<----I---+
~----~
a) initial texture
b) time = 16.75 J.Ls
von Mises strain = 0.21
c) time = 18.00 J.Ls
von Mises strain = 0.45
with the same pattern as the strong initial anisotropy. (The
yield anisotropy for the random distribution was z 1.5%,
with no particular pattern.) By 15 f-ts, the yield surfaces of
the B = 3° cell are essentially the same for both random and
strong initial textures.
The evolution of yield anisotropy in the e = 52° cell, like
the evolution of texture, follows a different pattern. In accor
dance with the texture changes, we see some persistence of
2646 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 d) time = 19,00 f.l-s
von Mises strain = 0,61
e) time"" 30,00 /-Ls
von Mises strain = 2.71
FIG. 13. (0002) pole figures for the e = 5Y cell, strong initial t~xture, Con
tours are 6,12, ... ,42 mrd for (al; 1,2, ... ,19 mrd for (b)-(el.
strong yield anisotropy, plus a variety of shapes of the yield
surface, as the patterns of preferred orientation shift.
We consider first the evolution of the yield surface for
strong initial texture (Fig. 16). The persistence ofthe initial
preferred orientation is apparent here. At the onset of defor
mation, Fig. 16(a), the initial yield anisotropy, in principal
axes, is :::::63%; the anisotropy at 16.75 fLs is :::::24%, still
large after a von Mises strain of ::::: 22 %. This is not a smooth
Sheila K, Schiferl 2646
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30a) initial texture c) time = 19.00 fLs
von Mises str'ain = 0.61
b) time = 16.75 fLs
von Mises strain = 0.21 d) time ~o 30,00 fLS
von Mises strain = 2.71
FIG. 14. (0002) pole figures for the (J = 52' cell, random initial texture. Contours are 1,2,3 mrd. Pole intensities for the initial texture vary from 0 to 2.2 mrd,
with no particular pattern.
change, however; the yield surface passes through a variety
of anisotropic shapes during this time. After 45% strain, at
18 f.ls, the yield is still significantly anisotropic (;::; 12.5%)
but the maximum and minimum positions have shifted. This
is not equivalent to the compression yield anisotropy in the e = 3° cell. In the () = 52° cell, the principal axes [ 1] and r 2 J
are rotated ;::; 30° relative to the corresponding laboratory
axes, and the compressive and tensile yields are approxi
mately equal, After 19 JLs the yield surfaces do not change
significantly in shape, and give a weak anisotropy of ;::;6%.
The variety of shapes of the yield surface is also charac
teristic ofthe e = 52° cell with random initial texture, but the
anisotropies are weaker, varying from :::::6% to almost 9%.
The differences between yield-surface evolution in the e = 52° cell and in the (J = 3° cell are a function of the differ
ences in texture evolution. The most striking differences are
for the riner with a strong initial texture. In the (J = 3° cell,
both the strong preferred orientation and the strong yield
anisotropy dissipate relatively quickly, within < 1.5 ps and
< 22% von Mises strain. In the e = 52° cell, the strong tex
ture and the corresponding yield anisotropy dissipate more
slowly (within :::::3 ps, and ;::;50% von Mises strain).
2647 J. Appl. Phys .• Vol. 66, No.6. 15 September 1989 Neither cell becomes isotropic, but the new yield anisotro
pies are relatively weak.
For random initial texture, both e = 3° and 52° cells ap
pear to evolve a weak compression-type yield anisotropy ear
ly in the deformation, but this pattern does not remain.
In the next section we consider the consequences of
these results for jet behavior, and for penetrator simulations
that include texture effects.
v. SUMMARY AND CONCLUSIONS
In this study, we have investigated the possibiiity that
crystallographic texture (or preferred orientation) can have
important effects on soHdjet behavior. There are some indi
cations that liners fabricated to have certain strong textures
can produce jets with markedly improved properties; there is
also considerable information from metal-forming applica
tions that certain strong textures can produce desirable me
chanical properties. We would lik.e to exploit these effects in
designing penetrators.
There are several points to be considered when dealing
with texture in the context of a deforming liner:
Sheila K. Schiferl 2647
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:3052 S:!
a) time == 13.75 p..s
von Mises strain == 0.00
s,
~t\ : I
52 53
b) lime '" 14.50 j.lS
von Mises strain "" 0.07
81
c) time =: 14.69 ILs
von Mises strain = 0.14
(1) Texture can produce large mechanical anisotropies
if single-crystal anisotropies are large.
(2) The texture, and the corresponding mechanical ani
sotropy, change as the material deforms.
(3) Texture evolution depends on the kind of deforma
tion, as well as on the crystal structure. It is mediated by
single-crystal mechanisms.
(4) Ifwe can specify a deformation path, we can use the
major single-crystal mechanisms (slip and twinning) to cal
culate texture evolution in a polycrystaUine material, and
the resulting yield anisotropies.
2648 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 SE S3
d) time == 15.00 f.J.S
von Mises strain == 0.22
SI
(.
82 5:1
e) time == 30.00 p:s
von Mises strain == 2.66
FIG. 15. Deviatorie yield loci in the system of principal strain for the e = 3'
ceil, strong initial texture. The [3] direction is normal to the jet axis. The
onset of plastic deformation occurs at ;:::: 13.75 f-ls; (a) represents the yield
ing behavior of the initial texture.
We have concentrated here on typical deformation
paths during liner collapse, and on the potential effect of
initial texture on subsequent jet behavior. In particular, we
have calculated the evolution of textures, and the corre
sponding yield anisotropies, during collapse of a hemispheri
cal titanium jet liner: (l) For random initialtexture, (2) for
a strong initial texture, (3) for a region of the liner near the
jet axis «(J = 3° cell), and (4) for a region of the liner origin
ally distant from the jet axis ((} = 52" ce!l) ,
From our results for titanium we can make the follow
ing conclusions:
Sheila K. Schiferi 2648
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30a) time == 15.75 J.J.s
von Mises strain = 0.00
b} time = 16.75 jJ.S
von Mises strain == 0.21
c) time'" 18.00 J.l.s
von Mises strain == 0.45
( 1) Yield anisotropy, traceable to a strong initial orien
tation, is only significant at early times during liner collapse
(0-3 f-ls after the start of deformation for our model).
(2) Even before the jet is well fanned, the material is
unlikely to bear any significant traces of the initial texture.
Instead, the metal will have evolved textures and yield an
isotropies characteristic of the most recent deformation.
(3) The effect of strong initial texture persists consider
ably longer in parts of the liner far from the axis than in the
axial region. This is probably a consequence of the greater
importance of twinning to accommodate deformations
2649 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 d) time == 19.00 IJS
von Mises strain = 0.61
e) time"" 30.00 j.J.S
von Mises strain:: 2,71
FIG, 16. Deviatoric yield loci in the system of principal strain for the e = 52' l'eH, strong initialtexture. The l3] direction is normal to the jet axis.
The onset of plastic deformation occurs at 0::: 15.75 f.1-s; (a) represents the
yielding behavior of the initial texture.
along the axis. The complicated and changing deformation
modes for the (J = 52° cell may also be less efficient in dis
persing the initial texture than the simple compression and
tension near the axis.
( 4) The yield surface for the e = 52° cell, for a strong
initial texture, does not simply become less anisotropic dur
ing Hner collapse, but evolves through a variety of shapes,
(5) A random initial texture evolves weak preferred ori
entations and corresponding yield anisotropies in the first
few f-lS of deformation. These do not necessarily match the
texture evolution from strongly textured liners.
Sheila K. Schiferl 2649
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130.209.6.50 On: Mon, 22 Dec 2014 17:17:30These points are specific to our particular mechanical
model for titanium, but the general conclusions and the pro
cess should be applicable to other hexagonal materi.als, and
other defonnation paths. With the exception of the third
point above, the general conclusions should also be applica
ble to other crystal structures. In particular, the loss of infor
mation about initial texturefollowing a large deformation is
seen for many fabrication processes. There are exceptions to
this rule,32 but only if certain symmetries are present in ini
tial textures and subsequent deformations.
The limitation of initial texture-induced anisotropies to
early times helps narrow the search for the mechanisms of
initial-condition effects on jet behavior. We do not need to
trace initial textures from the undeformed liner through
breakup. Instead, initial texture effects must influence jet
behavior through changes in material flow, localization, etc.
induced at early time. In particular, if flow patterns in a jet
are affected, the velocity gradient, and hence the eventual
breakup, would probably be affected. For other penetrator
designs, such as EFPs,33 which can be particularly sensitive
to small changes in material properties, texture effects may
be larger than in jets. In some EFPs, complicated flow pat
terns early in deformation are typical; the possibility of al
tered flow patterns suggests differences in the final
shape obtained.
ACKNOWLEDGMENTS
The author would like to thank J. N. Johnson (Los Ala
mos) for many valuable discussions. H.-R. Wenk graciously
helped check out the texture code, and C Tome provided an
early version of the pole figure graphics. This work was sup
ported by the Department of Defense and the Department of
Energy, through the Joint DoD/DOE Munitions Technolo
gy Development Program.
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'<0L. E. Murr, ibid., pp. 607·-673.
'lD. N. Williams and D. S. Eppe!sheimer, Trans. AIME 194, 615 (1952).
'"Ref. 7, p. 544.
"S. P. Marsh, Los Alamos National Laboratory Report No. LA-9538-MS,
October, 1982.
Sheila K. Schiferl 2650
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1.342514.pdf | Magnetoresistivity in a NiFeCo/Ta multilayer thin film with elevated substrate
temperature
J. H. Hur, C. S. Comstock, A. V. Pohm, and L. A. Pearey
Citation: Journal of Applied Physics 64, 6113 (1988); doi: 10.1063/1.342514
View online: http://dx.doi.org/10.1063/1.342514
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137.149.200.5 On: Sun, 30 Nov 2014 18:17:59Magnetoresistivity in a NifeCo/Ta multilayer thin fUm with elevated substrate
temperature
J. H. Hur, C. S. Comstock, A. V. Pohm, and L A. Pearey
Electrical and Computer Engineering Department, Iowa State University, Ames. Iowa 50011
T~e effects of s~bstra:e tempe~ature on magnetoresistive (MR) ratio of the NiFeCo mutilayer
thm films were mvestlgated. Films were fabricated by rf sputtering with substrate temperature
elevated to 200 and 300 ·C prior to deposition. MR ratios increased by an average of 5% at
2OO·C and 7.7% at 300 ·C, as compared with the films deposited on unheated substrate.
INTRODUCTION
A multilayer structure of two ferromagnetic layers and
a nonferromagnetic conductive middle layer has been used
for magnetoresistive (MR) memory cells and transducers. I
In order to have appropriate signal levels from these ele
ments, it is desirable to have a high MR ratio. A ternary aHoy
(65-wt. % Ni-15-wt. % Fe-20-wt. % Co), which is non
magnetostrictive, was used for the magnetic layers? Tanta
lum is a conductive metal and appears to have a much higher
sheet resistance than NiFeCo because it is thinner than the
NiFeCo layers in this structure. When tantalum is used as
the middle separation layer, most of the sense current will
flow through the top and bottom magnetic layers parallel to
the plane of the film. Tantalum was also used as protection
layers to prevent the magnetic layers from oxidizing. This
was done because tantalum forms tough self-protective ox
ides through heat treatment :in oxygen or anodic oxidation.
A study showed that multilayer films, with NiFeCo as the
two ferromagnetic layers and a 20-.A tantalum intermediate
layer, exhibited good magnetostatic coupling? A previous
study showed that the MR ratio of a multilayer structure
increased by an average of 15%-22% and the resistance de
creased by an average of 7%-10% by annealing after depo
sition.4
Larger grain size can be obtained by increasing the sub
strate temperature during deposition. This is due to a corre
sponding increase of the mobility of target atoms condensing
on the surface of the substrate, which allows the film to de
crease its total energy by growing larger grains.5 Collins and
Sanders studied the effects of substrate temperature on the
MR ratio for NiFeCo single layer :films deposited by elec
tron-beam evaporation.6 They found that the MR ratio in
creased with increasing substrate temperature and that the
increase was mainly due to the decrease in resistivity. In this
paper, multilayer films were fabricated by rf sputtering, and
were studied to determine the effect of elevated substrate
temperature on the MR ratio. No attempt was made to cor
rect the results for the current shunting effect caused by the
tantalum layers.
EXPERIMENTAL PROCEDURE
The substrates were heated up to 200 or 3OO·C before
depositing the five layers of the film. 3-in. silicon wafers with
silicon dioxide passivating layers were used as substrates.
Temperatures were maintained constant during deposition.
All the films were deposited at Iowa State University by rf sputtering with argon pressure at 5-6 mTorr. A 6-0e exter
nal field was applied parallel to the plane of the film during
deposition to induce the uniaxial anisotropy of the films in a
direction perpendicular to the flat edge of the 3-in. silicon
wafer. 100 A of tantalum was deposited as a first layer to
prevent oxygen from the silicon dioxide from diffusing into
the first magnetic layer. A nonferromagnetic tantalum mid
dle layer, between 40 and 60 A thick, was deposited between
the nonmagnetostrictive NiFeCo layers. Each NiFeCo
layer was 250.A.. thick. Finally, l00.A.. of tantalum was depos
ited on top to protect the second NiFeCo layer from oxida
tion. AU five layers were deposited consecutively without
breaking a vacuum. Thicknesses of the films during the sput
tering process were measured by an Inficon model XTM
thickness and rate monitor. The B-H hysteresis looper meth
od was used to measure the coercive force lie' the anisotropy
field H k' and the saturation magnetization M,. In particular,
H k was evaluated by applying a large magnetic field to deter
mine the value of M, on the CRa screen. Then a small mag
netic field was applied parallel to the hard axis. This field
produced a straight line trace, which was extrapolated to the
Ms value, giving rise to the value of Hk•
MR ratios were measured automatically by using a Z-
100 PC and a rectangular four-point probe, with a rotating
magnetic field of 900 G to saturate the films in a desired
direction. After bei.ng deposited at a substrate temperature
of 200 "C, the films were then annealed in a separate anneal
ing oven at 300 °Co Four sample wafers were each divided
into four pieces. One piece of each wafer was annealed at
300 ·C. Each wafer was annealed for a different amount of
time. An external field of 100 Oe was applied in a direction
TABLE 1. Data for films with 200 'C substrate temperature.
Middle
layer He II. Ms R MRratio
(A) (De) (De) (Oe) (mm (%)
40 0.72 9.6 0.396 1140 2.45
40 0.684 9.6 0.396 1085 2.58
40 0.72 9.6 0.396 1150 2.45
SO 0.612 9.6 0.432 1125 2040
50 0.684 9.6 0.396 H2O 2.47
50 0.576 11.52 0.396 1126 2.38
60 0.792 10.8 0.432 1080 2.55
60 0.72 9.6 0.432 1120 2.50
60 0.72 9.6 0.414 1I20 2.55
6113 J. Appl. Phys. 64 (10), 15 November i 988 0021-8979/88/226113-02$02,40 @ 1988 American Institute of Physics 6113
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137.149.200.5 On: Sun, 30 Nov 2014 18:17:59TABLE H. Data for films with 300 ·C substrate temperature.
Middle
layer He Hk ,'14, R MRratio
(A) (De) (Oe) (De) (mn) (%)
40 0.648 9.6 0.396 1076 2.70
40 0.576 11.52 0.378 1090 2.55
40 0.612 9.6 0.396 1092 2.58
50 0.504 9.6 0.396 1120 2.48
50 0.756 11.52 0.414 !l15 2,57
50 0,684 9.6 0.378 IllO 2.45
60 0,648 9.6 0.396 1087 2.53
60 0.648 9.6 0.396 1160 2.50
60 0.702 9.6 0.396 1120 2.50
paranel to the easy axis ofthe film during annealing. A form
ing gas, 15% hydrogen in nitrogen, was used to prevent oxi
dation. MR ratios were measured again on the same films
after the annealing step.
RESULTS AND DISCUSSION
Data resulting from films deposited with substrate tem
peratures of 200 and 300 °C, respectively, are shown in Ta
bles I and II. TheRe, Hk, andMs values are almost the same
as the films deposited without elevated substrate tempera
tures. MR ratios were increased by an average of 5% at
200"C and 7.7% at 300 °C, as compared with the films de
posited on unheated substrates. The maximum MR ratio
was 2.7%. The resistance of the films measured in this study
(with elevated substrate temperatures during deposition)
was almost the same as the resistance measured for films
with no substrate heating but annealed after deposition.3
The MR ratios of the films were not as high as expected. It is
believed that the first tantalum protection layer did not pre-
TABLE III. Data for films deposited at 200 'C substrate temperature and
annealed at 300 ·C. B stands for before annealing. A stands for after anneal-
ing.
He Hk M,
Middle Annealing
la{;'er time B A B A B A
(A) (h) (Oe) (De) (Oe)
40 1 0.648 0.666 9.25 iO.3 0.171 0.171
40 2 0.576 0.756 13.2 13.2 0.216 0.216
40 4 0.54 0.72 to. 3 10.3 0.18 0.18
40 8 0.666 1.08 10.8 10.8 0.171 0.171
SO I 0.72 1.332 12.0 10.B O.IB 0.171
50 2 0.12 1.332 10.8 10.8 0.216 0.216
SO 4 0.648 1.296 13.2 11.3 0.216 0.216
50 8 0.432 0.792 12.0 t2.0 0.216 0.216
60 1 0.792 1.296 12.0 10.8 0.171 0.171
60 2 0.72 0.936 12.0 12.0 0.198 0.198
60 4 0.792 1.188 13.2 13.2 0.216 0.216
60 8 0.792 1.368 10.3 10.3 0.189 0.189
6114 J. Appl. Phys., Vol. 64, No.1 0, 15 November i 988 TABLE IV. Data for films deposited at 200'C substrate temperature and
annealed at 300 'C, B stands for before annealing. A stands for after anneal-
ing.
Resistance MRratio
Middle Annealing
layer time B A B A
(fl.) (h) (mn) (%)
40 1 1312 1327 2.63 2066
40 2 1437 1428 2,57 2.61
40 4 1370 1372 2.54 2.S0
40 8 1399 1399 2.55 2.50
50 1 1400 1388 2.52 2.56
50 2 1425 1413 2.50 2.54
50 4 1411 1415 2.59 2.55
50 8 1403 1396 2.52 2.54
60 1 1348 1323 2.68 2.75
60 2 1369 1370 2.55 2.64
60 4 1390 1392 2.72 2.70
60 8 1304 1288 2.63 2.70
vent oxidation of the first magnetic layer from silicon diox
ide. An increase of the grain size compensates for a decrease
in magnetic material, which would explain the reason why
the resistance did not change as much as expected.
Tables HI and IV demonstrate magnetic properties of
the films before and after annealing at 300 °C. There were
hardly any changes in most of the properties except in He.
The increased He values suggest that the films were pinhole
coupled after annealing.
Our study showed that elevating the substrate tempera
ture for the multilayer film deposition obviously did not
have as much of an effect on the MR ratio as annealing the
film after deposition.
CONCLUSION
MR ratios of NiFeCo multilayer thin films were in
creased by elevating the substrate temperature during depo
sition. Values to as high as 2.7% were measured. This in
crease was not found to be as pronounced as the increase
caused by annealing the film after deposition. An investiga
tion correlating grain size, resistivity, and MR ratio, with
substrate temperature is being continued.
IA. V. Pohm, J. M. Daughton, C. S. Comstock, H. Y. Yoo, andJ. H. Hur,
IEEE Trans. Magn. MAG·23, 2575 (1987).
2c. H. Tolman, J. AppL Phys. 38,3409 (1967).
'L. A. Pearcy, M.S. thesis, Iowa State University, 1987
'J. H. Hur, C. S. Comstock, A. V. Pohm, and L. A. Pearey, I. AppL Phys.
63,3149 (1988).
'C. Neugebauer, Condensation, Nucleation, and Growth of Thin Films
Handbook of Thin Film Technology (McGraw-Hill, New York, 1970).
"A. J. Collins and I. L. Sanders, Thin Solid Films 48,247 (1978).
Hur eta!. 6114
......... -....•......•..•••. ;.:-:.:.:: ............ .
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1.457091.pdf | The rheology of Brownian suspensions
G. Bossis and J. F. Brady
Citation: J. Chem. Phys. 91, 1866 (1989); doi: 10.1063/1.457091
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Downloaded 29 Aug 2013 to 128.104.46.196. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissionsThe rheology of Brownian suspensions
G. Bossis
Laboratoire de Physique de la Matiere Condensee, Universite de Nice, Parc Valrose 06034
Nice Cedex, France
J. F. Brady
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
(Received 15 September 1988; accepted 27 March 1989)
The viscosity of a suspension of spherical Brownian particles is determined by Stokesian
dynamics as a function of the Peclet number. Several new aspects concerning the theoretical
derivation ofthe direct contribution of the Brownian motion to the bulk stress are given, along
with the results obtained from a simulation of a monolayer. The simulations reproduce the
experimental behavior generally observed in dense suspensions, and an explanation of this
behavior is given by observing the evolution of the different contributions to the viscosity with
shear rate. The shear thinning at low Peclet numbers is due to the disappearance of the direct
Brownian contribution to the viscosity; the deformation of the equilibrium microstructure is,
however, small. By contrast, at very high Peclet numbers the suspension shear thickens due to
the formation of large clusters.
I. INTRODUCTION
Predicting the rheological behavior of concentrated sus
pensions poses a difficult theoretical problem primarily for
two reasons. First, the hydrodynamic interactions appear on
several different scales. There are short-range lubrication
forces between particles, which are essentially two-body
contributions. There is an intermediate range in which
many-body hydrodynamic interactions are important. And
finally, there are also long-range, divergent, interactions that
must be properly "renormalized." Second, the exact knowl
edge of the forces and stresses for a given configuration of the
particles is not sufficient to determine the rheology, because
an average over the different configurations sampled by the
particles is needed. These configurations are themselves the
result of the interplay between the external driving force
(the imposed shear flow) and the "internal" hydrodynamic,
interparticle and Brownian forces; thus, the system is com
pletely coupled.
We have recently developed a numerical simulation
method, called Stokesian dynamcis, that deals with these
different aspects (cf. Ref. 1 for a review). In the case of
purely hydrodynamic interactions (i.e., without interparti
cle forces or Brownian motion), and with configurations
sampled from a Monte Carlo hard-sphere distribution, the
viscosities obtained by simulation2 as a function of the vol
ume fraction <p, are in excellent agreement with experimen
tal results, for example those reported by Van der Werff et
al.3 Furthermore, the simulations show the importance of
the lubrication forces in the increase of the viscosity with
increasing concentration.
In preceeding papers4•5 we have described how to intro
duce Brownian motion into the evolution equation for the
particle trajectories, and have discussed the changes in the
suspension microstructure and the self-diffusion coefficient
with increasing shear rate. In this paper we wish to focus on
the rheology of Brownian suspensions and in particular, re
late the change in the viscosity with shear rate to the chang
ing microstructure. In order to save computation time we shall follow our previous studies and simulate a monolayer
of identical spheres. While perhaps not directly quantitative
ly comparable with experiment, the resulting evolution of
the viscosity with shear rate should be qualitatively accurate.
In the first part of this paper (Sec. II) we give the gen
eral relation for the various contributions to the bulk stress
and offer an alternative "microscopic" derivation of the so
called direct contribution due to Brownian motion. In Sec.
III we present the simulation results for the viscosity and the
structure as a function of the Peclet number. In the discus
sion we compare the simulated viscosities with experiment.
II. THEORY
The calculation of the average or macroscopic stress in a
homogeneous suspension has been given by Batchelor6•7; the
deviatoric part of the stress is given by
N
-(l/V) L raFa· (l)
a=l
(l:) and (E) are, respectively, the macroscopic averages of
the stress and rate of strain tensors defined by an integral
over the volume of the suspension:
(.) = (l/V) Iv dr. (2)
I.T. stands for an isotropic term of no importance for the
rheology of the incompressible suspension. Sa' the stresslet
exerted by the fluid on the rigid particle a located at position
ra, is the symmetric and traceless part of the first moment of
the force distribution integrated over the particle surface Aa :
Sa = (l/2) r {(r-ra)u+u(r-r a) JAo
-(2/3 )I(r -ra)'u }·n dr. (3)
Here u is the stress tensor in the fluid, i.e., u = -pI-
1866 J. Chern. Phys. 91 (3),1 August 1989 0021-9606/89/151866-09$02.10 © 1989 American Institute of Physics
Downloaded 29 Aug 2013 to 128.104.46.196. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissionsG. Bossis and J. F. Brady: Rheology of Brownian suspensions 1867
+ 21][Vu + (Vu)t] withp the local fluid pressure, Vu the
local fluid velocity gradient, and 1] is the viscosity of the
suspending fluid. The normal n points into the fluid.
The final term in Eq. (1), (1/ V) ~r a Fa, is the stress
due to the interparticle forces. Fa is the non-hydrodynamic
external force exerted on particle a: the common example
being the force due to an interparticle potential V(rl, ... ,rN).
(Note, a constant external force such as gravity may be in
cluded in the definition of Fa since it does not affect the
deviatoric part of the bulk stress.)
An analysis of the different components of the bulk
stress has already been given, both in the context of dilute
solutions? and in an approximate treatment of concentrated
suspensions,8 but we wish here to clarify certain points that,
perhaps, appear more transparently in the context of a nu
merical simulation.
The local hydrodynamic stresslet of particle a is ob
tained with the help of the Faxen law linking the stresslet to
the local rate of strain tensor e(r) evaluated at the particle's
center:
Sa = (20/3)1T1]a3[1 + (a2/1O)V2]elr~ra' (4)
Equation (4) is valid for spherical particles, but generaliza
tions to nonspherical particles are possible. The local field
el r ~ ra differs from the average rate of strain (E) firstly be
cause of the excluded volume due to the finite size of the
particle (this is the equivalent of the well known cavity field
in electrostatics), and secondly because of the nonhomogen
eous (on the particle scale) repartition of the other particles
around the reference particle. This difference between the
local rate of strain tensor and the average one is used indi
rectly in the renormalization procedure of Batchelor and
Green9 and explicitly by BedeauxlO to obtain a Clausius
Mosotti-like formula for the viscosity.
In our approach through numerical simulation, we
model an infinite suspension by periodically replicating the
basic unit cell and use periodic boundary conditions. The
divergent and conditionally convergent hydrodynamic in
teractions are renormalized by O'Brien's method, II and the
convergence of the resulting interactions are accelerated us
ing the Ewald summation technique. 12 This amounts to re
moving the k = 0 terms in the reciprocal lattice sums. 13
From the linearity of the governing Stokes' equations
we may write the stresslets of the N particles as I
S= -R~u'(U-(u»+R~E:(E)-rFP, (5)
where S = (SI,SZ,,,,,SN) is a column vector containing the
N particle stresslets. R~u and R~E are part of the grand resis
tance matrix defined by
[F] = _ [R:u R:E]. [U -(u)] + [FP p]. (6)
S Rsu RSE -(E) -rF
In Eq. (6) U stands for the translational/rotational ve
locities of the N particles and (u) is the average velocity at
the center ofthe particles. F and S are, respectively, the total
force/torque and stresslet exerted on the N particles by the
fluid and by the interparticle forces FP• The interparticle
force contribution to the bulk stress given in Eq. (1) is the
- r FP term in Eq. (6); r denotes the vector of particle posi-
tions. The star notation indicates that Ewald sums have been performed on the infinite periodic lattice. The resistance ma
trix R~u, etc. are purely geometric quantities, being func
tions of the instantaneous particle configuration only.
At low particle Reynolds numbers, the total force F is
zero, and the particle velocities are given by
U = (u) + R~u I. (FP + R~E:(E». (7)
The velocity in (7) does not include the contribution
from Brownian motion; in the absence of an imposed flow or
interparticle forces, the particles do not move. Brownian
motion can be included by integrating the Langevin equa
tion,I.4,14 but, for our purposes in discussing the stress we
only need to add a Brownian component UB (t) to Eq. (7).
The total stress is then obtained from the second line of Eq.
(6) :
S = -(R~u'R~u I'R~E -R~E):(E)
-R~U'UB -R~u'RFUI'FP -rFP. (8)
To compare with previous expressions used in the literature
for the bulk stress, we write
S = SH + SI + SB, (9)
where
SH = - (R~u' R~u I. R~E -R~E ):(E) ,
SI= -(R~u'R~ul+rI)'FP,
SB = - R~U·UB(t).
Here I is the unit isotropic tensor. ( lOa)
(10b)
( lOc)
Unlike the deterministic velocity U in Eq. (7), the
Brownian velocity UB (t) fluctuates with a characteristic
time equal to the Brownian relaxation time 'TB = m/61T1]a,
which is generally several orders of magnitude smaller than
the time interval at required for the particles to move a sig
nificant fraction (10-2_10-3) of their radius (or interparti
cle spacing). In addition to producing the Brownian dis
placement, these rapidly fluctuating particle velocities
propagate (instantaneously in the limit of an incompressible
fluid) a velocity field whose perturbations by the N particles
give rise to the Brownian stress. The average of this
Brownian stress over a time interval at~ 'T B is different from
zero because both R~u and UB (t) depend on the configura
tion of the particles which fluctuates at the rate ofUB (t). In
the appendix it is shown that:
SB = -1/ at ldl R~u' UB(t)dt
(11)
where the configuration-space divergence is with respect to
the last index of R~u I.
Owing to the symmetry of the grand resistance matrix
we have
(12)
so this quantity represents the velocity of a particle resulting
from the imposed rate of strain (E) [cf. Eq. (7)]. We can
make a connection with the work of Batchelor? by noting
that for two particles (a and {3) alone in the fluid (i.e., pair
wise hydrodynamic interactions), the components of the
tensor (R~u I)ap· (R~E)aP reduce to the quantity CaP, de-
J. Chem. Phys., Vol. 91, No.3, 1 August 1989
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fined by Batchelor, giving the relative velocity of two spheres
in a linear shear flow:
Cjkl(r) = -(rjrkrJ2r)(A -B) + (1I6)rIDjkA
-0/4 )(rjDkl + rkDjI )B, (13)
where r = r a -r (3 and A and B are functions of I r I = r only.
The stresslet in Eq. (11) thus becomes Sjk = -kT V I Cjkl,
which is Batchelor's result, where he used the concept of a
"thermodynamic" force. Our result is, perhaps, a bit more
direct, provides a microscopic definition and is not restricted
to pairwise additivity. That the two definitions agree is, of
course, satisfying.
Our Langevin derivation of the direct Brownian stress
also serves to indicate its hydrodynamic origin, for it is ulti
mately linked to the motion of the fluid through the hydro
dynamic resistance matrices. If the hydrodynamic interac
tions did not change with relative position or orientation of
the particles, then there would be no divergence in ( 11 ) and
no Brownian stress. For an isolated spherical particle,
Rsu . Rpul is a constant, namely zero, and SB = O. Thus the
direct Brownian stress is proportional to q; 2 for dilute con
centrations of spherical particles and results from the diver
gence of the relative velocity [C in Eq. (13)] with particle
separation. For nonspherical particles, however, Rsu' Rid
is not, in general, zero for an isolated particle, and there is
generally an 0 (q;) direct Brownian contribution to the bulk
stress. Indeed, for spheroidal particles, the orientational di
vergence ofRsu' Rid is nonzero. For an isolated spheroidal
particle described by the orientation vector p, Eq. ( 11) gives
a contribution to the bulk stress (~B) = -31JkT/3 (pp),
where (pp) is an orientational average and /3 is a function of
the aspect ratio only. 15 This is precisely the result first pro
posed by Kirkwood and Auerl6 and Giesekusl7 and used by
Hinch and Leal. 18.19 (See also Brenner20 for a complete sum
mary of the properties of axisymmetric particles. )
Using the above expressions for the particle stresslet, we
may write the bulk stress in Eq. (1) as
(~) = I.T. + 21J(E) + (N IV){(SH) + (Sf) + (SB)},
(14)
where (SH) = ( liN) ~a = INS;: is the number average par
ticle stresslet, and SH, Sf and SB are given by Eqs. (10) and
( 11 ). Equation ( 14) is true for any configuration of arbitrar
ily shaped and sized particles. It applies instantaneously (on
time scales larger than 7' B ) and therefore can also be used for
time-dependent flows, such as oscillatory shear or start upl
cessation experiments; in this case, the impressed rate of
strain (E) and flow (u) are now functions of time. Note also,
that even in the absence of interparticle forces (FP = 0) and
even if the magnitude of the direct Brownian stress is small,
despite the appearance of Eq. (10a), the hydrodynamic
stress is nonlinear in the rate of strain (E) due to the fact that
the particle configurations depend upon both hydrodynamic
and Brownian forces. This latter dependence is the so-called
indirect effect of Brownian motion on the stress: Brownian
motion influences the structure, which in tum influences the
configurational average of Eq. (lOa).
Further progress can be made in the interparticle force
contribution to the bulk stress if we restrict ourselves to pair-wise interparticle forces. Most colloidal forces of interest are
well represented by pairwise interparticle interactions, so
this is not a severe restriction. Making use of Eq. (12), (Sf)
from Eq. (lOb) becomes
N
(Sf) = -(liN) L (R1ul
'R1E + rI)a 'Fa
a=l
= -(1IN) L L Aa . Fa{3' (15)
(3 a
Here, Aa (rl ... rN) = (R~u I. R~E + rl)a is the ath compo
nent of this tensor, and when multiplied by a straining flow
E, it gives the actual velocity of particle a due to this strain
ing flow. F a{3 (r a -r (3) = -F {3a is the force on particle a
due to /3 and is only a function of the separation between a
and /3. Introducing the N-particle probability distribution
function P N (r I ... r N) for N identical particles, Eq. (15) be
comes without approximation
(Sf) = -J (AI -AZ)2'F12PI/I(r2/rl)dr2' (16)
where
(AI - A2)2
== [lI(N -2)!]
X J (AI -A2)PN-2I2 (r3· .. rNlrlr2)dr3· .. drN (17)
is the conditional average with two particles fixed at r I and
r 2' PI/I is the probability density for finding a particle at r 2
given that there is a particle at r I'
Note in Eq. (16) that it is only through the hydrody
namic interactions that information on three particle distri
butions, etc. is needed. In the absence of hydrodynamic in
teractions, Al -A2 = (rl - r2)1, and Eq. (16) depends
only on pair-particle information. Under the assumption of
pairwise hydrodynamic interactions, we approximate
where the last identity follows the notation of Batchelor7 [cf.
Eq. (3)]. Thus, with pairwise hydrodynamics, Eq. (16)
becomes
(S~A) = -J [C(r12) +r12I]'F12PI/2(rzlrl)drz,(19)
where the subscript PA is to remind us of the pairwise hydro
dynamics.
Equation (19) should be contrasted with the work of
Russel and Gast8 [their equation (31) ] where they have the
potential of mean force (V 12 Vrnf = V 121n g) rather than the
actual force (or potential) between two particles
(F 12 = -V 12 VI2). This difference is significant and can
have an enormous impact on the values of the stress that is
calculated. Our derivation here shows clearly that it is the
actual two-body interparticle potential that enters into Sf,
and not the potential of mean force. The potential of mean
force does, of course, play an important role in a theoretical
development of the evolution equation for the pair-distribu
tion function and possesses a good physical interpretation as
a "force" in this context. But, this mean force cannot neces-
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sarily be carried over directly as if it were a true force into the
calculation of the bulk stress. Indeed, the above shows that
such a carry over is incorrect. 2 1
One final general point that can be made with regard to
the interparticle force contribution to the bulk stress is in the
case of a hard-sphere potential. A hard-sphere interparticle
force is pairwise additive, so Eq. (16) applies. The hard
sphere interparticle force is only nonzero when the particles
touch; F\2 = (r\2/lrd) 8( Ird = 2a), where 8 is a delta
function on the surface of contact Ird = 2a, a being the
particle radius. The (x,y) component of the tensor
(AI - A2) 'r\2 is the relative velocity of particles 1 and 2
along their line of centers due to a straining flow. This rela
tive velocity approaches zero linearly with the surface sepa
ration, i.e., I (AI - A2) 'r12I-0(g), where g = (r\2 -2a)/
2a, as g -+ O. This is true for any two particles and with the full
many-body hydrodynamic interactions. With pairwise hy
drodynamics I (AI - A2) 'rd ~4.077 g as g -+0, and only
the coefficient changes in going to many-body interactions,
not the linear scaling with g. Thus, since IFd ~0[8(g)],
for hard spheres, the integral in Eq. (16) is proportional to
sg8(g)dg, which is zero. With hydrodynamic interactions
the hard-sphere potential makes no contribution to the bulk
stress. This is also the case with the particle trajectories:
R~u 1. FP = 0 for hard spheres in Eq. (7) because IR~u 11
-O(g) also. With hydrodynamic interactions the hard
sphere potential has no dynamic significance. The interparti
cle force that appears in the particle velocity (7) and the
bulk stress (1 Ob) is an actual interparticle force of electro
static or colloidal origin.
In our simulations to be discussed in the next section,
the relative viscosity of the suspension is defined by the ratio
of the xy component of the bulk stress (~Xy) to the xy com
ponent of the rate of strain (Exy), where we are imposing a
simple shear flow with (ux) = r.v, with y the shear rate.
Nondimensionalizing the elements of the grand resistance
matrix by 61T1]a, 61T1]a2 and 61T1]a3, according to their respec
tive dimensions; all lengths by the particle radius a; the time
by a2/ Do, where Do = kT /61T1]a is the diffusion coefficient of
an isolated particle; the interparticle force by kT fa; and the
stress by 61T1Ja3y; the relative viscosity becomes
with
N
1]~=(9/2)cp(1IN) I (S;:)Xy' (21a)
a=I
N
1]~ = -(9/2)cp(1/Pe)(1IN) I (Aa'Fa)xy , (21b)
a=l
N
1]Br= -(9/2)m(I/Pe)(I/N) "[V (R*-I'R*)] T L a FU FE xy'
a=l
(21c)
The over bar is to indicate a time average over the course of
the dynamic simulation.
The fundamental parameters that appear are the vol
ume fraction cp of particles and the Peclet number Pe
= 61T1Ja3y/kT measuring the relative importance of shear
and hydrodynamic forces. Pe-+O implies Brownian motion dominated behavior, while Pe-+ ao implies hydrodynamic
dominated. Note that neither 1]~ nor 1]~ diverge as Pe-+O as
the scaling in Eq. (21) might indicate. As Pe-+O, (1/
N)~(') is O(Pe) in both expressions so that the contribu
tions to the stress are actually O( I ) as Pe -+ 0 (cf. the discus
sion by Batchelor7). Although we determine the complete
bulk stress, we shall only discuss the viscosity here, normal
stress differences will be discussed elsewhere.
We close this section by repeating here, for ease of read
ing, the evolution equation for particle positions formed
from integrating the Langevin equation (see Bossis and
Brady4 for a complete discussion):
~x = Pe{ (u) + R~u-1. [R~E:(E) + FP] }~t
+ V·R1u- I~t + X(~t), (22)
(X) = 0, and (X(~t)X(~t) = 2R1u- I~t,
where X is a random displacement.
III. SIMULATIONS RESULTS
We have discussed elsewhere,4 the use of Stokes ian dy
namics with Brownian motion to determine particle motion.
The only new point is the calculation of the Brownian stress
SB given by Eq. (11). We have performed simulations for a
monolayer of identical spheres; in this case the convergence
problems associated with the long-range hydrodynamics in
teraction are less important because the local rate of strain
on a reference particle due to a stresslet located at a distance
r decreases as 1Ir3, and the integral over a monolayer is con
vergent. So, in principle, we have no long-range problem in
the calculation of the viscosity. Nevertheless, if we assume a
linear perturbation of the pair-distribution function PIll (r)
as a function of the Peclet number, which must be the correct
asymptotic form as Pe-+O, we can write
PIll (r) = ng(r) = ngo(r)[ 1 -(Pe/2)f(r)(xy/~)],
(23)
and we can show by solving a two-sphere convection-diffu
sion equation for a monolayer5 that the deformation func
tionf (r) decreases as 11 r at large distances. Thus one might
fear that the use of periodic boundary conditions would per
turb not only the long-range structure (which would not be
critical for 1Ir asymptotic behavior of the Brownian stress
in a monolayer), but also the short-range behavior off (r). If
the short-range structure were perturbed, the value of the
Brownian or interparticle stress would depend on the size of
the box. Similarly the hydrodynamic stress SH contains a
part coming from the velocities of the particles, which could
also depend on the size of the unit cell. We have checked this
cell dependency of the stress in two ways:
( 1) First, we have used the Ewald summation with a
replication of the planar unit cell on a cubic lattice so that the
whole 3D system consists of equally spaced planes with a
distance between the planes equal to the length of the unit
cell. The hydrodynamic viscosity 1]~ has been calculated at .
zero Peclet number, because for a purely Brownian suspen
sion, we can generate the configurations with a Monte Carlo
hard-sphere simulation, which is very fast, and then calcu
late the average of SH on uncorrelated configurations. The
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2
1.5
1
0.5
f ( r )
0
-0.5
-1
-1.5
2 8. o o
• o
• •
o o 0
.0 • •
·0
00
o ~i o •
• 0 •
3 o • o
• o
4
hydrodynamic viscosity obtained for an area fraction
qJ A = 0.45 with Ewald sums and 25 particles was: (7J~) Ew
= 0.77 compared to (7J~)PBC = 0.72 with periodic bound
ary conditions; for a higher density: qJ A = 0.6 we find
(7J~)EW = 2.74 and (7J~)PBC = 2.55. This change (~7%),
is very moderate and of no consequence for our analysis.
(2) Second, we have checked the deformation function
f (r) and the Brownian stress SB for a Peclet number ditfer
entfrom zero: (Pe = 0.5) with either 25 or49 particles in the
unit cell. The comparison is represented in Fig. 1. We can see
that the deformation functionf(r) is the same, within un
certainty, in the region 2 < r < 5. The precision is not suffi
cient to detect any long-range behavior, but in any case, this
does not matter for the Brownian stress since we obtain
0.58 ± 0.05 for 25 particles and 0.53 ± 0.05 for 49 particles.
In brief the use of periodic boundary conditions does not
seem to influence the determination of the stress for a mono
layer. Furthermore, we are more interested in a study of the
evolution of the viscosity with shear rate rather than in the
absolute value of the viscosity of a monolayer.
The results for the viscosity as a function of the Peclet o o o
o • •
5 •
o o o
6 FIG. 1. Simulation results for the defor
mation function! (r) for hard spheres de
fined in Eq. (23): (0) 49 particles (.) 25
particles .
number are summarized in Table I and plotted in Fig. 2. We
have used two kinds of systems at the same areal fraction:
qJ A = 0.453. The first one is composed of hard spheres
(there is no interparticle potential but the spheres do not
overlap due to the hydrodynamic lubrication forces as dis
cussed in Sec. II). This is a reference system and we shall
discuss it in considerably more detail than the second system
where we have added a soft interparticle repulsive force
FP = -V V derived from a Debye-Huckel potential
V(r)/kT= Ce~K(r~2)/r. (24)
We have chosen C = 950 and K = 12 so that pi' a/kT is of
order one for Pe = 1 and a distance between two spheres
corresponding to the formation of a square lattice.
The second and third column of the table give the num
ber of steps and the time step either in units of a2/ Do for
Pe< 1 or in units of lIr for Pe > 1. For 25 particles a run of
30 000 time steps represents approximately one hour on a
Cray 2. 7J~ -(5/3)qJ A and 7J~ represent, respectively, the
hydrodynamic viscosity coming for the shear flow (minus
the self part which is 5/3 qJ A for a monolayer instead of
TABLE I. Results ofthe simulation of a monolayer of25 identical hard spheres at an area fraction tp A = 0.453
for different Peclet numbers. The second column is the number of steps of the run; the third column is the time
step nondimensionalized by a21 Do for Pe < 1 and by y-I for Pe> 1. The three following columns give the
hydrodynamic (minus the self part) , the Brownian, and the total relative viscosity of the hard-sphere suspen
sion. The last column is the total relative viscosity of the spheres with a repulsive Debye-Huckel potential.
Pe NSTEPS /:'t
0 10000
0.25 90000 10-3
0.375 60000 10-3
0.5 30000 2X 10-3
1 20000 2X 10-3
10 20000 2X 10-3
102 25000 2X 10-3
103 20000 2X 10-3
10' 20000 2X 10-3
00 20000 2X 10-3 'TJ~ -5/3 tpA
0.72 ± 0.01
0.70 ± 0.01
0.71
0.71
0.72
1.04
1.19
1.27
1.51
1.90 'TJ~
0.91"
0.80 ± 0.05
0.66 ±0.05
0.58 ±0.05
0.50
0.185 ± 0.Q1
0.023
2X 10-3
1.6X 10-4
0 'TJ~s
3.39
3.25
3.12
3.04
2.97
2.97
2.96
3.02
3.26
3.65 2.99
1.99
2.29
3.05
3.65
a Value estimated by extrapolation according to a quadratic scaling of the two lowest Pe values reported in the
table.
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4.0..-----------------------,
Extrapolated Pe -> 0 Limit
1.5 Pe·1 =0
o Total viscosity
o Hydrodynamic viscosity
D. Brownian viscosity
0.0 ~--l...,----l...,----l...,---~~--'_:_--'":--~.
1.0.2 10.1 100 101 102 103 1()4 105
Pe
FIG. 2. Relative viscosity as a function of the Peclet number for a mono
layer of hard spheres: (-0-) total relative viscosity; (--/:1--) Brownian con
tribution: 1J~; (-0-) hydrodynamic contribution without the self part: 1J~
-5/3 'PA'
Einstein's 5/2 <p) and the Brownian viscosity of this hard
sphere suspension. By hard-sphere suspension we mean a
suspension of particles that interact uniquely through hy
drodynamic and Brownian forces; there are no interparticle
forces. We can see that the hydrodynamic part remains con
stant with a value of O. 71 ± 0.01 from Pe = 0 to Pe = 1 and
then rises up to "'~ = 1.9 for Pe = oc. It is worth noting that
for Pe = 104 even if the Brownian motion is very small (it
scales as Pe -I) its influence is still quite important since "'~
= 1.51 instead of 1.9. The Brownian contribution at zero
Peclet number has been extrapolated from a quadratic de
pendency on Peclet number: ",:(Pe) = ",:(0) -A Pe2.
General consideration about reversing the direction of shear
in simple shear flow requires that the viscosity be a function
of the square of the Peclet number. 22
The total relative viscosity ("'~S in Table II) is presented
in Fig. 2. The qualitative behavior is quite similar to that
observed experimentally.23-25 We observe a shear thinning
region at low shear rates and then a plateau followed by a
shear thickening region which begins between Pe = 103 and
Pe = 104. This behavior can be easily understood by looking
at the change in the local structure with the shear rate.
The Brownian viscosity is given by the relation (21c);
and, as noted before, if we consider pairwise hydrodynamic
interactions it reduces to
TABLE II. Cluster statistics as a function of the Peclet number. If the gap
between two spheres is smaller than Ee they belong to the same cluster. S,
and S2 are, respectively, the average size and average mass of the clusters
[cf. Eqs. (26) and (27)].
P, Ee = 10-3 Ee = 10-2 Ec = 10-'
S, 1.006 1.025 1.305 0.25 S2 1.0115 1.052 1.671
S, 1.054 1.372 2.34 100 S2 1.117 1.\936 5.25
S, 2.07 2.76 4.79
00 S2 5.17 7.67 13.06 "': = -(27/161T)(<p2/Pe) f W(r)xy;,.2 g(r)dr, (25)
where W(r) is a known function of the separation distance r
between the two spheres; at large distances (actually r> 4a)
it decreases as 1/~ for a monolayer5 and 1/';; for a 3D sus
pension,7 whereas for two particles at contact W = + 6.96
for a monolayer and W = + 6.37 in 3D. At low Peclet
numbers the deformation of the pair-distribution function is
linear in the Peclet number as expressed by Eq. (23) and we
get a constant value as Pe -> O. At higher shear rates the angu
lar deformation of g( r) no longer responds linearly, and ap
pears to saturate at high Peclet numbers in the range
HX) < Pe < 10 000, as can be seen in Fig. 3 of Bossis and
Brady.4 On the other hand, the function W(r) has no singu
larity for r = 2a and decreases rapidly as a function of r.
Thus we expect that the integral in Eq. (25) will become
constant at high shear rates and that the viscosity will de
crease as Pe -1 as the scaling in Eq. (25) indicates. This is
indeed what we find numerically for Pe > 10.
This apparent Pe -1 decay of the Brownian viscosity
cannot, however be the ultimate scaling as Pe -> oc. The gen
eral considerations about reversing the direction of shear in
simple shear flow, predict that the Brownian stress should
ultimately decay as Pe - 2 as Pe -> oc. That this should be the
case can also be seen from Eq. (25) by noting that at
Pe -1 = 0, g( r) is an even function of x (reversing the direc
tion of flow does not change the structure), and thus the
integral in Eq. (25) is zero. Perturbation from the infinite
Peclet number state should proceed in inverse powers ofPe,
i.e., g(r)-goo(r) +Pe-lg_l(r) + ... as Pe->oc, and
g _I (r) will be odd in x. Thus, the "': -Pe-2 as Pe-> oc.
The simulation results shown in Table I are not, appar
ently, at high enough Peclet number to detect the proper
scaling as Pe -> oc . The same can also be said ofthe low Peclet
number results. The extreme limits of high and low Pe pose
numerical difficulties as the deformation of the microstruc
ture is slight, requiring a very high level of statistical accura
cy.
The diminution of the Brownian viscosity with the Pe
clet number is responsible for the shear thinning behavior
since the hydrodynamic part remains constant for Pe < 1.
The increase of the hydrodynamic viscosity accounts for the
shear thickening part, and we shall see that it comes from the
formation of transient clusters. In the absence of Brownian
motion, experiments26 and simulations27 on a monolayer
have demonstrated the existence of clusters whose size in
creases with the volume fraction of solids. These situations
correspond to an infinite Peclet number. When Brownian
motion is added, it efficiently destroys the larger clusters
[principally through the action of V' Ri'ul in Eq. (22)] as
can be seen in Fig. 3 where we have plotted the percentage of
spheres belonging to clusters which contain at least N
spheres as a function of the size (in number of spheres) of
each cluster. We see that for Pe = 0.25 there are no clusters
of three or more spheres, whereas for Pe = 104,40% of the
spheres belong to clusters of 3 or more and at infinite Peclet
number 68% belong to clusters of 3 or more. The large dif
ference between the two curves for Pe -1 = 0 and
Pe-I = 10-4 shows that a very small amount of Brownian
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100
o
20 (,
o ·0
5 7
nsphere
FIG. 3. Percentage of spheres belonging to clusters which contain at least N
spheres: (-e-) Pe -I = 0; (-0-) Pe = \0"'; (-.-) Pe = 0.25.
motion (10-4) is still very efficient in breaking clusters. We
have chosen 10-2 radii for the separation distance €e which
defines that two spheres belong to the same cluster. This is
quite reasonable since 10-2 also represents the characteristic
range of the lubrication forces. In any event, changing the
criterion to define a cluster does not change the qualitative
behavior as can be seen from Table II where we have listed
the number and the mass averaged moments of the cluster
distribution, defined by
(26)
and
(27)
where ns is the number of clusters containing S particles.
For each definition of the minimum separation €e we ob
serve the same trend demonstrating the growth of cluster
size with Peclet number.
This formation of clusters is clearly correlated with the
increase of the hydrodynamic viscosity, but the relationship
is not obvious at first sight. For a given volume fraction, if we
form spherical clusters of radii a' such that a'ia = (N I
N') 1/3 (where Nand N' are, respectively, the number or
particles of radius a and a' per unit volume), it amounts to
rescaling all lengths by a' and the viscosity will be un
changed. (For a monolayer we have a 1/2 as opposed to a 1/
3 power). In fact, there is some fluid imprisoned between the
spheres inside the cluster and the new radius a' will be slight
ly larger than a(N IN') 1/3, which will contribute to increase
the effective packing fraction and so the viscosity. For non
spherical clusters, however, the hydrodynamic stress is pro
portional to the cube of the larger dimension situated in the
plane of shear; so, for the same number of particles per unit
volume, elongated clusters will contribute much more to the
viscosity than spherical ones. We have calculated a charac
teristic size Le of the clusters by inscribing the centers of the
particles in a rectangle and taking its diagonal. If we com
pare with the same quantity Ls calculated for a cluster of 4 spheres (square arrangement), and for 7 and 19 spheres
(hexagonal packing) we get, respectively, the ratios Lei
Ls = 1.9, 1.65, and 1.4, respectively, showing that, on aver
age, the clusters are elongated and the elongation is more
pronounced for the smaller ones. Furthermore, for a given
number of spheres, this shape ratio is quite insensitive to the
value of the Peelet number. These results clearly show that
for hard-sphere suspensions the shear thickening is associat
ed with the formation of elongated clusters, whereas the
shear thinning is due to the nonlinear behavior of the Brow
nian stress coming directly from the nonlinear deformation
of the local structure.
IV. DISCUSSION
Up to now shear thickening behavior has been observed
for monodisperse systems in the presence of interparticle
forces (often due to a stabilizing double layer). For coated
silica spheres which exhibit a hard-sphere structure, no di
latant behavior has been observed by Van der Werff et al.,3
but the maximum Peclet number (;:::: 102) in these experi
ments is probably too low to observe the shear thickening
predicted here, and there is a need for higher Peclet number
measurements in order to see dilatancy in hard-spheres sus
pensions. (From Table I we see that Pe = 104 is needed be
fore any shear thickening could be detected. )
The effect of a purely repulsive force on the rheology is
given by the interparticle viscosity 1]~, [cf. Eq. (21 b) ] .
There is now a new parameter-the nondimensionalized
force F' and a detailed study of soft-sphere rheology is be
yond the scope of this paper. Nevertheless, we have per
formed one simulation with the Debye-Huckel potential
given by Eq. (24) for several different Peclet numbers in
order to see if we recover the same qualitative behavior as for
hard spheres. The results listed in the last column of Table I
show that this is indeed the case with a minimum at Pe = 102
which is much deeper than for the hard-sphere potential.
This behavior-a decrease of the viscosity at high Peclet
numbers when the range of the repulsive force increases
has been experimentally observed. 25
If we use pairwise hydrodynamics, Eq. (21 b) for the
interparticle viscosity reduces to the form
1]~ = -(27/161T)(tp2/Pe) f r(1-A)f P(r)xylrg(r)dr,
(28)
wherefP (r) is the nondimensional (by kT la) interparticle
force and A is the hydrodynamic function in ( 13). The form
of 1]~ is very similar to that for 1]~ with pairwise hydrodyna
mics, Eq. (25); the only change needed is to replace W( r) by
r( 1 -A )fP (r). One should thus expect that the interparti
cle viscosity should behave in a manner analogous to the
Brownian viscosity, provided that r( 1 -A )fP (r) is of the
same general form as W(r). At large separations [r> K-I in
Eq. (24)] fP falls off rapidly as does W(r). At short dis
tances, however, the form offP (r) will be important in de
termining the viscosity; r(1 -A )fP (r) ;::::2(r -2)fP (r) as
r->2, and, providedfP (r) is less singular than 1/(r -2), 1]~
will behave as 1]~. For the interparticle force used here this is
the case; f P reaches a large, but finite, value as r -> 2, and 1]~
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shear thins as Pe -1 in the large, but not infinite, Peclet num
ber range. Again, as Pe -+ 00 we should see an ultimate decay
as Pe-2 from flow reversibility arguments.
Even if the repulsive interparticle force is singular as
r -+ 2, we can still estimate the asymptotic form of 7J~ for large
Pe. SupposethatfP (r) ;':;;S-a ass = r -2-+0, wherea>O.
As the Peclet number increases, there will be a nearest neigh
bor peak in g(r) formed on the upstream side of the refer
ence particle, i.e., where the shear forces along the compres
sive axis balance the repulsive forces. This balance will occur
when Pe = fP (S); Pe represents the shear force normalized
by kT I a. The peak in g( r) will become very sharp and high,
such that the dominant contribution to 7J~ in Eq. (28) will be
from the region near maximum S m of g( r). Hence, in order
of magnitude Eq. (28) becomes
7J~;.:;;(q;2/Pe)SmfP(Sm). (29)
But,JP (Sm) ;.:;;Pe from the balancing of shear and interpar
ticle forces, and Eq. (29) becomes
7J~;.:;;q;2Sm. (29a)
Finally, assumingfP (S) ;':;;S-a, we have Sm ;.:;;Pe -(I/a), giv
ing
(30)
Thus, regardless of the form of the repulsive interparticle
force, it too shear thins, with an exponent depending on the
nature of the singular form of the force near contact.
Since the interparticle viscosity vanishes in the limit
Pe -+ 00 and since the microstructure approaches that of a
hard-sphere system, we should always see an ultimate shear
thickening of the suspension owing to the formation of elon
gated clusters. The effect of a repulsive interparticle force on
cluster size is very similar to that of Brownian motion shown
in Fig. 2 and Table II. The precise value of the Peclet number
or dimensionless shear rate will, of course, depend on the
particular interparticle force, but the qualitative trends re
main the same. The effect of the repulsive interparticle force
is to delay the formation of the clusters and so the onset of
shear thickening but dilatancy should always be observed
due to the increase of 7J1j, with the viscosity reaching a con
stant asymptote as Pe-+ 00.
Experimental studies of suspensions do not seem to ver
ify this predicted "hydrodynamic" dilatancy. In Brownian
suspensions with repulsive interparticle forces,24 there has
been observed a shear thinning region, followed by shear
thickening, followed by a further region of shear thinning,
but no ultimate shear thickening. Two separate regions of
shear thinning can be explained by the fact that both the
Brownian and interparticle force contributions to the bulk
stress shear thin, and the juxtaposition in dimensionless
shear rate where these two shear thinning mechanisms occur
can produce either one or two regions of shear thinning. The
proper juxtaposition depends, of course, on the detailed
form of the interparticle force and no general statements can
be made.
The lack of any observations of an ultimate shear thick
ening behavior as the shear rate increases could be due sim
ply to the fact that large enough shear rates (or Peclet num
ber) have not been investigated experimentally. In the Brownian suspensions studied here, a Peclet number in ex
cess of 104 is needed in order to observe the shear thickening,
and with the Debye-Huckel repulsive potential an even
higher shear rate is needed. There may be other explana
tions, however, that mask the ultimate shear thickening be
havior, such as the formation of plug flow regions at high
concentrations and shear rates, precluding the treatment of
the suspension as a homogeneously sheared material. The
sensitivity of the hydrodynamic viscosity to cluster forma
tion (the cluster size increases with increasing volume frac
tion27) makes the viscosity particularly sensitive to edge and
boundary effects during an experiment. Further, well de
fined and controlled experiments with the simultaneous
measurement of viscosity and microstructure are needed in
order to answer some of these intriguing questions.
APPENDIX
Stresslet due to Brownian motion
According to Eq. ( 11 ), the Brownian stresslet is defined
by
(AI)
During a time at the Brownian velocity UB (t) will give
a random displacement that is characterized by its two first
moments:
(aXR) = 0 and (aXRaXR> = 2Dat,
and a convective displacement: aXe = V· Dat, where X is
the 6N displacement (rotation-translation) vector and
D = k1RicJ is the 6N X 6N diffusion tensor. These
Brownian displacements can be obtained from the N-parti
cle Fokker-Planck or Smoluchowski equation for the distri
bution function P N (r 1···r N ):
(A2)
where V is the 6N velocity vector coming from the external
flow or interparticle forces.
According to Lax28 and Zwanzig29 the corresponding
Langevin-type equation for the total velocities of the parti
cles can be written as [note that there is a sign error in the
Eq. (23) of Ref. 31]:
(dXldt) = V + a·V·a + a·fR = V + UB, (A3)
where a is the square root of the diffusion tensor, D = a· a + ,
and fR a 6N random force which satisfies:
(f:(t)f:(s» = 2opqo(t -s),
(fR) = o. (A4)
With the expression (A3) for the Brownian velocity (A 1)
becomes:
1 Sodt SB= -- {Rsu·a·V·a+Rsu·a·fR}dt. (AS) at 0
The quantities Rsu . a· V . a and Rsu . a depend on time,
through the change of the positions of the particles in time.
To evaluate Eq. (AS) we use a first-order development for a
quantity A (t):
A [X(t)] =A [X(O)] + (VA)·dX(t),
with from Eq. (A3):
J. Chem. Phys., Vol. 91, No.3, 1 August 1989
Downloaded 29 Aug 2013 to 128.104.46.196. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions1874 G. Bossis and J. F. Brady: Rheology of Brownian suspensions
d X(t) = (V + 0" V ·O')t + 0'(0)' L fR(S)ds.
Thus we have
or using:
_1_ j6.t dtfqR(t)f!(s) = (fqR(t)f!(s» at Jo
1 16.t -- Rsu'O"fRdt=Vp(R~::-O'km)O'pm' at 0 (A7)
Putting Eqs. (A6) and (A7) into Eq. (AS) we get for the
Brownian stress:
Sff = -(Jp (R ~J/O'kmO'pm» ,
or since D = 0"0'+ = kTR;;u\
Sff = -kTJp(R ~J/R k7, 1) (i,j,k,p = 1, ... 6N),
which is Eq. (11). (A8)
IJ. F. Brady and G. Bossis, Annu. Rev. Fluid Mech. 20, III (1988).
2R. J. Phillips, J. F. Brady, and G. Bossis, Phys. Fluids 31,3462 (1988).
3J. C. Van der Werff, C. G. de Kruif, C. Blorn, and J. Mellema, Phys. Rev.
A 39,795 (1989). 4G. Bossis and J. F. Brady, J. Chern. Phys. 87, 5437 (1987).
'G. Bossis, J. F. Brady, and C. Mathis, J. Colloid Interface Sci. 126, 1
(1988).
6G. K. Batchelor, J. Fluid Mech. 41, 419 (1970).
'G. K. Batchelor, J. Fluid Mech. 83, 97 (1977).
8W. B. Russel and A. P. Gast, J. Chern. Phys. 84, 1815 (1986).
9G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 401 (1972).
100. Bedeaux, J. Colloid Interface Sci. 118,80 (1987).
"R. W. O'Brien, J. Fluid Mech. 91, 17 (1979).
12C. W. J. Beenakker, J. Chern. Phys. 85,1581 (1986).
I3J. F. Brady, R. J. Phillips, J. C. Lester, and G. Bossis, J. Fluid Mech. 195,
257 (1988).
140. L. Ermak and J. A. McCammon, J. Chern. Phys. 69, 1352 (1978).
"For a derivation note that the time rate of change in orientation dp/
dt = fl·p + P [E·p -p(p·E·p) 1 wherep = ('> -1)/(,> + 1) is a func
tion of the aspect ratio r of the particle and fl is the vorticity tensor.
I6J. G. Kirkwood and P. L. Auer, J. Chern. Phys. 19, 281 (1951).
I'H. Giesekus, Rheol Acta 2, 50 (1962).
18E. J. Hinch and L. G. Leal, J. Fluid Mech. 52, 683 (1972).
19L. G. Leal and E. J. Hinch, J. Fluid Mech. 55, 745 (1972).
2°H. Brenner, Int. J. Multiphase Flow I, 195 (1974).
2 I Note also that Eq. (29) in Russel and Gast (Ref. 8) is incomplete as they
have neglected an a(Pe) contribution due to the deformation of the po
tential of mean force with shear (cf. discussion in Ref. 5). The errors in
Ref. 8 have recently been corrected in N. J. Wagner and W. B. Russel,
Physica A ISS, 475 (1989).
22See, for example, R. B. Bird, R. C. Armstrong, and O. Hassager, Dynam
icsofPolymeric Liquids (Wiley, New York, 1977), Vol. I, p. 141, as well
as Ref. 18-20.
231. M. Krieger, Adv. Colloid Interface Sci. 3, III (1972).
24R. L. Hoffman, Adv. Colloid Interface Sci. 17, 161 (1982).
2'H. M. Laun, Angew. Makrornol. Chern. 123,335 (1984).
26C. Carnoin, R. Faure, R. Blanc, and J. F. Roussel, Europhys. Lett. 3, 419
(1987).
21J. F. Brady and G. Bossis, J. Fluid Mech. ISS, 105 (1985).
28M. Lax, Rev. Mod. Phys. 38,541 (1966).
29R. Zwanzig, Adv. Chern. Phys. IS, 325 (1969).
J. Chem. Phys., Vol. 91, No.3, 1 August 1989
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1.344264.pdf | The fractal nature of the cluster model dielectric response functions
L. A. Dissado and R. M. Hill
Citation: J. Appl. Phys. 66, 2511 (1989); doi: 10.1063/1.344264
View online: http://dx.doi.org/10.1063/1.344264
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Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsThe fractal nature of the cluster model dielectric response functions
L. A. Dissado and R. M. Hill
Departmeni of Physics, King~~ College London, The Strand, London WC2R 2L5: England
(Received 1 August 1988; accepted for publication 16 May 1989)
Calculable fractal circuit models are used to show that the cluster model response functions
result from the combination of two types ofseIf-similarity. The analysis is extended to the
molecular scale where the cluster model is seen to be based on sequential relaxation processes.
An outline is given of the physical origin for such behavior, and the self-similar processes are
identified with the basic concepts of (i) an efficient (compact) exploration of a fractal lattice
and (ii) self-similarity in the contacts between internally connected regions (clusters). The
relationship of the cluster model parameters nand m to system dimensionalities are derived for
a number of cases.
I. INTRODUCTION
Linear dielectric (and mechanical) response measure
merits are common techniques which have the important
facility of allowing one to follow the regression of spontane
ous structural (dipolar or nonpolar) fluctuationsl over sev
eral decades of time (typically 10 -10_104 s) or, equivalently,
frequency. For this reason the existence offractional power
laws2 in relaxation dynamics has been established unambig
uously and shown to be the ubiquitous pattern of behavior. 3,4
Such a widespread and specific deviation from exponential
ideality5 implies that the fundamental physical principles
governing relaxation have a general form6 different from
that of a completely random process. Over the last decade
the physical basis for the power-law behavior has been the
subject of a great deal ofinterest,6-·17 and it has been pointed
out that despite differences in physical detail all the pro
posed models are based in a hierarchy of self-similar pro
cesses.6,15,17 It has therefore been suggested6,17 that self-simi
larity (fracta! behavior) is a fundamental feature of
relaxation in real materials, However, most models7,8,13.15,16
identify only one region of fractal behavior which crosses
over at long times (low frequencies) to a nonfractal (Euclid
ean) behavior. In the two distinct classes of materials that
can be identified, viz., those which possess bound dipoles
and those that possess potentially mobile charges, these
models predict a crossover to random relaxation processes 1 5
and uniform de transport,16 respectively, It has been ar
gued6,9.1o on the basis of experimental observation1 that the
relaxation of bound dipolar systems involves a crossover to a
different form of self-similarity at long times. A similar be
havior has also been found to occur when mobile charges
face irregular interruptions of their transport paths, 17,IR This
identification of two different fractal regions in the observed
dielectric relaxation is strengthened by its analytical deriva
tion for a simple deterministic fractal circuit model, 19 It is
the intention here to demonstrate the equivalence of the
theoretical response functions previously derived9.18,2o to
those of a deterministic fractal circuit, 19 and thereby identify
the basic factors leading to the observed behavior. These
basic requirements are found to be the existence of two inter
woven forms of self-similarity, one of which dominates the
response at high frequencies and the other at low frequen
cies. In a further development the theoretical functions wiil be shown to be equivalent in detail to more general fractal
systems than that of the deterministic fractal circuit. Here
the response originates with specific regions of the dielectric
containing dipoles (or ions) whose position can be altered by
an electric field. The lack of ideal (or close) molecular pack
ing that allows such rearrangements yields a structural flexi
bility which extends over a "defect" region or duster con
taining both dipoles (ions) and their local environment. 9
One form of self-similarity therefore corresponds to the in
ternal dynamics of these regions.6 Since the ;egions are limit
ed in spatial extent any sample of the material will contain
macroscopic quantities of the same type of defect. Thus the
second form of self-similarity refers to the way in which the
response of the macroscopic system is built UP from its re
gional (cluster) components.6 These two seif-simiIar re
gimes are a natural consequence of systems composed of
interwoven regional groups rather than site dipoles. Our ul
timate aim is to establish the physical origins for the two
fractal regimes of relaxation and to open discussion on the
values of the power-law exponents, so that the information
inherently available from response measurements may be
correctly interpreted and understood.
II. CLUSTER MODEL RESPONSE FUNCTIONS
Two distinct classes of dielectric response have been
identified from the cluster model, 9.1~,20 namely that of bound
dipoles6,9,lo,2o and that of potentially mobile charges,18 In
both cases the response functions that have been derived
have been shown to give excellent agreement with experi
mental data.9.lO,18 That of the former (bound dipole) class
has also been compared with a variety of empirical functions
which have been proposed as descriptions of dielectric relax
ation, and it has been shown that where significant differ
ences between theoretical and empirical functions occur the
former gives a substantially better description of experimen
tal data. 10,2 1 In this section we shall quote the pertinent re
sponse functions of the cluster model and outline its basic
construction. The reader is referred to the original pa
pers9,10.18 for further details,
A. Bound dipole case
Here the complex susceptibility (X) is defined in terms
of the Gaussian hypergeometric function 2FJ (,;;) as9•20
2511 J. AppL Phys. 66 (6), 15 September 1989 0021-8979/89/182511-14$02.40 @ 1989 American Institute of PhYSics 2511
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsx(m) = x'(m) -iX" (m)
= X(O){(1 + im/{i)p Y-!
X 2Fl (1 -n,l -m;2 -n;(l + iM/Mp) ~-I]}
= lim (00 e-;,ote-Et¢;(t)dt, (1)
<,-.0 Jo
with the response function 4>(t) determined by the conflu
ent hypergeometric function IF] (;;) as9,10,20
<I>(t)/<I>(O) = (Nt) --"(mpt) --n exp( -(upt)
and X IF] (1 -m;2 -n;(upt)
=(Ns)-n(up l""[ny)t]-n
Xexp[ -rcy)t Jy g(y)dy
r(y) = wp [yllntj(l + ylfm) L
yu-m)/m I d [r(Y)/Mp11'
g~)= =1 . m( 1 + yllm)2 dy (2a)
(2b)
(3)
(4)
In deriving these expressions it is considered that a per
turbation has been applied to the system at zero time which
consists of a number of structural displacements equivalent
to local dipoles. The initially independent dipole motions in
an undisplaced environment evolve into motions correlated
over progressively larger numbers of environmental and di
pole sites22 ( 0: t) with a correlation index n (0 < n < 1) such
that the contribution per site to the dipolar displacement is
proportional to t ~-n. These correlated groups are termed
clusters and contain a characteristic number Nt; of sites at
the characteristic time (w p) -\ for relaxation of a local di
pole in its instantaneous environment, with (Nt;)~ n in Eq.
(2) being the fractional dipole contribution per site in the
characteristic cluster and <P(O) the site contribution in the
absence of correlated displacements.
The asymptotic limits of the index n are such that n = 0
defines a system in which the local dipoles remain indepen
dent during relaxation whereas n = 1 refers to displace
ments which become funy correlated, somewhat like an
overdamped normal mode.
This coherent period of evolution is interrupted by inco
herent events initiated at random which fragmcnt/aggre
gate23 the growing cluster either by correlating some portion
orits sites with another such cluster, i.e., interc!uster trans
fers, or by disconnecting them to form new clusters. These
events cause an originally uniform cluster array to evolve
into an ensemble characterized by the stationary distribu
tion density g(y). The rearrangements involved in this reor
ganization propagate through the system with a correlation
indexed by m (0 < m < 1). Here the asymptotic limits are
such that zero corresponds to isolated identical fragmenta
tion events which leaves the distribution as an array ofiden
tical clusters. At the other extreme a value of unity corre
sponds to an ideally connected sequence of fragmentation
events leading to an exponential distribution of decreasing
cluster sizes.
The response function <P(t), in the form ofEq. (2b), is
defined as the average of the contribution per site weighted
2512 J. AppL Phys., Vol. 66, No.6, 15 September 1989 2 3 4 5 6
tal log [frequency] ( Hz)
'3
~
en .:l -1 • 0
,,"00
• 0
-4 -3 -2 -1
ibl Log [frequency J (Hzj
FIG. 1. Dielectric response data showing loss peak behavior. Ca) The a
dielectric response of the nematic fOim of OHMBBA (see Ref. 10) the
original data measured by lohari (see Ref. 47). The normalized data of the
real and imaginary components of the susceptibility are indicated by the
points. The continuous curves have been obtained from the cluster model
response function with m =, 0.85 and n = 0.61. For comparison the Kohl
rIlusch response function, which is indicated by the dashed curves, has been
fitted to the high-frequency CPA region and the zero-frequency real magni
tude. (b) The diclectric response of poly (vinyl acetate) from the measure
ments of Johnson et al. (sec Ref. 48). The original data is given as the con
tinuous curves as it was obtained by transformation from the time decay.
The cluster model response, with m = 0.79 and n = 0.56, is indicated by the
open circles and the Kohlrausch response by the crosses.
by the fractional probability that a site is part of a given
cluster (index y) in the instantaneous ensemble.1O Earlier
work'l,20 derived <P(t), equivalently, as the average at time t
of the relaxations that result from all possible rearrange
ments initiated during the period of observation t.
On the basis of this model the susceptibility function
exhibits a peak in the loss component X" (w) with power
laws as the high-and low-frequency limits
X'({i) ccX"((v) o:w" -1, m>{i)p'
X" (w) 0: X' (0) -X' (w) cc (urn, 0) <wp' (5)
The extent to which the theoretical function describes ex
perimental data is illustrated in Fig. 1. The best fit ofthe data
to the Fourier transformation of the Kohlrausch decay func
tion,
d\ll(t) d{ [ I-n]} -<I>(t) = ---= -exp -(cupf) , dt dt (6)
predicted by a number of models13•15 is also shown in this
figure for comparison. It can be seen that whereas the two
expressions agree in the high-frequency limit where the pow
er laws are derived as a result of self-similar processes,b only
the cluster model predicts the second power-law regime
which is observed at low frequencies. This discrepancy has
been found to occur in all cases of dielectric response where
deviations between the two functions can be detected. 10,21,24
L. A. Dissado and R. M_ Hill 2512
I Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsSo Potentially mobile charges
Systems containing mobile charges are potentially capa
ble of supporting a bulk de current even although this may be
blocked by electrode interface effects.2~ However, when the
coherent displacement of charge was constrained to finite
sized clusters (e.g., as in adsorbates or pore systems) rather
than extended over the whole system in conduction bands, it
was recognized that the duster model predicted a different
class of behavior. IS This class is characterized by a current
response to a step-up/step-down in field which decays con
tinuously at long times as t I -m (0 < m < 1) and is thus cor
rectly termed a dielectric response. Such weakly decaying
currents can be difficult to observe in time domain experi
ments but are much easier to identify in the frequency do
main where the susceptibility formally diverges as a power
law w -m at a low frequencies. An example given in Fig. 2
shows experimental data together with the theoretical SIlS
ceptibility function derived from the cluster model III for this
process, termed quasi-de (q-dc) transport by the authors.
In this case
X(w) =X(wc){O +iwlw,,)n-I
X2F1 (1-n,l + m;2 -n;(1 + iwlCclc )"-1 n,
(7)
for which the high-and low-frequency limits
X'(w) <xX"(w) CXW,,·l, UJ>(})c. (8a)
(8b) X' (w) <X X" (liJ) <X (J). m, (I) < We
are illustrated in Fig. 2. The corresponding response func
tion is given by
<t»(t)I<P(O) = (Nt) -"(wet) -n exp( -wet)
(9a)
roo
=(Nr;)--"(UcJ [r(z)tj-n
o
xexp[ -r(z)t )Z-I g(z)dz. (9b)
Expression (9b) is derived from the published function 18 in
Appendix A and
r(z) = [<dztlml(1 +zum)J, (10)
while g( z) is the samefunction (of z) as expression (4).
Some fractal features of this form of response have been
discussed previously in Ref. 17 where it was termed anoma
lous low-frequency dispersion" (ALFD) and index m was
denoted by p in order to distinguish it from that of class (a)
as was done in other earlier works.18,25 The cluster model
from which expression (7) is derived has been given here in
very general terms, which can be expected to encompass sev
eral of these features. Its physical description is simplest
from the point of view of a continuous polarization by an Olc
field. At high frequencies (W> We) potentially mobile
charges correlate their individual displacements to generate
a coherent charge displacement, with the number of sites
involved increasing with the period (w -I). Thus, although
the displacement contribution per site varies as ((u -11 -n,
where n is a correlation index (0 < n < 1) as before, this must
be multiplied by the number of sites coherently connected to
give the displacement (polarization) per charge as propor-
2513 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 -3
u-
-5
'3
u -7
0'1
0 --l
-9 t
-2 0 2 4
Log [frequency] {Hz}
FIG. 2. Dielectric response data exhibiting mobile charge behavior. Experi
mental data for the dielectri.c response of a leaf from the plant Nicotiana
Solanceae (see Ref. 49) measured with the electric field perpendicular to
the jeaf surface, The continuous curves show the fitted cluster model re
sponse function ofEq. (7) for potentially mobile charges with m = 0.985,
n = 0,80, we = 9X 102 Hz, and C(w, ) = 6.5x 10-1 F. This example has
been chosen as it shows the form of the response in isolation from other
parallel or series components unlike most other case.s (see Ref, 18 and 49).
tional to w" --I. Here the limit of zero for n corresponds to
independent mobile charges (i.e., a de current) and that of
unity to rigidly displacing groups. At the frequency We the
groups (clusters) are correlated to their characteristic ex
tent and contain a number Nr; of sites, with the displacement
per site a fraction (Nr; ) -n of that in the uncorreiated system.
When W < We' incoherent transfers of charges between clus
ters fragment the clusters and allow charge separation to
occur over ranges greater than the characteristic coherence
length. Here, as before, the index m (0 < m < 1) defines the
degree of correlation between the intercluster transfers that
transport the charge through the system. Thus a value of
unity for m corresponds to an ideally correlated sequence of
incoherent transfers and a de current, whereas a value of
zero describes a system in which the polarized clusters can
not be connected by transfers and remain identical.
The equivalent relaxation current, defined by ~(t), fol
lows a path in which at first a progressively larger number of
displaceable charges ( 0::: t) are coherently coupled such that
the displacement per charge site is proportional to t _ .. n. This
is followed by charge recombination which starts at a time
(t)c-I and as the system proceeds to equilibrium involves an
increasing number ofpartialiy correlated interduster trans
fers in sequence, Here the mobile charge can be considered to
have coherently polarized a cluster of characteristic coher
ence size prior to being incoherently transported to a recom
bination site with further polarization of all intervening clus~
ters on the transport path. IS
lit DIELECTRIC RESPONSE AND DETERMiNISTIC
FRACTAL CIRCUITS
Regular (deterministic) fractal circuits are currently at
tracting interest for a variety of reasons. Firstly, and perhaps
most importantly, they are exactly solvable so that basic con
cepts can be directly examined. 16 Secondly, they can serve as
idealized models for percolation systems26,27 and hierarchi-
LA Dissado and R. M. Hill 2513
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionscal memories,28 whilst also providing a simple explanation
for the well-known appearance of constant phase angle re
sponses at insulation/electrode interfaces. 16.29.30
Most circuit models consider only one type of hierarchy
and thus give a single constant phase angle element in the
response (where appropriate26•27). However, the porous
electrode model of Sapovapo shows how two different kinds
of self-similar hierarchy can be combined to give responses
with the forml'} of the two classes described in Sec. It We
have, therefore, chosen this model to illustrate the fractal
composition of dielectric response and demonstrate the
equivalent features of the duster model.
Ao The Sierpinski carpet electrode
This model system,30 an example of which is shown in
Fig. 3, consists of a conducting block oflength L and side ao
through which electrolyte-containing square cylindrical
pore channels run, and which is separated from planar coun
terelectrodes by thin electrolyte layers. The fractal nature of
the model is expressed by the pore cross-section pattern and
is defined by the number ratio N and size ratio a between
pores of successively smaller size, i.e.,
N= Nq+1/Nq,
a=aq/a q+j,
where there are Nq pores of side aq
from the size of the block. 01a)
( llb)
each reduced q times
In this version of the model each pore acts as a transmis
sion line coupled to the electrode via the wall capacitance
(Fig. 4). The total capacitance of the system is thus
C(X)=CoX-1/2i NQ-la-3QI2tanh[(xaq)1I2L (12)
q ~-I
where Co is determined from the surface capacitance per unit
area 6. as
Co= 46.a{~,
and x is the normalized frequency
x = iw/o)o'
with
(UO = Go/Cb.pL 2),
and p is the electrolyte resistivity. (13)
(14a)
( 14b)
The asymptotic behavior ofEq. (12) can be obtained by
rescaling x, giving a recursion relationship for C(x);
C(x/a) = CoX--I12 I Nq -Ian -3q)/2 tanh [ (xaq--1)1/2j
q~-l
(15a)
= C(x)Na--1 + Coa--1x--1/2 tanh(x1/2). (1Sb)
The last term in Eq. (ISb) dominates when w> Wo and the
system exhibits a one-dimensional (1D) diffusion appropri
ate to the electrolyte within individual pore channels, 16 with
C(x)-Coa-l(ax)-1/2, (U>(UO° (16)
However, when w < mo/ a, expression (15b) reduces to
C(x/a)~C(x)Na-l+Coa-1, w<(f)oIa, (17)
and the frequency dependence is now controlled by the
2514 Jo Appl. Phys., Vol. 66, No.6, 15 September 1969 FIG. 30 Examples of Sierpinski carpet electrodes. (a) The carpet electrode
is shown displaced from its position in the complete cell for clarity. The cell
has two electrically paralleled counterelectrodes. The fractal cross-section
al arrangement here has N ,= 5 and a = 3, giving a surface dimensionality of
d, = 104650 (b) A carpet electrode with N = 2 and a = 3 giving a surface
dimensionality of 0.631. In the particular configuration shown here it is
clear that the dimensionality would be expected to lie below unity.
cross-sectional geometry ofthe pore system, with successive
ly smaner pores contributing in fun to the capacitance as the
frequency w drops below the inverse time constant of their
particular circuit, i.e., Wq = a,/(b.pL 2).
Two different types of solution to the low-frequency re-
FIG. 4. Schematic representation of a discrete component transmission line
with all resistive and capacitive elements being of equal value and giving a
response equivalent to classical diffusion.
L. A. Dissado and R. M. Hill 2514
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(a)
o
...-.-2
LJC) ~I __ ~~ __ ~~ __ ~! __ -b __ ~~ __ ~~
" -5 0 5 -3 -u
(b)
-2
FIG. 5. Computed responses for Sierpinski carpet electrodes. In each case
20 self-similar embeddings were used in the computations. (a) The low
frequency divergent response for N = 5 and a = 3 giving d, = 1.465 and a
low-frequency exponent m of 0.465 [cf. Fig. (3a)]. (b) The convergent
response, exhibiting Ii peak in the loss component, for N = 4, a = 8 with
d, = 0.6666, and a low-freque!lcy power-law exponent m = 0.333).
lationship, Eq. (17), exist depending on whether N /a is less
than or greater than unity. 19 In the former case the total pore
perimeter and hence the capacitance converges as all the
pores contribute with x approaching zero, and the solution
takes the form
C(x) = Co(a -N) -IA Ix", x < 1, (18)
with v related to the surface dimensionality of the pore sys
tem ds' which is defined by
o <ds = !n(N)/ln(a) < 1
through
v= 1-d .. (l9a)
(20)
This solution, a computed example of which is shown in Fig.
5, exhibits a loss peak with the same form as the bound dipole
response of Sec. II A. In particular, the low-frequency de
pendence of the loss component, C II ((j) a: X" (w), has the
power-law form (.urn (with m = Ivl) rather than the contin
ually varying behavior of the Kohlrausch function in the
same frequency region.
On the other hand, when N / a is greater than unity the
constant term in Eq. ( 17) becomes irrelevant and the capaci
tance (perimeter) diverges as x approaches zero. In this case
the solution takes the form
C(x)=Ax-1vl, x<l, (21)
where again v is related to ds through Eq. (20). Here, how
ever,
1 <ds = In(N)/ln(a) <2, ( 19b)
where the upper bound results from the requirement that the
2515 J. Appl. Phys., Vol. 66, No.6, i5 September 1989 pore cross-sectional area must converge. Thus this class of
solutions have the same form as that of the quasi-mobile
charge response of Sec. II B, and a computed example is
given in Fig. 5. Here the low-frequency capacitance
C' (ill) 0:.. X' (ill), and the loss component diverge as (j) -m with
m = Ivj = 11 -ds i. (22)
It must, however, be realized that the power-law divergence
is an expression of the self-similarit y31 of the system to
successive rescalings by the factor a and wiH be truncated in
real systems at the large and small limits where the self
similarity changes or fails. In the present model the cross
over to diffusion behavior «(u-1(2) corresponds to trunca
tion at the largest pore, whilst a saturation in capacitance
would occur at the smallest pore size, which could not be less
than a molecular diameter or unit cell in real systems. Thus a
constant phase angle response requires no greater range of
relaxing "subcircuits" (or time constants) than the self
similarity of the system is capable of supporting.
Unlike the cluster model of Sec. II the electrode model
in its present form is restricted to an exponent n of 0.5 in the
high-frequency region by the transmission line response of
individual pores. This restriction can, however, be lifted if
the pores themselves are considered to have a fractal geome
try in the bulk of the electrode. Two model systems which
may be adopted for this purpose have been considered by
Liu.16•32 In one case each pore can be thought to ferm a
conducting frame having the geometry of a Sierpinski gasket
capacitively connected to the electrode block at each gasket
junction. Electrically the system is a generalization of the
transmission line circuit with the equal resistances and capa
citances replaced by self-similar units as indicated in Fig. 6.
Such a model may be realized physically if the pores are
formed as a multiply connected conducting system such as a
percolation cluster. Alternatively we may consider the pores
as forming a self-similar branched tree,16.29 reducing in
width at each branching. Again the electrolyte in the pore
system is capacitively connected to the walls and the trans
mission line is converted to the circuit description of Fig. 7.
Both these pore systems exhibit the required form of
response. A resistance-capacitance series response arises
from either the sections of the Sierpinski gasket or the largest
cross-sectional pore branch at frequencies ill in excess of
(C,R,.) -I, where Rs is the sectional (largest pore branch)
resistance and Cs its wall capacitance. When (I) < (C,R,) --I
a constant phase angle (CPA) behavior C( (j)) a: (i(j)) n -lOC_
curs as the self-similar circuits of the pore system come into
play. Here16•32
n = 1 -~ d/(O + 2), (23)
where df is the dimensionality of the fractal structure, and
(} + 2 that of a random walk on the fractal defined by the
radial distance R to time relationship
(24)
In the branched pore system e = -1 and Eq. (23) reduces
to
n = 1 -df = 1 -In(Nb ) 11n (/3) = 3 -Dp, (25)
where N h is the number of new branches and f3 -1 the ratio of
L. A. Dissado and R. M. Hill 2515
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FIG. 6. Development of a scaled transmission line response from a Sier
pinski gasket in which the gasket elements are resistances and each junction
oftwoedges has a capacitanceoq C to aground plane. (After Ref. 32.) (a)
One section of a gasket with A and the other two equivalent vertices at a
common potential. (b) The development from the structure in (a) to the
transmission line shown in (c) by means of delta/star transformations. The
symbols G, b, c, d, etc., are used to indicate equivalent sections but as no
current passes through these vertices they play no part in the extended trans
mission line.
Po = (3/R) + hoC;
Q _ 2i(liC( 1 + hoRC) (3 -.\-iwRC) .
0-- 3 + 2iwRC '
Pp + I = PI' (3Pp + 2Qp )/(5P" + 2Q,,);
Qp+! = Qp{3Pp + 2Qp)IPp' P> -1.
pore widths (cross-sectional areas) at successive branchings
(/3> Nb ). D p is the dimensionality of the internal pore sur
face.
In the finite-sized geometry of the present model the
CPA region is truncated at low frequencies when the system
responds as a whole by a constant capacitance Cp represent
ing the effective wall capacitance of the whole pore. For a
constant length (fixed number of self-similar embeddings)
pore system, the terminal capacitance and the frequency at
which saturation occurs will both be proportional to the side
a p of the pore cross-section at the surface, just as with Eqs_
(13) and (14b), i.e.,
Cp = Aap./,(L), (26a)
wp = (CpRp)-l = ap(ilp)"-lg(L), (26b)
wheref(L) and g(L) are functions of the (constant) length.
Therefore, these generalized pore systems can be arranged
such that their cross sections on the outer surface form a
fractal system as before. leading to a second constant phase
angle as low frequencies the exponent for which is dependent
upon the fractal dimension of the surface through Eqs. (20)
and (21). The appearance of two CPA regions can thus be
seen to be due in this model to two different kinds of self
similarity, that is, one which relates the longitudinal pore
system to the size of the input pore entering the surface and
effective at high frequencies, and a second which relates the
surface cross-sections of the pores to that of the largest pore,
and effective at low frequencies.
2516 J. Appl. Phys., Vol. 66, No, 6, 15 September 1989 (b)
FIG. 7, Self-similar branched porous electrode system shown in cross sec
tion in (a) can be given a circuit description as ill (b) by associating the
electrolyte in the pores with a resistive path that is capacitively coupled to
the walls of the pores.
B. Relationship between the carpet electrode and
cluster models
Although both forms of self-similarity involved in the
model of Sec. III A are geometrically regular it has been
shown that the features of the branched pore system are re
tained if randomness is introduced29 into the branching ratio
l¥~? and scaling ratio /3, and we can probably expect the same
to be true for the surface structure as long as self-similarity is
retained as an average property. In this way these models can
be forced towards the more stochastic picture of the cluster
model, and here we shall identify the equivalence between
them.
L, A, Dissado and R. M, Hill 2516
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsFirst let us look at the high-frequency region, (0 > Wp (or
we). Here the effective contribution to the susceptibility in
Eq. (1) originates from <P(t) in the range O<t<o)p- I (or
w,:" 1). Since r(y)/wp<l [r(z)/wc<l] for aHy(z), the ex
ponentialfactor of <I> (t) in Eqs. (2b) and (9b) can be taken
to be unity, and the response is governed by the time power
law, giving
¢Ua) 2:a -n«p(t) 0:: (fa) -n
and the CPA behavior (27a)
X(u;/a) 2:a1 ". "X(w) cc (w/a) n -1, (27b}
independent of the form of the functiong(). Thus the region
of the cluster model in which the site motions become dy
namically connected within a cluster corresponds to the de
velopment of self-similar subcircuits within individual frac
tal pores. Using Eqs. (23) and (24), the site contribution at
time t, proportional to [r ( ) t) -", can be related to the flum
ber of sites visited per step in a random walk on a fractal, 16.32
i.e.,
(28)
Thus the dynamically connected duster moti.ons can be
thought of as the result of a random walk of an interaction
perturbation on a fractal lattice.33
The fuU relaxation of individual clusters occurs in the
frequency range w <Wp (We) and here the response is gov
erned by the form ofthe distributiong(x) dx (wi.th x = y,z)
. just as in the electrode model it is determined by the self
similarity of the pore cross sections. Here the cluster expres
sions can be converted into equations with the form of Eq.
( 17) by using the approximations
g(x) :;;,;x( 11m) .. 1, O<X< 1,
g(X)~X .(lIm)-1, 1<.x<00, (2Ba)
(2gb)
and dividing the integrals over y(z) into the two ranges 0-1
and 1-00. In this way only the o~ I range was found to
make any substantial contribution to the scaling relationship
at frequencies less than (up (wc). For the bound dipole case
the resu.lt is
(29)
where X 0 is a frequency dependent function rapidly ap
proaching a constant value for (() < wP' and given by
xyd(yllm)dto (30)
A comparison with Eq. (17) identifies
N / a = a· m and 1 > m = 1 -ds > 0 (31 )
as previously, and Xo with the "static" contribution of the
largest pore. The integral over yin (30) arises because ofthe
continuum nature of the duster model as compared to the
discrete format of the electrode model. The form of the
equivalence between the two cases can be identified by tak
ing the ratio of the effective relaxation frequencies and am
plitudes for the lower (l) and upper (u) bounds of the inte-
2517 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 gral. Thus
((Jpayjlm yjlm
and W a"I/m p :J'u. =--=- (32a)
y1lyu = a-m, (32b)
w hieh are the ratios expected if a single reduction of scale in
the discrete model is replaced by a continuum. The integral
over yin Eq. (2b) is therefore the continuum equivalent in
the range O<y< 1 of the discrete pore electrode model with y
representing the amplitude contribution ( 0: Nqaq) at a giv
en scale (q), wpylim representing the relaxation frequency
( ex: aq) at that scale, and the increment g(y)dy (equal to
d[ r(y)/wp J) representing the incremental change in relax
ation frequency, i.e., providing the frequency mesh for the
response function. The continuation of the integral from
y = 1 to the lower bound of zero describes the infinite em
bedding of the fractal surface system which though unphysi
cal will not cause difficulties because the susceptibility con
verges giving a power -Ia w dependence, and Eq. (18) will be
obeyed over the range of self-similarity.
The quasi-mobile charge case is different onty in that the
susceptibility diverges and we obtain
x(w/a) = a"'x«(v) + Xc,
with
Xc = «PoN 5 nwc i"" e"-;,," iZ_~aI_ m a exp( -wcazllmt)
Here
am=N/a (33)
(34)
(35)
and m is given by Eq. (22) as in the appropriate case of the
electrode model. The relaxation frequency (wczum) in this
case behaves in the same way as that in the bound dipole
model, Eq. (32a), and approaches zero as the scale size (aq )
approaches zero. However, the amplitude factor ( a: Nqoq)
in the continuum expression (9b) diverges as the relaxation
frequency ((UcZllm ex Oq) approaches zero, and is represented
by Z -I in the integral over z.
The analysis presented in this section has shown that the
cluster model expressions (2b) and (9b) can be regarded as
equivalent continuum forms of the discrete pore electrode
model. The dusters are to be taken as the internally self
similar pores and the instantaneous cluster distribution g(x)
X dx in the range O<x < 1 defines the fractal arrangement of
the pore (cluster) cross section. However, this only accounts
for a part of the cluster distribution. The other part of the
distribution with y(z) in the range 1 <y(z) < 00 corresponds
to relaxation frequencies in the range wp (we) to wp/2
«(oj2) and we would expect it to influence the shape of the
response in the region of the crossover between the two pow
er-law regions and, as we have shown, to have negligible
effect on the asymptotic frequency dependencies. In terms of
the interpretation of the cluster model as a continuum equiv
alent of the electrode mode! ofthis section, this portion of the
distribution corresponds to aggregated clusters (i.e., pores
with aggregated cross sections). This possibility does not
L, A. Dissado and R. M. Hill 2517
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsexist for the deterministic geometry of the discrete pore elec
trode model and thus we find discrepancies between its cal
culated response functions and those of the cluster model in
the crossover (peak) regions even though they have identi
cal form in the high-and low-frequency limits, Therefore,
although the combined self-similarities of the deterministic
(discrete) fractal electrode model may contain many of the
features of the cluster model, in particular the existence of
two power-law regions, the full range of structural fluctu
ations contained in the dynamics ofthe cluster model are not
allowed for.
IV. A MOLECULAR SCALE FRACTAL
INTERPRETATION OF THE CLUSTER MODEL
Since an ideal circuit comprised of an ideal capacitor
and resistor in series combination relaxes exponentially in
time, it is often used as a representation of an independently
relaxing dipole. Thus the circuit model of the previous sec
tion can be related to molecular systems by identifying the
smallest (irreducible) series subcircuit as individual re
sponding dipoles. Electrical combination of molecular di
poles, so defined, give larger-scale subdrcuits and a CPA
(power-law) response when scale self-similarity is pre
served. In these terms the high-frequency CPA response
originates with the self-similar connection of dipoles within
finite regions (clusters), each of which possess a specific
relaxation frequency.9.10 Self-similarity in the factors gov
erning the cluster relaxation frequency then leads to the low
frequency power-law response." These last two statements
define the basic framework for the fractal interpretation of
dielectric response via the cluster model, and when applied
to molecular (ionic) systems requires us to abandon the con
cept of independent dipoles in favor of connected motions
within the duster. Such dynamic behavior will have a gen
eric relationship with lattice and molecular vibrational
modes and the cluster model has been shown previously9,10
to extend naturally into this region without the disadvan
tages of divergence or lack of time symmetry appropriate to
arbitrarily introduced power-law (t -n) and exponential de
cays.
Fractal circuit models can be expected to most closely
resemble self-similar heterogeneous materials. In principle,
the properties of the ideal subcomponents can be measured
and it is analytically simple to relate amplitude and time
scale to the subcomponent size. However, molecular sys
tems13•15 do not have such an obvious general formalism,
and the subsequent sections will be denoted to examining the
cluster model in this context. Particular attention will be
paid to the self-similarity of the cluster relaxation frequen
cies since this originates from a parallel arrangement in the
circuit models of Sec. III, whereas it is much more likely to
be serial in bulk molecular systems.9.D
A. Bound dipole systems
Here we seek a fractal interpretation of the cluster mod
el sufficiently general to be capable of application to the
widespread systems and relaxation mechanisms9 whose re
sponse the model is known to reproduce. 9, to Mechanistic
2518 J. Appl. Phys., Vol. 66, No.6. 15 September 1989 and system details are expected to determine the values of
the parameters <Po, (J)p, Nt;, n, and m.
Turning to the defining expression of the cluster model,
expression (2b), we first identify the contribution per site
from a duster y at time t as
[N(y,t)] -n = [Nt;r(y)t J -ny, (36)
and the cluster relaxation frequency as ny), with Eq. (4)
relating wp g(y)dy to the frequency mesh d[r(y)]. These
relationships correspond to those determined in Sec. Ill.
Equation (36) shows that the number of dipolar sites N(y,t)
forming a cluster increase until it reaches N(y)
(37)
when r(y)t is unity. At iimes beyond this value further in
crease in the number of sites is cut off by the exponential
decay, which has been shownlO to replace the t -n behavior
which ceases at the time [r(y)] --'. During the period of
power-law decay the contribution [to <P (t)] for the com
plete cluster y is
[N(y,t)] I -n, (38)
and the power law reflects the self-similarity of the cluster at
different stages of its development, i.e., the cluster at time 2t
is isomorphic with that at time t, if the number of sites at 2tis
measured in units of twice the size used at t. Remembering
that the response originates with dipolar (vector) displace
ments of molecular dipoles or ions a pictorial representation
of this process can be obtained if we regard the site displace
ments to form a dynamic connection along a convoluted
path in space.9 In this case the contribution from N sites will
vary as N f with 0 <I < 1, since the largest contribution will
occur when each site is free to contribute additively (f = I)
and the smallest when the sites are "locked" into a fixed
contribution if = 0). Here
n=l-J, (39)
and we may recover a form for n similar to that of Eq. (23)
by taking the convoluted path of the contribution to be a
"chemical" or "minimum" path34 with fractal dimensionali
ty de. Progressive connection in such a system wiU also in
clude pendant groupings which do not contribute to the
overall "chemical path contribution" so that the dimension
ality of the whole system df> de' The "contribution path"
length is therefore given in terms of the total number of sites
N, as
(40)
and hence
n=l-dc/dr,
which has the sense ofEq, (23), i.e., that of an inefficient use
of the fractaHy arranged contributors. Such a picture would
be equally applicable to dipoles which on displacing between
potential minima influence the potential surface on which
neighboring dipoles move9,22 (e.g., in polymers and dipolar
solids), as to nominally free rotating dipoles in a liquid
whose motions connect to displace the tip of a joint dipole
around the surface of a sphere. Appendix B outlines the way
in which this region of relaxation can be related to the evolu
tion of configuration entropy.
L. A. Dissado and R. M. Hill 2518
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsThe low-frequency power-law region of the cluster
model originates from the self-similarity of the cluster relax
ation frequencies which in this case are related to their self
consistent cluster size via
[r(y)] -1 = CWp)-l(l +y-lim)
= ((Vp)--l{l + [N(y)/N,;-r1m}. (41a)
By remembering that N" is the number of connected sites
required to give a unit dipole contribution in a cluster of size
N, Eq. (41a) can be rewritten as
(4lb)
whereM(y) {= [N(y)INs-r}isthenumberofcharacteris
tic unit dipole groups (with N'; sites) contained within the
unit dipole group of the cluster {with [N(y)] n sites}.
Equation (4 I b) describes relaxation as a sequential (se
ries) process in contrast to the "parallel" arrangement of
Sec. Ill, When isolated [N(y)/N,;- ..... 0] the representative
site possesses a relaxation time (wp) ~ 1, however, connec
tion to other sites increasing N(y) causes it to experience an
increasing number M(y) 11m of nonconnected contacts
necessitating sequential relaxation of the contacted dipoles.
The extent of the characteristic cluster is defined through
Eq. (41h) as the duster for which an unit-dipole groupings
are in nonconnected contact with another such group. Con
versely it is possible that the characteristic cluster size deter
mines the frequency (wp/2) below which relaxation in
volves other clusters sequentially, as in ferroe1ectrics.35
A general picture of relaxation can now be built up in
which a progressive connection of dipole displacements
forming a "chemical path" is interrupted dynamically by
nonconnected contacts such as sterk hindrances, structural
strains, and order defects,15 or brownian motion leading to
an instantaneous distribution of dusters. Near individual di
poles relax by the time (w p ) --I, acting as the first stage in .the
sequential relaxation oflarger connected groups, By the time
2 (Wp) --1 two stages of the sequence have been completed,
relaxing aU self-similar fragments up to clusters of the char
acteristic size. At longer times the sequence still extends to
the complete relaxation of larger connected regions (i,e.,
self-similar aggregates of the characteristic cluster). This
picture of relaxation is very close in form to the serial relaxa
tion of constraints proposed by Palmer et al. 13 as a model for
the a response (rubbery/viscoelastic phase) of glass-form
ing materials, from which, however, it differs in giving the
low-frequency power-law behavior when combined with the
connection process, rather than being the origin of the high
frequency CPA behavior.
A comparison with Sec. III shows that it is the conver
gence of the contribution amplitude ( a: y) as y approaches
zero and N(y) infinity, together with the power-law depen
dence of r(y) upon y that gives the low-frequency power
la w behavior. However, here Eq. (41 a) shows that the self
similarity in [r (y) ]-I extends throughout the range from
self-similar fragments of the characteristic cluster to formal
ly infinite aggregates [of zero weight in the integral in Eq.
(2b)]. This self-similarity is expressed through the power
law dependence of the number of sequential relaxation
2519 J. Appl. Phys., Vol. 66. No.6, 15 September 1989 stages M, (y) upon M(y), i,e.,
[M,(y)Jm = M(y). (42)
Here M(y) measures the dipole group of cluster y in units of
the characteristic dipole group [(Ns) n], and Eq. (42) ex
presses the geometry of the group on this scale in terms ofthe
number of "contacts" forcing sequential relaxations. A di
mensional interpretation for m can be obtained if the dipole
group [N(y)]" is considered to be composed of (Ng)" sized
"segments" joined together at contact nodes. In this case a
value of unity for m corresponds to a linear (one-dimension
al) arrangemeni of characteristic segments, while smaller
values anow for branching and loops of mUltiple contacts.
Use of Eqs. (42) and (3) shows that a value of m identically
equal to zero only allows for clusters of size Nt with all
subcharacteristic fragments relaxing freely at a frequency (up
while any duster aggregates require an infinite time for re
laxation. Thus here the number of contacts changes discon
tinuously from zero within the characteristic cluster to infin
ity at the characteristic cluster boundary. The system is
therefore one of internally deformable clusters with infiexi
ble boundaries between one another, yielding a rigid large
scale structure. Materials in a glassy state can be expected to
lie close to this limit with m approaching zero.9 Since the
clusters in these circumstances are disconnected from each
other, their dimensionality (on the Nt scale) is effectively
that of a point, that is, zero. Thus in its serial form the inter
pretation of the cluster model parameter m is reversed from
that obtained for the parallel version of Sec, III. In contrast
to the near rigid limit of m --0 we expect materials with
m -> 1 to allow the relaxation to flow through the system via
weakly cross-linked lines of nonconnected contacts, Le., the
fluid limit. This limit applies to relaxation in liquid systems,9
and in water, for example, the contacts may be taken as the
reversed molecule defects which terminate hydrogen-bond
chains.36
Expression (2b) for ¢(t) is given by the integral over
the incremental current contribution per site as it takes part
serially in all the sequential relaxations defined through y,
An equivalent parallel definition can be had by taking r (y) /
{u as the effective number of alternative relaxation channels
(i.e., parallel addition of relaxation probabilities), in which
case g(y)dy, as given in Eq. (4), becomes the probability
density for a site to relax via one of the alternatives with
frequency (probability per unit time) r(y), and we recover .. 1 . f th 1 t ' I 9.20 the ongma constructlOn 0 e c user moae .
The present analysis shows that the difference between
the Kohlrausch and cluster model function for ¢ (t) arises
because the connection self-similarity ofthe cluster (giving
t -n decay) ceases to exist10 at times [r(y)]-l and each
individual cluster crosses over to the Euclidean behavior of
exponential decay,34,37 but with self-similarly related decay
times and amplitUdes generating a second power-law re
gime.6 In contrast, the Kohlrausch function combines self
similarity in the form of a time-dependent rate constant
( ex: t -n) together with the random nature of a first-order
(unimolecular) rate equation, Le.,
-<t>(t) = dif;(t) = -(Up (wpt) -"¢(t). (43)
dt
L. A. Dissado and R. M. Hill 2519
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsIn this case the same dynamic self-similarity is presumed to
extend indefinitely as relaxing processes explore space and
time to relax displaced centers at random. 15.38
B. Quasi-mobile charge systems
Niklassen 17 has discussed this form of response for the
two cases of conduction on an infinite percolation cluster
and on a distribution of dusters. In both cases he finds m to
be given by the exponent ofa fractal time processl5.!7 (D,),
though n differs in the two cases and is dependent upon D,
for the distribution case. Here we shaH examine the cluster
model version of this process, which is known to describe
experimental data throughout the frequency range, because
we feel that it serves to give a clear physical picture for the
origin of fractal time processes.
Starting with expression (9b) we must identify the COll
tribution per site as
[N(z,t)] -11 = [Ni; r(z)t] -"z--t, (44a)
and hence the number of connected sites N(z) at the time of
relaxation (charge recombination), rr(z)] -I, is given by
(44b)
As in Sec. IV A the t n decay in ~ (t) arises from self
similarity in the connected displacements of the mobile
charges within the duster with the number of sites per unit
dipole increasing as [N(z,t)]" and the cluster polarization
contribution as [N(z,t) J 1-n. Asin Sec. III we may associate
this process with the inefficient (compact) exploration of
the duster fractal matrix by a mobile charged pseudoparticle
seeking an immobile counter charge for recombination. 3M
The term inefficient in this case means that not all steps of
the pseudoparticle reach a new site. The expressions given
for n by Niklasson 17 are
n = 1 ______ d ___ _
B+2+d(l-D,)/D, (4Sa)
for the case of an infinite duster, and
S n = 1 -------=:---------
S + t + dv( 1 -D,)/ Dr (450)
when a distribution is considered. In this case s is the expo
nent for the divergence of the dielectrical constant, t the de
conductivity exponent, and v the correlation length expo
nent in percolation theory. In both cases the purely geomet
rical inefficiency of exploration is supplemented by trapping
and detrapping from centers with a long-time power-law tail
in the waiting time distribution39 for which the number of
detrapping events is proportional to t D,. When this process is
not present Dr must be set to unity, and expression (45a)
recovers the geometrical circuit result of Sec. HI with (45b)
as its stochastic equivalent.
Niklassonl7 also identifies D, as m, however, the circuit
model of Sec. III provides an example in which the self
similarity determining the low-frequency CPA is completely
independent from that of the high-frequency region, and m
and n are not related. Thus although some evidence exists for
this interrelationship in inorganic oxidesl7 it is not an essen-
2520 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 m 1. 0 ,..--• ........,.:c1Ill;IIIII ..... r: .... .....",I: .. "-:-r/ -----, ·...,.·/0.-, 0 ..... I. • I ., ,
I 0 0 ,'0
It '0 t 0' 0 i / a 0
, I
O.S --f rf 0/ , I
0 '0 / , ,
/ 0/
I /
I
I / I , /
II L _t ~
0 ~ i
0.5
1 -n 1,0
FIG. 8. Plot ofihe exponent m as a function of the high-frequency exponent
(1 .~ n). Niklassen's relationships between m and (j -n) are indicated by
the dashed curves and his reported experimental values by the open circles
(taken from Ref. 17). The filled circles are experimental values taken from
data investigated by the authors and reported in Refs. 45 and 49. The sizes of
the data points gives an estimate of the accuracy of the data values.
tial feature of this type of dielectric response, as indicated in
Fig.8.
We now examine the low-frequency CPA region of the
cluster model with a view to clarifying its origin. As in Sec.
III its appearance is due to a divergence in the contribution
amplitude ( a: z--J) together with a power-law approach to
zero for r(z), as z approaches zero. From Eqs. (10) and
(44) we find
[nz)l--l = «(uc)-l{l + [N(z)/N,; ]-nlm}. (46a)
Here we see that the range 0 < z < 1 and 0 < r(z) < wJ2 is
contributed by the subcharacteristic-sized clusters N(z)
< lIlt... Again the relaxation is sequential but instead of the
smaller clusters relaxing rapidly as part of the sequence for
the larger ones (e.g., by removing constraintsl3) the con
verse applies for this process. As previously shown, we can
express the relaxation time [r (z) ]-I through the number of
sequential steps .!i,( (z) as
(46b)
withMs (z) given in terms of the cluster dipole group in units
of the characteristic dipole group, i.e.,
[M.I (z)] -m = [N(z)/ N,;-r = M(z). (47)
The picture of the relaxation process that can be obtained
from these expressions has the cluster whose dipole group,
[N(z) ]", is infinite [N(z) --> 00] relaxing in a time (we) -\
following a self-similar exploration by the charge which ex
tends to the whole matrix because of the infinite size of the
connected group. This infinite cluster contribution appears
with zero weight in the integral of expression (9b) and the
response must thus be regarded as that of a system below the
percolation limit. Clusters with finite size connected dipolar
groups relax via 1 -1-lvI, (z) sequential (incoherent) steps,
with the number of steps increasing as the size of connection
decreases.18 We can thus take the sequential process as one
in which fast recombination relaxations in large connected
clusters eliminate connections from the system, rather like
L. A. Dissado and R. M. Hill 2520
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsburning out the red (single-connected) bonds of a percola
tion system.40 The self-similar fragments of the infinite clus
ter now require an incoherent transfer across the lost con
nection in order to achieve recombination. Again the
characteristic cluster is defined by a value of unity for Ms (z)
and is thus the one for which each dipole group of (Ns) n
connected sites requires one incoherent transfer for relaxa
tion. The characteristic cluster is thus the one in which aU
dipole groups are singly disconnected from each other, and
its size will be related to the characteristic correlation length
for a charge pseudopartic1e. Self-similar subcharacteristic
groups with [N(z) J n < (Nt;) n experience an increasing ex
tent of disconnection as recombination proceeds and the re
sidual groups become smaner. It is these fragments that give
the low-frequency CPA behavior, and i.ts power-law index is
dependent upon the self-similarity of the lost connections
across which incoherent transfers must be made. As in the
previous subsection it is clear that if m is unity the number of
disconnections scale with the number of fragments
[M(z)] -I and the connectivity is linear. We may expect
most systems in this class to lie close to this limit because of
their near conductive nature. The other extreme of zero for
m limits the size of the cluster to its characteristic value
within which the charge is absolutely trapped possessing a
recombination frequency We' This limit cannot be expected
when the system contains potentially mobile charges.
The picture we have here may be reconciled with the
fractal waiting time process I 7.39 if the traps are conceived to
be the clusters of the present process with, for example, the
large clusters responding faster than the smaner ones be
cause of their larger screening and weaker binding which
must, however, be self-similarly related, Nonetheless the
structural interpretation given here could be equally valid
giving an origin for the low-frequency CPA in terms intrin
sic to the duster distribution structure of the subpercolative
systems. It is of course possible that a fractal waiting time
process could supplement the index Tn for subpercolative
systems (no infinite cluster) and give m above the percola
tion limit, providing a change of exponent which should be
testable.
As previously an equivalent parallel definition can be
obtained from r(z), allowing us to identify g(z)dz (equal to
d [nz)/wc]) as the probability density for a site to be in
volved in a relaxation process with a connection over N(z)
sites. It should be appreciated however that it is a "steady
state" description of a system that is continually fluctuating
during relaxation.9•23
Vo THE INTERPRETATION OF DlEL.ECTRIC
MEASUREMENTS
Only four parameters, namely the exponents nand m,
an amplitude X(O) [X({J}c) J and characteristic rate Olp (we)
are available to characterize an isolated response in the die
lectrical spectra. Within the context ofthe cluster model the
amplitUde and rate will be modified from their independent
site values by dynamic connections between cluster sites.
They will, however, remain related to the single-site pro
cesses and their variation with temperature and pressure can
2521 J. Appl. Phys., Vol. 66, No.6, i5 September 1989 be used to obtain information as to the local relaxation
mechanism. The nonexponential behavior characterized by
exponents nand m occurs as a result of the manner in which
the site relaxations are interconnected, and should not be
regarded as a particular relaxation process of itself. Instead
different modes of connection arising in various relaxation
contextsl5,41 will yield different values for the exponents. A
molecular understanding of the relaxation dynamics can
thus only be obtained by incorporating all the information
available into a complete picture, and some discussion in
these terms for typical response patterns has already been
made. 9
In the cluster model the presence of alternative orienta
tions (local positi.ons) for site dipoles (charges) allows the
structural environment of a responding site to be displaced
during relaxation. An expanding zone of disturbance (clus
ter) is formed, in which the displacements of originating
dipole and environment sites are connected dynamically.
The perturbation responsible for the connection33 acts via
changes in the Ioca! potential surfaces and explores the
structural matrix in a compact manner. That is, in a given
volume of matrix (R df) many sites are visited more than
once, i.e., they are multiply connected to each other. Thus
the clusters of the model are not necessarily formed by re
gions of static distortion, but are rather transient zones of
disturbance whose extent may be determined either by the
relaxation time as for dipolar centers in ionic crystals, or by
structural constraints in the case of the f3 response of glasses.
The exponent 11 is not determined solely by the dimensionali
ty of the structure that is connected but reflects the dynamic
nature of the cluster through the involvement of an explora
tion (time) exponent [i.e., e + 2 in Eq. (23) ]. This concept
of a compact exploration, in the sense used by de Gennes,42
unifies all the theoretical models of the t -" dielectric re
sponse that do not rel.y on a distribution of independent re
laxation times. Klafter and Shlesinger15 have shown that a
number of such models can be reduced to the same algebraic
form. Here the Glarum defect-diffusion modei43 was found
to define n through a compact exploration of the matrix by a
defect seeking a frozen dipole to relax. The hierarchical con
straint mcdeI13 presents a more subtle example, with the
system undergoing a compact exploration of the dipole ori
entation configurations before relaxation of a given level can
be achieved. This definition can also be extended to ultrame
tric spaces,41 where the compact exploration takes place in
the energy space of the barriers to activated displacements.
In aU these models the power-law relaxation arises from se1f
similarities in the space explored and the time process of
exploration. However, when the exploration is controlled
solely by geometrical factors the value of n is temperature
independent, whereas for the energy space it is linearly de
pendent on temperature [Le., n = 1 -(kT I f:A )1n b where b
is the branching of the activation energy tree based on an
activation energy A]. If a waiting time distribution with a
long-time tail is incorporated into these models, a multipli
cative factor (D,) is introduced15,41 into 1 -n which may
also be proportional to temperature if the distribution is re
lated to activated processes.44 Because of the ratio of the
dimensionalities in the definition of n and the possible subor-
L. A. Dissado and R. M. Hill 2521
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsdination by D, (Ref. 46), there will be no one specific value
of n appropriate to each model even for materials with a
particular structural arrangement unless the manner of dy
namic connection is also the same, Here, however, it may be
expected that the different values of n would He close togeth
er.
It is possible to regard all the fractal-type models dis
cussed above as specific cases of the cluster model with dif
ferent forms for the amplitude and characteristic rate. How
ever previous interpretations based on the cluster model9,45
have leaned towards a geometric understanding of n (i.e.,
exploration of entropylO rather than energy space), and it
should be noted that n is rarely, if ever, observed experimen
tally to be temperature dependent, except at phase transi
tions where the structure is known to alter.
The existence of a low-frequency power law is unique to
the cluster model response function although we have
shown 19 that it can occur in a relatively simple deterministic
fractal circuit as a result of an interwoven self-similarity.
Other fractal models either assume that the system follows
the same self-similar construction indefinitely in which case
a stretched exponential results, or a crossover to a Euclidean
space (noncompact exploration) occurs giving an exponen
tial cutoff.15,41 In the cluster model the connected distur
bance zones (clusters) are of finite size when relaxation
starts to occur via an irreversible transfer of energy to the
heat bath (dissipation). It is now possible for relaxation in
one cluster to influence relaxation in another cluster, leading
to connected relaxation sequences in the system of clusters
rather than the random relaxation of independent clusters.
This dynamically interconnected dissipation process re
places the energy sharing that is responsible for the evolution
of clusters at short times. The relationship of the low-fre
quency power-law exponent m to the dissipative process can
be seen from the equation ofmotionlO for $(1):
d 2cp(t) +.l (2 + n + ill t) dCP
dt2 t P dt
. 1 + 2" [n + wpt(1 + m)]<l>(t) = O. (48) t
At times shorter than those of lattice frequencies t -1 this
expression transforms theoretically into a modified osciHa
tor equation appropriate to the spreading out of the site dis
placements involved in the later cluster formation, Le.,
d2$(t) + t(2 + n)(; d<l>(t) _ n(;2 <I>(t) = 0
dt 2 (1 + i~·t) dt (1 + itt) 2 '
(49)
but at long times, OJp t > 1, it becomes a modified dissipation
equation governed by the exponent m,
d$(t) + 1 + m Il>(t) = O.
dt t (50)
Some discussion of the physical origin of this process has
been given in Sec. IV A where it was attributed to noneon
nected contacts between the surfaces of different clusters
originating with the same type of dipole center. This is a
geometrical (structural) interpretation and should lead to
temperature independent values of m, with zero being the
limit when the relaxations are confined to independent clus-
2522 J. AppL Phys., Vol. 66, No.6, 15 September 19S9 ters. When relaxation (dissipation) Bows ideally from dus
ter to cluster m approaches unity. An alternative view ofthe
transfer (of charge) between clusters is given in Niklasson's
suggestion 17 that it is governed by the long-time tail of a
waiting time distribution for detrapping. This gives Dr for m
and in some cases a temperature dependence.44 Although
experimentally m is more susceptible to temperature than n,
this is usually only strong at cryogenic temperatures. Thus in
most cases this feature of relaxation dynamics is also deter
mined by the geometrical arrangement of the interc1uster
boundaries.
When all the information available from dielectric re
sponse measurements is assembled in the manner outlined
above a picture can be developed that will show not only
what local mechanisms would be involved if the environ
ment were rigid, for example, an activated barrier process or
rotational Brownian motion, but also how motions at differ
ent sites are connected dynamically during the lead up to
relaxation. In the absence of a detailed analysis a general
picture of the dynamics can be had, an example of which is
shown in Fig. 9 for a cluster-forming process appropriate to
the a relaxation of glasses above their Tg• Some idea can also
(a)
(b)
(c)
(d)
(e)
FIG. 9. A schematic reprcscntation of self-similar displacement motions
(a)-Cd) on a chain and their combination (e) to give the overall relaxation
(from Ref. 10). The figure shows the early stages ofclusier formation, with
the cluster region expanding along the chain as larger groups of sites are
dynamically conne.cted to the originating nonequilibrium site indicated in
(a). Such a picture may be taken to represent the molecular displacements
involved in the a response of amorphous polymers such as PMMA with the
arrows denoting tilt: displacement of the polar side groups. In this case the
chain is that of the polymer and the presence of other chains, whkh may
introduce potential barriers, is implied. Alternatively the chain may repre
sent only a set of dipoles whose dynamics are interconnected as a result of
sterk interactions; again the arrows denote the displacement of the dipoles.
This latter picture is more appropriate to the displacement of hydroxyl po
lar groups attached to long molecules as in the a response of the nematic
glass-forming OHMBBA material.
L. A. Dissado and R. M. Hill 2522
Downloaded 21 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsbe gained of the way in which relaxations in different regions
influence one another as energy is transferred through the
system to be dissipated in the heat bath. For example, the {3
relaxation of glassy states typically has large values of
n ( ..... 1) and small values of m ( --> 0). As discussed in Sec. IV
this type of response originates with dynamically connected
relaxations restricted to cluster regions which are nearly iso
lated from each other, i.e., it is almost impossible to extend
them by aggregation. The connection within the cluster is
such that the gross dipole length remains almost the same
regardless of the number of units that become dynamically
involved, that is a highly compact exploration (() + 2
-+ large} or a highly convoluted path of dipole displacements
(dc-->O).
VI. CONCLUSION
Previous analyses of experimental data'l·1O·17.21 have
demonstrated that the cluster mode! provides a very good
description of dielectric susceptibility. Its unique feature is
the presence of two power-law regions of frequency depen
dence and we have shown here that this can be attributed to
an interweaving of two forms of self-similarity. Analytically
solvable fractal circuit models offractal series-fractal paral
lel combinations are found to be identical in their asymptotic
frequency dependence to the cluster model although the lat
ter is essentially sequential in form.
The fractal interpretation of the model achieved here
has allowed the origin of the high-frequency CPA region to
be identified as a compact self-similar exploration of a fractal
matrix, either by a charged entity (potentially mobile charge
case) or a connecting perturbation (bound dipole case). In
either case the frequency exponent of the response, (n -1),
is defined by a ratio of the fractal dimensionaIities. At low
frequencies the mobile charge and bound dipole cases are
distinguished by a diverging or a converging contribution to
the response, respectively. In the former case a CPA re
sponse results while a power-law behavior for X" (UI) is ob
tained in the latter. The origin for both behaviors lies in a
self-similarity of the individual cluster relaxation times
which arise from self-similarity of the contacts between dis
connected clusters expressed through the index m. A de
tailed expression for m has as yet been achieved only for the
fractal circuit models where the contact system is replaced
by a fractal surface whose dimensionality determined m.
However, the form of this combination of self-similarities is
of a sufficient basic nature as to occur in a wide range of
materials as would be expected from the widespread applica
bility of the response function.
ACKNOWLEDGMENT
The authors wish to acknowledge the assistance given to
them by John Pugh in disentangling the electrical properties
of the Sierpinski gasket.
APPENDIX A
The response function ¢ (t) for the partially mobile
charge case (b) was derived in Ref. 18 in the following form:
2523 J. App!. Phys., Vol. 66, No.6, 15 September 1989 <P(t) (N) --n t --Ilt
( t ) --= • (tJe exp -(u, 1 41(0)" 0 '
(Al)
This time average over a dynamically fluctuating array of
relaxing currents can be converted into an average over an
equivalent ensemble of effectively independent instanta
neous contributions by the technique adopted in Ref. 10 for
the bound dipole case (a) which leads to expression (2b).
Here we define the ensemble variable z through
Z-I=tj-m(t-t\)m,
hence
tl = tzllml(1 + zllm) = t [r(z)/(Uc]' CA2)
(A3)
and can version of the integral variable from t I to z leads in a
straightforward manner to expression (9b).
APPENDIX B
In the cluster model the connected intrac1uster motions
are considered to be the result of perturbation which binds
the cluster together during relaxation from an initial state in
which an dipoles (charges) move independently (i.e., a dis
ordered duster), whereas if formed in vacuo such a cluster
can be defined to have an ideal binding energy of Em per
dipole. In the condensed media considered the binding ener
gy will be reduced to nEm per particle (0 < n < 1). Clearly
the limits of n = 1 and C correspond to clusters formed as
particles with specular boundaries and dissociated clusters
of independent dipoles, respectively. During the evolution of
the cluster the available binding energy is considered to con
nect the dipoles together in all possible sequential arrange
ments, running from independent sites, through pairs up to a
complete sequence of all sites. By treating a site within the
cluster in a similar manner to that in which a "bare" particle
becomes "clothed" in particle physics, its dipole (or cur
rent) contribution is found to decay in the power-law form
t -, as a result of an infrared divergence in the clothing in
teraction.
We have previously related the power-law decay to a
time-dependent change in the activation configuration en
tropy of reI ax at ion by considering Eq. (2b) to be the addi
tion of incremental relaxation currents whose rate constant
is time dependent,3g Le.,
r(f)p XJ exp[ -f"(y)t Jy[r(y)tJ -"d [r(y»).
()
(Bl)
Neglecting the effect of the cluster distribution by taking aU
dusters to be of the characteristic size the rate constant takes
the form (tJp (Nc;(tJpt) -n which can be rewritten in terms of
an activation free energy [to U -TLl.s(t)] by
Wp(NgUlpt} -n = vexp{ -(/j,U /kn + [/j,S(t)lk H.
(E2)
In an expression of this type the configuration entropy term
t:.S(t) defines the statistical probability of achieving a suc-
l. A. Dissado and R. M. Hill 2523
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nate, which is attempted at the rate v. When IlS> a the re
laxation coordinate of the group of Ng dipoles can be entered
along more than one vibration coordinate per site, whereas
for IlS < 0 the site vibrations must combine into specific dis
placement configurations to be effective.
Noting that the formal zero time limit of Eq. (B2) islO
(up' the time power law can be associated with the time-de
pendent change of t:.S( l) during cluster formation,
(lIk)[.clS(t) -.clS(O)] = --nln[Ns(t)]
(B3)
with
Ng (t) = Ng(upt<N#,. (B4)
This reduction in .clS reflects the requirement for specific
configurations during relaxation as the N#,. dipoles of the
characteristic cluster become connected. The loss of config
uration entropy on cluster connection is thus
nN~ (tHn[ Ng (0) withEq. (B3) giving the contribution per
dipole. The limit of zero for n refers to a cluster remaining
disconnected, whereas a value of unity corresponds to a situ
ation in which connection occurs via all possible sequences
[I.e., exp(Nt.clSglk) = N~ss=;Ng!]. Fractional values of n
refer to systems in which a representative dipole takes part in
just a fraction ofthe sequences potentially available to the Nt,
dipoles of the cluster, and for which the sequences involved
are self-similar to scale changes.
A similar interpretation can be placed upon the fractal
description of Sec. III and IV when it is realized that using
Eq. (24) (N!; (I) ] 11 can be expressed as
[N,,(t) r= [R(t) jf) ~2/[R(t) ]df, (BS)
which is the total number of sequential exploration steps
connecting the system per unit volume. Just as above, we can
regard Eq. CBS) as the number of distinct exploration (con
nection) sequences per site, and define the configuration en
tropy of the dynamically connected cluster as the explora
tion entropy of the fractal matrix.
The relationship between the fractional power laws and
configuration entropy is not confined to dielectric relaxa
tion. It has previously been established by de Gennes46 in a
different context (i.e" viscosity). Here the absence of tied
endpoints to polymer chains allows segmental motions se1f
similarly to explore the configurations available to the chain
in the polymer melt. Thus a viscosity exponent can be de
fined with the same kind of fractal interpretation as is given
to n in Eg. (25). Here 8rjO: (iw)-n with n = -l/(vz),
where V-I is equivalent to df, being defined via the fractal
mass (N) relationship R 0::. NV, and z is the time exponent
defined through 'T 0::. R z.
Although the discussion has been restricted to the char
acteristic cluster it will apply equally wen to all clusters inte
grated over in Eq. (Bl). Here we can define a cluster en
tropyO,10 for each value of the indexy (i.e.,-n In [N(y,t) l)
and for the fluctuations of the clusters about the characteris
tic size (Ns)' Such fluctuations will add a further contribu
tion to the total entropy of the cluster array. The reader is
referred to Refs. 6 and 10 for further details.
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Dissado, and R. M. Hilt J. Biot Phys. 12, 1991 (1984); R. M. Hill and L.
A. Dissado, J. Phys. C. 17, bOOl (1984); L. A. Dissado, R. M. Hill, C.
Pickup, and S. H. Zaidi, Appl. Phys. Commun. 5,13 (1985); R. M. Hill
anelC. Pickup,J. Mater. Sci. 20, 4431 (1985); L. A. Dissado, Comm. Mol.
Cell. Biophys. 4, 143 (1987); R. M. Hill, L A. Dissado, J. Pugh, M.
Broadhurst, C. K. Chiang, and K. J. Wahlstrand, J. BioI. Phys. 14, 133
( 1986); L. A. Dissado, R. C. Rowe, A. Haidar, and R. M. Hill, 1. Colloid.
Intcrfacc Sci. 117, 310 (1987); K. Pathrnanathan, L. A. Dissado, and R.
M. Hill, J. Matter. Sci. 20, 3716 (1985).
46p. deGermcs, Scaling Concepts in Polymer Physics (Cornell University
Press, Ithaca, NY, 1979).
PG. P. Johari, Philos. Mag. B 46,549 (1982).
48G. E. Johnson, E. W. Anderson, and T. Furukawa, IEEE Trans. CEIDP,
258 (1981).
40R, M. Hill, L. A. Dissado, and K. Pathmanathlln, J. Bio!. Phys. 15, 2
(1987).
L. A. Dissado and R. M. Hill 2524
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1.344045.pdf | Thermochemistry of alkylarsine compounds used as arsenic precursors in
metalorganic vapor phase epitaxy
R. M. Lum and J. K. Klingert
Citation: Journal of Applied Physics 66, 3820 (1989); doi: 10.1063/1.344045
View online: http://dx.doi.org/10.1063/1.344045
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/66/8?ver=pdfcov
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128.114.34.22 On: Sun, 30 Nov 2014 13:02:14Thermochemistry of alkylarsine compounds used as arsenic precursors
in metalorganic vapor phase epitaxy
R. M. Lum and J. K. Klingert
AT&T Bell Laboratories, Holmdel, New Jersey 07733
(Received 19 May 1989; accepted for publication 21 June 1989)
Despite their increased safety, alkylarsine compounds have not generaily replaced arsine
(AsH3) in the metalorganic vapor phase epitaxy (MOVPE) of GaAs because of carbon
incorporation and high background doping levels. We have studied the thermal decomposition
of AsH] and its alkyl derivatives (methyl, ethyl, and butyl compounds) to determine the
impact of the thermochemistry on growth processes. The thermal stability of the As-precursor
compounds was found to decrease in the order AsH] > Men AsH) _ tl > Et3As > t-BuAsH2• We
report the first evidence for production of diarsine (As2H..) from t-BuAsH2 and for formation
oflower substituted methyl arsine homologs from Me3As and Me2AsH. The presence of these
species is strong evidence that decomposition of the alkylarsines occurs via a free-radical
mechanism. Formation of carbon-free arsenic products appears to be the key difference
between t-BuAsH2 and the more highly substituted alkylarsines in attaining high quality films
by MOVPE.
I. INTRODUCTION
Alkyl substituted arsine compounds are attractive alter
natives to arsine for the metal organic vapor phase epitaxy
(MOVPE) of GaAs because they are typically low vapor
pressure liquids and can be stored and handled more safely
than the high-pressure gas cylinders used for arsine. We have
investigated the growth characteristics of several alkylarsine
compounds in previous studies,I.2 and found that films
grown with different As precursors exhibit significant dif
ferences in growth rate and electrical properties. This sug
gests that the underlying growth chemistry and reaction ki
netics are greatly affected by the molecular configuration
and degree of hydrogen atom substitution of the alkylarsine
compound. Design of effective new arsenic sources for the
MOVPE process thus requires an understanding of the de
tailed role of the hydrocarbon and hydrogen radicals in the
overall reaction chemistry. In this paper we report mass
spectrometric studies of the thermochemistry of arsine and
the alkylarsines in hydrogen. Data are presented on the ther
mal stability of the As precursors, and on the composition
and formation rates of the resulting volatile decomposition
products. The reactions controlling decomposition of the
precursor compounds are identified, and insights are ob
tained on the potential of alkylarsine reactants for different
CVD processes.
The As precursors investigated in this study were AsH)
and the corresponding alkylarsinc derivatives from the series
RnAsH3 II (n = 1-3), where R represents methyl, ethyl,
and butyl groups. The physical properties of these com
pounds are listed in Table 1. The alkylarsines are all low
vapor pressure liquids and were used as received with no
further purification. Their room-temperature vapor pres
sures range from 5 Torr for Et3As, which represents a low
limit convenient for MOVPE applications, to 400 Torr for
Me::!AsH. Although the toxicity of the alkylarsines has been
found to generally increase with the number of As--H bonds
in the molecule,2 the low vapor pressure of these compounds
significantly reduces their safety hazard. It EXPERiMENT
The thermal decomposition experiments were per
formed in hydrogen at atmospheric pressure in a quartz
flow-reactor tube (0.5 em diam, 100 em long). A resistively
heated gold-coated tubular furnace was used to heat the gas
es in the flow reactor. To more closely simulate MOVPE
growth conditions, the input partial pressure of the As-pre
cursor reactant was kept at 10-3 atm, and the residence time
of the gases in the flow reactor was adjusted to be similar to
the transit time of gases over the hot susceptor in our growth
reactor (0.5 s). The decomposition behavior of the As pre
cursors was determined by increasing the furnace tempera
ture in a stepwise manner and measuring the volatile pyroly
sis products at the outlet of the reactor with a quadrupole
mass spectrometer (VG Instruments model SXP600). The
gases were introduced into the spectrometer through a sili
cone membrane inlet. The membrane separator acts as an
effective barrier to the hydrogen carrier and eliminates the
requirement for intermediate pumping stages ahead of the
mass analyzer chamber. Mass analysis was performed using
electron impact ionization at electron energies of 70 e V.
TABLE I. Physical properties of arsine and the methylarsine homologs.
Compound
Arsine
AsH, mp
ee)
Trimethylarsine -87.3
Me,As
Dimethylarsine ~ 78
Me2AsH
Triethylarsine -91
Et3As
tertiary-Butylarsine -I
t·BuAsH2 bp PV3.P
eCl (20 'C)
-62.5 15 atm
50.2 238 Torr
36 405 Torr
140 5 Torr
69 124 Torr
3820 J, Appl. Phys, 66 (8), 15 October 1989 0021-6979/89/203820-04$02.40 (c) 1989 American Institute of Physics 3820
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128.114.34.22 On: Sun, 30 Nov 2014 13:02:14III. RESULTS
A. Thermal stability of the As precursors
A comparison of the thermal decomposition of the dif
ferent As precursors is presented in Fig. 1. AsH3 is the most
stable compound with a decomposition onset temperature of
approximately 575 "c. This is loo·C higher than the onset
observed for the methylarsines, Me3As and Me2AsH, whose
decomposition is already more than 50% complete by
550 ·C. The ethyl and butyl compounds are even less stable,
with 50% decomposition occurring at approximately 500
and 450 ·C, respectively. The relative thermal stability of the
As precursors decreases in the order AsH3> Me" AsH3 n
> Et3As > t-BuAsH2• This is consistent with a decreasing
C-As bond strength as the size of the hydrocarbon group in
the alkylarsine compound increases, and supports a free ra
dical mechanism for thermal decomposition in which the
breaking of the C-As bond is the rate determining step. A
similar trend has been observed for Te, Hg, and Cd metalor
ganic compounds3 as the number of carbon atoms in the
alkyl group is increased. This effect was ascribed to de1ocali
zation of the free-radical electron charge by neighboring or
ganic groups.
The data in Fig. 1 represent the first comprehensive
study of the thermal decomposition properties of AsH3 and
the alkylarsines in the same reactor under identical experi
mental conditions. Although the same relative ordering in
alkylarsine thermal stability has been observed in low-pres
sure (20-50 Torr) studies,4 the absolute values of the 50%
decomposition temperatures were significantly lower than
reported here. For example, decomposition of t-BuAsH 2 in
the low-pressure reactor was 50% compiete by 290 ·C, as
opposed to 450°C as shown in Fig. 1. This compares with
375°C reported from measurements5 obtained in a flow
reactor similar to the one used in this work. A similar spread
exists in the 50% decomposition temperatures measured for
AsH1 by various ex situ techniques.6-!() These variations in
dicate the difficulties involved with attempts to directly cor
relate results obtained from different reactors, and empha
size the importance of obtaining comparative measurements
in a single system.
100
w
(,) 80 Z
;§
Zm 60 ::>.-=:
~§
w€ 40
>~
~ 20 -' w
a::
0
300 400 500 600 700
TEMPERATURE "C
FIG.!. Thermal decomposition of As-precursor compounds determined
from mass spectrometric measurements of the uecrease iii the parent ion
signal as a fUliction of temperature.
3821 J. Appl. Phys., Vol. 66, No.8, 15 October 1989 B. Gassphase decomposition products
Measurements were also obtained on the composition
and formation rates of the volatile decomposition products.
During decompositon of t-BuAsH2, shown in Fig. 2, isobu
tene (C4Hg) and isobutane (G~H!{)} are observed as the ma
jor hydrocarbon products, while AsH] is the predominant
arsenic product. These results agree with the low-pressure
studies4 where C4H!O was observed as the dominant product
at low temperatures and C4H!( at high temperatures. This is
in contrast to the flow reactor measurements of Ref. 5 which
indicated that C4HIO was the dominant product at all tem
peratures. However, the most important aspect ofihe data in
Fig. 2, which differs from both of the earlier studies. is the
observation of significant amounts of diarsine (As~H4)' De~
tection of this species has a fundamental imnact on the inter
pretation of the reaction mechanism contrdlling decomposi
tion of t-BuAsH z.
The formation of As2H4 was postulated in the radical
decomposition mechanism proposed in Ref. 4, but was not
detected. Whether this was due to the molecular beam sam
pling techniques used in that work, for example, or to a slight
misalignment of the 1 DO-,am sampling orifice is not known at
present. However, the failure to detect this species in the
flow reactor system of Ref. 5 appears to be related to the gas
residence time in that reactor. As shown in Fig. 3 the ASzH4
signal decreases with residence time due to its reactivity and
vanishes for times in excess of 1 s. The experimental condi
tions for the measurements in Ref. 5 were chosen to keep the
flow velocities in the pyrolysis reactor similar to those typi
cal of an atmospheric pressure growth reactor (5-10 cm/s).
However, this resulted in gas residence times greater than 5
s, which may account for the absence of detectable amounts
of As2H4•
The data presented in Figs. 1 and 2 provide strong sup
port for the radical decomposition mechanism proposed in
Ref. 4 for t-BuAsH2• That model is based on homolysis of the
parent molecule,
(1)
foHowed by radical recombination reactions to form C H 4 g,
C4HIO, AsH3, and ASzH4-
(CH3hC' + (CH3)3C' -C4HS + C .. Hw, (2)
>-I--
00 Z ....... WUl
i--~ zC: -::I W' :>€ _aI
'""'~ :s w a::
300 o C4HgAsH2
400 500 600
TEMPERATURE (0C) 700 800
FIG. 2. Major volatile products from decomposition of t-BuAsH2•
R. M. lum and J. K. Klingert 3821
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128.114.34.22 On: Sun, 30 Nov 2014 13:02:1450r-----~------_.------_.------,
~ 40
.~
C
:::I
..ci 30
~
~20 I
N
~ 10 •
OL-------~------~------~~----~ 10-3 :0-2 iO-1 i 10
CELL RESIDENCE T!ME (sec)
FIG. 3. Variation in the diarsinc signal intensity with gas residence time in
the flow reactor.
(CH3hC' + AsH1'->C4HB + AsH"
AsHz' + AsH2' ->As2H4• (3)
(4)
The observation of a radical decomposition scheme for
t-BuAsH~ led us to investigate the possibility of similar reac
tions for t-he other alkylarsines, Earlier studies II of the pyro
lysis of Me1As indicated that it decomposed via loss ofmeth
yl radicals in a manner completely analogous to that
observed4,9 for Me,Ga decomposition with formation of
CH4 as the major volatile product:
(CH3kAs->CH3' + (CRI)2As'. (5)
Isotopic labeling of the Me3Ga decomposition products in
deuterium4•9 revealed that CH3D was the major product,
indicating that hydrogen atom abstraction reactions by
methyl radicals are the primary source of methane in a hy
drogen ambient:
CH3' + H2->CH4 + H', (6)
No volatile arsenic products from MeJAs were reported in
Ref. 11 other than, presumably, AS2 and AS4 which would
tend to deposit on the cooler sections of the reactor.
Our data on the decomposition products from both
Mc3As and Me2AsH are shown in Fig. 4, Although CH4 is
confirmed as the major hydrocarbon species, the data also
provide the first reported evidence for formation of volatile
As products. These take the form of the corresponding lower
methylarsine homologs; i.e" Me2AsH and MeAsH2 from
Me3As [Fig, 4 (a) ], and MeAsH2 from Me2AsH r Fig,
4(b) ]. Formation of these species is ascribed to radical re
combination reactions involving hydrogen atoms produced
via reaction (6) and the corresponding methylarsine radical
formed during homolytic cleavage of the parent compound,
e. g., reaction (5):
H· + (CH\) zAs' --> ( CH.J) 2AsH, (7)
H· + (CH3)AsH' -+ (CHl)AsH2• (8)
A similar radical decomposition mechanism has been
proposed4 for Et3As, where recombination reactions of ethyl
radicals with themselves and with ethylarsenic radicals to
form C2H4• C2H .... , fl-C4H 10 and Et2AsH were determined to
be the most kinetically favored:
(9)
3822 J, Appl. Phys" Vol. 66, No.8, 15 October 1969 t;" CH4
• CH3AsH2 (x 2)
400 500 600 700 800
TEMPERATURE (OC)
FIG, 4, Major volitile products from decomposition of (al Me,As; (b)
Me,AsH; and (e) Et,As,
CZH5' + C2H,;, --+ n-C4HlO, (10)
C2HS' + (CzHs)zAs' --.CZH4 + (C2Hs)2AsH. (11)
However, the data shown in that work were limited to the
hydrocarbon products and no evidence was presented for the
actual formation of EtzAsH.
Our measurements of the Et3As decomposition prod
ucts are plotted in Fig, 4(c). For the hydrocarbon species
these show a relatively larger C2H4 signal compared to C2H6
in agreement with Ref. 4. Although a mass signal corre
sponding to EtzAsH (ml e = 134) is observed, its tempera
ture profile I Fig, 4( c) I is not characteristic of a decomposi
tion product. Since recent gas chromatography mass
spectrometry measurements 12 also rule out the possibility
that this species is present as a contaminant in the Et]As
source material, its formation appears to be due to ion-mole
cule reactions in the ionizer. Unfortunately, the occurrence
of such reactions masks any contributions to the Et2AsH
signal that could be attributed to reaction (11).
IV. DISCUSSION
Although the effects of catalytic reactions at different
surfaces (e.g., GaAs) were not examined in this work, pre
vious studies5 have indicated that the overall alkylarsine de
composition behavior and pyrolysis products were not sig
nificantly affected by the addition of Me3Ga. The
thermochemistry data accumulated in this study enable se-
R. M, Lum and J. K. Klingert 3822
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128.114.34.22 On: Sun, 30 Nov 2014 13:02:14lection of the most effective alkylarsine compound for a par
ticular CVD process. Singly substituted alkylarsines, e.g., t
BuAsH2, appear to be best suited for MOVPE applications
since they form hydrogenated arsenic species upon decom
position (e.g., AsH3 and As2H4), which result in films with
reduced carbon incorporation. Funy and doubly substituted
alky larsines, on the other hand, form arsenic products which
still retain a C~~As bond and yield films with unacceptably
high carbon levels. In addition, the lower stability of methyl
and ethyl radicals further increases carbon incorporation
compared to butyl compounds.
For similar reasons t-BuAsH2 also appears to be the best
alkyl arsine for metalorganic MBE. However, to take advan
tage of the unique t-BuAsH2 thermochemistry the pre
cracker furnace should be operated at temperatures below
500°C to maximize formation of AsH] radicals. This is con
trary to common practice 13 in which the cracker is operated
at 1000 °C to ensure formation of AS2 species. At these high
temperatures any benefit in using t-BuAsH2 to reduce car
bon incorporation is lost.
Finally, for hot-wall CVD processes, e.g., hydride vaper
phase epitaxy, differences in thermochemistry are less im
portant due to the longer residence times of the gases at ele
vated temperatures. This tends to drive the reactions further
towards equilibrium so that the predominant arsenic species
in the growth zone are AS2 and As4• In such cases the purity
of the source material is a more important consideration
than its molecular composition. 14
V, CONCLUSIONS
In summary, we have measured under identical experi
mental conditions the thermochemistry of the As precur
sors currently ofinterest for MOVPE. Their relative thermal
stability was found to decrease in the order
AsH3> Men AsH3 _ n > Et}As > t-BuAsH2, consistent with
3823 J. Appl. Phys., Vol. 66, No.8, 15 October 1989 the decreasing strength of the C-As bond. We report the
first evidence for production of As2H4 from t-BuAsH2 and
for the formation of lower methylarsine homologs from
Me3As and Me}AsH. The presence of these species provides
strong evidence that decomposition of the alkylarsines oc
curs via a free-radical mechanism. Formulation of carbon
free arsenic products appears to be the key difference be
tween t-BuAsH2 and the more highly substituted
alkylarsines in attaining high quality films by MOVPE.
ACKNOWLEDGMENT
The authors are grateful to D. W. Kisker for use of the
quadrupole mass spectrometer and for helpful discussions.
'R. M. Lum, J. K. Klingert, and M. O. Lamont, J. Cryst. Growth 89, 137
( 1988).
'R. M. Lum, J. K. Klingert, and D. W. Kiskcr, J. App!. Phys. 66, 652
(1989).
'w. E. Hoke, P. J. Lemonias, and R. Korenstein, J. Mater. Res. 3, 329
(1988).
'Po W. Lee, T. R. Omstead, D. R. McKenna, and K. F. Jcnsen, J. Cryst.
Growth 93,134 (1988).
'CO A. Larsen, N. I. Buchan, S. H. Li. and G. B. Stringfellow, J. Cryst.
Growth 93,15 (l988).
"J. Nishizawa and T. Kurabayashi. J. Electrochem. Soc. 130,413 (1983).
75. P. DenBaars. B. Y. Maa, P. D. DapkllS, A. D. Danner, and H. C. Lee, J.
Cryst. Growth 77,188 (1986).
"M. R. Leys, Chemtronics 2, 155 (1987).
"c. A. Larsen, N. I. Buchan, and G. B. Stringfellow, App\. Phys. Lett. 52,
480 (J988).
lOR. Luckeralh, P. Tommack, A. Hertling, H. J. Koss, P. Balk, K. F. Jen
sen, and W. Richter. J. Cryst. Growth 93, 151 (1988).
lip. W. Lee, T. R. Omstead, D. R. McKenna, and K. F. Jensen, 1. Cryst.
Growth 85,165 (1987).
I2R. M. Lum, J. K. Klingert, and E. T. Johnson (to be published).
13M. B. Panish, J. Cryst. Orowlh 81,249 (1987).
141). N. Buckley, in IIl-V Heterostructuresfor Electronic Plwtonic Devices,
edited by C. W. Ttl, V. D. Mattera, Jr., and A. C. Gossard, Materials
Research Society Proceedings Vol. 145A (Materials Research Society,
Pittsburgh, PA, 1989).
R. M. Lum and J. K. Klingert 3823
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1.343013.pdf | Controlled conductivity in iodinedoped ZnSe films grown by metalorganic vaporphase
epitaxy
Akihiko Yoshikawa, Hiroshi Nomura, Shigeki Yamaga, and Haruo Kasai
Citation: Journal of Applied Physics 65, 1223 (1989); doi: 10.1063/1.343013
View online: http://dx.doi.org/10.1063/1.343013
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/3?ver=pdfcov
Published by the AIP Publishing
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41Controlled conductivity in iodine .. doped ZnSe films grown by metalorganic
vapor-phase epitaxy
Akihiko Yoshikawa, Hiroshi Nomura. Shigeki Yamaga, and Haruo Kasai
Department 0/ Electronic Engineering, Faculty of Engineering. Chiba University. 1-33, Yayoi-cho,
Chiba-shi, Chiba 260, Japan
(Received 1 August 1988; accepted for publication 27 September 1988)
Iodine-doped ZnSe films have been grown on GaAs by low-pressure metalorganic vapor-phase
epitaxy using dimethylzinc and hydrogen selenide as reactants. In order to accompUsh an
accurate control of the carrier concentration in the films over a wide range, ethyliodide diluted
to 1000 ppm was used as a dopant source. It has been shown that the carrier concentration can
be changed in the range from 1015 to 1O!9 cm-3 by varying the flow rate of ethyliodide.
Furthermore, the films with carrier concentrations below 10lg cm -3 exhibit strong blue
emission with suppressed deep level emissions. The origin of blue emission has been ascribed to
the iodine donors incorporated during growth. According to the results shown, it has been
conduded that iodine is a superior donor dopant for ZnSe from a standpoint of the
controllability and reproducibility of electrical and photoluminescence properties of the n-type
films over a wide range.
I. INTRODUCTION
ZnSe is one of the most promising materials for efficient
blue light emitting diodes (LEDs), because of its wide direct
band gap of 2.67 e V at room temperature. Since it has been
reported that low-resistivity n-type ZnSe films can be grown
at fairly low growth temperatures by metalorganic vapor
phase epitaxy (MOVPE) 1-3 and molecular-beam epitaxy
(MBE),4 many attempts to achieve conductivity control in
n-type epitaxial ZnSe films have been performed by doping
with group-III and group-VII donors, such as AI, Ga, In, Cl,
and 1. 1-11 Among these donor elements, it has been reported
that group-VII elements are superior to group-HI elements
with respect to the electrical and photoluminescence proper
ties of the films. 10 That is, in the case of the group-VII do
pants, it is rather easy to obtain highly conducting films
which exhibit strong blue near-band-edge emission with sup
pressed deep level emission.
Recently, Shibata, Ohki, and Zembutsu f I have attempt
ed iodine doping of MOVPE ZnSe using ethyliodide as a
dopant source, Since iodine is the least active among group
VII elements and alkyliodide decomposes at a lower tem
peratare than other group-VII alkyis, I! ethyliodide has been
considered an efficient and useful dopant source in low-tem
perature epitaxy, such as MOVPE. Ethyliodide is liquid at a
standard state and its vapor pressure is too high from a
standpoint of a dopant source ( ~ 110 Torr at room tempera
ture). Therefore, when the flow rate of ethyliodide is con
trolled by adjusting both the flow rate of carrier gas and the
bubbling-cylinder temperature, as in the case of ordinary
liquid metalorganic sources, it is fairly difficult to control its
flow rate with high accuracy especially in an extremely low
flow-rate region. This has resulted in a high flow rate of the
dopant source and consequently in heavily iodine-doped
ZnSe films. 11 Then, details on the electronic and photolumi
nescence properties of iodine-doped ZnSe films over a wide
carrier-concentration range are not given as yet.
In order to accomplish an accurate control of the flow rate of ethyliodide in an extremely low flow-rate region, we
have attempted to dilute it with a buffer gas to a concentra
tion of 1000 ppm. Then, iodine-doped ZnSe films have been
grown by low-pressure MOVPE over a wide flow-rate range
of ethyliodide. In this paper, we report electrical and photo
luminescence properties of iodine-doped ZnSe films over a
wide carrier-concentration range. It will be shown that elec
trical properties, such as resistivity and carrier concentra
tion of ZnSe films, can be controlled over a wide range by
using iodine as it dopant. Furthermore, it will also be shown
that iodine-doped ZnSe films exhibit strong near-band-gap
photoluminescence with suppressed deep-level emission
when the carrier concentrations are below IOlll em -3.
It EXPERIMENT
Iodine-doped ZnSe layers ( -I-f1,m thick) were deposit
ed on semi-insulating (100) GaAs by low-pressure (-0.4
Torr) MOVPE.12 Dimethylzinc (DMZn) and hydrogen se
lenide (Hz Se), diluted to 1 % and 10% in helium and hydro
gen, respectively, were used as reactants. EthyHodide, which
was diluted to 1000 ppm in helium, was used as a dopant
source. Typical growth conditions are summarized in Table
1. In the growth system used in this study, DMZn and
ethyliodide were used in a completely gaseous state as wen as
TABLE I. Typical growth conditions.
Substrate
Growth temperature eCl
Reactor pressure (Torr)
Growth rate (ftm/h)
Flow rate (ftmollmin)
DMZn (1% in He)
HzSe (\0% in Hz)
CzHsI (0.1% in He)
Film thickness (I'm) (100) GaAs
300 (260-330)
-0.4
~(J.5
4
200
0.067
-I (40--200)
(0.0034-3.1 )
1223 J. Appl. Phys. 65 (3).1 February 1989 0021-8979/89/031223-07$02.40 © 1989 American Institute of PhYSics 1223
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41H2 Se. That is, every source material was charged together
with an appropriate buffer gas into a conventional high-pres
sure gas cylinder. 12 A stainless-steel bubbler, often used for
transporting liquid metalorganic sources, was not used in
the present work. Then, our growth system looks like a sim
ple conventional CVD system, though it is in fact a MOVPE
system.l2 Therefore, in our growth system, operation for
growth is very simple and the flow rate of all source gases can
be easily and accurately controlled. The reason why the buff
er gas for ethyliodide and DMZn is not hydrogen but helium
is to prevent their dissociation in a cylinder. l2It may be pos
sible and likely that both ethyliodide and DMZn react with
hydrogen and decompose into elemental iodine and zinc
even at room temperature, respectively. This is because the
bonding energies between these elements and alkyIs are fair
ly low. (The bonding energy for Zn-CH, is as low as 44.5
kcallmol, and that for I-C2Hs can also be estimated to be
low from the fact that the bonding energy for I-CH, is 56
kcallmol.l3)
The GaAs substrate was etched in a mixture of 5:1:1
H2 SO 4 :H2 O2 :H2 0 at 60 ·C, followed by etching in boiling
HCl. No heat treatment nor gas etching ofthe substrate was
performed in the reactor before growth. Electrical properties
were measured by the van cler Pauw method in the tempera
ture range from 77 K to room temperature. Ohmic contacts
to the films were made by depositing In drops followed by
annealing in vacuum at about 300 fiC for 5-10 min. Photolu
minescence spectra were measured at about 18 K and room
temperature, using a O.64-m monochromator with a recipro
cal dispersion of 0.8 um/mm. A 6-mW He-Cd laser operat
ing at 325 nm was used as an excitation source. In order to
assign the emission peaks in the excitonic-emission region,
reflection spectra were measured by using the same mono
chromator. Furthermore, crystallinity of the films was char
acterized also by a conventional x-ray diffraction analysis.
Film thicknesses characterized were about 111m if not speci
fied.
m. PROPERTIES OF UNDOPED ZnSe FILMS
Electrical and photoluminescence properties of nomi
nally undoped ZnSe films will be briefly summarized. The
growth system used in this study is essentially the same as
that reported previously,3.12.14 but a newly designed suscep
tor has been used in this work In the old reactor, a sheathed
heater was used as a heating element and the efficiency of
heat transfer between the element and the susceptor was not
so good in the pressure range below 1 Torr. This caused the
undesired temperature rise of the heating element itself, re
sulting in a presence of an extremely high-temperature por
tion in the reactor. In contrast, in the new susceptor, the
heating element is embedded in it. According to this, one of
the contamination sources in the reactor has been eliminat
ed. This has resulted in an improvement in the properties of
undoped films, i.e., the concentration of the residual donors
in the films has been drastically reduced.
First, photoluminescence (PL) spectra of the nominal
ly undoped ZnSe films measured at 18 K are shown. Figure 1
shows the growth temperature dependence of the I~L spectra
1224 J. Appl. Phys., Vol. 65, No.3. 1 February 1989 Photon Energy (eV)
2<80 2.78 276
r ZnSe t Ix Tm = 18K
til
C
'" Tg=280·C FIG< 1. Growth temperature
dependence of the photolumi
nescence spectra in the exci
tonic emission region of the
typical undoped ZnSe films.
c\.-.LiLU..J.-'::=;:=::::::::,,----1
4400 4500
WavelengthCA)
in the excitonic emission region. Dominant peaks are those
originating from the recombinations of free excitons (Ex)
and excitons bound to neutral donors (Ix)' Observations of
a fairly strong Ex line and a clear separation between Ex and
1, lines are indicative of a good crystallinity of the films. It is
shown that the intensity of Ix line decreases with growth
temperature. This indicates that the residual impurities in
the films are donors and their concentration decreases with
temperature. As for the electrical properties of the undoped
films, however, the resistivity is too high to measure by a
conventional van dec Pauw method.
IV. ELECTRICAL PROPERTIES OF IODINEBDOPED ZnSe
FILMS
Figure 2 shows how the carrier concentration at room
temperature varies with the flow rate of ethyIiodide. All the
films were grown at 300 fiC and [VI} I [II] molar ratio of SO.
lt is shown that the carrier concentration can be changed
ZnSe:j Tm" R. T. Tg "300·C
E
-1 Y 10 E
.L: o
10-3
~0~.0~1----0~.O-5-0~.-1-----0-5--1~.O-----5~.O
C2 Hs! Flow Rate (f.JmQI/min)
FIG. 2. Dependence of the carrier concentration at room temperature on
the flow rate of ethyliodide. AI! growth conditions except the flow rate of
cthyliodide are kept unchanged.
Yoshikawa et al. 1224
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41widely from the order of 1015_1019 em -3 by varying the flow
rate of ethyliodide. The maximum carrier concentration ob
tained is 8 X 1018 em -3 and the corresponding minimum re
sistivity is 3.7X 10 -3 n cm. This has been achieved ata max
imum flow rate of ethyliodide and if the flow rate can be
much higher, much lower resistivity films will be obtained.
Anyway, the observed values of maximum carrier concen
tration and minimum resistivity are almost the same as those
already reported for chlorine-doped and iodine-doped ZnSe
films, grown by MBE9 and MOVPE, II respectively. The
crystallinity of the heavily iodine-doped films was character
ized by x-ray diffraction measurement. The full width at half
maximum (FWHM) of (400) ZnSe for CuKal was about
5.25 arcmin, which was as good as that of undoped ZnSe
films.
As for the electron mobilities at room temperature, they
are as high as 400-460 cm2 IV s in the films with carrier
concentrations below 5 X 1017 cm-3. However, they tend to
decrease with carrier concentration up to 230 cm2;V s. Con
sidering the film thickness is as low as 1 {-tm,15.16 observed
values of the electron mobility are considered very high.
Memory effect in doping ZnSe with ethyliodide was ex
amined by characterizing the undoped ZnSe films grown
just after the growth of the most heavily iodine-doped films.
The resistivity of the films was extremely high and the PL
properties were just similar to those of truly un doped ZnSe
films shown in a previous section. Thus it has been found
that the ethyliodide is a superior dopant source for ZnSe
from a viewpoint oftne controllability and reproducibility of
electrical properties of the n-type films.
Dependence of electrical properties at room tempera
ture of ZnSe films on the growth temperature under a con
stant flow rate of ethyliodide (0.067 pmol/min) has been
investigated and the results are shown in Fig. 3. The carrier
r~se:! Tm = R. r
C2HSl "O.067pmol/mi n
Growth Temperature (. C if)
3 :> 10 ;;-.
E u
FIG. 3. Growth temperature dependence of electrical properties at room
temperature of iodine-doped ZnSe films.
i225 J. AppL Phys., Vol. 65, No.3, 1 February 1969 concentration steeply decreases with growth temperature.
This is probably attributed to the decrease in the sticking
coefficient of ethyliodide at high temperatures. One may
consider the observed temperature dependence is attributed
to the increased concentration of some compensation
centers in the films grown at high temperatures. If this is
true, the compensation ratio NA IN D (i.e., the ratio of the
concentration of acceptorlike compensating center to that of
incorporated donor center) in the films grown at high tem
peratures should be close to unity. However, as discussed in
a following paragraph, the compensation ratio ofthe films is
much lower than unity. Therefore, we consider that the tem
perature dependence is attributed to the effect of decreased
sticking coefficient of the dopant with temperature. Recent
ly, similar marked temperature dependence of the sticking
coefficient of the dopant has been observed in antimony dop
ing in ZnSe by MBE.17 Another notable feature shown in
Fig. 3 is that the doping efficiency of iodine is highest at
260°C within the examined temperature range. This indi
cates that a temperature as low as 260 °e is high enough for
the di.ssociation of ethyliodide. From a viewpoint of an effi
cient dopant source in low-temperature epitaxy, ethyliodide
is found superior too.
Figure 4 shows the dependence of the electrical proper
ties of ZnSe films at room temperature on the [ethyl
iodidel/[H2Se] molar ratio under a constant flow rate of
ethyliodide. The growth temperature was 300 °e. In this ex
periment, only the flow rate ofH2 Se was varied and all other
growth conditions were kept unchanged. It is shown that,
even though the flow rate of ethyHodide is kept unchanged,
the carrier concentration remarkably increases with (VIlli
[VI} source-gas molar ratio. Considering the fact that io
dine substitutes on Se sites in ZnSe, this result is considered
reasonable, because the concentration ofSe vacancy tends to
-~ -C
<11
<J
C o u
~ ""[ HZ Se Flow Rote (iJmo!/min)
300 200 100 50
ZnSe:1 Tm = R.T. Tg = 300·C Vl
e2HSl = O.067umo!{min 103 :>
0.2 ;::;.
E
$
?:
:D o
::2:
FIG. 4. Dependence of the electrical properties of iodine-doped ZnSe films
at room temperature on the [cthyliodide JI [H2Se I molar ratio. In this ex
periment. only the flow rate ofH2Se is varied and that of ethyliodide is kept
unchanged.
Yoshikawa et at. 1225
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41Temperature (K)
400 200 100
ZnSe:l~ . ~.".,... ......
r J{ Tg" 2 8 0 .C --'-x_"-'_
;:; 1017
f 'E
u
c:: o
~ t
~ 1016
u c:: o u
o i ! ! ,
10
FIG. 5. Temperature dependence of the carrier concentrations of iodine
doped ZnSe films for different growth temperatures. Three curves are
shown also as typical examples for different doping levels.
decrease with an increase in the flow rate of Hz Se, resulting
in a decreased probability of the doping efficiency of iodine.
Temperature dependence of the carrier concentrations
for different growth temperatures is shown in Fig. 5. Three
curves are shown also as typical examples for different dop
ing levels. The compensation ratio and the donor ionization
energy ED can be calculated from the above results using the
wen-known formula for nondegenerate statistics18;
n(n + N.4 )/(Nj) -NA -n) = (NJg)exp( -EvlkT),
(1)
where n is the electron concentration, N D and NA, are the
concentrations of donors and compensating acceptors, re
spectively, Nc is the density of states in the conduction band,
g is the degeneracy factor and assumed to be 2, and k and T
are the Boltzmann constant and absolute temperature, re
spectively. The solid lines through the experimental points
represent the best fit of Eq. (1) to the experimental values.
The parameters used in obtaining the fit are listed in Table
II. First, it should be noted that the compensation ratios are
sufficiently lower than unity. As discussed in a previous
paragraph, this indicates that the growth temperature de
pendence of the electron concentration shown in Fig. 3 can
not be explained by the mechanism of increased compensa-tion centers with temperature. The estimated
donor-ionization energy decreases with electron concentra
tion. In the heavily doped films grown at 280 ·C, the estimat
ed donor concentration 1s4.2 X 1017 cm 3. This value is high
enough for impurity banding and tailing of states, resulting
in 11 extremely small donor ionization energy. In the lightly
doped films grown at 320 ·C, the estimated activation energy
is 29 meV, which is very close to the hydrogenic donor ioni
zation energy (29 ± 2 meV). 19 In the intermediately doped
film grown at 300°C, however, the estimated value is 20
me V, which is slightly less than the hydrogenic donor ioniza
tion energyo This reason is not clear at present, but it has
been reported that, in the intermediately doped ZnSe films,
the values of donor ionization energy determined from the
temperature dependence of the carrier concentration are of
ten somewhat smaner than those determi.ned by an optical
measurement.7-9
Figure 6 shows the temperature dependence of the elec
tron mobility for different doping levels, which correspond
to the films shown in Fig. 5. The low electron mobility in the
heavily doped film grown at 280"C is attributed to the in
crease in ionized-scattering centers. In the lightly and inter
mediately doped films, the electron mobility increases with a
decrease in temperature because of a decrease of polar-opti
cal phonon scattering. Considering that the thickness of the
film grown at 320°C is as low as 1 pm, the remarkable in
crease in electron mobility with a decrease in temperature is
indicative of the crystaUinity of the film being very good,
According to the data shown above, it has been shown
that iodine is a useful donor dopant for controlling the elec
trical properties ofZnSe widely. However, it should be noted
that its doping efficiency greatly depends on the growth pa
rameters, especially growth temperature and [VII]I[VIJ
source-gas molar ratio.
Vo Pl PROPERTIES OF IODINE-DOPED ZnSe FILMS
Photoluminescence spectra at room temperature of
typical iodine-doped ZnSe films with different doping levels
are shown in Fig. 7. It is shown that the lightly doped films
exhibit strong blue near-band-gap emission at around 4610
A (2.69 eV), which probably originates from recombina
tions between bound electrons and free holes. In these films,
emissions from deep centers are very weak. However, as the
carrier concentration increases, the broad deep level emis
sions observed in 5000--7000 A (about 1.7-2.4 eV) become
dominant. Since the spectra are modulated due to the effect
of optical interference in the film and many "peaks" can be
observed in the spectra, the origin for the emissions cannot
TABLE II. Electrical parameters of iodine-doped ZnSe films obtained by fitting the temperature dependence of the carrier concentration to the formula for
non degenerate statistics.
Growth
Sample temperature C2HsI EI> NI> NA
No. ee) (pmol/min) (meV) (1016 em 3) (lO"cm-') NAIND
SE8825 280 0.067 0.000 12 42 63 0.15
SE8842 300 0.013 20 4.5 12 0.27
SE8827 320 0.067 29 1.6 5.9 0.37
1226 J. Appl. Phys., Vol. 65, No.3, 1 February 1989 Yoshikawa et al. 1226
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41if)
:>
"'
N
Ii:
u
,... -
.0
0
~
C
~ -u
<II
W 103
x Tg= 2BO'C
102
70 iOO 200 300 400
TI&mperature ( K )
FIG. 6. Temperature dependence of the electron mobility in iodine-doped
ZnSe films with differellt doping levels, which correspond to the fiims
shown in Fig. 5.
be determined. They are probably the emissions from com
plex centers such as the copper-green (eu-G) and the self
activated (SA) centers. However, as discussed later, the ori
gin for deep centers in heavily doped films is uncertain.
Figure 8 shows the dependence of the peak intensities of
both the blue and the deep level emissions on the flow rate of
ethyliodide. Correspondence between the flow rate of
ethyliodide and the carrier concentration in the films at
room temperature is also given by the upper abscissa. Similar
results have already been reported by Shibata, Ohki, and
Zembutsu. i J But, it should be noted that they have shown
the growth temperature dependence of photoluminescence
properties in the films grown under a constant ethyliodide
flow rate. The carrier concentration in their films has been
varied due to the effect of decrease in carrier concentration
with growth temperature. On the other hand, the films
shown in Fig. 8 were grown at a constant substrate tempera-
K'--~=-~-- .~--~
6.7X1015
5000 6000 7000
Wave-length (A)
FIG. 7. Photoluminescellce spectra at room temperature oftypica[ iodine
doped ZnSe films with different doping levels.
1227 J. AppL Phys., Vol. 65, No.3, , February 1989 -c
,x
0.01 Carrier
1016 Concentration (cm-3 )
1~7 IdS ,d9
Trn = R. T.
Tg = 300'C
x Deep-Level
EmiSSion
0050.1 0.5 10 5.0
CZHSI FlowRa!e (fjmo!!min)
FIG. 8. Dependence of the peak intensities of the blue and the deep level
emissions on the flow rate of ethyliodid<:. Correspondence between the flow
rate of cthyliodide and the carrier concentration at room temperature is also
given hy the upper abscissa.
ture, i.e., 300 ·C, and the carrier concentration in the films
was varied by changi.ng the flow rate of the dopant source.
Therefore, the effect only of doping levels on the lumines
cence intensity can be considered in the present data shown
in Fig. 8. It is shown in this figure that, in lightly doped films,
the blue emission is dominant and its intensity increases with
carrier concentration. This result indicates that the origin of
the blue emission relates to the iodine donors incorporated
during growth. However, the intensity reaches maximum at
around the carrier concentration of lOIS cm -3, and it de
creases with carrier concentration in heavily doped films. In
lightly and intermediately doped films, the intensity of deep
level emissions also increases with carrier concentration, but
the intensity is remarkably low compared with that of the
blue emission. However, as shown in the figure, the deep
level emissions become dominant in the heavily doped films.
Furthermore, the origin of deep levels probably relates in
part to complex centers between the iodine and Zn vacancy
(VZn), such as (I-Vztl) centers.9•11 However, it should be
noted that more complicated complex centers may relate to
the origin of deep levels. Since the I-VZIl centers are singly
ionizable acceptorlike centers, which act as carrier compen
sating centers in donor-doped films. Therefore, if the con
centration ofI-VZn centers is very high and if it exceeds the
concentration of shallow donor, the carrier concentration of
the films should decrease remarkably. However, as shown in
Fig. 2, the carrier concentration increases monotonically
with flow rate of ethyliodide within the experimental condi
tions examined in this work. Then we consider somewhat
more complicated complex centers are introduced in the
films due to the effect of heavy doping. The decrease in PL
intensities of both the blue and deep level emissions indicates
that the crystallinity in the heavily doped films is remarkably
degraded due to heavy doping.
The carrier concentration at which the intensity of blue
emission becomes the same level as that of the deep level
Yoshikawa et al. 1227
<" ••• ,-••••• -•••• '.~.-'-.' •• '.' ••• -.-. T. ••• .-••••• -.-.-.-.-••••••• ~.-;................... .... • • • • •• • .-, .-.-. ·.-~'.·.·;·.v.-.·.·.~.·.·.~.:.:.:;:.;.:.:.:.:.:.:.:;.x. ;.;.;.;.;.:.:;0;.:.;.;.:.:.;.:.:;;:.;.:.:.:.:.:.:.:.:.:;; .•.•. <;'.O;';>;>.',~.'-' • , •••••
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41emissions is about (2-3) X 1018 em -3. This value is almost
the same as that observed in chlorine-doped ZnSe films
grown by MBE.9 However, it is slightly smaller compared
with that observed in iodine-doped ZnSe films reported by
Shibata, Ohki, and Zembutsu.lI We consider that this is
probably attributed to the difference in growth temperature
between both cases.
Figure 9 shows the dependence on doping levels of PL
spectra in the near-band-gap emissions at room temperature.
In the heavily doped films, which are funy degenerate, a
notable wavelength shift and broadening of the emission
linewidth are observed. This is attributed to the effect of
impurity banding and the Moss-Burstein shift which are of
ten observed in heavily doped semiconductors.20
Figure 10 shows the PL spectra at 18 K of typical iodine
doped ZnSe films with different doping levels, which corre
spond to those shown in Fig. 7. It is shown that the excitonic
emissions are dominant in the films with carrier concentra
tions below lOl8 em -3. Deep level emissions such as the cop
per-green and the self-activated emissions tend to be com
parable in magnitude with the excitonic emission in the
heavily doped films. Figure 11 shows the emission spectra in
the excitonic emission region for different doping levels. In
lightly doped films two emission peaks are observed The
dominant peak Ix originates from recombinations of bound
excitons at neutral donors. Another peak E", is from recom
binations of free excitons. Furthermore, a very weak emis
sion 11 is observed at around 4455 A (2.781 eV), which is
attributed to the recombinations of bound excitons at deep
centers. As the carrier concentration increases, the Ix line
becomes dominant and the broadening of the linewidth is
observed. In the heavily doped films, the Ix line remarkably
shifts toward shorter wavelengths together with asymmetric
Photo") Energy (eV)
3.0 Z.9 2.8 2.7 2.6 2.5
ZnSe:!
...
o 4.3x1()18
>-
·iii
~ 6.0:<1 at?
C
c:. 2.0xla17
2.8Xl016
4000 4500
Wavelength (A) 5000 FIG. 9. Dependence on
doping levels of the photo
luminescence spectra in the
ncar-hand-gap emissions at
room temperature.
1228 J. AppL Phys., Vol. 65, No. 3,1 February 1989 4000 Photon Energy (eV)
2;5
5000 6000
Wavelength(A) 6.7 xl 015
7000
FIG. 10. Photoluminescence spectra at 18 K of typical iOdine-doped ZnSe
films with different doping levels, which correspond to those shown in
Fig. 7.
broadening with a tail extending to a longer wavelength. As
already pointed out,9 these are attributed to the decreased
binding energy of bound exciton!> due to the screening effect
of donor electrons on excitons and the Stark effect due to the
charged impurities in bound excitonsY These observations
are indicative of the films being heavily doped.
VI. CONCLUSION
Iodine-doped ZnSe films have been grown on (100)
GaAs by low-pressure metalorganic vapor phase epitaxy us
ing dimethyl zinc and hydrogen selenide as reactants. In or
der to accomplish an accurate control of the carrier concen
tration over a wide range, ethyliodide diluted to 1000 ppm
was used as a dopant source. It has been shown that the
carrier concentration at room temperature can be changed
Photon Enorgy (oV)
2.84 2.82 2.80 2.78 2.75
ZnSe:1 Tm=18K
Tg = 300'C
Carrier
Concentrc1ion
at R.i. (cm-J)
7.4xl018
,=-= __ -:-:-,=,L~"::"":;;::::"'_.,....I 2.0 x 1015
4350 4500
FIG. 11. Photoluminescence spectra in the excitonic emission region of the
iodine-doped films with different doping levels.
Yoshikawa et al. 1228
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41in the range from 10 l 5 to 1019 em -3 by varying the flow rate
of ethyliodide. The electron mobility at room temperature in
lightly doped I-j.tm-thick films is as high as 460 cm2 IV s. It
has been found that the doping efficiency of ethyliodide re
markably depends on the growth parameters, especially
growth temperature and [VII]![VI] source-gas molar ra
tio. This has been attributed to the effect of the decreased
sticking coefficient of iodine with temperature and source
gas molar ratio.
Photoluminescence properties at room temperature and
at 18 K have also been investigated for the films with differ
ent doping levels. In the lightly and intermediately doped
films, the room-temperature luminescence is dominated by a
strong blue near-band-edge emission with suppressed deep
level emissions. The origin of the blue emission has been
ascribed to the iodine donors incorporated during growth.
In the heavily doped films with carrier concentrations above
1018 cm -3, the luminescence is dominated by deep-level
emissions. This has been attributed to the formation of deep
complex centers due to the effect of heavy doping. Further
more, no memory effect has been observed in doping ZnSe
with ethyliodide even in the films grown just after the growth
of the most heavily iodine-doped films.
According to the results shown, it has been concluded
that iodine is a superior donor dopant for ZnSe from a stand
point of the controllability and reproducibility of elecrical
and photoluminescence properties of the n-type films over a
wide range.
ACKNOWLEDGMENTS
This work was partly supported by Grant-in-Aid for
Scientific Research on Priority Areas, New Functionality
Materials Design, Preparation and Control, from The Min
istry of Education, Science, and Culture. The authors wish
1229 J. Appl. Phys., Vol. 65, No.3, 1 February 1989 to express their gratitude to Dowa Mining Co., Ltd. for the
supply of the GaAs substrate.
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lOR. N. Bhargava, J. Cryst. Growth 59,15 (1982),
21lT. S. Moss, G, J. Burrell, and B. Ellis, Semiconductor Optoelectronics
(Butterworth, London, 1973), p. 48.
21H. Kukimoto, S. Shionoya, S. Toyotomi, and K. Morigaki, J. Phys. Soc.
Jpn. 28,110 (1970).
Yoshikawa et al. 1229
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205.208.120.231 On: Sun, 30 Nov 2014 13:02:41 |
1.343236.pdf | Deep traps at the interface of SiO2 and InP grown by molecularbeam epitaxy
A. A. Iliadis, S. C. Laih, E. A. Martin, and D. E. Ioannou
Citation: Journal of Applied Physics 65, 4805 (1989); doi: 10.1063/1.343236
View online: http://dx.doi.org/10.1063/1.343236
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/12?ver=pdfcov
Published by the AIP Publishing
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138.26.31.3 On: Mon, 22 Dec 2014 08:37:32Deep traps at the interface of Si02 and inP grown by molecular-beam epitaxy
A. A. lliadis, S. C. laih, E. A. Martin,a) and D. E. Ioannou
Electrical Engineering Department, University of Maryland, College Park, Maryland 20742
(Received 22 June 1988; accepted for publication 22 February 1989)
Deep level transient spectroscopy (DLTS) was employed to study for the first time the
interface between deposited Si02 and n-InP( 100) grown by molecular-beam epitaxy (MBE).
The DLTSspectra exhibited three weB-defined interface peaks II' 12, and 13, Comparison
between MBE grown layers and bulk samples clearly showed a different interface trap
configuration, with II being common to both types of samples and 12 and (, being
characteristic of the MBE samples. Two different thicknesses of Si02 were found to produce no
observable change in the DL TS signatures of the MBE samples. Peaks 12 and 13 were
associated with the rronequilibrium processes of MBE growth, and the data suggested that
these interface traps were derived from the semiconductor side of the interface.
I. INTRODUCTION
Recently the molecular-beam epitaxial (MBE) growth
of InP has shown promising results 1.2 and has attracted corr
siderable attention because of the wide range of potential
applications of this semiconductor in high-speed electronic
and optoelectronic devices.
A main difficulty in the fabrication of devices based on
InP is the low Schottky barrier height (<1>0 =0.5 eV) of this
semiconductor, resulting in the "soft" and "leaky" current
voltage (/-V) characteristics of the gate electrodes. For this
reason, most InP FETs use insulated gate technology to pro
duce either a metal-insulator-semiconductor (MIS) type of
device3 (thick gate insulator 600-1000 A) or an enhanced
gate bamer height device" (thin oxide 20-100 A) using a
particular oxidation process to unpin the Fermi level at the
interface. This metal-insulator-semiconductor approach is,
unfortunately, not without problems too. Native oxides
grown thermally or electrolytical.ly on InP are generally of
poor stability and low resistivity. Deposited oxides on the
other hand, like Si02, have been favored5 because of better
thermal stability and higher resistivity. However, the resul
tant SiOz/lnPinterface, which is of critical importance to
the electron transport in the device,6,7 is not yet clearly un
derstood. When MBE grown InP is used in the MIS struc
tures, very limited data on the charge trapping at the Si02/
InP interface appear in the current literature.
In this study we report for the first time deep level tran
sient spectroscopy CDLTS) studies of electron traps at the
SiOz/lnP interface ofMBE grown InP which show features
unique to MBE growth and have implications to our current
understanding of energy states at the oxide-semiconductor
interface.
It EXPERIMENTAL PROCEDURE
The lnP epitaxial layers were grown by MBE from solid
sources on (100) n-type or semi-insulating InP substrates at
two different growth temperatures, 450 and 530 ·C, under
phosphorus (P 2) stable conditions. The grown layers were
unintentionally doped n type with a carrier concentration
a) Also with Aerospace Technology Center Allied-Signal Aerospace Com
pany, 9140 Old Annapolis Road, Columbia, MD 21045. (N D -NA ) ranging between 7 X 1015 and 3 X 1016 cm -3 as
determined by electrochemical C-V profiling. Liquid encap
sulated Czochralski (LEC) InP( 100) undoped
(ND -NA = 2x 1016 cm-3) control samples were pro
cessed simultaneously, under identical conditions, for
comparison with the MBE grown layers. Both types of sam
ples were chemically etched first in buffered HF. then in
H2S04:Hz02:HzO foHowed by a final buffered HF etch to
remove any remnants of the native oxide. The samples were
then mounted quickly into the plasma-enhanced chemical
vapor deposition reactot: for SiOz deposition. The deposition
was done in a flow of silane and nitrous oxide at 250 ·C as
described in Ref. 8. The thickness of the deposited SiO? films
ranged between 100 A llnd 500 A. Aluminum dots for ~etal
insulator-semiconductor contacts and Au-Ge pads for oh
mic contacts were deposited in a conventional thermal evap
oration vacuum system. The DLTS measurements were
carried out in the temperature range between 90 and 350 .K
using a Polaron-BioRad DLTS system. Prior to the DLTS
measurements, the AlISi02InP MIS structures were evalu
ated by capacitance-voltage (C-V) measurements at 300 K.
The high-frequency C-V characteristics were typical of MIS
structures with well-defined accumulation, depletion, and
inversion regions. These structures allowed the DLTS tech
nique9 to probe most of the upper half of the energy gap, both
at the interface as well as in a substantia! part of the bulk of
the InP layers. Thus, both interface and bulk traps were ob
tained.
III. RESULTS AND DISCUSSION
The DL TS spectra of the MBE samples grown at the
Iow-(450°C) and the high-(530·C) temperature regimes,
and that of the LEC control sample, are shown in Figs. 1, 2,
and 3, respectively. It is evident from the spectra that the
DLTS signatures ofthe MBE and LEC samples differ signif
icantly. A larger number of peaks is observed in the MBE
samples, indicating that the nonequilibrium processes in
volved in MBE growth may result in a high number of in
strinsic and extrinsic defects. ! It is also evident that the low
temperature ofMBE growth produces the largest number of
4805 J. Appl. Phys. 65 (12), 15 June 1989 0021-8979/89/124805-04$02.40 © 1989 American Institute of Physics 4805
.. .' .•.•.•... ~ •.•.•. ;:-.: •.•.•. -. .•.•••••••••••• ~ .. ,..:.:.;.~.:.:.: •.•.•.•.•. ~ •• ; ......... '7.: •.• :.:.:O:.:.; •••••••••• ~ ••••• ~.:.:.:.:.:.:.:.: ••• .> •••• ;<;~.:.:.:.:.:.:.;o:.:-; ••••• ,:.·.·.·.:.~.:.:.:.:.:.:·:·x·:-.:·:·.·.-.~-..·.·.·.·;>.:.:-.:.~.:-:.:.;.~.:.:., •.•..••.•.• -.•. ---
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138.26.31.3 On: Mon, 22 Dec 2014 08:37:32AI/SiOz/lnP
MBE #148
110 150 190 230 270 310 340
TEMPERATURE (K)
FIG.!. DLTS spectrum ofMBE No, 148 grown at 450 'C. Interface peaks
I" [2' and 13 are clearly observed here. Reverse bias: ~ 1 V; filling pulse: 0
V; pulse width: I liS; and rate window: 80 s-' upper graph, 4 s-' lower
graph.
peaks, possibly due to the reduced surface mobility of the
arriving species during growth.
DLT~ spectra for two different Si02 thicknesses (100
and 500 A) are shown in Fig. 4 for the high-temperature
MBE sample (peak II has been omitted from this figure in
order to expand the scale). The DL TS signature of the inter
face remains unchanged for the two oxide thicknesses.
A total of six peaks (II' 12, /3' BI, B2, and B3) are ob
served in the spectra. These are designated by the letter / for
peaks related to the Si02/InP interface or by the letter B for
peaks related to the bulk of the layers. Such designation is
achieved by examining the shift of the peaks under different
filling pulses (Vf ) and/or reverse biases (V R ). According
to Ref. 9, the position of peaks due to interface traps changes
with Vi, and/or VR• while the position of peaks due to bulk
traps remains unchanged. This is clearly shown in Fig. 5 for
interface peak h The shift of this peak with Vr is evident
here. Similar shifts were observed for peaks 12 'and 11, No
shifts were observed for peaks Bl• Bz• and B3• Thus, i't was
determined that peaks I!, 12, and 13 are due to interface traps,
whereas peaks Ri• B2• and B3 are due to bulk traps. This
study is mainly concerned with the interface peaks II> 12, and
13,
(f)
(f)
~
...J Al/SiOz/InP
MBE #139 II
x 5.0
o~~~~~~~~~
110 150 190 230 270 310 :J5()
TEMPER.ATURE (K)
FIG, 2. DLTS spectrum ofMBE No. 139 grown at 530 'CO Interface peaks
I, and I, are observed here. Reverse bias: ~ 3 V; filling pulse: 0 V; pulse
width: I ms; and rate window: 80 s -'.
4806 J. AppL Phys., Vol. 65, No. 12, 15 June 1989 I/O AI/Si0 2!InP
LEe ** 1
81 II
150 200 250 300
TEMPERATURE (K) 350
FrG. 3. DLTS spectrum of LEe No. I for comparison with the MBEsam
pies. Except for interface peak I, no other interface peaks are observed. Re
verse bias: -1.5 V; filling pulse: 0 V; pulse width: 1 ms,and rate window:
2005-'.
The capture cross sections and energies of the interface
states responsible for the observed peaks can be deter
mined9•10 from the Arrhenius plots of the thermal emission
rates, as shown in Fig. 6 for peak 13, for two bias levels. The
densities of these states can be obtained from the magnitude
of the DLTS peaks using the analysis of Ref. 9, provided the
densities are not higher than typically ~ 1012 cm -2 eV-1•
For higher densities this analysis provides only an estimate
of the trap density, and simulation 10 is required to obtain
accurate values.
Peak II is a relatively broad peak and it is observed in aU
our MBE and LEe samples. Under the present bias levels,
the corresponding trap capture cross section was
()' 00 "'" 9 X 10-16 cm2 and the trap energy around midgap.
Following the analysis of Ref. 9, the value of the trap density
AI/Si0 2/InP
MBE:# 139
TG=530°C
100 150 200
TEMPERATURE (K) Si02
100A
500 A
250
F.IG. 4, DLTS spectrum ofMBE No. 139 for 500 and 100 A of deposited
S102• No changes are observed in the spectrum for the two thicknesses of
Si02, Reverse bias: 3 V; filling pulse: 0 V; pulse width: 1 ms, and rate win
dow: !ODD s "
Wadis etal. 4806
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138.26.31.3 On: Mon, 22 Dec 2014 08:37:32~ AI/SlO.lInP
::l MBE fi 139 II
.0 .9 V.=-3.0 V
..J « z
~
(jJ
(j)
!..J a
200 250 300 350
TEMPERATURE (K)
FIG. 5. Temperature and shape change with filling pulse V, showing that
peak I, ofMBE sample No. 139, is originating from the Si02/InP interface.
Reverse bias: -3 V; pulse width: 1 ms; and rate window: 20 s '.
was calculated to be between 2Xl014 and 4X1014
cm -2 e y -l, which is much higher than the limit of applica
bility of the analysis and must therefore be taken as an esti
mated value.
As this peak is present in all our samples, intrinsic sur
face states are believed to be responsible; the definition of
intrinsic surface states as given by Spicer and co-workers 11 is
adopted here. Surface states around the mid gap of ( 100) InP
have been reported previously, although at lower densities
( 1012 em -2), for bare surfaces 12 and for surfaces with depos
ited phosphorus. 13 The high trap density observed may be
related to the processing of the surface prior to SiOz depo
sition.
Peak 12 is a relatively sharp peak and it is observed in the
low-temperature MBE sample. Its presence in the DLTS
spectrum of the high-temperature samples could not be veri
fied due to overlapping by the bulk peak RI• The capture
cross sections of the traps corresponding to this peak are of
the order of 1O-!I cm2, the energies between 0.44 and 0.58
eV and the density estimated to be between 2X 1013 and
4X 1013 cm -2 eV--·I• The range of energy of these traps is in
good agreement with the energy of an interface level ob
served by Williams and co-workersl4 at 0.4 to 0.5 eY from
the conduction band and attributed by Dow and Allen 15 to a
phosphorus antisite defect.
Peak I, is the sharpest of aU interface peaks and is ob
served in all the MBE samples. The capture cross section is
f7 =2x 10.-14 cm2, the energy is between 0.22 and 0.24 eV
(Fig. 6), and the density is estimated to be between 5 X 1013
and 9XlO13 cm-2ey--1• An interface level has been ob
served previously by Dow and Allen 15 at around 0.1 e V from
the conduction band and also by Yamaguchi and Ando!6 at
around 0.16 e V and was attributed in both cases to a phos
phorus vacancy. Although peak 13 is close in energy to these
interface levels, further studies are needed to establish a de
finitive link between this trap and the surface defect it is
associated with.
These data demonstrate that MBE grown and LEC
grown InP have a different trap configuration at the SiOz!
InP interface. Peaks 12 and 13 are found to be characteristic
of the MBE layers. As the conditions for surface treatment
4807 J. App!. Phys., Vol. 65, No. 12, 15 June 1989 PEAK 13
IOO~I __ ~~ __ ~~ __ ~~ __ ~r_~r~
74 7.8 8.2 8.6
IOOO/T (liT)
F!G. 6. Arrhenius plots of the thermal emission rates of peak I, for reverse
biases of (a) 2.5 V and (b) 3.0 V.
and SiOz deposition were kept the same for both types of
samples and different thicknesses of Si02 were shown to
leave the interface unchanged, the comparison leads to the
conclusion that the interface traps (12,]3) must be derived
from the semiconductor side of the interface. These traps
must therefore depend upon the MBE growth mechanisms.
This is a valid assessment in view of the nonequilibrium pro
cesses involved in the MBE growth of lnP which usually
result in a high number of intrinsic and extrinsic defects!
during growth. If this is indeed the case and the interface
traps are derived from the bulk but with modified energy
positions, then our data lend support to the defect model of
Spicer and co-workers II and in particular the work of Dow,
Sankey, and Allen 17 suggesting that interface levels are de
rivatives of bulk antisite and vacancy defects.
IV. CONCLUSION
We have used the DLTS technique to study for the first
time the interface between Si02 and n-InP grown by MBE.
Three wen-defined interface peaks (1], 12, and 13) are ob
served in the DLTS spectra. Two different thicknesses of
Si02 are found to produce no observable change in the
DL TS signature of the MBE samples. A comparison of
MBE and LEC grown samples shows that peak It is com
mon to both types of samples and it is probably due to intrin
sic surface states. Peaks 12 and l.~ are found to be characteris
tic to the MBE growth. The data suggest that these traps are
derived from the semiconductor side of the interface, and as
such they depend on the nonequilibrium process of MBE
growth.
'A. A. I1iadis, K. A. Prior, C. R. Stanely, T_ Martin, and G. R. Davies, J.
App!. Phys. 60, 213 (!986).
2W_ T. Tsang, R. C. Miller, F. Capasso, and W. A. Bonner, App!. Phys.
Lett. 41, 467 (1982).
'E. A. Martin, O. A. Aina, A. A. Iliadis, M. R. Mattingly, and L. H.
Stecker, IEEE Trans Electron Devices Lett. EDI.·9, 500 ( 1988).
'0. Wada, A. Majerfeld, and P. N. Robson, Solid-State Electron. 25. 381
( 1982).
'M. J. Taylor, D. L. Lile, and A. K. Nedoluha, J. Vac. Sci. Techno!. B 2,
522 (1984).
6D. L. Lile, J. Vac. Sci. Techno!. B 2,3496 (1984).
7H. H. Wieder, Surf. Sci. 132,30 (1983).
Iliad is eta/. 4807
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138.26.31.3 On: Mon, 22 Dec 2014 08:37:32"K. P. Pande, E. A. Martin, D. Gutierrez, and O. Aina, Solid-State Elec
tron. 30, 253 (1987).
oK. Yamasaki, M. Yoshida, and T. Sugano, Jpn. J. App!. Phys. 18,113
(1979).
"'F. Murray, R. Carin, and P. Bogdanski, J. App!. Phys. 60, 3592 (1986).
IIW. E. Spicer, P. W. Chye, P. R. Skeath, C. Y Suo and I. Lindau, J. Vac.
Sci. Techno!. 16, 1422 (1979).
12J. M. Moison and M. Benso!lssan, Surf. Sci. 168,68 (1986).
4808 J. Appt. Phys., Vol. 65, No. 12, 15 June 1989 13R. Schachler, D . .T. Olego, J. A. Baumann, L. A. BUllZ, P. M. Raccah, and
W. E. Spicer, App!. Phys. Lett. 47, 272 (1985).
"'R. H. Williams, A. McKinley, G. J. Hughes, V. Montgomery, and I. T.
McGovcm, J. Vac. Sci. Techno!. 21, 594 (1982).
"J. D. Dow and R. E. Allen, J. Vac. Sci. Techno!. 20, 659 (1982).
16M. Yamaguchi and K. Ando, J. Appl. Phys. 51, 5007 (1980).
17J. D. Dow, O. F. Sankey, andR. E. Allen, App!. Surf. Sci. 22, 937 (1985).
lliadis etal. 4808
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On: Mon, 22 Dec 2014 08:37:32 |
1.340623.pdf | Light scattering from thermal magnons in thin metallic ferromagnetic films
J. F. Cochran and J. R. Dutcher
Citation: Journal of Applied Physics 63, 3814 (1988); doi: 10.1063/1.340623
View online: http://dx.doi.org/10.1063/1.340623
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/63/8?ver=pdfcov
Published by the AIP Publishing
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193.0.65.67 On: Mon, 22 Dec 2014 10:29:25Light scattering from thermal mag nons in thin metallic ferromagnetic films
J< F< Cochran and J. R. Dutcher
Department of Physics, Simon Fraser University, Burnaby, B. c., V5A lS6, Canada
A computer program has been written with which the complex resonant frequency can be
calculated for a thin ferromagnetic metal film sandwiched between a nonmagnetic metallic
substrate and a nonmagnetic metallic overlayer. The calculation includes exchange and
magnetic damping having the Gilbert form. The program has been used to investigate the
sensitivity of thin-film resonant frequencies to the resistivities of the overlayer, the substrate,
and the magnetic film. It is concluded that the presence of an overJayer and of a substrate are
unimportant for the analysis of Brillouin scattering data from films less than 100 A thick:
uncertainties in the absolute value of the frequency shift of the scattered light-typically
1 :200-are greater than, or comparable with, the frequency shifts caused by an overlayer or a
substrate.
In this paper we make a quantitative assessment of the
effect of a metallic substrate and of a thin metallic overlayer
on thin film magnon frequencies. Experiments using Bril
louin scatteringl--8 have shown that boundary effects are
small, but it has yet to be shown that they are negligible if
accurate magnetic parameters are to be obtained from Bril
louin scattering data.8,9
The theory ofBriHouin scattering for thin, unsupported,
nonmetallic films has been carried through by Carnley, Rah
man, and MillslO using an application of the fluctuation
dissipation theorem from statistical mechanics. We have
chosen to attack this problem using the approach of Wol
fram and DeWamesl1 in which Maxwell's equations and the
Landau-Lifshitz equations for the magnetization are used to
calculate the normal modes of the system. We consider a
system composed of a magnetic film backed by a nonmagne
tic metallic substrate and covered by a nonmagnetic metal
overlayer. The x, y axes are in the plane of the film; z is
directed into the substrate and is parallel with the film nor
mal. The external magnetic field is directed along x, and the
in-plane component of the mag non wave vector is directed
along y (only magnetic excitations which propagate normal
to the applied magnetic field are considered). The ground
state of the system is assumed to be uniformly magnetized.
The surfaces of the magnetic film are taken to be at z = 0 and
at z = d. The front surface of the overlayer is located at
Z= -d,.
For this geometry, Maxwell's equations for the magneti-
cally active modes become
aex 1 a -= ---(h +417m ) (la) Jz c at y y ,
ae" 1 J -=--(hz + 417mz) , (lb) Jy c at
ahz Jhv 41T0' -" =--e . (1c) Jy az c x
The displacement current density has been neglected in (Ic)
because at microwave frequencies it is very small compared
with the conduction current density. Similar equations de
scribe the fields in the nonmagnetic metals except that
my = mz =0.
Solutions of Maxwell's equations are sought which are proportional to the factor ei( qy-m,). The disturbances in the
vacuum, overlayer, and substrate must all be proportional to
this same factor in order that the tangential components of
ex and hy may be continuous everywhere across the inter
faces at z = -dl, Z = 0, and z = d. The wave vector q is
real, and in a Brillouin scattering experiment it is determined
by the wavelength and the angle of incidence ofthe incident
laser light. 8 From the outset the frequency f, where OJ = 217"1,
is taken to be a complex quantity. The real part of the fre
quency is, of course, the resonant frequency of a normal
mode; the imaginary part of/must necessarily be negative
since the amplitude of a normal mode which has been stimu
lated by an impulse must die away with time due to magnetic
dissipation and eddy current damping. Solutions of Max
well's equations are sought which have a z dependence ~ eikz
where, by definition, the imaginary part of k is taken to be
positive. In the nonmagnetic metals, Eqs. (I) fully specify
the dependence of the wave vector k upon frequency. For
example, in the metallic overlayer, the wave vector kl is giv
en biZ k ~ = -q2 + (i18~), where 8i = c2/417OJO'I and (71
is the conductivity of the metal in esu. In the vacuum the
conductivity is, of course, zero and one must include the
displacement current density in Maxwell's equations.
In the magnetic metal Maxwell's equations alone do not
determine the allowed values of the wave vector; they serve
only to provide one set of relationships between the compo
nents of the magnetization and the magnetic fields. From
Eqs. (1) one finds
417my = -(! + i82k 2)hy + i82qkhz ,
417m2 = i(?qkhy -(1 + ilPq2)hz • (2a)
(2b)
A second set of relationships is provided by the Landau
Lifshitz equations of motion for the magnetization which,
when linearized, can be written in component form asl3
2A (J2
my) (iOJ) ---2--Hzmy - -mz = -Mshy,
M, Jz r (3a)
2A (J 2mz) (iW) ---~--Hvmz + -mv = -Mshz· Ms Jz- " r" (3b)
In these equations A is the exchange stiffness parameter and
the magnetomechanical ratio, r, is positive and is given by
g( el2mc). The effective fields Hy and Hz are
3814 J. Appl. Phys" 63 (8), 15 April 1988 0021-8979/88/083814-03$02.40 @ 19813 American Institute of Physics 3814
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193.0.65.67 On: Mon, 22 Dec 2014 10:29:252Aq2 .( ())) ( G ) Hy =H+---E ---+ay' M, y yMs (4a)
2Aq2 .( (u \ ( G ) Hz =H+---l -) --+az, M, y yMs (4b)
where H is the externally applied dc field and G is the Gilbert
magnetic damping parameter. The terms ay' ax represent
effective fields due to magnetocrystalline anisotropy. Equa
tions (2) can be used together with Eqs. (3) to obtain two
homogeneous equations for the magnetic field components
hy, hz• The requirement that these equations have a nontri
vial solution leads to a secular equation which is cubic in k 2:
where
PI = i(2A IMJj2) 2 ,
Pz = (2A IM,81f![1 + io2ql]
+ i(2A IMso2)(Hy + Hz + 417M3) ,
P3 = i{2A IMs02)(q282)(Hy + Hz + 477Ms)
+ (2A IMs02)(Hy + Hz + 8;rMs)
+ i[ ByHz -(Wly)2] ,
P4=i02q2[BzHy -(W/y)2] + [ByB, -(w1r)2].
In the above expressions Bv = Hy + 41TM." Bx
= Hz + 4-rrMs , and 02 = c2/4-rrw(7, wh"ere (7 is the conduc
tivity in esu of the magnetic metaL The general solution of
the combined Maxwell's equations and Landau-Lifshitz
equations is specified by six independent wave amplitudes 14:
a forward propagating and a reverse propagating wave for
each of the three wave vectors k" k2, k3 which satisfy Eq.
( 6). The six wave amplitudes in the magnetic slab must be
chosen so as to satisfy six boundary conditions. These are,
explicitly, at z = 0:
(i)
where
a=
(ii)
(iii) [(k1Iko) + 1]
[(kj/ko) -1]
and atz= d:
(iv)
3815 .J. AppL Phys, , Vol. 63, No, S, i5 April 19S8 (v)
(vi)
Conditions (0 and (iv) are required to ensure contin
uity of ex, hy across the slab surfaces. Conditions (ii), (iii),
(v), and (vi) are Rado-Weertmanl5 pinning conditions de
rived from a surface pinning energy density having the form
E, = Ky (myIMs)2 + Kz (m;JAi, )2. The complex frequen
cy OJ must be chosen so that the determinant of the coeffi
cients of the six homogeneous equations for the six field am
plitudes formed from (i)-(vi) vanishes. This is a very
difficult program to carry through algebraically, but one
which presents a relatively uncomplicated numerical prob
lem.
Having calculated a normal mode frequency it is a com
plicated but straightforward matter to calculate the fraction
ofthe incident optical energy which is scattered into a partic
ular direction, and to calculate the frequency distribution of
the scattered light.S, Ie.. I? The frequency of the scattered light
is shifted from the frequency of the incident light by ±fR'
where /R is the real part of the magnetic normal mode fre
quency. Ifthe normal mode is lightly damped the frequency
spectrum of the scattered light is a Lorentzian distribution
whosehalf-powerfrequencywidthistl/= 2/rwhere -1/7
is the imaginary part of the normal mode complex frequen
cy.8
The frequencies of the lowest modes have been listed in
Table I for an isotropic film having the magnetic properties
ofiron, 18 for an applied in-plane magnetic field of 1 kOe, and
for in-plane wave vectors typical of a backscattering experi
ment using 5145-A laser light. For the sake of completeness
we have also included a calculation of the frequency using
the Damon-Esbach theoryl9 for a magnetic insulator with
out exchange and having no losses, as weU as a calculation
for a metallic magnetic material having magnetic losses but
no exchange torques. The no-exchange frequencies lie re
markably close to the Damon-Eshbach frequencies. The
discrepancy decreases with increasing q and increasing mag
netic field, but increases with increasing thickness, rising
from approximately 1 :5000 for a lO-A-thick film to ! :300 for
a l00o~A-thick film. Even with the inclusion of exchange,
the resonant frequencies for the lO-A-thick film are within a
few percent ofthose calculated using Damon-Eshbach theo
ry. Of course, as is to be expected, exchange becomes more
important as the wave number of the excitation and the
thickness of the film increases.
The frequencies calculated for the "Norma! Case" (a
silver substrate and a 40-A gold ovedayer) are compared in
Table 1 with the frequencies calculated for no overlayer but a
silver substrate (column 5), and for a 40-A. overlayer and a
substrate both of which have the very large resistivity value
of 100 n em (column 6). Changing the resistivities of the
overlayer and substrate produces a change of approximately
1 :500 for the 100-A. film and for the smallest value of q. The
difference decreases for larger magnetic fields and for larger
values ofthe in-plane wave vector. The resonant frequency is
very insensitive to the resistivity of the magnetic film. The
J. F. Cochran and J. R. Dutcher 3815
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193.0.65.67 On: Mon, 22 Dec 2014 10:29:25TABLE 1. A comparison of the resonant frequencies, / (in GHz), of a system composed of a metallic magnetic film ofthickness d covered by a 40-A. layer of
gold (resistivity = 2.44 X 10-6 !} em) and mounted upon a silver substrate (resistivity = 1.59 X 10-6 n cm) for an applied magnetic field of 1.0 kOe. The
wave-vector component of the excitation parallel to the film surface and perpendicular to the magnetic field corresponds to that fOT backscattered 5145-A.
wavelength light incident at e = 10' (q = 42 413 cm I) and al4S· (q = 17 2707 cm-'). The properties of the magnetic film are taken to be those ofiron
having no magnetocrystalline anisotropy: saturation magnetization, 41TM, = 21.55 kOe; exchange parameter, A = 2.0X 10 6 erg/cm; g = 2.09; Gilbert
damping parameter, G"~ 7.0X 107 Hz; resistivity = I.OX 10 -5 n crn. Frequencies for the loo-A-thick magnetic film are listed for the lowest normal mode
(the uniform mode) and for the first exchange mode whose wavelength is A. = 2d.lt has been assumed that the magnetization is unpinned at the film surfaces.
(a) An iron film (except that A = 0) sandwiched between a 4O-A. gold overlayer and a silver substrate. (b) An iron film mounted on a silver substrate and
covered with a 40-A-thick layer of gold. (c) An iron film mounted on a silver substrate but having no overlayer. (d) An iron film mounted on a substrate
whose resistivity is 100 n cm and covered by a 4O-A.-thick layer of a material whose resistivity is 100 n em. (e) A magnetic film haYing the magnetic
properties of iron but its resistivity has been increased to 10-3 n em, mounted on a silver substrate and covered by a 40-A-thick overlayer of gold.
Thickness
angle
d= lOA
8= 10·
d= lOA.
()= 45°
d= 100 A
d= 100 A.
8=45" Damon
Eshbach
frequency
(GHz)
21.9798 No-exchlLTlge
meta! film'
frequency
(GHz)
--i 0.2373
21.9799 Normal
caseb
frequency
(GHz)
14.2226
-i 0.0953
15.5188
-i 0.0822
16.6112
-i 0.2371
96.7929
-i 0.2294
22_3769
-j 0.1110
96.9833
-i 0.2298
frequencies listed in the last column have been calculated for
a magnetic film whose resistivity has been increased two or~
ders of magnitude (from 1O~-5 to 10-3 fl em). The resulting
frequency shifts are less than 1: 105•
The authors would like to thank the Natural Sciences
and Engineering Research Council of Canada for grants and
a scholarship (l.R.D.) which supported this work.
'B. Heinrich, K. B. Urquhart, J. R. Dutcher, J. F. Cochran, A. S. Arrott,
D. A. Steigerwald, and W. F. Egelhoff (these proceedings).
2A. P. Malozemoff, M, Grimsditch, 1. Aboaf, and A. Bnmsch, J. Apr!.
Phys. 50, 5885 (1979).
'R. E. Camley and M. Grimsditch, Phys. Rey. B 22,5420 (1980).
4p, Griinberg, M. G. Cottam, W. Vacl!, C. Mayr, and R. E. Carnley, J.
App!. Phys. 53, 2078 (l982}.
5p. Kabos, W. D. Wilber, C. E. Patton, and P. Griinberg, Phys. Rev, B 29,
6396 (1984).
·P. Kabos, C. E, Patton, and W. D. Wilber, Phys. Rey. Lett. 53, 1962
(1984).
3816 J. Appl. Phys .. Vol. 63, No. B, 15 April 1988 Exchange, High resistivity Increased resistivity
no overlayer overlayer and substrated of magnetic metale
frequency frequency frequency
(GHz) (GHz) (GHz)
14.2227 14.2194 14.2226
-i 0.0943 -i 0.0765 -i 0,0953
15.5188 15.5188 15.5188
-i 0.0812 -i 0.0770 -i 0.0822
16.6125 16.5790 16.6113
_. i 0.2270 -i 0.0781 -i 0.2358
96.7929 96.7929 96.7929
-i 0.2294 -i 0.2294 -i 0.2261
22.3770 22.3765 22.3769
-i 0.1019 -i 0.0784 -i 0.1114
96.9833 96.9833 96.9833
-i 0.2297 -j 0.2297 --i 0.2269
7G. Srinivasan and C. E. Patton, J. App!. Phys. 61, 4120 (1987).
"J. R. Sandercock, in Light Scattering in Solids III. edited by M. Cardona
and G. Giintherodt (Springer, Berlin, 1982), Chap. 6.
"Carl E. Patton, Pl!ys. Rep. 103,251 (1984).
lOR. E. Camley, Talat S. Rahman, and D. L. Mills, Phys. Rev. B 23. 1226
(1981 ).
liT. Wolfram and R. E. DeWames, Phys. Rev. B 4,3125 (1971).
12In the program which we wrote, the displacement current was included in
Eq. ( I c) for the substrate and overlayer in order to be able to approach an
insulator limit.
"William Fuller Brown, Jr., Micromagnetics (Krieger, Huntington, New
York, 19781, Chap. 3.
!4W. S. Ament and G. T. Rado, Phys. Rev. 97,1558 (1955),
15G. T. Rado and J. R. Weertman, J. Phys. Chern. Solids 11,315 (1959).
"'W. Wettling, M. G. Cottam, and J. R. Sandercock, J. Phys. C 8, 211
(1975).
17L. D. Landau and E. M. Lifshitz, Electrodynamics o/Continuous Media
(Pergamon, Oxford, 1960), Chap. XIV.
I" Anisotropy was ignored in the calculations for Table I because it has no
direct effect on the frequency shifts caused by the electrical properties of
an over/ayer or substrate or on shifts due to the conductivity of the mag
netic layer. Such anisotropies do have a profound effect on the resonant
frequencies themselves, but that will be the subject for further work.
IYR. W. Damoll and J. R. Eshbach. J. Phys. Chem. Solids 19, 308 (1961).
3816
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1.344943.pdf | Rareearth promoters of semiconductor oxidation: The case of GaAs(110)/Yb
S. Chang, P. Philip, A. Wall, X. Yu, and A. Franciosi
Citation: Journal of Applied Physics 67, 4283 (1990); doi: 10.1063/1.344943
View online: http://dx.doi.org/10.1063/1.344943
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59Rare-earth promoters of semiconductor oxidation: The case
of GaAs(110)/Yb
s. Chang,a) P. Philip, A. Wall, X. Yu, and A. Franciosi
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis,
Minnesota 55455
(Received 25 October 1989; accepted for publication 15 January 1990)
Synchrotron radiation photoemission studies show that thin Yb overlayers (0.3-4.1)
monolayers) enhance the oxidation of GaAs ( 110) surfaces. The magnitude of the promotion
effect varies as a function of Yb coverage. The oxidation reaction products involve several
nonequivalent oxidation states of As and Ga. The specific catalytic activity of the pure divalent
Yb overlayers in promoting GaAs oxidation appears lower than that of Sm overlayers
containing both Sm2+ and Sm3+ species. The spectroscopic signature of the oxidation reaction
products, instead, is compellingly similar for the two rare-earth promoters. We propose that
the oxidation promotion mechanism is related, in both cases, to the decomposition of metal!
semiconductor interface reaction products upon exposure to oxygen, and that the rare-earth
atomic valence has only a limited influence on the promotion mechanism.
I. INTRODUCTION
Thin overlayers of the low-electronegativity, rare-earth
metal 8m substantially increase the Sic 111 )-02 and
GaAs( 110)-02 reaction rates.l On GaAs both divalent Sm
and trivalent Sm species contribute to the observed catalytic
activity. 1 We tentatively associated the formation of two dif
ferent As oxidation products (oxides or arsenates) with the
presence of two types of reaction intermediates involving,
respectively, divalent and trivalent Sm. In this study we spe
cifically address the correlation between the nature of the
oxidation reaction products and the rare-earth metal valence
by examining the activity of divalent Yb overlayers in pro
moting the oxidation of GaAs( 110) surfaces.
We selected Yb as a test case since its valence has been
well characterized at metal/semiconductor interfaces and
during oxidation, and because of the relatively simple inter
face morphology observed for GaAs/Yb.2.3 Studies of the
GaAs( 110)/Yb interface by Nogami et al.4 have demon
strated that Yb atoms are in the divalent electronic configu
ration 4114 During the oxidation of elemental Yb films,5.6
Yb) + species have been identified in the resulting oxidized
layer. No mixed-valent Yb emission was observed in either
case. Yb exhibits a relatively abrupt reacted interface mor
phology with semiconductors, with evidence of room tem
perature interdiffusion on GaAs( 110) in a limited range of
Yb coverages [1-2 monolayers (ML)], in contrast with
what has been observed for GaAs/transition metal inter
faces. 2.3.7
We focus here on the relationship between specific activ
ity for oxidation promotion and rare-earth valence through a
comparison of results for Sm and Vb, and we explore the
relationship between oxidation promotion and GaAs/Yb in
terface morphology. We found that Sm and Yb promote the
formation of compellingly similar oxidation reaction prod
ucts regardless of their different initial valence prior to oxy
gen exposure, and that oxidation promotion occurs through
oJ Present address: Xerox Webster Research Center, Webster, NY 14580. the decomposition of rare-earth Ga and rare-earth As inter
face reaction products.
II. EXPERIMENTAL DETAilS
The experiments were performed on GaAs( 110) sur
faces obtained by cleaving in situ n-type, Te-doped,
4 X 4 X 10 mm1 oriented single crystals at operating pressure
< 5 X 10-11 Torr. Yb was deposited from a resistively heat
ed W coil at pressure < 2.5 X 10-10 Torr. The metal COver
age (J was measured with a quartz thickness monitor and is
given in mono layers (ML) in terms of the GaAs( 110) sur
face atomic density (I ML = 8.85 X 1014 atoms/cm~). Oxy
gen exposures were performed by isolating the ion pump
from the spectrometer and maintaining a constant oxygen
pressure (10-7_10-5 Torr) for appropriate lengths of time.
The pressure was monitored with a low-emission ion gauge
that did not face the sample surface in an attempt to mini
mize the excitation of molecular oxygen. Exposures are
given in Langmuirs (L) throughout the paper
(I L = 1 sX 10-6 Torr).
The photoemission measurements were conducted by
positioning the sample surface at the focus of a monochro
matic synchrotron radiation beam and a commercial hemi
spherical electron energy analyzer. The synchrotron radi
ation emitted by the I-GeV electron storage ring Aladdin at
the Synchrotron Radiation Center of the University of Wis
consin-Madison was dispersed by means of a grazing inci
dence "grasshopper" Mark II monochromator, or a 3-m to
roidal grating monochromator. The total energy resolution
was less than 0.3 eV for studies of the Ga 3d core levels
(hv = 6OeV) and As 3d core levels (hv = 85 eV), and about
0.4 eV for the valence band results, as determined from the
width of the Fermi level cutoff in valence band spectra from
thick metal films evaporated in situ onto GaAs( 110).
Selected results for the As 3d, Ga 3d, Yb 5p, Yb 4f core
levels and for the valence band emission are shown in Figs.
1-5 in the form of angle integrated photoelectron energy
distribution curves (EDCs). In each figure, the EDCs are
shown in relative units, after normalization to the mono-
4283 J. Appl. Phys. 67 (9), 1 May 1990 0021-8979/90/094283-08$03.00 @ 1990 American Institute of Physics 4283
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59GaAs/Yb·O z
As 3d cores
.---- 0 L
lOooL hv= 85eV
Ybcoveraee
4
1, 1 1\ (ML)
I il/,l \ x~ ,J,
I \
x2 ~ __ d~
6 S 4 3 2 I 0 -I -2 -3 -4
Relative Binding Energy (eV)
FlG. 1 As 3d core emission from GaAs/Yb at h" = 85 eV before (dashed
line) and after (solid line) 10 \ L of oxygf:l1 exposure. We show results for
the fr"e GaAs( 110) surface (bottom-mo£t EDC) and for surfaces with Yb
(lverlayers of increasing thickness (disl'h.~ed upward). The zero of the
binding energy ~I:ale is referred to the position of the As 3d core levels from
the cleaved surface prior to Yb deposition. The vertical bars I-A mark the
no~ition of oxidized As 3d features observed by Landgren el al. (Refs. 8 and
~) during oxidation ofGaAs and associated by these authors with As atoms
l'oordinated with 1 to 4 oxygen atoms. respectively. Yb overlayers enhance
the oxidatIOn of As at all Yb coverages explored.
chromator throughput, monitored by means of a Ni mesh
\QCalW near the monochromator exit slit. EDCs for the core
lev.:::!: emisi>ioi1 are showi1 anef subtraction of a smooth sec
ondary electron background (approximated with a third or
der polynomial).
ill. RESULTS AND DiSCUSSION
A. Coveragecdependent oxidation promotion
In Fig. 1, weshowth~As 3dcoreemissionathv = 85 eV
before (dashed line) and after (solid line) exposure to 103 L
oxygen. The bottom-most EDCs were obtained for the free
GaAs( 110) surface, while spectra displaced upward show
the effect of Yb overlayers of increasing thickness. The zero
of the binding energy scale corresponds to the initial position
of the As 3d core level in flat band conditions, prior to Yb
deposition and oxygen exposure.
Deposition of Yb on the GaAs ( 110) surface (dashed
line) yields a rigid shift of the 3d core levels to lower binding
energies reflecting a band bending of 0.65 ± 0.05 eV. Well-
4284 J. Appl. Phys .. Vol. 67. No.9. 1 May 1990 ! J
J GaAs(Yb.01
Ga 3d and Yb 5p cores
---. 0 L
-IOOOL
Yb5p
1
1314
t6 t4 t2 to J " , " , ,
, I
4
Retative Binding Energy (eV) hv= 6lJeV
(ML)
o
o ·2
FIG. 2. Ga 3d and Yb Sp core emission from GaAs/Yb at hv = 60eV before
(dashed line) and after (solid line) a 10' L oxygen exposure. We show re
sults for the cleaved GaAs( 110) surface (bottom-most EDC) and for sur
faces with Yb overlayers of increasing thickness (displaced upward). The
zero of the binding energy scale is referred to the position of the Ga 3d core
levels from the cleaved surface prior to Yb deposition. The vertical bars 1--4
mark the position of oxidized Ga 3d features observed by Landgren et al.
(see Refs. 8 and 9) during oxidation of GaAs. Yb overlayers enhance the
oxidation of Ga at all Yb coverages explored.
defined line shape changes in the 0.3-1.4 ML coverage range
in Fig. I reflect the emergence of emission from a second 3d
doublet shifted by -0.7 eV to lower binding energies relative
to the main line.4 This new 3d contribution appears as a
shoulder 1.0-1.5 eV below the zero of the binding energy
scale in the low coverage spectra of Fig. I (Yb coverages
0.3..;0..;1.4 ML) and dominates the overall spectrum for
coverages ;> 1.9 ML. The formation of this new chemically
shifted As 3d component has been observed by Nogami et
al.4 and associated with the formation ofYb·As arsenidelike
reaction products following atomic interdiffusion across the
GaAslYb interface.
Exposure of the free GaAs surface to 1 <P L of oxygen
(bottom-most EDC, solid line) yields a rigid shift of the 3d
emission to lower binding energies (reflecting a band bend
ing of 0.5 eV) and some broadening of the core line shape,
mostly determined by a change in the surface· related core
level contribution. 8-10 The relatively small changes in the As
3d emission and the lack of chemically shifted As 3d features
Chang etal. 4284
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59GaAs/Yb
Valence Band
----0 L --lOOOL
-xl/4
-xl/4 hv~ 60eV
Bulk
Surf ~1 Yb
~ ~ coverage
11'11 (ML)
,~1111i1 ," ~':
I t 27.5
.~ ---xl/2 --,I',
I I
I I " ::>
!:
.~
-.:; j I I 4.1
\
e:. -xl/4 ,'1/1
?> ---x 1/2 I I
I I '§ ---7
~ I I
I
-= • 1\
=::;~ /\ /11\
.---7~-----)./ \ 1.9 ~
'. i\ 1\ , I -~1/4 III1 I I ---~~~--_________ LL4
-xl/2
---xl ,i
t'I'1 : 11\
I I
I
---~---------_I I
-xl/2
---xl
---;:;,
/-, Din Curve
/ ". /\ ,....
xS I \ I'
/ \ I I f'
--' \ I \ / \ '_j \ /'" I
" I I
16 14 12 10 8 6
Oindmg Energy (cV) o
FIG. 3. Valence band and Vb 4/emission at hv = 60 eV for GaAs/Yb be
fore (dashed line) and after (solid line) exposure to 103 L of oxygen. The
bottom-most EDC is for the free GaAs( 110) surface, and the second bot
tom-most curve (dashed-dotted line) was obtained by subtracting the un
oxidized spectrum from the spectrum of the same surface after oxygen expo
sure. Other spectra displaced upward show the effect of Vb overlayers of
increasing thickness. Before oxidation the valence emission is dominated by
the Vb + 24/ final state mUltiplet. Vertical bars mark the surface and bulk 4/
contributions. After oxidation the valence band includes ° 2p emission near
5.5 eV, and the Vb+J 4/ final state mUltiplet in the 7-13 eV region.
emphasize that in this exposure range only submonolayer
oxygen coverages can be obtained on the free GaAs ( 110)
surface at room temperature.8,9
A large enhancement of As oxidation is observed in the
presence of Yb overlayers, with the emergence of well-de
fined oxidized As 3d features on the high binding energy side
of the main line in Fig, 1, At the lowest Yb coverage explored
(0_3 ML, second bottom-most EDCs in Fig, 1), exposure to
oxygen yields a new oxidized As 3d feature at 2,75 eV, in-
4285 J. Appl. Phys., Vol. 67, No.9, 1 May 1990 :? '2
;:J
~
.~
" B .s
" 0 tl l
f GaAs/Rare-earth-l000LOl
As 3d cores
4
Yb
0,3 ML
Sm
0.3 ML hv= 85eV
6 5 4 3 2 ° -I -2 -3 -4
Relative Binding Energy (eV)
FIG. 4. As 3d emission at hi-= 85 eV from GaAs/Yb-O, (top) and
GaAs/Sm-O, (bottom), at a metal coverage of 0.3 ML (at which both rare
earths are divalent prior to oxidation) and a 10' L oxygen exposure (solid
circles). We also show (solid line) the result of a least-squares fit of the As
3d lineshape in terms oftwooxidized As and one unoxidi~ed As 3d doublets
(dashed line). Vertical bars I to 4 mark the position of oxidized As 3d fea
tures observed by Landgren et al. (see Refs. 8 and 9) duringUaAsoxidation
and associated by the same authors with arsenic atoms coordinated with 1
to 4 oxygen atoms, respectiVely.
creased emission in the 0-2 e V range, and removal of the
emission from the Yb-As arsenidelike phases at the interface
(shoulder at -1.0 eV in the unoxidized spectrum). The
main oxidized As 3d feature shifts to higher binding energies
at higher Yb coverages and appears at 3,2 eV for a metal
coverage of 4.1 ML (topmost EDC in Fig, 1, solid line),
Such a shift is similar to that observed by Su et aI, II during
oxidation of elemental As, and assigned by these authors to
the formation of As20y 12.13 For comparison, we also indi
cate with vertical bars 1 to 4 in the topmost section of Fig, 1
the position of oxidized As 3d features observed by Land
gren et al,K.9 during oxidation of the free GaAs( 110) surface
at high oxygen exposures (10"'_1014 L), The position of the
vertical bars in Fig. 1 takes into account the variation in band
bending between the results of this work and those of Refs. 8
and 9. Landgren et aI, associated features 1-4 with As atoms
coordinated with 1 to 4 oxygen atoms, respectively, Com
parison with our results for GaAs( 110)/Yb oxidation sug
gests the coexistence of severai nonequivalent oxidation
states for As within the reaction Qroducts in our results.
After oxidation, residual As 3d emission is observed
near the pinned As 3d position at --0,65 ± 0,1 eV. The
corresponding broad line shape is likely to reflect the partial
superposition of unoxidized As emission with 3d contribu-
Chang etal. 4285
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59~
c:
::J
-e
<t:
?;>
:;;
c:
" " c:
~
-"' " 2 " 0:: GaAs/Rare-earth-IOOOL O2
As 3d cores
Yb
14 ML
Sm
14M1.
' ..
6 5 .\ 2 0 ·1
RciJti\c Binding Energy (eVI hv= 85eV
2 ·3 -4
FIG. 5. As >,d emission at h" = 85 eV from GaAs/Yb-O, (top) and
GaAs/Sm-O. (bollom), at a metal coverage of 1.4 ML (at which Sm is
mixed valent'prior to oxidation), and a 10' L oxygen exposure (solid cir
des). We abo show (,,)lid line) the result of a least-squares fit of the As 3d
IlIlc shape in terms of three oxidized As and one unoxidized As 3d doublets
(dashed line) Vertical bars I to 4 nu,,\; the position of oxidized As 3d fea
tures observed by Landgren ct af. (Refs. 8 and 9) during GaAs oxidation
and associated by the same authors w~th arsenic atom, coordinated with 1
to -t l1X~gen atoms. respectively. Sm and Yb o\crlayers promok the forma
t il>ll of similar oxidalic))1 reaction products.
tions from As atoms in low oxidation stati:'''' If we use the
area shared by {'fort; pair of oxidized-unoxidized spectra in
Fig. I as a rough ",',~:imate of the unoxld,:cd As 3d emission
intensity, we ob{~t',;t that for Yb COVi:ti,ges "> I ML the total
emission intensity from oxidized l\S species in the 0-5 eV
range tracks the initial emission btc-Hsity from the Vb-As
reacted phase" prior to oxygen exposure. This, together with
the changes in line shape observed upon oxidation in Fig, I,
indicates that As oxidation occurs through the irreversible
decomposition of the arsenidelike reaction products at the
interface.
In Fig. 2 we show the Ga 3d and Yb 5p core emission at
hv = 60 eV before (dashed line) and after (solid line) expo
sure to 103 L of oxygen. The bottom-most EDCs show re
sults for the free GaAs ( 110) surface, while spectra displaced
upward show the effect ofYb overlayers of increasing thick
ness, The zero of the binding energy scale corresponds to the
initial position of the Ga 3d core level in flat band condi
tions, I~
Yb deposition onto the cleaved Gil-As surface yields Yb
5p emission features in the 3-5 and 9-11 eV binding energy
range, a rigid shift of the Ga 3d core levels to lower binding
energies due to band bending, and changes in the Ga 3d line
shape. The line shape changes are due to the emergence of a
4286 J. Appl. Phys., Vol. 67, No.9, 1 May 1990 low binding energy Ga 3d component visible as a shoulder at
-I eV in the EDCs for coverages 0.3;;;8< 1.4 ML This
component becomes the dominant Ga 3d contribution in
EDCs for 8;;; 1.9 ML Low binding energy components of
this kind have been observed during GaAs reaction with
Sm,l" Ce,I6 and Yb,~ and associated with the formation of
Yb-Ga alloyed species. A shift of about 0.4 eV to lower bind
ing energies is observed for the Yb 5p core levels when spec
tra for 8 = 0.3 ML coverage are compared to those for (};) I. q
ML This is also qualitatively consistent with Yb-Ga alloy
ing, since Pauling's electronegativity difference suggests
charge transfer from Yb to Ga in the alloy. At low Yb cover
ages, the alloy would be Ga rich, with large shifts to higher
binding energies of the Yb core levels and relatively minor
modification of the Ga 3d line. At higher Yb coverages, the
alloy would be Yb rich, the Yb 5p emission would converge
to the metallic situation, and the Ga 3d emission would ex
hibit a shift to lower binding energies as a result of charge
transfer,
At the highest coverage explored (27.5 ML), no residu
al Ga 3d or As 3d emission could be detected within an ex
perimental uncertainty of about 2%-5%. Changes in the Yb
emission also reflect the establishment of an elemental Yb
type of emission, For example, in the topmost EDC of Fig. 2
(dashed line), two partially resolved Yb 5p components are
observed with an energy difference of about 0.6 eV. We asso
ciate the higher binding energy doublet with a surface-shift
ed contribution, and the low binding energy doublet with
bulk Yb emission, in analogy with the results of Refs, 4 and
17-19 for elemental Vb, A similar effect is observed in the 4/
results,
Exposure of the free GaAs( 110) surface to 103 L of
oxygen (bottom-most EDC in Fig. 2, solid line) yields a
rigid shift of the Ga 3d core levels due to band bending, and
some broadening of the core line shape, The presence of Yb
overlayers on GaAs( 110) causes a substantial increase in
the Ga oxidation rate, as indicated by the formation of well
defined oxidized Ga features on the high binding energy side
of the main line. In particular, a shoulder in the 0-0.5 eV
range for O. 3 < 0< 1.4 ML evolves into dominant broad struc
ture centered at about 0.3 eV at Yb coverages 0"> 1.4 ML For
comparison, in the upper section of Fig. 2 we mark with
vertical bars I to 4 the position of the oxidized Ga 3d features
observed by Landgren et aI, K,'J during oxidation of the free
GaAs ( 110) surface at high oxygen exposures ( 106_1014 L) ,
The broad oxygen-induced Ga 3d feature observed in Fig. 2
indicates the coexistence of several nonequivalent Ga oxida
tion states within the reaction products.
A quantitative analysis of the overall Ga 3d line shape in
terms of different oxidized 3d components was not attempt
ed due to the close energy spacing expected for the different
oxidized 3d component, R,9,20 and due to the superposition of
the Ga 3d line with broad structure in the 0-6 eV range in
Fig. 2, deriving from 0 2s (Ref. 21 ) and Auger contributions,
The presence of this broad structure also complicates the
interpretation of the highest coverage spectra (27,5 ML) in
Fig. 2, where it dominates in the 0-6 eV range. In any case,
the results of Fig. 2 provide evidence that enhanced Ga oxi
dation is observed in the presence ofYb overlayers, and that
Chang eta!. 4286
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59the Ga oxidation process is accompanied by a parallel de
crease in the emission from the Yb-Ga alloyed phases at the
interface ( -1-- 2 eV, dashed line, in Fig. 2) throughout
the entire Yb coverage range explored.
Exposure to oxygen also yields large changes in the Yb
5p emission, namely a 3-3.4 eV shift to higher binding ener
gies of the 5p core levels, a sharp increase in the 5p full width
at half maximum (FWHM), and a variation of the apparent
5P3/2 -5P1/2 "spin-orbit" splitting from 6.0 (before oxida
tion) to 6.6 eV (after exposure to 103 L of oxygen). Such
changes indicate that most Yb atoms within the escape depth
are oxidized. The large oxidation-induced chemical shift of
the 5p core levels mostly reflects the valence change of the
Yb atoms from Yb2+ to Yb3+, and the corresponding differ
ence in intra-atomic screening of the 5p core hole.21-23 The
valence change is also clearly observed in the 4/ results to be
discussed in the next paragraph. The observed change in the
apparent spin-orbit splitting and FWHM of the 5p3/2-5P1/2
core features is likely to reflect changes in the 5p-4/multiplet
coupling, which is of the same order of magnitude of the
spin-orbit splitting for shallow core levels of the rare-earth
metals.22
Oxidation-induced changes in the Yb electronic config
uration are also clearly depicted in Fig. 3, where we show the
valence band and Yb 4/ emission from GaAs/Yb at hv = 60
e V before (dashed line) and after (solid line) exposure to
103 L of oxygen. The bottom-most EDC (dashed line) in
Fig. 3 shows the valence band emission from the free
GaAs ( 110) surface. The dash-dotted curve was obtained by
subtracting the band-bending-corrected GaAs( 110) spec
trum from an EDC from the same sample after 103 L of
oxygen exposure. Other spectra displaced upward show the
effect of Yb overlayers of increasing thickness. The zero of
the binding energy scale corresponds to the position of the
Fermi level, EF•
Even at the lowest Yb coverages explored, the 4/ cross
section at hv = 60 eV dominates the GaAs sp valence band
emission, so that prior to oxidation in Fig. 3 (dashed line) all
spectral features in the 0-3 e V range for 0 < B < 1. 9 reflect
the 4/ 13 final state doublet deriving from the photoionization
ofYb2+. For B-1.9 ML, broadening of the 4/ doublet sug
gests the presence of new 4/ contributions. These are clearly
observed for B = 4.1 and 27.5 ML when a well-defined Fer
mi level is also observed. The final EDC for () = 27.5 ML is
very similar to that of Yb metal,17.18 with two 4/ doublets
shifted 0.6 eV from each other and each exhibiting a spin
orbit splitting of 1.3 eV. By analogy with the results of Refs.
17 and 18, we attribute the two 4/ doublets to emission from
Yb surface and bulk atoms.24 Our results for the unoxidized
GaAslYb interface are in good agreement with those of No
gami et 01.,4 who reported GaAslYb reaction in the 1-2 ML
coverage range, and the gradual formation of a layer of me
tallic Yb (Ref. 4) at coverages > 2 ML.
Exposure of the free GaAs surface to 103 L of oxygen
yields limited emission of oxidation-induced valence states,
mostly accounting for an emission feature centered at -5.8
eV in the difference curve of Fig. 3 (second bottom-most
spectrum, dash-dotted line), in agreement with the results of
Refs. 8 and 9. When Yb overlayers are present, the oxidized
4287 J. Appl. Phys., Vol. 67, No. 9,1 May 1990 valence band emission is dominated by 0 2p-induced fea
tures at -5.5 eV. The characteristic Yb2+ 4/emission with
in 3 eV of EF vanishes, and is replaced by Vb-related cover
age-dependent features at 11.5,9.3, and 7.7 eV. Results by
Schmidt-May et aU for the oxidation of elemental Yb show
that the valence band emission is dominated by Yb3+ 4/12
final state multiplets located in the 7-13 eV binding energy
range, and are qualitatively consistent with those in the top
most section of Fig. 3 (solid line). We conclude that expo
sure of GaAs/Yb to oxygen yields oxidation of most of the
Yb atoms within the sampling depth, and a corresponding
Yb2+ _ Yb3+ valence transition. This change in the Yb elec
tronic configuration affects the Yb 5p emission in Fig. 2
through a modification of the intra-atomic screening of the
5p core hole, and 5p-4/multiplet coupling.
B. Microscopic picture
Our results for the GaAs/Yb interface prior to oxygen
exposure in Figs. 1-3 are in general agreement with those of
Nogami et a/.4 The presence of a chemically shifted reacted
As 3d doublet in Fig. 1, and an alloyed Ga contribution in
Fig. 2, together with the character of the 4/ emission in Fig.
3, supports the contention that interface reaction yields ar
senidelike species and Yb-Ga alloys involving divalent Vb.
In our results we find no evidence, however, for the existence
of a critical coverage of 1 ML, below which no atomic inter
diffusion would reportedly take place.4 Our results show a
monotonic interface evolution throughout the 0.3-4.1 ML
Yb coverage range. In this range, the attenuation rate of the
As 3d and Ga 3d core emission intensity as a function ofYb
coverage is very similar.25 At higher Yb coverages the faster
attenuation rate of the As relative to the Ga emission may
reflect trapping of As atoms in the interface region and the
progressive dilution of Ga in the Yb overlayer reported by
Nogami et al.4
Upon exposure to 103 L of oxygen, the relative integrat
ed emission intensities from the As 3d, Ga 3d, and Yb 5p
core levels in Figs. i and 2 show only minor changes, sug
gesting that the profile of the relative concentration of the
different elemental species in the direction perpendicular to
the surface is not strongly affected by the oxidation process.
The presence ofYb overIayers, however, enhances the oxida
tion rate of As and Ga atoms, as indicated by the large oxi
dized core contributions in Figs. 1 and 2. The formation of
oxidized As and oxidized Ga species in Figs. 1 and 2 is ac
companied by a parallel decrease of the core emission from
the Vb-As and Yb-Ga reacted phases at the interface. This
suggests that the observed enhanced As and Ga oxidation
rates is related to the presence of the Vb-As and Yb-Ga reac
tion products at the interface, and that oxidation takes place
either through the decomposition of such products or
through the formation of ternary oxides.
Abbati et al.26 have proposed that the enhancement of
the Si oxidation rate in the presence of several transition and
near-noble metal overlayers is related to the dynamic de
composition of semiconductor Imetal interface reaction
products. Such species would exhibit a higher affinity for
oxygen than the elemental semiconductor, due to the metal
lic density of states at the EF which favors chemisorption
Chang etal. 4287
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59processes, and because of the "broken" sp' hybridization of
the semiconductor atoms.2
1> The metal/semiconductor
phases would decompose in the presence of oxygen, releas
ing semiconductor atoms for oxide formation. The metal
atoms \vOltld recombine with new semiconductor atoms,
further disrupting the semiconductor substrate in an oxida
tion-induced dynamic process.
The model of Abbati et al.26 can, in principle, be ex
tended to a number of GaAs/metal systems because of the
similarity of the electronic structure of arsenide and silicide
phases 27.28 and because of the expected high affinity for oxy
gen of the overlayer-Ga intermetallics. In the case of
GaAs ( 110) -Vb, a decomposition of the semiconductor
metal interface reaction products upon oxidation is consis
tent with the results of Figs. 1-3. However, the dynamic
character of the decomposition is ruled out by three main
observations. First, the characteristic Yb-As and Yb-Ga
core features in Figs. I and 2 are irreversibly removed upon
oxidation. A dynamic decomposition should correspond to a
steady-state concentration of Vb-As and Yb-Ga phases be
low the oxidized layer, while we observe a rapid attenuation
of the characteristic Vb-As and Yb-Ga spectral feature rela
tive to the unoxidized As and Ga emission features. Second,
the overlayer atoms appear fully oxidized following a IOJ L
oxygen exposure (Fig. 3), so that they do not remain "pris
tine,,20 to recombine with semiconductor atoms. Third, we
observe no subst;mtial change in the relative intensities of the
Vb, As, and Ga core emission upon oxidation. This rules out
drastic rearrangements of the atomic concentration profile
in the direction normal to the interface, and suggests that Yb
remains near the over layer surface rather than forming a
steady-state semiconductor-metal reacted layer below the
oxide. ,', We conclude that oxidation promotion in the case of
GaAs/Yb-O, may be related to the decomposition of semi
conductor-metal interface reaction products, but that such a
decomposition is certainly not dynamic in the sense of Ref.
26. We speculate that the thermodynamics of this system
favors location of the metal atoms at the surface-vacuum
interface (in analogy with a number ofSi/metal-oxygen sys
tems involving low e1ectronegativity metals"'-" rather than
at the semiconductor-oxide interface, as in the case of several
Si/transition metal-oxygen and noble metal-oxygen sys
tems. ,,,
The role of rare-earth valence in determining the over
layer oxidation promotion activity can be examined by
comparing results for Yb and Sm overlayers. On Si ( III ) we
have observed little promotion activity at low Sm coverage
( < 1 ML). when a Sm:' + overlayer is present at the surface.
On the other hand, the presence of interface reaction prod
ucts involving Sm' + species at coverages > 1 ML yields
large oxidation promotion effects.' On GaAs( 110), we ob
served that Sm' + ({j < 0.3 ML) and mixed valent Sm species
({i> 0.3 ML) appear to promote the formation of different
types of oxidized-As phases. '
In Figs. 4 and 5 we directly compare results for the
GaAs/Yb-O:, and GaAs/Sm-O:,. 12 We show results for the
As 3d emission at hv = 85 eV for Yb overlayers (topmost
section) and Sm overlayers (bottom-most section) of simi
lar thickness (0.3 ML in Fig. 4 and 1.4 ML in Fig. 5) after
4288 J. App!. Phys., Vol. 67, No.9, 1 May 1990 exposure to 103 L of oxygen. The coverage of 0.3 ML in Fig.
4 corresponds to a mostly divalent state ofSm at the inter
face, while the coverage of 1.4 ML in Fig. 5 corresponds to a
Sm" + ISm' I mixed valent state. Yb overlayers include only
divalent atoms at all coverages prior to oxidation (see Fig.
3) .
The experimental data in Figs. 4 and 5 (solid circles) are
shown in arbitrary units, together with the results of a fit
(solid line) in terms of up to four As 3d components. Each
component was taken as a 3d doublet including two spin
split subcomponents, with spin-orbit splitting and branching
ratio fixed at the values obtained from the free GaAs( 110)
EDCs prior to metal deposition and oxidation. Each 3d sub
component was approximated with a Lorentzian function
convoluted with a Gaussian function. The Lorentzian full
width at half maximum (FWHM) was also fixed at the pris
tine GaAs (110) value.11 A least-squares fitting procedure
was used to determine energy position, intensity, and Gaus
sian FWHM of the different As 3d subcomponents. A single
Gaussian FWHM was used for all of the oxidized As sub
components in Figs. 4 and 5.1>·'4 The individual As 3d doub
lets resulting from the fitting procedure are also shown
(dashed line) in Figs. 4 and 5. In the topmost sections of
Figs. 4 and 5 we show with vertical bars I to 4 the position of
the oxidized-As features observed by Landgren et al. K.'J dur
ing oxidation ofGaAs, and associated by these authors with
As atoms coordinated with I to 4 oxygen atoms, respective
ly. Unfortunately, an analogous study could not be per
formed in the case of the Ga 3d core levels for which the
different oxidized components are too closely spaced in ener
gy, and oxidized and unoxidized features are partiaIIy super
imposed to the complex, coverage-dependent Sm 5p line
shape. I
The results of the fits in Figs. 4 and 5 show several simi
larities in the effect ofSm and Yb overlayers. In Fig. 4 diva
lent Sm promotes the formation of oxidized As 3d features at
0.65 ± 0.05 and 2.8 ± 0.05 eV (bottom-most section), while
the main emission feature at -0.55 ± 0.05 eV corresponds
to unoxidized As emission. The corresponding result for Yb
(topmost section) yields oxidized As 3d features at
0.55 ± 0.05 and 2.7 ± 0.05 eV, with relative amplitudes sim
ilar to those observed for Sm. The presence of at least two
oxidized As 3d features indicates the coexistence of relative
ly low and relatively high oxidation states for As (vertical
bars 1-4) within inhomogeneous oxidation reaction prod
ucts.
In Fig. 5 the fitting procedure in the case of mixed-va
lent Sm overlayers (bottom-most section) yields oxidized
As 3d components at 0.5 ± 0.1, 1.9 ± 0.1, and 2.7 ± 0.1 eV,
and a feature corresponding to emission from unoxidized As
at -0.5 ± 0.1 eV. In the presence of Yb"+ (topmost sec
tion), exposure to 10' L of oxygen yields oxidized As 3d
features at 0.6 ± 0.1, 1.9 ± 0.1, and 2.8 ± 0.1 eV, with the
main As substrate emission at a relative binding energy of
-0.5 ± 0.1 eV. In Figs. 4 and 5 we note that binding ener
gies and relative intensities of the oxidized As 3d features are
compellingly similar in the case of Yb and Sm overlayers.
The major difference appears to be a generally higher specif
ic activity1) for oxidation promotion of Sm relative to Vb,
Chang eta/. 4288
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128.59.222.12 On: Thu, 27 Nov 2014 09:42:59possibly related to higher interface reactivity of Sm. 36
A comparison of the results of Figs. 4 and 5 indicates
that at low metal coverage the reaction products involve
mostly high and low As oxidation states, while at coverages
above 1 ML an additional product involving an intermediate
oxidation state for As is detected. Without kinetic data it is
not possible at this time to determine if this additional oxida
tion state corresponds to an arsenate phase or to a substoi
chiometric binary oxide which appears when the oxidation
reaction becomes diffusion limited. We emphasize, in any
case, that a compellingly similar behavior is observed in the
presence of Sm and Yb overlayers, suggesting that the for
mation of different oxidation products in the presence of
Sm2 + versus mixed valent Sm species I is not the result of the
rare-earth valence transition, but rather a consequence of the
coverage dependence of the composition of the semiconduc
tor/metal interface reaction products. The properties of
these interface reaction products determine the oxidation
enhancement effect.
We suggest that the rare-earth valence has a relatively
small role in determining the oxidation promotion activity of
rare-earth overlayers on GaAs, and that the activity de
pends, instead, on the oxygen-induced irreversible decompo
sition of arsenidelike species and overlayer-Ga intermetal
lics formed at the interface upon metal deposition.
IV. CONCLUSION
Thin Yb overlayers promote the oxidation of As and Ga
at the GaAs( 110) surface during room temperature low
pressure reaction with oxygen (103 L). The reaction prod
ucts involve several nonequivalent oxidation states for As
and Ga atoms. Oxygen-induced decomposition of the arsen
idelike species and overlayer-Ga intermetallics present at the
GaAs/rare-earth interface is consistent with the observed
behavior, but contrary to the case of transition and near
noble metal on Si the decomposition is not a self-sustaining
dynamic process, at least under the reactions conditions ex
amined. Comparison of results for Sm and Yb overlayers on
GaAs( 110) indicates that the two rare earths promote the
formation of compellingly similar oxidation reaction prod
ucts, regardless of their different initial valence prior to oxy
gen exposure. We suggest, therefore, that the rare-earth va
lence has a limited effect on the microscopic mechanisms
which determine the oxidation promotion activity of the
overlayer.
ACKNOWLEDGMENTS
This work was supported in part by ONR under Grant
Nos. NOOO14-84-K-0545 and NOOO14-89-J-1407, and by the
Center for Interfacial Engineering of the University of Min
nesota. We thank the whole staff of the Synchrotron Radi
ation Center of the University of Wisconsin, Madison, sup
ported by the National Science Foundation, for their
cheerful assistance.
's. Chang. P. Philip, A. Wall, A. Raisanen, and A. Franciosi, Phys. Rev. B
35,3013 (1987).
'G. Margaritondo and A. Franciosi, Ann. Rev. Mater. Sci. 14,67 ( 1(84).
4289 J. Appl. Phys., Vol. 67, No.9, 1 May 1990 'See, for example, L. J. Brillson, Surf. Sci. Rep. 2. 123 (1982).
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257 (1982).
"A more precise determination of the chemical shift involved would re
quire for us to know the As 3d binding energy in elemental As, As,OJ'
GaAs, GaAs/Yb, and GaAslYb-O, relative to a common reference level.
If we use the vacuum level, as recommended by a number of authors [see,
for example, R. E. Watson and M. L. Perlman, Struct. Bonding 24, 82
( 1975) I, we need reliable values of the work function for each of these
systems, which are not available. For example, work function values of
3.75 and 5.1 eV have been reported for elemental As II and no work func
tion value is available for As,OJ' Ifwe use the work function values for As
and GaAs, and the results ofSu et 01. (see Ref. II) to estimate the As 3d
chemical shift due to As,OJ formation on GaAs, we obtain values of2.9 or
4.25 eV, depending on which work function value we employ for As.
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a value of 3.75 eV for the work function of elemental As from photoelec
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dicted instead a value of 5.2 eV based on the systematics of the work func
tion in the periodic table, and concluded that the value reported by Raisin
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work function with atomic number Z. The value of 5.2 eV proposed by
Michaelson is actually similar to the value of 5.1 eV reported earlier by R.
Schulze, Z. Phys. 92. 212 ( 1934).
I.p. E. Eastman, T.-e. Chiang, P. Heimann, and F. J. Himpsel, Phys. Rev.
Lett. 45, 656 ( 1980).
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17M. H. Hecht, A. J. Viesca;" I. Lindau. J. W. Allen, and L. I. Johans,on. J.
Electron Spectrosc. Rdat. Phenom. 34, 343 (1984).
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lat. Phenom. 18,43 (1980).
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(1982). observed a shift of2.2 eV of the Ga 3d core levels during oxidation
of metallic Ga and associated the shift to the formation ofGa,O,. If one
takes account of the changes in band bending and refers the bi~ding ener
gies to a common vacuum level (Refs. 10 and II). the position of [he Ga
3d line in Ga,O, should he dose to the position of vertical bars 3 and 4 in
Fig.2.
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Physics, Vol. 27 (Springer. New York, 1979).
"See A. Franciosi, J. H. Weaver, P. Perfetti. A. D. Katnani, and G. Mar
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6519 (1978).
24The higher intensity of the surface-related component relative to the bulk
component in the results of Fig. 2 (Yb 5p) vs Fig. 3 (Yb 4]) may be attrib
uted to the higher surface sensitivity of the Yb 5p results. Photoemission
results for Yb films in Refs. 17 and 19, in 1. Lindau and W. E. Spicer, J.
Electron. Spectrosc. Relat. Phenom. 3, 409(1974), and in F. Gerken, J.
Barth, R. Kammerer, L. I. Johansson, and A. Flodstrom, Surf. Sci. 117,
468 (1982), indicate that the minimum photoelectron escape depth oc
curs at electron kinetic energies between 5 and 40 eV. For a photon energy
of60eV, the kinetic energiesofthe 5pand 4fphotoelectrons are 25-30 and
52-56 eV, respectively. Thus, the surface-to-bulk intensity ratio should be
higher for the 5p cores than for the 4/ c(}r~ at .. "';"."",. ... ,,'-"' .. \ ... , p"""'= ==
gy.
"S. Chang and A. Franciosi (unpuhlished). See also Ref. 4.
'hI. Abbati, G. Rossi. L. Calliari. L. Braicovich, I. Lindau. and W. E. Spicer,
J. Vac. Sci. Techno!. 21,409 (1982).
"A. Franciosi, S. Chang. P. Philip, e. Caprile, and J. Joyce. J. Val'. Sci.
Chang eta/. 4289
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
128.59.222.12 On: Thu, 27 Nov 2014 09:42:59Technol. A3. 933 (1985).
'" A. Franciosi. P. Philip, S. Chang. A. Wall. A. Raisanen. N. Troullier, and
P. Soukiassian, in Proceedings of the 18th International Conference on the
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gapore. 1987), p. 141.
'" A. Franciosi, P. wl.l.ld".sian, P. Philip, S. Chang, A. Wall, A. Raisanen.
and N. Troullier, Phy •. Rev. B 35, 910 (1987).
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35,4176 (1987); P. Soukiassian. T. M. Gentle, M. H. Bakshi, and Z. Hur
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"No results are yet available for Sit III )/Yb-O" so that an analogous com
parison of the effect of Si and Yb overlayers on the oxidation of Si is not
possible at this time.
"The fit for the pristine GaAs( 110) surface yields a bulk As 3d doublet and
a surface-related doublet shifted by 0.43 eV relative to each other. The
4290 J. Appl. Phys., Vol. 67, NO.9, 1 May 1990 values of this parameter, and all other fitting parameters obtained from
the fit, were in good quantitative agreement with the literature. See, for
example, Ref. 14.
'·The Gaussian FWHM reflects the instrumental energy resolution and
possible disorder-induced broadening. The assumption of a constant
Gaussian FWHM for all of the oxidized subcomponents is therefore not
strictly justified a priori. However, such an assumption was required to
limit the number of fitting parameters, and yielded satisfactory fits, with
quantitatively consistent values of the fitting parameters as function of
exposure and photon energy.
J5 As a rough measure of the specific activity we take the overall intensity of
the oxidized core features normalized to the metal coverage.
'''The GaAs/Sm interface (see Ref. 7) exhibits larger disruption and higher
interdiffusion than GaAs/Yb (see Ref. 4). A. Fujimori, M. Grioni, and J.
H. Weaver, Phys. Rev. B 33,726 (1986) calculated the heats of reaction
for GaAs/rare-earth interfaces. They report values of --56 kcallmol
for trivalent rare earths and --46 kcallmol for divalent rare earths.
Chang etal. 4290
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1.102762.pdf | Effects of surface hydrogen on the air oxidation at room temperature of HF
treated Si(100) surfaces
N. Hirashita, M. Kinoshita, I. Aikawa, and T. Ajioka
Citation: Appl. Phys. Lett. 56, 451 (1990); doi: 10.1063/1.102762
View online: http://dx.doi.org/10.1063/1.102762
View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v56/i5
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Downloaded 10 Jun 2013 to 128.252.67.66. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissionsEffects of surface hydrogen on the air oxidation at room temperature
of HF",treated SI(100) surfaces
N. Hirashita, M. Kinoshita, I. Aikawa, and T Ajioka
Oki Electric Industry Co., Ltd., VLSI Research and Development Laboratory, Higashi-asakawa, Hachioji,
Tokyo 193, Japan
(Received 1 September 1989; accepted for publication 20 November 1989)
Thermally stimulated desorption and x-ray photoelectron spectroscopy were used to study the
air oxidation at room temperature ofHF-treated Si( 100) surfaces. The desorption results
indicated an appreciable density of hydrogen at the surface. Air oxidation experiments with
predesorbing surface hydrogen were carried out and an obtained linear relationship between
the amount of H2 desorption and oxidation indicated that the oxidation was allowed by Hz
desorption. The surface hydrogen was also found to be stable in air at room temperature and to
contribute to a retardation in air oxidation of the surface.
As the dimensions of integrated circuits are progressive
ly reduced in the submicron regime, the presence of native
oxide greatly influences device fabrication processes. A re
tardation in Si oxidation rate in air at room temperature has
been reported for the HF-treated Si surface. 1,2 This was spe
culated to be due to chemical species terminating the Si dan
gling bonds. Multiple internal reflection infrared measure
ments showed the presence of Si H bonds on the
HF-treated Si surface at about a monolayer density.3A An
appreciable density of fluorine with a monolayer at the sur
face was observed by both ion scattering spectroscopy and x
ray photoelectron spectroscopy (XPS).5 The existence ofa
large amount of Si-CH2 in addition to Si-H and Si--O
was also reported for the surface. I Takahagi et aU recently
examined the Si surface prepared by an ultraviolet cleaning
followed by HF dipping with Fourier transform infrared
spectroscopy (FTIR) and ultraviolet photoelectron spec
troscopy, They reported the hydrogen termination of an or
der of a monolayer and its passivation effect against the
room-temperature oxidation of the surface. However, the
presence of Si-F, Si-OR, and nonbonding hydrocarbons
was also indicated by the XPS measurements. It is still not
clear which chemical species dominate the air oxidation at
room temperature fer the HF-treated Si surface.
We have investigated oxidation kinetics of HF-treated
SiC 100) surface in air at room temperature using XPS and
thermally stimulated desorption (TSD) measurements. An
appreciable density of hydrogen at the surface was con
firmed by a series of TSD studies. Surface kinetics of the
hydrogen is described to be connected with air oxidation.
XPS measurements were performed using a VG
ESCALAB-5 spectrometer equipped with a hemispherical
analyzer and a 600 W Mg K" x~ray source (1253.6 eV). The
analysis chamber pressure was in the 10 -10 Torr range and
the detector was placed at the surface normal direction. For
measuring the Si2p spectra, the spectrometer was operated in
a high~resolution mode using a path energy of 10 eV, which
provided the fun width at half maximum of 0.9 e V for the
Ag3d 5/2 peak. Desorption experiments were carried out by
the TSD apparatus equipped with quadrupole mass spec
trometer. The chamber was evacuated with a 300 {Is turbo
molecular pump and it reached pressures on the order of
7X 10-8 Torr without baking. Samples were externally heated with an infrared radiation lamp, which was able to
precisely control linear heating and cooling rates between
0.1 and 5°/s without significant increases in the background.
In this work the linear heating rate of2°/s was used to avoid
the effect of readsorption and background increases. (,
Commercially available polished CZ(100) wafers (p
type, 3.25-4.25 n em) were used in the present experiment.
The wafers were chemically cleaned by a conventional
HzS04/H20z solution and immersed in a 5% aqueous HF
solution, typically for 20 s, to remove chemical oxide formed
by the previous chemical cleaning. Subsequently they were
rinsed with de~ionized (Dl) water for 10 s and blown dry
with N 2. Resistivity of the used D I water was over 18
MO em and its total organic contamination was < 20 ppb.
The residual C, 0, and F were detected by XPS for the above
HF-treated Si and ratios of each signal with respect to the
Sizp intensity were < 0.25 for C, < 0.25 for 0, and < 0,03 for
F.
In desorption experiments for HF~treated Si surfaces,
desorption associated with C and F was not observed for the
highest temperature to 800°C. Only H2 desorption exhibit
ed characteristic peaks in the TSD spectra, A series of Hz
desorption spectra is shown in Fig. 1. An spectra, obtained
from SiC 100) surfaces having different air exposure time
after HF treatments and the HF-treated SiC 111) surface,
show two binding states of f3 I and /3 2 ,as shown in Fig. 1.
The maximum temperature of each desorption was 440·C
for /3 2 and 500°C for /3 l states. Crude evaluation according
to Redhead's ploe yielded binding energies of2.l eV for the
{32 state and 2.3 eV for the/3 I states. Similar spectra8 have
been observed for SiC 111) surfaces with a saturation cover
age of hydrogen prepared by H exposure on the cleaved and
annealed surface in an ultrahigh vacuum chamber. Gupta
and co-workers ~ have recently studied hydrogen desorption
kinetics on porous Si surface by FTIR measurements and
mentioned thatp 2 andf31 states are second-order desorption
kinetics and are attributed to the dihydride and monohy
dride surface species, respectively. Therefore, the existence
of both desorptions observed in this work indicates that the
majority of the surface dangling bonds of the HF -treated Si
are covered with hydrogen. The surface hydrogen is also
found to be rather stable in air at room temperature, since
the essentially same desorption is observed for samples ex-
451 AppL Phys, Lett 56 (5), 29 January 1990 0003-695,/90/050451-03$02.00 (0) 1990 American Institute of PhysiCS 451
Downloaded 10 Jun 2013 to 128.252.67.66. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions~ 400
u:
N J:
C'l !:
:.e 200 o
~
C TSD
H!Sil1(0)
dT/dt=2?sec
o h // 200 400 600 800
Temperature Cc)
FIG. L H2 thermally stimulated desorption spectra from (a)-( c) HF
treated 5i ( 100) surfaces and (d) (Ill) surface with the following pre para
tion,:(a) just after the HF treatment, (b) after 2 days, (c) 14 days air expo
sure at room temperature following the HF treatment, and (d) just after the
HF treatment.
posed to air at room temperature even for two weeks after
HF treatments, as shown in Fig. 1,
The surface hydrogen was partially removed by control
ling the highest temperature Th during the TSD measure
ment. Samples were cooled to < 60 cC using the same linear
rate of 2°/s immediately after reaching the T", H2 desorp
tion was observed for 1~, > 400 OC but not for < 400°C. In
this sequence the pressure was < 3 X 10-7 Torr and read
sorption of hydrogen was not observed after cooling down
below 60 Pc. The samples were then loaded into the XPS
~ !:
::J
>-...
«l .... .....
:.0 ...
~
>-
.~
fI"I r.:
CI) ..... E,
c: 0 ... ....
~
"aJ 0 .... 0 J:
0.. a)
b)
c)
<I)
96 a)600"C
b)500"C
c)400'C
d) !iF Treatment
98 100 102 104
Binding Energy (eV)
FIG. 2. Si,p.1/2 photoelectron spectra ohtained from HF-treated Sir 100)
surfaces with (a)--( c) predcsorbing surface hydrogen and air exposure and
(d) the HF-trcated surface_ The surface hydrogen was partially prede
sorbed by varying the highest temperature in TSD sequence_ The highest
temperatures performed were Cal 400 'C, (b) SOO 'C. and (e) 600"C.
452 Appl. Phys_ Lett., Vol, 56, No. S. 29 January 1990 system and measurements were carried out. Typically, the
air exposure time during the loading was < 1 min. Obtained
Si2P spectra as well as the spectrum obtained from samples
just after the HF treatment are shown in Fig. 2. In order to
define the difference between the samples processed in var
ious T", the secondary electron background was subtracted
with a curve proportional to the integral of the spectrum and
the spin-orbit doublet was removed by a decomposition with
an energy separation and intensity ratio corresponding to
the known spin-orbit-split components, For Til > 400°C,
chemically shifted Si2P peaks resulting from the presence of
the suboxide and Si02, 10,11 are observed but not for T"
< 400 °C, as shown in Fig. 2. The arrows in Fig. 2 indicate
the expected position for the SiZv312 peaks for Si with 1,2,3,
and 4 oxygen ligands,lO The o~xide-induced Sizp peaks in
crease with increasing Th, as shown in Fig. 2. A concomitant
increase in 01s peak intensity was also observed with in
creasing Th, The oxidation was observed only when Hz de
sorption occurred for 1~, > 400°C.
A relationship between H2 desorption and the above
oxidation is quantitatively presented in Fig. 3. The amount
of H2 desorption, evaluated from the area below desorption
peaks, is plotted as a function of T;, in Fig, 3(a). The amount
of H) desorption linearly increases with increasing T" for
+-'
c
:::J
>-
.~ -e
~
'" OJ
<i:
-"" '" OJ c...
r:::
0
'';:::;
e-o en
Q.)
Cl
"C
W
.C:::
'" E 5 ;::: 200
/ 100
~ a
300 400 500 600
Ca) Highest Temperature("C)
O.6~-----------~
0.5
0.4
0.3
0.2 0 s· '0 I/"i,p ~ '2r\X"~ ,
0.1~
a 0 100 200
(b) Desorption Peak Area(arbitrary unit)
FIG. 3. (a) Amount of H, desorption, evaluated from the area under de
sorption peaks, as a function of the highest temperature ofTSD measure
ments. (b) Relationship between the normalized intensities of 0" lSi ': and
Si,1' (Ox)/Si,1' and the amount ofH" desorption.
Hirashita et ai 452
Downloaded 10 Jun 2013 to 128.252.67.66. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions> 400 cc. Normalized intensities of a,s peak and oxide-in
duced Si2P components [Si2P (Ox) L evaluated by the area
ratio to the Si2p peak from the Si substrate, are shown in Fig.
3 (b) as a function of the amount ofH2 desorption. The area
of Si2P (Ox) was evaluated by subtracting the spectrum of
the HF-treated Si. The normalized intensities of O's/Si2p
and Si2p (Ox) ISi2p present a good linear relationship with
the amount of H2 desorption. indicating that the surface
hydrogen prohibits oxidation. Appreciable offset ofO,jSi2p
at zero desorption is due to the hydroxy Is, since obtained O's
peaks were located at 532.5 e V for T" > 400 cC and differen
tiated by the hydroxyls of531.6 eV observed for T" < 400°C.
Combining the evidence of no desorption associated with C
and F, oxidation isjllst allowed by Hl desorption. The sur
face hydrogen predominately limi.ts air oxidation at room
temperature of the HF-treated Si surface but does not com
pletely inhibit the air oxidation. The air oxidation was de
tected by XPS measurements for the HF-treated Si exposed
to air for> 12 h. The retardation in air oxidation rate was
confirmed for the HF-treated Si to compare with samples
whose surface hydrogen was removed by heating to 600"C
with TSD apparatus. The present results suggest that the
retardation in air oxidation rate is due to the hydrogen passi
vation effect.
453 AppL Phys. Lett., Vol. 56, No.5, 29 January 1990 In summary, the HF treatment results in a signiik'<lnt
amount of hydrogen terminating to the Si dangling bonds.
Air oxidation experiments with predesorbing surface hydro
gen reveal that the surface hydrogen restricts oxidation. The
surface hydrogen is stable in air at room temperature and
contributes to the retardation in air oxidation rate of HF
treated Si surfaces.
The authors would like to express their appreciation to
S. Ushio for his advice and encouragement.
IA. Licciardcllo, O. Puglisi, and S. Pignataro, App\. Phys. Lett. 48, 41
(1986).
2T. Takahagi, I. Nagai, A. Ishitani. H. Kuroda, and Y. Nagasawa, J. App!.
Phys. 64, 3516 (1988).
3E. Yablonovitch, D. L. Allara, C. C. Chang. T. Gmitter, and T. B. Bright,
Phys. Rev. Lett. 57, 249 (1986)0
4y. A. Burrows. Y. J. Chabal, Go S. Higashi, K. Raghavachari, and S. B.
Christman, App\. Phys. Lett. 53,998 (\988).
5B. R. Weinberger, G. G. Peterson, T. C. Eschrich, and H. A. Krasinski, I.
Apr!. Phys. 60, 3232 (1986).
6D. A. King, Surf. Sci. 47, 384 (1975).
71'. A. Redhead, Vacuum 12, 203 (1962).
"G. Schulze and M. Henzler, Surf. Sci. 124, 336 (1983).
0p. Gupta, V. L. Colvin, and S. M. George, Phys. Rev. B 37,8234 (1988).
"'I'. J. Grunthaner, M. H. Hecht, F. J. Gnmthaner. and N. M. Johnson, J.
App!. Phys. 61, 629 (1986).
IIF. I. Himpsel, F. R. McFeely, k Taleb-Ibrahimi, J. A. Yarmoff, and G.
Hollinger, Phys. Rev. B 38, 6084 (1988).
Hirashita et at. 453
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1.345527.pdf | Electrical activity and structural evolution correlations in laser and thermally annealed
Asimplanted Si specimens
A. Parisini, A. Bourret, A. Armigliato, M. Servidori, S. Solmi, R. Fabbri, J. R. Regnard, and J. L. Allain
Citation: Journal of Applied Physics 67, 2320 (1990); doi: 10.1063/1.345527
View online: http://dx.doi.org/10.1063/1.345527
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/67/5?ver=pdfcov
Published by the AIP Publishing
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33Electrical activity and structural evolution correlations in laser
and thermally annealed As .. implanted SI specimens
A Parisini
CNR-Istituto LAMEL via de Castagnoli 1, 40126 Bologna, Italy
A. Bourret
Centre d'Etudes Nucleaires, Departement de Recherche Fondamentale, Service de Physique, 85X-38041
Grenoble. France
A. Armigliato, M. Servidori, S. Soimi, and R. Fabbri
CNR-Istituto LAMEL via de Castagnoli, 40126 Bologna, Italy
J. R. Regnard and J. L. Allain
Centre d'Etudes Nucleaires, Departement de Recherche Fondamentale, Service de Physique, 85X-38041
Grenoble, France
(Received 5 September 1989; accepted for publication 3] October 1989)
Laser-annealed and further thermally annealed arsenic implanted silicon specimens have been
investigated in a range of doses from 1 X 1016 to 5 X 1016 As/cm2, with different experimental
techniques: electrical measurements, transmission electron microscopy (TEM), double-crystal
x-ray diffractometry (DCD), and extended x-ray absorption fine structure analysis (EXAFS).
On the as laser-annealed samples, in the whole range of doses examined, a lattice contraction
of the doped layer has been evidenced by DCD, whereas, on the same specimens, EXAFS
measurements have shown the presence of a local expansion around substitutional As atoms.
The relationship between strain and carrier concentration has been found to be approximately
linear and can be described by the presence of a size and an electronic effect, as recently
proposed in the literature. The former effect represents the atomic size contribution, while the
latter is the strain induced by the variation of the conduction-band minima due to the doping.
After a subsequent thermal annealing in a low-temperature range (350-550 °C), a strong
deactivation of the dopant has been evidenced by electrical measurements. From the
experimentai results, a new model of the first step of the As deactivation phenomenon at low
temperature is proposed. It is described by the capture of two electrons from a pair of As
atoms in the second neighbor position in the Si lattice, leading to the formation of a positively
charged arsenic~vacancy cluster (As2 V) + , and to the emission of a negatively charged Si self
interstitial I -. This model takes into account the main phenomena that are experimentally
observed simultaneously to the As deactivation, i.e., the transition from a contraction to a
dilatation of the strain observed by DCD and the formation of interstitial loops, At relatively
high temperatures (650--900 °C), the hypothesis of the coexistence of the clusters and of the
observed precipitates has to be taken into account in order to explain the nature of the inactive
As. However, whether clustering or precipitation is the dominant phenomenon still remains an
open question.
I. INTRODUCTION
The first studies on the behavior and properties of As in
Si date back to the early sixties. As is wen known, during the
last 30 years the technological demand for integrated elec
tronics has led to the development of new preparation tech
niques of heavily doped semiconductor (low-and high-ener
gy ion implantation followed by rapid thermal annealing or
laser annealing) and to a renewed interest for their struc
tural characterization, \-3 Nevertheless, the behavior of As,
when heavily implanted in Si, still remains a puzzling prob~
lem. Clustering+ 8 and precipitation 9-tJ are the main phe
nomena proposed by several authors as conflicting hypoth
eses to explain the As deactivation process, In particular, the
precipitation has been proposed as the main phenomenon
responsible for the inactive As on the basis of Refs. 10-12.
This conclusion has been supported by the following:
For example, it is known that laser annealing of heavily
As~implanted Si specimens gives electrically active concen
trations well above the equilibrium value, Nevertheless,
further thermal annealing of these samples produces a
strong deactivation of the dopant, i.e., these alloys are meta
stable. ( 1) Thermodynamic considerations, to Le., analysis of
the deactivation kinetics during isothermal and isochronal
annealing; experimental evidence that equilibrium carrier
concentration is insensitive to the total amount of dopant,
but dependent on temperature only, and that a reverse an
nealing occurs;
(2) Transmission electron microscopy (TEM) obser
vations of As-related precipitates, 11
On the other hand, the results obtained from the more
recent cluster models have shown that:
( 1) A saturation value for the carrier concentration is
obtained if one considers, at the annealing temperature, the
2320 J. Appl. Phys. 67 (5). 1 March 1990 0021-8979/90/052320-13$03.00 @ 1990 American Institute of Physics 2320
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33capture reaction of a negative charge from two or more sub
stitutional As ions,8.13 This value is only slightly dependent
on the total dopant concentration.
(2) An As" V cluster is energetically favored over both
substitutional isolated As and substitutional As4Si configu
rations,14
Moreover, the experimentally observed discrepancy
between the precipitated and inactive As fractions, II as well
as the observation thai inactive As, unlike Band Sb, is mo
bile during high-temperature annealing,15,16 induce to also
consider the clustering mechanism as the responsible for a
significant fraction of the inactive As. This situation leaves
two main open questions that deserve a more accurate inves
tigation: (1) the relationship between the electrical activity
variations and the structural evolution of the metastable al
loys; and (2) the possible coexistence of significant duster
ing and precipitation phenomena in heavily doped Si sam
ples.
This work is an attempt to gain a deeper insight into
these problems by using two additional techniques to ana
lyze the same specimens investigated by transmission elec
tron microscopy and electrical measurements. These tech
niques, which have been only recently applied to these kinds
of problems, are extended x-ray absorption fine structure
spectrometry (EXAFS) and double-crystal x-ray ditfracto
metry (DCD).
In the foHowing, experimental results obtained on 1, 3,
and 5 X 1016 As/cm2 implanted Si specimens after laser and
thermal annealing in a temperature range 350--900·C are
reported. In Sec. II the main features of the sample prepara
tion techniques are reviewed and the experimental tech
niques employed for their characterization briefly described.
Section III is devoted to the presentation of the experimental
results obtained on the as-laser annealed samples, whereas
Sees. IV and V report the results of the thermal evolution of
these samples at low and high temperatures, respectively. In
Sec. VI, the results of Sec. III (as laser-annealed samples)
are discussed in the con text of the Yokota's suggestion 17 that
the strain in a semiconducting material results from both a
size (Vegard's law) and an electronic effect (model of the
deformation potentiaP!l). This latter approach has recently
been adopted by Cargill et al. 19 to exp1ain the observed dis
crepancy between EXAFS and DCD measurements on la
ser-annealed As-implanted specimens, i,e., a local dilatation
around As atoms and a global contraction of the laser an
nealed implanted layer, respectively.
In Sec. VII, a model of the first step of the As deactiva
tion phenomenon is presented, according to the experimen
tal results of Sec. IV (low-temperature annealed samples).
Finally, a brief discussion of the presence of clustering and
precipitation phenomena at high temperature is presented in
Sec. VIII.
II. EXPERIMENT
{lao} Czochralski (CZ) p-type silicon wafers have been
implanted with arsenic at an energy of 100 keV and at
fluences of 1,3, and 5 X 1016 As/cm2. Laser annealings have
been carried out at the implanted doses of 1 and 5 X 1016
As/cm2 with a Q-switched pulsed ruby laser, whereas a
232"1 J. Appl. Phys., Vol. 67, No.5, 1 March 1990 Xe-Cl exdmer laser has been employed to also anneal the
3 X 10]6 As/ cm2 implanted Si wafers. As will be seen, slight
differences in the experimental results obtained with the two
lasers do not affect the main conclusions of this work.
For ruby laser annealings a quartz wave guide has been
employed to obtain a uniform light spot of a diameter of 16
mm, while for the Xe-Cl excimer laser a fast scanning of a
square light spot of 16 mm2 has been permitted to cover the
whole area of the samples, with a 10% superposition
between adjacent spots. Both these types oflaser annealings
have been performed in air with an energy density of 1.9
J/cm2• Thermal annealings have been performed in an N2
atmosphere in a range of temperatures from 350 up to
900 "C.
TEM observations have been carried out by a lEOL 200
CX electron microscope operating at 200 keY. The weak
beam (WB), and high resolution electron microscopy,
(HREM), modes have been employed on ion milled cross
section and chemically etched plan-view specimens. In the
HREM mode, the point-to-point resolution was of about
0.25 nm at 200 ke Vo Carrier concentration and mobiiity have
been obtained from resistivity and Hall effect measurements
using a van der Pauw geometry.
As to the DeD measurements, a paranel (n, -n) dou
ble-crystal configuration has been used. The 400 reflection
has been employed, with the eu Ka 1 radiation, for the mon
ochromator and the specimen. To minimize the effects
caused by the specimen bending (see Sec, HI), O.6-mm
thick specimens have been used.
Finally, electron yield EXAFS measurements have been
performed at the synchrotron facility of LURE (Paris) us
ing a Si {331} channel cut monochromator and a detector
developed by Tourillon et alo20 Auger and secondary elec
trons emitted following the core-hole relaxation ionize a he
lium atmosphere (multiplication factor of about 50). The
electron flow is then detected as a function ofthe incident x
ray energy. A specially designed rotating sample holder has
also been used during the energy scan in order to significant
ly reduce the contribution of Bragg peaks superimposed to
the EXAFS signal.
III. EXPERIMENTAL RESULTS: LASER ANNEALED
SAMPLES
The characterization of the supersaturated alloys ob
tained directly after Xe-Cl excimer laser annealing of 1, 3,
and 5 X 1016 As/cm2 implanted Si specimens has been car
ried out with electrical measurements, TEM, DCD, and EX
AFS. Electrical measurements indicate a complete electrical
activation of the implanted dose up to the value of 3 X 1016
As/cm2, whereas the active As fraction is of about 80% at
the dose of 5 X 1016 As/cm2, in agreement with previous
measurements 10,12 obtained on ruby laser annealed Si speci
mens implanted in the same range of As doses. It is well
known that the strong As redisiribution, occurring duri.ng
the liquid phase epitaxial recrystallization induced by laser
annealing, gives rise to an approximately box-shaped As
concentration profile. The extension in depth of the plateau
region of the carrier concentration profiles is of about 150
Parisini et al. 2321
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33nm for both Xe-Cl and ruby laser annealing operating at the
same energy density of 1.9 J/cm2•
In the whole range of doses examined, TEM observa
tions have not revealed the presence of any extended defect
and in this sense the epitaxial recrystallization can be consid
ered as perfect. However, it is well known2! that the implant
ed dopant atoms (as wen as the pointlike defects possibly
present in this type of specimen) can lead to a strain in the
laser annealed implanted layer. This strain is directed along
the axis perpendicular to the specimen surface
(61 = Ad j d1 ), the lattice continuity of the laser annealed
implanted layer on the Si substrate having been, in the pres
ent case, always confirmed by cross-sectional HREM obser
vations. From DeD rocking curves, one gets information
only on e1' whereas residual strain in the plane parallel to the
specimen surface (ell = Ildlll d:! ), if any, can be determined
by diffraction from lattice planes inclined with respect to the
surface. As TEM observations exclude the presence of ex
tended defects, and hence of misfit dislocations, Ell = O.
However, a parallel mismatch between the surface and the
depth position corresponding to the extinction length of x
rays results from the bending of the wafer induced by the
doped layer. If this mismatch were evaluated from the inves
tigated samples by using the mechanical model reported in
Ref. 22, one would verify that the parallel strain is of the
order of 10-7, i.e., completely negligible. In the absence of
<:11 ' the perpendicular lattice mismatch in the relaxed state,
Aala, is obtained from the measured AdLldL by the for
mula23
l1a ell I1d1
2C12 + elJ -;J;' (1)
a
representing the variation of the hydrostatic strain l1al a due
to the lattice coherence of the laser-annealed implanted layer
on the 8i substrate (crr and C12 are the Si elastic constants).
Figure 1 shows the DCD rocking curves obtained on the
1, 3, and 5 X 1016 As/cm2 implanted Si specimens after
Xe-Cl exdmer laser annealing. At the doses of 3 and 5 X 1016
7 t -r---,--
6 r-
5 f
~o-.: 4 ~
$2 t 3. t-I
2f
: ['~_J __ ~_~~_~ __ ~_~~_J
-200 a 200 400 600
.1-8> (arcsec)
FIG. l. DeD rocking curves (reflectivity R vs angular displacement t:.O)
obtained on samples implanted with Ix 10'6 As/em -2 <triangles),
3><IO'6As/cm 2 (squares),and5X10'oAs/cm -0 (circles),afterXe-CI
excimer laser annealing. The continuous curves represent the fits given by
the simulation program.
2322 J. Appl. Phys., Vol. 67, No.5, 1 March 1990 Asl ern 2, a satellite peak is clearly observed at ~e > 0 (A()
being the angular distance between the satellite and the Si
substrate peak) corresponding to a contraction of the laser
annealed implanted layer, while at the lowest As dose no
indication of the presence of a strained layer is directly ob
tainable from the DCD rocking curve.
As will be shown in Sec. V, the strain of this layer is
mainly due to the presence of the substitutional As atoms,
whose depth distribution after liquid-phase epitaxy is not
uniform. For a nonuniform distribution of the dopant, the
corresponding depth profile of the strain 61 can be obtained
only by computer simulation of the neD rocking curves.
The description of the computer code used to obtain the
strain profiles has been published elsewhere.24 The comput
ed strain profiles corresponding to the three doses examined
have been superimposed in Fig. 2. The comparison of these
strain profiles with SIMS25 and carner concentration pro
files26 shows that the region of maximum strain (Ej
> 5 X 10-4 up to a depth of about 150 nm) does correspond
to the richest As region (N As;;' 1 X 1021 em -3). EXAFS
measurements at As-K edge allow one to determine the local
environment of the As atoms. In this work, the first neighbor
As-Si distance d AsoSi , and the corresponding As coordination
number, N, are reported.
In the whole range of implanted doses, these experi
ments have revealed that around As atoms the first neighbor
shell is composed of Si atoms only, with N 2!t 4 and d A"Si
= 2.41 ± 0.01 A, indicating a local expansion of 0.06 A
with respect to the pure Si first neighbor distance dSi,gi
= 2.35 A. These results agree with the EXAFS measure-
-4
-3 --------,
I
f
I
I
I
!
i
i
I
I
I
«
I
I
50 ---,
I
I ,
I
I e ___ ...
I
I ,
100
depth [nm] 150
FIG. 2. Computed depth profiles of the perpendicular strain fC[ deduced
from the corresponding DeD rocking curves in Fig. 1. The heavy, the light.
and the dashed lines refer to the doses of 1, 3, and 5 X 10'0 As/em -2, re
spectively.
Parisini et al. 2322
••••••••• j ••.•..•
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33ments of Erbil et al.27 obtained on Si specimens doped with
0.1,0.7 and 7 at. % As.
Therefore, in terms of the first-order elasticity theory,
one is facing the same apparent contradiction already re
ported by Cargill et al.19; while EXAFS results reveal a local
dilatation around substitutional As atoms, DCD measure
ments indicate a global contraction ofthe laser annealed im
planted layer. In Sec. V, it will be seen how these results can
be explained.
After laser annealing, post-thermal treatments of the su
persaturated alloys of As in 8i results in the formation of
extended defects and in a strong deactivation of the electri
cally active As. II To study the As deactivation it is useful to
anneal the supersaturated specimens in a wide range of tem
peratures. However, to understand the deactivation mecha
nism, the first step of the process, i.e., the onset of any agglo
meration of As atoms, must be experimentaUy evidenced.
This can be accomplished only at low temperatures, where
the deactivation rate is reasonably slow. To this end, a tem
perature range between 350 and 550·C has been chosen, as
the deactivation occurs in this interval for experimentally
accessible annealing times (Sec. IV). Conversely, the evolu
tion of this situation towards the thermodynamical equilibri
um can be better investigated in a higher-temperature range,
between 650 and 900·C (Sec. V).
IV. EXPERIMENTAL RESULTS: lOW· TEMPERATURE
THERMAL EVOLUTION (35(}-550 ·C)
In the temperature range 350-550 ·C, the thermal evo
lution of laser annealed samples has been followed on 1, 3,
and 5 X 1016 As/cm2 implanted specimens by electrical mea
surements, DCD, EXAFS, and TEM.
A. Electrical measurements
The deactivation process is tirst foHowed by isothermal
annealing in a temperature range 350-550 °C, at the interme
diate implanted dose of 3 X 1016 As/cm2• The a, b, and c
curves of Fig. 3 represent the isothermal evolution of the
sheet carrier concentration for the Xe-CI laser-annealed
3 X 1016 As/cm2 implanted specimens at the temperatures of
3 ----.--------~-T------.----I--~
3 x 10'6 As/cm2 J
C\I
'E 2 ·350 'C
.. 375 ·C
.400 ·C -I -~
~
1 - J
o t ____ ~_~L ___ ~~ ___ L-j
o 5 10 15 20
t [h]
FIG. 3. Isothermal evolution of the sheet carrier concentration for Xe-CI
excimer laser annealed 3 X }O'6 As/em -2 implanted specimens, at the tem
peratures of 350, 375, and 400·C.
2323 J. Appl. Phys., Vol. 67, No.5, 1 March 1990 350,375, and 400 ·C, respectively. From this figure, one can
see, as just pointed out in Sec. III, that a complete electrical
activation of the implanted dopant has been obtained after
laser annealing.
Furthermore, two samples annealed at 350 ec for 42 h
and at 4oo·C for 21 h have been subsequently annealed at
450·C for 15 min. After this second anneal, a further de
crease of the sheet carrier concentration of about 5% is ob
served, in both cases, with no evidence of a reverse anneal
ing. On the contrary, the occurrence of this phenomenon
should be evidence ofthe presence of As precipitation. Elec
trical measurements have shown that the As deactivation is
more rapid the higher the implanted dose. In fact, for a ther
mal annealing at 450 ·C for 4 h, an inactive As fraction of
about 60% and 90% for the lowest and highest doses, re
spectively, is observed, It is worthwhile to note that these
strong deactivation phenomena occur in a range of tempera
tures (350-550 ·C) where no evidence of As diffusion has
been detected by SIMS analysis.25
B. OeD measurements
The samples implanted at 3 X 1016 As/cm2 and isother
mally annealed at 350"C have also been characterized by
DeD measurements. Figures 4(a) and 4(b) represent the
computed strain profiles obtained on these specimens from
the corresponding DCD rocking curves, showing that im
portant structural modifications take place at this annealing
temperature. In particular, these profiles reveal the evolu
tion by which the contraction observed after laser annealing
is transformed into a dilatation. The main features of this
evolution are as follows:
[ <I) iii
-4 --, --laser annealed ·1
-3 ~.-} -----"+ 350°C, 10mln -1
-2 ---,,+ 350·C,20min .
CONTRACTION
~ t-------<-<::;;~--~ -~---J
0.;-1 _. ______________________________ j
(Y)
Q_7~kd :=:l
1 --Iaser+ 350 "C,40min
-6 -: -----.: .350°C,80min 1 :; i I -'350,"840m,"]
:~ J~-L~ _____ L_ CONTRACTION j
,----( o --------i"-- -+-----1-=_-;;;._~-;,i.:~-.:-- .... -t..~~~
i.. -_j , __ I
!--; -DILATATION __________ .1 ___________ ~ ____ _
o 100 200
Z fnmJ
FIG. 4. Computed depth profiles of the perpendicular strain E, obtained
from DCD measurements performed on Xe-CI laser-annealed 3 X 1016
As/em -2 implanted specimens, isoth::rmally treated at 350 'c. For sake of
clarity the figure has been split up into two parts, the annealing times rang
ing from 0 to 20 min in (a) and from 40 to 640 min in (b). Note in (b) the
transition from a contraction to a dilatation of the doped layer.
Parisini et al. 2323
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33-5~
-4
-3
-2
"'~ 1 L 'b-J --laser annealed I
----- ,,+ 450·C 4 h ]
---. .. + 550·C:lh .
.... 0 ""-'-=-'-=--=--=->-11 ---t-~- __ ,~ ... f~~r --
~l, _.J __
"'!to.l~ ______ ,... ... _, •• £d-[-,J,
i 2
DILATATION r-'-'; 3 i.'-'L._._._._._.j --L.. ____ . __ -'--_
o 100 200
Z [nmJ
FIG. 5. Computed depth profiles of the perpendicular strain /', obtained
from DCD measurements performed on ruby-laser-annealed 5 X 10 1(.
As/cm' 2 implanted specimens, thermally annealed at 450 and 550'C. The
profile obtained on the as laser-annealed sample is also reported for com
parison. Note that a complete recovery of the negative strain occurs at the
higher temperature.
(1) After annealing at 350·C for 10 and 20 min (see
Fig. 4( a) J, the maxim um of the strain profile observed in the
laser annealed specimen decreases by about 20% and a
strain peak forms at the surface.
(2) The strain value of this peak increases considerably
after 40 min of annealing [Fig. 4(b)], while only minor var
iations are observed in the tail region of the profile for this
annealing time.
(3) A region of small positive (dilatation) strain is ob
served after 80 min annealing, starting from about 110 urn
from the surface. In the specimen annealed for 640 min, this
positive strain increases considerably and moves towards the
specimen surface where the negative strain is strongly de
creased.
A confirmation of the occurrence of the reversal of the
strain sign on annealing has been obtained in the tempera
ture range 450-550·C by DeD measurements on 1 X lOll>
and 5 X lOU> As/cm2 implanted Si specimens. The computed
strain profiles obtained at this latter dose, on the ruby laser
annealed specimen and on the ones subsequently annealed at
the temperatures of 450 and 550 ·e, are shown in Fig. 5. At
450 ·C a residual negative strain is observed in a 40-nm-wide
surface layer, while a complete recovery of the negative
strain is detected after the thermal treatment at 550 ·C.
From Figs. 4 and 5, it is possible to conclude that the transi
tion from a contraction to a dilatation of the laser-annealed
implanted layer starts from the tail of the observed strain
profiles, the positive strain region tending to move towards
the specimen surface on further annealing.
TABLE I. EXAFS values of d""" and N for 3 X lOl" As/cm2 samples.
d",,, (A) N
Sample (± 0.01 A) :i: (10-7-20%)
Laser 2.41 4
Laser + 350"C 40 min 2.41 2.9
Laser + 350 "C 640 min 2.38 2.7
2324 J. Appl. Phys., Vol. 67, No.5, i March 1990 c
b
a
i
100 !
200 850t
,
300 Z(nm)
..
FIG. 6. WB cross-s<.'Ction TEM micrographs of ruby-laser-annealed
I X J 016 As/em -2 implanted specimens, subsequently heat treated at
550°C for 3 h (a), at 650 'C for 2 h (b), and at 850 'C for 30 min (e).
C. EXAFS measurements
First neighbor As-Si distances and As coordination
numbers obtained by EXAFS measurements28 on the
3 X 1016 As/cm2 implanted specimens annealed at 350·C for
40 and 640 min are reported in Table I and compared with
the values obtained from the laser-annealed samples. From
this table, it is observed that while no variation of d As:Si is
detected after 40 min of annealing, the longest annealing
time reduces this distance to the value of2.38 A, characteris
tic of the monoclinic SiAs compound,z9 Concerning the As
coordination number, as soon as the specimens are submit
ted to the first thermal annealing, it is observed a decrease by
one (1'1 ~ 3) of the val ue obtained on the laser -annealed sam
pIe (the accuracy of the N value ranges from 10% to 20% ) .
At the implanted dose of5 X 1016 As/cm2, EXAFS mea
surements on the specimens annealed at 450 and 550 ·C have
yielded a value of dA;Si = 2.39 ± 0.01 A and an As coordi
nation number N ~ 3, confirming the behavior already ob
served for the isothermal treatments at the dose of.3 X 1016
As/cm2.
D. TEM observations
In the low-temperature range considered, the presence
of extended defects has been revealed by TEM observations.
as shown in the WB images of Figs. 6(a) and 7 (a), for the
doses of 1 X 1016 and 5 X 1016 As/cm2, respectively. At both
these doses, small {113} interstitial loops begin to appear in
Parisini et ai 2324
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33d
c
b
a
I
100 i 200 I 300 Z(nm)
"
FIG. 7. WB cross-section TEM micrographs of ruby-laser-annealed
5 X 10"6 As/em -2 implanted specimens, subsequently heat treated at
450 'C for 4 h (a), a\ 550 'C for 3 h (b), at 650"C for 2 h (c), and at 750 'C
for 1 h (d).
a layer centered at about 150 nm from the specimen surface,
i.e., beyond the plateau region of the As SIMS profile.25
V. EXPERIMENTAL RESULTS: HIGH-TEMPERATURE
THERMAL EVOLUTION (650-900 "e)
In the temperature range 650-900 "C, the thermal evo
lution of ruby laser-annealed samples has been followed by
1 X 10\6 and 5 X 1016 As/cm2 implanted specimens by elec
trical measurements, DCD and TEM.
A. Electrical measurements
Isothermal electrical measurements have been per
formed at 900 °C on ruby laser-annealed 1 X 1016 As/cm2
implanted Si specimen. As shown in Fig. 8, an initial very
rapid decrease of the carrier concentration (for an annealing
time of 3 s, an inactive As fraction of about 40% is observed,
corresponding to a reduction of the carrier concentration
from 1 X 1021 to 4 X 1020 em·· 3) is followed by a much
smaller 20% decrease up to an annealing time of 30 min. The
carrier concentration for this latter time (2X 1020 em -3 )
corresponds to the equilibrium value of the active As con
centration at this temperature.9,W,12
In spite of the lack of experimental points below 3 s, the
behavior of Fig. 8 seems to indicate that the As deactivation
occurs in two steps.26 In the temperature range 650-900 ·C,
due to the rapidity of the process, it is possible to follow only
the second step of the deactivation phenomenon, in which
the carrier concentration slowly decreases up to the equilib
rium value.
2325 J. Appl. Phys., Vol. 67, No.5, 1 March 1990 (\J ,
E
.£
z
(0
"0 ... 10 as laser
annealed
0.8
0.6
t
04 ~
I Ln
0 I 1_1016 As/cm2
T = 900 ·C
101 102
teft [sec] 103
FIG. 8. Isothermal evoluti()n of the sheet carrier concentration for ruby
hIser-annealed I X 1016 As/em -2 implanted specimens, at a temperature of
900'C.
B. TEM observations
For the doses 1 X 1016 and 5 X 1016 As/cm\ a prelimi
nary TEM analysis of the defects present in ruby laser-an
nealed specimens thermally annealed from 450 up to 900 °C
has been previously reported,25 For the purposes of this
work, the results of this electron microscopy analysis per
formed in the WB and HREM modes can be summarized as
follows:
(1) At the dose of 1 X 1016 As/cm2, two types of defects
are observed, i.e., perfect and faulted interstitial loops and
As-related precipitates.
(2) The concentration of the Si self-interstitiais bound
ed by loops, Co reaches its maximum value at the tempera
ture 0[750 "C, where C[ ;::;6X 1019 em -3.
(3) At both the doses considered, a low density of very
sman As-related precipitates (about 2 nm in diameter) is
visible only in specimens annealed at relatively high tem
perature (;;;. 850 "C). The observed precipitated As fraction
does not explain the total inactive As.
To complete this investigation further TEM observa
tions have been performed on ruby laser annealed 5 X 1016
As/cm2 implanted specimen. As an example of the typical
faulted loops observed at this As dose after thermal treat
ment, one can see in Fig. 9 an HREM image of a {lIl}
extrinsic Frank's loop. Further analysis has confirmed that
all the observed loops can be identified as Si. self-interstitial
aggregates, no evidence of an As segregation phenomenon at
the defects being in fact observed.
The thermal evolution of the depth distribution of these
Parisini et al. 2325
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33FIG. 9. HREM image of an interstitial Frank loop observed on the same
specimen as in Fig. 7(d).
defects is shown in the cross-sectional WB TEM images of
Figs. 6 and 7 for the doses of 1 X 1016 and 5 X 1016 As/cm2,
respectively. At the lower dose (Fig. 6) with increasing an
nealing temperatures the loops tend to reach the specimen
surface, which is actually attained after a 30-min annealing
at 900 ·CY At the higher dose (Fig. 7) the specimen surface
is reached by the loops already after a 3 h annealing at
550 ·C.
C. DCD measurements
DCD rocking curves have also been obtained on
lXlOl6 and 5XI016 As/cm2 implanted Si specimen, an
nealed in the temperature range 650-900 ·C. Nevertheless,
at both doses, the strong diffuse scattering (Huang scatter
ing) produced by the long-range strain field associated with
the dislocation loops (see Figs. 6 and 7) does not anow a
reliable simulation of the rocking curves obtained by double
crystal diffraction. 30 Therefore, the nCD results relative to
the samples annealed at high temperature are not reported.
VI. DISCUSSION: LASER ANNEALED SAMPLES
As shown in Sec. III, a global contraction has been
found by DCD measurements on laser annealed samples im
planted at doses of 1,3, and 5X 1016 As/cmz. The reasons
why this negative strain can be attributed to the As atoms
can be summarized as follows:
( 1) A quite good agreement is found between the ob-
2326 J. Appl. Phys., Vol. 67, No.5, 1 March 1990 served negative strain distribution and the SIMS and carrier
concentration profiles.25,26
(2) Carbon atoms, possibly present in the specimens as
the result of a contamination effect during the implantation
process, could equally well give rise to a contraction of the
laser-annealed implanted layer. Nevertheless, it is known
that these atoms are very stable on the Si lattice up to anneal
ing temperatures of about 900 ·C.31 The strong variations of
the computed strain profiles observed at the annealing tem
perature of 350°C (see Fig. 4) anow one to rule out this
hypothesis.
(3) The presence of vacancies, caused by an imperfect
liquid-phase epitaxial recrystallization, could also give rise
to a contraction of the laser-annealed implanted layer. An
estimate of the vacancy concentration necessary to produce
all the observed negative strain gives values ranging from
1 X 1021 to 5x 1021 cm --3 over a 150 nm wide layer.26 The
high degree of electrical activation measured on these speci
mens makes such high vacancy concentrations quite unlike
ly. On the other hand, x-ray diffractometry oflaser-annealed
Sb-and Ga-implanted Si specimens has shown a global dila
tation of the laser-annealed implanted layers.21,32 This dem
onstrates that laser annealing does not give rise systematical
ly to a contraction of this layer, indicating that one is really
in presence of a dopant effect.
From these remarks it descends that the observed strain
distribution is mainly due to the As atoms, even if minor
effects due to relatively low vacancy concentrations cannot
be a priori excluded (see Sec, VII). Therefore, what remains
to be explained is the discrepancy between the lacal dilata
tion around As atoms, observed by EXAFS, and the global
contraction evidenced by DCD on the same laser annealed
samples.
On the basis of the deformation potential model of Bar
deen and Shockley, 18 Yokota17 suggested that in a semicon
ducting material the hydrostatic strain Aa/ a, given by a car
rier concentration lIT, can be decomposed into two
contributions, namely
Aa (/la) (tia) -= -. + -= (!3size +/3.)N, a o sIze ae (2)
where for As in Si
-= (3sizeNAs = ----, ( Ila) lIT As (or)
\ a size CSt rSi (3)
CSt' or/ r Si' and N As being the Si atomic density, the relative
difference between the tetrahedral covalent radii of As and
Si and the As concentration, respectively, and
(4)
where B is the Si bulk modulus and Ec is the Si deformation
potential constant. 33 Expression (3) is the Vegard's law con
tribution ( or atomic size factor) to the strain ~a/ a, whereas
( 4) represents the electronic contribution to Aa/ a , i.e., the
hydrostatic strain induced by the variation of the conduc
tion-band minima due to the doping.
For As in Si, a positive contribution to !.ia/ a is expected
from the atomic size factor. To comply with the experimen
tally observed contraction of the laser-annealed implanted
Parisini et al. 2326
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33layer, the electronic contribution must be negative ({Je < 0
and E,. > 0) and represents the dominant contribution to
fla/a.
This argument has been used recently by Cargill et al.19
to explain the observed discrepancy between DCD and EX
AFS measurements on a Nd:Y AG laser-annealed Si speci
men implanted at a dose of 6 X 1016 As/cm2, and to give an
experimental estimate of {J e and Ec. These authors have ob
tained f3e = -(1.8 ± 0.4) X 10 -24 em3 and Ec
= 3,3 ± O.7eV in qualitative agreement with the more re-
cent theoretical estimations of these parameters.34,35
Nevertheless, it is important to stress than an experi
mental confirmation of this hypothesis has to show that the
strain tl.a/a varies linearly with the carrier concentration.
Figure 10 reports the average strains, i.e., the values of the
integrals of the computed strain profiles divided by their to~
tal width, as a function of the average active As concentra
tion. Open and full triangles in this figure represent the aver
age values of the tetragonal strain (b.d1/d1) and of the
hydrostatic strain (tl.a/a), respectively [see (1) ]. From this
figure, one sees that the negative strain increases on increas
ing As concentration, The observed strain variation follows
a law of the type < !1a/ a) 0: N x with 0.7 < x < 1.2, i.e., not far
from linearity.
Within the accuracy of the measurements, one can say
that the observed strain variation as a function of the active
As concentration is compatible with the deformation poten
tial model on the basis of (2). From the slope of the straight
-2.0
o L-______ ~ ______ _L_ _____ ~ __ ~ 012
10-21 N 3
FI G. 10. Average strains (Ad I d) (i.e., the integrals of the computed strain
profiles divided by their total widths) obtained from the strain profiles
shown in Fig. 2, as a function of the correspondi.ng sheet carrier concentra
tions. Open and full triangles represent the average perpendicular strain
{t:.d,ldj) and the hydrostatic strain (Aa/a), respectively.
2327 J. Appl. Phys., Vol. 67. No.5, 1 March 1990 line representing < !1a/ a) in Fig. 10, {3 exp = f3 As + {3 e
= -(0.5 ± 0.2) X 10-24 eml is obtained. To obtain a val
ue of f3c one has to evaluate the atomic size parameter !3si,.e,
i.e., to choose the reference endpoint structures for the appli
cation of the Vegard's law to As in Si.
Following Cargill et al. 19 one can take the diamond cu
bic Si and a hypothetical sphalerite AsSi as endpoint struc
tures.For the sphalerite AsSi, it is possible to define a natural
As-Si bond length,36 making use of the d A"Si value ob
tained from EXAFS measurements!9:
d ';.'~\;i = jd As:Si -jdSiSi = 2.43 ± 0.02 A.
Using this latter value in the Vegard's law expression, one
obtains {Jsizc = + (1.4±0.3)xlO -24 emJ. It is worth
while to remark that this latter value is very similar to the
one obtained from the Vegard's law application to the mono
clinic SiAs endpoint structure, i.e., !3si'c = + (1.5 ± 0.2)
X 10' 24 em3.26 Assuming the {J size value for the sphalerite
AsSi compound, from the experimental value f3 exp it is ob
tained
!3e = (3exp -(3size = -(L9±O.5)XlO-24 em3 (5)
and
Ec = -3B{J" = 3.5 ± 0.9 eV, (6)
in good agreement with the corresponding values obtained
by Cargill et al. ]9
VII. DISCUSSION: lOW-TEMPERATURE THERMAL
EVOLUTION (350-550 0c)
From TEM observations and the reverse annealing ex
periment (see Sec. IV D and IV A), it has been shown that
no evidence of an As precipitation phenomenon has been
detected in the temperature range considered. In the absence
of precipitation, the formation of electrically inactive clus
ters of As atoms is the alternative hypothesis that can be
invoked to explain the As deactivation mechanism.
Several cluster models have already been presented in
the literature, describing, in the formalism of chemical ther
modynamics, the capture reaction of one or more negative
charges from the positive As ions. These models can be di
vided into the two following main classes:
(1) Arsenic-vacancy clusters, ASm V, in which the cap
tured negati.ve charge is represented by a negatively charged
vacancy5,7; and
(2) clusters of As atoms only, As~!, corresponding to
the capture of one or more eiectrons.4,6,8
AU these models are based on high-temperature data
(800-1200 °C) of the chemical and the active As concentra
tions. In this temperature range, the thermodynamic equi
librium is attained after short annealing times and the law of
mass action is therefore applicable to the capture reaction
considered. In this way, Tsai et af.s have shown that the AS3
cluster model (corresponding to the capture of only one
electron at the annealing temperature) succeeds in giving a
saturation value for the carrier concentration (only slightly
dependent on the total As concentration), in agreement with
the more recent experimental estimates of the high-tempera
ture equilibrium value of the active As concentration.37,38
Parisini et ai. 2327
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33It is worthwhile to make some critical remarks about
these models:
( 1) Guerrero et al. 13 have pointed out that a saturation
value for the c.arrier concentration always exists if the clus
tering process is governed by the capture of a negative charge
at the annealing temperature. This leads to the conclusion
that these types of models cannot distinguish between nega
tively charged vacancy or electron capture reactions.
(2) These models summarize a series of successive steps
of the As deactivation of which the first is too rapid to be
observed at high temperatures.
(3) They do not take into account the formation of ex
tended defects and precipitates that are actually observed in
the same temperature range (see Sec. IV D).
A study of the low-temperature structural evolution of
the metastable alloys obtained in the present case by laser
annealing of the implanted specimens can conversely lead to
evidence the fundamental interactions of the As atoms with
the Si lattice and with the point defects, i.e., the first step of
the As deactivation phenomenon.
A, A model for the first step of the As deactivation
phenomenon
In Sec. IV, it has been shown that two main phenomena
are observed simultaneously to the low-temperature As de
activation, i.e., the recovery of the negative strain and the
formation of interstitial loops. As to the negative strain re
covery, one has to stress that this phenomenon is in qualita
tive agreement with the expected annealing behavior of the
negative strain (b.a/ a) e induced by the electronic effect. In
fact, as shown in Sec. VI, being (/:;,a/a)e proportional to the
carrier concentration, a decrease of this negative strain is
expected on increasing As deactivation. Moreover, it is seen
that the thermal evolution of the negative strain recovery
(Figs. 4 and 5) and of the depth distribution of the intersti
tial defects (Figs. 6 and 7) follows the same mechanism, i.e.,
they both start from the deeper region of the laser-annealed
implanted layer, then move towards the specimen surface on
further annealing.
This strongly suggests that, in a temperature range
where As diffusion is not present, the formation of Si self
interstitials is connected to the recovery of the negative
strain and hence to the As deactivation phenomenon. This
implies that the alternative hypothesis of the formation ofSi
self-interstitials during the liquid-phase epitaxial recrystalli
zation, previously invoked to explain the calculated C1 val
ues in the observed loops,25 has to be rejected, being not
compatible with the DeD measurements performed on the
laser-annealed samples (contraction of the laser annealed
implanted layer; see Sec. III).
Conversely, the formation upon annealing of these in
terstitials can take place where two or more immobile As
atoms (there is no diffusion in this temperature range) are
already present in second neighbor position in the Si lattice
(in the laser-annealed samples no As atom has been detected
by EXAFS measurements on the first neighbor shell). In
fact, the capture of one or more electrons can set on a deacti
vation process leading to a slight displacement of the As
second neighbors with an increase of the local lattice defor-
2328 J. Appl. Phys., Vol. 67. No.5, 1 March 1990 mati on around these atoms. This deformation can in turn be
released by the formation of a vacancy with the consequent
emission of a Si self-interstitial.
A study of the kinetics order of the isothermal deactiva
tions at the dose 3 X 1016 As/cmz (Fig. 3) can state the pre
vious hypothesis more quantitatively. The kinetics order can
give, in fact, an indication of the number of species partici
pating in this phenomenon, i.e., as in the present case the As
atoms are fixed in the Si lattice, of the number of electrons
captured in the first step of the As deactivation. The kinetics
equation used is the following;
_ ds = kf;-n 123 dt !:>, n = , , ... , (7)
where
NA + (I) -NAlim1 gU)= S s (8) Ntot _ N1im
. As-f
and NAg' , Ntot, and N~:\ represent the electrically active
concentration at time t, the total As concentration
[Ntot = NAS+ (0): complete activation], and the limiting
value of N As + for the process considered (if only one mecha
nism is responsible for the deactivation phenomenon, this
value represents the equilibrium carrier concentration).
For N1im the value Nlim = O.2Ntot = 4x 1020 cm -3 As -1-- As +
has been taken. This arbitrary choice can be justified observ
ing in Fig. 3 that the asymptotic value of for NAs + is close to
this value, whereas the equilibrium carrier concentration ex
trapolated at 350-400 °C is much lower: N ~r;, = 4 X 1018
cm-3. This indicates that at higher temperatures or for
longer annealing times other reactions follow the first one, as
described by (7).
By integration of (7), with different n values, the order
of the deactivation kinetics has been determined. The best fit
of the experimental data is obtained for n = 2, as reported in
Fig. 11 where a second-order kinetics is observed in the
whole range of temperatures examined. As pointed out pre
viously, this means that the first step of the As deactivation
phenomenon is governed by the capture of two electrons.
It is further proposed that the initial cluster of fixed As
atoms is formed by a pair of these atoms in second neighbor
position on the Si lattice; that this is a reasonable assumption
is also supported by the direct detection of As-As pairs in
recently reported perturbed-angular-correlation experi
ments.39
This discussion can be summarized with the following
model of the first step of the As deactivation process:
(9)
Concerning the final products of the reaction (9), one can
observe that the deactivation phenomenon can start in a re
gion where the formation of the 5i self-interstitial, I, and of
the cluster Asz Vis energetically favored. This region is iden
tified with the region of the electric junction where the pres
ence of an intense electric field can decrease the formation
energy of the final products by means of a charge separation
phenomenon. The formation of a negatively charged Si self
interstitial, 1-, and of a positively charged cluster,
(AszV) + , in this region explains the experimentally ob-
Parisini et a/. 2328
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:3314 K=4.2.10-2
T=400 "C
12
10 ~ 1 1 i
8 t 1 ......
6 r l i
oJJJ\ ........ .....
4 ,..-
~~
#-~ -3
K= 3.9 ·10
2 T=350 "C
0
0 200 400 600 800 1000 1200
t [min]
FIG. 11. Isothermal evolution ofthe As deactivation. plotted as the integra!
ofEq. (7), which shows that a second-order kinetics fits the experimental
data. Specimens: Xe-Cllaser-annealed 3 X 10'6 Askm 2 implanted wa
fers.
served onset of the negative strain recovery and of the self
interstitial aggregation at the deeper region of the laser-an
nealed implanted layer.
Furthermore, with increasing As deactivation one ex
pects that the boundary between the deactivated and the not
yet deactivated region (n + In) moves towards the specimen
surface, in agreement with the experimental results obtained
in TEM and DeD (see Sec. IV).
To ascertain whether the first step of the deactivation
occurs through a unique mechanism, as assumed by the
model, the activation energy Ea for this process has been
determined from the isothermal electrical measurements
shown in Fig. 3. In Fig. 12, the Arrhenius plot of the time
required to decrease the initial value of the carrier concen
tration by 33%, 50%, and 66% is represented for the
3 X 1016 Asl cm2 implanted specimens. This plot yields a val
ue of Ea = 1.9 ± 0.1 eV up to the highest inactive As frac
tion considered, in good agreement with the value of
2.0 + 0.1 eV obtained by Lietoila et al.,9 in the same range of
temperatures, on Ar-laser annealed 1 X 1016 As/cm2 im
planted specimens. This demonstrates that only one mecha
nism operates in the temperature range considered almost
up to a deactivated As fraction of 66%.
Reaction (9) is also supported by the local atomic ar
rangement of the As atoms. In fact, these atoms in the Asz V
cluster have the same local configuration as that in the mon
oclinic SiAs compound, where they are bounded to three Si
atoms at an average distance of2.38 A,29 The present model
is therefore supported by the experimental EXAFS results,
showing that after the first thermal annealing the first neigh
bor As-Si distance and the As coordination number tend to
the values typical of this compound.
Moreover, according to (9), a dominant role should be
played by the total number of As atoms in the second neigh-
2329 J. Appl. Phys., Vol. 67, No.5, 1 March 1990 FIG. 12. Arrhenius plot oftlle time reqnired to decrease the initial value of
the carrier concentration by 33%, 50%, and 66% (from bottom to top) in
specimens doped with 3 X 1016 As/cm2. The values reported in the figure
represent the corresponding activation energies Eo'
bor position, (NAs )NNN, in the laser-annealed Si lattice. To
get more information about the initial As distribution, a
Monte Carlo computer simulation has been performed to
calculate (NAS )NNN for different As-implanted doses, im
posing the absence of As atoms in first neighbor position, as
suggested by EXAFS measurements (see Sec. Ill). The re
sults of this calculation are shown in Table n. From this
table, one can observe that the proposed deactivation mecha
nismshould be importantfor doses ;;;, 1 X 1016 As/cm2,where
the As fraction that could be deactivated by this process
ranges from 12 % to 51 % of the total As dose. Nevertheless,
the value of N~';!N = 6.8 X 1020 cm -3 (inactive As-fraction
value of 34%) obtained at the implanted dose of 3 X 1016
As/cm2 (Table II) corresponds to a value of N~~.
~ L3 X 1021 cm -3 which can only take into account the
very early stage of the As deactivation phenomenon and
does not agree with the previous estimate of this value de
duced from the experimental results of Fig. 3, i.e., N~":+
= 4 X 1020 em -3. This finding deserves some more re
marks.
At the dose on X 1016 As/cmz, from the experimental
results of Figs. 3 and 11, it is seen that a unique mechanism
(constant Ea value) is responsible for the first step of the
TABLE n. Computer simulated values of N~::N and Ct.
implanted As Initial As
dose concentratioll N~::N ,C~h C~x"
(10" em 2) (l020 em 3) (10'9 em -3) (l0'9 em -') (10'9 em 3)
6 4.0 2.89 1,45
10 6.7 8.07 4.03 6
30 20 68.5 34.2 18
50 33 169 84.5 30
Parisini et al. 2329
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33deactivation phenomenon up to a deactivated As fraction of
about 70%, i.e., the value of N ~7 I = 4 X 1020 cm -3 is con
sistent with the experimental data. Therefore, the following
two hypotheses can be argued to explain the previous dis
crepancy:
(1) 8i self-interstitials, created in accord with (9),
could increase the total number of As atoms in the second
neighbor position by interstitialcy diffusion. Nevertheless,
the effect of this process has to be a mere redistribution of the
dopant atoms, since no evidence of a broadening of the As
chemical profile is in fact observed experimentally in this
low-temperature range. 25
(2) The calculated values of N~~N, reported in Table
n, could underestimate the real number of As atoms in sec
ond neighbor position. These values have been obtained by
random generation of the As atoms on the Si lattice with the
only limiting condition of the absence of As atoms in first
neighbor position, i.e., imposing a strong repulsive potential
between these atoms. As shown, this calculation fails in deo
scribing quantitatively the experimental situation, indicat
ing that the distribution of the As atoms on the 8i lattice
could not be random in nature and that attractive interac
tions between As second neighbors could exist, leading to
greater values of N~~N.
Actually, excess As-As next nearest neighbors have
been detected in a laser-annealed 6X 1016 As/cm2 Si-im
planted specimen by EXAFS measurements, 14 which could
support the latter hypothesis. Unfortunately, in this sample
an inactive As fraction of about 30% is expected (see Sec.
III) so that from these measurements it is not possible to
deduce the total number of As second neighbors around sub
stitutional active As atoms, that is, the number of interest for
the proposed deactivation mechanism. Therefore, at present
it is not possible to discriminate between these two hypoth
eses. Further experimental investigations are necessary to
obtain information about the initial As distribution in the 8i
lattice.
In Table II, the Si selfointerstitial concentrations pre
dicted by the present model, (C1) th [one Si self-interstitial
produced for each (As2) 2 -+ pair J are also compared with
the corresponding experimentally observed values, (C[ )"X9
(see Sec. IV). Concerning this comparison, the observed dis
crepancy between the (C[ rh and (C[ )exp values for doses
;;,3 X 1016 As/cm2 can be easily explained considering that
only a fraction of the produced Si seIf-interstitials can con
tribute to the formation of the interstitial agglomerates ob
served by TEM (see Sec. IV). This is still more valid consid
ering that, as shown in the previous discussion about the
values of N~;:N reported in Table II, the C~h values have to
be considered as lower limits of the Si self-interstitial concen
trations produced by the proposed mechanism.
Finally, one has to remark critically that the present
model does not explain the variations of the negative strain
at the specimen surface [see Sec, IV and the negative peak in
Figs. 4(a) and 4(b)] observed on 350 ec annealed speci
mens implanted at the dose of 3 X 1016 As/cm2. A likely
explanation of this phenomenon is the presence of oxygen
vacancy defects at the specimen surface, caused by a migra
tion towards the surface of laser induced multivacancy deo
2330 J. Appl. Phys., Vol. 67, No.5. i March 1990 fects. For example, it has been shown recently that, while
vacancies are mobile in Si at temperatures of about 150 K,40
divacancies migrate in Si at temperatures of about 450-500
K,41 i.e., for temperatures comparable to the annealing tem
perature at which this phenomenon have been observed.
This explanation does not contradict the proposed deactiva
tion model if one observes that the migrating defect, in the
temperature range considered, is the divacancy whose intero
action with As atoms is likely to be weak.
VIII. DISCUSSION: HIGH~TEMPERATURE THERMAL
EVOLUTION (650-S00 °C)
While in the previous section, from the low-temperature
experimental results of Sec. IV, it was possible to propose a
model for the first step of the As deactivation phenomenon,
the mechanism by which these metastable alloys attain the
thermodynamic equilibrium still remains a matter of specu
lation. For example, in a temperature range from 650 to
900 ec where As diffusion cannot be neglected, one can easi
ly envisage the growth of the AS2 V clusters with the conse
quent formation of ASm V agglomerates. In support of this
view, recent total-energy calculations performed by Pandey
et aZ. 14 have shown that an AS4 V cluster is energetically fao
vored over both substitutional isolated As and substitutional
As4Si configurations. Nevertheless, one has to take into ac
count the presence of As precipitates that are actually de
tected by TEM observations, in this temperature range.
Therefore, if one considers that these clusters are the
nuclei for the As precipitates, two main hypotheses can be
advanced26,42; (1) Only As precipitation essentially occurs
at high temperature. In this case at least a part of the ob
served discrepancy between precipitated and inactive As
fractions can be explained by the limited visibility of the very
small precipitates in HREM observations.43 (2) Clusters
and precipitates coexist in equilibrium with the active As
fraction.
Moreover, it has been correctly remarked recently44
that the electrical measurements, which show that the car
rier concentration after thermal equilibration is insensitive
to excess dopant, can hardly attain a sufficient accuracy to
rule out the cluster model. This remark further suggests that
the above second hypothesis has to be taken into account.
IX. CONCLUSiONS
In this work laser-annealed and further thermally an
nealed (350-900 °C) 1,3, and 5 X 1016 As/cm2 Si-implanted
specimens have been investigated. On the as laser-annealed
samples it has been shown, by DCD and electrical measure
ments, that the relationship between the strain and the car
rier concentration is not far from linearity. This finding alo
lows one to consider the experimental results obtained on
these samples by DCD and EXAFS measurements as proof
of the Yokota suggestion that the strain aa/ a results from
both a size and an electronic effect. The size effect represents
the Vegard's law contribution to aa/a, while the electronic
effect is the strain induced by the variation of the conduction
band minima due to the doping. In this way it has been possi-
Parisini et al. 2330
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155.33.120.167 On: Tue, 02 Dec 2014 05:52:33ble to confirm the explanation first proposed by Cargill et
ai.,19 that the contraction of the laser-annealed implanted
layer observed by nCD is the result of the prevalence of the
negative electronic effect on the positive size effect, whereas
the local expansion observed by EXAFS measurements
around As atoms is essentially a measure of this latter effect.
The values of /3. and Ec also agree with previous experimen
tal estimates. 19
On the samples further thermally annealed in a low
temperature range (350-550 'C), the experimental results
obtained by electrical measurements, TEM, OeD, and EX
AFS, have allowed one to propose a model for the first step
of the As deactivation phenomenon. The proposed deactiva
tion mechanism considers the formation of an (As2 V) +
duster and the ejection of a Si self-interstitial, !<-, starting
from the capture of two electrons from a (As2) 2 + pair of
substitutional and immobile As atoms in second neighbor
position in the Si lattice. It is proposed that this reaction
starts in the region of the electric junction, where a charge
separation phenomenon can favor the formation of the nega
tively charged Si self-interstitial and of the positively
charged As-vacancy cluster.
This model allows one to explain the experimental ob
servations showing that the As deactivation phenomenon is
simultaneous to the onset of the negative strain recovery and
to the formation ofSi self-interstitial aggregates (interstitial
loops) in the deeper region of the laser-annealed implanted
layer. Moreover, this model is supported by EXAFS mea
surements indicating that, for all the As doses considered,
the As-Si first neighbor distance as wen as the As coordina
tion number tend to the values characteristic of the SiAs
compound, i.e., of a compound where the local configura
tion of the As atoms is the same as in the AS2 V cluster.
After thermal equilibration, attained with short anneal
ing times in a high-temperature range, it is not yet clear
whether precipitation or clustering is the dominant phenom
enon. Nevertheless, in the light of the proposed first step of
the As deactivation mechanism and of the experimental ob
servation of the presence of As related precipitates, the hy
pothesis of the simultaneous presence of clusters and precipi
tates in equilibrium with active As has to be taken into
account. Further experimental investigations are necessary
to determine the nature of the initial distribution of the As
atoms in the laser-annealed 8i lattice and to better identify
the structure of clusters and precipitates. The EXAFS tech
nique, which has proven to be a powerful tool of structural
investigation, should be usefully employed to answer these
still open questions.
ACKNOWLEDGMENTS
The authors are indebted to R. Angelucci for the carrier
profiles, L. Correra and S. Nicoletti for the laser annealings,
G< Tourillon for the assistance in the use of his detector for
EXAFS,and D. NobiH for useful discussion. The technical
assistance of E. GabHli and R. Lotti (ion implantation), P.
Negrini and G. Pizzochero (furnace annealings and test pat
tern preparation), and C. Bouvier, C. Closse, F. CorticeUi,
A. GaruUi, and D. Govoni (electron microscopy) is also
gratefully acknowledged. This work is partially supported
2331 J. AppL Phys., Vol. 67, No.5, i March 1990 by an E. E. C. Contract No. ST2J-0068-1-1 and by C. N. R.
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1.575741.pdf | Friction and wear properties of thin films of carbon with diamond structure prepared by
ionized deposition
Katsuzo Okada and Yoshikatsu Namba
Citation: Journal of Vacuum Science & Technology A 7, 132 (1989); doi: 10.1116/1.575741
View online: http://dx.doi.org/10.1116/1.575741
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.70.241.163 On: Mon, 22 Dec 2014 13:58:39Friction and wear properties of thin films of carbon with diamond structure
prepared by ionized deposition
Katsuzo Okada
Departmento/Mechanical Engineering, Facultyo/Engineering, Yamanashi University, Takeda-4, Ko/u 400,
Japan
Yoshikatsu Namba
Department o/Electrical Engineering, Faculty o/Technology, Tokyo Noko University, Koganei, Tokyo J 84,
Japan
(Received 28 April 1988; accepted 1 October 1988)
The friction and wear properties for thin films of carbon with diamond structure, prepared by
ionized deposition, slid with copper have been examined in a pressure range of5 X 10-4 to 105 Pa.
The friction coefficient shows a tendency to decrease with the increase of pressure and it is < 0.2
because the surfaces of thin films of carbon with diamond structure are very smooth. The specific
wear rate of copper sliders decreases as the pressure becomes lower. However, no wear is detected
on thin films of carbon with diamond structure.
I. INTRODUCTION
Diamond shows the largest wear resistance because it is the
hardest of all materials. Lives of bearings, shafts, and sleeves
may be lengthened if they are made of diamonds.
The friction resistance is expressed as the sum of two
terms, one of which represents the shearing and the other the
ploughing process. I
If a diamond with a sharp edge is slid on metals, it will
tend to dig into metal surfaces during sliding, and produce
grooves. Therefore, the larger the surface roughness of dia
mond, the greater the friction resistance. The friction resis
tance for the combination of diamond and metals would be
come small because of weak adhesion between them if the
ploughing process is negligible.
There are two methods, in principle, for the preparation of
thin films with diamond structure, i.e., chemical vapor depo
sition (CVD) and plasma vapor deposition (PVD). The for
mer produces films having large surface irregularities be
cause polycrystals whose diameters are distributed in a
range of 1 to 10J1m grow on substrates.2 The latter, however,
shows flat surface films, because the crystal grain is very fine,
that is, the mean grain size is < 0.1 J1m.J But, there are few
reports on friction and wear on diamond films.
The purpose of this paper is to evaluate the friction and
wear behavior of sliding over contacts between copper
sliders and flat thin films of carbon with diamond structure
prepared by ionized deposition.
II. EXPERIMENTAL
Thin films of carbon with diamond structure were pre
pared with the modified apparatus, whose original design
has been described in a previous paper. 3 The main modifica
tion was the deflection of the ion beam with the aid of mag
nets, so that the ion beam could reach the Si substrate with
out the deposition of neutral particles, such as carbon
clusters and soot, on the surface of the carbon films. Pure
copper sliders with a radius of curvature of -100 J1m pre
pared by electropolishing were used.
Figure 1 shows a schematic diagram of the friction tester used in the experiment. The copper slider on a rotating thin
film of carbon with diamond structure was fixed on a rigid
pole through a spring leaf on which two strain gauges were
cemented for the measurement of friction force. Sliding was
carried out in a range of 5 X 10-4 to 1 X 105 Pa after atmo
spheric air has been pumped out. The films were rotated at a
rate of 30 rpm and sliding speed was -3.0 cm/s. Normal
loads applied to the slider were in a range of 30 to 300 g.
Specific wear rates of sliders and thin films of carbon with
diamond structure were obtained from the difference
between the weights before and after the sliding test. A mi
crobalance was used to measure the wear. Great care was
used in removing and attaching sliders to the spring leaf. The
carbon films were rubbed with soft cloths, then cleaned with
acetone using ultrasonic cleaner in order to remove the wear
debris from the film surfaces after the sliding test.
III. RESULTS AND DISCUSSION
Figure 2 shows the scanning electron microscope (SEM)
photograph of a thin film of carbon with diamond structure.
The film surface is indicated by A, its vertical section by B,
and the substrate by C. I t has been observed that (i) the film
surface is smooth because an edge line of the film appearing
between a and b seems to be straight, and (ii) there exist pits
like H, whose mean size was 8 flm. Item (i) has been also
revealed using a noncontact high-precision optical surface
roughness measuring technique4 as shown in Fig. 3. The
3
evacuation FIG. I. Schematic diagram of
friction tester: (I) spring leaf,
(2) strain gauge, (3) weight, (4)
slider, (5) diamond film, (6)
motor, and (7) bearing.
132 J. Vac. Sci. Technol. A 7 (2), Mar/Apr 1989 0734-2101/89/020132-04$01.00 © 1989 American Vacuum Society 132
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b
8
c
FIG. 2. View of diamond phase carbon film depm,ited on Si wafer.
maximum height of irregularity, except pits, is 8 nm and the
mean pitch is 0.4 f.lm. Next, item (ii) is discussed in detail.
Lots of pits are observed when the substrate and ion source
were aligned well. But there were a fewer pits when both
were set out of alignment. Therefore, it can be considered
that they might be produced as a result of carbon clusters
and soot coming from the ion source sticking on the surface
of the film.
The friction was recorded during 2 s for each 1 min. The
variation over time of the friction coefficient for 2 s is shown
in Fig. 4. The friction coefficient varies from 0.12 to 0.19,
and the average calculated by computer is 0.15.
Figure 5 shows friction coefficient versus time for 60 min
at a load of 30 g in both high vacuum at a pressure of
5 X 10-4 Pa and atmospheric air. It is recognized that (i) the
friction coefficient for vacuum is greater than that of atmo
spheric air (the former is 0.20 and the latter 0.15) and (ii)
the friction coefficient has small fluctuations. In addition, it
first increases, then reaches a steady state for both curves.
The relationships such as those shown in Fig. 5 were ob
tained from various kinds of applied loads.
Figure 6 shows the relationship between applied load and
friction coefficient which indicates the mean value for a du
ration of 60 min. It is clear that (i) thefriction coefficient for
atmospheric air is smaller than that of vacuum in all the
loads and (ii) friction is independent of load over a range of
30 to 300 g without correction for the apparent area of con
tacts. Item (ii) corresponds to ionized carbon films reported
by Ente.'
No change of friction coefficient with respect to sliding
directions on thin films of carbon with diamond structure
has been observed because of the fine polycrystallization.
The friction coefficient on natural single diamond has de
pended on the crystal orientation of the sliding direction. (,
::1=: -=~~~r-=- ··f~L-'--'
~F~-'~_=
FIG. 3. Surface roughness of diamond phase carbon film.
J. Vac. Sci. Technol. A, Vol. 7, No.2, Mar/Apr 1989 0.4,---------------------,
.~ 0.3
.':::::'
-0.1
OL-----~------L------~------~ o os 10 15 20
: [ere (sec)
FIG. 4. The variation over time of friction coefficient for 2 s.
Next, track surfaces on thin films are discussed. Figures
7(a) and 7(b) show optical photographs of the track sur
faces on thin films where (a) was obtained in high vacuum at
a pressure of5 X 10-4 Pa and (b) in atmospheric air. Lots of
wear particles found in Figs. 7 (a) and 7 (b) are classified
into three types: (i) small metal particles like A, (ii) rolling
pin-type particles like B, and (iii) large metal particles like
C.
Small metal particles are found evenly on both surfaces as
shown in Figs. 7(a) and 7(b). The number of small metal
particles per unit area on both surfaces is almost the same,
that is, -3 X 104/mm2. The mean particle size is 0.4 f.lm,
which is nearly equal to the mean pitch of the surface irregu
larity on thin films as shown in Fig. 3. Therefore, it may be
considered that small metal particles could be formed on
film surfaces as a result of normal sliding wear.7
Figure 8(a) is an enlargement ofa part of Fig. 7(a). Roll
ing-pin-type metal particles with a long axis perpendicular
to the sliding direction are observed as if wear debris of an
eraser are oriented to be normal to the rubbing direction.
Bright parts in rolling-pin-type metal particles such as those
marked P are observed. However, no rolling-pin-type metal
particle is found on track surfaces taken in atmospheric air
as seen in Fig. 7 (b). Therefore, it may be conjectured that
small metal particles would subsequently roll up over sliding
and generate rolling-pin-type particles, since wear metal
particles generated in vacuum could be expected not to be so
c
"' .:': 0.4
:::: 03 "' . o u
oL-----~------~-------+------~ o 15 30
time(mm)
FIG. 5. Friction coefficient as a function of time for 60 min. 60
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~ 03
.S! .....
Qj 8 0.2 0-0-00--0-0-0-0-0-0 in vacuum
c o
~ 01
'..... o-o-<~>---"--eo,---,o --0---,,---" ina i r
o
FIG. 6. Friction coefficient as a function of applied load for both in vacuum
at a pressure of 5 X 10-4 Pa and in atmospheric air.
much contaminated with oxide in comparison with those
generated in atmospheric air.
This can be supported also by the following two facts. The
first one is that the roughness of worn copper sliders for
vacuum is a little bit coarser than that of atmospheric air, as
shown in Fig. 9 where (a) and (b) were obtained in high
vacuum and atmospheric air, respectively. The second one is
that the mean length of the rolling-pin-type metal particles
obtained at a load of 30 g increases as pressure decreases,
which is shown in Fig. 10, because the lower the pressure, the
more active the adhesion. Rolling-pin-type metal particles
have been also reported on friction between mild metals in
vacuum.8
The mean size of large metal particles like C, as shown in
Fig. 7, is 11 /Lm. Figure 8 (b) is an enlarged photograph of a
large metal particle. The surface of the large metal particle is
found to be rather fiat, which corresponds to wear particles
reported by Reda et al. 6 Large metal particles are sometimes
directly observed to be located at pits, as seen in Fig. 7
marked C\. Therefore, it may be assumed that excessive sur
face shear stress causes the complete breakdown of parts of
copper sliders and generates larger metal particles.
No wear has been detected on thin films, while the differ
ence between the weights before and after the sliding test
could not be detected.
Figure 11 shows the wear and friction behavior of copper
sliders slid on thin films as a function of pressure in a range of
5 X 10-4 to 1 X 105 Pa at a constant 000 g. It is clear that (i)
Sliding Direction of Copper Slider
=-
(a) ( b)
FIG. 7. Optical photographs of diamond surfaces after sliding: (a) in vacu
um at a pressure of 5 X 10-4 Pa and (b) in atmospheric air.
J. Vac. Sci. Technol. A, Vol. 7, No.2, Mar/Apr 1989 Sliding Direction of Copper Slider
(a) (b)
FIG. 8. SEM photographs of wear metal particles: (a) in vacuum at a pres
sure of 5 X 10-4 Pa and (b) in atmospheric air.
the friction coefficient shows a tendency to decrease when
pressure increases and (ii) specific wear rate increases as
pressure increases. Item (i) mentioned above can be ex
plained as follows: the adhesion process between copper
sliders and wear particles becomes active as pressure de
creases because both the worn slider surface and wear parti
cles are easy to keep clean. Item (ii) is also explained as an
effect of adhesion, that is, the slider is more difficult to wear
as pressure becomes lower because of the repeated adhesion
of wear particles to the slider.
Thin films of carbon with diamond structure have good
friction and wear properties in both vacuum and atmospher
ic air as mentioned above. Moreover, results obtained may
suggest that they could be used for mechanical sliding parts
such as bearings, shafts, and so on. Further studies of thin
films of carbon with diamond structure deposited on metals
such as Mo, W, and Fe alloys are needed along with friction
and wear tests over a long time.
After sliding, friction parts of thin films of carbon with
diamond structure were observed by transmission electron
diffraction (TED). No change of TED patterns for friction
parts has been observed in comparison with those taken
from thin films before the sliding test, which has been report
ed in the paperY It may be supposed from the above-men
tioned result that the maximum normal stress of ~ 28 NI
cm2 calculated from the copper worn area was not enough to
deform thin films of carbon with diamond structure plasti-
(a) Sliding Direction
~
(b)
FIG. 9. SEM photographs of worn copper surfaces: (a) in vacuum at a
pressure of 5 X 10-4 Pa and (b) in atmospheric air.
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4.0
E
:::l.
3.0
1.0 o
L
o
v .. ----__ w. _______ v ________ ~--------
O~~~~~~~~~~~
104 162 100 102 ld
pressure, Pa
FIG. 10. Pressure vs lengths of rolling-pin-type particles.
cally. In characterizing CVD films, Raman scattering mea
surement is extensively used 10 as well as diffraction. There
fore, the characterization of thin films of carbon with
diamond structure measured by Raman scattering spectros
copy must be studied, induding a comparison between thin
films of carbon with diamond structure before and after the
sliding test.
Friction has some bearing on surface electric structure.
However, it was very hard to study effects of electric struc
ture for thin films of carbon with diamond structure because
of a residual pressure of 5 X 10-4 Pa during the sliding test.
In order to study the relation between friction and electric
structure, experiments were carried out with the friction
equipment installed in the chamber of an Auger micro
probe. II All friction test were performed under ultrahigh
vacuum of 2 X 10 -7 Pa. A normal load applied to the copper
slider was 50 g. Sliding speed was 0.1 mm/s. The value of the
friction coefficient was 0.21 which was nearly the same one
for 5 X 10-4 Pa shown in Fig. 11. Bombardment with 1-keV
electrons for thin films of carbon with diamond structure
showed the increase in friction coefficient to 0.43. This sup
ports that friction may depend on the bonding conditions. It
has been reported by PepperI2,13 that electron bombardment
affects friction, that is, low friction is associated with the
diamond surface devoid of gap states whereas high friction is
associated with the diamond surface with gap states. There
fore, it may be conjectured that electric structure for thin
films of carbon with diamond structure would be corre
sponding to that of the diamond. However, much more defi
nite information on thin films of carbon with diamond struc
ture for electric structure must be required.
IV. CONCLUSIONS
The friction and wear properties for thin films of carbon
with diamond structure prepared by ionized deposition, slid
with copper, have been examined in various ranges of pres
sure. The main results obtained are as follows:
J. Vac. Sci. Technol. A, Vol. 7, No.2, Mar/Apr 1989 ~
N~ 10 0----------0_ 0.2
E
----~/: c Ln CI.> '9 u ><
CI.>~ '+--
Q;
~ 0 u
iii 5 0.1 c <V 0 :;: /v u u '--~v '+--
U
CI.> Q.
Vl
164 162 100 102 104 0
pressure, Pa
FIG. 11. Relations between pressure and both the specific wear rate and the
friction coefficient.
(i) Thin films of carbon with diamond structure as grown
by ionized depositing have very flat surfaces and their sur
face roughness is < 8 nm.
(ii) The friction coefficient, which shows a tendency to
decrease with the increase of pressure, is < 0.2.
(iii) The specific wear rate of copper sliders decreases as
pressure becomes lower. However, no wear is detected on
thin films of carbon with diamond structure.
ACKNOWLEDGMENTS
The authors are grateful for the cooperation of the experi
mental works of both Mr. T. Shimizu of Yam an as hi Univer
sity and Mr. E. A. Heiderpouv and Mr. M. Morikawa of
Tokyo Noko University in Japan. Thanks are due to a
Grand-in-Aid for Scientific Research in 1987-1988 for fi
nancial support.
IF. P. Bowden and D. Tabor, The Friction and Lubrication o/Solids (Ox
ford University, New York, 1964), Vo\. I, p. 90_
2H. Tsai and D. B. Bogy, J. Vac. Sci. Techno\. A 5,3287 (1987).
'T. Mori and Y. Manba, J. Vac. Sci. Techno\. A I, 23 (1983).
4T. Kohno, N. Ozawa, K. Miyamoto, and T. Musha, App\. Opt. 27, 103
(1988).
5K. Enke, Thin Solid Films 80, 227 (1981).
"Y. Enomoto and D. Tabor, Proc. R. Soc. London Ser. A 373, 405 (1981).
7 A. A. Reda, R. Bowen, and V. C. Westcott, Wear 34, 261 (1975).
"N. Soda and T. Sasada, J. Jpn. Soc. Lubr. Eng. 10, 125 (1965).
9y. Namba, J. Wei, T. Mohri, and E. A. Heidarpour, J. Vac. Sci. Techno\.
A 7,36 (1989).
1(IR. J. Nemanrich, J. T. Glass, G. Lucovsky, and R. E. Shorder, J. Vac. Sci.
Techno\. A 6,1783 (1988).
11M. Uemura, K. Okada, A. Okitsu, and N. Takahashi, ASME Wear Mat
er. 107 (1983).
"s. V. Pepper, J. Vac. Sci. Techno\. 20, 213 (1982).
"s. V. Pepper, J. Vac. Sci. Techno\. 20, 643 (1982).
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1.575786.pdf | Effect of magnetic field on plasma characteristics of builtin highfrequency coil
type sputtering apparatus
Mutsuo Yamashita
Citation: Journal of Vacuum Science & Technology A 7, 2752 (1989); doi: 10.1116/1.575786
View online: http://dx.doi.org/10.1116/1.575786
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/7/4?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 128.252.67.66 On: Tue, 23 Dec 2014 01:24:29Effect of magnetic field on plasma characteristics of built-in
high-frequency coil type sputtering apparatus
Mutsuo Yamashita
FacultyofEngineering, Osaka Electro-Communication University, Hatsu-cho, Neyagawa, Osaka 572, Japan
(Received 24 January 1989; accepted 6 March 1989)
The effects of a perpendicular magnetic field on the plasma characteristics of a high-rate
sputtering apparatus with a built-in high-frequency (HF) coil were investigated. When the
proper perpendicular magnetic field, between 20 and 30 G, was applied to the plasma region, the
plasma density markedly increased and the lowest limit of the operating gas pressure could be
reduced from 1.3 X 10-3 to 2.45 X 10-4 Torr. The optimum perpendicular magnetic-field
strength regularly increased with an increase in the operating HF at pressures of 5 X 10-4 Torr or
less, but was little affected by the other discharge parameters, such as HF power and target
voltage. The frequency of the largest harmonic component of the HF voltage, detected from the
plasma region, agreed with the electron cyclotron frequency calculated from the optimum
magnetic-field strength. Therefore, it is suggested that a resonancelike phenomenon occurred in
the plasma region.
I. INTRODUCTION
In the sputtering method for producing thin film, increased
plasma density and reduced operating gas pressure improve
the results, both in terms of film formation rate and quality
of the formed thin film. Therefore, the following methods
are widely employed: (i) application of an external magnetic
field; (ii) incorporation of a thermionic emission system;
and (iii) combination of methods (i) and (ii). For example,
in the case of magnetron type and opposite-facing type sput
tering apparatus, the plasma is confined and the effective
path of the energized plasma electrons is increased by means
of method (i). 1-5 In the tetrode (or triode) type sputtering
system, method (iii) is used to improve sputtering charac
teristics, but the use of active gas may shorten the service life
of the filament electrode.6 Suganomata et al.7 superimposed
both the L-coupled rf discharge and the static magnetic field,
which is parallel to the axis of the high-frequency (HF) coil,
on the sputter type ion source. Oechsner et al. developed
sputtered neutral mass spectrometry (SNMS),8.9 in which a
plasma of27.12 MHz was inductively excited under electron
cyclotron wave resonance; resonance conditions were ad
justed by the change of a superimposed static magnetic field.
In the last two cases, an exciting HF coil was located outside
the glass discharge chamber, preventing the transmission of
the electro-magnetic field and limiting the run time of the
apparatus when the inner wall is coated with sputtered me
tallic material.
The author developed a high-rate sputtering apparatus
with a built-in high-frequency coil for high-density plasma
generation, and reported its fundamental characteristics. 10
An outline of the results is as follows:
(i) A plasma with a density of the order of W12cm -3 was
generated in the sputtering region without an external static
magnetic field, because the plasma could be confined within
the HF coil. Consequently, the deposition rates for various
materials, including ferromagnetic materials, were marked
ly increased.
(ii) The target current increased linearly with the HF
power, but was practically independent of the target voltage; the deposition rate could be independently and linearly con
trolled by changing either the HF power or the target vol
tage.
(iii) The target current density was much higher than that
of other sputtering methods at target voltages below -300
V and its gas pressure dependence was very small compared
with that of conventional dc diode sputtering systems, in
cluding the magnetron and opposite-facing types.
(iv) The degree of ionization of the sputtered atoms im
pinging on the substrate surface was considerably high.II.12
As described above, this apparatus offers some advan
tages in controllability of the deposition rate and in stability
during extended operation, and may be a very useful method
for energy controllable high-rate ion plating. On the other
hand, the lowest limit of operating gas pressure is
-1.3 X 10-3 Torr; this value is an order of magnitude larger
than that of the magnetron and opposite-facing type sputter
ing apparatuses. To reduce the lowest limit of the operating
gas pressure, and to increase plasma density, a perpendicular
magnetic field, whose direction is held perpendicular to the
axis of the exciting HF coil, was applied to the plasma re
gion. The effect of this magnetic field on the plasma charac
teristics is described in this paper.
II. EXPERIMENTAL APPARATUS
The experimental apparatus used has been reported in de
tail elsewhere. I I Therefore, only the outline of the apparatus
will be described. Figure 1 shows the fundamental structure
of this apparatus. To produce dense plasma, an exciting HF
coil 90 mm in diam, and consisting of four turns of 5 mm Ti
wire, was positioned between a disk target (usually 50 mm
ifJ) and a substrate holder in a conventional dc diode sputter
ing apparatus. This HF coil influences the following very
important functions: (i) applying HF energy to the plasma
region; (ii) constructing the impedance matching circuit
between HF electric circuit and plasma with two variable
condensers, VCl and VC2; (iii) confining plasma and in
creasing plasma density. External static magnetic field,
which is perpendicular to the axis of the HF coil, was applied
2752 J. Vac. Sci. Technol. A 7 (4), Jul/Aug 1989 0734·2101/89/042752·06$01.00 © 1989 American Vacuum Society 2752
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(j) Target
<2l HF coil
(J) Variable leak valve
© Base plate
$ Plasma screen grid
(Q) Shutter
Q) Substrate holder
® Radio frequency choke coil
® Bias resistance (Ra) Water Cooled
FIG. I. Schematic diagram of the built-in HF coil type sputtering apparatus
( B,: superimposed perpendicular magnetic field, B II: parallel magnetic
field).
to the plasma region using two permanent magnets located
on two sides of the sputtering chamber (SUS 304, 160 mm
tP X 100 mm H). The strength of the magnetic field was ad
justed by changing the distance between these magnets and
the center of the HF coil. The nonuniformity of the applied
magnetic-field strength was kept under 4% at all parts of the
discharge space. The HF power frequencies used were 7, 14
(or 13.56), 21, and 28 MHz. HF voltage was detected using
a small antenna inserted into the plasma region; frequency
spectrum was analyzed via a spectrum analyzer (Hewlett
Packard, Type-1740A).
III. EXPERIMENTAL RESULTS AND DISCUSSION
Figure 2 shows the target current, which is closely related
with the plasma density, as a function of applied perpendicu
lar magnetic field,B 1 , whose direction is held perpendicular
to the axis of the HF coil, at various Ar discharge gas pres
sures. Sputtering conditions were as follows: the HF power
and its frequency were 300 Wand 13.56 MHz, respectively;
the target was a Ti disk 50 mm tP (effective area:20 cm2); the
target voltage was -500 V. HF discharge continued with-
....... «
E ......
I-
Z
W a: a:
:::I u
I
W 700
400
300
(!) 20 a:
~
100 HF: 13.56 MHz. 300 W
Vr:-SOO V
o 0 20 40 60 80 100
B ... (G)
FIG. 2. Target current as a function of the applied perpendicular magnetic
field strength, B, , at various Ar gas pressures [frequency: 13.56 MHz, tar
get:Ti disk 50 mm '" (20 em')].
J. Vac. Sci. Technol. A, Vol. 7, No.4, Jul/ Aug 1989 out Bl at gas pressures above 1.3 X 10-3 Torr, but suddenly
stopped when Bl rose above a certain value. HF discharge
occurred only when the proper Bl was applied at gas pres
sures < 1.3x 10-3 Torr; the range of B1, in which the HF
discharge continued, diminished with discharge gas pressure
decrease. For example, the magnetic field ranged between 15
and 38 G, when discharge gas pressure and HF power were
5 X 10-4 Torr and 300 W, respectively. B1ma., i.e., the per
pendicular magnetic field at which the target current
reached maximum, hardly shifted with a change in dis
charge gas pressure below 5 X 10-4 Torr (The mean-free
path of the plasma electrons is larger than the dimensions of
the plasma region; the disturbance of the electron trajectory,
due to gas collision, becomes slight).
Figure 3 shows the target current and deposition rate as a
function of the discharge gas pressure. Curves A and A'
show the characteristics obtained when Bl = O. The lowest
limit of operating gas pressure is 1.3 X 10-3 Torr. Although
this lowest limit slightly depends on HF power, it is indepen
dent of the target voltage. Curves Band B' show the charac
teristics obtained when Bl = B1max (optimum value for each
gas pressure). This magnetic field produces the most re
markable effect at a low-pressure range below 5 X 10-3 Torr.
When an optimum magnetic field between 20 and 45 G was
applied to the plasma region, not only did the plasma density
markedly increase, but the lowest limit of the operating gas
pressure diminished from 1.3 X 10-3 Torr to 2.45 X 10-4
Torr where the mean-free path of the sputtered atoms is esti
mated to be -20 cm and most of sputtered particles can
reach the substrate without gas collision. Consequently, the
gas pressure range, in which the deposition rate exhibits its
maximum, changed from 1 X 10-2 Torr to 1.2x 10-3 Torr;
the maximum deposition rate increased by -2.5 times.
On the other hand, when a parallel magnetic field, B II '
whose direction is held parallel to the axis of the HF coil, was
applied, the target current and the sputtering rate were de
creased with an increase in B II; the lowest limit of the work
ing gas pressure was hardly improved. The detailed discus
sion has been reported elsewhere. 13
700 HF:13.56 MHz. 300 W ....... « Vr:-500 v B E 600 Target: 5011. 20cm2 (Ti )
Coil: 9cmJ!l. 3.5 T I-500 Z 3' w d a:: 400 a:: w :::J f-U 300 <{ a:
I- z UJ 200 Q (!)
a:: )--f-
VJ « 100 0 I- 0.
W Cl 0 10'4 10-3 10-2 10-1
GAS PRESSURE ( Torr)
FIG. 3. Target current and deposition rate as a function of the discharge gas
pressure. Curves A and A' show characteristics obtained with B, = O.
Curves Band B' show characteristics obtained with optimum perpendicular
magnetic field strength.
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Figure 4 (a) shows the target current as a function of the
perpendicular magnetic-field strength,B 1, for various HF
powers, at a discharge gas pressure of 5 X 10-4 Torr and a
frequency of 14 MHz. The target current increases with an
increase in the HF power. Although B1max is almost inde
pendent ofHF power at such a lower discharge gas pressure,
it increased with an increase in the HF power at gas pres
sures above 1 X 10-3 Torr, this HF power dependence be
coming stronger with an increase in discharge gas pressure.
For example, when HF power was increased from 200 to 500
W, B1max linearly changed from 34 to 45 Gat 5 X 10-3 Torr.
Such HF power dependence also appeared at frequencies of
7,21, and 28 MHz. Figure 4 (b) shows the target current as a
function of the external perpendicular magnetic fields for
two different target voltages, i.e., -1000 and -60 V
(where the inflow of plasma electrons is eliminated and only
-~
E -.... z
~ a:
=> u
~
~
la)
C'
E -300
200
100
0
300
~200
l1J a: S u
tij100
i 0 PAr : 5x 10-4 Torr
f:14~
10 20 30 40 50
Bol (G)
HF: 14~z.IIXJW
F\r: 5xl0-4Torr
00 10 20 30 40 50
Ib) Bo&. (G)
FIG. 4. Target current as a function of the perpendicular magnetic field
strength, Bjo for various HF powers (a), and two different target voltages
(b) (discharge gas pressure: 5 X 10-4 Torr, frequency: 14 MHz).
J. Vac. Sci. Techno!. A, Vol. 7, No.4, Jul/Aug 1989 ions are drawn in), under the conditions where discharge gas
pressure is 5 X 10-4 Torr, and HF power and frequency are
400 Wand 14 MHz, respectively. No particular change is
seen in B1max with the target voltage in this figure. This was
also independent of other sputtering parameters, such as dis
charge gas pressure, operating HF power and frequency.
These results suggest that plasma generation is mainly
caused by HF energy, and that the target voltage is rather
insignificant in the generation of dense plasma.
Figure 5 shows the relationship between target current
and external perpendicular magnetic field for various high
frequencies at a discharge gas pressure of 5 X 10-3 Torr and
an HF power of 300 W. B1ma. increases with an increase in
frequency and exhibits some consistency. Each curve for 21
MHz and 28 MHz has a sharp peak at 20 and 25 G, respec
tively. Figure 6 (a) shows the frequency spectrum of the
induced HF voltage with applied HF power and fundamen
tal frequency (jl) of 300 Wand 13.56 MHz, respectively,
but the discharge was suspended. Only the fundamental Cf.. )
component appeared. Figure 6 (b) shows the frequency
spectrum during discharge with a discharge gas pressure of
5 X 10-3 Torr and Bl of O. As soon as the discharge oc
curred, the/. component quickly diminished but many har
monic components, especially the 2nd U; ), increased. The
reduction of the /. component means that the applied HF
energy was absorbed efficiently to generate the dense plas
ma. Generation of the 2nd harmonic component can be ex
plained as follows: The instantaneous HF power changes
with double frequency of the operating frequency, because
HF voltages of both ends of the HF coil change alternately
over time. Then, plasma density corresponding to the ioniza-
I
Z W a:: a:: a
I
W
<.!) a:: 400
PAr 5 X 10-3 Torr
~ 100 HF 300 W
Vr -500 V
OL-~--~~--~~--~~--· o 10 20 30 40 50 60 70 80
BJ. (G)
FIG. 5. Relationships between target current and perpendicular magnetic
field, Bjo for various HF frequencies (discharge gas pressure: 5x 10-3
Torr, HF power: 300 W).
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f 2 3 4 5 6 7 8 9
f 2 3 4 5 6 7 8 9
f 2 3 4 5 6 7 8 9
FIG. 6. Frequency spectrum of induced HF voltage [discharge gas pressure:
5XIO-' Torr, HF power: 300 W, fundamental frequency (j, ):13.56
MHz]. (a): without discharge. (b): during discharge without B1• (c): dur
ing discharge with B1 of 39 G. (Number shows the order of each harmon
ic).
tion frequency also changes with double frequency of the
operating frequency. The growth of harmonics of a higher
order is caused mainly by following three items: (i) The
ionization frequency does not change sinusoidally, even if
the electric field strength changes sinusoidally over time.
(ii) The waveform of the HF voltage across the HF coil is
markedly distorted due to the nonlinearity of the plasma;
many harmonics grow. (Details of this distortion will be de
scribed later.) (iii) Some harmonic components are pro
duced by the frequency mixing action caused by the plasma
nonlinearity. Therefore, it is considered that the waveform
chart of plasma density consists of many sinusoidal waves
with difference periods and amplitudes, i.e., many harmonic
components. When Bl was superimposed on the plasma re
gion, the frequency spectrum was greatly changed. This phe
nomenon markedly appeared near Blmax in Fig. 5. For exam-
J. Vac. Sci. Technol. A, Vol. 7, No.4, Jul/Aug 1989 pIe, Fig. 6 (c) shows the frequency spectrum when Bl is 39
G. The 8th (fs) component markedly grew as compared
with Fig. 6 (b). This value (39 G) is almost the same as
Blmax for 13.56 MHz in Fig. 5 (40 G). These frequency
spectra also depended on the discharge gas pressure.
Figure 7 shows the relationships between the target cur
rent and the external perpendicular magnetic field for var
ious high frequencies under conditions where the discharge
gas pressure is 5 X 10-4 Torr and the HF power is 400 W.
The Blmax for each curve was hardly affected by discharge
parameters such as HF power and target voltage at such a
low discharge gas pressure. Blmax increased with an increase
in the operating HF and exhibited remarkable consistency.
That is, when 6 G is subtracted from the value of Blmax for
each frequency, the electron cyclotron frequency,f;, calcu
lated from the remaining magnetic-field strength, B ~max ,
shows a value -4 times as high as the fundamental frequen
cy, J. , of the operating HF power. Figure 8 shows the fre
quency spectrum during discharge under conditions where
the discharge gas pressure is 5 X 10-4 Torr and Bl is 26 G.
The 4th ~) component extremely increased, and the 8th
(fs) component decreased, as compared with the spectrum
in Fig. 6. The frequency of the h component is 54.24 MHz,
which approximately agrees with the electron cyclotron fre
quency /; (56 MHz) calculated from B ~max (20 G) for
13.56 MHz in Fig. 7.
It is well known that when the electron cyclotron frequen
cy calculated from the applied magnetic-field strength
agrees with the frequency of the electromagnetic wave in the
plasma region, electron cyclotron resonance (ECR) occurs;
the plasma electron is preferentially excited, and thereby the
plasma density is extremely increased. The experimental re
sults suggest that an ECR or an ECR-like phenomenon oc
curred between Blmax and a specific harmonic component of
the operating HF power. This resonance has a remarkable
effect at lower discharge gas pressures (below I X 10-3
Torr).
300
7 MHz -4
E -
~ 200 z w a: 0:
:::J
U
100
~ PAr: 5xlO-4Torr W (!) HF:400W 0: Vr : -500 V ~
0
0 10 20 30 40 50
B.L (G)
FIG. 7. Relationships between target current and perpendicular magnetic
field strength, B1, for various frequencies (discharge gas pressure: 5 X 10-4
Torr, HF power: 400 W).
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f 2 345 6 7 8 9
FIG. 8. Frequency spectrum of induced HF voltage (discharge gas pressure:
5 X 10-4 Torr, B,: 26 G, HF power: 400 W, fundamental frequency (f),:
13.56 MHz). (Number shows the order of each harmonic).
The waveform of the HF voltage was distorted, as shown
in Fig. 9, during operation. The reason for this distortion can
be explained as follows: The HF coil was mounted inside the
sputtering chamber, and was grounded through two variable
condensers (VCl and VC2 ) as shown in Fig. 1. Many elec
trons enter the HF coil and form a large electron current, Ie,
when the potential of the HF coil indicates a positive value
with respect to the plasma potential. This Ie charges capaci
tors (VCI. VC2 etc). Thereby, the HF coil is negatively bi
ased up to the terminal voltage of these capacitors. On the
other hand, although the motion of the ions hardly follows in
the change of the electro-magnetic field, the ions flow into
the HF coil and form an ion current, Ii, because the potential
in most parts of the HF coil (except near both ends) is kept
negative for all periods of the HF cycle. This Ii discharges
the capacitors and shallows the bias voltage of the HF coil.
Consequently, a self-bias voltage of --110 V is automati
cally impressed upon the HF coil. The mechanism of this
action is similar to that of generating a negative target vol
tage in a conventional rf sputtering apparatus. A time con
stant, T, is given by T = C' R, where C is the total capaci
tance, including an equivalent plasma capacitance, and R is
the equivalent plasma resistance corresponding to the plas
ma density. In the present apparatus, T is estimated to be
-10 -7 s. This time constant is closer to the period of applied
HF (7.37x 10-8 s, at 13.56 MHz). Therefore, in a steady
state, the bias voltage of the HF coil ripples greatly; the
waveform of the terminal voltage is extremely distorted, as
shown in Fig. 9. Consequently, the plasma is excited with
o level
FIG. 9. Potential waveform of end of HF coil with respect to sputtering
chamber wall (HF power: 300 W, fundamental frequency: 13.56 MHz,
discharge gas pressure: 5 X 10-4 Torr, B,: 26 G). horizontal axis: 2 X 10-"
s/div; vertical axis: 100 V /div.
J. Vac. Sci. Technol. A, Vol. 7, No.4, Jul/Aug 1989 both the fundamental and harmonic components of the ap
plied HF energy.
The perpendicular magnetic field, B l' is also useful in
plasma confinement. When electrons collide with the dis
charge gas, D1, i.e., the diffusion constant of the plasma elec
trons which cross a perpendicular magnetic field, B l' is giv
en by
Dl = D /(1 + w~r), (1)
where D is the diffusion constant when Bl = 0, We is the
electron cyclotron frequency and 7' is the mean time of colli
sion. If w~ r <en, B 1 has no effect on diffusion. When
w~r> 1, Eq. (1) can be simplified as follows:
Dl = D /w~r = kTv/mw~, (2)
where v is the frequency of collision and m is the mass of the
electron. For example, when the discharge gas pressure is
5 X 10-4 Torr, Bl is 30 G and the energy of the electron is
100 eV, the Larmor radius of electron and the value of We 7'
become 1.12 cm and 44 rad, respectively. Therefore, w~ r > 1
is satisfied, and Bl takes part in plasma confinement at pres
sures below 10-3 Torr. However, results shown in Figs. 7
and 8 suggest that the effect of the resonance phenomenon is
larger than plasma confinement effect in operating gas pres
sure reduction and plasma density increase.
IV. CONCLUSIONS
The effects of the perpendicular static magnetic fields on
the discharge characteristics of a built-in HF coil type sput
tering apparatus were examined. HF discharge continued
only within a certain limited magnetic field at a discharge
gas pressure of < 1.3 X 10-3 Torr. Optimum magnetic-field
strength, where the target current becomes maximum, in
creased regularly with an increase in applied HF, but was
hardly affected by discharge parameters such as HF power
and target voltage, at pressures of 5 X 10-4 Torr or less.
These experimental results correspond to the frequency
spectrum of the HF voltage detected in the plasma region.
When the optimum magnetic field was applied to the plasma
region, not only did the plasma density increase remarkably
at lower discharge gas pressure, but the lowest limit of the
operating gas pressure could be reduced from 1.3 X 10-3 to
2.45 X 10-4 Torr. Therefore, it can be expected that this
method permits realization of high-rate formation of high
quality thin film.
ACKNOWLEDGMENTS
The author would like to acknowledge the continuing
guidance and encouragement of Emeritus Professor T. Ta
kagi, Professor I. Yamada, and Associate Professor J.
Ishikawa of Kyoto University, and Professor T. Koshikawa
of Osaka Electro-Communication University for his helpful
advice.
'N. Hosokawa, T. Tsukada, and T. Misumi, J. Vac. Sci. Techno!. 14, 143
(1977).
2J. A. Thornton, J. Vac. Sci. Techno!. 15,171 {I978).
's. Kadokura, T. Tomie, and M. Naoe, IEEE Trans. Magn. 17, 3175
(1981 ).
4y. Hoshi, M. Naoe, and S. Yamanaka, Trans. lnst. Electr. Commun. Eng.
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 128.252.67.66 On: Tue, 23 Dec 2014 01:24:292757 Mutsuo Yamashita: Effect of magnetic field on plasma characteristics 2757
Jpn. J65-C, 490 (1982) (in Japanese).
5y' Niimura, and M. Naoe, J. Vac. Sci. Technol. A 5,109 (1987).
oZ. Oda, T. Asamaki, H. Muta, and T. Mizonobe, Oyo Buturi, 36, 281
(1967).
7y. Saito, Y. Mitsuoka, and S. Suganomata, Rev. Sci. Instrum. 55, 1760
(\984).
8H. Oechsner, Plasma Phys. 16, 835 (1974).
J. Vac. Sci. Technol. A, Vol. 7, No.4, Jul/Aug 1989 9H. Oechsner, and E. Stumpe, Appl. Phys. 14,43 (1977).
10M. Yamashita, J. Vac. Sci. Technol. A 7, lSI (1989).
"M. Yamashita, in Proceedings o/the International Ion Engineering Con
gress ISIAT'83 and IPAT'83. Kyoto (Institute of Electrical Engineers of
Japan, Tokyo, 1983), p.385.
12M. Yamashita, Jpn. J. Appl. Phys. 26, 721 (1987).
13M. Yamashita, Nucl. Instrum. and Methods B 37/38, 194 (1989).
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 128.252.67.66 On: Tue, 23 Dec 2014 01:24:29 |
1.98675.pdf | Interface contribution to the capacitance of thinfilm AlAl2O3Al trilayer structures
A. F. Hebard, S. A. Ajuria, and R. H. Eick
Citation: Applied Physics Letters 51, 1349 (1987); doi: 10.1063/1.98675
View online: http://dx.doi.org/10.1063/1.98675
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/51/17?ver=pdfcov
Published by the AIP Publishing
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129.22.67.107 On: Mon, 24 Nov 2014 17:43:37Interface contribution to the capacitance of thin"'film A( ... ~U203 .. AI trnayer
structures
A. F. Hebard, S. A. Ajuria,a) and R. H. Eick
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
(Received 6 August 1987; accepted for pUblication 28 August 1987)
A dual-gun reactive ion beam sputtering technique has been used to reproducibly fabricate
A1203 dielectrics with low electrical loss for controlled thickness ranging from approximately
10 to 360 A.. The linear dependence of the reciprocal capacitance on dielectric thickness of
AI-AI20J-AI triIayer structures incorporating this dielectric reveals a significant contribution
from an interfacial capacitance in serres with the geometric capacitance. Room-temperature
measurements of both the de resistance and the frequency-dependent complex impedance
demonstrate that, with respect to bulk, there is an enhanced frequency-dependent dielectric
tosS associated with this interfacial capacitance.
The constantly shrinking size of circuit elements in mi
croelectronic applications necessitates a thorough under
standing of physical processes occurring on length scales ap~
proaching atomic dimensions. This is particularly true for
thin-film capacitors where attributes such as frequency-de
pendent loss, electric field breakdown strength, and charge
storage capability become strongly modified as the electrode
separation is decreased. The nature of the Si/Si0 2 interface
in very large scale integrated technology is just one example
of the importance of increased understanding of these is
sues. I An indication that interface processes begin to be
come significant in the limit of smail electrode separation
can be found in the work of Meadz on Ta-Ta20s -Au and
Ta-Ta20S -Bi tunneling structures in which it was shown
that for dielectrics thin enough to allow direct electron tun
neling it is necessary to model the total capacitance as a se
ries combination of an interfacial capacitance and a geomet
rical capacitance. This interfacial capacitance was shown to
vary in proportion to the electronic density of states of the
Au and Bi counterelectrodes. Such a dependence is based on
the notion that an electrode with a low density of states has a
larger charge penetration depth with a correspondingly
smaner capacitance.2 There are, however, serious theoreti
cal objections3 to this interpretation which are based on the
question of which electric field boundary conditions to use at
the metal-dielectric interface. The physics of the situation is
further complicated by polarization and space-charge effects
which have the effect of creating a "blocking" capacitance at
the interface.4•5 Although a complete theory is lacking, the
microscopic origin of these effects is suspected to be in
fluenced by the presence of electrons trapped with a finite
lifetime in localized states near the interface. 6
The research reported here is motivated by this same
question concerning the behavior of the capacitance of thin
film metal-insulating-meta! trilayer structures when the
electrode separation d is reduced towards zero. We have
chosen for simplicity to study the symmetric AI-Alz03-AI
system in which there is only one metallic element. The
3) 1986 recipient of all AT&T Bell Laboratories Cooperative Research Fel
lowship award. presently at MIT. Cambridge, MA. A1203 dielectric with predominantly ionic bonding and large
band gap is wen known in tunnel junction and artificial bar
rier applications 7 for its low leakage and pinhole~free cover
age. In contrast to the work by Mead,2 our AIzO} dielectric
is grown with known thicknesses so that the dependence of
capacitance on absolute rather than relative thickness can be
determined. Interpretation of electrical impedance data on a
sequence of AI-A1203-Al thin-film capacitors with varying
thickness is based on a model in which dc conduction pro
cesses are ascribed to afrequency-independent shunt resistor
in parallel with a capacitor having a frequency-dependent
dielectric constant. We find that the total measured capaci
tance em arises from a geometric capacitance Cb with
"bulk" dielectric constant in series with an interfacial ca
paci.tance Cj• Interestingly, the magnitUde of Cj is an appre
ciable fraction of C b over the entire thickness range (d,;;; 3 60
A). As a consequence, the frequency-dependent loss is COIl
siderably enhanced over that of the bulk, an enhancement
which becomes especially pronounced at low frequencies.
A dual-gun reactive ion beam sputter deposition tech
nique is used for the fabrication of the AIz03 dielectric. A
beam of xenon ions from the first gun, the deposition gun, is
directed onto an Al target at an incident angle of approxi
mately 45°. Simultaneously, a beam of oxygen ions from the
second gun, the etching gun, impinges directly on the rotat
ing substrate which is in a location outsi.de of the first ion
beam. Oxide growth on the substrate thus occurs under dy
namic nonequilibrium conditions in the presence of a plasma
of incoming aluminum atoms and oxygen ions. By careful
tuning of ion beam intensities the rate of oxide accumulation
can be adjusted to be slightly greater than the rate of oxide
erosion. The net oxide growth rate of approximately 4 A. per
minute is thus slow enough to allow a homogeneous wel1-
compacted film to grow. Transmission electron microscopy
examination confirms a homogeneous void-free amorphous
filmS which is consistent with increased packing densities
commonly found in films prepared using ion-assisted depo
sition processes. ".10
Eight capacitor samples, each in a cross configuration
with an area of 4X 10-4 cm2, are prepared simultaneously.
The Al electrodes are deposited through photoresist masks
1349 Appl. Phys. Lett. 51 (17). 26 October 1987 0003-6951/871431349-03$01.00 © i 987 American Institute of Physics 1349
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129.22.67.107 On: Mon, 24 Nov 2014 17:43:376
.. 100 Hz 5 + de +
lL
~ 4
'" E
~
E 3 1 (,)
"-
-\ <t
2
~ !
°0 100 200 300 400
0
DIELECTRIC THICKNESS (Al
FIG. L Plot of the reciprocal area! capacitance vs dielectric thickness 100
Hz (circles) and dc (crosses). The solid line is a regression of the 100 Hz
data.
from thermal sources. Pricr to the deposition of the dielec
tric the base electrode is sputter cleaned with the beam from
the erosion gun. After the deposition of the dielectric the
sample is exposed to atmosphere for preparation of the coun
terelectrode mask. Variation in the time of this exposure
does not cause significant changes in the electrical properties
of the samples. The dielectric thickness d is inferred from
quartz crystal monitor readings calibrated with respect to
optical interferometric measurements 011 the thicker sam
ples. Electrical measurements are made both at dc and at ac
(50 Hz to 40 kHz) with special care being taken to assure
linearity by using voltage levels of 100 mV or less.
The capacitance Cb associated with the bulk dielectric
can be written in the form Cb = K€oA Id, where If is the per
mittivity of the bulk dielectric, A is the area, and d is the
thickness. The effect of an interface capacitance Ci is includ
ed by modeling the total measured capacitance C", as a series
combination of Cb and C,. One thus expects the reciprocal
areal capacitance to have a linear dependence on d with a
nonzero intercept at d = 0, i.e.,
(1)
C(w)
c::
--c;t-~ 0 f-
U
~ 0,5
;z
0 I f-
<:( J IL 01, I./')
.~ if)
0 O.05r-
I III .. .. I e. Q 00 e
0011 e III $ " ..
I I ! $9 0 el
106 107 108 109 10\0 1011
Ro (.Q.)
FIG. 2. Logarithmic plot of the dissipation factor JJ vs the de resistance Ro
for those films in Fig. 1 for which Ro was small enough to be measured in the
linear regime. The solid line is a guide to the eye which identifies the points
plotted in Fig. 3.
1350 Appl. Phys. Lett., Vol. 51, No. 17,26 October 1987 30 I
oc
0 f-2.5'
u 2.0 -it
2:
1.5~ 52
f-
<1:
il..
in 1O~ ..
(f)
0 oJ .. *
~I 6
0°0 2 4 6 8 10
Rd (10-7.0.-1 )
FIG. 3. Linear plot ofD vsR 0-"forthedata points adjacent to the solid line
in Fig. 2.
This dependence is verified in the Fig. 1 plot of A I Cm vs d for
80 junctions made in 10 separate depositions. A value for K of
9.03 is calculated from the slope of the solid line regression
fit through the 100 Hz data (solid circles). This value of K is
somewhat higher than typical thin-film values of slightly less
than 8.5 found in the literature. tl,l2 These results thus indi
cate that a void-free high quality dielectric has been obtained
with the two-beam deposition technique. The high quality of
the dielectric is also confirmed by measurements of a lower
bound to the dc leakage resistance of 1012 n for all samples
with thicknesses greater than 32 A. The low leakage currents
associated with these high resistances enabled accurate qua
sistatic measurements (crosses in Fig. 1) taken with a Cou
lomb meter using a 10-8 integration time. The closeness of
these de data to the 100 Hz data indicates an almost negligi
ble amount of low-frequency dispersion.
The salient feature of Fig. 1 is the rather large zero
thickness intercept on the inverse capacitance axis from
which the value CJA = 1.62 .uF/cm2 can be calculated.
The crossover thickness at which Ci = C b occurs at a rela
tivelY robust value of 50 A. For smaller d the interface con
tribution dominates the capacitative part of the impedance.
If the two interfaces are assumed to be equivalent, we find a
value of 3.24 ,uF/cm2 per interface. Interestingly, the as-
0.Q16
.... '" " 0.012 "
" it: ••• • • -' " -~ 0008 • • "
0.004 ~-.. ~ ! • '" f .... ! e • " " " e " .. S t 1 .. .. .. .. ..
I
0) I I I I
10 100 1000 10000 100000
FREQUENCY (Hz)
FIG. 4. Plot of the ratio of the imaginary to the real part of the permittivity
vs frequency for film thicknesses of :::::10 A (squares), 22 A (diamonds)
212 At. (circles), and 360A (triangles). '
Hebard, Ajuria, and Eick 1350
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129.22.67.107 On: Mon, 24 Nov 2014 17:43:37sumption of a vacuum dielectric for Ci (K = I) implies a
plate separation of 2.7 A, a distance comparable to nearest
neighbor atomic separations. However, the alternative ex
planation13 of a two-layer composite dielectric cannot be
ruled out.
It is reasonable to suspect that Ci and Cb should have
different frequency dependences.12•14 To investigate this
possibi.lity, we model the electrical response of our trilayer
structures (inset of Fig. 2) as a paranel combination of Ii
frequency-independent resistance Ro and a frequency-de
pendent capacitance C(UJ) with compiex permittivity
K(UJ) = K' (UJ) -iK" (al). The real part of C is equal to Cm.
The dc resistance Ro is included to take into account conduc
tion processes such as tunneling and thermaIiy activated
hopping which become important as d is made small. It is
straightforward to show that the experimentally measured
dissipation. factor D, defined as the ratio of the real and
imaginary parts of the complex admittance, can be written in
the form
K"(al) d D=--+ (2)
K' «(1) UJ£oK' «(1) )ARo
The logarithmic plot in Fig. 2 of D vs Ro includes all of the
data in Fig. 1 for whi.ch Ro was sman enough to be measured
in the linear regime (Le., d,32 A.). There are clearly two
regions of behavior: a region, depicted by the solid line, of
large D and small Ro where the second term ofEq. (2) domi
nates and a region of lower D and higher Ro where the first
term ofEq. (2) dominates. For the thicker dielectrics with
unmeasurably high Ro. D decreases further to a bulk-domi
nated lower bound of approximately 0.006. Replotting the
data in Fig. 2 on a linear scale versus R 0-!, as is done in Fig.
3, reveals the expected linear dependence predicted by Eq.
(2) when Ro is small. From the slope of the regression fit
solid line in Fig. 3, a value for the capacitance per unit area of
1.58pF/cm2 is obtained. Since these data with smallRo only
apply to the ultrathin dielectrics where Ci dominates over
Cb, it is not surprising that this number is close to the result
2C;lA = 1.62 J.lF/cm2 calculated from the data in Fig. 1.
These results thus tend to validate the use of a frequency
independent value of Ro in a finite frequency (100 Hz) anal
ysis using Eq, (2). A similar analysis could be used at higher
frequency providing that series lead resistances can be kept
small enough. In practice, this condition occurs for our films
at frequencies less than 100kHz.
For capacitors with high shunt resistance the second
term in Eq. (2) can be ignored and a measurement of Dis
equivalent to a measurement of the rati.o K" (tV )IK' «(1)). Fig-
1351 Appl. Phys. Lett., Vol. 51, No. 17,26 October 1987 ure 4 is a plot of this ratio versus frequency for a series of
dielectric films which increase in thickness from tens of A
(top) to 360 A (bottom). These data dearly show increased
dielectric loss at low frequencies due to the interface capaci
tance.
In conclusion, we have shown in this letter that interfa
cial processes can make a substantial contribution to both
the magnitude and frequency dependence of the capacitance
of thin-film trilayer structures. Values ofCm cannot be used
with impunity to calculate dielectric thickness! The result
win always be too large because of the presence of a series
connected Ci which forces the inequality C m < Cb• This ac
counts for the experimental observation that dielectric
thickness inferred from capacitance measurements is always
larger than the thickness inferred from tunneling. 3, II
Roughness considerations are also important as the tunnel
current is dominated by the thinnest portion of the barrier
whereas the capacitance is a measure of the arithmetic aver
age of the barrier thickness. Finally, in the absence of elec
trode effects,3 we conjecture that for an ideal interface the
magnitUde of C; has as a lower bound the capacitance asso
ciated with a vacuum dielectric between two parallel elec
trodes with nearest neighbor interatomic spacing. This con
jecture is consistent with the results reported above and with
previously reported work on high-quality Ta20s and MgOx
films.2,i3
The authors appreciate useful and stimulating discus
sions with A. T. Fiory and A. F. J. Levi.
'F. J. Feigie, Phys. Today October, 47 (\986).
le. A. Mead, Phys. Rev. Lett. 6, 545 (1961).
3 A. K. Theophilou and A. Modinos, Phys. Rev. B 6, 801 (1972).
4J. G. Simmons, J. Phys. D 4,613 (1971 l.
sD. S. Campbell, Vacuum 27, 213 (1977).
6J. Halbritter, Z. Physik B 31,19 (1978).
7J. B. Damer and S. T. Ruggiero, IEEE Trans_ Magn. MAG-23, 854
(1987).
's. Nakahara (private communication).
·P. J. Martin, J. Mater. Sci. 21, I (1986).
10J. J. McNally, G. A. AI-Jumaily, andJ. R. McNeil, J. Vac. Sci. TechnoL A
4,437 (1986).
!lO. Meyerhofer and S. A. Ochs, J. App/. Phys. 34, 2535 (1963).
!2F. Argall and A. K. Jonscher, Thin Solid Films 2,185 (1968).
Jj A. F. Hebard, A. T. Fiory, S. Nakahara, and R. H. Eick, Appl. Phys. Lett.
48,520 (1986).
"A. K. Jonscher and J. M. Reau, S. Mater. Sci. 13, 563 (1978).
Hebard, Ajuria, and Eick 1351
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129.22.67.107 On: Mon, 24 Nov 2014 17:43:37 |
1.341630.pdf | Effect of substrate photoexcitation on channel conduction in a modulationdoped Al x
Ga1−x As/GaAs heterostructure
P. H. Jiang, Y. J. Huang, W. K. Ge, D. Z. Sun, and Y. P. Zeng
Citation: Journal of Applied Physics 64, 2488 (1988); doi: 10.1063/1.341630
View online: http://dx.doi.org/10.1063/1.341630
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/64/5?ver=pdfcov
Published by the AIP Publishing
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:32Effect of substrate photoexcitation on channel conduction in a
modulatlon .. doped AlxGa1_xAs/GaAs heterostructure
P. H. Jiang,a) Y. J. Huang, W. K. Ge, D. Z. Sun, Y. P. Zeng
Institute afSemiconductors, Chinese Academy a/Sciences, P.o. Box 912, Beijing ]()()(J83, China
(Received 5 January 1988; accepted for publication 9 May 1988)
If a modulation-doped AIGaAs/GaAs heterostructure is illuminated by light, photoexcitation
of deep levels in the GaAs substrate leads to some interesting enects. Below 100 K, the
heterostructure shows a persistent photoconductivity effect. Moreover, a strong persistent
channel depletion is observed at low temperatures when a small negative voltage is applied to
the substrate contact (backgate). The latter effect is explained by a double-layer model of
GaAs where the GaAs side of the heterostructure consists of ( 1) a buffer layer and (2) a semi
insulating substrate. Under illumination, most of the applied negative voltage drops across the
very thin buffer layer, and the enhanced electric field in the layer exerts a very strong influence
on the conducting channel.
I. INTRODUCTION
In modulation-doped heterostructures, a large energy
gap material such as A]GaAs is grown epitaxiaUy on a
smaller energy-gap material, such as GaAs. The structures
are grown by molecular-beam epitaxy (MBE) or metal
organic-chemical-vapor deposition (MOCVD). A very
abrupt interface between the two materials is achieved. Do
nor dopant atoms are placed in the AIGaAs, sometimes sep
arated from the GaAs by an undoped AIGaAs spacer layer,
whereas the GaAs is undoped. Some of the electrons from
the donors are transferred from the AIGaAs into the GaAs
and form a quasi-two-dimensional electron gas (2DEG) in a
triangular potential wen near the heterojunction. The 2D EG
manifests itself as a conducting channel at the interface, but
is sufficiently removed from the ionized donor impurities so
that impurity scattering is reduced and very high mobility is
obtained.
The sheet carrier concentration of the 2DEG, and hence
the conductivity of the conducting channel, can be modula
ted by an electric field perpendicular to the interface. For
example, in the high electron mobility transistor (HEMT)
structure, a metal gate is formed on top of the AIGaAs layer
("front gate"), and the carrier concentration of the 2DEG
can be controlled by the voltage between the gate and the
channel. A metal layer can also be formed on the bottom of
the GaAs substrate ("backgate"). The voltage between the
backgate and the channel ("substrate bias") has qualitative
ly the same effect on electron concentration and sheet con
ductivity of the channel as that by the front gate. 1 Since the
thickness of the GaAs layer on the substrate side of the heter
ointerface is large compared to the thickness of AlGaAs on
the top side, the effectiveness of the backgate modulation is
small compared with that by the front gate modulation.
It is found that if the sample is cooled down to low tem
peratures ( < 100 K) in the dark and then illuminated, the
electron concentration and sheet conductivity ofthe channel
increase. If the light is turned off, electron concentration and
a) Current address: Electricity Division, National Bureau of Standards,
Gaithersburg, MD 20899. sheet conductivity decay in a few seconds to lower steady
values, which are higher than the original values in the dark.
The original values can only be restored again by warming
the sample up to room temperature and cooling it again in
the dark. This phenomenon is known as persistent photo
conductivity (PPC). 2
In a previous paper,3 we reported two thresholds of
PPC, 0.8 and 1.1 eV, They are related to two independent
mechanisms: ( 1 ) electron photoexdtation from chromiurn
related deep levels in a semi-insulating (SI) GaAs:Cr sub
strate and (2) photoionization of donor complex (DX)
centers in AIGaAs.
The combined influence of illumination and negative
substrate bias was reported by Kastalsky and Hwang." They
observed strong persistent depletion of the channel, but did
not investigate this effect in detail and its mechanism re
mains unclear. In this work we investigate, in detail, the in
fluence of both illumination and substrate bias on the con
ducting charme!. For the first time, the mechanism of
persistent channel depletion at low temperatures is ex
plained by a double-layer model of GaAs. The experiments
were carried out with photon energies between 0.8 and 1.1
eV, lower than the threshold of DX center photoexcitation in
AIGaAs, but higher than the threshold of deep center pho
toexcitation in a semi-insulating GaAs substrate. The en
hancement of substrate conductivity under illumination
turns out to be the crucial factor responsible for the strong
persistent decrease in channel conductance with the applica
tion of negative substrate bias.
It EXPERIMENTAL PROCEDURES
The modulation-doped AIGaAs/GaAs heterostruc
tures were grown by MBE. 5 A high-purity GaAs buffer layer
of a thickness of 1-3 fLm was grown on a SI GaAs:Cr sub
strate. It was followed by an undoped AIGaAs spacer layer
of thickness 10 nm, a Si-doped AIGaAs layer of thickness 60
nrn, and finally a 20-um-thick un doped GaAs cap layer. The
Al mole fraction x = 0.3, and the doping concentration in
AIGaAs was 1 X 1018 em -3. The samples for measurements
2488 J. Appl. Phys. 64 (5), 1 September 1988 0021-3979/88/172488-07$02.40 @ 1988 American Institute of Physics 2488
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:32were made in van der Pauw geometry with photolithogra
phically defined patterns and In-alloyed ohmic contacts.
The conductivity and Hall coefficient were measured at
77 and 4.2 K in low magnetic fields ( < 0.3 T). Components
of the resistivity tensor Pxx andpxv were measured at 4.2 K in
high magnetic fields. The electron concentration of the
2DEG was determined by Shubnikov-de Haas (SdH) oscil
lations of Pxx versus magnetic field B.
The sheet electron concentrations before illumination
ranged from 3 X 10 II to 7 X 1011 em'-2, the mobilities were
5 X 104 to 4 X 105 cmZ IV s at 4.2 K and varied from sample to
sample.
The sample was illuminated from the AIGaAs side of
the heterostructure with the following sources of light:
InGaAsP injection laser (A = L3 pm, photon energy 0.95
eV), GaP red light emitting diode (LED) (A = 0.7 Itm,
photon energy 1.77 eV), and a high-intensity grating mono~
chromator. The laser and LED were immersed in liquid ni
trogen near the sample for 77-K measurements. For 4.2-K
measurements, they were placed outside the cryostat and the
light was conducted through an optical. fiber to the sample in
liquid helium. For continuously variable photon energies, a
high-intensity grating monochromator was used as the light
source illuminating the sample through a window on the
cryostat.
m. EXPERIMENTAL RESULTS
A. Persistent photoconductivity (PPC)
In order to observe the substrate effect on PPC, the sam
ple was cooled to 77 K from room temperature in the dark,
then the measurements were made by exposing the sample to
monochromatic light with photon energy 0092 eV and ob
serving the decay of channel resistivity with time. The chan
nel resistivity at first exhibited a fast decay and then became
saturated at some lower value. After switching off the illumi
nation, the reduced channel resistivity persisted over a very
long time.
The substrate contact was either floating or connected
to one of the channel contacts, and the resulting saturated
channel resistivity under illumination was different, as
shown in Fig. 1, in which the variation of channel resistivity
R with time t is presented. The saturated channel resistivity
under illumination was dependent only upon the substrate
connection and was independent of the connection history.
When the substrate was floating, a voltage of Vr) = + 0.6 V
was developed on substrate contact with respect to the chan~
nel. When the substrate was connected to the ch.annel, a
current I, = 6 X 10-11 A was found to be flowing out from
the substrate contact. The appearance of the open-circuit
voltage and the short-circuit current with the illumination
clearly demonstrated that the electrons were photoexched
from the deep centers to the conduction band of the GaAs
substrate. These electrons could diffuse and then be swept
into the channel. Since their recombination with ionized
deep centers was prohibited by the macroscropic electric
field, these electrons remained in the channel after switching
otfthe illumination. This phenomenon is in fact the familiar
photovoltaic effect, where the conducting channel and sub
strate form a kind of "junction."
2489 J. Appl. Phys .• Vol. 64. No.5. 1 September 1988 1.00
0.90 I
"I
~ ~------------
~ l !
! F I ! ,
I
I I
I
LIGHT -------...-j DARK
I I
5 I I
I I
!
I
B6GS7
T =77K
t (min)
FIG. L Photoconductivity effect of heterostructure under illumination
with light of photon energy 0.92 eV. F: substrate contact floating, as shown
by upper-left inSet. S: substrate contact short connected to the channel
contact, as shown by upper-right in~et. Ro: channel resistivity before illu
mination.
SdH measurements were made at 4.2 K and the results
are shown in Fig. 2. From the periodicity oftne SdH oscilla
tions, the electron concentration of 2DEG can be deter
mined. From the depth of the minima of the SdH oscilla
tions, the presence of any parallel conducting layer other
~9G
0.8
0.6
T ,..
::rnA ."
3GO 'il
In 0.2
6 ,
i
00
j 200
86693
T:4.2K
100
" ' . , , ' ..
\J
'J
0 0
FIG. 2. Variation of Px., with magnetic field B. The SdH plots (B mi.: vs
integer i) are shown as inset, from which the 2DEG concentration nw can
be determined. The measurements were made in the following sequence:
(I) after cooling thesllmple in darkness (11m ~. 4.2 X 10" em -7); (2) illu
minated by light of photon energy 0.95 eV (flw :co 5.6X 10" em .,); (3)
illumination by light of photon energy 1.77 eV (11m = 6.0X 10" cm . 'J;
and (4) after tllming olIillumination (nm = 6.0X 10" em' ').
Jiang etal. 2489
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:32than 2DEO can be ascertained. It can be seen that the elec
tron concentration of the 2DEG has a more than 30% in
crease under illumination with light of photon energy 0.95
eV, but the effect of parallel conductance is small. The situa
tion was different when the sample was under the light from
the GaP red LED ( 1.77 e V), In this case, there was a further
increase of 2DEG electron concentration (less than 10%),
but a strong magnetoresistance was superimposed on the
familiar oscillatory SdH curve, indicating the formation of a
second conducting layer in AIGaAs. (,
The following conclusion can be drawn from the experi
mental facts, When the sample is illuminated by light with
photon energies between 0.8 and 1.1 eV, the responsible
mechanism for the PPC effect is the photoexcitation of elec
trons from deep centers in the SI GaAs substrate, and their
subsequent transfer into the channel.
B. Substrate bias effect under illumination
At low temperatures (77 K), when a bias was applied
between the substrate and one of the channel contacts under
continuous illumination with light of photon energy 0.95 e V,
the variations of channel resistivity and bias current through
the substrate are shown in Figs. 3 and 4, respectively. The
polarities of voltage and current are shown in the inset of Fig.
3. The relaxation processes are evident with the tum on and
turn off of the substrate bias under constant illumination. It
can be noticed that there were very large charging and dis
charging current transients. Under constant illumination,
the saturated values depended only on the substrate bias ap
plied and were independent afthe past history. As shown in
Fig. 3, a strong enhancement of channel resistivity with neg
ative substrate biasing was observed, but only a slight reduc
tion took place when the voltage was positive.
The relationship between these saturated values of sub
strate current and substrate bias voltage was highly nonoh
mic (see Fig. 4). The saturated substrate current had differ
ent values for different polarities of biasing. For positive
biasing, the "junction" between channel and substrate was
15
10
5
!
(I I;
j
(I V!l: -6V
~~
-..
-4V
-2-'L
",2 AI 't6V
2. 3 "
t(min) 86087
T=77K
5 6 7
FIG. 3. Typical variation of channel resistivity with substrate bias under
continuous illumination ( 0.92 eV). At t = 0 the substrate voltage is
changed from zero to V. and then turned off. Ro is the channel resistivity
with zero substrate bias under illumination.
2490 J. Appl. Phys" Vol. 64, No.5, 1 September 1988 ... < g 1.5
lo()
0.5 ,
Vg=-4V 0 I
I
/ , , , ,
I
I (I !'---'
-0.5
-1.0
-1.5 o '(-
2 Vg=D Vg".4V (I
r-'
86081
T=77K
4
FIG. 4. Typical variation of substrate current with substrate bias under con
tinuous illumination ( 0.92 eV). The substrate voltage is changed from zero
to -4 V and then turned off. Later it is changed from zero to + 4 V and
then turned off.
"forward" biased, and the high-density 2DEO as a source of
electrons could supply a large current which was limited by
the SI substrate. For negative biasing, however, the "junc
tion" was "reverse" biased, and the magnitude of current
was much smaller.
This substrate bias effect is related to the PPC effect
described above. When the substrate contact was discon
nected from the channel, an open-circuit voltage was devel
oped across the "junction" under illumination, and the sub
strate contact then had a higher potential than the channel.
This is equivalent to a sman positive voltage applied to the
substrate, giving rise to a slight decrease of channel resis
tance.
In order to determine the variation of carrier concentra
tion and mobility in the channel, Hall measurements were
carried out at 77 K in low magnetic fields (-0.1 T) with
iHumination oflight (0.95 eV) and various substrate biases.
The saturated values of electron concentration n, sheet con
ductivity a, and the electron mobility f.l = oi en are shown in
Fig. 5 as functions of the substrate bias, Their dependencies
are very similar to that obtained by Stormer, Gossard, and
Wiegmann I in the dark, but the voltage scale is three orders
smaller than that of the latter work. The variation of electron
concentration with negative substrate voltage was linear; the
dependence followed the behavior of a simple capacitor
model An = CAVg Ie, where C, the capacitance per unit
area, is proportional to the slope of the linear relation. With
application of negative biasing, the channel conductivity
showed a dramatic decrease. Complete depletion of the
channel with resistance between contacts in excess of 107 n
was observed with application of negative voltages beyond
-10 V. The mobility decreased with increasing negative
voltage, as explained by Stormer and co-workers. i For com
parision, the effect of the substrate bias on the same sample
in the dark was also measured at 77 K. The variation of
electron concentration with negative voltage was also linear,
Jiang eta!. 2490
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:327
II 86087
'l'e 5 T: 1'71<:
~ .. :g
3
2
12
'" > 10 ;:;.
5 8 g " !b)
~ 4
:<
_1.0
(CI
! .. ~
_~10~-k~~~_5~~~~~~
Vg(\ll FIG. 5. Variation of carrier
concentration n, electron
mobility f.1. and sheet con
ductivity 0' with substrate
bias voltage Vg under illu
mination (0.95 eV). From
the linear variation of f!
with Vg, the slope
eAnIAV.=9.8XIO-9 FI
cm2 was calculated.
but the calculated capacitance was many orders smaller than
that obtained under illumination.
The transport properties were also measured at 4.2 K in
strong magnetic fields. The carrier density determined by
the SdH oscillations is attributed solely to 2DEG in the
channel. The presence of the parallel conducting layer can be
estimated from the minima of the oscillations.7 The in
fluences of negative bias on transport properties in dark and
under illumination are shown in Figs. 6 and 7, respectively.
In most cases, the effect of parallel conductance in AlGaAs
is not significant. The carrier concentrations determined by
the low magnetic field Hall measurements and by SdH oscil
lations in high magnetic fields are approximately equal. The
bias dependences of carrier concentrations measured at 77
K, as shown in Fig. 5, were reproduced at 4.2 K.
When the sample was illuminated by white light from an
incandescent lamp, the strong enhancement of channel resis
tivity with application of negative bias was also observed.
But the same effect did not appear under illumination by the
GaP red LED. This might be due to the strong absorption of
its 1.77 eV photons by the AIGaAs layer, preventing the
light from reaching the substrate.
C. Persistent channel depletion
It has already been shown that under the combined ac
tion of illumination and negative substrate bias at low tem
peratures, a dramatic increase of channel resistivity, and
even channel depletion, may take place. The typical vari
ation of channel resistivity after turning off illumination and
bias is shown in Fig. 8. After turning off only the light, the
channel resistivity will persist for a very long time. After
turning off both the light and the substrate bias, the en
hanced channel resistivity clearly relaxes toward its previous
value, but it still is not close even several hours later.
2491 J. Appl. Phys., Vo!. 64, No.5, 1 September 1988 2 86093
T:4.2K
c.a
OJ>
0.4
()'2
a
~ 0.4 l!
0.. 0.3
0.,2
0.1
()
0.2
B,TJ
to 86093
4.21'1
8
6
Oi
l& fb)
~
0::4
2
IHTl
FIG. 6. Substrate bias effect on transport properties of heterostructure in
the dark. (a) Pxx vs E, the numbers of occupied Landau levels are indicated
at the corresponding minima and (b) P xx vs B, the numbers of occupied
Landau levels are indicated at the corresponding plateaus.
IV • ANALYSIS OF EXPERIMENTAL RESULTS
In a modulation-doped AIGaAs/GaAs heterostruc
ture, the GaAs side consists of two layers of different proper
ties. A high purity GaAs buffer layer was grown on top ofSI
GaAs:Cr substrate. The former is of high purity grown by
MBE with a thickness of the order of several Il-m, the latter
has a thickness of several hundreds of jlm. There is a large
number of deep centers in the SI substrate, but the exact
concentration of deep centers is unknown to us. When the
substrate is illuminated by light with a suitable photon ener
gy, the electrons can be photoexcited from these deep
centers, and, therefore, under illumination, the resistivity of
Jiano stal. 2491
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:3215 86093 "11=-20" -18v
4
3
2
-0.8
"'" ~ OA • r.l Q2
().6
006
1)..4
0.2
(US
IUD
IlO5
°0
10
8 4.2K
lal
Cal
86093
4.21<
fbI
FIG. 7. Substrate bias effect on transport properties of heterostructure illu
minated by light with photon energy 0.95 eV. (a) P.x vs D, the numbers of
occupied Landau levels are indicated at the corresponding minima and (b)
Pxv vs S, the numbers of occupied Landau levels are indicated at the corre
sponding plateaus.
the substrate will be lower than that of the high-purity buffer
layer. The photoconductivity of the substrate is the crucial
factor responsible for our observed experimental results.
As mentioned above, the substrate 1-V characteristic in
the stationary state under constant illumination is highly
nonohmic. The "junction" between the conducting channel
2492 J. Appl. Phys., Vol. 64, No.5, 1 September 1988 3 iiQht+dark
; , ,
0 Vg:;;:~4V: 0
£2 .......
IX
86067
T=71K
0
0 20 40 60
t(min)
FIG. 8. Typical variation of channel resistivity R after turning offillumina
tion and substrate biasing. The substrate voltage is changed from zero to
-4V under illumination of light ( 0.95 eV). Ru is the channel resistivity
with zero bias. Later, the illumination and then the biasing are turned olf.
and substrate is "forward" biased with positive substrate
voltage, and the "forward" current has a large magnitude
with the 2DEG as the source of carriers injected into sub
strate. The "junction" is "reverse" biased with negative sub
strate voltage, and the "reverse" current is smaner than the
"forward" one. In the fonowing, the attention is focused on
the situation of "reverse" biasing. In analyzing the effect of
substrate bias. the photovoltaic effect will be neglected in the
first approximation.
The structure and parameters of the two layers are
shown schematically in Fig. 9(a). Let db andd, be the thick
nesses, Eo and E, the electric field strengths, Ib and Is the
currents, Po and Ps the resistivities ofthe layers, and Vb and
Vs the voltage drops across the layers. The suffix b refers to
the buffer layer, and the suffix s refers to the SI substrate. Let
Q be the charge at the interface between the two layers and
Qs be the charge at the substrate contact. Then we have
20EG
/"
V Eb
---'"
la) ~ It!
< -
buff .. ,
-
(bl Es ..-
Is .......
substrate
.;-
V 9 b.lrate
ontact V:u
f--(1)
(2)
FIG. 9. Double-layer model for the GaAs side of the heterostructure. (a)
Schematic drawing for the heterostructure (not to scale) and (b) equiva
lent circuit of the double-layer model.
Jiang etal. 2492
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:32dQs I-Is =--, dt
Q= Cb Vb -C, V" (3)
(4)
Qs = Cs V" (5)
where Rb = P b d blA and R s = P sd,! A are the resistances
and Cb = ££oA Idb and Cs = £€oA Ids are the capacitances of
the two layers, A is the area of the heterostructure. This
structure has the very simple equivalent circuit, as shown in
Fig.9(b).
These equations can be easily solved for constant Vg, aU
of the solutions have an exponential factor with time con
stant
(6)
The saturated values for the stationary state are as follows:
Vb=RbVgI(Rb+Rs)' (7a)
V, =RsVg/(Rb +Rs), (7b)
Eb = Rb Vgldb (Rb + Rs),
Es =R,Vg/ds(Rb +R,),
Q= (RbCb -RsCs)Vg/(Rb +Rs),
1= Ib = Is = VgI(Rb + Rs}· (8a)
(8b)
(9)
( 10)
We have ds ~db' hence, Cs <Cb• As a result of the iUumina
tionp, <Pb and thenR/J/db~RJds' or RbCb ~RsC,. Thus,
Eb ~Es in the stationary state, and the 2DEG is affected by
an enhanced electric field from the substrate side with ap
plied negative bias while under illumination.
The field affecting the conducting channel is EI>' which
bears a linear relation with electron concentration n in the
2DEG. Thus, by applying Gauss' Law to the 2DEG we have
An = EEob.Eb/e = €EoAVgRbledb (RI; + R,). (II)
If we treat the negative substrate bias effect on the channel
with a simple capacitor model, the effective width of dielec
tric between the capacitor electrodes can be denoted by dew
and we have
(12)
which is somewhat larger than db'
The transient response can be analyzed by the simple
equivalent circuit in Fig. 9(b). Since C£ <Ch, C, can be ne
glected in the analysis. We also continue to ignore the photo
voltaic effect in the first approximation. As the applied bias
changes abruptly from zero to a negative value, Cb is
charged by a current with initial value Vg IRs. When the
stationary state is attained, the current has a saturated value
determined by Eq. ( 10). Meanwhile, there is a sheet of nega
tive charge Q at the interface between buffer layer and SI
substrate determined by Eq. (9). Conversely, if the applied
bias changes abruptly from a negative value to zero, Cb is
discharged and the negative interface charge disappears.
The switching transient shown in Fig. 4 can be com
pared with the theoretical analysis. The large switching tran
sient in the substrate current indicates that Rb > Rs. i.e.,
Pbdb >Psd". From the curves we get 7= 6.7 S,
Rb = 1.3 X 1010 n, R, = 5.3 X 109 fl, and Cb = 1,8 X 10-.9
F. The latter agrees with the capacitance calculated from the
values of A and db'
2493 J. App!. Phys., Vol. 64, No.5, 1 September 1988 TABLE 1. Comparison of thicknesses determined by experiments (dd')
and from MBE growth parameters (d,,).
Sample ddf (pm) dh (pm)
86087 1.15 I
86089 1.06 J
86090 1.90 2
R6093 3.22 3
III the dark, we also have a linear variation of 2DEG
concentration with negative substrate bias, which can be ex
plained by a simple capacitor model with dielectric thickness
of the order of 500 tim, corresponding to the thickness db
+ d,. Under illumination, the variation of 2DEG concen
tration can also be explained by a simple capacitor model
with a very thin dielectric layer of thickness deff, which is
only a little larger than db and two to three orders smaner
than db + ds' Some data ofiHuminated samples are shown in
Table I, in which db were determined by MBE growth pa
rameters and det!· were calculated from the n vs Vg relation.
The results strongly suggest that the model is satisfactory.
Namely, if the negative bias is applied during continuous
illumination, most of the bias voltage is dropped across the
buffer layer, giving rise to 11 significantly enhanced depletion
effect on conducting channel.
After turning off iHumination, the resistivities of both
layers are iarge. The negative sheet charge Q between the
buffer layer and substrate is "isolated" at the interface,
/lIG .. /I.
("l
(b)
(C) \1 , ,
! ~ , , buffer 51 GaAs
substrate
[]
-lOOOV
;/V'~f!J! hV
~ +
-2V
FiG. 10. Energy-band diagrams of the heterostructure under various condi
tions of experiment: (a) in the absence of both illumination and substrate
biasing, (b) with application ofa large negative substrate bias (e.g., -1000
V for illustrative purpose) in the dark, and (c) combined influence of small
negative substrate bias (e.g., -2 V) and illumination with light (0.95 eV}.
Jiang etal. 2493
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:32meanwhile the electric field Eb, and hence the channel resis
tivity, remain nearly unchanged. After turning off both illu
mination and substrate biasing, the sheet charge Q and elec
tric field Eb disappear slowly, as shown in Fig. 8.
The energy-band diagrams depicting the above explana
tion are shown in Fig. 10. Figure lO(a) shows the situation
in the absence of external influences, Figure lO(b) refers to
the situation with negative substrate biasing in the dark,
where a very large voltage is required for the channel deple
tion. If the negative substrate bias is applied under illumina
tion, however, the energy-band diagram is that shown in Fig.
We c). Most ofthe applied bias drops across the buffer layer
and channel depletion occurs with rather small negative
bias.
V. CONCLUSIONS
In modulation-doped AIGaAs/GaAs heterostructures,
the effect of the substrate on the conducting channel has
been studied in detail. At low temperatures, the PPC effect is
observed with light (photon energies between 0.8 and 1.1
eV) and its magnitude depends on the connection of the
substrate contact. Application of a bias between the sub
strate and the 2DEG channel has a strong effect on channel
conduction under illumination, The effect is two to three
orders of magnitude stronger than that in the dark. The con
ducting channel can be totally depleted with a relatively
small negative bias, and that depletion persists after turning
2494 J. Appl. Phys., Vol. 64, No.5, i September 1988 off the illumination. These effects can be explained by a dou
ble-layer model of GaAs: a very thin buffer layer upon a
thick 31 substrate. Under illumination, the resistivity of the
S1 substrate is small compared with that of the buffer layer,
so that most of the negative bias drops across the buffer lay
er. The "field effect" of negative biasing is thus greatly en
hanced by this much reduced effective thickness bearing the
negative bias.
ACKNOWLEDGMENTS
The authors would like to thank J. Zhou and J. L. Gao
for the loan of equipment, M. Y. Kong for support in prep
aration ofMBE grown wafers, and C. Van Degrift for help in
the preparation of this manuscript. This work was supported
by the National Natural Science ·Foundation of China,
'H. L. Stormer, A. C. Gossard, and W. Wiegmann, App!. Phys. Lett. 39,
493 (198l).
2M. I. Nathan, Solid-State Electron. 29, 167 (1986).
3M. Q. Dong, W. K. Gc, P. H. Jiang, D. Z. Sun, and Z. G. Cheng, Chin. J.
Semicond. 9, 99 (l988).
4A. Kastalsky and J. C. M. Hwang, Apr). Phys, Lett. 44, 333 (1984).
5Z. G. Chen, J. B. Liang, D. Z. Sun, y, H. Huang, and M. Y. Kong, Chin. 1.
Semicond. 5, 694 (1984).
'S, Luryi and A. Kastalsky. App\. Phys. Lett. 45, 164 (1984 J.
7E. F. Schubert, K. Ploog, H. Dambkes, and K. Hcime, AppL Phys. A 33,
63 (1984),
Jiang etal. 2494
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138.251.14.35 On: Thu, 18 Dec 2014 06:16:32 |
1.584501.pdf | The coherence factors of excimer laser radiation in projection lithography
K. A. Valiev, L. V. Velikov, G. S. Volkov, and D. Yu. Zaroslov
Citation: Journal of Vacuum Science & Technology B 7, 1616 (1989); doi: 10.1116/1.584501
View online: http://dx.doi.org/10.1116/1.584501
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/7/6?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 134.245.224.26 On: Thu, 25 Dec 2014 00:35:17The coherence factors of excimer laser radiation in projection lithography*
K. A. Valiev, L. V. Velikov, G. S. Volkov, and D. Yu, Zaroslov
Institute of Physics and Technology, Academy of Sciences of the USSR, Moscow, Krasiko1!st., 25-a
(Received 1 June 1989; accepted 24 July 1989)
The spatial coherence of the excimer laser radiation seriously affects the quality of the images
being reproduced by diffraction limited optics in photolithography. It is shown that the coherence
parameters of excimer laser radiation exceed the necessary level in 102_103 times. To decrease the
coherence down to the optimal level a fly's eye element is used. The concept of Kirchhoff integrals
has been applied to calculate the mutual intensity function transformation by the illuminator of
the projection system equipped with fly's eye element.
I. INTRODUCTION
The coherence properties oflight sources used in projection
lithographic systems strongly affect the photomask image
quality reproduced on semiconductor wafer. To find out this
dependence it is necessary to provide careful study of coher
ence properties of different sources and to work out methods
for the primary source coherence variation. The fundamen
tal principles of light coherence are stated in Refs. 1-7. It
follows from the theory that a light wave illuminating an
object (photomask), as well as reconstructed image, always
have a certain degree of coherence, including the case of
almost incoherent (fj correlated) source. Coherence proper
ties of laser sources are widely varied. The degree of coher
ence of excimer lasers used as pulsed UV sources for projec
tion photolithography, is relatively small. However, the
application of these lasers for projection lithography needs
to have their coherence reduced by 2 orders of magnitude.
The light coherence decrease is equivalent to its divergence
increase; it may be done by beam scanning in the limits of the
numerical aperture of the optical system 7 or by fly's eye ele
ment application. 8
Current work deals with: (1) parameters being used for
the description of the light coherency; (2) experimental
measurements of the coherence of the discharge pumped ex
cimer laser radiation; (3) variation of the light coherence by
application of the intracavity slit apertures and fly's eye ele
ment; (4) computer simulation of coherence variation for
the light transformed by the fly's eye element; (5) demon
stration of image pattern quality dependence on the degree
of coherence of the exposure radiation.
It THE PARAMETERS BEING USED FOR THE LIGHT
COHERENCE DESCRIPTION
Let us consider an arbitrary centered optical system
which tranforms the traveling light wave front. The statisti
cal properties (coherence) of the light wave are transformed
too. The most complete information about light wave coher
ence properties is contained in the transverse correlation
function:
(E(r,t)E(r + s,t)*) B t ( s) = ---'---'--'----'---'----'-::----,-,-,-
( IE(r,t) 12) < IE(r + s,t) 12») I/~
r(r,r + s,t,t)
( < 1 E (r, t) 12) ( i E (r + s,t) 12) ) 1/2 ' (1)
*Published without authors' corrections, where E is the electric field of the light wave, r is a two
d~mensional radius vector which is orthogonal to the optical
axis of the system, s is a spatial interval, r = (EE*)-the
mutual intensity function, ( > means the temporal averag
ing. We define the radium r c of transverse coherence (corre
lation radius) by the following expressions:
(2)
Figure 1 presents the optics of projection lithography sys
tem; S, the light source; C, the condenser; M, the mask (its
plane coincides with the plane of condenser) 11; 0, the plane
of the entrance pupil of the lense; W, the plane of mask image
which coincides with the surface of the resist film 011 the
wafer.
The light wave is transformed by lense systems in such a
way that for two conjugate planes M and W
rc( W) = mrc(M), (3)
where m is a magnification. Usually the magnification of the
mask image is equal to m = 1:10 or 1:5.
Equality (3) is the special case of more general statement:
for centered optical systems the variations of light beam ra
dius a(z) and transverse coherence radius rc (z) obey the
same law and their relation is an invariant6;
c= rc(z)la(z) = const. (4)
This invariant is called the coefficient of coherence.
When a point source is imaged by a lense with numerical
aperture NA the radius of the formed image is equal to
ra = O.61A I(NA). (5)
It is evident that ra is a radius oftransverse coherence on the
wafer plane when a 8-correlated source is positioned onto
s eM o w
FIG. I. The projection lithography system with Kohler type of illumination:
condenser C creates an image of the primary source S in the entrance pupil
of the \elise O.
1616 J. Vac. Sci. Techno!. B 7 (6), Nov/Dec 1989 0734-211X/89/061616-04$01.00 @ 1989 American Vacuum Society 1616
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the mask plane. If we choose r a as a natural scale of r" value,
then we can introduce a dimensionless coherence fa~tor 0'
1!O' = Yc (W)IY a =?O' = 0.6lA IrNa rc (W)]. (6)
Substitution of C = rc (z)la(z) into Eq, (6) gives
0' = (O.6U INA) [1!a( W)C], (7)
where a ( W) is the radius of light beam in the image plane
(chip's size). The formulas (4), (6), and (7) express
the relation between the coherency parameters
rc IX C, fc IX (T, C ex 0'.
The optimal value of coherence factor was determined
empirically in the interval of values O'ot>! :::;:0.3-0.7 (e.g., Ref.
7) . Corresponding to O'opt = 0.7 optimal values of coherency
parameters rc and C are (for A = 0.3 pm, NA = 0.3,
a( W) = 10 mm, m = 1: 10): rc ( W) = O.6U I(NAu) :::;:0.9
11m, 'c (M) = 9,0 ,am, CoPt = rc (W)la( W) = 9.0X 10-5.
Let us compare these optimal values with measured values
for excimer lasers radiation,
The measurements of correlation radius and length were
carried out with the modified Michelson interferometer. JO
The cavity of excimer laser was pumped by transverse dis
charge between two Al electrodes (X direction; interelec
trode gap = 20 mm, electrode length = 700 mm). The out
put laser beam cross section is lOX 20 mm2, pulse duration
= 20 ns, energy "" 100 mJ, In our experiments a spectral
unnarrowed laser radiation was used.
The measured transverse coherence function is anisotrop
ic (the value of Yc depends on the direction in laser beam
cross section): the values of rex = 150 pm and rcy "" 750 f.1m
differ in five times. Using Eqs. (4) and (6) one can find the
value of coherence coefficients: C,,=7.5XlO-', Cv
""",75xlO-3•
Cy may be increased by appropriate decreasing of intraca
vity aperture slit width (d). The obtained results are shown
on Fig. 2. Decreasing the slit width led to the narrowing of
radiation angle distribution and therefore, the increase of the
coherence coefficient. Narrowing the linewidth
(LU. = 0.005 nm) by insertion of a dispersive element
(Fabry-Perot etalon, for instance) inside the laser cavity
would result in an insignificant increase of the coherence
coefficient.
Thus transverse coherence of excimer laser radiation ex
ceeds the optimum level for projection lithography
Copt"'" 10-4 two (Cx ""'" 10-2) or three (Cy "'" 10-1) orders of
magnitude. Hence, the illuminator oflaser projection system
has to contain special elements for the transverse coherency
reduction. We suppose an array of short focusing lenses
(fly's eye) to be the most suitable in this case.8
III. COHERENCE TRANSFORMATION BY LASER
ILLUMINATOR EQUIPPED WITH FLY'S EYE
ELEMENT
The scheme of the investigated projection system is shown
on Fig. 3. Fly's eye (25x25 mm") consists of 25 square
microlenses (5 X 5 mm2 and! = 10 mm focal length of each
lenslet). We see that the correlation radii (fe, and r,y ) of the
radiation incident on fly's eye are less than lenslet size fj = 5
J. Vae. Sci. Technol. 8, Vol. 7, No. S, Nov/Dec 1989 1617
D. J ~
0.2 \
~,,-, ,,-,
~---"-------------0.1
0.0
d. mm
FIG. 2. The coherence coefficient of the excirner laser radiation vs the width
(d) of its intracavity apertures.
mm. Thus, in the fly's eye's focal plane a virtual source is
created in the form of the array of approximately mutually
incoherent "point" sources. Condenser C transfers the vir
tual source (an array of spots) into the lense entrance pupil.
The mask is positioned in the back focal plane of condenser.
Thus every arbitrary point of the mask is illuminated by the
light irradiated from all mutually incoherent points of vir
tual source, This determines the low degree of coherence in
the mask illumination, It may be said that the fly's eye ele
ment divides the wave front into mutually incoherent parts
and condenser provides summation of these parts on the
mask and image planes.
The coherence coefficient of the system was determined
by computer simulation, The mutual intensity function of
the primary radiation measured in Ref. 10 we approximate
as usual by Gaussian:
r(1"1,r2,z) =Ioexp{ -(Xj-xz)2 _ (YI-Y2)2}. (8)
2~x 2~y
The expression for the mutual intensity r(rl,r2,z) transfor
mation from z to z' plane,
FIG, 3. The Kohler-type illumination system equipped with the fly's eye
clement used for the projection printillg.
••••••••••••••••••••••• --. ••••• -.-•••••••••••••••• -••• -.-.-•••• ".-.-.-,-.-.-.-.- •• -••• -•• ~ .•••••• ' •••• ; ••••••••• ~ •••••••••••••••••••••• ' ••••• '~ •• ' ••••• ~.:.:.:.:.:.:.:.:- ................... ; •• -••• -••• -.-.-.-.-.".;. "." ••• "." ••• , •.•. n '.' ' .•.•.• , •••••• ,' ••
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f'(r;,r;,z)
= (IlZ)-2 f f dr1 dr2 f'(r1,r2,z)T(rl)T(r2)*
<0/ .v/
XexpUk [f(rl -r; )2 + (z _ Zf)2
-~ (r2 ~-r~)2 + -{z -Z')2 ]} (9)
was consequently applied for two intervals: fly's eye con
denser, condenser mask. The first interval included the fly's
eye phase transformation T(r), the second one included the
condenser lense phase transformation. d is the integration
surface of the corresponding aperture.
If the fly's eye consists of (2N + 1) 2 square lenses of 8 X 8
size and off, focal length one can find the phase tranforma
tion function:
{al C
5.0.10-4
4.5.10- 4
.3.0 10-4
1.5.10- 4
10 -5 ----·--T
0.0 0.1
Vy, %
80
fbI 0.0 0. 1 0.2 0.2 0 . .3 0.4
0 . .3 0.4 0.5
FIG. 4.(a} The coherence coefficient in the mask plane as a function of
coherence coefficient C", of the primary radiation. Curves (1) and (2)
show anisotropic correlation function. Curve (3) shows an isotropic
correlation function. Corresponding a values and its optimal interval
are shown too. (b) Inhomogeneity V = (1m .. -1m," )/(lmax + 1m'n)
X 100% of photomask illumination as a function of coherence coefficient of
incident beam. Curves 1 and 2 present anisotropic [ (Cx)o
= 1.2 10--2, (Cy)o -variable J and isotropic [( Cx)o
= (Cy)o -variable 1 correlation functions accordingly.
J. Vac. Sci. Techno!. e, Vol. 7, No.6, Nov/Dec 1989 1618
NN
T(r) = LL rect{(x/28) -(1I2)}
l,n~ N
Xrect{(yI20) -(n/2)}exp{ -jk [(x -18)2
+ (y-n8)2]1(2/,.)}, (10)
{ 1,
rect(X) = 0, (11) ixl<0.5
I I . ,x >0.5
The phase transformation function of the condenser lense is
T(r) = exp{ -jkr2/(2Fc)}. (12)
The focal length of the condenser lense Fc = 200 mm,
ZI = 330 mm, 22 = 200 mm.
The results of computer simulation are shown on Fig. 4.
Coherence coefficient CyO was chosen to be a process vari
able (its value depends on the width d of intracavity slit
apertures). The main result is that the fly's eye element re
duces the coherence coefficient close to the optimal value
[Fig. 4(a)]. This is caused by superposition of mutually
incoherent light beams on the photomask plane. We see that
the interval of optimal values O"opt = 0.3-0.7 corresponds to
the initial values of the laser radiation coherence in isotropic
case CxO = CyO = 0.1-0.2. In the case of anisotropic correla
tion function we have to choose the value of the width of slits
in the x direction, if we want to be in the interval of optimal 0"
(a)
(b)
FIG. 5. Optical photographies of microimages, produced on the positive
resist film under XeCI excimer laser projection exposure. Ca) The square,
two-dimensional fly's eye, containing 5 X 5 = 25 microlenses was uniformly
illuminated by laser beam. (Cx)" = 0.02, (Cv)o = 0.3. (b) The linear, one
dimensional fly's eye. containing only 5 microlcnscs positioned along Y
axis, was uniformly illuminated by XeCl-laser beam. (C, 10 = 0.1, (C,.)"
= 0.3. The coherence of the primary radiation along x direction is the same
in cases (a) and (b). The increase in ( C, ) 0 (b) is explained by the decreas
ing of the light beam diameter along x direction in the case (b).
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values. The high quality microimages were obtained in this
case [Fig. 5(a)].
The main restriction on the initial increasing of the beam
coherency is connected with the growth of intensity inhomo
geneity on the mask and wafer planes. The last resulted from
the interference of partially coherent beams formed by dif
ferent elements of the fly's eye system. As one can see from
the computer simulation results presented in Fig. 4(b), only
the light beams which have the strongly anisotropic correla
tion functions may be successfully used in the illuminators,
containing fiy's eye element. In this case [curve 1 in Fig.
4(b)] we have a very low level ofinhomogeneity ofil1umina~
tion in the mask plane.
It is evident that the intensity inhomogeneity as well as
light coherency on the photomask plane will be maximum if
only mutually coherent beams are superimposed. Experi
mentally it may be produced by linear, one-dimensional fly's
eye. The shape of microimage distortions in this case is
shown on Fig. 5(b).
IV. CONCLUSIONS
( 1 ) The coherence parameters of excimer laser beam are
102_103 higher than the optimal values. The correlation
function is strongly anisotropic.
J. Vac. Sci. Technol. S, Vol. 7, No.6, Nov/Dec 1989 1619
(2) The simulations and experimental measurements
show that an illumination system equipped with fly's eye
element can reduce the values of coherence coefficients
down to optimal level providing an essential microimage
quality improvement. For this purpose laser beams with
strongly anisotropic correlation function would be used. All
image distortions like speckles and double edges are elimin~
ated in this case.
'M. Born and E. Wolf, Principles of Optics (Pergamon, N.Y., 1964).
2E. W. Marchand and E. Wolf, J. Opt. Soc. Amer. 64,1219 (1974).
'E. Wolf, J. Opt. Soc. Amer. 68, 1597 (1978).
4A. T. Friberg, SPIEProc.194, 55 (1974).
'J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, N.Y.,
1968).
"S. A. Akhmanov, Yu. E. Dyakov. and A. S. Chirkin, Introduction to Sta
tistical Radiophysics IJnd Optics (Nauka. Moskva, 1981).
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State Techno!. 115 (1980).
Mil. N. Kotletzov, Microimages. Reproduction and Control (Mashinos
troenie, Leningrad, 1985).
9G. S. Landsberg, Optics (Nauka, Moskva, 1976).
10K. A. Valiev, L. V. Velikov, G. S. Volkov, and D. Yu. Zaroslov, Soviet
Quant. Electron. 14, 1266 (1987).
"If plane Mis aribitrarily moved from plane C planes (S,O) and planes
(M, W) should remain conjugate.
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1.2811617.pdf | Ballistic Electron Transport Through a Narrow Channel is Quantized
Anil Khurana
Citation: Physics Today 41, 11, 21 (1988); doi: 10.1063/1.2811617
View online: http://dx.doi.org/10.1063/1.2811617
View Table of Contents: http://physicstoday.scitation.org/toc/pto/41/11
Published by the American Institute of PhysicsSEARCH (j DISCOVERY
James Cronin and his high-energy-
physics collaborators from the Uni-
versities of Chicago and Michigan are
in the process of surrounding the
Fly's Eye detector with an extensive-
air-shower array of unprecedented
capability, covering a quarter of a
square kilometer and studded with
underground muon detectors. Half of
its 1089 scintillators should be oper-
ational before the end of next year.
—BERTRAM SCHWARZSCHILD
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7. W. Ochs, L. Stodolsky, Phys. Rev. Lett.
33, 247 (1986).
8. M. Drees, F. Halzen, Phys. Rev. Lett. 61,
275 (1988).
BALLISTIC ELECTRON TRANSPORT THROUGH
A NARROW CHANNEL IS QUANTIZED
The electrical conductance of a short
and narrow conducting channel is
quantized in units of 2e2/h, a team of
experimenters from the Netherlands
recently reported. The effect was
independently observed by experi-
menters at Cambridge University at
much the same time as its discovery
by the Dutch group. In the new effect
the conductance of the channel,
which connects two-dimensional re-
servoirs of electrons, remains con-
stant at an integral multiple of 2e2/h
for a range of channel widths but
jumps sharply to the next higher
integral multiple of 2e'2/h at some
critical values of the width.
The step-like behavior of the con-
ductance of a narrow conducting
channel (see the figure on the right),
even though it arises in the absence of
a magnetic field, is reminiscent of the
quantum Hall effect, in which the
Hall conductance of a two-dimension-
al electron gas in the presence of a
strong magnetic field shows steps at
successively higher multiples of e'2/h
when the magnetic field is decreased.
But unlike in the systems that show
the quantum Hall effect, where the
motion of electrons is diffusive, the
electron motion is ballistic in the
systems that show the new effect.
Ballistic transport
In systems, such as GaAs-AlGaAs
heterojunctions, used in the study of
the quantum Hall effect, electrons are
scattered repeatedly by impurities
and imperfections; the electron mo-
tion from one end of the sample to the
other is therefore diffusive. But in
the high-mobility GaAs-AlGaAs sam-
ples the Dutch and Cambridge experi-
menters used, the elastic mean free
path, or the average distance betweenConductance of a
narrow channel
connecting two rwo-
dimensional reservoirs
of electrons increases
in sreps of 2e2/h when
rhe width of the
channel increases. The
more negative rhe
gate volrage is, the
narrower rhe channel
is. (Adopted from
reference 1.)
-1.6 -1.4
GATE VOLTAGE (V)
successive scatterings by impurities
and imperfections, is much larger
than the length of the conducting
channel connecting the two two-di-
mensional regions that act as electron
reservoirs. This so-called ballistic
transport of electrons in small, submi-
cron-sized systems has been of great
interest in the past few years because
of the new insights it provides into the
mechanisms of electron transport in
solids. Advances in molecular-beam
epitaxy, which is used for the fabrica-
tion of high-quality heterostructures,
have given further impetus to these
studies. The experimenters observed
the quantization of the conductance
in a high-mobility GaAs-AlGaAs
structure when the width of the
connecting channel was comparable
to the Fermi wavelength of the elec-
trons in the reservoirs, or, in terms of
energy levels, when the temperature
was smaller than the separation be-
tween successive energy levels of the
electron system. (The Fermi wave-
length is the de Broglie wavelength of
the electron in the highest occupied
energy level in the electron reservoir.)- 1.2 -1.0
The experiments were done at a
temperature of a few tenths of a
kelvin. Both groups have observed
well-defined plateaus up to about 2 K.
The prefactor 2 in the new quan-
tum of conductance arises from spin
degeneracy of electron states. When
this degeneracy is lifted by applica-
tion of a magnetic field parallel to the
two-dimensional electron gas, the
Cambridge group reports, new pla-
teaus appear between those already
found in the absence of the magnetic
field. The steps in the conductance
then appear at values that are inte-
gral multiples of e2/h. The Cam-
bridge group has observed plateaus at
conductance values up to (30)e2/h.
Point-contact spectroscopy
The Dutch and Cambridge groups had
very different motivations for study-
ing the transport properties of a
narrow conducting channel. Michael
Pepper of the Cambridge group told
us that the group was interested in
studying the transition between diffu-
sive and ballistic regimes of electron
transport in one and two dimensions
PHYSICS TODAY NOVEMBER, 1988 21as the channel width was changed
and impurities and imperfections in
the samples were reduced. Pepper
also pointed out theoretical work by
Yoseph Imry (Weizmann Institute,
Israel), which had suggested the possi-
bility of some structure, or feature, of
magnitude e2/h appearing in the con-
ductance as the transport became
more ballistic. Henk van Houten
(Philips Research Laboratories, Eind-
hoven, The Netherlands) told us that
the Dutch group, by contrast, discov-
ered the new quantization somewhat
unexpectedly in the course of its
attempts to study point-contact spec-
troscopy in two dimensions.
Point-contact spectroscopy, which
in its simplest form is a study of the
current-voltage characteristics of a
small—almost point-like—conductor
in contact with a metal or a semicon-
ductor, is an important experimental
technique for studying scattering of
electrons in solids. Of particular in-
terest to the Dutch experimenters
was an extension of the simplest
technique that uses two point con-
tacts. By application of a transverse
magnetic field the beam of electrons
injected into the metal or semiconduc-
tor from the first point-like contact is
focussed at the other contact, which is
at a distance shorter than the elastic
mean free path. Because the shape of
electron trajectories in a magnetic
field is related to the shape of the
Fermi surface, this form of point-
contact spectroscopy, called trans-
verse electron focusing, has proved to
be extremely effective in the study of
Fermi surfaces in solids.
It is difficult to insert external
point contacts into a two-dimensional
system. The experimenters therefore
decided to create such a contact "in-
ternally." They deposited a gate on
the surface of the heterostructure,
which is about 500 A above the two-
dimensional electron gas (see the
figure on page 23). When a negative
voltage was applied to this gate, the
two-dimensional electron gas under it
was depleted of free electrons. The
gate consisted of two narrow collinear
strips separated by a gap, so that
application of a negative voltage to it
split the two-dimensional electron gas
into two parts that were in electrical
contact only through the narrow
channel under the gap between the
gate electrodes. The width of this
channel could be varied, even though
the separatio n between the gate elec-
trodes was fixed, by increasing (in
magnitude) the voltage applied to the
gate. This method for making narrow
channels in heterostructures was de-
veloped by the Cambridge group in
1986; the Cambridge group has alsoused this method for studying elec-
tron transport in one dimension.
The Dutch team studied the trans-
port properties of one point contact,
partly to test their ideas about fabri-
catin g such contacts in two dimen-
sions, before moving on to their goal of
electron focusing using two point
contacts. They were surprised to find
that the conductance of the contact
showed step-like behavior indicatin g
quantization as the channel width was
increased (see the figure on page 21).
Besides van Houten, the Dutch
team consisted of Bart J. van Wees,
Leo P. Kouwenhoven and Dick van
der Marel (all from Delft University
of Technology), Carlo W. J. Been-
akker and John G. Williamson (Phil-
ips Research Laboratories, Eindho-
ven) and C. Thomas Foxon (Philips
Research Laboratories, Redhill, UK).)
The Cambridge University group con-
sisted of Pepper, David A. Wharam,
Trevor J. Thornton, Richard New-
bury, Haroon Ahmed, John E. F.
Frost, David G. Hasko, David C. Pea-
cock (also at General Electric of UK),
David A. Ritchie and Geb A. C. Jones.
The Dutch team has studied the
propertie s of two point contacts in two
dimensions.3 When the two-dimen-
sional sample is placed in a magnetic
field normal to the electron gas, the
voltage at the contact used as a
collector shows peaks at values of the
magnetic field for which the distance
between the two contacts is an inte-
gral multiple of the diamete r of the
classical cyclotron orbit. This effect,
in which the motion of electrons is
similar to that of ions in a mass
spectrometer, is striking evidence for
the ballistic transport of electrons in
the two-dimensional sample. At very
high values of the magnetic field—
above 1.5 tesla—the peaks are de-
stroyed and plateaus characteristic of
the quantization of the Hall conduc-
tance appear. Van Wees told us that,
unlik e the behavior expected for the
regular quantum Hall effect, the
quantized value of the Hall conduc-
tance in these experiments is deter-
mined by the quantized values of the
conductance of the narrow channel
that is used as an external probe.
The usual laws for the addition of
resistances do not apply to the quan-
tized resistance of narrow channels.
The Cambridge group reports that
when one or more such channels are
connected in series, the resistanc e of
the assembly is equal to the highest
resistance in the series, not to the sum
of the resistances connected in series.4
An electron waveguide
The new discoveries raise a fundamen-
tal question: Why should the conduc-tance of a narrow conducting channel,
longer than it is wide, connecting two
high-quality two-dimensional reser-
voirs of electrons increase discontinu-
ously in steps of 2e2/h when the
channel width is increased? The elec-
tron reservoirs are free of impurities
and imperfections, so that the proba-
bility that electrons will pass through
the channel without being scattered is
very high; and the temperature is low
enough so that electrons are also not
significantly scattered by phonons.
Should not the conductance then be
given by some expression from classi-
cal physics that counts the number of
electrons passing through the channel
per unit time and per unit difference
in the applied voltage? But in that
case the conductance should increase
linearly with the width of the channel!
Indeed, the system might show such
behavior if the width of the channel
were much larger than the Fermi
wavelength, or, more precisely, if the
temperature were higher than the
difference between successive energy
levels in the electron system. In the
experiment, however, the channel
width—a few tenths of a microns—is
of the same order of magnitude as the
Fermi wavelength. (In two dimen-
sions, the Fermi wavelength varies
inversely as the square root of the
electron density, and the electron
density in heterostructure devices is
typically on the order of 1015-1016
electrons/m2.) The quantum mechan-
ical wave nature of electrons is there-
fore essential in understanding the
observed quantization.
According to Douglas Stone (Yale
university), the best analogy for un-
derstanding quantum mechanical
ballistic transport through a narrow
channel connecting two large reser-
voirs is that of a waveguide. A
waveguide transmits only radiation
whose frequency is higher than a
specific cutoff frequency. In a rectan-
gular waveguide, for example, the
cutoff frequency for a given mode is
determined by equating the wave-
number of the radiation in free space
with the mode's transverse wavenum-
ber. The idea of the cutoff frequency
of a waveguide helps us to understand
the quantization because increasing
the width of the channel may be
looked upon as introducing, at some
critica l values of the width, new
propagating modes in the channel.
The quantum mechanical formula
for conductance relevant to the exper-
iment reads
G = (2e2M)TrTTr
where T is the transmission matrix
for the channel. (Again, the prefactor
22 PHYSICS TODAY NOVEMBER 1968SEARCH 0 DISCOVERY
Cross section of a GaAs (yellow) ond AIGoAs (orange) hererosrrucrure
used in rhe experimenrs on quantized conductance. The two-
dimensional electron gas, here shown as occupying a region of finite
widrh (black), is or the interface between rhe GoAs ond AIGaAs layers
Two gold electrodes (blue) that act as gates are deposited on the
AIGaAs layer using electron-beam lithography. A narrow conducting
channel is formed when a negative voltage is applied to rhe gates
depleting free elecrrons or carriers from rhe regions enclosed by rhe
dashed lines.
2 in the formula arises from the spin
degeneracy of the electron gas.) This
formula is a variant of one that Rolf
Landauer (IBM Yorktown Heights)
wrote down more than 20 years ago.
There has been a lot of controversy
since the beginning of this decade
concerning the correct mathematical
expression that describes the result of
a measurement of the resistance of a
small quantum mechanical system.
The above form of the Landauer
formula applies when the sample
whose resistance is to be measured is
in contact with large reservoirs that in
turn are connected to the external
leads.
The quantization of the conduc-
tance observed by the Dutch and
Cambridge experimenters follows im-
mediately from the above formula if
one assumes that in ballistic trans-
port each mode is transmitted
through the channel without being
reflected or scattered into other
modes—that is, if T only has diag-
onal elements, so that there is no
mixing of modes, and if the diagonal
elements are unity for modes allowe d
by the channel width and zero for
other modes. Arguments such as this
had been discussed by Imry, and the
two experimental groups used it in
their papers to explain their observa-
tion of the quantized conductance.
But this simple argument does notdescribe the real experimental situa-
tion, in which two wide regions are
connected by a narrow channel. The
above simple explanation therefore
leaves unanswered questions such as:
Why is the transition from one step to
the next so sharp, and what does the
slope between steps depend on? How
wide are the steps? How sensitive are
the steps to changes in temperature
and sample quality?
Stone and Aaron Szafer (Yale Uni-
versity) have modeled the experimen-
tal situation as two wide waveguides
(for the reservoirs) connected by a
narrow waveguide and have done
detailed calculations for the transmis-
sion probabilities of various modes.
Their analysis predicts that the con-
ductance steps may develop some
structure at low temperatures due to
resonance scattering. Such structure
has also been discussed by George
Kirczenow (Simon Fraser University).
Both the experimental groups have
reported that at low temperatures the
conductance steps in some of their
samples develop features that depend
on the channel geometry. L. I. Glaz-
man, G. B. Lesovick, D. E. Khmelnits-
kii, R. E. Shekhter (Institute of Solid
State Physics of the Academy of
Sciences of the USSR) have presented
an analytical solution that shows the
quantized behavior of the conduc-
tance for an experimentally realisticsituation.5 Horst Stormer (AT&T
Bell Labs) thinks, however , that more
theoretical and experimental work is
needed to decide whether a true point
contact is sufficient or whether a
channel of finite length is necessary
for the quantization.
If the quantization of the conduc-
tance of a point contact in two dimen-
sions could be explained so readily,
why was the discovery somewhat
accidental? Why was the quantiza-
tion not predicted theoretically, even
though hints of the possibility of such
an effect did appear in theoretical
papers? The theoretical hints, includ-
ing those that appeared in work on
the scanning tunneling microscope,
were not pursued very enthusiastical-
ly, Landauer said, because no one
believed that the conditions necessary
to observe the effect could be realized
in an experimental system.
Unlike the Hall conductance in the
quantum Hall effect, which has been
found to be quantized to an accuracy
of about 1 part in 107, the conductance
of a narrow channel is expected to be
quantized to an accuracy no better
than about 1 part in 103. The new
quantization is also expected not to be
as robust to variations in temperature
and quality of the samples as the
quantization in the Hall effect is. It is
therefore unlikely that the new quan-
tization effect will be readily used as a
resistance standard. Meanwhile, the
significance of the new effect for
developing new submicron electronic
devices is being investigated. The low
temperatures at which the effect oc-
curs make it unlikely that any signifi-
cant application will be developed
soon. But there are excited murmurs
among experts that the effect might
someda y make possible devices that
exploit, in Stormer's words, diffrac-
tion effects arising from the wave
nature of electrons.—ANIL KHURANA
References
1. B. J. van Wees, H. van Houten, C. W. J.
Beenakker, J. G. Williamson, L. P.
Kouwenhoven, D. van der Marel, C. T.
Foxon, Phys. Rev. Lett. 60, 848 (1988).
2. D. A. Wharam, T. J. Thornton, R. New-
bury, M. Pepper, H. Ahmed, J. E. F.
Frost, D. G. Hasko, D. C. Peacock, D. A.
Ritchie, G. A. C. Jones, J. Phys. C 21,
L209 (1988).
3. H. van Houten, B. J. van Wees, J. E.
Mooij, C. W. J. Beenakker, J. G. Wil-
liamson, C. T. Foxon, Europhys. Lett. 5,
721 (1988).
4. D. A. Wharam, M. Pepper, H. Ahmed,
J. E. F. Frost, D. G. Hasko, D. C. Pea-
cock, D. A. Ritchie, G. A. C. Jones, J.
Phys. C. 21, L891 (1988).
5. L. I. Glazman, G. B. Lesovick, D. E.
Khmelnitskii, R. E. Shekhter, Pis'ma
Zh. Eksp. Teor. Fiz. 48, 218 (1988). •
PHYSICS TODAY NOVEMBER 1988 23 |
1.2811199.pdf | Profiles in Publishing Poductivity
Paula E. Stephan Sharon G. Levin
Citation: Physics Today 42, 10, 151 (1989); doi: 10.1063/1.2811199
View online: http://dx.doi.org/10.1063/1.2811199
View Table of Contents: http://physicstoday.scitation.org/toc/pto/42/10
Published by the American Institute of PhysicsLETTERS
continued from page 15
DRESDEN REPLIES: Both Akira Isihara
and R- Byron Bird observe that al-
though Hendrik Kramers wrote only
one paper on polymer statistics, that
paper had an enormous and lasting
influence. This observation is in com-
plete harmony with the ideas ex-
pressed in my paper: Kramers's con-
tributions to statistical mechanics,
few as they are, are gems full of
technical mathematical innovations,
combined in a most original way with
deep physical insight.
I am most thankful to Isihara and
Bird for calling attention to yet an-
other one of Kramers's seminal con-
tributions, which like many others
has not always received the recogni-
tion it deserves. This particular pa-
per was not mentioned in the original
article for lack of space, so it is
gratifying that these letters give an
idea of Kramers's contribution in this
area, especially his unusual and per-
haps unexpected use of Riemannian
geometry.
The thesis by R. M. F. Houtappel to
which D. ter Haar calls attention
was clearly strongly influenced by
Kramers. The elegant mathematics,
the ingenious way in which explicit
group theory is avoided in a cleve r
adaptation of Bruria Kaufman's
method—these are as characteristic
of Kramers as his signature. Thus
Kramers was certainly aware of and
explicitly conversant with the devel-
opments in the Ising model that
followed the celebrated Kramers-
Wannier paper. In that sense my
statement that Kramers never
worked on the Ising model after
World War II is too strong. He clearly
stayed informed and thought about it.
Still, I believe that the general idea I
expressed is probably correct. Com-
paring Kramers's intense, deep preoc-
cupation with the Ising model during
the war years with his subsequent
more casual involvement, almost by
proxy, indicates to me that his own
personal involvement declined sharp-
ly if not precipitously. Of course
Kramers, even if only casually inter-
ested, could make contributions of
such depth and brilliance that any
totally committed investigator would
have been pleased and proud to have
made them.
I believe that all the correspondents
and I agree that Kramers was an
unsurpassed master in using and
inventing mathematical procedures
that were miraculously suited to the
elucidation of physical problems in
statistical mechanics.
MAX DRESDEN
Stanford Linear Accelerator Center
8/89 Stanford, CaliforniaProfiles in
Publishing Productivity
We recently completed a study of
publishing patterns of PhD physicists
trained and employed in the United
States.' We were particularly inter-
ested in the relationship between
publishing activity and age. Because
the average age of physicists, and
scientists in general, has increased
dramatically in the past 10-15 years,
a concern of US science policy makers
is whether this older group is as
productive as a younger group was a
decade or two earlier. Given the
inherent difficulty of measuring re-
search productivity, and given that
there is some evidenc e that publish-
ing is a reasonable measure of produc-
tivity,2 our study focused on the rela-
tionship between publishing activity
and age. Specifically, we counted the
number of journal articles authored
in a two-year period. Adjustments
were also made to this count for the
number of coauthors as well as for the
quality of the journal in which each
article was published, where quality
was measured by the impact the
journal has on the science literature
as reflected by citation practices.3
Physicists in the 1973, 1975, 1977 and
1979 Survey of Doctorate Recipients,
administered biennially by the Na-
tional Research Council, were includ-
ed in the study.4 Information on their
publishing patterns was taken from
the Science Citation Index with the
cooperation of the Institute for Scien-
tific Information.
Past work by Stephen Cole5 and by
Alan E. Bayer and Jeffrey E. Dutton6
on age-publishing profiles of physi-
cists suggests that article production
increases until early middle age and
declines thereafter. Cole's sample
was restricted to physicists employed
in doctorate-granting departments in
the late 1960s, while Bayer and Dut-
ton's sample consisted of physicists
employed at colleges and universities
during the 1972-73 academic year. A
strength of the SDR data base used in
our study is that it is drawn from a
later period and includes scientists in
five employment sectors: graduate
academic (universities offering a PhD
in physics), nongraduate academic,
Federally funded research and devel-
opment centers, government, and
business and industry.
Our results for physicists in aca-
demic employment are somewhat dif-
ferent from those of Cole or Bayer and
Dutton. In particular, when we
grouped our sample by five-year age
intervals, we found that for physicists
in graduate departments the produc-
tivity of the 35-39-year-old group isClean
cheap
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PHYSICS TODAY OCTOBER 1989151always significantly less than that of
their younger colleagues, and output
does not rebound to the pre-age-35
level for any age group. On the other
hand, publishing activity does not
continuously decline with age, al-
though it does decline in the last years
of the career regardless of the way
articles are measured.
For physicists in nongraduate phys-
ics departments, the story is different.
Although output is highest for the
youngest group, until age 45-49 out-put never differs at the 5% level of
significanc e between the youngest
and older groups. Those 45-54 years
old, on the other hand, produce signif-
icantly less than the youngest of their
colleagues, while the 55-59-year-olds
publish more, perhaps because pro-
ductive physicists are lured into the
nongraduate sector from the graduate
sector toward the end of their careers,
or perhaps because less productive
scientists tend to retire earlier.
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152 PHYSICS TODAY OCTOBER 1989peak output is also produced by those
under 35; for the next ten years
output dramatically declines. It then
increases or stays fairly stabl e for the
next ten years, after which it again
declines. Government is the only
sector in which the peak productivity
occurs in the middle of the career, not
the beginning. In business and indus-
try, publishing activity declines until
age 49, then increases for ten years
before declining again. This age pat-
tern for business and industry is not
inconsistent with what Donald C.
Pelz and Frank M. Andrews7 found in
the 1960s.
Our results also suggest that the
age-publishing profiles depend upon
how one measures publishing activ-
ity. The profiles are generally steep-
est when the article count is adjusted
for quality, suggesting that the young
are more likely to publish in presti-
gious journals. On the other hand, as
physicists age, the straight count and
the count adjusted for coauthorship
converge, showing that a dispropor-
tionate amount of early output is
coauthored. This result holds in all
sectors and is contrary to the view
that older physicists, through their
administrative roles, "ride piggy-
back" on the shoulders of younger
physicists.
The age-publishing profiles dis-
cussed thus far are drawn from cross-
sectional data. Since different age
groups are observed at the same time
in a cross-sectional analysis , the age
effects found may be contaminated by
what are called cohort or genera-
tional effects. If, for example, physi-
cists in their sixties come from a
particularly weak cohort and physi-
cists their thirties from a particularly
strong cohort, we would infer aging
effects from a cross section even if
they did not exist.
There are several reasons to believe
cohort effects might be present. One
theory—more popular, we might add,
among social scientists than physical
scientists—is that certain cohorts
may be at a disadvantage because
their members were educated prior to
a major innovation in theory or ex-
perimental technique. If one sub-
scribes to a "latest educated are best
educated" philosophy, this would im-
ply that the decline in publishing
activity with age may be an artifact of
"vintage" and not a true aging effect.
On the other hand, the best vintage
need not always come from the latest
cohort, since science does not always
advance smoothly but may experi-
ence for a time what are eventually
regarded as "false turns."
Perhaps the most important rea-
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PHYSICS TODAY OCTOBER 1989153research productivity, particularly as
manifested in article counts, is
strongly affected by characteristics of
the employing institution. In partic-
ular, there is strong evidence that
physicists employed in top PhD-
granting departments and Federally
funded R&D centers are more likely
to publish than their colleagues in
places where resources are scarcer
and the environment is less condu-cive to research.8 It is clear that not
all generations of physicists have had
equal access to the most productive
sector. Indeed, one need only look at
the pages of PHYSICS TODAY to see
how job opportunities for physicists
have changed over time. A cohort
particularly hurt was that of the late
1960s and early 1970s—the cohort
from which the "young" in our study
are drawn.
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AVS Show—Booth #315 Circle number 137 on Reader Service CardFinally, some have expressed con-
cern that the average ability of new
science PhDs has declined in recent
years as the best and brightes t in our
society have been draw n into the
lucrative professions of law, business
and medicine.9
Because our data allowed us to
observe physicists as they aged over a
six-year period, we were able to draw
inferences concerning the presence of
cohort effects and to see whether true
aging effects exist once we controlled
for these cohort effects. Using an
econometric technique that controls
for both cohort and aging effects, we
found evidence that except for parti-
cle physicists employed in PhD-grant-
ing departments, true aging effects
exist. Furthermore, when we held
the aging effects constant, we found
evidence that for the period of our
study the latest PhD cohorts were not
the most productive in any of the
subfields of physics we studied.
References
1. P. E. Stephan, S. G. Levin, "Demo-
graphic and Economic Determinants of
Scientific Productivity," Georgia State
U., Atlanta (1987).
2. R. Evenson, Y. Kislev, Agricultural Re-
search and Productivity, Yale U. P.,
New Haven (1975).
3. E. Garfield, ed., SCI Journal Citation
Reports, Institute for Scientific Infor-
mation, Philadelphia (1975).
4. National Research Council, Science, En-
gineering, and Humanities Doctorates
in the United States, 1979 Profile, Natl
Acad. Sci., Washington, D. C. (1980).
5. S. Cole, Am. Sociol. Rev. 84(4), 958
(1979).
6. A. E. Bayer, J. E. Dutton, J. Higher Ed.
48(3), 259 (1977).
7. D. C. Pelz, F. M. Andrews, Scientists in
Organizations, revised edition, U.
Michigan P., Ann Arbor (1976).
8. J. S. Long, Am. Sociol. Rev. 43, 889
(1978).
9. H. R. Bowen, J. Schuster, American
Professors: A National Resource Imper-
iled, Oxford U. P., New York (1986).
PAULA E. STEPHAN
Department of Economics
and Policy Research Program
Georgia State University
SHARON G. LEVIN
Department of Economics
2/89 University of Missouri, St. Louis
Dread Shortage in the
Nation's Breadbasket?
In the December 1987 issue (page 9),
George E. Pake writes: "Through its
extensive nationwide system of re-
search universities, centers of basic
research are ubiquitous in the vo.
154 PHYSICS TODAY OCTOBER 1989 |
1.340334.pdf | Field effects in semiconductor doubleinjection devices
R. Stawski and K. L. Ashley
Citation: Journal of Applied Physics 63, 5571 (1988); doi: 10.1063/1.340334
View online: http://dx.doi.org/10.1063/1.340334
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/63/11?ver=pdfcov
Published by the AIP Publishing
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23Field effects in semiconductor double .. lnjection devices
R. Stawski and K LAshley
Department of Electrical Engineering, Southern Methodist University, Dallas, Texas 75275
(Received 10 November 1987; accepted for publication 18 January 1988)
An analysis ofhigh~field effects in semiconductor double~injection devices is presented. Exact
and approximate numerical solutions are developed, which include the electric field
dependence of carrier mobilities and capture coefficients. The model assumes that the current
is entirely field driven and that charge neutrality applies. The current-voltage characteristics
are obtained in the square-law and threshold vohage regions. A comparison is made between
the present analysis and a previous, more approximate, analytical formulation which was
similarly based on a modification of the square law. The validity of approximations made in
the development of the models is discussed. The conditions, under which high-field effects
have a significant influence on the current-voltage characteristics, are determined.
I. INTRODUCTION
The study of semiconductor double-injection devices
provi.des valuable information on various electronic proper
ties of the device material. The modeling of the current-vol
tage characteristics of double-injection devices is of consid
erable interest for practical applications such as sensors and
high-voltage switches.
In double-injection devices electrons and holes are in
jected from the cathode and anode, respectively. into the
bulk of a high-resistivity semiconductor doped with deep
impurities. The properties of the impurities and the trans
port parameters of the bulk material influence the shape of
the current-voltage characteristics. The segment of the char
acteristic from the square law to the threshold is of particu
lar interest and has been studied extensively. Solutions for
this case have been presented either in analytical or numeri
cal form by Ashley,! Ashley and Milnes,2 Ashley, Bailey,
and Butler,3 Deuling,4 and Zwicker et al.,5 and more recent
ly by Migliorato, Margaritondo, and Perfetti, (, and Ashley
and Stawski. 7 The field dependence of mobilities and capture
coefficients has been included in solutions obtained by Wa
gener and Milnes,R Hurm, Hornung, and Manek,'! and Ash
ley and Stawski.7 An analytical formulation for the thresh
old voltage region that i.ncluded field-dependent parameters
was presented in Ref. 7. The approach was based on a modi
fication of the square law7 which accounted for the reduction
of the effective device length due to the penetration of a low
field region from the anode. It contained the following sim
plifying assumptions: (1) hole current is negligible and elec
tron current is constant and equal to the total current; (2)
hole density is constant and equal to the thermal density; (3)
electronic parameters are considered field independent in
the low-field region. The validity of the above assumptions
and the limitations of the simplified model are assessed by
developing a second, more general model and an exact solu
tion, both containing field-dependent parameters.
We first review the square-law regime and the modified
square law which includes the effective length reduction.
The square law is then obtained through a second, more
general approach which includes field-dependent mobilities
and capture coefficients. The effective device length is deter
mined by considering field-dependent parameters in the low-field region. The more general approach and the model from
Ref. 7 are compared with an exact solution to assess the
conditions under which those approximate models are valid.
The exact solution is obtained by introducing into the meth
od of Ref. 3 the electric field dependence of electronic pa
rameters.
II. THEORETICAL MODELS
A double-injection device of configuration p+ -p-n+ is
considered. The P region contains deep lying acceptors of
density NR and shallow donors of density ND, with
N R > N D· This is represented by the energy-band diagram of
Fig. 1. The shanow donors provide compensating electrons
for the deep acceptors and are assumed not to play any other
role in the electronic behavior of the p region. The acceptor
level is considered sufficiently deep for the density of ther
mal holes Po, to be small compared to NR and ND• i.e.,
Po < N R ,N D' The recombination of electrons and holes at the
deep level is characterized by capture coefficients Yn and Yp'
respectively, with rp» Yn for an acceptorIike impurity.
The model assumes that the current is entirely field driv
en and that the diffusion current is negligible. This is justified
for "long" p+ -p-n+ structures where the p region is several
diffusion lengths long. 10 It is also assumed that charge neu
trality applies which limits the results to the case ofrelativeIy
high magnitudes of Po' The lower limit of Po corresponds to
the condition that the dielectric relaxation time is approxi
mately equal to the low-level electron lifetime.3
The injection of electrons and holes into the p region
occurs when the p+ region, "anode," is biased positive with
respect to the n 1-region, "cathode:' The applied bias is as
sumed to appear almost entirely across the p region. The
anode and cathode are considered to be infinite sources of
carriers for the center region. With increasing bias the cur
rent-voltage characteristic evolves through the following re
gimes: Ohm's law, square law, threshold, and negative resis
tance. In the square-law regime the current is carried
essentially by injected electrons and the J-V characteristic is
given by2
(1)
5571 J. Appl. Phys. 63 (1 1), 1 June 1988 0021-8979/68/1 15571-i 2$02.40 © 1988 American Institute of Physics 5571
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23( a)
v
p
o L L x-
( b )
FIG. 1. (a) Equilibrium energy-band model for a p-type semiconductor
with a deep acceptor <recombination center) at BR and a shallow donor at
ED' (b) Schematic diagram of ap' -p-n+ structure.
or in the normalized form by
IN = (VV~, (2)
where J is the current density, Vis the applied voltage, (To is
the thermal equilibrium conductivity (0'0 = q Il~ Po), qis the
electron charge, f.l~ and p~ are the electron and hole field
independent mobilities, L is the length of the p region,
'T nL is the electron lifetime at thermal equilibrium,
'T"L = 1!(y,; PR" ),PRo is the equilibrium density ofunoccu
pied recombination centers, and y,: is the field-independent
electron capture coefficient. The normalized current den
sity, J N' and the normalized voltage, VN• are defined as
IN = Jf.ln7"Ij(Lo-o) and VN = Vf.lIl'Tn1jL 2.
As the bias increases, the recombination centers near
the anode become largely depopulated of electrons due to an
increasing level of hole injection. This results in the forma
tion of a high conductivity low-field region near the anode
which progressively moves into the bulk of the p region. The
bulk can therefore be regarded as consisting of two distinct
regions: a low-field region near the anode and a high-field
region near the cathode. As the low-field region progresses
into the p region the J-V characteristics departs from the
square law and enters a transition regime that leads to the
threshold. A good approximation for this porti.on of the
characteristics is obtained. by a modification of the square
law which involves the reduction of the effective device
length.7 The modified square law is given by
J = (V.u~rnIPoV2/(L -K'J)3,
where
K' = [1 -b In(1 + 1/b) ]!(qnRo y,;NR), (3)
where b = f1~/f1~' NR is the density of recombination
centers, and nRo is the equilibrium density of recombination
centers occupied by electrons. The threshold voltage can be
5572 J. Appl. Phys., Vol. 63, No. 11, 1 June 1988 detennined from the above relation and the condi.tion dV /
dJ = O. It is given by
(4)
As discussed in Ref. 7, this approach allows for the in
clusion of the field dependence of mobilities and capture co~
efficiems, while still retaining tractable results. This is par
ticularly true when solutions are developed for the threshold
voltage region and not for the entire segment of the square
law. In this case the magnitude ofthe electric field is limited
to a narrow range and simplified expressions offield-depen
dent parameters can be used. Accordingly, the modified
square law can be extended to include field-dependent mo
bilities and capture coefficients of the form:
J.l.,p (E) = J.l~.p( E;p ) l!(3n.p
,
(E r )Un,p -112
rn,p (E) = y,:.P ;p , (5)
where f1~.P and 'fn,p are the field-independent mobilities and
capture coefficients, respectively, /3 n.p and an,p are con
stants, and E ~.P and E ~.P are critical field strengths at which
mobilities and capture coefficients become field dependent.
The modified square law which includes field-dependent pa
rameters was obtained in Ref. 7 and is given by
<r+2)r-t-l Vr+-l J=C p,°rLo- (6) (r+1)y+2 n n ° (L-K'J)Y+2
where
r = an + 1/2 -lI!3" -lI!3p
1 (E ~ )"'n-112
-=--------:-:::-------:--:-:-
C (l -l//3p )(E~) 1If3"(EP 1//31'
An expression for the threshold voltage including high-field
effects is obtained by combining Eq. (6) and the condition
dV IdJ = 0 with the result
(r+ 2)!/(y+I)(r+ 1)1 + lI(r->-l) V. -....:..!:--C--....:...... __ '-'-'--'--__ _
th -(r+3)H-2/(r+ l)
L 1+2/(r+ I}
X (7)
(Cp~rnLaoK')1I(r+ I)
As is discussed in Ref. 7, with field-independent parameters
the modified square law, Eq. (3), provides a good approxi
mation of the exact solution in the threshold voltage region.
However, when high-field effects are included, this is not
always the case as win be shown in the following.
III. GENERALIZED APPROACH FOR THE MODifiED
SQUARE LAW
A. Extended model for the high~field region
In the original derivation of the square law, Eq. (1),
wh.ich served as the basis for Eqs. (6) and (7), it was as
sumed that the hole density was constant and equal to the
thermal hole density, Po, and that the hole contribution to
the current was negligible. In the present formulation, both
of those restrictions are removed. The results may therefore
R. Stawski and K. L. Ashley 5572
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23be used to assess the conditions under which those assump
tions are valid.
As will be shown, it is usually a valid approximation to
neglect p in the current equation insofar as p < n for current
density magnitudes in the square-law region, and up to, and
above that corresponding to the threshold voltage. However,
the manner in which p is reflected in the current divergence
may require that p be allowed to be significantly different
from Po. This can be more properly clarified from the rel
evant system of equations which is as follows: The current
equation
I = q(lln (E)n +,up (E)p]E,
the continuity equation
1 dJn ---= 11 Yr/(E)PR' q dx
and the recombination kinetics equation (8)
(9)
ny,,(E)PR =pYp(E)n R -poYp(E)(nRJpR..)PR' (to)
where nand P are the electron and hole densities, respective
ly, E is the electric field, In is the electron current density,
and n Rand P R are the nonequiHbrium densities of occupied
and unoccupied recombination centers, respectively. In this
casepR and fiR will, respectively, be set equal tOPR" and nR".
This is consistent with charge neutrality and is justified
whenever n,p<PR' which will generally be true in the high
field region.
From this system of equations the current density and
the voltage across the high-field region can be obtained. The
! J-V characteristic for the entire P region, which consists of
the high-and low-field regions, is obtained by accounting for
the reduction of the length of the high-field region toL -L',
due to the penetration of the low-field region of length L I
into the device. This follows the approach described in Ref. 7
as the modification of the square law and which resulted in
Eqs. (3) and (6).
In the derivation of Sec. II, P was set strictly equal to Po.
This condition, when used with P R = P R" (or n R = n R.., ),
eliminated the use of the recombination kinetics equation,
i.e., the right-hand side was exactly equal to zero. Retention
of that equation here, by havingp#po will provide for appli
cation to a broader range of situations which can obtain
when field dependence of electronic parameters is included.
It is notable that unlike the results of Sec. II, the present
development will contain rp (E) as a parameter.
Substitutingp from Eq. (8) into Eq. (10) gives
n = tf;(E)b(E)nR./PR" J (1 _ W'), (II)
1 + tf;(E)b(E)nR/PRo q/-l .. (E)E
where
fjJ(E) = Yp (E), beE) = {-ttl (E) • r .. (E) /l-p (E)
Ifl' = q/-lp (E)poE .
J
MUltiplying Eq. (11) by gP .. (E)E, differentiating, and sub
stituting dJ"ldx from Eq. (9), results in
y .. (E) .£(1-W') = [IfjJ(E)b(E)O -Ifl') d[~(E)b(E)J _ ( (E) +Ed#p(E2.)]dE .
PRo #" (E) E 1 + ¢(E)b(E)nRJpRo dE qpo Pp dE dx (12)
Equation ( 12) can be simplified by introducing the approxi
mation ~"< 1, which is valid when the characteristic has
evolved well into the square law. The resulting equation can
otherwise be obtained by initially neglecting the hole current
in Eq. (8). Therefore, the assumption made in Ref. 7 that the
hole current is negligible and that the electron current is
constant and equal to the total current is wen justified. This
is especially true when the J-V characteristic has reached the
threshold voltage region. The difference between the present
approach and the one which resulted in Eq. (6) is thus mani
fested in the presence of the first term, within the parenthe
sis, on the right-hand side of Eq. (12).
For obtaining solutions for the J-V characteristic we use
the functional forms for field-dependent mobilities and cap
ture coefficients which apply for a broad range of electric
field. These are
()
(E) = f-l",p
fln,p 1 EIEp. + n.p
(E) = y,;.P Y",p a 1 + (EIE~,p) n,p (13)
Here E ~,p and E ~,p are the magnitudes of electric field where
the mobilities and capture coefficients assume half of their
5573 J. Appl. PhyS., Vol. 63, No. 11, 1 June 1988 I
field-independent values ,u~.P and .y~,p. In Appendix A, solu
tions are given which are obtained using the approximate
forms of field-dependent parameters, Eq. (5). However, as
may be noted there, those solutions still require numerical
evaluation and are subject to serious error if a proper selec
tion of parameters (such as a /I,p' f3 fl,p' E ~:.P' and E ~.P ) is not
made for a given segment of the J-V characteristic. Use of the
simplified forms does not provide, in this case, a significant
benefit in the form of computational ease, as is shown in
Appendix A, and hence the choice was made to use the more
accurate forms.
The current expression is obtained by first substituting
general expressions offield-dependent parameters, given by
Eq. (B), into Eq. (12). Integrating the resulting equation
gives
(14)
R. Stawski and K. l. Ashley 5573
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23with one boundary condition E = Eo at the cathode x = L,
and a second condition E = E'atx = L', which is the bound
ary between the high-and low-field regions. The function F
is defined as follows:
F= (an/E~)(E/E ~)a,,~ I
1 + (E/E~/'r.
(0: /E'Y)(E /Er)ap~ \
p P P
l/E~ +----'--
1 + EIE; l/E~
1 +EIE~
At the first boundary condition x = L the magnitude of the
electric field, Eo. is determined as the lowest value of the field
for which the integrand in Eq. (14) is positive. This follows
from an examination ofEq. ( 11), which, when multiplied by
qj.tn (E}E, gives an expression for the electron current, In, as
a function ofthe electric field E. Using this expression, it can
be shown thatJ" is not a monotonic function of E. However,
physical arguments indicate that J n should be a decreasing
function of E in the high-field region. The physically mean
ingful part of the solution is obtained in an interval of the
electric field that is limited at the cathode x = L by a bound
ary value Eo, such that for E> Eo the electron current de
creases monotonically with E. This is consistent with having
the following conditions satisfied in the high-field region:
dJnldx> O,dE Idx <0, anddJ,,/dE <0 (with thex-axisori
entation chosen here). The value of Eo is determined as the
largest zero of the integrand in Eq. (14).
The second boundary condition corresponds to the re
duction of the length of the high-field region toL -L t, when
the low-field region penetrates a distance L ' from the anode
into the device. An expression for the length of the low-field
region is given in Sec. III B that follows. A solution of Eq.
(14) is obtained by first choosing a value of J and then ad
justing the value of the parameter E' until both sides ofEq.
(14) are equal. The voltage across the high-field region is
obtained as follows:
v= -fE dx dE dE
=f..L~7nLUfJrE' E2[1 + (E/E~)""]
J J/;.~ 1 +E/E~
r 1 J
X (1 +EIE~)2 -00
X F ] dE.
1 + r/>(E)b(E)nR/PR" (15)
The voltage is evaluated by substituting into Eq. (15) values
of J and E' that are solution of Eq. (14), and integrating.
B. Length of the iow~fleld region
The modified square law, Eq. (3), and its extension that
includes field-dependent parameters, Eg. (6), were derived
by accounting for the reduction of the length of the high
field region to L -L', due to the penetration of a low-field
5574 J. Appl. Phys., Vol. 63, No. 11, 1 June 1988 oflength L ' into the device. An expression for the length of
the low-field region was obtained in Ref. 7 through an ap
proximation of the exact solution, and was given as
_ b In( (1 + b)Yo)l,
1 + byo j
(16)
whereb = ,u~/,u~, and Yo = nlpatx = L '. The magnitude of
Yo corresponds to the crossover point or boundary between
the low-and high-field regions. It was shown in Ref. 7 that
the field at the crossover on the high-field region side can be
expressed in terms of Yo as
Eh (Yo)
=!...[ [1-yoi,;PR../(rj!nR.,)] -(Yo -1)Po/PR,,].
(To 1 + byo
(17)
An expression for the electric field in the high-field region
can also be obtained as an intermediate step in the derivation
of the modified square law. This expression evaluated at the
boundary x = L' gives
Eh(L,)=[2J(;;-Lf
)]1/2
0 (18)
j.tn7nLUO
At the boundary, the two expressions, Egs. (17) and (18),
are equal. This equality provides a means for obtaining Yo as
a function of J which in turn can be substituted into Eq. (16)
to yield a value for L '.
A more approximate form of L' is obtained for Yo> 1,
which is
L'= J l-~ln 1 +!!L .
[ 0 ( 0 )]
qnR.. i:,NR ft~ J.l~ (19)
This result is in agreement with that obtained by MigIiorato
et al.6 which was based on the assumption that most of the
recombination centers are fined with holes, i.e., that
PR z,NR, and that the boundary x = L' is defined by
n = n R,,' The boundary condition n = it R
Q' together with the
local neutrality relation n = p + n R,,' is in effect equivalent
to having Yo> L
Equations (16) and (19) weredetived with theassump
tion that in the low-field region mobilities and capture coeffi
cients can be considered field independent. In the present
analysis this assumption is removed and an assessment of its
validity can be made.
When the field dependence of electronic parameters is
introduced into the low-field region, the manner in which
the variables are related in the resulting expressions (Appen
dix B) prohibits a direct application of the method from Ref.
7 which led to Eq. (16). In the method from Ref. 7 a general
expression of the electric field in the low-field region was
derived from the charge neutrality relation in terms of the
parameters y = nip. This expression for the electric field
was subsequently simplified and substituted into the contin
uityequation for electrons from whichEq. (16) for L! result
ed. In the present case, with field-dependent parameters, a
difficulty arises from the fact that a general expression for
R. Stawski and K. l. Ashley 5574
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23the electric field in the low~field region cannot be obtained in
analytical form, as it is apparent from an examination ofEg.
(B9). However, an approximate expression of the low field
can be directly obtained from the observation that the ap
proximate form of the electric field given in Ref. 7 can be
otherwise obtained by assuming that in the low-field region
most of the recombination centers are filled with holes, i.e.,
PR ,;::;NR• With this assumption the charge neutrality rela
tion can be simplified to n -p = n Ro' Substituting into the
charge neutrality relation expressions of i1 and p, given in
Appendix B as Eq. (B6) and Eq. (B7), results in an expres
sion for the field in the low-field region. This is
(20)
where z = J I[ qpP (E)pE] as defined in Appendix B.
The electron continuity equation, Eq. (B2), integrated
over the low-field region only, gives an expression for the
length of the low-field region. This is
(21)
with E given by Eq. (20) andpR replaced by NR according
to the previous assumption. The lower limit of integration,
Za' corresponds to the onset of the square-law regime for
which at the anode n = p. Substituting the condition n = p
into the variable z gives Za = 1 + f1n (E)I{tp (E)
:::::; 1 + J.l~ I p~. The upper limit of integration, zo. corresponds
to the boundary between the low-and high-field regions. For
a given value of the electric field at the boundary on the high~
field side, E I, the magnitude of Zo can be obtained by numeri
cally solving the charge neutrality relation, Eq. (B9), given
in Appendix B.
A more approximate expression for L I is given in Ap
pendix C, where, in addition to the assumptionpR ,;::;NR• the
boundary between the low~ and high-field regions is assumed
to occur for n = nRo'
The degree of approximation introduced into the pres
ent approach by assuming that PR :::::;NR can be reduced
without increasing the level of complexity of the method.
For this, the expression for PR given in Appendix B as Eq,
(B8) can be simplified by removing the field dependence of
mobilities and capture coefficients and by neglecting the
field-dependent term in the denominator, The resulting
expression is
WithpR given by Eq. (22), the expression for the field in the
low-field region, Eqo (20), has to be modified by replacing
n R" with P R -P R,,' This modified equation for the electric
field is then substituted into Eq. (21) to give an expression
for the length of the low-field region. In the fonowing section
it will be shown that PR given by Eq. (22) considerably im
proves the accuracy of the present method especially for
larger ratios of i,! I y~.
5575 J, Appl. Phys .. Vol. 63, No. 11, 1 June 1988 IV, COMPUTATION OF THE CURRENT~V(n. TAGE
CHARACTERISTICS
In the fonowing, the equations developed in Sec. In are
used to eval.uate the influence of field effects on the J-V char
acteristic and in particular on the threshold voltage. These
results are compared with solutions obtained from Eq. (6) of
Sec. II and from an exact solution, which is given in Appen
dix B. A modified form of Eq. (6) is used in the present
computation. The modification consists of including in the
derivation of Ref. 7 general expressions of field-dependent
parameters, given by Eq. (13). In this manner, differences
between solutions which may result from the use of approxi
mate forms of field-dependent parameters are eliminated
from the comparison. The exact J-V characteristic is used to
assess the validity of the approximate models.
We also compare solutions obtained with, and without,
including the field dependence of electronic parameters in
the low~field region. It might be expected that since the elec
tric field is relatively small in the low-field region, the effect
on parameters would be negligible. However, as will be
shown, although the effect on the threshold voltage is slight,
effects on the current magnitUde in the negative resistance
region can be significant.
The set of parameters used in computations might be
representative of SUn devices at 77 K. The field-dependent
mobilities, given by Eq. (13), are well represented, as was
shown in Ref. 7, by the following parameters:
f.L~ = 1.86 X 104 cm2 V--Is -1, J.l~ = 0.63 X 104
cm2 v--! S-1 Ef' = 650 V cm-I Ell = 1100 V cm--1 For , n j p •
the field-dependent capture coefficients, given by Eq. (13),
the following values were used: i,! = 10--10 cm3 S--I,
~ = 10-7 em3 g--I EY = 75 V em-I EY = 600 V cm--!
~ p 2 n , p s
and an = a p = 2. All the values related to the capture coeffi
cients were taken in correspondence with those obtained by
Hurm et ai. '} except for f},. Other parameters used in compu
tations were: NR =2XlO16 cm-3 and ND
= 1 X 1016 cm--3•
A. Comparison of approximate models
In this subsection a comparison is made between the
approximate model from Eq. (6) and the model from Sec.
III. The exact solution is used to assess the validity of the
approximate models. The parameters used in the compari
son are chosen to make evident those differences that result
from approximations introduced in the high-field region.
The choice of a particular model for the length of the Iow
field region has negligible effect in this case.
A plot of the normalized threshold voltage, V~, versus
the logarithm of L is shown in Fig. 2(a) for Po = 1010, 1011,
and 1Ol2 cm --3. For each value of Po three curves are shown:
the exact solution (solid lines), the approximate model from
Eq. (6) (dotted lines), and the model from Sec. HI (dashed
lines). Where the threshold voltage is constant and indepen
dent of L, field effects on parameters are negligible. [Note
Eq, (4) and the definition of the normalized threshold vol
tage, V~=,u~rnLVth/L2.J The results indicate that for
large magnitUdes of Po, the exact solution and the two ap-
R. Stawski and K. l. Ashley 5575
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23proximate models are essentially identical for small values of
L where the field effects are absent. For increasing device
lengths, the model from Sec. HI closely follows the exact
solution, while the approximate model from Eq. (6) shows a
slight deviation. For lower values of Po a significant differ
ence appears between the approximate model from Eq. (6)
and the solution generated from the model of Sec. III. The
difference is especially large for shorter devices and tends to
diminish as the length increases. This is a reflection of the
limits of validity of the square law, Eq. (1), on which the
approximate solution, Eq. (6), was based. In the derivation
of those equations it was assumed, for example, that the hole
density was constant and equal to the thermal hole density,
Po' In the formulation of Sec. HI this restriction was re
moved. It was noted that the solution obtained in Sec. III
differed from the one which resulted in Eq. (6), by the pres
ence of the first term, within parenthesis, on the right-hand
sideofEq. (12). The second term, within the same parenthe-
104,..-________________ ---,
"" .. ,,, .. ,",,., Ci~Zl~~1§~
( a )
,
10 100
DEVICE LENGTH (,'~m)
10 100
DEVICE LENGTH (,.cm) 500
500
FIG. 2. Theoretical plot of the normalized threshold voltage, V~, YS the
device length, L. For each value of Po three curves are shown: exact solution
(solid lines), the model from Eq. (6) (dotted lines), and the model from
Sec. III (dashed lines). A comparison is made for: (a) r~/r;, = 1000, (b)
Y},/r;, = 100.
5576 J. AppL Phys., Vol. 63, No. 11, 1 June Hl88 sis, on the right-hand side ofEq. (12), is directly proportion
al to the thermal hole density, Po. As Po becomes smaller, the
contribution of the second term becomes less significant and
the first term gains in importance. The presence of the first
term affects the accuracy of the solution for lower values of
Po' The lack of this term in the solution leading to Eq. (6) is
primarily responsible for the error that affects the threshold
voltage magnitude. The model from Sec. III provides a very
good approximation of the exact solution for shorter device
lengths. For the purpose of estimation of the threshold vol
tage in longer devices, both models are sufficiently close to
the exact solution.
A second plot ofthe normalized threshold voltage, V~,
versus the logarithm of L is shown in Fig. 2 (b) for Po = 1011,
1012, and 1013 cm~3. In this plot the field-independent hole
capture coefficient r~ is changed to 10-8 cm3 8-1• This re
duces the ratio of capture coefficients, ~//,;, to a 100. The
curves are labeled in the same manner as in Fig. 2 (a). The
remarks made in relation to Fig. 2 (a) also apply in this case.
However, for this ratio of Yn/~ a significant difference ap
pears between the model from Sec. HI and the exact solution
for lower values of Po' The difference is due to the approxi
mationpR ~NR that is made in the model for the low-field
region. With the introduction of a more accurate expression
for PR' such as the one given in Eq. (22), into the model of
the low-field region the correspondence with the exact solu
tion is greatly improved. This is evident from the long
dashed curve which was obtained with the more accurate
expression for P R .
The threshold voltage depends on the square of the de
vice length (L 2) in the case offield-independent parameters.
This is apparent in Eq. (4). When field effects are present,
the simplified approach leading to Eq. (7) suggests that the
threshold voltage is proportional to L I + 2/( y + [). The extent
to which this form of dependence on the device length is
supported by the more accurate solution from Sec. III is
exhibited in Fig. 3. The figure shows a piot of the threshold
voltage versus the logarithm of L for Po = lOW, 1011, and
ld
1d
~ (5 10' >
w
100 Cl
~ 0 > 10-' c
\ Iii iii
100 500
DEVICE LENGTH (." m )
FIG. 3. Theoretical plot of the threshold voltage, V~, vs the device length,
L. SOlutions are obtained using the mode! from Sec. HI (solid lines).
R Stawski and K. L. Ashley 5576
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:231012 cm-3• Solutions obtained using the model of Sec. III
(solid lines), that include the field dependence of electronic
parameters in the low-field region, are compared to the L 2
dependence resulting from Eq. (4), and to the L I + 21( r + I)
dependence obtained from Eq. (7). The results indicate that
for sman magnitudes of L, the threshold voltage is propor
tional to L 2, while for large L, a lower power dependence is
observed. As the value of Po is decreased, the departure from
an L 2 dependence occurs at smaller device lengths. It is seen
that for Po = 10 Hl em -3 and for shorter device lengths, the
threshold voltage displays a larger power dependence than
L 2. This also occurs for Po = lOll and 1012 cm--3 but to a
much lesser extend, and therefore it is not apparent on the
plot. For longer device lengths, the reduction of the thresh
old voltage, due to the field dependence of electronic param~
eters, can be significant.
B. Field effects In the low&field region
In this subsection a comparison is made between two
solutions derived both from the model of Sec. III. One solu
tion is obtained with, and the other without, the inclusion of
the field dependence of electronic parameters in the low-field
region. The exact solution is again used as a reference for the
comparison.
J-V characteristics were calculated using three formula
tions. These are: (l) model from Sec. III A with Eq. (16);
(2) model from Sec. III A with Eq. (21); (3) the exact solu
tion. A plot ofthe normalized current density, J N. versus the
normalized voltage, VN, is shown in Fig. 4 for L = 1, 10,50,
200, and 1000 J..lm. The three cases are represented, respec
tively, by dotted, dashed, and solid curves. The plot is made
for Po = 1012 cm-3, r,: = 10-9 cm3 S-I, and ~
= 10-6 cm3 S-l. These results indicate that for small mag
nitudes of L, the influence of field-dependent parameters on
the length of the low-field region is negligible, while for large
L, a substantial difference appears. When the length of the
l~+-----~-J---r-~~--f-r~'r------~--4
10 100
NORMALIZED VOLTAGE 300
FIG. 4. TheoreticalJ- V characteristics for various device lengths. Solutions
obtained using the model from Sec. III with (dashed lines), and without
(dotted lines), including field effects in the low-field region, are compared
with the exact solution (solid lines).
5577 J. Appl. Phys., Vol. 63, No.11, 1 June 1988 low-field region includes field-dependent parameters, the
transition from the square law through the threshold voltage
region and into the negative resistance region, occurs at low
er currents and lower voltages as the length of the device
increases. Although both the maximum current of the nega
tive resistance region and the threshold voltage are reduced,
the former represents the strongest effect on the J-V charac
teristic.
The threshold voltage is also obtained using the three
formulations described in the previous paragraph. Figure 5
shows a plot of the normalized threshold voltage, Vtj;, versus
thelogofL forpo = 1012cm--3, r,: = 1O~\ 10-9, and lO-H)
cm3 S-1 while maintaining the ratio r,:/~ constant and
equal to 10-3, For each value of r,; three curves are shown:
the exact solution (solid lines), the model from Sec, HI in
cluding Eq. (16) (dotted lines), and the model from Sec. III
including Eq. (21) (dashed lines). It is seen that the influ
ence of field-dependent parameters on the length of the low
field region, and through it on the threshold voltage, is most
significant for large magnitudes of the electron and hole cap
ture coefficients, and for long devices. The results also indi
cate that the field dependence of electronic parameters must
be included in the low-field region to provide good corre
spondence between the model from Sec, In and the exact
solution for longer device lengths.
A plot of the spatial variation of the electric field and
electron density across the low-field region is shown in Fig.
6. The injection level into the low-field region corresponds to
a normalized current density IN = 6 X 104• The plot is made
for p = 1012 cm-3 .11 = 10-9 em38-1 ./J = to-6 em3 n , rtf .. ,rp
s -1, and L = i 000 J..lm. The vertical bars at the end of each
curve represent the boundary between the low-and high
field regions. The junction p+ -p is positioned at xlL = O.
This plot illustrates the effect offield-dependent parameters
on the length of the low-field region in accordance with Eq.
(21). The curves labeled (b), (c), (d), and (e) are obtained
from Eq. (21). The curve labeled (a) results from Eq. (16)
500-
w 0 ;=; '-' 0 >
a -' 0
I (f) w a::
j:s
Q
W t::; -' « ;:;;
0:: 0 z
20 -.
1 10 500
DEVICE LENGTH (,.un)
FIG. 5. Theoretical plot of the normalized threshold voltage, V~, V5 the
device length, L, with r;: as a parameter. The model from Sec. HI with
(dashed lines). and without (dotted lines), including field effects in the
low-field region, is compared with the exact solution (solid lines).
R. Stawski and K. L. Ashley 5577
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23I
.--.. 1017 ~ld
,.., f I d e E E u [ tJ
---Ii> );'
>-t t:: g Vl z I w w c:: 0
z u cr 0 >-'" i3 g ..J
W
c:i 10'" 10'
0.0 0.1 0.2 0.3 0.4
NORf"lAlIZED DE ViCE LENGTH, X/L
FIG. 6. Theoretical plot of the spatial variation of the electric field and elec
tron density across the low-field region. All solutions, except (a), are ob·
tained with including field effects in the low-field region.
and corresponds to the case offield-independent parameters.
Curve (d) is obtained with E ~ = 6.5 X 104 V cm -1 and E ~
= 1,1 X lOS V cm --I. Curves (b) and (c) are obtained with
E~ = 450 V cm--1 and E;, = 150 Vern-I, respectively.
Those results indicate that the length of the low-field region
increases significantly when the electron capture coefficient
is reduced through field effects. It is also seen that a large
decrease of electron and hole mobilities results in a compara
tively smaner increase in the length of the low-field region.
c. Comparison of models for the low~field region length
Two solutions derived from the model from Sec. III
with different expressions for the length of the low-field re
gion are compared. One solution is obtained with L ' given by
Eq. (21) and the other by using Eg. (C3) from Appendix Co
The expression for L j derived in Appendix C is based on one
additional assumption which is not made in the approach
leading to Eq. (21), The assumption made in Appendix C
relates to the boundary between the low-and high-field re
gions which is assumed to occur for n = n R,,'
A plot of the normalized threshold voltage, VI};, versus
the logarithm of Po is shown in Fig. 7 for ~/Y,; = 100 and
1000. The plot is made for short (L = 5 /-f.m) and long
(L = 500 Jlm) devices. For each value of L three curves are
shown: the model from Sec. HI with Eq. (21), nh (dashed
lines); the model from Sec. III with Eq. (C3), V;h (dotted
lines); and the exact solution, V~h (solid lines). The results
indicate that for r;:1'fn = 1000 the two approximate solu
tions fonow closely the exact solution except for the highest
magnitudes of Po. This is a reminder of the limit of validity of
the approximation P R = PRo on which the model for the
high-field region in Sec. III is based. As the magnitude of Pu
increases, the electron and hole densities make an increas
ingly important contribution to the charge neutrality rela
tion and cannot be assumed negligible in comparison to P R" •
For lJ.},lr;, = 1000 and for short devices the threshold
voltage is proportional to Po-112, while for longer devices it
5578 J. AppL Phys., Vol. 63, No. i 1,1 June i 988 ld -!---r--r-r-r-r-r-m---,--r..,..,..,...,.,.,.,-...,.......,...-,....,.....,.,.,....-r-r-r-r,"",,",
~ ~ ~ ~ ~
-3 (eM ) THERMAL HOLE DENSITY
1lf-,r------------------------r-------- •
...... ., .................. .,
'.
.... , ..... , ..... " '. " " ",
" '.
L=500u.m
-3 THERMAL HOLE DENSITY (eM )
Fl G. 7. Theoretical plot of the normalized threshold voltage vs the thermal
hole density. v" (til) represents the exact solution; V, (th) and Vz (th) are
based on the model from Sec. III with L ' given by Eq. (21) and Eq. (C3),
respectively. A comparison is made for: Ca) Y,:/r~ = 1000, (b)
y':/r;, = 100.
shows a lower power dependence, close to Po-1/3. The depar
ture from a Pr,-liZ dependence, that is due to the presence of
field effects, is supported by the simplified approach leading
to Eq. (7) which suggests that the threshold voltage should
be proportional to Po -1/( y +-lJ. It is evident in the plot for
y}'1y" = 100 and L = 5 Jim that the threshold voltage dis
plays a substantially larger power dependence than Po-lI2 as
the value of Po is decreased. This also occurs for
r;:/Y,: = 1000 but to a much lesser extent, The deviation
from the Po-!l2 power dependence is increased for a lower
ratio of r~/Y,; because in the expression of the voltage, Eq,
( 15), the second term within parenthesis on the right-hand
side ofEq. (15) is inversely proportional to the ratio r;:1y",
The presence of this term enhances the difference between
the solution of Sec. III and the one which resulted in Eq. (4).
Therefore, as the ratio Y;Ii,; becomes smaller, the contribu
tion of this second term increases and the solution deviates
from the Po-1/2 dependence which is suggested by Eq. (4) in
R. Stawski and K. L. Ashley 5578
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23the case of negligible field effects.
In the plot for Y},/-I,. = 1000 the exact and approximate
solutions tend to differ for smaller magnitudes of Po but are
still sufficiently close for the purpose of estimation of the
threshold voltage. As ij,/r;, becomes smaller, a significant
difference appears between the exact and approximate soIu~
tions for lower values of Po. The accuracy of the approximate
solutions for f),/Y,. = 100 can be considerably improved by
using in the model of Sec. III the expression for P R given by
Eq. (22). The resulting approximate solution provides an
excellent approximation of the exact solution.
v. CONCLUSIONS
The approximate analytical and numerical models with
field-dependent parameters which were presented in this pa
per and in Ref. 7 were based on the modified square law and
included a number of simplifying assumptions. The solu
tions, which were obtained in Sec. IV for the current-voltage
characteristics and the threshold voltage, indicate when the
assumptions which were made in the approximate models
are valid and demonstrate the conditions under which the
field dependence of electronic parameters is a factor in the
result. A comparison between the approximate models and
the exact solution was made to determine the range of pa
rameters in which each one of the assumptions would have a
significant effect on the accuracy ofthe approximate models.
The conclusions related to the validity of the assump
tions can be summarized as follows:
( 1) The assumption that the hole density in the high
field region is constant and equal to the thermal hole density,
Po. is not valid for lower magnitudes of Po-As the ratio ~ / ~
is reduced this assumption becomes unjustified even for
higher magnitudes of Po.
(2) For lower ratios of capture coefficients, r,;/Y,:, the
assumption that in the low-field region most of the recom
bination centers are filled with holes, i.e., thatpR 'ZNR, is not
accurate. A more complete expression for PR' which allows
for a spatial variation of P R in the low-field region, has to be
used instead.
(3) The effect of the field on the electronic parameters
in the low-field region cannot be assumed negligible. For
longer devices and large capture coefficients, field effects can
significantly affect the length of the low-field region, and
through it the threshold voltage and the current magnitude
in the negative resistance region of the characteristic.
( 4) For higher magnitudes of Po the assumption that in
the high-field region the density of unoccupied recombina~
tion centers is equal to their thermal equilibrium density, i.e.,
PR 'ZPRo' becomes inaccurate as the density of free carriers
increases.
In general, however, a good correspondence is obtained
between the approximate and exact solutions over a wide
range of parameters. The advantage of approximate models
in comparison to the exact solution is that they require con
siderably shorter computations and therefore are particular
ly suitable for modeling purposes"
It can be seen from the solutions presented in the pre-
5579 J. Appl. Phys" Vol. 63, No.1 i. 1 June i 988 vious section that the effects on the current-voltage charac
teristic and on the threshold voltage, associated with high
fields are not negligible. Those effects are particularly signif
icant for long devices made of semi-insulating material with
low thermal carrier densities and doped with impurities with
large capture cross sections. At lower magnitUdes of ~/~,
high-field effects are even more pronounced. With high-field
effects present the threshold voltage increases slower than L 2
with increasing device length and slower than Po 112 with
decreasing thermal hole density. This reduction of the
threshold voltage, compared to the case where high-field ef
fects are absent, occurs at shorter device lengths as the mag
nitude of Po decreases or as the magnitude of capture coeffi
cients increases.
The theoretical plots of the previous section can be in
vestigated experimentally by measuring current-voltage
characteristics of forward biased devices, of various lengths,
at different temperatures. The temperature variation will ad
just the thermal hole concentration to the desired range. For
example, for SUn devices, with the set of parameters used
here, a change in the thermal hole concentration from 1010 to
1012 cm-~3 can be achieved by a temperature change from
100 to 135 K approximately. Double-injection devices made
of semi-insulating GaAs could be studied at room tempera
ture since, for example, chromium-doped GaAs can be ob
tained with resistivity greater than 107 n cm at 300 K. 1 J The
high resistivity of GaAs is dependent upon midgap impurity
levels such as chromium II and iron, 12 and defect levels such
as EL213 and EL014 in undoped GaAs. Chromium and iron
both introduce deep acceptor levels in GaAs with ionization
energies of Ec -0.63 eV and Ev + 0.52 eV, respective
ly.IS In undoped semi-insulating GaAs the deep donor level
EL2, shallow carbon acceptors, and oxygen~related ELO are
the predominant levels. The understanding of mid gap deep
levels in GaAs has become increasingly important for the
improvement of material quality in GaAs integrated circuits
and optoelectronic devices. The mechanism of double-injec
tion offers a reliable technique for studying the various pa
rameters of semi-insulating materials and the properties of
defect levels.
Assuming that the velocity field relationship is known,
the models that were presented in this paper and in Ref. 7 can
be used as a tool for determining the field dependence of
capture coefficients of deep impurities. The theoretical mod
els can be fitted to experimental J~ V characteristics of short
and long devices to determine separately the low-and high
field parameters of capture coefficients. Measurements of
the threshold voltage can be fitted to the analytical model of
Ref. 7 to yield the field dependent electron capture coeffi
cient. Further details of this type of measurement on double
injection devices are described in Ref. 8. It is also notable
that to apply the models of this paper to the case of GaAs
appropriate expressions of field-dependent mobilities have
to be introduced into the formulation. Such expressions are
given in Ref. 16.
Other factors which could affect the results of measure
ments are impact ionization and the Poole-Frenkel effect.
With the set of parameters used here, measurements of the
threshold voltage at Po = WIG em -3 would create fields in
R. Stawski and K. L. Ashley 5579
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23the order of !03-lif V cm-1 for devices oflength 100--500
/-lm. It has been reported by McCombs!7 that in indium
doped silicon fields in the range 103_104 V em _.-1 are suffi
cient to cause impact ionization to occur. McCombs!7 also
observed that hi this range of electric field the thermal hole
concentration can be increased by enhanced emission due to
the Poole-Frenkel effect. IS The models of this paper should
be extended to include both impact ionization and the
Poole-Frenkel effect when electric fields of this magnitude
need to be considered.
APPENDIX A: EXTENDED MODEL FOR THE H!GH-FIELD
REGION WITH SIMPLIFIED FORMS OF FIELD
DEPENDENT MOBILITIES AND CAPTURE
COEFFICIENTS
It was discussed in Ref. 7 that simplified expressions of
field-dependent parameters, Eq. (5), can be used in the case
when the magnitude of the electric field is limited to a nar
row range, such as the threshold voltage region. The use of
asymptotic approximations of field-dependent mobilities
and capture coefficients requires that a proper choice of ex
ponents a /l,p and f3 H,p be made for different portions of the J
V characteristic. The attractive side of this approach is that it
allows for a simple analytical formulation, such as Eq. (6),
to be obtained. Substituting those simplified expressions of
field-dependent parameters, given by Eq. (5), into Eq. (12)
results in
Jdx = [~ rpL f.-L~ EY' _ EY']dE (AI) co Co' I ttn rnL(To 2(TO rnL fll!
where YI' Y2' Ch and Cz are constants given by
YI = an -~ -lI/3n -l//3p•
and Y2 = ap -! -lI/3p,
1 (E~)an- 112
c;= (1_1/f3p)(E~)l/fJn(E~)l/fJp'
-= (an -ap + lIf3p -lIf3/! )(E~)an- 1/2
0- 1J/3p)(E~)l/f3"(Epap- 112
(To=q/-l~Po, rnL = lI(pR"r~),
TpL = lI(nRo~)'
Integrating Eq. (At) results in
J(L -x)
Clfl~rnLaO E y, + 1 _ E 6' + 1
J ".a l' r E y, + 1 -E y, + I ___ ~ 0 (A2)
CPo fl~rnL r2 + 1
with the boundary condition E = Eo at the cathode x = L.
At the boundary x = L the magnitude of the electric field,
Eo, is determined as the lowest value of the field for which
theright-handsideofEq. (A2) is positive. This follows from
the discussion in Sec. III A. The second term on the right
hand side of Eg. (A2) is nonzero only for an =lap or
f3 n =lf3p. The voltage across the device is obtained from
V = -f E dx and Eq. (At) which together give
5580 J. Appl. Phys., Vol. 63, No. 11, 1 June i 988 C 81.0 r Q; E y, 1-2 _ E y, + 2 V = 1 r-n nL 0 0
J Yl +2
C E 1'z + 2 _ E 01', -'" 2
:1 0 --/-l T L ------C2 P P Yz + 2 (A3)
The current and voltage expressions, represented by Eqs.
(A2) and (A3), respectively, are related through the pa
rameter E. The J-V characteristic is obtained by substituting
into Eq. (A3) values of J and E that are the solution of Eq.
(A2).
It was shown in Ref. 7 that when simplified expressions
of field-dependent mobilities and capture coefficients are
used, the coefficients a",p and"B n,p have to be adjusted as the
J-V characteristic evolves. Since the second term in
Eg. (A3 ) depends on differences (an -aD) and
( 1//3 p -1/ fJ n ), a poor choice of a /t.p and f3 n,p may lead to
largely inaccurate results.
APPENDIX B: EXACT SOLUTION FOR
QUASINEUTRALITY WITH FIELD~DEPENDENT
PARAMETERS
The system of equations for the development of an exact
solution with field-dependent mobilities and capture coeffi
cients consists of the current equation
J = q[ lln (E)n + flp(E)p]E,
the continuity equation
1 dJp ---d =nr,,(E)PR' q x
the recombination kinetics expression (D1)
(B2)
y" (E)nPR = rp (E)p(N R -PR) -Yp (E)pO(nR./PRn )PR'
(B3)
the charge neutrality relation
P + N D -n -NR + PR = 0, (B4)
and expressions for field-dependent mobilities and capture
coefficients
ll~.p j.£",p (E) = _-':".:.:2.. __
1 +EIE~.p
Yn (E) = ~,p
,p 1 + (E lEY )an.p
fI.P (B5)
For simplifying expressions the following transformed vari
ables are defined:
z = J I (q/-lp (E)pE) , If = EUolJ
b(if) =/-lnUf)lflpUf), c(W) = Yn(W)lrp(W),
with
Using Eq. (DI) we obtain
R. Stawski and K. l. Ashley 5580
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23(B6) (B7)
and Substituting nand pinto Eq. (B3) and solving for P R yields
NR
PR =----------------------------------------1 + (z-l)c(~)/b(~') +zlf[,up(If)l,u~](nRJPRJ (B8)
Expressions of n, p, and P R can in turn be used in Eq. (B4) to give
[f.J,~ (_1 __ ex -1)) _ PRo ](1 + (z _ 1) c(lf) + z~ .up Of) nRo) + NR = o.
z~ .up (E) /-tn (E) / Po b( ~) .u~ PRo Po (B9)
The solutions for the electric field in the low-and high-field regions can be obtained as a function of the parameter z by locating
numerically the roots of Eq. (B9). A complication arises since Eq. (B9) depends on the current J through Jln.p ( If) and
r n,p (If), The current is computed starting with the continuity equation (EZ) which can be arranged into the form
dz qnrf/(If)PRr
dx J (BIO)
Using Eqs, (B6) and (B8) to eliminate nand p R in Eq. (B 10) results in
dx= J.un(lf) ~
O'orn(lf/)NR j<'tf,z) ,
where
The current is obtained by integrating Eq. (Ell) over the
low-and high-field regions. The low-field region, 'tf [, is con
tained in the interva1 0 < x < L' (anode, x = 0) and in the z
parameter range Za < Z < Zo [anode, n = p and
Za = 1 +.u,,(E)/.up(E);:::;l +Il~/fl~]. For the high-field
region, cg h' the intervals are L; < x < L (cathode where
'tf I = 'tf hand z = Z m ), The current expression becomes
J= O'oNRL (iZ" fln Cifl I )dz
Za rn(~I)f('tfI'Z)
+ f'm Iln ('tf h )dz ) -1
)"', Yn('tfh)j('tfh,z) (B12)
Equation (B 12) is an equation which implicitly contains J in
the right-hand side. A solution ofEq. (B12) is obtained by
first choosing a value of J and then successively adjusting the
value of Zo until the equality is satisfied. An expression for
the voltage is obtained from V = -S E dx and Eq. (B 11),
which together give
J2 [("" fl,,(iff[)~[dz
v= c?oNR Jza rnClfi[)j('tfI,z)
ron fl,,('tfh)~hdz ] (B13)
+ Jz" rn (,15\) f( 'tf h'Z) ,
The voltage is evaluated by substituting into Eq. (B 13) val
ues of I andzo that are the solution ofEq. (B12). The square
law, threshold region, and the negative resistance region can (Bll)
APPENDIX C: APPROXIMATE EXPRESSION FOR THE
LENGTH OF 1..0WnFIELD REGION
A more approximate expression for L ' is derived here,
where in addition to the assumption PR ;:::;NR used in Sec.
III B, the boundary between the low-and high-field regions
is assumed to occur for n = n R" •
In the present method, which follows, it is assumed that
most of the recombination centers are fined with holes, i.e.,
that PR ;:::;NR• and that local neutrality is satisfied with
n = P + nR,,' The system of equations consists of the current
equation, previously given as Eq. (8), and of the continuity
equations for electrons and holes, given by
1 dJn 1 dIp ---= ---=nr,,(E)PR· q dx qdx (CO
Combining the continuity equations with the condition
n -p = n R,,' and substituting n from the current equation
results in
dx = __ fl_,,_C_E_) __
rn (E)N R (1 + ~*)
X[l + EO + ~*) d.u,,(E}
tt .. (E) [1 + beE) 1 dE
(C2)
all be generated with Zo comprised in the range Za <ZO<Zm' where
5581 J. Appl. Phys., Vol. 63, No. 11,1 June 1988 R. Stawski and K. L. Ashley 5581
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137.149.200.5 On: Tue, 02 Dec 2014 19:23:23b(E) = ftn (E) ,
Jlp (E)
Substituting into Eq. (C2) field-dependent mobilities and
capture coefficients from Eq. (13), and integrating the re
sulting equation, gives an expression for the length of low
field region
L ' = fE, ftn (E) ~
Jo Yn (E) NR
( ftp(E) (E'~-E~)
X /-Ln (E) + /-Lp (E) (E~ + E}(E~ + E)
+ 1 l)a
l+EIE~ {JI[q,up(E)nR..]+E} ,
(C3)
with one boundary condition E = 0 at the anode x = 0, and a
second condition E = EI at x = L '. The boundary x = L I is
defined, foHowing Ref. 6, by the condition n = n lin' which,
when substituted into the current equation, gives EI = J I
[q/-l" (E,)nRn] orrearrangedE, = J l(qp~nR" -J /E~). It
is notable, that the first term within parenthesis on the right-
5582 J. Appl. Phys., Vol. 63, No. 11, 1 June 1988 hand side of Eq. (C3), vanishes if the electron and hole mo
bilities have the same field dependence, i.e., if E ~ = E ~, or if
the field dependence is removed from the development.
'K. L. Ashley, Ph.D. thesis (Carnegie-Mellon University, Pittsburgh,
1963;.
2K. L Ashley and A. G. Milnes, J. Appl. Phys. 35, 369 (1964).
'K. L. Ashley, R. L. Bailey, and I. K. Butler, Solid-State Electron. 16, 1125
(1973).
4H, J. Deuiing, J. Appl. Phys. 41, 2179 (1970).
sH, R.. Zwicker, B. G. Streetman, N. Holonyak, Jr., and A. M. Andrews, J.
App!. Phys. 41,4697 (1970).
6p. Migliorato, G. Margaritondo, and P. Perfetti, J. App!. Phys. 47, 656
(1976).
7K, L. Ashley and R. Stawski, J. Appl. Phys. 62, 1484 (1987).
gJ. L. Wagener and A. G. Milnes, Solid-State Electron. 8, 495 (1965).
9V. Hurrn, J. C. R. Hornung, andO. Manck, J. App!. Phys. 58, 588 (1985).
10M. A. Lampert and A. Rose, Phys. Rev. 121, 26 (1961).
"M. Otsubo and H. Miki, J. Electrochem. Soc. 124,441 (1977).
12H. Hasegawa, K. Kojima, and T. Sakai, Jpn. J. Appl. Phys. Hi, 1251
(1977).
!lG. M. Martin, A. Mitonneau, and A. Mircea, Electron. Lett. 13, 191
(1977).
14J. Lagowski, D. G. Lin, T. Aoyama, and H. C. Gatos, App!. Phys. Lett.
44,336 (1984).
I~S. M. Sze, Physics a/Semiconductor Devices, 2nd ed. (Wiley, New York,
1981).
16K. Horio, 1. Ikoma, and H. Yanai, Semi·Insulating III-V Materials, Kah
Nee-Ta (Shiva, Nantwick, 1984), p. 354.
17A. E. McCombs, Jr. and A. G. Milnes, Int. J. Electron. 32,361 (1972).
IKJ. Frenkel, Phys. Rev. 54, 647 (1938).
R. Stawski and K. L. Ashley 5582
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1.584517.pdf | The influence of ion scattering on dry etch profiles
J. Pelka, M. Weiss, W. Hoppe, and D. Mewes
Citation: Journal of Vacuum Science & Technology B 7, 1483 (1989); doi: 10.1116/1.584517
View online: http://dx.doi.org/10.1116/1.584517
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Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 160.36.178.25 On: Tue, 23 Dec 2014 08:35:51The influence of ion scattering on dry etch profiles
J. Pelka, Mo Weiss, W. Hoppe, and D. Mewes
Fraunhofer-Institutfiir Mikrostrukturtechnik (IMT), DilienburgerStr. 53, D-1OOO Berlin 33, West Germany
(Received 30 May 1989; accepted 21 July 1989)
A si.mulation study is presented using a new version of the simulation program ADEPT
(advanced simulation of dry-etching process technology), which is a subset of the process
simulator COMPOSITE. Based on some aspects of plasma physics, a model was developed that
allows for the calculation ofimportant properties of a collisional sheath by Monte Carlo methods.
These properties have great influence on the anisotropy of dry-etch processes. Angle/energy
spectra of ions and fast neutrals can be gained from the model and can be used as input data for
profile simulation. A simulation study is presented showing several profile phenomena. A short
discussion is included on sidewall protection by polymer deposition, and on surface diffusion.
t INTRODUCTION
In today's semiconductor fabrication, dry etching is based
on reactive ion-etch processes and plasma-etch processes,
whereas the technology of the future is believed to be reac
tive ion-beam etching. A common problem of all these tech
niques is a lack of understanding of the coupling among reac
tor, plasma, and etch processes. Therefore, simulation of
dry-etch processes is still in its infancy_
Modem technology requires the ability to fabricate fea
ture sizes with dimensions below 1 f1m. Several effects, such
as ion scattering and sidewall passivation by polymers, as
wen as surface diffusion of etchants, have to be taken into
account during process development in order to achieve an
isotropic and highly selective dry-etch processes. Several au
thors have dealt with the problem of ion transport within a
plasma sheath,I-6 which is surely the main consideration
with respect to anisotropic etch processes.
Sheath length and mean free path for ion/neutral colli
sions are generally in the same order of magnitude. In several
cases, the sheath length will even be significantly larger than
the mean free path. Therefore, ion scattering cannot be ne
glected in sub-fIm technology.6.7 As seen in many experi
ments, ion scattering leads to barreling and rounded bot
toms. Etch rates are dependent on the feature size.8
Experimental investigations suffer from the superposition
of several effects and from the usually unknown surface
chemistry. Simulations allow for a separation of different
mechanisms. Therefore, simulation studies can help to im
prove the understanding of the origin of profile phenomena.
To obtain a suitable simulation tool, the module "dry
etching" of the process simulator COMPOSITE9•1O was ex
tended to deal with ion scattering in a plasma sheath, depo
sition of polymers from the plasma, and surface diffusion of
etching particles within an etched trench.
In a first step, a model was developed in order to describe
ion distribution, voltage drop, and electrical field within the
sheath of a coHisionless rf glow discharge. These data can be
used as the basis for a Monte CarIo simulation of ion flight
paths considering elastic scattering as well as charge transfer
collisions. By the definition of an effective mass, the influ
ence of the scattering could be brought into the sheath model
in order to get an approximation for a collisional sheath. The Monte Carlo simulation results in angle energy spectra that
can be used as input data by a subsequent profile simulation.
Based on some general consequences gained from our cal
culations, as well as from the results of other authors,5,6 a
simulation study on the influence of different scattering dis
tributions on etch profiles was performed. Furthermore,
some aspects of deposition of polymers and a first approxi
mation of surface diffusion effects were included in this
study. Many profile phenomena can be simulated by super
position of these effects.
II. SHEATH MODEL
An rf plasma can be divided into three regions of very
different properties. The first one is the neutral plasma body.
The second one is the plasma sheath, which is a distinct
space-charge region. Between these two regions there is a
quasineutral transition region. The properties of the transi
tion region and the space-charge distribution within the
sheath itself are responsible for the transport of ions from the
plasma to the wafer.
The decisive properties of the transition region are sum
mari.zed by Bohm II in his criterion. He found that ions can
only cross the sheath if they reach the sheath boundary with
a minimum velocity V;) of
vo>·JkTe/m-;,
where mj is the ion mass and kTe represents the temperature
of the electrons, The concentration of the charge carriers
(ions: nt, electrons: ne) decreases from the plasma to the
sheath boundary to
ni(O)~ne(O) = ne{J exp( -1/2)~O.6n«().
neG is the carrier concentration in the neutral plasma body.
Other authors have shown that the Bohm criterion can be
written with an equal sign, ifvo is interpreted as the mean ion
velocity.12 For the following calculations, the Rohm crite
rion was assumed to be
vo = {kTe/m~,
Furthermore, the ions were assumed to be monoenergetic at
the sheath boundary to simplify the calculations. Therefore,
the ion current density Ji at the sheath boundary can be
expressed as
1483 J. Vac. Sci. Techno!. B 7 (6), Nov/Dec 1989 0734-211X/39/061483-05$Ol.00 @ 1989 American Vacuum Society 1483
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Ji = enj(O)-jkTe/m j,
where e represents the elementary charge. This current is
normally indicated as ion saturation current.
The sheath is assumed to be collision-free and recombina
tion of carriers is neglected. In this case, the ion current will
not change within the sheath. If Ish represents the sheath
length, we obtain
Ji = Ji (0) = J;C(h)'
The conservation of energy yields the relation between ion
velocity Vi and local potential Vex),
miv~(x)/2 = miv6/2 -eV(x).
Inserting the ion velocity at the sheath boundary Vo and in
troducing the abbreviation ue = kTc/e, we obtain
Vi (x) = voJr~2.v(x)7U~.
The continuity of the ion current mentioned above results in
nj (x)vi (x) = const = nj (O)vo'
Inserting Vo and vj(x) and combining the result with Pois
son's equation yields
Eo.fl -2V(x)/u~
eO.6neO 1
Up to this point, the electrons that are also within the
sheath have been neglected. Contrary to the heavy and inert
ions, the electrons are able to cross the sheath region due to
the time-dependent rffield in the normally used frequency of
13.56 MHz. Their contribution to a stationary model of the
sheath can only be considered by averaging. Furthermore,
the electrons are assumed to have a Boltzmann energy distri
bution. The local electron distribution is then given by
ne (x) = n,<j exp [ V(x)/u e ].
As a first-order approximation, Vex) is assumed io be the
same potential distribution as for the ions. This is not reany
true, because the real contribution of the electrons has to be
calculated as the time average of the electron concentration,
using a time-dependent potential distribution.
Now Poisson's equation yields, under consideration of
electrons and ions,
-:0 ne() { ~1-=-2~x);U:-
-exp [ V(x)/u e] }.
The solution of this differential equation was made numeri
cally. The sheath length, the distribution of electrical field
and potential, and the distribution of electrons and ions
within the sheath can then be obtained from this solution. As
input parameters, the bias voltage, the electron temperature,
and the electron density within the plasma have to be known.
All three values can be determined easily by probe measure
ments.
As an example, Fig. 1 depicts the carrier distribution with
in a sheath based on a set of data obtained from an Ar dis-
J. \taco Sci. Technol. S, Vol. 7, No.6, Nov/Dec 1989 r--l
rt')
I
< E
(.)
en
( o 6.0
4.0
2.0
0.0 0.0 I
I . I /
11/ !
i i~
: .1
:1
i /11 i !i
) \' .. 1
/ : ,I
\1
1\ i" ....
0.2 [°14-
X emJ 1484
i I
I i
1 i J J
I
I I
i
I
i I
0.6
FIG. 1. Carrier concentration in the sheath of an Ar rf glow discharge (pres
sure p = 30 m Torr, power P = 30 W, bias voltage Vdc = 176 V, electIOn
density n,{1 = 0.96>< 10'0 em" electron energy kT, ~~ 3.3 eV, plasma po
tential VPL -~ 31 V, floating potential Va = -16 V). -ion concentration,
.. , electron concentration, -~ -charge density, .' -' -sheath boundary.
charge in a standard RIE reactor (pressure p = 30 mTorr,
power P = 30 W, bias-voltage Vee = -176 V, plasma po
tential Vpt = 31 V, floating potential VII = -16 V, elec
tron density in the plasma body lleO = O.96X 1010 cm-3,
electron energy kl~ = 3.3 eV). Although collision pro
cesses are still neglected, the calculated sheath length of
(h = 0.32 em agrees well with the dark space length ob
served during the experiments.
m. COLLISION PROCESSES
All considerations made above assume the sheath to be
collision-free because it simplifies the calculations. How
ever, the mean free path for ion/neutral collisions is only half
the length of the calculated sheath length and for higher
pressure, the ratio between mean free path and sheath length
will be even smaller. Therefore, the collision processes
between ions and neutrals cannot be neglected in most cases.
Elastic collisions, linked with a change in flight direction
and a change in kinetic energy of the colliding partners, have
to be taken into account for all fast particles (ions and neu
trals) with thermal background gas molecules at rest. Fur
thermore, charge transfer collisions of fast ions with the
background gas have to be considered. In the case of Argon,
the total collision cross-sections for both scattering mecha
nisms are in the same order of magnitude, with the charge
exchange cross section slightly higher than that for elastic
scattering. l:l
A computer program was developed that calculates scat
tering processes by means of Monte Carlo methods. Elastic
collisions as well as charge transfer processes can be taken
into account. Flight paths of ions can be recorded. Up to 500
fast neutrals generated by the collision cascades can be
traced. Results gained by this program were presented in
Ref. 7.
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3.0 I:
I I I I I I 1 :
I
1
I I i I E 2'°1
1 I I I
::: !~\ttm,·t~·,t--i-
0.0 20.0 40.0 6Q.O 80.0
angle [deg.J
F[G, 2, Impact angle distribution for ions and neutrals on the wafer surface
referring to the plasma sheath of Fig. I. The probability for a particle to hit
the wafer surface under a particular angle is shown. Total collision cross
sections after Ref. 13, -ion distribution. ---neutral distribution.
Although the program has considered only the total cross
sections and a hard sphere model, the results are comparable
to those of other authors.3-6 Charge transfer processes lead
to broad energy distributions, because the energy of an ion
will be completely transferred to the neutral, whereas the
new ion has to be accelerated again. Elastic scattering results
in an angle distribution for ions and accelerated neutrals
with a peak at zero degrees, related to particles that are un
scattered and a scattered part with a maximum somewhere
around 15 deg. During an elastic collision, energy and mo
mentum will be shared between ion and neutral according to
the collision parameter. The distribution of the impact an
gles for both ions and neutrals is shown in Fig. 2, referring to
the data already used in Sec. U.
To complete an initial description of a collisional sheath,
the results of the Monte Carlo simulation were fed back into
the model for the collision less sheath. By an iterative proce
dure the mean ion energies computed by the two methods
were aligned. An effective mass was introduced in the sheath
model in order to take into account the influence of the ion!
neutral collisions on the ion mobility within the sheath. This
effective mass was found to increase with the pressure and
the mean free path to sheath length ratio, respectively. Using
the cross-section data of argon from Ref. 13, the effective
mass increases from approximately l.1m; for a mean free
path to sheath length ratio of 0.7 to -3.5 at a ratio of 5.
IV, PROFILE SIMULATiON
Because of the lack of data for relevant etch gases, the
general results mentioned above were used as input informa
tion for profile simulation. The etch module of the process
simulator COMPOSITE 10 was extended to handle angle dis
tributions of etching particles computed by the Monte Carlo
program, as well as arbitrary given distributions or analyti
cal approximations. The particle fiux towards a surface
J. Vac. Sci. Techno!. B, Vol. 7, No.6, Nov/Dec 1989 1485
point is calculated by integrating the angle distribution func
tion over the shadow window, taking into account the angle
of incidence. For example, a point located in open space is
not shadowed. It has a shadow window from
-17/2 to + 17/2. The shadow window of a point inside a
trench is defined by the mask geometry and the aspect ratio
of the trench, The flux of the etching particles towards the
wafer surface was assumed to be proportional to the etch
rate. An energy level can be defined during the Monte Carlo
simulation in order to suppress the influence onow energetic
particles. Values between 1 and 10 eV were found to be ap
propriate.
Figure 3 depicts the principal differences in dry-etch pro
files for some basic impact angle distributions. Similar to an
isotropic distribution, a Gaussian-shaped scattering distri
bution with a standard deviation of 30 deg results in a strong
barrel-like underetching and a significant decrease of the
etchrate with increasing aspect ratio [Fig. 3 (a) J. Using
scattering profiles obtained by the Monte Carlo simulation,
strawberry-shaped profiles can be achieved [Fig. 3(b)J.
These profiles arc due to the superposition of the influence
on the etch rate by scattered particles and the influence by
unscattered ones. Strawberry-shaped profiles are known, for
example, from etching deep trenches into silicon by means of
CBrFJ as the etch gas. lot
By using narrow distribution functions with small stan
dard deviations, etching becomes more directional but the
barreling effect is still visible for small feature sizes. Etching
a 0.2-JLm trench into a tri-level resist system, for example,
results in dove-tail profiles that are wider at the bottom than
beneath the mask [Fig. 4(a) V The corresponding simula
tion [Fig. 4(b)] uses a Gaussian-shaped scattering distribu
tion with a standard deviation of 5 deg and 100% overetch
jng. During the over-etch time, the shape changes from
barrel-like to the dove-tail profile.
AU etch profiles calculated under consideration of scat
tered particles show rounded bottoms that are due to the
variation in the shadowing window when moving from the
middle of a trench towards the sidewalk Therefore, the par
ticle flux at the base of a step can be only half of the flux on a
plane surface.
Vo SIDEWALL PASSIVATION
Using, for example, halogenated hydrocarbons such as
trifluormethane (CMF 3) as an etch gas, sidewall passivation
is achieved by polymer deposition. The passivation layer is
F7 \ 1<) \
i
!
\"._.-/! -
: I L __________ J l ________ ._ . .J
{al (o}
FIG. 3. The influence of ditfercnt scattering distributions on etched profiles.
The simulations show a n,S-pm trench, a 2.0-JiIll trcnch, and a step. (a)
Gaussian distribution, (I' = 30 deg. (b) Distribution obtained by MOllte
Carlo simulations referring to the data used in Fig, 1.
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(al
fbI
FIG. 4. The influence orion scattering on sub-pm trenches. (a) SEM picture
of a O.2-ltm wide and I-Jim deep trench into a trilevel resist system showing
a dovetail profile. (b) Corresponding simulation using a Gaussian distribu
tion with a = 5 deg and 100% overetching.
built up by polymerizing particles from the plasma. Some
times, redeposition of reaction products results in a similar
effect.
The sidewall passivation is able to suppress underetching,
as shown in Fig. 5. A scattering distribution is modeled by
using a directional (anisotropic) rate for unscattered, high
energetic particles and a cos4 approximation for the scat
tered part with lower energy. Figure 5(a) depicts the result
ing profile without sidewall passivation. The calculation
shown in Fig. 5 (b) is based on the following assumptions:
lal ]
I
I LJ \
\ ! I~
Ib)
FIG. 5. The influence of sidewall passivation. (a) No sidewall passivation.
(b) Sidewall passivation by polymer deposition. Rates were chosen to be
have like 5:2: I (directional:scattered:polymel·ization).
Jo Vac. Sci. Techno!. B, Vol. 7, No.6, Nov/Dec 1989 1486
FIG. 6. The influence of surface diffusion, feature size = 0.2 [lm. (a) No
surface diffusion, anisotropic etching assumed. (b) Surface diffusion length
A, = O.l/tm. (c) Surface diffusion length A, = 0.5 pm.
(a) the high-energetic (anisotropic) etch component is able
to suppress the building of a protective layer, (b) the scat
tered particles will etch chemically, (c) a polymer layer will
reduce the chemical etch rate by an exponential function
R(d) = R(O)exp( -d fA),
A was chosen to be 1 nm, (d) polymerization is carried out
by thermal particles; their angle distribution is isotropic, (e)
the rates are chosen to be at a ratio of5:2:1 (directional:scat
tered:polymerization). The result is shown in Fig. 5 (b). The
etch profile is anisotropic and a very thin polymer layer is
found at the sidewall.
VI. SURFACE DIFFUSION
Using low-pressure etch processes, only a few particles are
simultaneously within sub-flm~sized trenches and collisions
between these particles become unlikely. Therefore, an iso
tropic etch rate as in wet etching or high-pressure dry etching
of several micrometer wide trenches no longer exists. An
"isotropic" undercut only occurs by surface diffusion of
etchants or by particle reflection within the trench.
As a first approximation of these effects, surface diffusion
can be simulated by an exponential decay of the number of
diffusing particles into the shadowed regions, which was as
sumed to be proportional to the etch rate. Figure 6 shows
three calculated 0.2 pm profiles. Figure 6(a) depicts the sit
uation without any surface diffusion, in which only aniso
tropic etching occurs. Figure 6(b) shows the process consid
ering surface diffusion with a diffusion length of
As = 0.1 pm, whereas Fig. 6 (c) depicts the results for a dif
fusio1l1ength of As = 0.5 pm. It is important to note that the
sidewalls in Figo 6(b) are vertical, although an undercut oc
curs. In Fig. 6 (c), an "isotropic" profile is demonstrated.
VII. APPLICATION TO A REAL PROCESS
During the development of a deep-trench process using
CBrFJ as etch gas, several nonideal results were obtained.
One strawberry-like profile is shown in Fig. 7(a). It was
etched in a MIE3001-reactor CLeybold GmbH) using a
pressure of 12 Pa, an rfpower of200 W, and a bias voltage of
..... ~ ...
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lal
~-___ J I
I I
(b)
FIG. 7. Strawberry-shaped profile obtained from a nonideal CBrFj process.
(a) SEM micrograph: the mask gap is 2.S-.um wide, the trench is S-/Lm
deep. (b) Corresponding simulation considering ion scattering and surface
diffusion. Rates were chosen to behave like 4:3 (directional:scattercd); sur
face dilfusionlength was chosen to be n.s flm.
400 V. The mask gap is 2.5-pm wide. Based on the sheath
model presented above, the ion transport through the sheath
was simulated. The scattering distributions were approxi
mated using a cosine function for the scattered part and an
anisotropic (vertical) component with a ratio of 3:4 for the
resulting etchrates. First calculations without consideration
of other effects already have shown satisfactory results. In
troducing the surface diffusion with a surface diffusion
length of 11, = 0.5 pm, the simulation yielded the profile
shown in Fig. 7 (b). Although some deviations can be seen at
the bottom of the trench, the simulation agrees well with the
experimentally obtained result. The real trench is somewhat
narrower at the bottom than the simulated one. This is prob
ably due to passivation effects caused by redeposited reac
tion products. Similar effects are known from redeposition
during ion milling.
The same parameters can be applied to other feature sizes
and etch depths, although some adjustments may be neces
sary if the feature size is varied too much. This shows that the
model is reasonable, but the coupling between the param
eters is not yet fully induded.
J. Vac. Sci. Techno!. B, Vol. 7, No.6, Nov/Dec 1989
--" ......... , •• "'~ .• "-'-' ••• -•.• -.-.-.-••• ' ••• '.'.~ ••••••• '.'.'.>.' ••••••••••.• ;.:.;.:.:.:.~.-.~ •.• 1487
VIII. CONCL.USIONS
The new version of the module "dry etching" of the pro
cess simulator COMPOSITE is able to consider effects such
as ion scattering, sidewall passivation by polymer depo
sition, and surface diffusion of spontaneously etching parti
cles. A model for the plasma sheath is included in order to
allow calculations of the ion transport to the wafer surface.
Based on this model of a collisional sheath, a simulation
study was presented showing the influence of ion scattering
on etch profiles. In combination with a model for sidewall
passivation by polymer deposition and a rough model for
surface diffusion of etchants, a nonideal trench process was
simulated. The results show good agreement with the experi
ment. Furthermore, most profile phenomena known from
dry-etch profiles can be simulated by a combination of the
three models described above, although there is still no mod
el that delivers all the necessary parameters.
ACKNOWL.EDGMENTS
The authors would like to thank K. Bornig, P. Hoffmann,
and F. Heinrich for helpful discussions, K. Griindorff for
preparing the drawings, and W. Pilz for the experimental
support. Finally, the authors acknowledge the helpful com
ments on the simulation program given by H. Hubner. This
work was supported by the German Ministry of Research
and Technology (BMFT).
'e. B. Zarowin, 1. Electrochem. Soc. 130, 144 (1983).
2e. B. Zarowin,J. Vac. Sci. Techno!. A2, 1537 (1984).
.IM. J. Kushner, J. App!. Phys. 58. 4D24 (1985).
4D. A. Fisher, B. E. Thompson, and H. H. Sawin, Mat. Res. Soc. Symp.
Proc. 68, 231 (1986).
'B, E. Thompson and H. H. Sawin, J. App!. Phys. 63, 2241 (1988).
'J. I. Ulacia F. and J. P. McVittie, J. Appl. Phys. 65, 1484 (1989).
'J. Pelka, H. -CO Scheer, P. Holfmann, W. Hoppe, and Ch. Huth, Micro
electron. Eng. 9,503 (1989).
"W. Pilz, H. Hiibner, F. Heinrich, P. Holfmann, and M. Franosch, Micro
electron. Eng. 9, 491 (1989).
9J. Lorenz, J. Pelka, H. Ryssel, A. Sachs, A. Seidel, and M. Svoboda, IEEE
Trans. CAD, 4, 421 (1985).
,oJ. Pelka, K. P. Muller, and H. Mader, IEEE Trans. CAD, 7,154 (1988).
"D, Bohm, in Characteristics of Electrical Discharges in Magnetic Fields,
edited by A. Gulthrie and R. Waherling (McGraw-Hill, New York,
1949).
12K. -U. Riemann, Thesis, Ruhr-Universitiit Bochum, 1977.
uS. Chapman, Glow Discharge Processes (Wiley, New York, 1980).
14W. Pilz (private communication).
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1.456740.pdf | Excitation of chemical waves in a surface reaction by laserinduced thermal
desorption: CO oxidation on Pt(100)
T. Fink, R. Imbihl, and G. Ertl
Citation: The Journal of Chemical Physics 91, 5002 (1989); doi: 10.1063/1.456740
View online: http://dx.doi.org/10.1063/1.456740
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/91/8?ver=pdfcov
Published by the AIP Publishing
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:13Excitation of chemical waves in a surface reaction by laser-induced thermal
desorption: CO oxidation on Pt(100)
T. Fink, R. Imbihl, and G. Ertl
Fritz-Haber-Institut der Max-Planck-GesellschaJt, Faradayweg 4-6, D 1000 Berlin 33, West Germany
(Received 2 June 1989; accepted 26 June 1989)
If a pte 1(0) sample is kept at steady-state conditions of O2 and CO partial pressures and
temperature which are similar to those for the occurrence of autonomous temporal oscillations
in the rate of CO2 formation, then the surface will be largely covered by adsorbed CO which
inhibits oxygen adsorption and keeps the catalytic rate low. Irradiation of a small spot with a
high power laser pulse causes momentarily local thermal desorption of CO and creation of a
reaction front which propagates as a chemical wave across the surface area, as was monitored
by the excursion of the integral reaction rate and locally by means of a work function
(~oxygen coverage) probe placed at several mm distance from the spot of irradiation. The
velocity for wave propagation rises from about 2 mm/min at 480 K to 4 mm/min at 507 K and
is not noticeably dependent on the partial pressures. The mechanism is closely related to that
for self-sustained kinetic oscillations of this system and exhibits the typical features of trigger
waves: Coupling between autocatalytic reaction and diffusion, as well as the occurrence of a
refractory period during which the system is "dead," and of a threshold for the intensity of the
excitation.
I. INTRODUCTION
Spatial concentration variations in a reacting system
which propagate with time are called chemical waves. I They
are frequently a consequence of the nonlinear coupling be
tween reaction and diffusion under conditions far from equi
librium and may occur with systems exhibiting sustained
temporal oscillations or excitability. The latter describes the
effect that a small local perturbation of one of the control
parameters governing the rate of the reaction initiates a large
response of the reactivity of the system, followed by its re
turn to its initial steady state. Chemical waves were observed
as early as 19062 and were frequently considered as models
for nerve conduction, although their velocity is usually
many orders of magnitude smaller. Systematic investiga
tions of these effects were mainly concentrated on homoge
neous reactions in solution, viz., the famous Belousov-Zha
botinsky (BZ) reaction for which concentration differences
are easily made visible through changes in color. With a het
erogeneously catalyzed reaction occurring on a uniform
metal surface, monitoring of variations of adsorbate cover
ages, signalling the propagation of chemical waves, is less
straightforward and requires more elaborate probes. The
catalytic oxidation of CO on pte 1(0) under low-pressure,
isothermal conditions represents an oscillatory surface reac
tion which had been extensively investigated in the past few
years.3-6 The mechanism responsible for the occurrence of
temporal oscillations in the rate of CO2 formation is based on
the CO-induced 1 Xl<=! hex phase transformation of the
surface structure which is associated with a change in oxy
gen sticking coefficient and hence catalytic activity. A scan
ning LEED technique applied during sustained temporal
oscillations demonstrated that these structural transforma
tions propagate wavelike across the macroscopic surface
area.3,6 (See note added in proof. ) The present paper reports on the results of a study in
which chemical waves were triggered by external excitation,
based on the following idea: Under steady-state conditions
( Peo, Po" T), the adsorption of oxygen and hence the for
mation of CO2 is known to be inhibited if the CO coverage is
too high. If for such a situation the CO coverage is momen
tarily and locally reduced, this spot will be able to adsorb
oxygen and to initiate the formation of a reaction front
which propagates across the surface. Such "holes" in the CO
adlayer were created through local temperature rises by an
infrared pulse laser causing thermal desorption. The integral
response of the system was monitored through recording the
reaction rate by means of a quadrupole mass spectrometer,
while the spatial propagation of the perturbation was detect
ed by a small work function probe (monitoring the variation
in coverage) placed at some distance from the location of the
laser excitation. In this way not only the creation of chemical
waves in an excitable surface reaction could be demonstrat
ed, but also their parameters for existence as well as veloc
ities of propagation were determined. The experimental
findings can be consistently interpreted on the basis of the
previously developed mechanism for the occurrence of ki
netic oscillations with the same system.
II. EXPERIMENTAL
The experiments were performed in an ultrahigh vacu
um (UHV) chamber evacuated by a turbomolecular/ion
getter/titanium pump combination down to a base pressure
of 1 X 10-10 mbar. The system was equipped with LEED,
two quadrupole mass spectrometers (QMS) (one of them
differentially pumped by a 150 {'Is turbomolecular pump)
and a piezoelectri~ driven Kelvin probe for work function
measurements [Fig. 1 (a)]. The Pt(100) single crystalsam
pIe was of quadratic shape (7 mm X 7 mm) and had a thick-
5002 J. Chem. Phys. 91 (8), 15 October 1989 0021-9606/89/205002-09$02.10 © 1989 American jnstitute of Physics
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:13Fink, Imbihl, and Ertl: Chemical waves in a surface reaction 5003
0) b)
Pt(100) Single Crystal
QMS1
Kelvin Probe
'\/
d=3-5mm FIG. 1. Experimental setup used for
the ignition and detection of chemical
waves in the system Pt( lOO)/02/CO.
Nd-Glass
Laser
1062nm
15OI-Is
0.6-1.0J m--'1
I I
1: : I I
I I
I I
I ............ -~
L.-_+----' 70% Laser Mirror
Laser Head
100% Laser Mirror
He-Ne Laser
ness of 1 mm. Surface preparation was done in the usual way
by electrochemical polishing followed by cycles of heating in
10-6 mbar oxygen and argon ion sputtering. The crystal was
heated resistively through two Ta support wires spotwelded
to its upper and lower edges. The temperature was moni
tored by a NiiNiCr thermocouple and kept constant within
± 0.1 K by a feedback-stabilized regulation system. For in-
troducing the reactants CO and O2, a feedback-stabilized gas
inlet system was used, so that the pressure in the chamber
was kept constant to ± 0.1 %. The purity of the gases was
5.0 for O2 and 4.7 for CO (both Linde AG).
For the ignition of chemical waves, a pulsed neodymium
glass laser (A = 1062 nm, pulse duration 150 Its) with a
maximum output energy of 1 J/pulse was used. Focused to a
spot of about 1 mm,2 a maximum power density of 0.7 MW /
cmz could be achieved. Such a device had been previously
developed for rapid and local thermal desorption.7
Variation of the pulse energy revealed that a threshold
in power density of 0.4 MW /cmz exists below which no CO
desorption could be detected. Above 0.7 MW /cm2 visible
damages on the Pt( 100) surface were observed. From the
peak height of the QMS signal at m/ e = 28, one can calcu
late that each laser pulse desorbs about 1 % of the total num
ber of CO molecules adsorbed on the Pt ( 100) single crystal
surface. Momentary temperature rises to 920 K with 0.3
MW /cm2 and to 2000 K at 0.8 MW /cm2 power density were
estimated. 8
For the detection of chemical waves, the experimental
setup displayed in Figs. 1 (a) and 1 (b) was used. In order to
avoid reflection and hence desorption from the walls of the
URV chamber, the laser was directed at normal incidence to
the Pt( 100) surface. The ignition of chemical waves was followed by simultaneous measurements of the work func
tion and the reaction rate. The reaction rate, which in the
10-4 Torr region had to be monitored via a differentially
pumped mass spectrometer, reflects the integral behavior of
the crystal surface. The local response of the surface was
probed by a Kelvin probe at a distance of 3-5 mm from the
spot hit by the laser pulse (Fig. 1 b ). The propagation veloc
ity of the waves was then determined by dividing the distance
d between the laser spot and the Kelvin probe by the time
delay between the ignition of the laser pulse and the response
of the Kelvin probe.
III. RESULTS
The kind of experimental observations made in the pres
ent work is best illustrated by a typical example (Fig. 2). The
URV system is operated as a flow system in which balance
between gas inlet and pumping speed establishes constant
partial pressures for Oz (Po, = S.6X 10-5 mbar) and CO
(Peo = 7.2 X 10-6 mbar) , while the sample temperature is
kept fixed at T = 481 K. Under these conditions, the surface
is essentially covered by adsorbed CO which inhibits disso
ciative oxygen adsorption, and as a consequence the steady
state rate of CO2 formation (as monitored by the mass spec
trometer, upper curve of Fig. 2) is low. The relative work
function 11 ct>, as simultaneously monitored with the arrange
ment depicted in Fig. 1 (b), is plotted as the lower curve of
Fig. 2. At t = 0, a single laser pulse with about 0.5 MW /cm2
power density is fired and causes momentarily desorption of
CO within the range of the irradiated spot. The reaction rate
(which is an integral property of the whole surface area)
starts to increase without any noticeable delay, passes
through a maximum, and returns to the initial low level after
J. Chern. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:135004 Fink, Imbihl, and Ertl: Chemical waves in a surface reaction
Pt(100) ICO 102
T =481 K
P02 =5.6x1(f5mbar
Peo = 7.2 x1Cfmbar -Laser :;
.2 j I =0.47 MW/cm
N 0 I u L-I
-
~ 200
9-
cO 0
0 2 4 6 8 10 12 14 16
t (min)
FIG. 2. Response of the reaction rate and of the work function after starting
a chemical wave with a laser pulse on a Pt ( 100) surface initially covered by
CO. The geometry shown in Fig. 1 (b) with d = 3 mm was used for the
detection of the propagating reaction front.
about 15 min. The work function, on the other hand, which
is monitored for a small area (-4 mm2) about 3 mm away
from the spot of irradiation remains at first unaffected by the
laser pulse. Only about 1.5 min later it rises steeply by about
250 mV and decays slowly to its initial value which is
reached again after the same time interval as does the reac
tion rate. This is considered as a clear manifestation of a
propagating reaction front initiated by the laser pulse.
The steep and local temperature rise associated with the
laser pulse created a hole in the CO adlayer by thermal de
sorption which enables appreciable adsorption of O2, As a
consequence the reaction is locally triggered. The propagat
ing reaction front causes removal of the adjacent CO mole
cules and the highly reactive O-covered 1 X 1 phase left be
hind this front grows continuously and causes continuous
increase of the reaction rate. A switch of the state of the
Pt( 100) surface from COad saturation to Dad saturation is
associated with an increase of the work function by about
400 m V. 6 During kinetic oscillations the integral work func
tion which is sampled over the whole surface area had been
found to parallel the reaction rate, since both are proportion
al to the Dad coverage. In the present case, however, there
exists a 1.5 min delay between the onset of the rate increase
and the rise of the local work function as recorded 3 mm
away from the trigger zone. This means that the reaction
front propagates with a velocity of about 2 mm/min.
Under the applied conditions, the reactive state of the
surface with high 0 coverage behind the reaction front is,
however, not stable. After some time the surface returns to
its initial state with high CO coverage via the 1 X 1 +::t hex
structural transformation steps which also underly the
mechanism for oscillatory behavior. The observed effects of
excitability and spatial propagation of the excited state are
characteristic features of a "chemical wave."
Now we turn to more detailed analysis of the various co
N
1/1
1/1
~
"2 .2' U)
c .2 -a. ..
0
1/1
~ Loser
I ~ ~ ~
I ~
o as
tls1 1.0 Pt(100)!COsot
T =300K
0.65 MW/cm2
0.63MW/cm2
0.56 MW/cm2
0.43MW/c~
FIG. 3. Evolution of the m/e = 28 QMS signal following laser-induced
thermal desorption of CO with varying power density.
phenomena. Essentially two conditions have to be fulfilled in
order to cause wave ignition: The laser power density has to
be high enough in order to enable substantial CO desorption
and the steady-state conditions Peo, Po" and T have to be
properly adjusted.
If the latter parameters are chosen appropriately, it was
found that a minimum laser power density of about 0.4
MW /cm2 is needed to excite a chemical wave. This is due to
the fact that the temperature rise within the irradiated area
persists essentially only for about 100 f.Ls, 8 during which peri
od it has to become high enough to enable appreciable ther
mal desorption of CO. Due to the very high heating rate, the
peak for thermal desorption will be shifted to much higher
temperatures than with ordinary thermal desorption spec
troscopy (TDS). A series of CO desorption traces recorded
with the QMS following single laser shots with varying pow
er is reproduced in Fig. 3 and directly confirms the existence
of such a threshold in power density for thermal CO desorp
tion, in agreement with previous findings.7 For the excita
tion of chemical waves, the power density of the laser pulse
had to exceed the threshold for CO desorption. Therefore
the primary effect which triggers a reaction front has to be
the laser-induced desorption of CO.
The external parameters (Po" Peo, n for the excit
ability of chemical waves are close to those for the occur
rence of sustained temporal oscillations which had been de
termined previously. 5.6 These are typically in the 10 -5_10-4
mbar partial pressure range and at temperatures around
480-520 K. The search for conditions of excitability can be
rationalized by cyclic variation of one of the external param
eters giving rise to hysteresis phenomena of the type as re
produced in Fig. 4. Here, at fixed Peo and T, the O2 partial
pressure was continuously increased and decreased again
while the reaction rate and the work function change a4>
were simultaneously monitored. Both quantities exhibit pro-
J. Chem. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:13Fink, Imbihl, and Ertl: Chemical waves in a surface reaction 5005
pt(100) ICOI02
T =480K
pco=2.0x1O-5mbar ,
~ast cycle (5 min)
N o u ....
vZZZZZZZZZZZ2ZZZZZZZZZZZZZZZh FIG. 4. Hysteresis in the reaction rate and
the work function measured with Pco' T
being kept constant, while Po, was slowly
varied in a cycle. The shaded bar indicates
the existence region for oscillations at
T = 480 K as determined in Ref. 5. ,...,...--
:':""<-slow cycle (40 min)
200
~ fast cycle (5min) ......
~ 0
o 1
nounced hysteresis effects. In the upper branch the surface is
covered by oxygen to an appreciable extent, while the lower
branch is due to the existence of an CO adlayer which inhib
its oxygen adsorption and hence product formation. The oc
currence of such hysteresis effects is a consequence of the
mechanism of the catalytic CO oxidation over platinum met
als9 and is per se not responsible for temporal oscillations or
spatial wave excitability. The latter effect may, however, be
exploited by momentarily disturbing the system while it is in
the lower reaction branch. This may lead to an excursion to
the upper reaction branch, followed either by a return to the
lower branch (excitability) or by sustained oscillatory be
havior.
The shapes of the hysteresis loops are strongly in
fluenced by kinetic limitations. This is, e.g., reflected by the
narrowing of the loop width if the cycling time is reduced
from 40 min (full line in Fig. 4) to 5 min (broken line). It is
mainly the upper branch which is responsible for this effect,
due to its instability as a consequence of the 1 X 1-+ hex sur
face structural transformation.
In addition, it was observed that the reactivity of the
Pt ( 1(0) surface and its hysteresis behavior is strongly affect
ed by the conditions of sample pretreatment (annealing tem
perature, oxygen pressure, etc.) as well as by preceding ki
netic oscillations. This can be traced back to the strong
dependence of the oxygen sticking coefficient on the pres
ence of surface defects, which in turn are affected by anneal
ing as well as surface reaction. 10,11 Kinetic oscillations are
associated with periodic structural transformations which
require considerable mass transport of Pt surface atoms.
More specifically, the hysteresis loop is broadened if several
cycles are run without intermediate sample annealing. While
the low oxygen pressure boundary remained essentially 4 5
fixed, the boundary at high Po, moved to higher values. This
explains why the conditions for sustained oscillations
(marked also in Fig. 4) extend over a larger range of Po,
than the single hysteresis loop which was started from a well
annealed surface.
The conditions for wave excitability were most conve
niently found by keeping T and one of the partial pressures
fixed, while the other one was stepwise varied between laser
shots. This is illustrated by Fig. 5, in which experiment Po,
Laser I j j
I I I ~
o 2
3.413.313.2
x 10-5mbar CO 4 6
t(min) Pt(100)/COI02
T =478K
:-4 P02 =3.6x,() mbar
.-5 Pco=3.2x10 mbar
I = O.SO MW/cm2
8 10
FIG. 5. The procedure for finding the conditions where the ignition of a
chemical wave was possible by a laser pulse by stepwise decreasingpco. The
wiggles in the work function trace are solely due to electronic effects.
J. Chern. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:135006 Fink, Imbihl, and Ertl: Chemical waves in a surface reaction
and Twere kept fixed, while Peo was stepwise reduced until
at Pco = 3.2 X 10-5 mbar the laser pulse was able to excite a
chemical wave. However, even for the CO pressures above
the critical value, firing the laser caused a slight instanta
neous rise of the reaction rate (but not of the work function),
signaling ignition of the reaction within the range of the illu
minated area which soon relaxes back to the initial steady
state without macroscopic wave propagation. The instanta
neous response of the reaction rate to the laser pulse offered a
convenient means for differentiating from spontaneous exci
tation (probably triggered by surface defects).
The example shown in Fig. 5 differs from the data repro
duced in Fig. 2 in so far, as in the present case not a single
wave front, but oscillatory behavior continuing over a longer
period of time was initiated. The different shapes of the reo,
and.6.<I> traces are consequences of the mostly irregular char
acter of the oscillations on pte 1(0) due to restricted spatial
coupling between various parts of the surface area. Another
example, exhibiting damped oscillations, is reproduced in
Fig. 6. Most probably the region excited by the laser flash
now emanates several consecutive wavefronts with strongly
decaying amplitUde.
Finally a case will be presented in which propagation of
the wave is so strongly damped in space that it even does not
reach the work function probe. For the conditions underly
ing Fig. 7, the laser pulse causes the reaction rate to show the
typical behavior for an excited wave, but the signal of the
Kelvin probe placed at 3 mm distance remains unaffected at
the level of the CO-covered surface. One notices that with
this example the surface was in an oscillatory state (albeit
with small amplitude) of the rate prior to each of the two
pulses. It is therefore likely that the surface was still in a
"refractory state" at the time of external perturbation and
hence the strongly damped response.
The existence of a refractory state is a general property
of an excitable medium, which means that the system is in
sensitive to further stimulations during this period. Only
Pt(100)/COI02
T =480K
P02 =8.1 x1(r4mbar
Peo = 3.7 x1cPmbar
I = 0.53 MW Icm2 Laser
j
~ 200
>e
o
4 12 14 16
t[min)
FIG. 6. Excitation of a pulse train with decaying amplitUde as a chemical
wave is triggered by a laser pulse. after the refractory time has elapsed can the system be excit
ed again by another pulse. The existence of such a refractory
period for the present system is demonstrated by the data
presented in Fig. 8. Additional laser pulses, at intervals be
fore the initial excitation had decayed, were obviously ineffi
cient in stimulating any noticeable response of either the rate
or the work function. Only after returning to the initial
steady state could a chemical wave be ignited again by a laser
pulse. Detailed experiments revealed that it is indeed the
relaxation of the reaction rate rather than of the local work
function which determines the termination of the refractory
period. This becomes plausible on the basis of the following
considerations: Since the reaction front propagates by re
moval of a CO adlayer, it is necessary that such a coherent
adlayer exists on its way. This is only warranted if the reac
tion rate has again reached its minimum steady-state value,
while this is not necessarily the case if the local signal from
the work function probe is considered. Returning now to
Fig. 7, the existence of low-amplitude oscillations indicates
that the surface is not uniformly covered with a high cover
age CO adlayer. Instead there will also exist patches either in
the hex state or covered by oxygen which inhibit propaga
tion of the chemical wave.
In order to compare the external conditions for excit
ability of chemical waves with those for the existence of sus
tained kinetics oscillations, a systematic series of experi
ments was performed at varying Po, and Peo for fixed
T = 480 K. At this temperature, the existence region for
oscillations had been explored previously.5 The resulting
data are plotted in Fig. 9. As can be seen, the conditions for
the excitation of single-pulse waves are near the high Peo
boundary of the existence region for oscillations. In those
cases for which single-pulse excitation was found for condi
tions amidst the oscillatory region, triggering of self-sus
tained oscillations was most probably prevented by the pres-
:::i B
'" 0 u L-
200
>e
9-0 <I Laser Laser Pt(100)/COI02
I I T =478K
I I -4 I I P02 =3.5x1O mbar :f\ :/\.. ~ .n-5 ...rJ ~ """" Peo=2.95xlU mbar
I I I =0.53 MW/cm
I I
I I
I I
I I
~ t-
o 1 2 3 456
t[min)
FIG. 7. An example of limited spatial propagation of a chemical wave
("damped wave") after excitation with a laser pulse. The wiggles in the
work function trace are caused solely by electronic effects.
J. Chern. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:13Fink, Imbihl, and Ertl: Chemical waves in a surface reaction 5007
....... ::;
d -N 8 ....
~ 200
9-
<l 0
o Laser Laser
~ !
4 8 12 16
t [min]
ence of spurious contaminations. Otherwise, for conditions
inside the oscillatory regime, indeed multiple wavefronts
were initiated by the laser pulse (marked by triangles). The
low-pressure limit of the oscillatory region is determined by
the CO-induced hex -+ 1 X 1 structural transformation, for
which a critical CO coverage is requiredy,12 For the same
reason no excitation of propagating chemical waves was ob
served near this low pressure boundary. Beyond the high-
10
8
'i:
0 .0 E 6 ..,
b ~
S 4 a.
2
00 2 Pt(100)/CO/02
T=480K
• I(
Pt(100) -(1x1) + eOad
4 6 8 10
Pee [1Q-5mbarJ
FIG. 9. The relation between the existence region for oscillations as deter
mined in Ref. 5 for T = 480 K and the parameter space in which various
types of chemical waves could be observed after ignition with a laser pulse.
X: damped wire; .: single pulse wave; T: multiple pulse wave. 20 Pt(1OO) ICOI02
T =480K
Pea= 7.2 .1O~mbar
-5
~=5.6.10 mbar
I =0.47 MW/cm2
24 28 FIG. 8. An experiment demonstrating the
existence of a refractory period for the exci
tation of chemical waves on Pt(100).
pressure boundary, on the other hand, only strongly damped
waves could be excited because of too efficient blocking of
the adsorption sites by CO.
Quantitative measurements of the velocity of wave
......
:::i
~
N
f5
~ 200
~ 0
>' 200
..5
~ 0 Laser
1
o 4 T =480K
T =507K
8 Pt(100)/COI02
-6 pco=7.2 -10 mbar
-5 po2=5.6 "10 Inbar
I =0.5 MW/cm2
d =2.6mm
12
t [min] -5 pco=1.94"10 moor
-4 P02 =3.17-10 moor
I =0.6 MW I cm2
d =3.0mm
16
FIG. 10. A comparison showing the different propagation velocities of
chemical waves at T = 480 K and T = 507 K.
J. Chern. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:135008 Fink, Imbihl, and Ertl: Chemical waves in a surface reaction
propagation turned out to be reproducible only to ± 30%.
This scatter is probably due to the high sensitivity with re
spect to the surface defect structure, which may vary in spite
of identical pretreatment procedures. The propagation ve
locities at 480 K range from 1.4 to 2.8 mm/min without any
clearly discernible systematic dependence on the partial
pressures, although the latter were varied by more than an
order of magnitude. The average value of about 2 mm/min is
in agreement with the velocity of propagation of the surface
structural transformation during sustained oscillations as
monitored previously by a scanning LEED technique. 3
It turned out, however, that the temperature had a
much stronger influence on the wave propagation velocity.
By raising the temperature from 480 to 507 K, it increased by
about a factor of 2 from 2 to 4 mm/min. An example for 507
K is shown in Fig. 10. Unfortunately, no larger range of
temperatures was accessible for experimental reasons. Be
low 480 K no waves could be excited, probably because their
propagation velocity was so low that stable conditions could
not be maintained for long enough periods of time. Above
507 K, on the other hand, partial pressures above 10 - 3 mbar
would have been required.
IV. DISCUSSION
The excitation of chemical waves by local external per
turbations in the present system is obviously closely linked
with spatial self-organization of autonomous kinetic oscilla
tions. The mechanism of the latter had been explored in de
tail in previous work4,6 and will be briefly recapitulated as a
starting point for the present discussion.
Kinetic oscillations occur under conditions for which
(dissociative) oxygen adsorption is rate limiting and the sur
face in its 1 X I phase is largely covered by adsorbed CO
which keeps the reaction rate low. Oxygen may, however,
preferentially adsorb at defect sites and from there react with
neighboring adsorbed CO molecules. In this way empty ad
sorption sites on the reactive 1 X 1 phase are created which
may adsorb additional oxygen with high sticking probabili
ty. The reaction rate and the work function increase, and a
reaction front propagates across the surface as experimental
ly demonstrated by scanning LEEDY; The low CO cover
age on these active 1 X 1 patches, however, causes these to
become metastable and to slowly transform into the hex
phase. For the latter, the oxygen sticking coefficient is negli
gibly small and hence the reaction rate and the work func
tion decrease parallel to the extent of this structural transfor
mation. As a consequence of the decreasing oxygen
coverage, the consumption of adsorbed CO by the reaction
will also be reduced. The CO coverage increases beyond the
critical value for the hex ...... 1 X 1 transformation which then
rapidly takes place and terminates one oscillatory cycle.
The essential difference between the mechanism for
these autonomous oscillations and that for the excitation of
individual chemical waves consists in the mode of triggering
the first step of oxygen adsorption. For autonomous oscilla
tions, this may happen all the time at the surface defects,
while in the present experiments such a trigger zone was
created by local desorption of CO by means of the laser
pulse. The reaction front requires a coherent CO adlayer for propagation. This effect is the reason for the observed refrac
tory time in the single wave excitation which, on the other
hand, determines the temporal periodicity of the autono
mous oscillations.
Before continuing the discussion on wave excitation by
external perturbations, we will first focus our attention again
on the role of surface defects whose importance became
again manifested in the present study. Their importance for
autonomous oscillations became already evident in previous
scanning LEED experiments which showed that propagat
ing waves of the structural transformation usually emanated
from the regions of the sample edges with enhanced defect
density.3,6 Such defect sites with increased oxygen sticking
coefficient were also introduced into the model for numeri
cal simulation.4 In these calculations it turned out that
waves were then repeatedly emitted from "edge" into "bulk"
compartments giving rise to (integral) temporal oscilla
tions, while without these defects the surface would have
remained in its low reactivity steady state.
Since there always exist numerous surface defects, from
where-according to this simple concept-continuously lo
cal reaction fronts are expected to be created, one may ask
why larger domains of the dense (but metastable) CO ad
layer form at all and are not spontaneously dissolved. As this
obviously does not happen, there must exist presumably a
competition between nucleation of a reaction front and inhi
bition by CO adsorption. This will depend on the CO cover
age and hence on the set of external parameters (Po" Peo,
and T) in a way as schematically illustrated by Fig. 11 for the
case of fixed Po" T, and variable Pea. Below PI no CO is
lands can be formed even on a perfect surface since the equi
librium CO coverage (in a mere CO atmosphere) would be
too low in order to inhibit oxygen adsorption and reactive
removal. (This is the range before the maximum in the rate
vs Pea curve is reached.) For PI <Pea <P2' CO islands are
formed, but numerous reaction fronts are created at defects
and no macroscopic pattern formation nor oscillatory be-
'0
~
E " c o no CO-islands. I unstable I metostable I stable
Seo small CO-islands. eO-adlayer eO-adlayer I spontaneous I I I reaction fronts, I
I
I
~high defect concentration
'" I I .
.... low defect concentratoon
................ I
I
FIG. II. A schematic plot demonstrating the different stability regions ofa
CO adlayer in CO/02 atmosphere, where either spontaneous reaction
fronts will be observed ( PI <Pea <P2)' or a stable/metastable CO adlayer
will result (P> P2)' All three boundaries (PI,P2' andp3) will depend on the
defect concentration.
J. Chem. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:13Fink, Imbihl, and Ertl: Chemical waves in a surface reaction 5009
havior will be observed. With increasingpco, however, more
and more of these defect sites will lose their ability to eman
ate far-reaching reaction fronts and larger patches of the
metastable CO adlayer are formed which may be subject to
macroscopic pattern formation and temporal oscillations.
Beyond P3 even this possibility will cease and the CO adlayer
becomes stable. This is the region in which even creation of a
locally and temporarily active zone by laser desorption will
cause only excitation of strongly damped waves, as marked
in Fig. 9 beyond the high Peo limit for sustained oscillations.
It should be mentioned that reaction fronts might nucleate
even on completely perfect surfaces due to local CO concen
tration fluctuations creating adsorption sites for oxygen, but
this effect of homogeneous nucleation will certainly be negli
gible in the presence of surface imperfections which exhibit
per se a higher oxygen sticking probability.
A higher defect concentration will necessarily extend
the oscillatory region over a larger pressure range. Such de
fects will, e.g., be created by the hex;::t 1 X 1 transformations
which are associated with a 20% variation in surface atomic
density. These surplus atoms form new islands with 25-100
A average diameters, depending on temperature, as verified
by scanning tunneling microscopy and computer simula
tions.13 The change in surface structure explains why in Fig.
4 the oscillatory range (after repeated structural transfor
mations) extends over a broader pressure range than the
hysteresis loop for a single cycle.
The excitability of the surface will, however, still be de
termined by the presence of the metastable CO adlayer on
the smooth (100) terraces necessary for wave propagation;
but since CO close to the defect sites will be consumed by the
reaction, these will act as sinks and as a consequence the CO
concentration on the flat terraces will become reduced by
surface diffusion. This effect stresses the importance of cou
pling between reaction and diffusion.
Now we return to the excitation of chemical waves by
external perturbations which in the present case consist in
local desorption of CO by the laser pulse. In this way mo
mentarily the oxygen sticking coefficient is enhanced and a
reaction front propagates. This represents an autocatalytic
step, since the reactive removal of adsorbed CO creates new
bare sites. Propagation takes place through coupling of the
reaction Oad + COad -C02 between adjacent sites and sur
face diffusion of COad (which is the most mobile surface
species). Previous numerical treatments of the oscillatory
mechanism in terms of the solution of differential equa
tions,4 as well as by applying the cellular automation tech
nique,14 had demonstrated that this type of coupling can
indeed produce wavelike spatiotemporal patterns as ob
served experimentally. By using experimental values for the
various parameters (activation energies, diffusion, constant,
etc.), even a reasonable estimate for the velocity of propaga
tion resulted from such calculations.4 The observed phe
nomena fulfill clearly the criteria of trigger waves which are
governed by the coupling between reaction and diffusion, 1,15
while kinematic waves as the second main type do not in
volve mass transfer between different regions of the reacting
medium, but are essentially an illusion caused by different
temporal oscillatory behavior of adjacent compartments. 1,16 The principal mechanism underlying excitation and
wave propagation in the present system is illustrated sche
matically by Fig. 12. The reaction zone may either grow to a
limited size and then shrink again, or it may propagate
across the whole surface area. In this latter case, the system
will either return to the initial steady state after a single pas
sage, or multiple pulse waves and temporal oscillations will
evolve. To a first approximation the reaction zone should be
of circular shape which expands with constant velocity, so
that the reaction rate should increase quadratically in time.
As can be seen from Figs. 2 and 5, this is roughly fulfilled at
the very beginning, but then obviously geometric limitations
come into play.
The velocity of propagation v p of a chemical wave deter
mined by reaction/diffusion is generally of the form vp
:::::: ~ D· K with D being a diffusion constant and K being an
"effective" (pseudo-first-order) reaction rate constant.1,2
One might expect that K depends not only on temperature,
but also on the concentrations of the reacting species. With
damped
wave Laser pulse
-r-Pt (100) surface
~~-+--Kelvin probe
single pulse
wave o CO covered
surface
fi3 0 covered
surface
multiple pulse
wave
FIG. 12. A schematic plot of the various types of chemical waves which
could be observed after excitation with a laser pulse.
J. Chem. Phys., Vol. 91, No.8, 15 October 1989
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141.210.2.78 On: Mon, 24 Nov 2014 20:39:135010 Fink, Imbihl, and Ertl: Chemical waves in a surface reaction
the present system, however, no significant dependence on
the partial pressures ( P02 ' Peo ) was found. This is probably
du~ to the fact that the reaction front always propagates into
a dense CO adlayer whose actual composition is not much
affected by the partial pressures. The value of v p :::::: 2 mml
min at 480 K and at pressures < 10-4 mbar should be com
pared with that of vp ::::::60 mmlmin derived by Dath and
Dauchoe7 for the same reaction occurring with polycrystal
line Pt films in the 103 mbar pressure range. In this work
again, chemical waves were initiated by laser irradiation.
Their propagation was monitored through local changes of
the electric resistivity caused by heating of the sample
through the reaction. It is quite remarkable that only a factor
000 difference in the wave velocity was found for these quite
different systems which varied by more than six orders of
magnitude in pressure!
The observed increase of v p with temperature is, on the
other hand, not surprising and is to be expected because of
the temperature dependence of both D and K. In an investi
gation with the homogeneous Belousov-Zhabotinsky reac
tion, Wood and ROSS18 derived for vp an effective activation
energy of 34 kJ/mol, whereby vp increased by about a factor
of 2 when going from 285 to 298 K, while with the present
system between 480 and 507 K again about a factor of 2
increase was found.
It is most remarkable that the essential features of chem
ical trigger waves were already recognized in the first report
on this subject by Luther,2 who even presented the basic
formula for the velocity of propagation:
(i) The processes propagating in a homogeneous medi
um are autocatalytic. In our case this is the removal of the
dense, metastable CO adlayer.
(ii) There exists a threshold for the intensity of the per
turbation. This corresponds to the minimum power density
of the laser pulse to initiate CO desorption to a sufficient
extent.
(iii) It takes a certain time to renew the excitability.
This refractory period is demonstrated by Fig. 8.
v. CONCLUSIONS
It has been demonstrated that chemical waves can be
ignited in the catalytic oxidation of CO if the conditions are
held such that a metastable CO adlayer exists on the surface
which keeps the reaction rate low. If the inhibitive effect of
the CO adlayer on oxygen adsorption is locally removed
through laser-induced thermal desorption of CO, a reaction
front is created which propagates over macroscopic dis
tances, e.g., the whole surface area. After the passage of the
reaction front, the system returns to the initial state of a Co-covered surface via the mechanism of the hex ~ 1 X 1 phase
transition. The mechanistic steps of the chemical wave are
identical to those of autonomous kinetic oscillations if one
replaces the role of the laser pulse by defects where the reac
tion fronts can nucleate periodically. This is supported ex
perimentally, since the parameter space where chemical
waves could be ignited coincides almost with the existence
region for self-sustained oscillations. The features which are
characteristic for trigger waves and which could also be ob
served on Pt(lOO), such as a spatially advancing reaction
front and the existence of a refractory period, follow directly
from the proposed mechanism. Quantitative measurements
revealed only a weak dependence of the front velocity from
the partial pressure conditions, but a significant influence of
the temperature was found. So the front velocity increased
by a factor of 2 from 2 to 4 mmlmin as the temperature was
raised from 480 to 507 K.
Note added in proof Findings were confirmed very re
cently with strongly improved lateral resolution by using the
method of scanning photoemission microscopy. 19
ACKNOWLEDGMENT
Technical assistance and the preparation of the draw
ings and graphs by S. Wasle is gratefully acknowledged.
I (a) Oscillations and Travelling Waves in Chemical Systems, edited by R. J.
Field and H. Burger (Wiley, New York, 1984); (b) J. Ross, S. C. Miiller,
and C. Vidal, Science 240, 460 (1988).
2R. Luther, Z. Elektrochern. 12, 596 (1906). For a commented English
translation of the paper, see R. Arnold, K. Showalter, and J. Tyson, J.
Chern. Educ. 64, 740 (1987).
3M. P. Cox, G. Ertl, and R. Irnbihl, Phys. Rev. Lett. 54,1725 (1985).
4R. Irnbihl, M. P. Cox, G. Ertl, H. Miiller, and W. Brenig, J. Chern. Phys.
83, 1578 (1985).
SM. Eiswirth, R. J. Schwankner, and G. Ertl, Z. Phys. Chern. N. F. 144, 59
( 1985).
6R. Irnbihl, M. P. Cox, and G. Ertl, J. Chern. Phys. 84, 3519 (1986).
7G. Ertl and M. Neumann, Z. Naturforsch. Teil A 27,1607 (1972).
8(a) D. Burgess, Jr., P. C. Stair, and E. Weitz, J. Vac. Sci. Techno!. A 4,
1362 (1986); (b) J. Ready, J. App!. Phys. 36, 462 (1965).
9T. Engel and G. Ertl, Adv. Catalysis 28, 1 (1979).
lOP. R. Norton, K. Griffiths, and P. E. Bindner, Surf. Sci. 138, 125 (1984).
IIR. Irnbihl, Thesis, University of Munich, 1984.
12R. J. Behrn, P. A. Thiel, P. R. Norton, and G. Ertl, J. Chern. Phys. 78,
7437 (1983); 48, 7448 (1983).
13(a) E. Ritter, R. J. Behrn, G. Potschke, and J. Wintterlin, Surf. Sci. 181,
403 (1987); (b) A. E. Reynolds, D. Kaletta, R. J. Behrn, and G. Ertl,
Surf. Sci. 218, 452 ( 1989).
14p. Moller, K. Wetzl, M. Eiswirth, and G. Ertl, J. Chern. Phys. 85,5328
(1986).
IS(a) A. T. Winfree, Science 175, 634 (1972); (b) E. J. Reusser and R. J.
Field, J. Am. Chern. Soc. 101, 1063 (1979).
160. Ortoleva and J. Ross, J. Chern. Phys. 60, 5090 (1974).
17J._P. Dath and J. P. Dauchot, J. Catalysis 115, 593 (1989).
18p. M. Wood and J. Ross, J. Chern. Phys. 82,1924 (1985).
19H. A. Rotermund, S. Jakphith, A. von Oertzen, S. Kubala, and G. Ertl, J.
Chern. Phys. (in press).
J. Chem. Phys., Vol. 91, No.8, 15 October 1989
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1.1141004.pdf | Design of an ultrahighvacuum specimen environment for highresolution transmission
electron microscopy
M. L. McDonald, J. M. Gibson, and F. C. Unterwald
Citation: Review of Scientific Instruments 60, 700 (1989); doi: 10.1063/1.1141004
View online: http://dx.doi.org/10.1063/1.1141004
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/60/4?ver=pdfcov
Published by the AIP Publishing
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44Design of an ultrahigh",vacuum specimen environment for high-resolution
transmission electron microscopy
M. L McDonald, J. M. Gibson, and F. C. Unterwa!d
AT&T Bell Laboratories, Murrayllill, New Jersey 07974
(Received 6 July 1988; accepted for publication 4 January 1989)
A JEOL 200CX high-resolution transmission electron microscope with point-to-point resolution
of2.5 A has been modified to achieve an ultrahigh-vacuum specimen environment (~1O 97). In
situ heating and evaporation are provided in the specimen viewing position, where high resolution
can be maintained at temperatures exceeding 600 0c. aUf design employs complete differential
pumping of the specimen chamber and the use of a He-cooled cyroshield at the specimen for best
vacuum attainment. Our design philosophy permits the instruments to be used for a wide variety
of in situ experiments, including low-pressure ( < 10 ]7) gas reaction.
INTRODUCTION
The desire to image atomically clean surfaces has led to the
development of ultrahigh-vacuum (UHV) (~1O --9 Torr)
specimen environments in transmission electron micro
scopes (TEM). Reported here are modifications made to a
JEOL 200CX high-resolution (HR) TEM to obtain an ul
trahigh-vacuum specimen environment and associated in
situ cleaning and thin-film deposition capabilities. Capabili
ties designed into the UHV TEM are maintenance of high
resolution at high temperatures and UHY, and the ability to
study in situ epitaxial growth and low-pressure gas-reaction
studies.
Venablesl performed the first experiments with a UllY
environment in a scanning electron microscope. The first
instrument to achieve moderately high resolution and Uny
was a JEOL 100B modified by Takayanagi et aF In their
group a more recent advance has been an ultrahigh-resolu
tion 0.4 A) I-MeV ultrahigh vacuum machine,1 although
the resolution has proved difficult to maintain at UHV. Oth
er experiments along the lines of Takayanagi et aI's 100B
have been carried out by Wilson and Petroff.4 Pappa et al.'
have obtained moderately high although not atomic-level
resolution at excellent vacuum by the use of thin-film aper
tures. The only commercially available UHV instrument, at
this time, is the Vacuum Generators HB-5, which only re
cently became equipped with in situ specimen cleaning, etc.!>
However, because of relatively poor signal/noise and our
primary interest being phase-contrast high resolution, this
instrument was not considered suitable for our needs. Proj
ects currently underway by lEaL/Xerox! and Philips/Ga
tan/AS. U. R to achieve similar lJHY TEMs to that described
here have not yet provided results. In contrast, the instru
ment described here has provided the first published
HRTEM images of clean Si surfaces.'! These included the
first bright-field phase-contrast images of the Si (111) 7 X 7
surface reconstruction.
EXPERiMENT
A UHY sample atmosphere can be provided in an elec
tron microscope by several methods. These are outlined in
Table 1. The URY cell is a limited area usually provided by cryopumping. The whole sample area conversion can be pro
vided by differential pumping or thin-film windows. The
windows, while simplifying the design, greatly reduce the
resolution. The design described here uses differential
pumping. Other microscopes have been designed with the
whole instrument at UHV or with various modifications as
previously stated, but have yet to provide UHV and high
resolution at an acceptable level for surface atomic resolu
tion.
The features which make our design unique are the fol
lowing: ( 1) The resolution of the microscope is not reduced,
but is maintained at the original design of the manufacturer
( < 3.0 A). The actual resolution depends on the objective
lens pole piece in use. (2) The entire sample area from con
denser to objective lens is maintained at UHV, which allows
the complete characterization of the atmosphere to which
the sample is exposed, The latter is accomplished with a
quadrupole residual-gas analyzer (RGA).
To improve the vacuum in the sample chamber, the fol
lowing design modifications were made: (1) The sample
chamber was isolated from the manufacturer's vacuum sys
tem and differentially pumped. (2) Larger pumps, pumping
manifolds, and ports were used. (3) Improved vacuum seals
were used. (4) Materials which were not vacuum compati
ble were replaced or removed from the sample chamber. A
URV sample air lock is also to be included to accept samples
TABLE L Comparison of different type DHV TEMS.
Electron microscope
HRTEMUHV UEV manufacture
TEM DHV cell sample area with growth chamber
Poor resolution High resolution VGHB-5STEM
Poor stability Good stability Poor SIN
Vibrations HR to 800'C Max resolution 5 A
Vacuum unknown Vacuum known Excellent vacuum
Fixed system Flexible system Flexible system
Restricted area Unrestricted area Large growth chamber
Sample restricted SampJe unrestricted Max resolution 200 A
Simple construction Complex construction Complex construction
Minor system Extensive system LargeMBE
modifications modifications Chamber added
700 Rev. Sci. Instrum. 60 (4), April 1989 0034-6748/89/040700-08$01.30 !.i: 1989 American Institute of PhYSics 700
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44from atmosphere or from another UHV chamber by means
of a UHV transfer case. Figure 1 is a block diagram which
shows the design schematically. Solid lines indicate the com
pleted portions of the design. At this time the ambient base
vacuum in the sample area is 5 X 10--9 Torr even though
several single sliding elastomer O-ring seals have yet to be
replaced. Much better results are expected in the future. The
local vacuum around the sample is considerably improved
by the use of a liquid-He-cooled cryoshield. At this point it
has been necessary to provide heating and evaporation facili
ties in the viewing position because of the inadequate am
bient atmosphere at other positions for Si surface cleanli
ness. This problem should be overcome in the near future by
replacement of the elastomer seals and the use of more ultra
high-vacuum compatible materials in the sample area.
The unmodified sample area of the JEOL 200CX con
sists of two parts. The upper portion is the "sample
chamber" which houses the upper beam tilt and compensa
tion coils, the top-entry sample air lock, and cartridge ma
nipulator. The lower portion is the objective-lens yoke which
houses the top-entry stage, lower beam tilt coils, and the
objective-lens pole piece. Both of these sections are con
structed of soft iron, which is part of the microscope's elec
tromagnetic shielding and completes the necessary magnetic
circuits. Figure 2 shows the microscope before modification
and the components affected by the URV conversion. FIG, 2, JEOL 200 ex HRTEM before conversion showing affected compo
nents. A, Sample chamber; D, objective·lens yoke; C, sample-exchange rna·
nipulator; D, sample air lock; E and F, stage x-y and tilt drive feed-through;
and G, objective-lens aperture mechanism.
The upper part of the UHV sample area is shown in Fig.
3. This piece replaces the original sample chamber as sup
plied by the manufacturer and separates the condenser lens
and objective-lens yoke. Our design separates the sample
chamber into two parts as shown in Fig. 4. This allows the
upper-beam tilt and compensation coils to be removed from
the UHV area by use of differential pumping without reduc-ing the 4-in.-diam side ports which are used for pumping and
specimen exchange. Our design increases the height of the
chamber by 3.2 cm. The increased separation of condenser
and objective lenses is readily dealt with by adjustment of
lens and correction coil currents, and leads to negligible
change in microscope operation. Height change in the over
all instrument involved minor microscope pumping modifi-
-.---'~
UHV
PUMPS I
AUXILIARY
SAMPLE
PREP
CHAMBER
__________ .J
CHAMBER
RESIDUAL
GAS
ANALYSER r' LIQUID HELIUM:
TRANSFER I
SYSTEM , GATE
VAl.VE -"", U
____ I
• E BEAM
CONDEr,._so,'!!, LENSES
TILT COILS
-~-"--~, ~.~ ~~->
GAS LEAK
-10'7,. VALVE ,1,1 I ___ "OIFFE~~!L~ __ ~_M"ING \",,$ 1 O~I----1 T~U~~
UHV SAMPLE CHAMBER • ---~r;; l-r--
VALVE ,
I
ION GAIIGE /
i MIRROR • II 1-SAMPLE r .. - AIRLOCK I
~ -r '" .
PYROIIII::;::OWJ'+ll, "" -I . !
CRVOSHIELD" \ ~-EVAPORATOR: I
SAMPLE~ j,.-,_, .~,
10o-T"'200'K GAS CAPILLARY
------ ~--- ----~---
... DIFFERENTIAL PUMPING L _____ ,_,~ ____ , ~, ________ ---.J
1 --~~--!-- ----j
I UHV
TRANSFER
CHAMBER -10-7 ..
IMAGING LENSES
VIEWING SYSTEM
FIG. I. Block diagram of our UHV microscope conversion.
701 Rev. Scl.lnstrum., Vol. 60, No.4, April 1989 UHV specimen environment 701
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44FIG. 3. UHY sample chamber. A, UHY sample chamber; B, high-vacuum
coil chamber; C, two 4-in. ports; D, two 2-in. ports; E, four I-in. ports; F,
beam tilt and compensation-coil adjustment-screw ports; G, electrical feed
through ports; H, pumping and Aux ports; and I, ditTercntial pumping
plate.
cations shown in Fig. 5. In the photograph of the specimen
chamber (Fig. 3), the implementation of differential pump
ing with the condenser-lens region can be seen. A differential
pumping tube oflength 2 cm and diameter 2 mm is mounted
in the hole just visible in the plate at the top of the chamber.
The differential pumping plate isolates the chamber from the
condenser lens, and the upper-beam tilt and displacement
compensator coils. The only electron optical components
which are in the differentially pumped area are the lower
beam tilt coils and the objective-lens pole piece.
The relative softness of the iron used in construction of
the sample chamber prohibited the use of Cn gasketlknife
UHV SAMPLE CHAMBER CROSS SECTION
COIL CHAMBER FIG, 5. LJHY pumping modifications,
edge seals directly to the chamber. Adapters are used
between the sample chamber and eu gasket-knife edge
flanges of standard dimensions, permitting the use of com
mercially available URV hard ward such as gauges, electri
cal and mechanical feed-throughs, etc. The adapters are
sealed to the chamber by elastomer O-ring seals which are to
be replaced with Au-coated Al C-ring seals. This design also
allows the use of Au wire seals with only minor modifica
tions of the adapters. Dynamic seals which cannot be re-
&. COMPENSATION COILS
:;Z:~~~f,?:l~.l!lfFERENTIAL PUMPING
SAMPLE CHAMBER'
PUMPING PORT
702 Rev. SCi.lnstrum., Vol. 60, No.4, April 1989 PLATE/TUBE
UHV specimen environment FIG. 4. URY sample chamber cross sec
tion.
702
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44placed with bellows seals are being converted to double 0-
ring seals with differential pumping between the seals.
The lower part of the sample chamber comprises the
objective-lens yoke which completes the magnetic circuit to
the upper part of the objective-lens pole piece. This has not
been substantially modified as yet and thus comprises the
weakest link in the URV system. The objective aperture has
been replaced with a bellows type and the mechanical mo
tion feed-throughs for specimen translation have been simi
larly altered. Pumping in this region is effected through a 1-
in.-dram port directly impinging on the specimen position
and reconnected for the URV system. This is shown in the
schematic Figs. 6 and 7. A difficulty with attempts to obtain
UHV in the specimen position of any HRTEM is the low
pumping speeds associated with narrow pole-piece dimen
sions. It is no consolation that the pressure in this region is
equally difficult to measure. The nearest gauge to the speci
men is in the upper sample chamber shown in Fig. 8. The use
of a cryoshield may thus be essential at the specimen position
to obtain reliably good vacuum.
The cryoshield surrounds the specimen cartridge end
with a 2-mm-diam hole in the end for specimen viewing. It is
cooled by conduction over a 5-in. length of shielded !-in. Cu
braid and rod from a liquid-He-cooled finger (Air Products
"Heli-Tran") shown in Fig. 9 which is maintained at a tem
perature of 4.2 K. The cooling power is 8 W, and experi
ments suggest that the temperature of the cryoshield is in the
vicinity of 30 K. Studies of the Si(111) 7 X 7 surface recon
struction,9 which forms and is stable only under UHV condi
tions, for over 1 h indicate a much improved vacuum in the
specimen viewing area within the cryoshie1d. Differential pumping between the lower part of the
specimen area and the objective lens is achieved through the
narrow gap in the lower part of the objective-lens pole piece
and objective stigmator pipe. The pumping system for the
URV sample area is comprised of a combination LN2-cooled
sublimation pump with a nominal speed of 1000 ( lIs) for N 2
and a 200 LIS for N 2 diode ion pump from Thermionics Lab.
This pumping system is shown in Fig. 10. (The original
pumping system was a slightly smaller Varian combination
pump.) This pump is attached to a 6-in. tee which will be
utilized as a sample-preparation chamber in the future. The
6-in.-tee is attached to the 4-in. side port of the microscope
sample chamber via a 6-in. gate valve. All seals in this part of
the system are the Cu gasketlknife edge type and the con
struction is of 316 SS. The estimated conductance-limited
pumping seed at the sample chamber is 390 LIS and in the
specimen position (without cryoshield) is 25 LIS. These
compare with the off-the-shelf manufacturers values of -10
and -1 LIS, respectively.
The entire UHV pumping region can be baked at over
200 °C, and when the valve is closed its base pressure is
-1 X 10 10 7. The UHV preparation chamber is fitted with
a residual-gas analyzer (Inftcon model Quadrex 200) which
permits analysis of gases in both the pumping and specimen
regions. Microscope baking is limited by the presence of
cooling water in the objective lens and other volatile compo
nents to ~ 80°C.
For prepumping of the sample chamber, a 50-LIS
Balzers turbomolecular pump (TMP), shown in Fig. 11, is
fitted. This TMP is used during baking to remove contamin
ants from the system and will be used to pump the UHV
UHV AREA CROSS-SECTION
COil CHAMB~R
SAMPLE CHAMBeR
WiNDOW BEAM TILT 8,
--l-l~---t-COMPENSATION COILS
P'I'ROMET:Q E-ION GAUGE
llPPE H OoLJEC TIVE
lOWER OBJECTIVI: LENS PUMPING PORT 2" PORT
SAMPLE STAGE
-I ..... ;;;;;;;;;;;;:;;~c ART RID G E
SAMPLE;t---,!,!.!;----fT--OBJECTIVE AP RTLIRE
OBJECTIVE STiGMATOR /JJ
DIFFERENTIAL PUMPING TUBE OBJECTiVE POLE PIECE
FIG. 6. URY area vertical cross section.
703 Rev. ScI. (nstrum., Vol. 60, No.4, April 1989 UHV specimen environment 703
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:442001/s ION PUMP
10001/s Ti SUBLIMATION PUMP
r f1-j----L! .. -..
-1.. RGA
4-1.5" at 15 Ir=-~J
/
PORTS FOR SAMPLE PREP SAMPLE PREP CHAM3ER
FIG. 7. UHV area horizontal cross section.
FIG. 8. UHV sampk chamber ion gauge.
704 Rev. Sci. instrum., Vol. SO, No.4, April 1989 UHV PUMPING SCHEMA TIC
~_Il
~l '._-=1
__ .J HOUGHING IYOKE PUMPING MANIFOLD
TUHBO PUMP
MICROSCOPE SAMPLE CHAMBER
FIG. 9. "Heli-Tran" on microscope.
UHV specimen environment 704
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44FIG. 10. UHV pumps on microscope.
FIG. 11. TMP manifold on microscope.
705 Rev. Sci. Instrum., Vol. 60, No.4, AprEi 1989 specimen exchanger under construction. The microscope
can be operated with the sample chamber pumped by only
the TMP if UHV is not needed; however, with the TMP
running the resolution of the instrument is -10 A. The base
vacuum of the specimen chamber pumped with only the
TMP is 10· 6r), The URV exchange mechanism will allow
samples to be introduced from atmosphere or another UHV
chamber via a UHV transfer case pumped by a battery
powered ion pump. The exchange mechanism will also be
used to move samples from the viewing position to the sam
ple-preparation chamber. At present a modified specimen
exchange mechanism from a JEOL 100 B TEM is used pre
pumped by a rotary pump.
Another advantage of the differential pumping design is
the ability to raise the specimen area pressure (:::::: 10-17)
while maintaining an operational pressure in the gun
( < 10-(7). This allows gas-reaction studies or the growth of
ices when the cryostagelO is installed. The system is fitted
with a calibrated leak valve (Fig. 11) for the introduction of
gases.
The original goniometer stage and tilting specimen
holding cartridge were replaced with ones of our own design.
The new stage and cartridge follow the same basic design as
the original equipment. The cartridge and stage have a ta
pered design which provides easy alignment during speci
men exchange. A guide pin in the cartridge and a slot in the
stage insure proper rotational alignment. The cartridge is
held solid in the stage by three spring-loaded blades which fit
into a groove in the cartridge. The new stage has four electri
cal connections which can be utilized individually or in
pairs. Flexible multistranded wires with soft vacuum-com
patible fiberglass insulation are used for connection to the
UHV feed-throughs. These wires do not transfer vibrations
or restrict movement. The electrical connections to the car
tridge are made by means of four spring-loaded silver con
tacts. In the present configuration the electrical connections
are used in pairs, two for specimen heating and two for evap
oration. The specimen-holding cartridge is shown in Fig. 12.
The cartridge body is constructed of phosphor bronze and
has silver electrical contacts with ceramic insulation. Two of
the electrical connections are connected to the Mo specimen
supports. Spring loaded Ta clips hold the specimen on the
end of the supports. The cartridge does not permit specimen
tilting, but provides excellent stability during heating. For
surface studies specimen tilting is not essential because of the
insensitivity of diffraction from very thin objects to small
tilts. The design of the specimen cartridge emphasizes the
need for stability in HRTEM, i.e., drift and vibration rates of
less than 0.5 A s I. By direct resistive heating, the overall
heat load is minimized, which aids stability by reducing ther
mal expansion in the stage and pole piece. This design also
allows more rapid temperature change and stabilization
than oven-type heating. The biggest disadvantage to direct
resistive heating is in measuring specimen temperature.
Since most surface preparation and crystal growth involves
temperatures in excess of 500 ee, we overcome this problem
by pyrometry on the specimen using a mirror, indicated in
Fig. 6. Pyrometry reveals that specimens of nonuniform
thickness heat relatively uniformly since heat generation is
UHV specimen environment 705
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44HEATING/EVAPORATION CARTRIDGE
I'll HAMiliL. SUPPORT
h IAMlJtlll eLI
IAM""I
FIG. 12. Specimen heating/evaporation cartridge.
dominant in thicker areas with lower electrical resistance.
Temperatures in excess of the melting point of Si
( 1412 °C) can be easily attained with this cartridge, without
evidence of excessive drift associated with stage and pole"
piece heating. However, at temperatures above 800 °C for Si,
the specimen exhibits a pulselike instability at times, which
is believed to be a result of local melting at the contacts.
Spring-loaded Ta clip contacts are employed for convenient
specimen exchange and the problem may be removed by spot
welding of the sample to contacts. However, stability is suffi
cient at temperatures up to 600°C for HRTEM. For exam
ple, Fig. 13 shows a 200-ke V image of a SiC particle in the
( 110) direction at ~ 600°C. These particles form during the
cleaning procedure for Si surfaces.
An evaporator has been built into a specimen cartridge
for molecular-beam epitaxial growth of thin films. Two of
the electrical connections are used for this evaporator, which
is electrically isolated by ceramic insulators. Connection be
tween the silver contacts and the Ta filaments is made by
means ofMo posts. Good electrical contact is maintained by
a spring held in place by the body cap. The spring presses on
an insulator which holds the filament in solid contact with
the Mo post. Filaments can be changed any time the car
tridge is removed from the sample chamber without expos-
706 Rev. Sci. Instrum., Vol. 60, No.4, April 1989 FIG. 13. SiC (110) 200-kcV lattice image ,~600 0c.
ing the chamber to atmosphere. Figure 12 shows the car
tridge and the Ta filament shaped so that the electron beam
can propagate through the center. The material which is to
be deposited is evaporated onto only one side of the Ta fila
ment, which faces down and evaporates only onto the speci
men.
CONCLUSION
In conclusion we describe a design for modification of a
HRTEM for an UHY specimen environment. The current
implementation as shown in Fig. 14 has achieved successful
high-resolution imaging ( ~ 3 A )of a clean Si surface for the
first time. The versatile design now allows a variety of differ
ent experiments at pressures from < 10-1 Torr to :5 10 9
FIG. 14. JEOL 200CX TEM after conversion of sample area to UHV.
UHV specimen environment 706
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44Torr and at temperatures ranging from room temperature to
30 or 1700 K. Further development will continue to improve
and expand the capabilities of this thin unique instrument.
ACKNOWLEDGMENTS
Assistance in the design of the DHV sample chamber by
JEOL USA, Inc., in particular M. Naruse and the skilled
machining by the Murray Hill Development Shop, in partic
ular A. G. Insano, is acknowledged.
'1. A. Venables, Ultramicroscopy 7,81 (1981).
2K. Takayanagi, K. Vagi, K. Kobayashi, and G. Honjo, J. Phys. E 11, 441
(1978).
707 Rev. Sci. (nstrum., Vol. 60, No.4, April 1989 -'K, Takayanagi. Y. Tanishiro, M. Takahashi, and S. Takahashi (discus
siolls).
4R. J. Wilson and P. M. Petroft'. Rev. Sci. Instrum. 54.1534 (\983).
'II. Poppa, K. Heinenann. and A. G. Elliot. 1. Vae. Sci. Techno!. 8, 471
(1971) .
"I'. M. Petroff. C. H. Chen, and D. 1. Werder, Ultramicroscopy 17, lH5
(1985).
'F, A. Ponce, S. Suzki, H. Kobayashi, Y. Ishibashi, Y. Ishida, and T. Eto, in
Proceedings of the 44th Annual Meeiing EMSA, Albuquerque, NM,
1986, p. 606.
"I'. R. Swann, J.5. Joncs, O. L. Krivanek, D. J. Smith, J. A. Venables, and
J. M. Cowley, in Proceedings of the 45th Annual Meeting EMSA Balti
more, MD, 1987. p. 136.
9J. M. Gibson, M. L McDmmld, and F. C. linterwald, Phys. Rev. Lett. 55,
1765 (1985).
wJ. M. Gibson and M. L. McDonald, Ultramicroscopy 12. 219 (19R3).
UHV specimen environment 707
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130.113.76.6 On: Wed, 17 Dec 2014 20:11:44 |
1.577075.pdf | Auinduced reconstructions of the Si(111) surface
T. Hasegawa, K. Takata, S. Hosaka, and S. Hosoki
Citation: Journal of Vacuum Science & Technology A 8, 241 (1990); doi: 10.1116/1.577075
View online: http://dx.doi.org/10.1116/1.577075
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/8/1?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.160.4.77 On: Fri, 19 Dec 2014 01:06:55Au-induced reconstructions of the Si(111) surface
T. Hasegawa, K. Takata, S. Hosaka, and S. Hosoki
Central Research Laboratory, Hitachi Ltd., Kokubunji, Tokyo 185
(Received 10 July 1989; accepted 1 September 1989)
Au-adsorbed structures ( -1 ML) on the Si ( 111 ) surface are studied using a scanning tunneling
microscope. In the initial stage of deposition, locally Au atoms are adsorbed onto the SiC 111)
surface with a 5 X 5 periodicity. At lower coverage, images showing a 5 X 2 periodicity are
recorded, in which there are a dark line and two atomic rows running in the [Tal] direction in a
five times period. In each atomic row, atoms are arranged in a two times period along the row. At
higher coverage, images showing a .J3 x.J3 structure are also recorded. In these images, in
addition to the.J3 x.J3 periodicity, there is an undulation which is explained as a phase shift of the
.J3 x.J3 structure.
I. INTRODUCTION
Scanning tunneling microscopy (STM) has received much
attention as a method for observing surfaces with atomic
resolution since Binnig, Rohrer, Gerber, and Weibel first
reported it. I In recent years, metal adsorbed structures on
semiconductors have been observed by using STM. For ex
ample, observations of Si(111)-.J3Ga,2-3 Si(111 )-.,J3ln,4
Si (111) -.,f3Ag, 5.6 and Si (111 ) -5Cu 7 have been reported.
Si ( 111) -.,J3Au studies were reported by Salvan et al.8 and
Dumas et al. 9 It has been reported in a reflection high-energy
electron diffraction (RHEED) study that Au-induced
Si ( 111) surfaces show four types of reconstruction, 5 Xl,
5 X 2, .J3 x.,f3, and 6 X 6, depending on Au coverage and an
nealing temperature. 10 Structures of 5 X 1 or 5 X 2 have been
reported by low-energy electron diffraction (LEED), II ion
scattering spectroscopy (lSS),12.13 x_ray,14 and /-l
RHEED15 studies, and some models have been proposed.
The models have a common feature in that there are two
atomic rows of adsorbed Au atoms running in the [Tal]
direction in a five times period. Some.J3 X .,f3 and 6 X 6 struc
tures have been reported by Auger electron spectroscopy
(AES),18 reflection electron microscopy (REM),17 ISS18.19
and LEED20 studies and three types of models have been
proposed: the honeycomb model,18 the simple hexagonal
model,20 and the trimer model. 19 The STM study by Dumas
et al.9 supported the trimer model, while the STM study by
Sal van et al.8 supported the simple hexagonal model. This
paper reports STM study ofSi( 111 )-5 X2 Au and Si (111)
.,f3 X .,f3Au structures to present additional information
about Au adsorbed structures on Si (111) surfaces.
II. EXPERIMENT
Details about the scanning tunneling microscope used in
this study have been previously described. 21,22 The following
is a condensed description. An electrochemical etched tung
sten tip was used. The STM has an inchworm system for
coarse control of the tip position in order to choose an obser
vation area in a lOX 10 mm2 field. The tripod type scanner
has a maximum scanning area of 300 X 300 A 2 and the fastest
scanning speed is 4 ms/ scan (2 s/image). This required that
STM images are recorded by a video tape recorder. All im-ages in this report are reproduced from that video tape.
An As-doped SiC 111) wafer(2 X 18 X 0.4 mm3, 0.5 n cm)
was chemically etched before being carned into a specimen
chamber. Base pressure of the specimen chamber was
4x 10-8 Pa. The specimen was cleaned by flash heating to
about 12OO'C in the ultra-high vacuum chamber; the pres
sure was kept below 1.5 X 10 -7 Pa during this cleaning pro
cedure. This process produced a clear 7 X 7 STM image.
Au was deposited from a resistively heated tungsten wire
basket onto this clean Si (111) -7 X 7 surface which was an
nealed at about 7OO'C during Au deposition. The sample
temperature was measured by an optical pyrometer. After
deposition, the sample was annealed for a few minutes at the
same temperature. STM observation was performed after
the specimen cooled to room temperature. Actual Au cover
age could not be measured since there was no monitoring
system attached to the STM. The amount of adsorbed Au
was estimated by deposition time, after examining the corre
lation between thickness and deposition time in another
vacuum chamber.
III. RESULTS AND DISCUSSION
A.5X2
The initial stage of Au adsorption on the Si ( 111) surface
is shown in Fig.1. This image was taken with the sample
biased at -2V, and at a tunneling current of 0.3 nA. Some
~1.~J
~ffJ
FIG. 1. An image of a Au-adsorbed Sit 111 ) surface. Imaging area is about
130X 110 A2. Locally adsorbed Au atoms are arranged with a 5 X 5 period.
241 J. Vac. Sci. Technol. A 8 (1), JanlFeb 1990 0734-2101/90/010241-04$01.00 © 1990 American Vacuum Society 241
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.160.4.77 On: Fri, 19 Dec 2014 01:06:55242 Hasegawa et al.: Au-induced reconstructions of Si(111)
brighter protrusions, corresponding to adsorbed Au atoms,
are arranged locally with five times periods along the [110]
direction and the [011] direction. The corrugation heights
of these brighter protrusions were 1.8 A. A 5 X 5 unit cell is
shown in Fig. I. Although not clear in this image, there is a
structure under these adsorbed Au atoms. This sample had
two types of terraces: one a clean 7 X 7 terrace with few ad
sorbed Au atoms, and the other a terrace on which a part of
adsorbed Au atoms was arranged with a 5 X 5 period. The
7 X 7 terraces were clear and noise free, but somehow Au
adsorbed terraces were always noisy, as in Fig. I. This means
that residual gases are adsorbed selectively onto Au ad
sorbed surfaces, and they are seen as noise. It is yet uncertain
whether the electron trapping effect in the surface2•3 or not
being of adsorbed gases in fixed sites makes these noise.
Another Au adsorbed Si ( Ill) surface is shown in Fig. 2.
This image was taken with -2V sample bias and a tunnel
ing current of 0.3 nA. Brighter protrusions, whose corruga
tion heights are 1.8 A, correspond to adsorbed Au atoms, the
same as in Fig. 1, but in this image, a 5 X 5 arrangement of
adsorbed Au atoms is not seen. An interesting feature of this
image is the presence of dark lines running in the [101] di
rection. These lines have a five times period with respect to
the [011] direction, and each adsorbed Au atom is next to
and on the left side of each dark line. Thus, it can be said that
adsorbed Au atoms are also on lines along the [101] direc
tion which have a five times period with respect to the [011]
direction. There is also a noisy area to the right of these dark
lines. These noisy signals were always present in areas where
residual gases were adsorbed. From this phenomenon it can
be concluded that the area next to dark lines has a structural
attraction for gases to adsorb.
There is also a periodic structure among brighter protru
sions. The periodicity is shown in Fig. 2 as a rectangular unit
cell which is coincident with a 5 X 2 structure. There seem to
be a few atoms in the unit cell, but a detailed structure is not
clear in this image.
Au adsorbed Si (Ill) surfaces, with a five times period
with respect to the [110] direction, are shown in Fig. 3. In
these images, adsorbed Au atoms appear as brighter protru
sions and dark lines are indicated by arrows. In Fig. 3(a)
FIG. 2. An image showing dark lines and noisy lines along the [lOll direc
tion and whose periodicity is five times. Arrow heads indicate some protru·
sions arranged with two times period with respect to the [loll direction.
J. Vac. Sci. Technol. A, Vol. 8, No.1, Jan/Feb 1990 .../'
"....
../'
y
.,./'
il
/' a
~
b 1J
.,...
~~O]
[J911J 242
FIG. 3. Images of Au-induced 5X2 reconstruction ofSi(lll). There are
two atomic rows along the [011) direction in a five times period. (a) An
image with a step running in the [011] direction. (b) An image showing a
dimer-like structure in each atomic row.
there is an atomic step running in the [011] direction. In the
majority of cases, dark lines run parallel to a step line.
In Fig. 3(a) it is clear that there are two atomic rows
running in the [011] direction in a five times period. It ap
pears that in each atomic row there are atoms having a two
times period arrangement with respect to the [011] direc
tion. From this characteristic of the image, the periodic
structure ofa unit cell shown in Fig. 3(a) is derived and its
periodicity is worked out to be 5 X 2. Most of the atomic rows
had a two times period along the [011] direction, i.e., there is
one atom in each two times period. But in the row indicated
by arrow heads in Fig. 3(a), there seem to be two atoms in
each two times period, and it seems that those two atoms
form a dimer-like structure.
Atomic rows in which there is a dimer-like structure hav
ing a two times period with respect to the [011] direction are
shown in the image in Fig. 3(b). In this image, a unit cell is
also shown. It is more clear in Fig. 3(b) than in Fig. 3(a)
that two atomic rows in a five times period seem to be on
both sides of the dark lines, and there is no obvious corruga
tion in the wide area between two atomic rows. Therefore,
there may be only two atomic rows in the second layer under
the brighter protrusions.
In this study it was observed that steps running along the
two times periods (parallel to dark lines) were straight, but
steps running along the five times period were not straight.
The direction parallel to the two times period was always
coincident with longer step lines, as previously reported in
the,u-RHEED study. 15 In the early stage of adsorption, five
times structures were formed from the underside of steps.
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.160.4.77 On: Fri, 19 Dec 2014 01:06:55243 Hasegawa sf al.: Au-induced reconstructions of Si(111)
Because no diffraction pattern was taken, it is uncertain
whether the obtained STM images were of a complete 5 X 2
structure. In any case, obtained STM images had two inter
esting features. One was that adsorbed Au atoms were ar
ranged with a five times period. The other was that there was
a five times period structure under brighter protrusions, and
there were two atomic rows in a five times period. There are
two possible explanations for these features.
One explanation is that Au atoms are adsorbed on the
SiC 111) surface with a five times period. Substrate Si atoms
are then affected by these adsorbed Au atoms and recon
struct to a 5 X 2 structure. Therefore, two atomic rows in a
five times period are made of Si atoms.
The other explanation is that two atomic rows in a five
times period are made of Au atoms. Thus, adsorbed Au
atoms already form a 5 X 2 structure on the Si ( III ) 1 X 1
surface. Surplus Au atoms forming a 5 X 2 structure are on
top of the initial 5 X 2 structure, and are observed as brighter
protrusions.
The phenomenon that there are two atomic rows in a five
times period is the same as in models previously proposed by
other methods,12-14 if we assume the second explanation.
Those models, however, do not explain well the dark lines
and the noisy area next to the dark lines. A detailed analysis
will be carried out and reported elsewhere.
B . ../3x../3
Images of a Au-induced Si ( III ) surface are also shown in
Figs. 4(a) and 4(b) in which the amount of adsorbed Au
was larger than that in Figs. 1-3. Figure 4(a) is an image
taken with -2 V sample bias and Fig. 4(b) is an image
taken with - 4 V sample bias. These two images were taken
in nearly the same area. In these images, there are periodic
protrusions arranged hexagonally whose corrugation height
is about 0.5 A, and their periodicity is .J3 x.J3R 30°. A unit
cell is also shown in each image. An arrangement of protru
sions in these images agrees well with the simple hexagonal
model or the trimer model, but does not agree with the sim
ple honeycomb model. Dumas et al. suggested the trimer
model because of triangular protrusions in images they ob
tained. However, the protrusions in images present study
obtained do not seem to have a triangular shape, and instead
look like those in a Oa-induced or an In-induced .J3 recon
struction reported by Nogami, Park, and Quate.2,4 Metal
atoms on Si have difficulty in being resolved,5 therefore, in
analysis of the current images, it is difficult to decide which
is the correct model, the simple hexagonal model or the
trimer model.
In addition to this .J3 periodicity, there is an undulation
whose amplitude is about 0.5 A in Fig. 4(a). The undulation
was observed over the entire .J3 X .J3 area with - 2 V sample
bias. It disappeared in the image with - 4 V sample bias.
This means that the undulation was caused by electronic
structure of the surface, rather than by a geometrical undu
lation. In Fig. 4(a), the brighter area has a complete.J3 x.J3
arrangement and the darker area has some distortion in its
atomic arrangement. The phase of a .J3 X .J3 structure is also
shifted 1/3 X .J3a between area A and area B. This phase shift
J. Vac. Sci. Technol. A, Vol. 8, No.1, Jan/Feb 1990 243
b
-.l.,/3 a
• • tt b. O· • • • · A. • • • b· b· • • · . p • • • • • • • • • • • • • • • • • • • • • • B. ·d ·d • • • • • • • • .q ·0 ·d • • • • • • • • • • • • •
C
FIG. 4. Images of Au-induced .j3x.j3 reconstruction ofSi(111). (a) An
image taken with - 2 V sample bias. The brighter area has complete .j3
x.j3 structure and the darker area contains some distortion. A phase is
shifted .j3a/3 between areas A and B. (b) An image taken with - 4 V
sample bias. The undulation seen in (a) is not visible. (c) Schematic dia
gram of.j3 X .j3R 30' arrangement containing a phase shift between A and B.
can be explained by the arrangement shown in Fig. 4(c).
The darker area between A and B is a transition region and
the registry of adsorbed Au atoms is different from that of
the brighter area. Thus, this undulation is most likely caused
by a mismatch between adsorbed Au atoms and the sub
strate Si layer.
IV. CONCLUSIONS
Si (111 ) -5 X 2 STM images have been presented for the
first time. In the structures, Au atoms were adsorbed with a
five times period and two atomic rows in each five times
period. Also Si ( III ) -.J3 X .J3Au STM images were shown.
In these images, protrusions are arranged hexagonally with a
.J3 X .J3R 30° period, but it is uncertain whether each protru-
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 130.160.4.77 On: Fri, 19 Dec 2014 01:06:55244 Hasegawa et al: Au-induced reconstructions of 5/(111)
sion consists of one Au atom or three Au atoms. An undula
tion whose corrugation height is about 0.5 A is also seen in
the image taken with - 2 V sample bias. It is caused by a
mismatch between adsorbed Au atoms and the substrate Si
layer.
ACKNOWLEDGMENTS
The authors wish to thank Dr. H. Ohbayashi and Dr. T.
Komoda of Central Research Laboratory, Hitachi Ltd. for
their constant advice and encouragement. They also thank
Dr. M. Ichikawa of Central Research Laboratory, Hitachi
Ltd. for his helpful discussion.
IG. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett. 49, 57
(1982).
2J. Nogami, Sang-il Park, and C. F. Quate, Surf. Sci. 203, L631 (1988).
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Rev. Lett. 61, 2867 (1988).
4J. Nogami, Sang-il Park, and C. F. Quate, Phys. Rev. B 36,6221 (1987).
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SR. J. Willson and S. Chiang, Phys. Rev. Lett. 58, 369 (1987).
6E. J. van Loenen, J. E. Demuth, R. M. Tromp, and R. J. Hamers, Phys.
Rev. Lett. 58, 373 (1987).
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8F. Salvan, H. Fuchs, A. Baratoff, and G. Binnig, Surf. Sci. 162, 634
(1985).
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IIH. Lipson and K. E. Singer, J. Phys. C 7,12 (1974).
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1486 (1985).
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789 (1989).
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16 (1989).
23M. E. Weiland and R. H. Koch, AppJ. Phys. Lett. 48, 724 (1986).
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1.576372.pdf | Different response of atomic force microscopy and scanning tunneling
microscopy to charge density waves
E. Meyer, R. Wiesendanger, D. Anselmetti, H. R. Hidber, H.J. Güntherodt, F. Lévy, and H. Berger
Citation: Journal of Vacuum Science & Technology A 8, 495 (1990); doi: 10.1116/1.576372
View online: http://dx.doi.org/10.1116/1.576372
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Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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microscopy to charge density waves
E. Meyer, R. Wiesendanger, D. Anselmetti, H. R. Hidber, and H.-J. GOntherodt
University oj Basel, Department oj Physics, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
F. Levy and H. Berger
Institute oJ Applied Physics, EPFL, PHB-Ecublens, CH-JOJ5 Lausanne, Switzerland
(Received 10 July 1989; accepted 1 August 1989)
We have studied the transition metal dichalcogenides IT-TaSi and IT-TaSe2 exhibiting charge
density waves (CDW) at room temperature by scanning tunneling microscopy (STM) and
atomic force microscopy (AFM) with atomic resolution. STM images are dominated by the
charge density wave modulation, while the AFM operated with an applied loading in the range of
10-8_10-7 N responds only to the atomic surface structure. Several possible explanations for this
experimental result are discussed, including differences in what STM and AFM are sensitive to, as
well as a possible local pressure dependence of the CDW state.
I. INTRODUCTION
The investigation of charge density wave phenomena in sol
ids is still of considerable interest, particularly the dynamics
of charge density waves I and the possible close relationship
between the charge and spin density wave state and high Tc
superconductivity. Z The static structure oflow dimensional
materials exhibiting CDWs has been studied extensively in
the seventies by using x-ray, neutron, and electron diffrac
tion.3 These experimental techniques are sensitive to the
CDW formation in the bulk and reveal the superlattice
structures related to the periodic lattice distortion (PLD)
which is accompanied by the charge modulation of the con
duction electrons. Helium scattering as an extremely surface
sensitive technique first proved that CDWs propagate up to
the topmost layer of the crysta1.4,5 The intensity of the super
structure peaks, e.g., for 1 T -TaS2 at 80 K was found to be as
large as that of the main Bragg peaks indicating a strong
deformation of the surface. The CDW corrugation, which
was determined to be of the same order of magnitude as the
atomic corrugation, was attributed to both a displacement of
the i(;ms and a change in the ionic radii as a direct conse
quence of the local charge modulation at each metal ion.
Recently, scanning tunneling microscopy (STM)6 has
proved to be a powerful technique to study charge density
waves at surfaces in real space and on a local scale.7 In con
trast to the diffraction experiments, STM is directly sensitive
to the charge modulation of the conduction electrons,
whereas the small displacements of the ions due to the PLD
(typically of the order of 0.01 nm) are difficult to detect by
STM. The question which we want to address here is how the
atomic force microscope (AFM)8 responds to the charge
density wave state. This question is of interest from two
points of view: (1) Concerning the AFM technique, the in
vestigation of CDW systems may provide further insight
into the relationship between the electronic surface structure
and the force response. This will hopefully lead to a better
understanding of what AFM is sensitive to. (2) Concerning
the CDW state, it may be interesting to investigate a possible
local pressure dependence of the CDW state by using AFM. In Table I we summarize the information provided by the
different experimental techniques.
II. EXPERIMENTAL
Single crystals of the transition metal dichalcogenides 1 T
TaS2 and IT -TaSez have been chosen as samples since they
exhibit a charge density wave state at room temperature.
Freshly cleaved surfaces remain free of oxides even in air
within the time needed for the AFM and STM experiments
as checked independently by Auger electron spectroscopy.
The AFM instrument used for the investigation of the 1 T
TaXz (X = S, Se) single crystals has already been described
earlier.9 For the experiments reported here, we used Si02
cantilevers produced by microfabrication techniqueslO with
spring constants between 0.3 and 1.0 N/m. The deflection of
the cantilever while scanning the sample is monitored by
electron tunneling between the rear side of the cantilever and
a STM tip. Therefore by removing the cantilever, the instru
ment can work as a STM. The forces acting between the
probing tip and the sample in the AFM experiment can be
evaluated from Zt (zs) plots, where z, is the movement ofthe
tip and Zs is the movement of the sample both perpendicular
to the sample surface. This is discussed in detail in a forth
coming publication. II All AFM measurements reported
here have been performed with repulsive forces in the range
of 10-8_10-7 N.
In Figs. 1 (a) and 1 (b) we present an AFM overview im
age showing a 340 X 340 nm2 area on the IT -TaS2 surface.
Several terraces separated by steps of various heights (one
and three times the unit cell height) can be identified. A
similar morphology was also observed on the 1 T -TaSe2 sur
face as studied by AFM and STM. After zooming into the
terraces, atomic resolution could be obtained by using both
techniques. In Fig. 2 we present an AFM image of a 8 X 8
nmz surface area on IT -TaSe2 obtained in the variable de
flection mode of operation where the tunneling current flow
ing between the r~ar side of the lever and the STM tip is
digitized. The atomic lattice is clearly resolved, whereas a
495 J. Vac. Sci. Technol. A 8 (1), JanlFeb 1990 0734-2101/90/010495-05$01.00 © 1990 American Vacuum Society 495
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'fABLE I. Information about CDW systems provided by different experimental techniques.
Experimental Bulk Surface
technique sensitive sensitive
X-ray diffraction X
Neutron diffraction X
Electron diffraction X
He scattering X
STM X
AFM X
superlattice structure due to the CDW state is totally absent.
This experimental result was confirmed for other 1 T -TaX2
samples as well and was found to be independent of the ap
plied loading in the range of 1O-x and 10-7 N. The lattice
soA
(a)
(b) 1T-TaSe2
AFM
3
J. Vac. Sci. Technol. A, Vol. 8, No.1, Jan/Feb 1990 Superlattice
structure
detectable
X
X
X
X
X
? Sensitive
toPLD
X
X
X
X Sensitive to
charge mod. of
condo electrons
X
X
constant on the 1 T -TaSe2 surface was determined to be
0.35 ± 0.01 nm, in good agreement with the bulk value of
0.3477 nm. An atomic corrugation of 0.02-0.04 nm could be
estimated. The absence of a superlattice structure in Fig. 2
FIG. I. AFM imageofa 340X 340 nm2
surface area on IT -TaS2. Several steps
can be observed with step heights be
ing multiples of the unit cell height
(0.586 nm). (a) Line-scan representa
tion, (b) perspective view.
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implies that a possible existent CDW corrugation is at least
an order of magnitude smaller than the atomic corrugation,
i.e., smaller than ~0.005 nm.
STM measurements have been performed on the same sin
gle crystal shortly after the data acquisition of the AFM
image shown in Fig. 2 by just removing the cantilever. In
Fig. 3 we present a STM image of a 8 X 8 nmz surface area on
1 T -TaSez obtained by current imaging with a mean tunnel
ing current of 1= 1 nA and a sample bias voltage of
U = + 30 m V. The image is dominated by the m X m
superlattice due to the CDW state as reported earlier.1Z In
another series of STM measurements on IT -TaSez, the
CDW superlattice structure and the atomic lattice could be
imaged simultaneously as shown in Figs. 4 (a) and 4 (b). The
CDW corrugation in this constant current STM image is
~0.27 ± 0.03 nm, whereas the atomic corrugation is
~0.08 ± 0.01 nm. The sample bias voltage was higher (0.45
V) than for the STM image presented in Fig. 3. However, the
ability to resolve the atomic lattice in addition to the CDW
superlattice by STM is believed to depend more on the state
of the tip than on the tunneling parameters.
Finally, we present a STM image of a 12 X 12 nm z surface
area on IT-TaSe z (Fig. 5) demonstrating that the CDW
superlattice persists right up to a step.
III. DISCUSSION
The different response of AFM to the CDW state in com
parison to STM and He scattering is certainly remarkable.
At present, we can give only qualitative arguments for this
experimental result, whereas a profound understanding can
be obtained only by a well elaborated theory which is hope
fully motivated by the presentation of this work.
It is well known that CDW formation results from a Fer
mi surface instability leading to both a periodic lattice distor-
o.lA/div
16A/div
J. Vac. Sci. Technol. A, Vol. 8, No.1, Jan/Feb 1990 497
tion (PLD) and a spatial modulation of the density of states
near the Fermi level. The latter can be probed directly by
STM which is therefore a highly sensitive technique for
studying the CDW state although the PLD seems to be be
low the detection limit of present STMs. On the other hand,
AFM is believed to respond to the total charge density at the
sample surface and should therefore be less sensitive to the
CDW state. Thus we can understand qualitatively the differ
ent response ofSTM and AFM. However, there remains the
problem of understanding the different experimental results
in AFM and He scattering experiments.
It has been shown \3 that the He-surface interaction ener
gy is basically proportional to the substrate total electron
density at the He site. The He scattering potential and the
surface total electron density are therefore directly related.
Thus we expect the corrugations derived from He scattering
and AFM experiments to be comparable in size. The He
diffraction pattern usually can be satisfactorily explained in
terms of scattering from a rigid wall, whose corrugation is
described by a shape function z = b(R) having the periodic
ity of the surface lattice. For CDW systems one can write5
b(R) = bo(R) + bcow (R),
where bo(R) describes the atomic lattice and bCDW (R) the
deformation induced by the CDW state. From the He scat
tering experiments on 1 T -TaSz at 80 K,5 an atomic corruga
tion of 0.052 nm and a corrugation of 0.037 nm due to the
CDW superlattice are derived. Even if one is concerned with
the derivation of the absolute amount of corrugation from
the He diffraction experiment, the results clearly indicate
that the atomic and the CDW corrugation should be of the
same order of magnitUde. This is in strong contrast to the
AFM results and can not simply be explained by a reduction
of the order parameter at 300 K in comparison to 80 K since
this reduction is only of a small amount due to the high
transition temperature (~600 K) between the normal state
16A/div FIG. 2. AFM image of a 8 X 8 nm2
surface area on IT -TaSe2 obtained
in the variable deflection mode and
with a loading of3 X 10-" N. Thepe
riodicity of 0.35 ± 0.01 nm agrees
well with the atomic lattice constant
(0.3477 nm) of IT-TaSe2•
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lA/div
16A/div
and the CDW state for the IT-TaX2 compounds. There
might be several other explanations for the different re
sponse of AFM and He scattering to the CDW state. One
possible reason might be the influence of local applied pres
sure in the AFM experiment. It is well known that transi-
2A/div
(a)
lOA/div
(bl
J. Vac. ScI. Techno\. A, Vol. 8, No.1, Jan/Feb 1990 16A/div 498
FIG. 3. STM image of a 8 X 8 nm' surface
area on IT-TaSe, obtained in the current
imaging mode (I = InA, U = + 0.030 V).
The image was acquired shortly after that
shown in Fig. 2 by removing the cantilever.
The .,ff3 x.,ff3 superlattice due to the CDW
state is dominant.
tions between different CDW phases in transition metal di
chalcogenides are highly pressure sensitive since pressure
leads to significant changes in the band shape for the layer
compounds by reducing their two-dimensionality.'4 For
1 T -TaX2, the transition temperatures Ttrans between differ-
lOA/div FIG. 4. STM imageofa 3.3 X 3.9 nm' surface
area on IT -TaSe, obtained in the constant
current mode (/ = InA, U = + 0.450 V).
The CDW superlattice and the atomic lat
tice can be observed simultaneously. (a)
Line-scan representation, (b) perspective
view.
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5A/div
40A/div
ent CDW phases usually decrease with increasing uniform
applied pressure by an amount of IdTtrans /dpl-3-5
K/kbar. The nonobservation of the CDW state by AFM
could be explained if we assume that a reduction of the tran
sition temperatures, or in general a depression of the CDW
state, occurs when local pressure is applied such as in an
AFM experiment where pressures of -100 kbar can be esti
mated for reasonable values for the area of contact of -1
nm2 and a loading of 10 -8 N. A further reduction of the
applied loading would be highly desirable in order to investi
gate a possible local pressure dependence of the CDW state,
but this has led to experimental difficulties so far. Instead we
have performed tunneling experiments with a conducting
cantilever where the tunneling image clearly showed the
CDW superlattice. By varying the tunneling resistance be
tween 30 M!1 and 300 k!1, a force change of 10 -9 N could be
determined from the lever deflection. Although we cannot
determine the absolute value offorce by this method, we can
give a lower limit for the force of about 10-9 N.
Finally, frictional forces may also play an important role
for the imaging mechanism of 1 T -TaX2 by AFM and may
lead to differences between AFM and He scattering results.
IV. SUMMARY
We have presented the first atomic resolution studies of
the charge density wave systems 1 T -TaS2 and 1 T -TaSe2 by
AFM showing the absence of a CDW modulation for an
applied loading of 10-8_10-7 N in contrast to STM and He
scattering experiments. Possible reasons for this absence
have been discussed, including the influence oflocal applied
pressure in the AFM experiment. Other explanations may be
given such as possible differences in the surface potential
probed in AFM and He scattering experiments. This prob
lem is left open for future theoretical work.
J. Vac. Sci. Technol. A, Vol. 8, No.1, Jan/Feb 1990 40A/div
ACKNOWLEDGMENTS 499
FIG. 5. STM image of a 12X 12
nm2 surface area on 1 T -TaSe2
obtained in the constant current
mode (l = 1 nA, U = + 0.400
V). The CDW superlattice is
shown to persist right up to a
step.
We would like to thank R. Buser and N. De Rooij (lnsti
tut de Microtechnique, Neuchatel) for the production of
Si02 cantilevers), R. Schnyder and A. Tonin for technical
help, and T. Richmond for proofreading the manuscript.
Financial support from the Swiss National Science Founda
tion and the Kommission zur Forderung der wissenschaftli
chen Forschung is gratefully acknowledged.
'For a recent review, see G. Griiner, Rev. Mod. Phys. 60,1129 (1988).
2Shiyou Pei, N. J. Zaluzec, J. D. Jorgensen, B. Dabrowski, D. G. Hinks, A.
W. Mitchell, and D. R. Richards, Phys. Rev. B 39, 811 (1989).
'J. A. Wilson, F. J. DiSalvo, and S. Mahajan, Adv. Phys. 24, 117 (1975).
4G. Boato, P. Cantini, and R. Colella, Phys. Rev. Lett. 42, 1635 (1979).
'P. Cantini, G. Boato, and R. Colella, Physica B 99,59 (1980).
"G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett. 49,57
(1982) .
7See, for example, R. V. Coleman, B. Drake, P. K. Hansma, and G. Slough,
Phys. Rev. Lett. 55, 394 (1985); R. E. Thomson, U. Walter, E. Ganz, J.
Clarke, A. Zettl, P. Rauch, and F. J. DiSalvo, Phys. Rev. B 38, 10734
(1988); X.-L. Wu, P. Zhou, and Ch. M. Lieber, Phys. Rev. Lett. 61, 2604
(1988); x.-L. Wu and Ch. M. Lieber, Science 243, 1703 (1989).
"G. Binnig, C. F. Quate, and Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986).
"E. Meyer, H. Heinzelmann, P. Griitter, Th. Jung, Th. Weisskopf, H. R.
Hidber, R. Lapka, H. Rudin, and H.-J. Giintherodt, J. Microsc. 152, 269
(1988) .
lOT. R. Albrecht and C. F. Quate, J. Vac. Sci. Techno!. A 6,271 (1988).
"E. Meyer, D. Anselmetti, R. Wiesendanger, H.-J. Giintherodt, F. Levy,
and H. Berger, Europhys. Lett. 9, 695 (1989).
12c. G. Slough, W. W. McNairy, R. V. Coleman, B. Drake, and P. K.
Hansma, Phys. Rev. B 34, 994 (1986).
"N. Esbjerg and J. K. Nl'lrskov, Phys. Rev. Lett. 45,807 (1980).
14See, for example, D. R. P. Guy, A. M. Ghorayeb, S. C. Bayliss, and R. H.
Friend, in Proceedings of the International Conference on CDW in Solids,
Budapest, 1984, edited Gy Hutiray and J. Solyom (Springer, Berlin,
1985), p. 80; F. J. DiSalvo, R. G. Maines, and J. V. Waszczak, Solid State
Commum. 14,497 (1974).
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1.344024.pdf | Optical and electrochemical studies of passive film formation in amorphous NiCrPC
alloys
D. B. Hagan, B. W. Sloope, and V. A. Niculescu
Citation: Journal of Applied Physics 66, 3942 (1989); doi: 10.1063/1.344024
View online: http://dx.doi.org/10.1063/1.344024
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/66/8?ver=pdfcov
Published by the AIP Publishing
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Amorphous layer formation on a Ni65Cr15P16B4 alloy by irradiation of an intense pulsed ion beam
Appl. Phys. Lett. 67, 206 (1995); 10.1063/1.114668
Formation and diffusion behavior of intermixed and segregated amorphous layers in sputtered NiCr films on Si
J. Appl. Phys. 73, 4023 (1993); 10.1063/1.352869
Chemistry of corrosion layers on amorphous FeNiCrPB alloys
J. Vac. Sci. Technol. 18, 722 (1981); 10.1116/1.570935
Magnetic Properties of Amorphous NiP Alloys
AIP Conf. Proc. 18, 646 (1974); 10.1063/1.3141790
Electrical Resistivity and Magnetic Susceptibility of Amorphous Cr–Ni–Pt–P Alloys
J. Appl. Phys. 42, 5184 (1971); 10.1063/1.1659916
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
130.63.180.147 On: Mon, 24 Nov 2014 13:07:33to be caused by formation of an amorphous layer at grain
boundaries. Thermal annealing after ion irradiation causes
irreversible compositional changes near the film surface. 14,15
We do not observe such severe segregation in our films even
though our doses and annealing temperatures are relatively
high. White et al. 16 found that the damage due to the films is
greater when they are implanted below 90 K. Our films may
have escaped this level of damage because they were im
planted at room temperature.
The above results show that a Y -Ba-Cu-O film can be
compensated for a Cu deficiency by ion implantation with a
significant improvement in zero-resistance temperature.
Better results may result with closer approach to the stoi
choimetric composition.
This work was supported by the Assistant Secretary for
Conservation and Renewable Energy, Office of Energy Stor
age and Distribution, Energy Storage Division, of the U.S.
Department of Energy under Contract No. DE-AC03-
76SF00098. The authors wish to thank Professor A. Zettl for
the use of resistance measurement apparatus, and Dr. K. M.
Yu for performing the RBS analysis.
IG. J. Clark, A. D. Marwick, R. H. Koch, and R. B. Laibowitz, App!. Phys.
Lett. 51, 139 (1987).
2G. J. Clark. F. K. LeGoues, A. D. Marwick, R. B. Laibowitz, and R. Koch, App!. Phys. Lett. 51,1462 (1987).
'R. H. Koch, C. P. Umbach, G. J. Clark, P. Chaudari, andR. B. Laibowilz,
Appl. Phys. Lett. 51, 200 (1987).
4M. Nastasi, J. R. Tesmer. M. G. Hollander, J. F. Smith, and C. J. Magiore,
Appl. Phys. Lett. 52, 1729 (1988).
'K. Char, A. D. Kent, A. Kapitulnik, M. R. Beasley, and T. H. Geballe,
App\. Phys. Lett. 51, 1370 (1987).
"R. M. Silver, J. Talvacchio, and A. L. de Lozanne, App!. Phys. Lett. 51,
2149 (1987).
7T. Aida, T. Fukazawa, K. Takagi, and K. Miyauchi, Jpn. J. App!. Phys.
26, Ll489 (1987).
"N. Terada, H. fham, M. Jo, M. Himbayashi, Y. Kimura, K. Matsutani, K.
Hirata. E. Ohno, R. Sugise, and F. Kawashima, Jpn. J. Appl. Phys. 27,
L639 (1988).
'iR. L. Sandstrom, W. L. Gallagher, T. R. Dinger, R. H. Koch, R. B.
Laibowitz, A. W. Kleinsasser, R. J. Gambino, B. Bumble, and M. F. Chis
holm, Appl. Phys. Lett. 53, 444 (1988).
lOS. H. Liou, M. Hong, J. Kwo, B. A. Davidson, H. S. Chen, S. Nakahara, T.
Boone, and R. J. Felder, App!. Phys. Lett. 52, 1735 (1988).
"I. G. Brown, J. E. Galvin, and R. A. MacGill, App\. Phys. Lett. 47,358
(1985).
"I. G. Brown, J. E. Galvin, and B. Feinberg, J. AppL Phys. 63, 4889
( 1988).
I3J. Biersack and W. G. Eckstein, AprL Phys. A 34,73 (1984).
14J. C. McCallum, C. W. White, and L A. Boatner, Mater. Lett. 6, 374
(l98g).
"N. G. Stoetfel, W. A. Bonner, P. A. Morris, and B. J. Wilkens, Mater. Res.
Soc. Symp. Proc. 99, 507 (1988).
'''A. E. White, K. T. Short, D. C. Jacobson, J. M. Poate, R. C. Dynes, P. M.
Mankiewich, W. J. Skocpol, R. E. Howai'd, M. Anzlowar, K. W. Bald
win, A. F. J. Levi, J. R. Kwo, T. Hsieh, and M. Hong, Phys. Rev. B 37,
3755 (\ 988).
Optical and electrochemical studies of passive fUm formation
in amorphous Ni-Cr~P~C aUoys
D. B. Hagan, 8. W. Sioope, and V. A Niculescu
Physics Department, Virginia Commonwealth University, Richmond, Virginia 23284
(Received 25 February 1988; accepted for publication 15 May 1989)
The investigation of passivation of an amorphous Ni-14Cr-17P-O.5C alloy in IN Hz S04
through anodic polarization and near-normal optical reflectance is reported. It was found that
the aHoy passivates with a current density of 10-I A/m2 extending to 1.0 V with current
density dependent upon surface morphology. In the transpassive region under constant current
density conditions the reflectance of the film exhibits strong interference phenomena and
overall exponential decay in intensity. The behavior of the system in this region is described
with a single thin-film optical model consistent with the formation of a chromium phosphate
deposit layer which increases in thickness at a rate of7 nm/s at a 1.67 mV /s sweep rate.
Amorphous nickel based alloys have been of interest for
their mechanical, magnetic, and corrosion properties. i5 In
particular, they display enhanced corrosion resistance and
passivity relative to crystalline alloys of the same composi
tion and passivity enhancement as a function of increased
concentration of certain metals, notably Cr and Mo. In the
Ni-Cr-type alloys the corrosion enhancement is due to the
formation of a passivating chromium oxyhydroxide film.b•i tcntiodynamic polarization and monochromatic reflectance
measurements on an amorphous Ni-14Cr-17P-O.5C aHoy in
order to obtain real time information on passive film forma
tion and surface morphology of this system.
The samples used (Mfr. Id, No. MBF65, provided by
Allied Corporation Metglas Products DivisionS) have a
nominal composition Ni-14Cr-17P-O.5C. They are pro
duced in ribbons, 5.0 em wide and 35 J-tm thick, and cut for
use in circular form with a 0.79 cm2 exposed area. The sam- In this communication we performed simultaneous po-
3942 J. Appl. Phys. 66 (8),15 October 1989 0021-8979/89/203942-04$02.40 @ 1989 American Institute of Physics 3942
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130.63.180.147 On: Mon, 24 Nov 2014 13:07:33SPECTROPHOTOMETER Le '--c O-M-P-U-T-E-R-~ PLO HER I
FIG. l. The block diagram of the instrument.
pIes, as supplied, had one shiny side and the other side some
what duller in appearance. The foils were analyzed by x-ray
diffraction and found to be uniformly amorphous. This
study was carried out with a computer-controlled instru
ment which allows simultaneous in situ measurements of
near-normal monochromatic reflectance for wavelengths
from 300 to 800 nm and several electrochemical processes. A
block diagram of the instrument is shown in Fig.1. Electro
chemical measurements have been carried out with a three
electrode potentiostat and cell which is an expansion of the
instrument which has been reported9 with enhanced com
puter capabilities. A standard Agi Agel reference electrode
was used. The potentiodynamic polarization was performed
at a sweep rate of 1.67 m V Is through the corrosion potential
up to 1,8 V in IN H2S04, The current limit imposed on the
system is 13.65 mA or a current density of 171 A/m2 with
the 0.79 cm2 sample area. The optical reflectance was mea
sured through a bifurcated fiber optics tube fitted in the elec
trochemical cell in a manner suggested by Puyn and Park to
and by Reed and Hawkridge.11 '" :r E
""-
<>:
>-II ....
iii z w
0 0 .... z w
0:: a::
:> -I
u
'" c
-' -2
-3L-~~--~------~------~
-0.2 0.2 0.6 1.0 1.4 1.8
POTENT:AL (A~/AgCI)
FIG. 2.l'otentiodynamic polarization of the dull and shiny sides ofMBF65
in IN H, S04 at a sweep rate of 1.67 m V Is.
Polarization current density and reflectance as a func
tion of potential were measured for dull, shiny, and polished
samples of both surfaces for multiple samples of the MBF65
with very good repeatability. Surface structure and mor
phology were investigated by scanning electron microscopy
(SEM) and energy dispersive x-ray dot mapping. X-ray
photoemission spectroscopy (XPS) spectra from the surface
of treated samples was performed with a Physical Electron
ics 5100 ESCA system with MgKa excitation. Film thick
ness was measured on polished samples with a Reichert po
larizing interferometer in 590-nm light. An Abbe
refractometer was used to determine the index of refraction
of the electrolyte at a temperature of 20°C.
SEM studies of the sample surfaces showed convolu
tions on the dun side while the shiny side was smooth and
3 ~------~~-------'--------~---------r--------,1.0
N 2i-,
E i "-« 1
>-I ~ t:
(J) z w
0 0 f-
Z
I.IJ ac
a;
:;:) -I
(.)
Cl
0
...I -2 REFLECTANCE
CURRENT DENSITY 0.8
o n::
"-
0.6 n::
w
0.4
0.2 (.) FIG. 3. Potentiodynamic polarization ofMBF 65
~ in IN H, SO. at a sweep rate of 1.67 TIl V Is with
t; normalized reflectance.
w
.-l
!.l.
W c::
-3 L-__ J-____ L-______ ~~ ______ ~ ________ _L ________ ~ 0
-0.2 0.2 0.6 i.0 1.4 1.8
POTENTIAL (liS Ag/Agel)
3943 J. Appl. Phys., Vol. 66, No.8, 15 October 1989 Hagan, Sioope, and Niculescu 3943
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130.63.180.147 On: Mon, 24 Nov 2014 13:07:33TABLE I. Single thin-film model optical parameters used in Eq. (1).
nrn
Electrolyte 400
532
Film" 400
532
Metal alloy" 400
532
Values obtained from the following:
a Refractometry of fluid at I. 7 V.
b Fit to curve. n k f3
1.36" O.Olb 0.25'
1.36" D.Oj" 0.0S'
1.58 0.019
1.58 0.019
1.81 3.12
1.81 3.12
C Absorption spectroscopy 0.245 mm I at 400, 0.055 mm I at 532 nrn.
"Values are for Cr2P04 (Ref. 16).
e By ellipsometry.
featureless. Semiquantitative analysis showed no measura
ble variations in composition of the two sides to within ap
proximately 1 ,urn depth. This is in contrast to the results
reported for a related system of amorphous Fe-Ni-Cr-C, 12, Ll
where a gradient of composition for chromium was found
with higher chromium concentration on the dull side of the
film.
The potentiomdynamic polarization measurements
(Fig. 2) yielded different characteristics of current density
in the region near the corrosion potential depending upon
the surface morphology. The dull samples exhibited an ac
tive region while the shiny side passivated spontaneously.
Since the current density curves for the polished dull and the
shiny sides are identical, only the results for the shiny surface
are reported. 14 The current density curve (Fig. 2), exhibited the gen
eral chararacteristics as those reported by Kawashima,
Asami, and Hashimoto15 for Ni-9Cr-lSP-SB in 2N H2S04
with spontaneous passivation and a comparable current den
sity in the passive region.
According to Hashimoto and co-workers,7 amorphous
alloys containing certain amounts of Cr and P passivate by
forming a film consisting entirely of hydrated chromium ox
yhydroxide [CrOx (OH)} 2x·nH20). Kawashima et alY
reported that a Ni-lOCr-20P alloy in IN /HCI showed pref
erential dissolution of nickel accompanied by increased sur
face concentrations of chromium and phosphorus yielding
chromium oxyhydroxide and chromium phosphate films.
Our results are consistent with the above and can be under
stood in terms of the dissolution ofNi from the surface, and
with the film-forming properties of Cr and P in amorphous
alloy systems.7,IS.16
Near-normal reflectance measurements were made in
situ at wavelengths of 400, 532, and 700 nm during anodic
polarization from the corrosion potential up to 1.7 V. Typi
cal results are shown in Fig. 3. As current increases at about
].0 V the reflectance exhibits an overall decay in intensity
with fluctuations which become quite uniformly periodic in
the region of constant current. The relative decrease in inten
sity is strongly dependent upon wavelength. The interfero
metric measurements of film thickness on a polished surface
anodically swept to the point of the first reflectance maxi
mum in 400-nm light indicated the presence of a surface film
about 130 nm thick. The above results suggest that overall
increase in absorption and the periodic fluctuations of the
reflectance can be related to a film-forming process with the
film thickness increasing with time and potential.
A simple model was developed which consists of a single
dielectric thin film with a single reflection at each of the two
0.8.--------,,--------,,--------,---------,--------,
0.7
o 0.6
0:::
......
0:::
w u z « t; 0.4
w
.....J u..
~ 0.3
0.2 MODEL 532 nm VV\
DATA
0.1 ~ ________ L-______ ~~ ______ ~ ________ ~ ________ ~
1.45 1.50 1.55 1.60 t.65 1.70
POTENTIAL (vs Ag/Agel)
3944 J. Appl. Phys., Vol. 66, No.8, 15 October 1989 FIG. 4. Plot of normalized reflectance of the sur
face and the theoretical single-layer model for
MRF65 (Ni-14Cr-IOP-0.5C) in IN H2S04 at 400
and 500 nm.
Hagan, Sioope, and Niculescu 3944
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
130.63.180.147 On: Mon, 24 Nov 2014 13:07:33interfaces: electrolyte/film and film/metal. Using the data
in Table I, the relative intensity, or reflectance, as a function
of film thickness t2 can be expressed as follows:
1= [exp( -2f3t.) 1 [ifo + (1 -ifo)~ exp( ~ 2at2)
+ 2uout (1 -~ )exp( -at2)cos(o) ], (1)
where 0"0 and U1 are the reflection coefficients at normal
incidence of the top and lower interfaces (a function of their
respective indices of refraction n and absorption k), a is the
film absorption coefficient equal to 4iTkoA, and 8 is the two
beam phase difference which is a function of the film thick
ness, its index of refraction, and the phase change of the
reflection from each interface. The electrolyte was taken as
an optical medium with an index of absorption f3 and thick
ness t •. For the index of refraction of the film we took
n = 1.58, the value for chromium phosphate reported in the
transpassive region in a similar system (Ni-IOCr-lOP) by
Kawashima 7 in IN HCI. Values of nand k for the untreated
polished surface are in general agreement with the published
values for nickeL 17
For a comparison of the results calculated from the
model and the experimental data, the potential was related
to thickness by assuming the increase in thickness between
successive reflectance maxima as 1/2 a wavelength of the
monitoring light. This comparison is shown in Fig.4 for
wavelengths of 400 and 532 nm. At both wavelengths the
overall exponential decay of reflectance shows good agree
ment with the predicted absorption by both the film and the
electrolyte. At both 400 and 532 nm the film growth rate is
approximately 7 nm/s at a 1.67 m V Is sweep rate. IS
We wish to acknowledge the very helpful suggestions and assistance of Dr. F. M. Hawkridge, Dr. D. D. ShiHady,
Dr. L. M. Vallarino, and J. Scrivener of the Virginia Com
monwealth University Chemistry Department and Dr. A. S.
Arrott from Simon Fraser University.
IH. Beck and H. J. Guntherodt, Eds., Glassy Metals II (Springer, Berlin,
1983).
2K. Hashimoto, in Passivity of Metals and Semiconductors, edited by M.
Fremont (Elsevier, Amsterdam, 1983), p. 235.
JR. B. Dieg\e, N. R. Sorcllsen, T. Tsuru, and R. M. Latanision, in Trealise
of Materials and Technology, edited by J. C. Scully (Academic, New
York. 1983), p. 59.
·V. A. Niculescu, J. Hammcrberg, and B. W. Sloope, Bull. Am. Phys. Soc.
30,521 (1985).
'V. A. Niculescu and J. Hammerberg, J. Electrochem. Soc. 123, 3, (1985).
"K. Hashimoto, Suppl. Sci. Rep. Res. lnst. (Tohoku Univ.), A-28 (1980).
7 A. Kawashima, K. Asarni, and K. Hashimoto, Corras. Sci. 24, 807
(1984).
'Allied Corporation Metglas Products Department, 6 Eastrnans Road,
Parsippany, NJ 07054.
°D. B. Hagan, V.A. Niculescu, and J. Spivey, Rev. Sci. lnstrum. 58, 468
(1987); 56, 2339 (1987); J. Electrochem. Soc. 123, C375 (1985).
lOCo H. Pyun and S. M. Park, Anal. Chern. 58, 251 (1986).
liD. E. Reed and F. M. Hawkridge, Anal. Chern. 59, 2334 (1987).
I~I. Nagy, T. Tarnoczi, M. Hosso, and F. Pavlayak, Proceedings of the Sym
posium on Rapidly Quenc:hed Metals (1983), p. 223.
,,]. Farkas, L. Kiss, A. Lovlas, P. Kovac~, and E. Geczi, Proceedings of the
Symposium of Rapidly Quenched Metals (1983), p. 367.
14D, B. Hagan, Thesis, Virginia Commonwealth University, Richmond,
VA,1988.
!SA. Kawashima, K. Asarni, and K. Hashimoto, J. Non-eryst. Solids 70,69
(1985).
I<'Masumoto and K. Hashimoto, Ann. Rev. Mater. Sci. e8, 894 (1978).
I7R. W. Ditchburn, Light, 3rd ed. (Academic, New York, 1976), p. 261.
ISD. B. Hagan, V. A. Niculescu, and H. W. Sloope, Mater. Res. Bull. 23,
1009 (1988).
Preparation and characterization of the fined tetrahedral semiconductor
UZnP fUm on quartz
K. Kuriyama, T. Katoh, and S. Tsuji
College of Engineering and Research Center of Ion Beam Technology, Hosei University, Koganei,
Tokyo 184, Japan
(Received 30 March 1989; accepted for publication 12 June 1989)
A direct wide-gap semiconductor LiZnP has been prepared by rapid evaporation onto a quartz
substrate. Various characterization techniques such as x-ray analysis, Rutherford
backscattering analysis, and scanning electron microscopy were used to evaluate the quality of
the films. Single-phase films were obtained by annealing during 40 min at substrate
temperatures ranging from 400 to 440 ·C. The grains in the films were oriented preferentially
to the < 111) direction with increasing substrate temperature. The optical transmission of the
LiZnP films was observed to the short wavelength beyond an absorption edge ( -600 nm) of
bulk materials, This suggests the existence of the imperfection such as accumulated impurities
at grain boundaries.
Recently, Wood, Zunger, and de Grootl have discussed
the susceptibility of zinc-blende semiconductors to band
structure modification by the insertion of small atoms at
their tetrahedral interstitial sites. Their electronic structure calculation has predicted that LiZnP [viewed as a zinc
blende-like (ZnP) -lattice partially filled with He-like Li +
interstitials] is a novel type of direct-gap semiconductor, not
encountered in any cubic III-V material. Among cubic III-
3945 J. Appl. Phys. 66 (8), 15 October 1989 0021-8979/89/203945-03$02.40 (1;) 1989 American Institute of Physics 3945
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130.63.180.147 On: Mon, 24 Nov 2014 13:07:33 |
1.343369.pdf | Ferroelectricferroelastic properties of K3Fe5F1 5 and the phase transition at 490
K
J. Ravez, S. C. Abrahams, and R. de Pape
Citation: Journal of Applied Physics 65, 3987 (1989); doi: 10.1063/1.343369
View online: http://dx.doi.org/10.1063/1.343369
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/10?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Phase transition dependence on composition in ferroelectric–ferroelastic K3−x Fe5F1 5 for 0≤x≤0.20
J. Appl. Phys. 67, 2681 (1990); 10.1063/1.345485
Mössbauer study of Fe2 +/Fe3 + order–disorder and electron delocalization in K3Fe5F1 5 at the 490K
phase transition
J. Appl. Phys. 67, 430 (1990); 10.1063/1.345219
Ferroelectric–ferroelastic Tb2(MoO4)3 crystal structure temperature dependence from 298 K through the
transition at 436 K to the antiferroelectric–paraelastic phase at 523 K
J. Chem. Phys. 72, 4278 (1980); 10.1063/1.439720
Variable frequency SAW resonators on ferroelectricferroelastics
Appl. Phys. Lett. 32, 129 (1978); 10.1063/1.89971
Domain wall dynamics in ferroelectric/ferroelastic molybdates
J. Appl. Phys. 46, 1068 (1975); 10.1063/1.322212
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141.210.2.78 On: Wed, 26 Nov 2014 07:15:31Ferroelectric-ferroelastic properti,es of K3FeSF1S and the phase
transition at 490 K
J. Ravez
Laboratoire de Chimie du Solide du CNRS, Uniuersite de Bordeaux L 351 cours de fa Liberation,
33405 Tafence Cedex, France
S. C. Abrahamss)
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
R. de Pape
Laboratoire desjiuorures, Universite du Maine, 72017 Le Mans, France
(Received 1 November 1988; accepted for publication 30 January 1989)
K3FesF IS has previously been predicted to be both ferroelectric and ferroelastic, with a phase
transition at 535 K, on ,the basis of the atomic coordinates given in Acta Crystallogr. Sect. B
29; 1654 (1973). Subsequently, the dielectric permittivity has been found to reach a maximum
at 495 ( 10) K as the dielectric loss undergoes a change in slope, characteristic offerroelectric
behavior. Furthermore, the heat capacity exhibits a A-type anomaly at 490( 10) K, with a
corresponding entropy change of M = 5.5 (2) J mol-I K -I. The entropy change at the phase
transition calculated from the predicted change in structure is 5.42 J mol-I K -I. Ferroelastic
domains present at room temperature disappear sharply on heating above 490( 10) K, as
K3FesFIs transforms from orthorhombic to tetragonal symmetry, and reappear on cooling
below 480( 10) K. The ferroelectric-ferroelastic properties in the orthorhombic phase are
shown to be fully coupled.
INTRODUCTION
Ferroelectric behavior has now been reported in six
structurally different families of inorganic fluorides, repre
sented by (NH4hBeF4,1,2 BaMnF4,3-S Li(N2Hs)BeF4•6
SrAIFs,7,8 Pb3(TiF6)2,9 and BaSGa3FI9'1O The phase transi
tion temperature in these fluorides varies widely with mate
rial, ranging from 176 K for (NH4)2BeF4 to 1070 K for
BaSGa3F 19' In the case of BaMnF 4, the crystal melts at a
lower temperature than that expected for the transition to a
higher-symmetry phase.
Structural criteria for predicting ferroelectricity in inor
ganic crystals have recently been developed. II The criteria
also allow an estimate to be made of the corresponding tem
perature at which the transition to the higher-symmetry
phase takes place. Preparatory to undertaking a systematic
examination of the atomic coordinates of all materials in
each of the polar point groups reported in the Inorganic
Crystal Structure Database, 12 an analysis was made in 1987
of the structural data listed therein for space group Pba2.
Ferroelectricity was thereby predicted in seven new inorgan
ic materials.13 Confirmation of the prediction made for
Na13Nb3S094 has now been presented.14 Experimental re
sults confirming the second of these predictions, for
K3FesF IS' is given below.
ATOMIC DISPLACEMENT BASIS FOR
FERROELECTRICITY AND FERROELASTICITY IN
K3Fe5F15
K3FesF 15 is reported to crystallize in the polar space
group Pba2, with a = 12.750(2), b = 12.637(2),
c = 3.986(2) A and two formulas in the unit cell at room
temperature. 15 The atomic arrangement exhibits a deforma-
a) Present address: Institut fiir Kristallographie der Universitiit Tiibingen,
Charlottenstr. 33, 0-7400 Tiibingen, Federal RepUblic of Germany: tion of the tetragonal tungsten bronze structure as found, for
example, in ferroelectric Ba3 TiNb40 15 (Ref. 16) and is com
parable to the orthorhombic distortion reported in ferroelec
tric Bax Sr2,5 _ x Nbs015.17 The xyz atomic coordinates 15 of
K3Fe5F 15 are presented in Table 1. Also given in Table I is a
related set of Xly'ZI coordinates for which the sense of the
polar c axis is reversed. Differences between the two sets of
coordinates lead to the atomic displacements ~ = x -'-x',
Lly = y -y', and Llz = z -Z'. The largest Llx or Lly displace
ment [for F(7) and F(8)] is 0.011 A, the largest Llz dis
placement [for F (5) and F ( 6)] is 0.638 A; the common Llz
displacement for Fe(2) and Fe(3) is 0.327 A.
The relationship between the two sets of coordinates
may be expressed as xyz = jixz + Ll, where Ll is the vector
sum Llx + Lly + Llz. Additional normal symmetry relation
ships used in deriving X'y'ZI values in Table I are the equiv
alence between xyz and xyz; ! -x, ! + y, z; and! + x, ! -y,
z. The primary coordinate relationship may also be ex
pressed in terms of the unit cell transformation:
abc = bac + Ll. (1)
It should be noted in Eq. (1) that the a axis is replaced by the
transposed b axis together with a change in sense, the b axis is
simply replaced by the transposed a axis, while the polar c
axis is reversed in sense.
The transformation in Eq. (1) may be interpreted as
showing that the a and b axes are ferroelastically inter
changed as the polar axis direction is reversed ferroelectri
cally, since the displacement Ll/2 is less than 0.32 A for all
atoms. II Considering the Fe-F bonds as the strongest and
least ionic in this crystal, the ferroelectric-paraelectric phase
transition temperature may be predicted by means of the
largest displacement required for an Fe atom to return to the
paraelectric m~rror plane at z =!, i.e., a displacement of
Llz/2 = 0.163 A, from the relationship, 18
3987 J, Appl. Phys, 65 (10), 15 May 1989 0021-8979/89/103987-04$02.40 © 1989 American Institute of Physics 3987
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141.210.2.78 On: Wed, 26 Nov 2014 07:15:31TABLE I. Atomic coordinates for K,FesF IS with reversed spontaneous polarization and reoriented spontaneous strain at room temperature.
Atom x :y z x' y' z'
K(1) 0 0 0 0 0 0
K(2) 0.1729(9) 0.6729(9) 0.008(11 ) 0.1729 0.6729" -0.008
Fe(1) 0 ! 0.501(9) 0 !a 0.499
Fe(2) 0.0763(4) 0.2135(4) 0.541(7) 0.0763 . 0.2136b 0.459
Fe(3) 0.7864(4) 0.0763(4) 0.541 (7) 0.7865 0.0763b 0.459
F(1) 0 ! 0.030(61) 0 ! -0.030
F(2) 0.2785(14) 0.7783(14) 0.549(19) 0.2783 0.7785" 0.451
F(3) 0.0734 ( 18) 0.2067(18) 0.041(23) 0.0734 0.2065c -0.043
F(4) 0.7935(17) 0.0734(18) 0.043(22) 0.7933 0.0734c -0.041
F(5) 0.3502(14) . 0.0065(13) 0.580( 12) 0.3497 0.0066c 0.420
F(6) 0.9934(13) 0.3497(14) 0.580( 12) 0.9935 0.3502c. 0.420
F(7) 0.1372(15) 0.0728 ( 14) 0.527(18) 0.1374 0.0719c 0.471
F(8) 0.9281(14) 0.1374(15) . 0.529( 18) 0.9272 0.1372c 0.473
"x' = ! -y, y' = ! + x, since xyz and ! + x, ! -y, z are equivalent positions in Pba2, and the sign of y in x' = ! -y is reversed.
bFe(2) and Fe(3) exchange identity,
CF(3) and F(4); F(5) and F(6); and F(7) and F(8) exchange identity.
(2)
in which .5Y is a force constant, k is Boltzmann's constant
and .5Y /2k=2.0X 104 K A. -z. The predicted transition
temperature Tc is hence 535 K from Eq. (2).
It may be noted'that Eq. (1) could be replaced by
abc::;::: bac + il'
followed, at a different temperature, by
bac = bac + il".
Such a two-step phase transition (or, alternatively,
abc = abc + il' followed by abc = bac + il") wcnIld be
readily detectable calorimetrically. As demonstrated below,
K3FesF IS exhibits a single-phase transition at 490 K, hence
Eq. (1) is indeed applicable with its requirement that the
ferroelectricity and ferroelasticity in K3FesF IS be fully cou
pled.
PREPARATION AND CRYSTAL GROWTH
Poly crystalline K3FesF IS was prepared by the method
of de Pape, 19 in which stoichiometric quantities ofKF, FeFz, .
and FeF3 are allowed to react at 1000 K under dry argon in a
sealed gold tube, thereafter maintaining this temperature for
15 h. The resulting microcrystalline product is dark brown
in color. Extending the length of heat treatment at 1000 K to
15 d promotes grain growth, leading to maximum dimen
sions for the single crystals thereby produced in this process
ofO.2XO.2XO.l mm. .
CRYSTAL DATA
K3Fe5FI5 crystallizes in the orthorhombic systemlS
with space group and lattice constants at room temperature
as given above. The measured density of 3.49(2) g cm-3
compares well with the calculated value of 3.52 g cm-3 for
two formulas in the unit cell. The spontaneous strain as giv
enzo byes = (a -b)/(a + b) == 4.45X 10-3. The coercive
stress E\2 required to rotate es by 90· could not be measured
quantitatively on the small crystals grown by the present
method.
3988 J. Appl. Phys., Vol. 65, No.1 0, 15 May 1989 OPTICAL STUDY
Examination of several single crystals in a Leitz Ortho
lux II Pol model polarizing microscope reveals the presence
of characteristic 90· ferroelastic domain patterns. On heat
ing the crystals, under flowing dry helium, the domains dis
appear sharply above 490( 10) K and reappear on cooling
below 480 ( 10) K. Crystals viewed. along the c-axis direction
become optically isotropic above Tc.
CALORIMETRIC STUDY
The heat capacity of K3FesF 15 was measured repeated
ly, on samples weighing 550-900mg, between 300 and 750 K
in a differential fluxmeter calorimeter. In initial measure
ments, each sample was encapSUlated in a gold tube sealed
under dry argon and placed within the alumina sample hold
er. Setting the microcrystalline sample directly within the
alumina holder under dry argon was later found to improve
the accuracy in measuring ilB. The specific heat undergoes a
A-type anomaly at 490( 10) K as shown in Fig. 1, with en
thalpy change ilB = 2700( 100) J mol-I and 'entropy
change ilS = 5.5(2) J mol-I K-I at Tc-
--" -;
'0 e
3
\.,)<>.
<l 100
50
450 500
TEMPERATURE (K) 550
FIG. I. Thermal dependence of the heat capacity ofK,FesF ls between 430
and 560 K.
Ravez, Abrahams, and de Pape 3988
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141.210.2.78 On: Wed, 26 Nov 2014 07:15:31DIELECTRIC PERMITTIVITY
The relative dielectric permittivity €; = Cx/Co, where
Co is the capacitance of the empty cell and Cx is the capaci
tance of the cell and sample, was measured under dry helium
at 102, 103, and 104 Hz as a function of temperature. Ceramic
samples were prepared by heating K3FesF 15 microcrystals,
in the form of I-mm-thick, 8-mm-diam disks, under a pres
sure of 10 kN cm-2 in sealed gold tubes under dry argon and
holding the temperature at 940 K for 1 h. Gold electrodes
were deposited on both disk faces by cathodic sputtering.
The resulting thermal dependence of the permittivity is
shown in Fig. 2.
The dielectric permittivity exhibits a sharp maximum at
495 ( 10) K in addition to a major change in the slope of the
dielectric loss at a temperature about 30 K below Tc. At 102,
103, and 104 Hz, respectively, the dielectric loss tan {j is
about 0.2,0.05, and 0.01 at 295 K rising rapidly to about 1.0,
0.4, and 0.1 at 455 K. Above 475 K, tan {j rises sharply and
nearly linearly to about 440, 80, and 11 at 575 K. Both di
electric anomalies are characteristic of a ferroelectric-para
electric phase transition. The dispersion of about 10 K ob
served in the permittivity maximum over the measured
frequency range is suggestive of dielectric relaxation. Strong
dispersion is characteristic of relaxor ferroelectrics.21.22
300
250
-'-III
>-
~ 200
i= I-
~
II::
W a.
u 150 g
w
15
w >
~ 100
w
II::
50
300 400 500
TEMPERATURE (K)
FIG. 2. Thermal dependence of the relative dielectric permittivity (E;) on
heating KJFeSF IS ceramic specimens between 300 and 550 K. Measure
ments at 102 Hz are represented by diamonds, at 10' Hz by squares, and at
104 Hz by circles.
3989 J. Appl. Phys., Vol. 65, No. 10, 15 May 1989 RESISTIVITY THERMAL DEPENDENCE
The possibility of a resistivity anomaly at Tc caused by
the expected disordering of the Fe2+ and Fe3+ ions above
the phase transition, see below, led to a series of resistivity
measurements with a Wayne-Kerr model B905 RLCbridge
made on gold-electroded disks under dry helium, at frequen
cies of 102, 103, and 104 Hz as a function of temperature. The
results are presented in Fig. 3. An inflection at about 490 K is
clearly discemable at each of the measured frequencies. The
dispersion at T < Tc is again characteristic of relaxor ferro
electrics.
FERROELECTRIC-FERROELASTIC PHASE
TRANSITION AT 490 K
K3FesF 15 is the first known fluoride to cr~stallize in a
distorted tetragonal tungsten bronze structure that possesses
the characteristic ferroelectric and ferroelastic attributes of.
this family. All atomic positions in Table I are within 0.25 A
of the corresponding posItIOns in ferroelectric
Ba3 TiNb401S.16 The origin offerroelectricity in the tungsten
bronzes is generally associated with the displacement of
atoms that form the strongest and least ionic bonds from the
centers of their oxygen atom octahedra. The dipoles that are
thereby produced in each octahedron are usually aligned in
the same sense and add to give a macroscopic spontaneous
polarization.
Simultaneous ferroelectricity and ferroelasticity in dis
torted tetragonal tungsten bronzes is well known, as in the
case ~fBa2+xNat_xNbsOls (Ref. 23) or Pb2KNbs015.24
The two properties are decoupled in the former and partially
coupled in the latter material. Replacing oxygen by fluorine
generally reduces Tc strongly; thus, in the case of
Ba2 _ x Nat + x NbS01S _ x F x' for example, substitution of 0
by one F atom per unit cell resulting in one F per 59 0 atoms
reduces Tc to about 225 K.2S It has indeed been found that
Tc is less than 300 K in all tetragonal tungsten bronzes inves-
tigated for which the ratio F/O;;;d/15.2s .
1O·L...,3:-:!O:=O---4:;-;oo;;;----::-:50~O,.----~600
TEMPERATURE (K)
FIG. 3. Thermal dependence of the resistivity in KJFesF" between JOOand
575 K. Measurements at 104 Hz are represented by diamonds, at IOJ liz by
squares, and at 102 Hz by circles.
Ravez, Abrahams, and de Pape 3989
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141.210.2.78 On: Wed, 26 Nov 2014 07:15:31It is hence of considerable interest to find a pure fluoride
with a distorted tetragonal tungsten bronze structure and
the moderately high value of Tc = 490 K, since this observa
tion demonstrates that the sharp decrease in Tc found on
replacing oxygen by fluorine cannot be due primarily to the
relatively high ionicity of the metal-fluorine bond.
The unit cell of K3FesF 15. contains 46 atoms. Above 490
K each atom has a unique disposition along the c axis either
at z = 0 or ! whereas on cooling through the pha·se transition
all atoms but K( 1) (see Table I) become displaced in one of
two possible directions, corresponding to an entropy change
of R In(88/46) = 5.39 J mol-I K-I, if all Fe atoms are re
garded as equivalent. However, the chemical formula
K3FesF 15 requires the presence of both Fe2+ and Fe3+ ions
for electrical neutrality. Examination of the orthorhombic
atomic arrangement at room temperature as given in Table I
leads to the inference that the twofold Fe( 1) site in space
group Pba2 is occupied only by Fe2+, whereas the fourfold
Fe(2) site contains Fe2+ ions and the independent fourfold
Fe( 3) site contains Fe3+ ions or vice versa. The disappear
ance of the domain pattern present below the phase transi
tion temperature, on heating through Tc' suggests a change
in symmetry from point group mm2 to 41mmm with the
twofold symmetry axis in the orthorhombic phase replaced
above Te by a fourfold axis; the most likely choice of space
group in the high-temperature phase is P 4lmbm. In this case
the phase transition at 490 K must be accompanied by a
disordered arrangement of Fe2 + and Fe3+ ions at the result
ing 8 ( j) position, with atomic coordinates for these two ions
close to 0.0763, 0.2136, ! above Te. The gain in number of
distinguishable orientations by either ion from 4 below to 8
above the phase transition, together with the ferroelectric
paraelectric configurational gain, corresponds to a total in
crease in entropy of R In(96/50) = 5A2 J mol-I K-I, in
excellent agreement with the experimental value of 5.5(2)
J mol-I K-I.
The inflection in resistivity at Te is entirely consistent
with a change from order to disorder among the Fe2+, Fe3+
ions at the transition. The Fe2+ IFe3+ order-disorder that
would hence accompany the ferroelectric-ferroelastic phase
transition is similarly expected to result both in magnetic
3990 J. Appl. Phys., Vol. 65, No. 10, 15 May 1989 susceptibility and Mossbauer effect anomalies at 490 K: ap
propriate measurements are in progress.
ACKNOWLEDGMENTS
I t is a pleasure to thank A. Simon, A. M. Mercier, and L.
Rabardel for their preparation and characterization assis
tance.
IR. Pepinsky and F. Jona, Phys. Rev. lOS, 344 (1957).
2M. Iizumi and K. Gesi, Solid State Commun. 22, 37 (1977).
3M. Eibschiitz, H. J. Guggenheim, S. H. Wemple,l. Camlibel, and M. Di
Domenico, Phys. Lett. A 29, 409 (1969).
4H; G. von Schnering and P. Bleckman, Naturwissenschaften 55, 342
(1968).
5E. T. Keve, S. C. Abrahams, and J. L. Bernstein, J. Chern. Phys. 51, 4928
( 1969).
6J._M. Palau and L. Lassabatere, C. R. Acad. Sci. Ser. B 273,714 (1971).
7S. C. Abrahams, J. Ravez, A. Simon, and J. P. Chaminade, J. AppJ. Phys.
52,4740 (1981).
8J. Ravez, S. C. Abrahams, J. P. Chaminade, A. Simon, J. Grannec, and P.
Hagenmuller, Ferroe1ectrics 38, 773 (1981).
9S. C. Abrahams, J. Ravez, S. Canouet, J. Grannec, and G. M. Loiacono, J.
AppJ. Phys. 55, 3056 (1984).
IOJ. Ravez, S. Arquis, J. Grannec, A. Simon, and S. C. Abrahams, J. AppJ.
Phys. 62, 4299 (1987).
"s. C. Abrahams, Acta Crystallogr. Sect. B 44,585 (1988).
12See F. H. Allen, G. Bergerhoff, and R. Sievers, Eds., Crystallographic Da
tabases (International Union of Crystallography, Chester, England,
1987).
13S. C. Abrahams, Acta Crystallogr. Sect. B (in press).
14S. C. Abrahams, C. D. Brandle, G. W. Berkstresser, H. M. O'Bryan, H. E.
Bair, and P. K. Gallagher, J. Appl. Phys. 65,1797 (1989).
15 A.-M. Hardy, A. Hardy, and G. Ferey, Acta Crystallogr. Sect. B 29, 1654
(1973).
16p. B. Jamieson and S. C. Abrahams, Acta Crystallogr. Sect. B 24, 984
( 1968).
17p. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, J. Chern. Phys. 48,
5048 (1968).
18S. C. Abrahams, S. K. Kurtz, and P. B. Jamieson, Phys. Rev. 172, 551
(1968). .
19R. de Pape, C. R. Acad. Sci. 260,4527 (1965).
2OS. C. Abrahams, Mater. Res. Bull. 6, 881 (1971).
21L. E. Cross, Ferroelectrics 76,241 (1987).
22A. Huanosta and A. R. West, J. AppJ. Phys. 61, 5386 (1987).
23p. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, J. Chern. Phys. 50,
4352 (1969).
24J. Ravez and B. Elouadi, Mater. Res. Bull. 10, 1249 (1975).
25J. Ravez, Rev. Chim. Min. 23, 460 (1986).
Ravez, Abrahams, and de Pape 3990
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1.343203.pdf | Liquid junctions for characterization of electronic materials. I. The potential distribution
at the Si/methanol interface
M. C. A. Fantini, WuMian Shen, Micha Tomkiewicz, and J. P. Gambino
Citation: Journal of Applied Physics 65, 4884 (1989); doi: 10.1063/1.343203
View online: http://dx.doi.org/10.1063/1.343203
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/12?ver=pdfcov
Published by the AIP Publishing
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:43Liquid junctions for characterization of eiectronic materia~s. t The potentia~
distribution at the SUmethano~ interface
M. c. A. Fantini, Wu-Mian Shen, and Micha Tomkiewicz
Department of Physics. Brooklyn College. CUNY, Brooklyn. New York 112JO
J. P. Gambino
IBM East Fishkill. Hopewell Junction. New York 12533
(Received 1 November 1988; accepted for publication 3 February 1989)
Photoelectrochemical cells consisting of n-type < lOO)-Si wafers in methanolic solutions of
ferrocene derivatives with LiCI04 as the supporting electrolyte have been analyzed using a
complementary set of impedance spectroscopy, electroreflectance, and current-voltage
measurements. The results were interpreted in terms of charge accumulation modes correlated
with junction parameters such as space-charge layer, surface states, Fermi-level pinning, and
the possible presence of an insulating layer at the interface. The impedance of these junctions is
interpreted in terms of an equivalent circuit. The Fermi level is partially pinned at a potential
about 0.2 eV below the conduction band and is completely pinned at potentials positive to
mid gap. The electroreflectance results agree well with the impedance. The effect of an HF
etching on the properties of the cells will be discussed. We have also compared the results in
the methanolic solution with an aqueous electrolyte. The potential distribution obtained in this
case is very similar to the ferrocene solution.
I. INTRODUCTION
Recently, solar conversion efficiencies that exceed 14%
were reported for n-Si in methanolic solutions of ferrocene
derivatives with LiCI04 as the supporting electrolyte. I
These cells were reported to be stable thus offering perhaps
the best argument in favor of the competitiveness of liquid
junction solar cells in comparison with their solid-state
counterparts. The mechanistic aspects of these cells were
investigated primarily through a detailed analysis of their
current-voltage characteristics. The small indirect gap and
the low e1ectronegativity ofSi makes the detailed analysis of
Si based devices by dielectric techniques among the most
difficult of the conventional semiconductors. Yet in terms of
applications. both in photovoltaic and electronics industries,
Si is without a significant rival.
This study is a first of a series of papers that summarize
our work on possible appiications ofSi/methanol interfaces
for scre:ning and understanding of the nature of the damage
afflicted t@Si during reactive ion etching (RIE). In this and
the following papers we will demonstrate the application of
photoreflectance. electroreflectance, and impedance spec
troscopy as complementary techniques to study the poten
tial distribution of the silicon/methanol interface before and
after etching. We will also compare the dielectric properties
of the liquid junction with metaljunctions, metal-oxide-sem
iconductor (MOS) configurations, and contactless configu
rations. In this paper we will. concentrate on the dielectric
properties of Si in liquid-junction configurations. both in
methanolic and aqueous electrolytes.
Ii. EXPERIMENT
The Si samples are n-type (100) wafers, with resistivi
ties between 0.8 and 2 n cm. We have studied these samples
in a conventional three-electrode cell, with Pt as the refer
.:nce and counterelectrodes. The methanolic solutions were
prepared using methanol which was distilled from Mg and oxidized and reduced dimethylferrocene in the following
concentrations:0.2M FeCpz, ImMFeCpt and 1M LiCI0 4
supporting electrolyte under nitrogen atmosphere. I The po
tential of this solution was measured as 0.138 V versus stan
dard calomel electrode (SCE). For the electro reflectance
measurements the ferrocene derivatives were diluted by a
factor of 20 since the absorption coefficient was found to be
too high. The aqueous electrolyte was composed of 0.25M
NH4F/ O.OIM K3Fe(CN)J O.OIM K4Fe(CN)JH20.2
We have analyzed as-grown (or original) samples, i.e., no
surface treatment, and also samples submitted to an HF etch
(5 wt. % in water) for 20 s. The objective of this etch is to
remove the native oxide layer on the Si surface. The electro
lytes were prepared with analytical grade chemicals and 18-
Mn resistivity distilled water.
The dark and photo J-V plots were obtained using an
IBM EC/225 Voltametric Analyzer in a three-electrode
configuration connected with an X-Y recorder 815M-Plota
matic, MFE. The light source was a Sylvania tungsten halo
gen ELH lamp and the light intensity at the electrode surface
was lOOmW/cm2•
The electro reflectance measurements were taken on a
fully computerized setup for modulation spectroscopies that
was described elsewhere.3 The modulation amplitude was
150 mV and the modulation frequency was 740 Hz. An the
spectra were measured at room temperature.
The impedance measurements were carried out in the
frequency range from 0.01 to 107 Hz. The measuring system
is based on a computer controlled combination of Sol art ron
1250 Frequency Response Analyzer for frequencies between
I. O,uHz and 65 000 Hz and an HP 3325A Synthesizer /Func
tion Generator connected to an HP 3575A gain-phase meter
for higher frequencies up to 107 Hz. The dc bias ( -0.7 V
< Bias < 0 V vs Pt) applied to the cell was introduced by the
Sol.artron or by an HP 6200B dc power supply controlled by
an HP 59501 A IB isolated D/ A power supply programmer.
4884 J. Appl. Phys. 65 (12). 15 June 1989 0021-8979/89/124884-07$02.40 @ 1989 American Institute of Physics 4884
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:43'" E
~ «
.§
>.
'iii c ...
Cl
C
~
::>
U IS
10
S
a
-0.6 -0.2
Polenliol (V vs. PI) 0.0
FIG. I. Current-potential response with chopped white light for unetched
(100) n-Si in methanolic solution of oxidized and reduced dimethylferro
cene in the following concentrations: 0.2M FeCp" I mM FeCp,' , and 1M
LiCIO. supporting electrolyte under nitrogen atmosphere. I Tungsten halo
gen ELH lamp with light intensity at the electrode surface of 100 m W Icm'.
The sweep rate is \0 mV Is.
The dc bias was monitored by a Keithley 192 programmable
DMM multimeter. All the components are interfaced to an
IBM-PC microcomputer via a GPIB card. The modulation
amplitude in all the experiments was 40 mV.
III. RESULTS
Figure 1 shows an example of the light-induced current
voltage characteristics of a Si sample in contact with the
methanolic solution in which the light source was chopped
at low frequency. In addition to the photovoltaic parameters
such as short-circuit current, open-circuit voltage, and a fin
factor, one can extract from such figures the turn-on poten
tial (the most negative potential for which charge separation
can be detected = -0.58 V vs Pt in the present case) and
the general behavior of the dark current. Figure 2 depicts the
dark and photocurrent-voltage curves of the Si in the same
electrolyte, before and after etching with HF. The main ef
fects of etching are increases in the short-circuit current and
in the fill factor. Typical values of the short-circuit current
20
N
E 15 ~
<l:
E
>. 10 -. iii
c cv 5 0
C
~ 0 b ............
......
.' .....
~ ___ .-::;_.aJc.~.~·~~·~·~·~·~ _____ ~ __
:J u
-5
-0.6 -0.4 -0.2 0.0
Potential (V VS. Pt)
FIG. 2. Current-potential curves of two samples: one original and the other
submitted to HF etching process. (a) Photoresponse ofHF etched Si. (b) of
unetched Si. and (cl dark response of both samples. Electrolyte and other
experimental conditions are the same as in Fig. I. Photovoltaic parameters
extracted from these curves: J", = 12.4 mA/cml and V~. = -0.503 V
(origina));J", = 16.3 mA/cm'; and v.", = -0.519V (afterHFetchingl.
4885 J. Appl. Phys., Vol. 65, No. 12. 15 June 1989 4.0,-------"""'11
0.3V
2.0r-----' O.OV
on Q
)( 0.0 FIG. 3. Electroreflectance spectra of
HF etched Si in the same electrolyte
as in Fig. I except for the dimethyl
ferrocenes that were diluted by a fac
tor of 20. as a function of the elec
trode potential vs Pt. The
modulation amplitude is 0.15 V and
the modulation frequency is 740 Hz. ~
~ -2.0t---- ..... -o.SSV
-4.0
3.0 3.4
EnerQY leV) 3.8
density (Jsc) and open-circuit voltage (Voc) are about 15
mA/cm2 and 0.5 V, respectively. The cells and the samples
were not optimized for efficiency.
Figure 3 shows the eiectrorefiectance, under different
bias conditions, for the sample submitted to the HF etching.
Figure 4 shows one of these spectra with the line-shape anal
ysis that will be discussed shortly. Figure 5 shows the poten
tial dependence of the amplitude of the peak for the Si sam
ple before HF etching (b) and after (a). In this figure the
potential dependence of the electrolyte electrorefiectance
(EER) amplitude is plotted for two potential excursion di
rections. The data were taken after equilibrium was reached
at each potential. Comparing Figs. 5(a) and 5(b) we ob
serve that the original sample presents a broader bias distri
bution and a small hysteresis effect in the potential sweep.
These features can be related to the presence of an oxide
layer on the top of the semiconductor. For both samples the
fiat-band potential can be observed as the potential in which
the signal changes sign. For the unetched sample the poten
tial is between -0.66 and -0.63 V vs Pt, depending on the
direction of the sweep and for the etched sample it is at
-0.51 V vs Pt. The Fermi level is partially pinned at a
potential about -0.4 V vs Pt and it is completely pinned for
positive potentials (reverse bias). HF etching reduces the
pinning, both due to the states dose to the conduction band
and in the reverse bias region, and also decreases the hystere
sis.
8.0~--------------------------~
.. -.
-8.0.~ ____ ~~ __ ~~ ______ ~ ____ ~
3.0 3.2 3.4 3.6 3.8
Energy (eV)
FIG. 4. Comparison of observed (points) and calculated (solid line) line
shape of the spectrum at O.OV vsPt. Fitting parameters: C = 6.4X 10 6; E.
= 3.407 eV; r = 0.17 eV; B = 4.18 rad; and n = 3.0.
Fantinietal. 4885
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:432.0....-----..,
(a)
1.0
~ O.O~--¥-------~
-..... a:: <l
-1.0 1.6r------.,
-2.0 -0.8~~::--~--=~ -1.0 -0.5 0.0 0.5 -1.0 -0.5 0.0 0.5
Potential (V vs. Pt)
FIG. 5. Variation of the amplitudes of the 3.4 eV EER peaks with the elec
trode potential: (a) after HF etching and (b) before etching. The potential
sweep rate was 5 min per experimental point. The lines are drawn for con
venience of inspection. The arrows indicate the direction of the potential
sweep.
Throughout this paper the term "Fermi-level pinning"
is used to describe a situation in which the difference
between the electrode potential and the flat-band potential is
independent of the electrode potential. This definition fol
lows the electrochemical practice in which equilibrium ex
periments are performed as a function ofthe electrode poten
tial which is measured relative to a non polarizable reference
electrode. Within this framework the rest potential (zero
bias) has no special significance. We assume here that the
electrode potential is a measure of the position of the Fermi
level relative to the standard electrode, and as a result Fermi
level pinning describes the situation in which the Fermi level
is pinned to the position of the band edges at the surface and
the barrier height is independent of the position of the Fermi
level relative to the reference electrode. This definition fol
lows earlier practice4 and it is a generalization of the defini
tion often used to describe solid-state devices in which the
term Fermi-level pinning is used only to describe the condi
tion under zero bias. Following this practice the terminology
of Fermi-level pinning and band-edge movement as a func
tion of potential becomes synonymous.
Figure 6 presents the potential dependence of the EER
amplitude using the aqueous electrolyte with the composi
tion described in the experimental section.2 The electrore-
2.0...------"""'\
.Q:. 0.0
0::
<I
-1.0
-2.01...-_.1....-_1-...._ ....
-1.0 -0.5 0.0 0.5
Potential (V vs. Pt) FIG. 6. The same as Fig. 5 but with
the aqueous electrolyte with the
following composlllon: O.25M
NH.F/ (l.Ol MK,Fe(CN)"IO.OIM
K4Fe(CN)"IH20.'
4886 J. AppL Phys., Vol. 65, No. 12, 15 June 1989 6~------------------~
5-
4
3
Q
Log f(Hz)
FIG. 7. Impedance response curves for HF etched n-Si in the methanolic
solution with the same composition as described in Fig. I. Potential is -0.2
V vs Pt. The symbols represent e.xperimental data for the real and imaginary
parts of the impedance. The solid lines represent numerical fits to the equiv
alent circuit shown in the left-hand comer.
flectance was very noisy and the photocurrent very small.
The behavior does not show the reverse bias pinning that was
observed with the methanolic electrolyte. The flat-band po
tential is around -0.81 V vs Pt.
Figure 7 presents typical impedance data and the fitting
with the equivalent circuit shown in the insert. Similar spec
tra were recorded for the etched and unetched samples over
the potential range that corresponds to forward bias condi
tions. A full analysis and proposed interpretation will be pre
sented in the discussion section.
Figure 8 shows the dark current-voltage plot of the
original sample. The same features were observed for the HF
etched one. In this figure we clearly notice a peak in the same
bias region where we observe the pinning of the Fermi level
from the EER data. The charge density which corresponds
to this peak is about 1.1 X 1016/cm2• Also, the photocurrent
voltage plot for the original sample (Fig. 1) only starts to
show photoeffect at potentials positive to -O.S V. We could
not fit the dark current to the diode equation with any rea
sonable ideality factor.
20r-----------------------~
N
~ -20 -.....
<.(
::l.
~ -60 >. -V>
C
~ -100
'E
~ -140
::l
U
-180L-.....,.-L::---~--__::::_'_:_-~~-~ -1.0 -O.S -0.6 -0.4 -0.2 0.0
Potential (V VS. Pt)
FIG. 8. Dark current-potential plot of the original sample in the methanolic
solution of the same composition as described in Fig. I. The calculated
charge density associated with the peak is shown on the figure.
Fantinietal. 4886
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:43IV. DISCUSSION
A. Electroreflectance
In the "low-field regime", 5 if one includes the possibility
that the Fermi level is pinned by surface states,4.b the ratio
between the modulated reflectance (~) and the reflectivity
(R) is given by
~ = -Ce
:d) [1-(;h) (d;;)] ~VL(ku), (1)
where e is the electronic charge, Nd the doping level, € the
dielectric constant, C h the capacitance of the Helmholtz lay
er (which corresponds to the entire surface covered with
states that can be charged and discharged upon modulation
of the surface potential), N" is the density of the surface
states, ~ V is the amplitude of the modulating voltage, and
L (ku) is a spectral line-shape function given by
L(ku) = Re [C(ku -Eg + ir) -n exp(iO)] , (2)
where C and 0 are amplitude and phase factors, n is a number
characteristic of the interband critical point, Eg is the energy
gap, and r is a broadening parameter related to the lifetime
of the majority carriers.
The electroreflectance ofSi in the 3.{}.-5.0eV regime was
analyzed in detail by numerous workers both in electrolyte
configuration 7 and in Schottky barrier configurations. K The
electrolytes were never chosen based on their stabilizing ef
fect and as a result the state of the surface and the potential
distribution at the interface were not well defined.
The electro reflectance of the indirect, fundamental
transition of crystalline Si was never reported due to its low
intensity.
The electroreflectance of Si in the UV region is very
complex. The 3.5 eV regime was proposed to be due to two
critical points8 E b and E. with the EI being the strongest
high-energy transition. In our experiments in liquid junc
tions we were never able to resolve these transitions. Since
we are interested primarily in the potential distribution and
not in the spectroscopic features, the spectra in this region
will be analyzed in terms of a single peak. In all cases it was
verified that around the rest potential, we are in the low-field
regime by working only in the linear regime of amplitUdes of
the EER signal versus the modulation. This modulation am
plitude was kept constant throughout the potential range.
Figure 4 is an example of a spectrum taken in the methanolic
solution at a potential of 0.0 V vs Pt and the corresponding fit
of the line shape to Eq. (2) with the following parameters:
Eg = 3.407 eV, r = 0.17 eV, 0 = 4.18 and n = 3.0, which
indicates a two-dimensional critical point. One can see that
the fit is excellent and there is no need to invoke a second
peak. This is not always the case and this issue will be further
discussed in a separate publication when we will compare
e1ectroreflectance and photo reflectance spectra of reactive
ion-etched Si.9 The potential variation of the amplitude of
the spectra are presented in Figs. 5 and 6. It is clear from
these figures that at positive potentials the Fermi level is
pinned in the methanolic solutions and is not pinned in the
aqueous solutions. We interpret this pinning to be due to
inversion of the surface that is facilitated by the presence of
the oxide layer. The Fermi level in this region is never com-
4887 J. Appl. Phys., Vol. 65, No. 12, 15 June 1989 pletely pinned in the samples that were subjected to HF etch
ing in which most of the oxide is removed. This effect is
much more pronounced in the aqueous electrolyte in which
the F-ions dissolve any oxide that is being formed. The
pinning region, observed at forward bias, is interpreted to be
due to surface states, as discussed below. One can, in princi
ple, derive more quantitative information based on fitting
these data to Eq. ( 1 ), Ii but since this equation is strictly valid
for the low-field regime, none of the two pinning regimes fits
the conditions for which this equation was derived.
B.lmpedance
For a simple case where one measures the impedance of
a single dielectric (abrupt junction between a semiconductor
and a metal or a concentrated electrolyte) one can construct
a generalized equivalent circuit as shown in Fig. 9. Csc is
usually the capacitance due to the space-charge layer, which
is assumed to be the fastest relaxing element. C; and 7,
= CjR; are the capacitances and their corresponding relax
ation times of charge accumulation modes such as various
surface states, minority carriers, and bulk states. Zd is a gen
eralized constant phase angle (CPA) element given by
Zd = N(1 + J0)7) -", (3)
where 0) is the angular frequency, and N, 7, and n are param
eters. Rs is the series resistance and Rp is the shunt resis
tance.
The inclusion of Zd extends the previously reported pro
cedure of relaxation spectrum analysis. 10 Zd in this form can
include contributions from static disorder such as poros
ity, II random mixture of conductor and insulator that can be
described by the effective medium approximation at percola
tion, 12 or an interface that can be described by a fractal ge
ometry. 13 It can also include contributions from a dynamic
disorder such as diffusion.
If one subtracts the frequency-independent, high-fre
quency resistance,
(4)
and calculates the resulting admittance, it is easy to show
that
c
FIG. 9. The generalized equivalent circuit of a single interface. Rp is the
resistance associated with the Faradaic current flow, Zd is a generalized
impedance associated with disorder either in the structure or in the dynam
ics (diffusion), C, and R, are associated with parallel charge aC{:umulation
modes with different relaxation times than the majority carriers such as
surface states or minority carriers, C", is the space-charge capacitance, and
R, is the series resistance.
Fantini et a/. 4887
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:432.0 5.0
(0) (b)
!9 4.0 • 1.5 Q
>< .,. 0 3.0 o
E 1.0 0 0
U N 0 • 2.0 u... 00
00
NO 0.5 '111 u 1.0
0
0.0 0.0 -0.8 -0.4 0.0
Potential (V VS. Pt)
FIG. 10. Mott-Schottky plots of n-Si in the methanolic solution described
in Fig. I. (a) HF etched sample. V", = -0.76 V vs Pt and Nd
=4.7XI0"/cm\ (b) Original sample. V", = -0.86 V vs Pt and N"
= 2.2X 1O"/cm'.
1 1 , "C;T; "C; -Z' =-R + JwCsc +w-L '.2 +Jw L
p I 1 + w-Tj I 1 + w2r;
+ N-'O + w2r;)n12(cos nO + Jsin nO), (5)
where tan 0 = WT.
For T~ 1 Eq. (5) can be viewed as the superposition of a
constant term, linear term, power-law term, and Lorentzian
terms with respect to the frequency. If the separation
between the time constants is large enough one can isolate
the respective terms and obtain all the parameters directly. If
the separation between the time constants is not large
enough and/or the system cannot be represented in terms of
a simple abrupt junction due to film formation, multiple
junctions, etc., some data fitting is necessary. In the latter
case one can get some degree of confidence if one fits the real
or imaginary components and checks it against the other
components. The uniqueness of the interpretation is then
checked against other techniques that provide complemen
tary information. Figure 7 illustrates the experimental re
sults for n-Si in the methanolic solution together with the
simplest equivalent circuit that was obtained. We could not
fit the results in terms of a single junction and we had to use
least-square procedures to obtain the fit. Figures 10-12 show
)( .. E
U
N · IL.
NU ,II)
U 4.0~-----"
0.0 0
-0''''.8:--~--:0:-'".4-:--'''''''~0~.O
Potential IV vs. Pt) FIG. II. Mott-Schottky plots of n
Si in the aqueous electrolyte de
scribed in Fig. 6. V,h = -0.79 V vs
Pt and No = 2.3 X JO"/cm:l.
4888 J. Appl. Phys., Vol. 65, No. 12, 15 June 1989 6.0r----------------.3.75 x 1015
o
Q
)( 4.0 o 2.50 X 1015 ~ o
'" E u c
Q)
Cl
Q) U:-
J: 2.0
u o o 1.25 X rol!S ~
o o 0 o o
O.O.~-__:::_L:,_--,..J---...L...--....JO.O -0.8 '0.6 -0.4 -0.2 0.0
Potentiol (V vs PI) ~ u
FIG. 12. Potential dependence of CH of the HF etched sample. The ordinate
depicts the charge density/eV.
the potential dependence of the two capacitive elements in
Fig. 7 for the various samples. Figures lO(a) and 10(b) de
pict the Matt-Schottky plotsl4•IS of the space-charge layer
capacitance Csc' for the HF etched sample and for the un
etched one. The flat-band potentials that were obtained from
the intercept are -0.76 V vs Pt for the HF etched sample
and -0.86 V vs Pt for the unetched one. The doping levels
were obtained from the slopes which yielded 4.7 X 1015/cmJ
for the etched sample and 2.2 X 1015/cm3 for the unetched
sample. The apparent difference in the doping level is due to
the increase in roughness due to etching. The pinning of the
Fermi level around -0.4 V vs Pt can be observed here better
than with the EER results. The 0.1 V shift in fi.at band due to
the removal of the oxide agrees well with the EER results.
However, the flat bands are about 0.2 V more negative than
that obtained from the EER. The primary reason for the
discrepancy is the difference in the composition of the elec
trolyte although some contribution due to the different am
plitude of the ac signal cannot be ignored. This is supported
by the results in the aqueous electrolyte shown in Fig. 11.
Here the flat band is -0.79 V vs Pt and the doping level is
2.2 X 1015/cmJ. The flatband here agrees within 0.02 V with
the EER results taken in the same electrolyte. The doping
level in this electrolyte is identical to the unetched sample in
the methanolic solution and the pinning of the Fermi level is
also evident here at about the same energy separation from
the conduction band as in the methanolic solution. If one
takes the capacitance of the Helmholtz layer to be -20
/-IF /cm2 then the number of surface states responsible for a
shift of 0.1 V for the HF etched sample is 1.6 X IOI3/cm2 and
about double that for the unetched sample. 16 The fact that
these states are present, with similar densities and energy, in
the methanolic and the aqueous electrolytes and also that
similar states can be identified in the corresponding
Schottky structures, 17 suggests that they are not due to inter
actions with the electrolytes .
CII and its corresponding RII are interpreted in terms of
absorption of the electrolyte at potentials negative to the sur
face states which cause the Fermi-level pinning. This inter
pretation is not based on the equivalent circuit, which place
these elements in series with the space-charge layer. An al
most equally good fit can be obtained by placing them in
parallel to the space-charge l.ayer which would have been the
case if these elements were interpreted to result from the
Fantini et al. 4888
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:43surface states that cause the Fermi-level pinning. The esti-
14/ 2 Th' . mated coverage from Fig. 12 is about 5 X 10 cm. IS IS
an order of magnitude greater than the number of states
calculated to be responsible for the Fermi-level pinning (or
the corresponding negative shift in the flat-band potential).
In addition, to account for the negative shift in the flat band,
one has to assutne absorption by the negatively charged
counter ions. Since almost identical shifts are observed for
the methanolic and aqueous electrolytes with no ions in
common, we were forced to assume that the Fermi-level pin
ning and its corresponding shift in the flat-band potential are
due to negatively charged surface states which are filled as
the Fermi level crosses the energy of these states. These
states are not coupled with the electrolyte, but the filled
states act as catalytic centers in the precipitation of the posi
tively charged redox species.
Zd was identified as due to a porous oxide layer that can
be almost completely removed by HF etching. Nand nr/ N
are the low-frequency resistance (WT~ 1) and the low-fre
quency capacitance of this layer. The exponent n is related to
the transport mechanisms within the material. Figure 13
shows that n is almost independent of potential, having a
value close to 0.6. This, and the sensitivity to HF etching,
strongly suggests that it results from transport through a
porous layer. Using the limiting values for Nand T one can
estimate the thickness ofthis porous oxide layer. For the HF
etched sample this value is about 3 A and for the original
sample it is 26 A. These numbers agree with the current
understanding of the oxide on unetched Si 18 which predomi
nantly originate from ex situ measurements. From the CPA
data one can, in principle, build a more detailed analysis of
the porosity profiles of this layer but the application of effec
tive medium theories to a layer with atomic thickness is sus
pect enough to prevent any further "analysis. " The presence
of a porous oxide layer on the surface of the semiconductor is
also supported by photo J-Vand electroreflectance measure
ments. The photo J-V characteristics of the ceH improve
after HF etching (Fig. 2), which is a well known procedure
to remove Si02• 19 The electroreflectance hysteresis effect in
the potential sweep, and the broader bias dispersion for the
original sample compared to the HF etched sample (Fig. 5),
are also consistent with the presence of an oxide layer on the
original sample.
n 1.0'1"-------------------.
0.8
000 0
0.6 000 0 0 0 0 0 0
0.4
0.2
o. 0 L---=-"~~_::____::_1_:___::_L:=___:::_L:::__~___::__:! -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
Potential (V vs. pt)
FIG. 13. The polential dependence of n [Eq. (3) 1 of the HF etched sample.
4889 J. Appl. Phys., Vol. 65, No. 12, 15 June 1989 V. CONCLUSIONS
Figure 14 represents the band diagram of the Silmeth
anol system in which we summarize these results.
Going from reverse to forward bias (V vs Pt increasing
negatively) on Fig. 14 we first observe the pinning of the
Fermi level due to the presence of the minority carriers in the
inversion region. The Fermi level is again partially pinned at
0.2 eV below the conduction band due to surface states. Ac
cording to our results the pinning is more pronounced for
non treated surfaces. This indicates that these states are cou
pled to the oxide layer. Finally the potential reaches the fl~t
band value, which is about -0.8 V vs Pt. The potential
distribution in the aqueous electrolyte is very similar to the
one in the methanolic solutions.
This potential distribution has to be reconciled with the
results of Rosenbluth and Lewis 1 in which they obtained a
linear dependence of the open-circuit voltage and the oxida
tion-reduction potential from which they conclude that the
Fermi-level of this system is not pinned. First we have to
emphasize that the two experimental methods in question of
analyzing Fermi-level pinning are sensitive to different pin
ning mechanisms. The method used by Rosenbluth and
Lewis I to analyze the variations of the open-circuit voltage
with the oxidation-reduction potential of the electrolyte, is
analogous to the analysis of the open-circuit voltage as a
function of the metal work function in metal-semiconductor
junctions, and monitors pinning due to coupling of the sur
face states with the electrolyte. The impedance and the EER
data that we present here monitor the charge accumulation
in the space-charge layer as a function of the position of the
Fermi level, and are sensitive to pinning of the space-charge
layer to alternative charge equilibration mechanisms such as
surface states, unpinning of the band edges through surface
charging, pinholes, pinning through the electrolyte, or any
other mechanism. Close analysis of Rosenbluth's results 1 re
veals that the Fermi level is unpinned over a potential range
of 0.4 e V which roughly corresponds to the energy difference
between the short-circuit potential and the potential of the
surface states, in full agreement with our data. Since they
were monitoring the open-circuit voltage, which is zero for
Vvs. Pt
-0.8
-0.5
o
0.5
1.0 BAND DIAGRAM
Fe (Cplz/
n -Si Fe (Cp); Metal
,,-,' .
porous ox ide
'-layer
FIG. 14. The proposed band·structure diagram of the Silmethanol that is
described in this work.
Fantini et al. 4889
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:43potentials negative to the potential of the surface states, one
cannot compare the data at potentials negative to that of the
surface states. The strong hysteresis that they observe can be
interpreted to be due to absorption of the electrolyte. The
kind of pinning that we describe here which results in a nega
tive shift of the band edges due to charging of the surface
states can be viewed as a combination of battery + photovol
taic cell and offers the possibility of a higher photovoltage.
The full implication of these possibilities in terms of a total
free-energy balance is beyond the scope of this paper, but
should be examined in more detail.
ACKNOWLEDGMENTS
This work was supported by IBM. One of us (M. F.)
wants to thank CNPq (Brazil).
1M. L. Rosenbluth and N. S. Lewis, J. Am. Chern. Soc. 108,4689 (1986).
'w. M. R. Divigalpitiya, S. R. Morrison, G. Vercruysse, A. Prat, and W. P.
Gomes, Sol. Energy Mater. 15, 141 (1987).
3M. Tomkiewicz and W. M. Shen, in Photoelectrochemistry and Electro
synthesis On Semiconducting Materials, edited by D. S. Ginley, A. J. No-
4890 J. Appl. Phys., Vol. 65, No. 12, 15 June 1989 zik, N. Armstrong, K. Honda, A. Fujishima, T. Sakata, and T. Kawai
(The Electrochemical Society, New York, 1987).
4R. P. Silberstein, F. H. Pollak, J. K. Lyden, and M. Tomkiewicz, Phys.
Rev. B24, 7397 (1981).
sD. E. Aspnes, Surf. Sci. 37, 418 (1973).
"M. Tomkiewicz, W. Siripa1a. and R. Tenne, J. Electrochem. Soc. 131,736
(1984).
7See, for example, M. Cardona, F.H. Pollak, and K. L. Shaklee, Phys. Rev.
154,696 (1967).
"See, for example, K. Kondo and A. Moritani, Phys. Rev. B 14, 1577
(1976).
oW. M. Shen, M. C. A. Fantini, F. H. Pollak, J. P. Gambino, H. Leary, and
M. Tomkiewicz (to be published).
10M. Tomkiewicz, J. Electrochem. Soc. 126, 2220 (1979).
11M. Kramer and M. Tomkiewicz, J. Electrochem. Soc. 131,1283 (1984).
12M. Tomkiewicz and B. Aurian-Blajeni, J. Electrochem. Soc. 135, 2743
(1988).
13H. S. Liu, Phys. Rev. Lett. 55, 529 (1985).
14W. Schottky, Z. Phys. 113, 367 (1939); 118, 539 (1942).
ISN. F. Mott, Proc. R. Soc. London Ser. A 171, 27 (1939).
16M. Tomkiewicz, J. Electrochem. Soc. 126, 1505 (1979).
17M. C. A. Fantini, W. M. Shen, J. P. Gambino, and M. Tomkiewicz (to be
published) .
I"J. W. Faust, Jr. and E. D. Palik, J. Electrochem. Soc. 130, 1413 (1983).
19J. L. Vossen and W. Kern, in Thin Film Processes (Academic, New York,
1978), Chap. V.
Fantini et al. 4890
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129.100.58.76 On: Tue, 02 Dec 2014 06:18:43 |
1.576302.pdf | Crystal structures and optical properties of ZnO films prepared by sputteringtype
electron cyclotron resonance microwave plasma
Morito Matsuoka and Ken’ichi Ono
Citation: Journal of Vacuum Science & Technology A 7, 2975 (1989); doi: 10.1116/1.576302
View online: http://dx.doi.org/10.1116/1.576302
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/7/5?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.105.215.146 On: Tue, 23 Dec 2014 23:57:38Crystal structures and optical properties of ZnO films prepared
by sputtering-type electron cyclotron resonance microwave plasma
Morito Matsuoka and Ken'ichi Ono
NTT Opto-electronics Laboratories, Tokai, Ibaraki 319-11, Japan
(Received 6 July 1988; accepted 1 April 1989)
This paper describes the crystal structure and photochromism of Zn oxide films fabricated by
sputtering-type electron cyclotron resonance microwave plasma. C-plane preferential orientation
and (101) plane preferential orientation are achieved in Zn oxide films deposited on glass
substrates below 200 ·C. These films have strong crystallite orientation. Films with (101) plane
orientation exhibit typical photochromic characteristics induced by x-ray irradiation.
Photochromism is probably caused by a color center, that is, the oxygen vacancy in Zn oxide
films. The absorption center exists in an energy range of 1.5 to 4 eV. The activation energy in the
fading process is -0.03 eV.
I. INTRODUCTION
Zinc oxide (ZnO) with a wurtzite crystal structure is well
known as an electroacoustic device material. In particular,
ZnO has been applied to surface acoustic wave (SAW) de
vices, I supersonic transducers,2 and supersonic oscillators. 3
ZnO films have also been of considerable interest for applica
tions such as window material for solar cells,4 gas sensors, 5
and saw devices because of their excellent electrical, optical
and acoustic properties.6
There have been two major goals in the study of ZnO
films. One is to prepare the well-oriented c-axis ZnO for
acoustic devices. The other is to achieve good optical trans
parency and low resistivity for transparent conductor.
Several techniques have been developed in recent years for
forming ZnO films on various kinds of substrates. These
techniques include evaporation, reactive sputtering,7-16 ion
plating,17 ionized cluster beam (ICB) deposition,18 and
chemical vapor deposition (CVD). 19
When the ZnO films are deposited by sputtering, the
film's crystallographic characteristics such as c-plane orien
tation strongly depend on sputtering conditions and sub
strate location. 12,13,16 During film deposition by convention
al sputtering, the film surface is bombarded by high-energy
particles, including argon ions reflected from the target, neg
ative ions emitted from the target surface, and ions acceler
ated from the plasma. High-energy particle bombardment
during deposition usually damages film surfaces and alters
film composition from the target composition. 16 One way to
avoid those problems is to thermalize particle energy by in
creasing the gas pressure. However, low ion energies in the
range of several to several tens of electron volts, which are
suitable for depositing films with good crystallographic
characteristics, 16 are also thermalized by increasing gas pres
sure. The lost energy must be compensated for by substrate
heating. As a result, the films end up being deposited at high
substrate temperatures.
On the other hand, well-oriented ZnO films have been
obtained by the facing targets sputtering (FTS) system at
low substrate temperature (Ts -300 ·C) and low gas pres-sure (Po, -0.1 Pa).16TheFTS system has been known as an
apparatus to deposit films without substrate bombardment
of several high-energy particles. 16
This indicates that films with good crystallographic char
acteristics can be obtained while avoiding substrate bom
bardment by high-energy particles during deposition. The
following conditions are believed to be necessary to form
well-oriented ZnO films with good surface smoothness: (i)
High-energy particle bombardment of the film surface dur
ing deposition should be suppressed and (ii) the sputtering
particles which land on the substrate surface should have an
appropriate energy level ranging from several to several tens
of electron volts. 16
Another factor which directly influences the electrical
and optical properties of ZnO is its defect structure. Oxygen
defects, in particular, are the most important factor. ZnO is
easily reduced by heating to 300 ·C, which leaves excessive
Zn remains in the compound.20 This is called an n-type ex
cessive semiconductor, in which metal ions are overabun
dant. It is well known that some compound semiconductors
such as CdS and ZnS exhibit photoluminescence properties
at their absorption edges, when the crystals are reduced, or
when Ag and Cu ions are doped in these crystals. ZnO also
exhibits typical photoluminescence properties caused by va
cancies and dopants.21 Consequently, the control of vacancy
density in ZnO is important in controlling its physical prop
erties.
From all the points of view above, to prepare the ZnO
films with good crystallographic characteristics, and also to
easily control the oxygen reactivity in the ZnO films, highly
reactive plasma with low-energy ion extraction to substrate
has been sought.
On the other hand, the sputtering-type electron cyclotron
resoanance (ECR) microwave plasma deposition appara
tus, hereafter called ECR sputtering, has been achieved for
preparation of high-quality films on the low-temperature
substrates.22,23 The ECR sputtering is the ECR microwave
plasma deposition employing cathode sputtering and real
izes film deposition under the plasma irradiation on the sub
strates. That is useful for obtaining high-quality films at low
2975 J. Vac. Sci. Technol. A 7 (5), Sep/Oct 1989 0734-2101/89/052975-08$01.00 © 1989 American Vacuum Society 2975
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substrate temperatures in a low gas pressure atmo
sphere.22-26 Extracted ions' energy levels, ranging from sev
eral to several tens of electron volts, can be controlled in the
system.25 Reactivity in compound films such as oxides and
nitrides is easily controlled by the ECR microwave plasma.
Moreover, substrate bombardment of several kinds of high
energy particles can also be suppressed in the system during
film deposition. 26
Consequently, the ECR sputtering is thought to be useful
for preparing ZnO films on low-temperature substrates and
for easily controlling the film's properties. Recently, the
ZnO films deposited by the ECR sputtering have been re
ported to exhibit photochromic characteristics.27 In this pa
per, the change in the film's crystallographic and optical
characteristics with preparation conditions for the ECR
sputtering are reported in detail.
ECR-sputtered ZnO films exhibit two types of preferen
tial crystallite orientation. One is c plane, and the other is
(101) plane. Many reports have been published on ZnO
films with preferential orientation in addition to c-plane ori
entation. These include (llO)-plane or (l()())-plane orient
ed films deposited by magnetron sputtering at low gas pres
sure,zs or (100) plane oriented films sputtered in a
hydrogen-added atmosphere.29 However, the (101)-plane
orientation has not been previously reported. Both of c-plane
oriented films and (101)-plane oriented films have strong
crystallite orientation. The films with (101 )-plane orienta
tion exhibit typical photochromic characteristics induced by
x-ray irradiation. The photochromism is probably caused by
a color center, that is, the oxygen vacancy ranging from 1.5
to 4eV.
II. EXPERIMENTAL PROCEDURE
ZnO films were synthesized by ECR sputtering. The
ECR-sputtering apparatus is shown in Fig. 1. Details of the
apparatus used in this study have already been described in
previous reports.24,26,27 The chamber comprised a resonance
cavity and a substrate chamber. The resonance cavity was a
cylinder of TEI13 standing wave mode for 2.45-GHz micro
wave. Magnetic flux density of 875 G was applied inside the
cavity. The generated plasma was accelerated along the
magnetic field divergent toward the substrate plate. The sub
strate plate, cylindrical target, and submagnetic coil were
located in the substrate chamber. The cylindrical target was
located at the cavity's bottom, and surrounded the plasma
stream. The target used was Zn metal with an inner diameter
of90mm.
Gas was introduced into the chamber in two ways. One
was to introduce pure oxygen gas into the resonance cavity,
and the other was to introduce oxygen gas into the substrate
chamber, and also, Ar gas into the resonance cavity. In the
former, oxygen gas flow rates were varied in the range 1-22
sccm, at pressures from 0.01 to 0.2 Pa. In the latter, the
oxygen gas flow rate was maintained at 15 sccm and Ar-gas
flow rate at 0.6std. cm3/min (sccm). Except as described in
Sec. IlIA, oxygen gas was introduced into the resonance
cavity.
Negative potential was applied to the target by dc power
J. Vac. Sci. Technol. A, Vol. 7, No.5, Sep/Oct 1989 FIG. 1. Apparatus of sputtering·type ECR microwave plasma (ECR sput
tering) used in this study.
supply. The oxygen ions in the plasma stream were acceler
ated to the target surface and sputter it. When Ar gas is also
introduced into the chamber (see Sec. IlIA), both Ar and
oxygen ions are accelerated to the target. These processes are
called reactive sputtering.
The substrate plate was electrically floated on the ground
shield and was movable parallel to the magnetic flux as
shown in Fig. 1. The glass substrate (Corning No. 7059) was
placed on the plate. Substrate temperatures were varied
between 40 and 300 ·C. Deposited film thickness was -0.08
jlm. Film preparation conditions are summarized in Table I.
The plasma diagnostics were perfonned by the emission
spectroscopic analysis. The ion energy and the energy dis
persion of the ions accelerated toward the substrate were
measured by the retarding method using mesh grids as de
scribed before.25
The crystal structures of the deposited Zn oxide films were
analyzed by the x-ray diffraction method and also by the
electron diffraction method. In particular, the crystallite ori-
TABLE. I. Typical ZnO preparation conditions byECR sputtering."
Oxygen gas flow (Fo, )
Oxygen gas pressure (Po,)
Substrate temperature ( T, )
Microwave power (Pelf)
Target applied voltage ( Va )
Film thickness (d)
Substrate 0.6-25 seem"
0.0I--D.2 Pa
20-300'C
l00-300W
300-600 V
0.08flm
Glass
"Oxygen gas was normally introduced into the resonance cavity. When
oxygen gas was introduced into the substrate chamber, Ar gas was also
introduced into the resonance cavity. Here, the Ar gas flow rate was main·
tained at 0.6 seem.
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entation was estimated by the rocking curve. This technique
is usually used for estimation of crystallite orienta
tion.9."-'3.'6 The standard deviation or the full width at half
maximum of the rocking curve is taken for the estimation of
the orientation. The oxgen reactivity and composition of the
deposited films were analyzed by the x-ray induced photo
electron spectroscopy (XPS).
Photochromic characteristics of the ZnO films were in
duced by x-ray irradiation emitted from the Cu target by 40-
mA electron beam bombardment at 40-keV energy. Optical
properties of the deposited ZnO films were measured by an
optical spectrophotometer in the wavelength range 150-
2500 nm.
III. RESULTS AND DISCUSSION
A. Method of introducing oxygen gas
First, two ways of introducing oxygen gas were tried. One
way was to introduce it into the resonance cavity. This is
called method A hereafter. The other was to introduce oxy
gen gas into the substrate chamber and also Ar gas into the
resonance cavity. This is called method B hereafter.
Figure 2 shows the typical x-ray diffraction diagrams of
ZnO films deposited on unheated glass substrates using these
two methods of introducing oxygen gas. The films deposited
by method A exhibited weak c-plane orientation. On the oth
er hand, the films deposited by method B exibited abnormal
plane's strong preferential orientation.
The abnormal-plane oriented films obtained in this study
have 2.54-..\ spacing. This spacing corresponds to a (101)
plane spacing of the ZnO compound, or a (002) plane spac
ing of un oxidized Zn metal. The oriented plane in the films is
probably the (101) plane of the ZnO compound, because,
similar to c-axis-oriented ZnO films, the films exhibit good
transparency of -80%-90% in a wide wavelength range as
described later (see Sec. III B), and they have an electrical
resistivity of > 100 n cm. The reflection high-energy elec
tron difraction pattern also exhibits weak spots correspond
ing to that of the (101) plane, which is not as clear as expect
ed from the strong uniaxial x-ray diffraction intensity.
uao,.:01
fII"I''''-
~ o
20 101 (a) F02:22.5scCM
(b) FA,:2.4.Fo2:15scCM
202
60 100
28 (deg.)
FIG. 2. Typical x-ray diffraction diagrams of ZnO films deposited on un
heated glass substrates using two ways of introducing oxygen gas into the
chamber. (a) Oxygen gas is introduced into the resonance cavity. (b) Oxy
gen gas is introduced into the substrate chamber and also Ar gas is intro
duced into the resonance cavity.
J. Vac. Sci. Technol. A, Vol. 7, No.5, Sep/Oct 1989 rocking 101
() FIG. 3. Typical rocking curve of (101 )-plane
preferentially oriented film.
The (101) plane orientation has not been previously re
ported yet, and exhibits much more excellent orientation
than the c-axis orientation as shown in Sec.lII B. The typical
rocking curve is shown in Fig. 3. The full width at half maxi
mum f).(}so reaches 0.2°. The (101) plane's orientation de
pends on the substrate temperature Ts; it improves as Ts
decreases, as shown in Fig. 4.
From the XPS analysis, the composition of the films are
Zn0I.03 for method A, and ZnOO.99 for method B. The va
cancy's density is higher in the film B than in the film A.
Moreover, as the substrate temperature increases, the oxy
gen composition increases, as shown in Fig. 4. These results
suggest that (101) plane's orientation is improved as the
oxygen composition decreases apart from stoichiometry,
and the c-plane orientation is improved in the films with
stoichiometric and with oxygen-rich compositions. Conse
quently, film composition is an important factor to control
the crystallite orientation. However, the difference in the
chemical shift of these films is not clear, because the shift of
the photoelectron energy profile for Zn, from Zn metal to the
ZnO compound, is only 0.47 eV. So, the detailed discussions
on the chemical states in the films have not yet been per
formed.
0.6
ZnO 1Jt1 x 0 on glass c
N
c
en 0.4 .Q ....
GI 'iii
~ 0 Q,
1.04 E
0 0
"' I.J
~ C ""l 0.2 1.02 ~
x 0
10 ..
x
,0
0.98
0 200 400
Ts (t)
FIG. 4. The relationships between substrate temperature T, and (101)
plane orientation 6.B,o and between T, and film composition. Composition
of X = I corresponds to stoichiometric one. Here, the films were deposited
by introducing oxygen gas into the substrate chamber. The 6.B,o is full
width at half-maximum of the rocking curve.
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FIG. 5. Plasma emission spectroscopic diagrams in methods A and B. These
correspond to Fig. 2.
As described above, the obtained crystal structure directly
depends on the method of introducing oxygen gas. The re
sults are explained as the difference in an ionization or acti
vation efficiency of oxygen in the plasma between the two
methods and also the vacancy density in the films.
Plasma emission spectroscopic diagrams are shown in
Fig. 5. Figure 5(a) corresponds to the plasma generated by
introducing oxygen gas into the resonance cavity. This cor
responds to Fig. 2(a). Figure 5(b) corresponds to the plas
ma generated by introducing oxygen gas into substrate
chamber. These correspond to Fig. 2(b). It is clear from
these diagrams that the activated particles, including oxygen
radicals O· and ions 0+ and O2 +, are clearly detected in the
plasma by introducing oxygen in the resonance cavity, and
the oxygen gases are much higher activated in the resonance
cavity than in the substrate chamber. These ions have an
energy ranging from several to several tens of electron volts.
This clearly shows that the gas is effectively activated in the
resonance cavity through the ECR. Accordingly, the films
deposited in a highly reactive plasma exhibit good stoichi
ometry and c-plane orientation.
From these results, it is concluded that the crystallite ori
entation directly depends on the activation efficiency of the
oxygen gas and the substrate temperatures during depo
sition. This means that the change in oxygen reactivity in the
films causes the change in crystallite orientation. The films
obtained by introducing oxygen gas into the resonance cav
ity have higher oxygen reactivity than those obtained by in
troducing oxygen into the substrate chamber. However, it is
surprising that the drastic change in crystallite orientation
occurs by such slight change (of a few percent) in film com
position. It is probably important to consider the change in
activation energy of the adatom's self-diffusion on the film
surface with reactive plasma irradiation.
B. Crystal structure
The oxygen gases are highly activated in the resonance
cavity as noted above. The crystal structure of the films de-
J. Vac. Sci. Technol. A, Vol. 7, No.5, Sep/Oct 1989 Fo2:22.5 seeM
12 seeM
9 seeM
60 100
2(J (deg.)
FIG. 6. Change in x-ray diffraction diagrams with oxygen gas How rate.
Here, the oxygen gas was introduced into the resonance cavity, and the
substrates were not heated.
posited by introducing oxygen gas into the cavity (that is
method A in Sec. III A) are described hereafter.
Figure 6 shows the changes in x-ray diffraction diagram
with oxygen gas flow rate. The films were deposited on un
heated substrates. Substrate temperature reached ~40 °C
during deposition. The c-plane orientation ofZnO improves
as the oxygen gas flow rate increases.
Figure 7 shows changes in x-ray diffraction diagram with
substrate temperature T,. The oxygen gas flow rate was
maintained at 22.5 sccm. The c-plane orientation improves
as Ts increases. The well-oriented ZnO films were obtained
at temperatures above 190°C.
Changes of crystallite orientation with the substrate tem
perature Ts and oxygen pressure po. are summarized in Fig.
8. The ECR-sputtered ZnO films exhibit two types of crys
tallite orientation as described in Sec. III A. One is c-plane
orientation, and the other is (101) plane orientation. The c
plane orientation improves as Ts increases, or as oxygen gas
flow rate increases. On the other hand, the (101 )-plane ori
entation improves as Ts decreases, or as oxygen gas flow rate
decreases. This is consistent with the results in Sec. IlIA.
These changes in crystallite orientation with sputtering
conditions are also consistent with the film composition, as
002
2
~
A
.n ......... "'" I 101 o
10 Fo2:22.5 seeM
T Ts: 260't
Ts: 190't
Ts:40'C
50 100
2(J (deg.)
FIG. 7. Change in x-ray diffraction diagrams with substrate temperatures.
Here, the oxygen gas was introduced into the resonance cavity and the flow
rate was maintained at 22.5 sccm.
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300
200 e
100 [c]
[101 ]
+[c] Peff:300w
Pdc:30 w
o
o 0.04 0.08 0.12
PO, (Pa)
FIG. 8. The change in crystallite orientation of ZnO films with substrate
temperatures T, and oxygen gas pressure Pm. Here, symbols 0,6, and.
correspond to a c-plane oriented film, a film with mixed orientation of the c
and (101 )-plane, and a (101 )-plane oriented film, respectively.
noted above. As the T, is increased, and as the oxygen gas
flow rate is increased, the oxygen composition in the films is
increased and the c-plane orientation improves.
Figure 9 shows the oxygen-gas pressure dependence of the
plasma emission intensity ratio of oxygen radicals and ions.
As the gas pressure increases, the luminescence intensity
from radicals in plasma increases. The change in plasma
emission spectra with oxygen gas flow rate are consistent
with the change in the film's crystallographic characteris
tics. This suggests that the neutral radicals also act as a ma
jor role in oxidation of Zn particles in the ECR sputtering.
Typical preferential crystallite orientations and their
rocking curves are shown in Fig. 10. The c-plane oriented
film was deposited at substrate temperature Ts = 200°C,
1.5 '" 'I
0* 7772
O~ 5586
0+ 4649
j 1.0-/0
o 0"/ 0/ 70~
,/
'f.. 0.5-I '/
o IIII1
0.01 , , ,I I -
FIG. 9. Change of emission intensity ratio of excited species including radi
cals and ions in a plasma.
J. Vac. Sci. Technol. A, Vol. 7, No.5, Sep/Oct 1989 rocking
002 2.2deg
004
-8 -4
~~~~~~~2~02~~J~ ~ A 0.2deg
60 100JL
28 (deg.) -O.B -0.4 0 0.4 0.8
8 (deg.)
FIG. 10. Typical x-ray diffraction diagram and rocking curve for c-plane
oriented and (101 )-plane oriented ZnO films.
and oxygen gas pressure P 02 = 0.1 Pa. The ( 101 ) -plane ori
ented film was deposited at Ts = 40°C, P 02 = 0.01 Pa. Both
films exhibit good orientations. In particular, the c-plane
orientation of ECR-sputtered film is much better than that
of rf-sputtered films. Typical rocking curves of the ECR
sputtered ZnO films and of the films deposited by a conven
tional rf sputtering are shown in Fig. 11. The rf-sputtering
apparatus consists of a planar target of 100 mm in diameter
and substrate. The sputtering was performed at a gas pres
sure of 2 Pa. Here, both film thicknesses are fixed at -0.08
11m, and the substrate temperatures were -200°C. The ori
entation improves as the thickness increases.
The (101 )-plane oriented films exhibit much better orien
tation than the c-plane orientated films. As shown in the
typical rocking curve of Fig. 10, the films have orientation
with the dispersion angle < 1°.
It is concluded that crystallite orientation can be easily
controlled by the oxygen gas flow rate and the substrate tem
peratures by also introducing oxygen gas into the resonance
cavity. That change is caused by the oxygen reactivity of the
films. The difference in the film composition between c
plane oriented films and (101 )-plane oriented films is 4% at
most.
Zn0002
-10 o ECR
SPUTTER
o (deg) 10
FIG. II. Comparison between c-plane rocking curves for ECR-sputtered
ZnO film and for rf-sputtered film.
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100 100
~
~
~
GI [C] 50 IJ 50 oriented GI r:: IJ «I r:: .. • 1:: ,
E r ¥ III ~ r:: lJ ~80nm GI «I ... a: l-
0
500 1500 2500
). (nm)
FIG. 12. Typical transmittance and reflectance spectra for c-plane oriented
ZnO film. Here, film thickness is 0.08 p.m.
c. Optical and photochromic properties
Typical transmittance and reflectance spectra of the c
plane oriented film and of the (101 )-plane oriented film are
shown in Figs. 12 and 13, respectively. Both films are 0.08
J..lm thick, and exhibit good transparency above 80% in wide
wavelength ranging from 300 to 2500 nm. The optical band
gap does not depend on the crystallite orientation.
The (101 )-plane oriented films with higher vacancy den
sity exhibit typical photochromic properties. These films are
darkened by x-ray irradiation. Changes in transparence
spectra of (101 )-plane oriented films with x-ray irradiation
are shown in Fig. 14. Absorbance increases in the wave
length range from 350 to 800 nm as x-rays are irradiated. A
typical absorption spectrum of films with x-ray irradiation is
shown in Fig. 15. The absorbance is estimated by change in
transmittance with x-ray irradiation for 4.5 h. The absorp
tion center exists at -2.8 eV.
Darkening and fading changes are also shown in Fig. 16.
The absorbance was measured at a wavelength of 450 nm.
These characteristics are obtained in many photochromic
materials/D•3! and also indicate that the ZnO films exhibit
typical photochromic characteristics.
100 100
~ 3
~
~
GI [101 ] IJ 50 50 r:: oriented GI
«I IJ ::: r::
«I 'E ..
III lJ ~80nm ~ r:: ~ «I GI ... a: I-
0
500 1500 2500
). (nm)
FIG. 13. Typical transmittance and reflectance spectra for (101 )-plane ori
ented ZnO film. Here, film thickness is 0.08 p.m.
J. Vac. Sci. Technol. A, Vol. 7, No.5, Sep/Oct 1989 100
~
GI 50 IJ r::
«I .. ..
'E
III r:: lJ ~80nm III ... I-0
300 500 700
). Cum)
FIG. 14. Change in transmittance spectrum of (101 )-plane oriented films
with x-ray irradiation.
The photochromic characteristics are usmilly exhibited in
a ZnO compound by ion doping of the crystaI.2!,32 Photo
chromic characteristics appearing in the ZnO films deposit
ed in this study are probably caused by their oxygen vacan
cies. X-ray irradiation probably excites electrons in the
crystal, and these electrons are trapped into the color centers
created by the oxygen vacancies.
These photochromic characteristics strongly depend on
the crystallite orientation. The better the (101 )-plane orien
tation, the more the film is darkened by x-ray irradiation.
Darkening is not observed in c-plane well-oriented films.
This result is consistent with the oxygen composition in the
films.
These results suggest that photochromic characteristics in
Zn oxide films deposited by the ECR sputtering depend on
the film's oxygen reactivity. The (101 )-plane oriented films
with many oxygen vacancies exhibit photochromic charac
teristics. These photochromic characteristics probably cor
respond to the color center caused by the oxygen defects in
Zn oxide films as described above. Moreover, oxygen defects
in the Zn oxide films can be easily controlled by using ECR
~
~ 40
GI IJ r::
III ..a ... 20 0
III ..a < ). Cum)
0.5 0.3
X-ray
4.5 hrs
at room temp.
101-f\
oriented \
film "\ J 0 c-
fP ~ oriented l 0 film
,.0 "'::. __ ""_
o 2 3 4 5
E), (eV)
FIG. 15. Typical absorption spectra caused by the color center in ZnO film
with x-ray irradiation at room temperature. Here, film thickness is 0.08 p.m.
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60
). :0.45.um
at room temp
~ 40
GI U
C .z ..
0
11
ct
0 2 3 40 40 80
(hours) (hours)
FIG. 16. Typical darkening and fading properties of (101 )-plane oriented
film with x-ray irradiation.
plasma, and the crystallite orientation can also be easily con
trolled.
Figure 17 shows typical temperature dependence of fad
ing rate of the absorbance excited by x-ray irradiation on the
(101 )-plane oriented film. The fading rate is estimated from
the model of darkening and fading process shown in Fig. 18.
The activation energy of Zn oxide films during fading pro
cess is -0.03 eV. The activation energy probably corre
sponds to the magnitude of energy in vibration or in rotation
of the excited oxygen vacancy. The vibration of vacancies is
usually promoted by electron excitation in an insulator.
Consequently, the activation energy of vacancy vibration in
the excited state is much lower than that in the ground
state.33 Thus, the obtained activation energy of ( 101 ) -plane
oriented Zn oxide films is reasonable. It is also comparable
with a alkyl-halide material. 33
These results indicate that the ECR plasma closely con
trols the oxygen reactivity and crystallite orientation of Zn
oxide films. The obtained ZnO films with (101 )-plane orien
tation may be applied to many photochromic devices.
~ 0.1
«
"" t;100 hours
E;0.03eV
0.01 L-_.....L. __ L-..:..a........L._----l o 20
FIG. 17. Typical temperature dependence of absorbance fading rate in
(101 )·plane oriented x-ray irradiated Zn oxide films.
J. Vac. Sci. Technol. A, Vol. 7, No.5, Sep/Oct 1989 o 4 104
t (hr)
IV. CONCLUSION FIG. 18. A model of darkening and
fading process with x-ray irradiation.
Zn oxide films were reactively deposited on low tempera
ture substrates below 200 °C by the ECR sputtering, which
can deposit films in a low gas pressure atmosphere without
any high-energy particle bombardment during film prepara
tion.
When oxygen gas was introduced into the cavity, the gas
was highly activated. This shows that the introduced gas is
easily excited through the electron cyclotron resonance.
The c-plane orientation improves when the oxygen gas is
introduced into the resonance cavity. On the other hand, the
(101 )-plane orientation improves when the gas is intro
duced into the substrate chamber. In particular, the (101)
plane oriented film exhibits strong preferential orientation
with a rocking-curve width ofO.2°.
These changes in crystallite orientation of ZnO films with
introducing methods of oxygen gas are caused by the film's
oxygen reactivity.
Also in the films deposited by introducing oxygen gas into
the resonance cavity, the c-plane orientation is improved as
the oxygen reactivity increases, and the (101 )-orientation is
improved as the reactivity decreases. The c-plane oriented
films deposited by this method also exhibit strong orienta
tion with a rocking-curve width of 2°.
Composition difference between the c-plane-oriented
films and the (101 )-plane oriented films is 4% at most. The
(101 )-plane oriented films with low oxygen-reactivity ex
hibit typical photochromic properties induced by x-ray irra
diation. These properties probably result from oxygen va
cancy, that is a color center, and they do not exist in the
c-plane oriented films. The darkened center exists at 2.8 eV.
The activation energy of the fading process is -0.03 eV.
These results indicate that ECR plasma is useful for con
trolling crystal structure and oxygen reactivity.
ECR-sputtered ZnO films with c-plane orientation may
be applied to many supersonic devices, and films with ( 101 )
plane orientation may be applied to many photochromic de
vices.
lAo J. DeVries, R. Adlen, J. F. Dias, and T. J. Wojcik, Abstracts, IEEE
Ultrasonic Symposium, St. Louis, Paper G-5 (1969).
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1.458528.pdf | Nonequilibrium computer simulation of a salt solution
S.B. Zhu, J. Lee, J.B Zhu, and G. W. Robinson
Citation: The Journal of Chemical Physics 92, 5491 (1990); doi: 10.1063/1.458528
View online: http://dx.doi.org/10.1063/1.458528
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205.208.120.10 On: Sat, 20 Dec 2014 11:10:11Nonequilibrium computer simulation of a salt solution
S.-B. Zhu, J. Lee, J.-B Zhu, and G. W. Robinson
Picosecond and Quantum Radiation Laboratory, Texas Tech University, Department of Chemistry
and Biochemistry, Lubbock, Texas 79409
(Received 1 June 1989; accepted 24 January 1990)
A nonequilibrium computer simulation is performed to investigate the relaxation of a realistic
polar solvent near a rapidly dissociating ion pair. The time evolution of the reaction
coordinate, the ultrashort time scale changes in solvation energy and solvent forces, the local
density response, the heating of certain librational degrees of freedom, and the time-dependent
polarization are studied during the first 125 fs of the reaction. It is found that the relaxation
behaviors in the anionic and cationic shells are very different. On average, the solvation process
under study takes about 30-40 fs to break the original cage. After another 50 fs, the solvated
ion pair reforms a new metastable structure, which feeds energy back into the reacting system
to break the cage further. This procedure is apparently repeated many times until dissociation
is complete. The results obtained in this work provide a graphic picture of some of the features
of ultrashort dynamics of ionic photodissociation reactions in a polar medium.
I. INTRODUCTION
The relaxation of water molecules in response to the
ultrafast excitation of a dipolar solute is an active area of
chemicall-6 and biological7 research. Enhancing current in
terest in this topic are the apparent failures of continuum
modelsS-1O revealed by modern laboratory techniques using
picosecond and femtosecond kinetic spectroscopies. In
stead, descriptions of solvation and solvent effects at the mo
lecular level seem to be required. Together with this new
experimental work, computer molecular dynamics (MD)
simulations have provided a powerful and complementary
tool for the better understanding of ultrafast dynamical
aspects of solvation in chemical reactions. 11-14 In nearly all
the simulations so far performed, attention has been focused
on the investigation of solvation response following step
function jumps in the solute's charge, 11,14 dipole momene3,
or quadrupole moment. 12
In the present work, we study a somewhat different sys
tem: the relaxation of polar solvent molecules in the vicinity
of a photodissociating solvated salt molecule. The excitation
can be viewed as the consequence of pumping with an ultra
short laser pulse, The rapid dissociation of the salt creates a
nonequilibrium ensemble. Unlike some of the previous in
vestigations in which the transitional solute is "clamped" at
certain fixed configurations, the full dynamical motion of
the solute15 is included in this study. In addition, instanta
neously responsive "electronic" solvent polarization, which
we believe to be crucial for a good description of real solva
tion over a wide range of experimental conditions, is taken
into account in the present work. Because of the short time
range investigated, the paper is addressed mainly to femtose
cond spectroscopists, who by becoming more familiar with
some of the effects described here, can devise ways through
which the effects can eventually be measured in the laborato
ry. II. NON EQUILIBRIUM MOLECULAR DYNAMICS
METHOD
The system under study consists of one Li+F-ion pair
dissolved in 255 polar solvent molecules, These solvent mol
ecules resemble water molecules in shape and in their vibra
tional and electronic properties. This system is constructed
first by containing 256 solvent molecules in a box with cubic
periodic boundary conditions. The dimensions of the box
(19.726 A)31ead to a density of 0.997 glcm3. As justified by
the results obtained, this sample size seems to be sufficient to
describe most of the properties to be discussed in Sec. III.
The key reason for this is that the processes studied are ultra
fast and the time elapsed ( 125 fs) during the simulation is so
short that perturbations from the dissociating ion pair do not
propagate to more distant solvent molecules during this
time. The only exception is the induced dipole moment for
which the long-range Coulomb interaction plays an essential
role. Similar calculations by other authorsll-14 have em
ployed about the same box size (212-504 molecules) with
out introducing appreciable size effects,13 even though their
computational times ranged into the picosecond regime.
To begin the simulation, one solvent molecule is re
placed by the ion pair. The classical many-body problem is
solved by the third order predict--estimate--correct algo
rithm of Beeman 16 with an integration time step of 0.25 fs.
Ninety-one independent sets of phase points equilibrated at
300 K are prepared. MD simulations are performed individ
ually for each set of phase points, These 91 independent re
laxation trajectories constitute a nonequilibrium ensemble
that can be used to determine the averages. As usual, the
velocities of the particles are measured in the laboratory ref
erence. The total momentum of the box of course remains
zero during the simulation. Further details about the meth
ods used here can be found in earlier publications. 15,17,1S
Developing a new polarizable liquid water model that
J. Chem, Phys. 92 (9), 1 May 1990 0021-9606/90/095491-06$03.00 @ 1990 American Institute of Physics 5491
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can be used over a broad range of temperature requires in
tensive effort and a large amount of computational
time. 17.19-24 Further reducing any realistic water model to a
sufficiently simple form so that ionic solutes can be included
without engendering unreasonably lengthy computer runs
presents an added computational enigma. While this will be
a focus of our future work, it is not the goal of this paper.
Rather, the solvent-solvent potential used is represented by
a TIP3P water model, modified by inclusion of both intra
molecular vibrational freedom and an electronic polariza
tion feature employed earlier. 17 A similar strategy has been
used before on SPC water to investigate intramolecular vi
brations.25•26 This simplifying strategy is not meant to im
prove the water-water potentials, since simply adding on
these two properties to an existing empirical model, whose
parameters have already been optimized for certain proper
ties of the pure liquid, disturbs the intermolecular potential
and structure causing the model to worsen for pure water
simulations.
The justification for this simplified approach is that we
can obtain at least a qualitative idea about the behavior near
an ionic reaction of a polar solvent resembling water without
an undue expenditure of computer time. The idea is that the
ion-solvent interactions are so much stronger than solvent
solvent interactions that the details of the latter, within rea
sonable bounds, are unimportant for obtaining an acceptable
picture of the local dynamics. Any new effects that are found
should thus show up when a better solvent model can be
employed. For example, a recent comparison27 made for re
sults from two sets of computer simulations, one with and
one without the inclusion of instantaneously responsive
"electronic" polarization in the solvent model, shows that
this polarization is crucial for adequately describing the re
laxation processes involved in the neighborhood of a rapidly
dissociating ion pair. The reason is simple. The strong elec
tric field of the ion pair induces a considerable dipole mo
ment in each of the neighboring solvent molecules. This ef
fect combined with the flexible intramolecular bonds
distorts the geometry of the solvent molecules and signifi
cantly perturbs both the ion-solvent and solvent-solvent in
teractions. None of the simple water models28-30 includes
these polarization corrections explicitly, but rather the po
larization is taken into account in an average way by intro
ducing effective point charges whose magnitudes are insensi
tive to the local electric fields. This scheme may be appropri
ate for simulating pure liquid water, but it cannot be correct
for studying the inhomogeneous interface between ions and
the polar solvent.
In the present work, the intramolecular potential is as-
TABLE I. Molecular parameters. sumed to be harmonic, having a quadratic form in the bond
stretches abl and ab2 and the "-0-" bending angle arp:
u =.£L[ab2 +ab2] +~[b a",]2 mIra 2 I 2 2 e 'f'
where be is the average 0-" bond length of the vapor phase
water molecule. The force constants employed are contained
in Table I.
To represent the electronic polarization, we allow the
point charges at the oxygen and hydrogen atoms to vary
according to the instantaneous local electric field. This type
of polarization model was first used by Zhu, Lee, and Robin
son31 in simulating liquid carbon disulphide in intense laser
fields. The model leads to a simple and computationally trac
table algorithm while retaining a basic feature of the polar
ization effect. For further convenience, the polarization cen
ter is chosen to coincide with the oxygen atom. It is known
experimentally32 that the water molecule possesses an iso
tropic polarizability a of 1.444 A3. The instantaneous in
duced dipole moment Dj (1) attime t of the ith molecule thus
has the same direction as that of the local field
(2)
The changes of the point charges reproduce this induced
dipole moment within the constraint that the entire mole
cule remains neutral. This local perturbation on a single
molecule propagates to long distance through the Coulomb
interactions and introduces a non-pair-additive contribution
to the potential. 17 Therefore, the dynamic influence of the
dissociating ion pair is not limited to nearest-neighbor sol
vent molecules.
To differentiate effects at different distances, we divide
the solvent molecules into three groups. To separate the ef
fects caused by the cation and anion, we further split each
group into two subgroups. Solvent molecules whose 0 atom
distance from the cation is less than 3.7 A form the PI or
"caging" shell. This definition is somewhat arbitrary. The
shell thus defined is certainly larger than the real equilibrium
first cationic shell but is suitable for studying the dynamical
features.
If the distance of the 0 atom to the cation is greater than
6.25 A, the solvent molecule is assigned to the P 3 shell. It is
of interest to know whether this shell possesses bulk solvent
properties. The region between these two shells is assigned as
the P 2 shell or the intermediate shell. Shells surrounding the
anion are defined in an analogous way and are referred to as
N 1, N2, and N3.
Force constants
(mdyn/A) Point charges
(electron charge) kcal!mol A-'
c, c, C4 q" A B f3 r
8.454 0.76\ 0.288 -0.10\ -\ 393582 750 6.321 0.8
J. Chem. Phys .• Vol. 92, No.9, 1 May 1990
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205.208.120.10 On: Sat, 20 Dec 2014 11:10:11Zhu et al.: Computer simulation solution 5493
IJ .... 151
~~
(
Q)
~151
0151
a..cp ..........
..............................................................................
41'11'11'1 51'11'11'1
Separation
FIG. 1. Position-dependent potential energies (in units of 100 cal/mol) for
the ground (solid curve) and excited (dotted curves) states of LiF used for
the simulation. The ion-ion separation is in units of 0.001 A).
In addition to the interactions with the surrounding sol
vent molecules, the ions are constrained by the Bom
Mayer33 potential
U (g) -Ae -[3'Li-F + qLi qF Li-F ---
rLi-F (3)
with a dissociation energy of 192.37 kcallmol and an equilib
rium bond length of 1.55 A to mimic the ground state ofLiF
in the vapor phase 34
The dynamics is addressed in the following manner. At
time t = 0, and according to the Franck-Condon principle,
the LiF molecule is pumped to an "electronically excited
state" from the instantaneous LiF bond length in the equili
brated ground state. This scheme was first employed by Wil
son's group35 for studying transient x-ray scattering of the I • 2
molecule. Exact excIted state data for LiF are not available.
Here we simply assume the excitation process is realized
through one additional exponential repulsive term, giving
for the total excited state potential,
U L~~F = Ae -[3'Li-F + Be -Y'L,-F + qLi qF
rLi_F (4)
The above equation gives a dissociation energy of53.30 kcal
/mol with a gas phase equilibrium bond length of 4.5 A.
Again, this solute model is not supposed to represent accu
rately any real chemical system. The results thus obtained
are meant only to provide a qualitative picture of the local
dynamics accompanying an ionic reaction in a realistic polar
solvent. These potential energy curves for the ground and
excited states of the ion pair are illustrated in Fig. I. A differ
ent excitation mechanism, which deforms the "electronic
clouds", has also been recently investigated. 27
III. RELAXATION PROCESS
When the intramolecular potential function of the ion
~air is abruptly changed from the stable ground state poten
tIal to the unstable excited state potential (see Fig. I), disso
ciation of the solute begins and the solvation relaxation pro
cess proceeds. In Fig. 2, the time evolution of the distance
between the two ions is illustrated. No actual dissociation is 5B1'1 758 II'lBl'l
Time (lit 1 fa)
FIG. 2. Time evolution ofthe ion-ion separation (in units of 0.001 A).
completed in the 125 fs time of the calculations, since the
slowly responding solvent is not able to diffuse into the va
cancy created by the ion-pair separation during this short
period. In other words, solvent friction on these short time
scales plays a role that essentially blocks the solute dissocia
tion. A similar system, the sodium chloride ion pair in TIPS2
water, was discussed earlier by Karim and McCammon. 36
Their study focused on the longer time dynamics of transi
tions between two quasistable states. They generated several
indc:pendent t.rajectories for this process by initially fixing
the Ions at a dIstance corresponding to the top of the barrier
in the potential of mean force. Because of our inclusion of
dynamic polarization and flexible bonds and the different
time scales and goals, there is little connection between that
work and the present simulations.
Plo~ted in Fig. 3 is the response of the solvation energy
(pot~ntIa~ energy between the ion pair and solvent). Again,
the diffUSive motion of the strongly structured solvent can
not keep up with the motion of the solute. It takes about 30-
40 fs for the solvent to respond to the abrupt change caused
by the initial excitation. This is indicated by the break up of
the original cage. After another 50 fs, the configuration of
the solute tends to stabilize as indicated in Fig. 2 and a new
cage is formed, leading once again to a metastable solute/sol
vent structure (Fig. 3).
Figure 4 compares the mean-square solvation forces act-
FIG. 3. Time evolution of the solvation energy (in units of 10 cal/mol).
J. Chern. Phys., Vol. 92, No.9, 1 May 1990
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,J
251'1 S01'1 750 11'11'11'1
Time (121. 1 f s)
FIG. 4. Time evolution of the mean·square solvent forces on the ions (in
units of kcal2 mol-2/ A 2). Solid curve for cation; dotted curve for anion
(the same for all remaining figures).
ing on the cation and the anion. According to the generalized
Langevin theory,37 this is equivalent to a space-time-depen
dent memory kernel M(X,T = t) for the solvent friction. Be
cause of the relatively rapid motion of the positive ion, its
memory kernel is considerably greater than that experienced
by the negative ion. Such dependences of the memory kernel
on the relative motional time scale of a solute particle have
been previously observed in MD simulations of cis-trans iso
merizations37,38 and dissociation-recombination reactions
in solution.39 The oscillations shown in Fig. 4 indicate at
tempts of the Li + ion to break out of the solvation cage.
After about 30--40 fs (three impacts on the cage), the cage
tends to soften and the pressure imposed by the cage de
creases rapidly.
Variations in the number of solvent molecules contained
in theP 1, P2, N 1, andN2 shells are displayed in Fig. 5. For
simplicity, we assume that the sizes of these shells around
each ion remain invariant during the dissociation process
and that the cationic shells always have the same diameter as
the anionic shells. In this way, we obtain information about
the variation of local densities. However, the different effec-
__ -L ___ L-L-._' ,
250 51'11'1 751'1
Time (121. 1 f s) .' . ......... :.
FIG. 5. Time evolution of numbers of molecules contained in PI and N 1
shells (upper curves, scaled by 0.00 1 ) and P 2 and N 2 shells (lower curves,
scaled by 0.01). tive radii of the solvated positive and negative ions, as evalu
ated from the solute-solvent radial distribution functions,
are not measured here. As a consequence, the differing abili
ties of these ions to attract neighboring polar solvent mole
cules are not investigated. In fact, the equilibrium solvent
densities near the interfaces of the cation and anion are al
most identical. The main cause of the different number of
solvent molecules contained in the first natural cage (not PI
and N 1 ) is the difference in size of these ions and their cages.
On the other hand, because of the relatively rapid movement
of the low-mass positive ion, the nonequilibrium local sol
vent densities do become distinguishible. As depicted in Fig.
5, the dynamical motions of the ions tend to decrease the
density in the neighborhood of the cation and to increase the
density in the anionic shell. After a sufficiently long relaxa
tion time, this difference in density tends to disappear
through solvent diffusion. As we have already mentioned in
an earlier paper, !5 the surrounding solvent cannot fully keep
up with the fast dynamical motions of the positive ion. This
motion has a tendency to erase the shell boundaries and gives
rise to a larger size of the cationic shell compared with the
heavier negative ion. Such separations of time scales of sol
vent 'and solute motions often play important roles in ultra
fast dynamical processes. 37
In their nonequilibrium computer simulations, Rao and
Berne!! and Maroncelli and Fleming!4 observed a dramatic
heating of the solvent in response to a change of the solute's
charge. Such heating is one of the features of non equilibrium
that might give rise to a departure from linear behavior. We
see similar temperature changes in the first, second, and
third solvation shells (see Figs. 6-14). Illustrated in Figs. 6-
8 are the center-of-mass (c.m.) mean-square velocities
(MSV) of solvent molecules in the various shells. Note the
vertical scale changes. These curves clearly show dramatic
increases of the local translational temperature caused by
the strong perturbation. It can also be noticed that the mo
tion of the positive ion raises the translational temperature of
its first shell (P 1) much more efficiently than the motion of
the negative ion raises the translational temperature of its
first shell (see Fig. 6). This difference, however, is not ob-
II
III "
........ ---_ ....
250 '.
'. ".
"........... ---· __ ---1
500 750 1 _
Time (0. Ifs)
FIG. 6. Time evolution of the mean-square velocities (MSY) for C.m. of
solvent molecules in P 1 and N 1 shells. The MSY values on the vertical axis
should be mUltiplied by 3 k8 T /1000 m. Solvent mass = m (the same for
Figs. 7-11)
J. Chern. Phys., Vol. 92, No.9, 1 May 1990
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205.208.120.10 On: Sat, 20 Dec 2014 11:10:11Zhu et al.: Computer simulation solution 5495
151
N -N
II! ...... .
N
251i1 ".
51i11i1 751i1
Time (li1. 1 f s) ......
llillillil •....•..
......
FIG. 7. Time evolution of the mean-square velocities for c.m. of molecules
in P2 and N2 shells.
vious for the P 2 and N 2 shells, while an opposite tendency is
found in the P 3 and N 3 shells (Fig. 7). In fact, heating in
these outer anionic shells is found to be at least as fast and
perhaps faster than that in the N 1 shell.
In order to understand the comparative effects of the
ionic motions on translational and rotational temperatures
of the solvent molecules, we plot in Figs. 9-11 the time evo
lutions of the mean-square velocity of the hydrogen atoms in
the various shells. Since the position of the oxygen atom is
close to the center-of-mass of the molecule, the translational
temperature is essentially determined by the oxygen motion,
while the temperatures of the rotations are determined pri
marily by the motion of the hydrogen atoms. Contrary to
what was observed in Fig. 6, the motion of the negative ion
now affects its neighbors more significantly. We therefore
conclude that the positive ion, which attracts the oxygen
atoms of the solvent, has more influence on the translational
temperature, while the negative ion, which attracts the hy
drogen atoms, raises the local rotational temperatures more
easily. The high frequency oscillations in the mean-square
hydrogen atom velocities indicate the presence of fluctu
ations caused by LiF intramolecular vibrations. This effect
151
Q)
N ......... _ ....•..... _ ... _. __ •.••....•..••...............•........•....
151 -N >-
Ul
~151
~ --
151 r-
151 -.-
251i1 51i11i1 7S1i1 llillillil
Time (lit 1 f s)
FIG. 8. Time evolution of the mean-square velocities for c.m. of molecules
in P 3 and N 3 shells. .............. . -.,. .....
'. :
. ...
""'._-... : .... : .. : .. : ....
2S1il S/IJEI 7SIil lllllillil
Time (121. 1 f.)
FIG. 9. Time evolution of the mean-square velocities for hydrogen atoms in
P I and N I shells.
on solvent rotational motion has been observed in previous
MD calculationslS and could be a subject of future experi
mental interest.
Figures 12-14 depict the total change oflocal tempera
ture in response to the photoinduced dissociation of the sol
ute. We see that instantaneous local temperatures in P 1 may
be raised to over 11 OOK, while the maximum temperature in
N 1 is only -800 K. This difference is partly caused by the
more rapid motion of the lightweight positive ion. Also seen
from these figures is the fact that the time required for P 1 to
reach its highest temperature is near 40 fs, while for N 1 it is
closer to 50 fs. The slower response in N 1 is consistent with
its smaller temperature maximum. These times are close to
the time required for the ion. pair to reach maximum separa
tion (see Fig. 2).
The rise time for the temperature in the P 2 shell is about
60 fs and is about 75 fs for N2. There is no significant differ
ence between P 3 and N 3 temperature increases, the rise
times being more gradual and reaching a lower maximum
than in the innermost shells. By comparing these curves, we
may estimate the propagation rate of the thermal flow. Clear
from these figures is the fact that solvent molecules sur
rounding the smaller, lighter weight positive ion because of
its shorter interaction distance should have a faster, more
151
N
N
N ....
0," •• . ", 0,: .:':' ..... : ..... : -" ...
FIG. 10. Time evolution of the mean-square velocities for hydrogen atoms
in P2 and N2 shells.
J. Chern. Phys., Vol. 92, No.9, 1 May 1990
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&
CD
CD
& -CD >
(f)
::::i:&
~
CD -
251!1 51!11!1 751!1 11!11!11!1
Time <l2l. 1 fa)
FIG. II. Time evolution of the mean-square velocities for hydrogen atoms
in P 3 and N 3 shells.
intense response to an abrupt ionic perturbation than solvent
molecules surrounding the larger negative ion.
The time dependences of the apparent mean-square-in
duced dipole moment (MSDM) per solvent molecule (J-t2)
are shown in Figs. 15-17. Because of the long range nature of
the forces here, and the relatively small sample size, one
must be somewhat cautious about all the details arising from
these particular calculations. The ion dynamics induces a
considerable dipole moment in each of the surrounding sol
vent molecules. In particular, the peak value of (J-t2) in the
P 1 shell may rise to values two to three times larger than the
equilibrium state value. The polarization effect i~ N 1 is
much weaker. It is interesting that a reverse order IS found
for the P3 and N3 shells; cf. Figs. 15 and 17. Two other
features regarding dynamic polarization of the solvent mole
cules should be mentioned here. First, the rise time for the
MSDMs are long in comparison with other properties and
there do not appear to be propagations. Instead, a long range
feature is observed, which is especially noticeable in the an
ionic shells. Second, while the negative ion seems more capa
ble of extending its influence to long range, the positive ion is
the most important at short range. We also observe these
features in the local heating of the solvent (refer to Figs. 12
and 13).
~
( "'. I ... /~'~, I
J : ..... '-.......--.'
.... .......... . ......... .1
... •••••••••••••••••••••..••••• I
.. ·······y···:::::_L __ .L ._L-L_ .L. __ ..I...-_L_~
25~ 5.Ul 751/J 11/J1/J1il
Time (0. 1 fa)
FIG. 12. Time evolution of the local temperature of P I and N I shells (in
units of 0.1 K, also Figs. 13 and 14). :.:.:.: ....
. ..... _ ..................... .
.'
251!1 51!11!1 151!1 11!11!11!1
Time (0. 1f s)
FIG. 13. Time evolution of the local temperature of P2 and N2 shells.
A general observation which can be made is that there
seems to be a wide variation in the ultrashort time response
of the solvent on the type of abrupt ionic perturbation im
posed here, the response characteristics depending on the
ionic mass, charge, and interionic distance, and also on the
type of measurement being made. This is truly a challenge
for theorists. Nothing seems to be getting very simple as the
molecular frontiers of time and space are approached. Glo
bal aspects of the solvation process are replaced by specific
characteristics caused by the detailed nature of the many
body interactions.
IV. CONCLUDING REMARKS
Nonequilibrium molecular dynamics calculations have
been performed in order to study the dynamical aspects of
solvation of a polar solvent in response to a sudden excitation
of an ion pair. Attention has been paid to the time evolution
of the reaction coordinates, the solvation energy, solvent
forces, local densities, and heating of different librational
modes of the solvent. The effect of solvent polarization and
the dissimilar responses of the cationic and anionic shells
have been studied. These dissimilar responses are partly
caused by the different masses and sizes of the various atom-
/ .. ---WVl . ....
• 0 -.:" .. ' .....
~... I ..... ,
.-....J...! --;:2±~1/J::---L-;=51/J;!.,!1!I;-...L.-7~1!I II!I~I!I
Time W.lfs)
FIG. 14. Time evolution of the local temperature of P3 and N3 shells.
J. Chern. Phys., Vol. 92, No.9, 1 May 1990
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205.208.120.10 On: Sat, 20 Dec 2014 11:10:11Zhu et af.: Computer simulation solution 5497
250 500 750
Time (f2l. lfs) 1000
FIG. 15. Time evolution of the apparent mean-square-induced dipole mo
mentinP 1 andN 1 shells [theunitsare7.35X 10-4 D2 (the same for Figues
16 and 17)J
ic entitites used and the different time scales of solute and
solvent motions. Coupled with these effects is the difference
in formal charge ofthe hydrogens and oxygens of the solvent
molecules. These differences have a dramatic influence on
local dynamic properties such as solvent densities, tempera
tures, and polarizations, and cause the solvent shells sur
rounding the smaller positive ion to respond to the perturba
tion differently than shells surrounding the larger negative
ion. The latter responds slowly, moderately, and over a long
er range; the former responds strongly, rapidly, and over a
shorter range. Moreover, the positive ion mainly influences
the translational motion, while the negative ion mainly in
fluences the rotational motions of the neighboring solvent.
From these studies, we can draw an intuitive picture for
primordial photoinduced ionic dissociation in a polar solu
tion. Excitation of the reacting system leads to a sudden
change of its electronic configuration. Consequently, huge
forces develop that are inclined to break the original solva
tion cage, which initially corresponds to the ground state
solvation cage of the system. Both the shape and size of the
cage resist this change. This stubbornness on the part of the
solvent decelerates the reaction process. As a compromise
151
151
151 ....
250 I
500 750
Time <0. 1 f s) I L._
1000
FIG. 16. Time evolution of the apparent mean-square-induced dipole mo
ment in P2 and N2 shells. 151
151
""Ot
Ul ..
: . ~: .. \. \:~'::4 '-: :.:-
..• ~ •• I." :
.: .... ~~ 0°
.-.:: .. " .. . . ...... '. : .. ~.:.::, :~, .. :;<:: .. \(: :: ... .
250 500 750
Time (f2l. 1 f s) 1111111111
FIG. 17. Time evolution of the apparent mean-square-induced dipole mo
ment in P 3 and N 3 shells.
reply, the reacting system achieves an intermediate metasta
ble configuration, around which the neighboring solvent at
tempts to reconstruct a new cage. During this period, solvent
friction may increase the kinetic energy of the solute through
feedback of the thermal energy from the locally heated sol
vent molecules. When the reacting system gains enough ki
netic energy, it launches another attack on the solvation
cage. This same procedure is repeated at lower and lower
amplitudes until some of the solvent molecules are able to fill
the vacancy created by the reaction. Separate cages for the
cation and anion are then formed and relative diffusion of
the two solvated ions separates them, completing the reac
tion process.
As some final notes, it is worth remembering that what
we have done in this paper does not bear necessarily on the
true mechanism of real ionic hydration reactions studied in
the laboratory. First of all, creation of the unstable ion pair
by artificial electronic pumping is not completely realistic.
Preceeding the nuclear dissociation of a real solute, there
occurs a change of electronic dipole on the ~ 1 fs time scale
of the electronic transition. This takes place before any of the
nuclei have a chance to respond, though the solvent elec
trons are certainly affected. Thus, the approximation of
time-independent point charges for the ion pair is an over
simplification. A more realistic electronic excitation process
has been investigated in other work.27
Another important point is that the run times used here
are very short, .;;; 125 fs. This is the order of, perhaps even
shorter than, the longitudinal relaxation time 'T L of water. 42
While many of the processes studied seem close to saturation
on this time scale, more interesting events may follow. For
example, the model for water used here has not been chosen
to give a good representation of the Debye rotation time 'TD
(~8 ps at 300 K).43 Thus, any processes involving high am
plitude molecular rotations of the solvent are absent from
these studies both because of the inadequacy of the potential
model and the short time duration of the MD. In future work
on this subject, the 'TD aspects of the problem will need to be
improved.
Quantum effects have also been omitted. The classical
results show a slowing down of the ionic dissociation because
J. Chem. Phys., Vol. 92, No.9, 1 May 1990
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205.208.120.10 On: Sat, 20 Dec 2014 11:10:115498 Zhu et af.: Computer simulation solution
of a complicated multistage caging effect. Could a low mass,
energy latent ion such as Li + use tunneling to speed up es
cape from its initial cage environment?
Finally, the energetics of the dissociation/solvation re
action described here do not match all laboratory problems
of interest. From Fig. 1, it can be estimated that most of the
time, an LiF molecule will be excited 20-40 kcallmol above
its gas phase dissociation energy. This excess energy in our
opinion can qualitatively modify the dynamics. In fact, our
ideas about proton dissociation/hydration from weak
acids44 require: (1) a realistic water model capable of pro
viding an accurate r D' (2) proton tunneling; and (3) energy
augmentation of the endoergic process through the forma
tion of strongly bound hydration structures. These aspects
have certainly not been addressed in previous MD simula
tions of ionic solvation, nor have they been here.
ACKNOWLEDGMENTS
Financial support at the PQRL has been shared by the
Robert A. Welch Foundation (D-0005, 46% and D-1094,
5%), the National Science Foundation (CHE8611381,
37%), and the State of Texas Advanced Research Program
(1306, 12%). Computer time was furnished by the Pitts
burgh Supercomputing Center.
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J. Chem. Phys., Vol. 92, No.9, 1 May 1990
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1.345286.pdf | Pt2Si formation: Diffusion marker and radioactive silicon tracer studies
M. A. E. Wandt, C. M. Comrie, J. E. McLeod, and R. Pretorius
Citation: Journal of Applied Physics 67, 230 (1990); doi: 10.1063/1.345286
View online: http://dx.doi.org/10.1063/1.345286
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32Pt2Si formation: Diffusion marker and radioactive silicon tracer studies
M. A. E. Wandt
Van de GraaffGroup, National Accelerator Centre, Faure 7131, South Africa
C. M. Comrie
Department of Physics, University of Cape Town, Rondebosch 7700, South Africa
J. E. McLeod
Van de GraaffGroup, National Accelerator Centre, Faure 7131 and Department of Physics,
University of Cape Town, Rondebosch 7700, South Africa
R. Pretorius
Van de GraaffGroup, National Accelerator Centre, Faure 7131, South Africa
(Received 20 June 1989; accepted for publication 4 September 1989)
The moving species during the formation of first-phase platinum silicide, Pt2Si, by thermal
annealing is identified with inert markers (Ti, Co, Ge, As) and radioactive 31St as a tracer.
Rutherford backscattering spectrometry is utilized to monitor the flow of atoms past the
marker during the silicide forming reaction, while the position of the tracer after the reaction is
determined by using sputter depth profiling and radioactivity measurements. Experiments with
thin-film structures employing a reference marker at the substrate silicon/amorphous silicon
interface and a mobile marker near the amorphous silicon/platinum interface clearly show a
shift of the latter marker towards the surface of the sample. The radioactive tracer, initially
embedded in nonradioactive silicon and metal, is moved from this position and concentrates at
the sample surface. The outcome of both marker and tracer studies is consistent with a picture
in which platinum diffuses during the formation of Pt2Si.
i. iNTRODUCTION
During the past decade silicide contact metallurgy has
been increasingly employed in advanced integrated circuit
metallization due to several of their advantages. In particu
lar, the low resistivity and high thermal stability of near
noble and refractory metal silicides makes these compounds
especially suitable as a replacement for polysilicon in the
production of gate electrode materials and low-resistance
interconnects. Among the materials of interest. self-aligned
silicides of platinum were among the first compounds to be
applied to a wide variety of integrated circuit structures. I
Lately this system has gained considerable importance in the
manufacture of Schottky barrier photodetectors.2
The platinum silicide layers are grown by annealing a
thin platinum film deposited on a silicon substrate. In a dean
system, with unlimited Si supply, the metal reacts with sili
con at temperatures above 200 °C, first forming a metal-rich
silicide, Pt2Si. When all the metal is consumed, the techno
logically important end-phase, PtSi, starts to grow at tem
peratures in the vicinity of 300°C. 3,4
Many investigations have been devoted to the under
standing of platinum silicide formation and the factors influ
encing the Pt-Si interaction. For example, reaction kinetics
of both Pt2Si and PtSi growth have been shown to depend
strongly on oxygen contamination of the metal film, increas
ing contaminant concentration slowing down the reaction
process.4,5 On the other hand, thin films of gold sandwiched
between the silicon and platinum layers have been demon
strated to enhance PtSi formation only.6 Other studies have
been concerned with the effect of nitrogen impurities on the
Pt-Si interaction,7 the redistribution of dopants, such as ar-senic, during Pt-silicide growth,8 the oxidation of platinum
silicide layers,9 the influence of different processes during
device fabrication,1O and the study of lateral diffusion cou
pIes. 11
In many instances results of these experiments are ex
plained in terms of the dominant moving species during sili
cide formation. Knowledge of the diffusants and the mecha
nisms of diffusion is essential for a complete understanding
of the interaction between metal film and silicon, and of the
influence of impurities on silicide growth. It is thus surpris
ing that with few exceptions12-15 no attempt has yet been
made to unequivocally pinpoint the diffusing species during
Pt2Si and PtSi growth. Employing a radioactive silicon trac
er, Pretorius et al. 12,13 deduced indirectly from second pha..'>e
PtSi results that platinum is the diffusing element during
first-phase Pt2Si formation. Zhao et al. 14 made use of a thin
molybdenum marker, the shift of which indicated predomi
nantly Pt motion in the case of thermally annealed Pt2Si,
while for ion mixing both species were involved in the atomic
transport. However, these researchers were mostly interest
ed in the initial reaction and experimented with thin (25-
um) Pt films, with the disadvantage of very small marker
movements. The same authors believed that Pt is the only
moving species in the thermal formation ofPt2Si, but recom
mended an additional independent study.15 Furthermore,
Tn 16 maintained that both Pt and Si diffuse during the for
mation ofthe metal-rich platinum silicide, but failed to pro
vide experimental evidence.
Discrepancies in these earlier reports prompted us to
reinvestigate the Pt-Si diffusion system. In this paper inert
marker and radioactive silicon tracer experiments are COD-
230 J. Appl. Phys. 67 (1), 1 January 1990 0021-8979/90/010230-07$03.00 © 1989 American Institute of Physics 230
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32sidered in detail with the aim of identifying the dominant
diffusing species (and possibly the diffusion mechanism)
during first phase Pt2Si formation.
It EXPERIMENTAL PROCEDURES
Polished single-crystal silicon wafers of (100) orienta
tion, p type (B doped), 1.5-4.0 n em, and a thickness of
approximately 0.5 mm were cleaved into 1 cm2 squares.
These were cleaned ultrasonically with trichloroethylene,
acetone, and methanol, followed by a rinse in deionized wa
ter. Immediately prior to loading into a vacuum chamber for
electron beam evaporation, the samples were etched in 20%
(v/v) hydrofluoric acid to remove the native oxide layer.
A. Marker
Thin film structures with a reference markerl5 at the
single crystal silicon/amorphous silicon interface and a mo
bile marker near the amorphous silicon/platinum interface
were prepared by consecutive electron beam evaporation of
marker (Ti, Co, Ge, or As), Si, marker, and Pt. The refer
ence marker was situated sufficiently deep in the structure
that its position was not altered during silicide formation.
Platinum film thicknesses ranging from 100 to 130 nrn with
corresponding silicon films of up to 300 nrn were deposited
at rates of less than 1.5 nrn/s. The marker elements were
evaporated at rates of about 0.1 nm/s and 0.5-1 urn thick
ness. The vacuum was always better than 8 X 10-5 fa during
evaporation.
For most marker investigations three different sets of
samples were produced in order to observe and minimize
possible effects of interface drag. 17 In the first set the mobile
marker was deposited between the amorphous silicon and
platinum films as described above, whereas in the second set
a 7.S-nm platinum layer preceeded the deposition of the
marker and capping platinum. In the third set an additional
5-nm Si layer was evaporated on top of the marker thus upon
a preanneal effectively embedding it in a layer of ~ 10 nm
Pt2Si. For each marker, a control sample with Si(lOO)1
marker/Pt structure, each layer 150 mn thick, was included
in the subsequent annealing sequence to study on a larger
scale any Si-marker-Pt interaction.
Thermal annealing was carried out in a vacuum quartz
tube furnace at a temperature of 285 ·C for times up to 30
min. Background pressure was less than 3 X 10-5 fa. The
marker movement was followed by 2 and 2.6 MeV 4He+
Rutherford backscattering spectrometry (RBS). Silicide
compounds formed were characterized by the height ratio of
the metal and silicon yields, while layer thicknesses and
marker position were extracted from simulated spectra fit
ted to experimental data,18 both before and after annealing.
B. Tracer
By now, radioactive 31Si (Si*) has been used on numer
ous occasions12.13.19 to determine the dominant moving spe
cies during silicide formation. While under certain circum
stances the interpretation of the experimental data is
ambiguous,20 the technique does have the advantage of not
introducing (chemically) foreign material into the diffusion
231 J. Appl. Phys., Vol. 67, No.1. 1 January 1990 system. In this investigation, 300-run Si was evaporated onto
the substrate silicon foHowed by approximately 50 nm radio
active 31Si and 140-nm platinum. Sets of 16 nominally identi
cal samples were prepared by deposition onto a 4 X 4 cm2
substrate.
The radioactive silicon was produced by 12-h neutron
activation of pieces of natural silicon (Cerac) with 99.999%
purity. Thermal neutrons are captured by 308i (natural
abundance 3.1 %) forming 31Si which is a ,B-emitter with a
half-life of 2.62 h, Before loading into the evaporator, the
activated silicon was subjected to the same cleaning se
quence as the substrate silicon to remove contingent surface
impurities. The decay of the 31Si was also followed by multi
ple beta counting of a reference sample with a Geiger
MiilIer detector to expose any deviation of the observed half
life from the tabulated one.
After deposition the samples were annealed in a vacuum
furnace at 285 ·C for 30 min, resulting in complete reaction
of the metal layer to Pt2Si. The activity profile was derived
from sectioned specimens using argon sputter etching to par
tially remove the grown silicide layer. The thickness of the
removed silicide was deduced from RBS spectra acquired
before and after sputtering. By varying the sputter time and
comparing normalized counts of the virgin and sputtered
specimen, each sample of a set provided one point on the
integrated activity profile. For comparison of this profile
with calculated profiles assumi.ng different diffusing species,
the exact amount of deposited radioactive silicon needs to be
known. A procedure based on evaporation of ~ 150 nm Si*
onto a thin aluminum foil of specific size was adopted to this
end. The quantity of Si'" on the aluminum was then deter
mined by weight difference (and RBS spectrometry), while
the Si* thickness on the specimens was derived by compar
ing normalized counts of the latter with those of a piece of
foil of same area.
iii. RESULTS
A. Marker
Figure 1 illustrates the general structure of samples with
reference and mobile marker before and after annealing. If
the layer of amorphous silicon, Si(a), is thick enough, the
substrate does not take part in the reaction and no atomic
transport takes place past the reference marker. Since matter
above the reference marker is conserved in the silicide form
ing reaction, the reference marker appears at the same ener
gy in RBS spectra acquired before and after complete trans
formation to Pt2Si. The separation of the two markers will
then vary according to which element constitutes the domi
nant diffusing species during the reaction. In the case of
platinum diffusion, Pt atoms move past the marker and
through the initially formed silicide layer, and react with the
underlying silicon. Thi.s causes an increase in marker separa
tion, until all metal is consumed and the marker reaches the
sample surface. Conversely, if silicon diffuses past the mark
er, the latter will be displaced deeper into the sample result
ing in a decrease in marker separation. If both species dif
fuse, the marker will be found somewhere between these two
limiting cases. Because of the pronounced difference in stop-
Wandt eta!. 231
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32"Refilfencil"
Marker Pt Diffusion
Si and pt
Dlffueion
SI Diffusion
FIG. 1. Schematic diagram showing the motion of a mobile marker relative
to a fixed reference marker after annealing a Pt-Si diffusion couple. The
reference marker is stationary at the single-crystal substrate silicon/amor
phous silicon [Si (xtal) lSi (a) J interface. During silicide growth the mark
er layer experiences a flux of platinum and/or silicon atoms past it with the
result of it being (a) expelled to the sample surface in the case of dominant
Pt diffusion, (b) situated within the band of Pt2Si in the event of both spe
cies diffusing, and (cl displaced deeper into the sample with Si diffusion.
ping powers of silicon and platinum, marker movement is
more dramatic in the event of Pt diffusion. The technique is
thus more sensitive for detecting metal diffusion.
Backscattering spectra of 2.6-MeV 4He+ particles ob-
250
"0
~150
o §
~100
50 -8' i
",-
GIl
. . ~
liS F pt
it ~-as deposited ~
......-
oos 28S"C-21mln
x7 )(85
lJ·:
o~~~~~~~~~~.-~~~~
250 300 350 400 450
Channel
FIG. 2. 2.6-MeV 'He' backscattering spectra obtained before (solid line)
and after (circles) thermal annealing of thin film structures delineated in
the insert. The silicon and germanium yields are magnified 7 and 85 times,
respectively. Surface positions for all thrce elements involved are indicated
by vertical arrows. Platinum diffusion manifests itself in a movement of the
marker towards the surface.
232 J. Appl. Phys., Vol. 67, No.1, 1 January 1990 tained from a virgin and an annealed sample are presented in
Fig. 2 for the germanium marker. The decrease in height and
widening of the Pt signal with the simultaneous appearance
of Si at its surface position indicate complete reaction. The
Ge part of the spectrum, magnified 85 times, shows an in
crease in marker separation with the expulsion cfthe marker
from within the sample to the surface upon thermal anneal
ing, pointing to Pt diffusion. However, since Ge does not
behave like a truly inert marker, but reacts with Pt to form
platinum germanides, as was observed with the control sam
ples, this conclusion may be questioned. For this reason the
experiment was repeated with a cobalt marker.
Figure 3 illustrates the similar movement of the Co
marker upon formation ofPt2Si. Since Co has a lower atomic
mass than Ge, no overlap of the marker signal with the Pt
peak occurred in the backscattering spectra and the energy
of the He + projectiles could be lowered to 2 MeV with the
benefit of improved depth resolution. The marker is seen to
shift towards its surface position, again implying platinum
diffusion. The control samples with thick Co/Pt layers, si
multaneously annealed with the marker specimens, showed
no reaction, neither bet\veen silicon and the marker dement,
nor between the latter and platinum, due to the relatively
high formation temperature ofCo2Si.21 However, in Fig. 3 a
drop in the peak height and broadening of the mobile
marker's cobalt signal is observed after silicidation. This
might stem from thickness variations between the two speci
mens or from the formation of a cobalt silicide at this inter
face. Yet, even in the latter case, the islands of cobalt silicide
will act as a proper marker, since adjacent CozSi and PtzSi
Energy (MeV)
300 1.4 1.6 1.8
g
~ i liS it --os deposited
250
Co
g ..-.
32 200 i i ~ & o. 28S"C-20min q;
5=
x70
Co
!
o~~~~~~ .. ~~~~~~~
250 0300 350 400 450
Channel
FrG. 3. 2-MeV 4He+ backscattering spectra obtained from Pt-Si diffusion
couples with a Co marker before (solid line) and after (circles) formation
of Pt2Si. Surface positions of marker and reacting elements are plotted as
vertical arrows. The drop in the height and broadening of the Pt peaks with
the concurrent change in the silicon yield is indicative of Pt2Si formation.
The shift of the marker towards the sample surface results from Pt diffusion.
Wandt etal. 232
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32would be immiscible due to different crystallographic struc~
tures, It follows that Co can be regarded as a good marker17
in the sense that it is inert and immobile during the studied
reaction,
The relative marker shifts for the formation of Pt2Si,
measured with respect to the.reference marker, as a function
of the amount of reacted silidde, are presented in Fig, 4 for
the Co marker. The plotting symbols relate to the three dif
ferent sets of samples analyzed, with triangles, circles, and
squares denoting the structures Si(xtal)/Co/Si(a)/Co/Pt,
Si(xtal)/Co/Si(a)/Pt/Co/Pt, Si(xtal)/Co!Si(a)/Pt/Co!
Si/Pt, respectively. The amorphous silicon layer, Si.(a) , was
in aU cases ~ 300 nm thick, the top Pt layer 100 nm, and the
Pt and Si layers embedding the marker 7.5 and 5 nm, respec
tively. The plot shows no difference in the diffusion behavior
of these structures, indicating that interface drag of the
marker did not occur, The solid lines in Fig. 4 correspond to
marker motions calculated with the assumption that only
one of the reaction partners moves during Pt2Si formation.
The data strongly support Pt as being the dominant diffusing
species.
In a similar experiment using a titanium marker, results
identical to those found with the cobalt marker were ob~
tained (cf. Table I).
In the arsenic marker investigation, it was extremely
difficult to maintain stable deposition conditions during the
evaporation of As, This element sublimes upon heating,
which resulted in subsequent volatilization of As from the
warm Si substrate. Oxygen absorbed in the porous As crys
tals used for evaporation, further complicated its use as a
180
........ 180
>-(!) 140
~ 120
~ -100 -.-4 .:= If.! 60
$.,
iV 80 .!lo:t
ra 40 :=
OJ 20
I> 0 .~ ~
~ -20 -Q)
M -40
-GO j
I,)
FIG, 4, Marker energy shift measured from RBS spectra as a function of
Pt2Si grown at 285 'C for various annealing times, The different symbols
refer to the three types of samples used to observe the possible effect ofinter
face drag: (a) marker at Si(a)/Pt interface (triangles); (b) marker embed
ded in platinum (circles); and (e) marker sandwiched between thin layers
ofPt and Si deposited on the opposite side of the particular thick layer ofthis
element (squares). The solid lines refer to the expected marker shift if either
Pi or Si diffuses exclusively,
233 J. Appl. Phys" Vol. 67, No. i, 1 January i990 TABLE 1. Marker separation before and after Pt,Si formation.
Marker
Ge" calculated
observed
Tia calculated
observed
Co' calculated
observed
Co" calculated
observed
Coc calculated
observed
a At SilPt interface,
b Embedded in Pc as-deposited
120
120
80
80
140
140
148
148
144
144
C Embedded in initial Pt2Si. Separation (keV)
Si diffusion Pt diffusion
108 180
176
72 108
120
104 296
282
112 296
292
112 300
288
marker, Some specimens, however, clearly showed transla
tion of the As peak from within the sample to the surface
after complete silicide formation. This is consistent with the
other marker results, showing that Pt diffuses under the de
scribed conditions.
Table I summarizes the results of the different marker
experiments conducted in this study. For each set of sam
ples, the separation of reference marker and mobile marker
are listed for the as~deposited specimen and after complete
Pt2Si formation, assuming silicon or platinum diffusion. Ex
perimental values were obtained from RBS spectra of fully
reacted samples, whereas calculated data were inferred from
computer simulations t8 of the thin film structures. For these
simulations, thicknesses of un annealed specimens were used
and complete conversion to PtzSi, with only one of the spe
cies moving, was assumed to have taken place. Discrepan
cies between calculated and experimentally observed marker
separations are thought to have their origin in small thick~
ness variations amongst the different samples, which are un
accounted for by the computer simulation. All. data are
clearly supportive of platinum diffusion.
Table I also shows that there is good agreement between
the results obtained using Co and Ge markers. This may be
regarded as surprising in consideration of the earlier as
sumption that the low formation temperature of platinum
germanides implies that Ge is not a true inert marker. The
reason that Ge does give reliable results is probably due to
germanium occupying silicon sites in the PtzSi lattice. Thus,
once formed, the Ge marker will be unaffected by Pt atoms
diffusing either along grain boundaries, interstitially or via
the metal sublattice.
B. Tracer
Initially the radioactive Si" tracer is located between the
metal and nonradioactive silicon (Fig, 5), After initial for
mation of a band of radioactive Pt2Si* the tracer is moved
from this position in a way which depends on the diffusing
species and diffusion mechanism during the reaction, In the
case of metal diffusion, platinum atoms migrate through the
radioactive layer, either along grain boundaries or via the
Wandtetal. 233
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32Pt Dlff.
Sl (GS/lnt)
Olffuslon
51 (G8/lnt)
and Pi Diff. ~
st (Vac) Dltt.
FI G. 5. Schematic representation of the expected distribution of a radioac
tive silicon tracer, Si*, supposing different diffusing species and mecha
nisms during the formation of Pt2Si from a Pt-Si diffusion couple. After
initial formation of a layer of radioactive Pt2Si*, the tracer profile uniformly
translates to the sample surface if plat inurn is the only moving species (any
mechanism). Silicon grain boundary (GB) or interstitial (Int) diffusion
leaves the marked Pt2Si* at the silicon/silicide interface. If the activity is
observed somewhere in between the former two limiting cases, both species
move simultaneously. Silicon vacancy diffusion (Vac) is thought to distri
bute the activity throughout the silicide (see Ref. 21).
lattice, without disturbing the silicon atoms. As a result the
tracer moves as a sharply defined band of radioactivity to the
surface of the sample, irrespective of the transport mecha~
nism (Fig. 5). On the other hand, if silicon diffuses by an
interstitial or grain boundary mechanism, nonradioactive
substrate silicon diffuses through the initial Pt2Si'" layer with
(almost) no exchange with the radioactive silicon. The ac
tivity thus remains within a layer at the substrate/platinum
silicide interface (Fig. 5). If the fluxes of both atomic species
are comparable a distribution somewhere between the two
extremes described above might be anticipated, in which the
Pt2Si* tracer is situated between two layers of nonradioac
tive Pt2Si. If silicon diffusion takes place by a substitutional
(vacancy) mechanism the tracer atoms in the initial Pt2Si*
win be displaced by the advancing nonradioactive silicon. A
radioactivity profile similar to that for metal diffusion might
then be expected if the random nature of substitutional diffu
sion is ignored. In practice, the randomness of the vacancy
movement win give rise to a broadening of the Sj* tracer
profile. In particular, Bartur and Nicolet22 pointed out that
for dominant lattice diffusion the mixing of the radioactive
Si* would be very thorough, resulting in a uniform (fiat)
activity profile (Fig. 5). In such a case, Lien20 has shown
234 J. Appl. Phys., Vol. 67, NO.1, 1 January 1990 that the information that can be obtained from a Sj* tracer
profile may be ambiguous, in that high silicon self-diffusion
in the silicide could produce the spreading, irrespective of
the dominant diffusing species or mechanism. However, as
Lien20 indicated, it is unlikely that a fiat Si'" profile will ever
result from metal diffusion since it is expected that the highly
mobile species is also the one which diffuses during growth.
Plots of residual radioactivity and its derivative, the ac
tivity concentration profile, measured as a function of depth
in the sample, are presented in Fig. 6. Also shown is the
expected decrease of activity for silicon grain boundary/in
terstitial and platinum diffusion calculated from the actual
amount of Si* deposited. The size of the vertical error bar
attached to each experimental point is determined by the
statistical uncertainty in activity counting, while the error on
the depth scale originates in the finite resolution of the RBS
technique. Within experimental error the measured activity
clearly follows the line for platinum diffusion. The Si* con
centration at the surface remains at 100% and the initial
band of radioactivity shows only very slight spreading. How
ever, some activity is still found beyond the expected depth
of Pt2Si*. We think this may be an experimental artifact
caused by sputter induced mixing of the Si and Si* at the
Pt2Si/Pt2Si'" interface during the sputter microsectioning
process.
r--I 100
~ 80 i...-l
I>.. 80
~ 70
+1 80 (,) -< 50
~ 40
30
·fi 20
~ 10 .,
100
~ eo
l-00oi ao •
d 70
~ 80 •
U 80
!;-40 •
.~ 30 :;.1 20 • (> -< 10 • 0
300 200 100 0
Pt2Si depth [n:m.]
FIG. 6. Percentage Si* remaining in the silicide after sputter ~ectioning
(top), and Si'" concentration (bottom) as a function of Pt2Si depth. The
solid lines indicate the expected decrease in activity if either platinum or
silicon is the dominant diffusion species. Although some spreading of the
Si" profile has occurred in the deeper parts of the sample, the data closely
follow the line for metal diffusion.
Wandtetal. 234
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32IV. DISCUSSION
Our observation that Pt is the diffusing species during
PtzSi formation lends credibility to various interpretations
of dopant and impurity behavior based on the assumption of
metal diffusion during this reaction. For example, Ho et al.7
studied the influence of nitrogen impurities on the Pt-Si reac
tion. Nitrogen implanted in the platinum film tended to ac
cumulate at the Pt/Pt2Si interface during silicide growth,
whereas nitrogen implanted into the silicon was incorporat
ed into the formed silicide, with a simultaneous broadening
of the nitrogen profile. These results are in accordance with
Scott's model ofimpurity redistribution23 accompanying si
licide formation by Pt diffusion. Similar conclusions were
reached by Fon et al.24 who investigated the formation of
platinum silici.des on slightly oxidized Si substrates. In their
study the remnants of the oxide layer were interpreted as
diffusion markers. The same reasoning is valid for experi
ments conducted by Nava et al. 5 who found oxygen original
ly contained in the metal film segregating at the PtzSilPt
interface. Another approach was presented by Song and
Chang6,25,26 who demonstrated that the growth rate of Pt2Si
shows little change, while that ofPtSi is greatly enhanced,
when a thin gold film is interposed between the substrate
silicon and metal layer. These authors argue that the en
hancement can be attributed to the increased supply of Si
due to the added out-diffusion of Si through the gold layer,
which acts as a good silicon diffusion source due to the low
Au-Si eutectic. This would expressly apply when silicon is
the dominant diffusing species. From the absence of an en
hanced growth rate in the case of Pt2Si it can thus be con
cluded that platinum is the main diffusing species during the
formation of this compound.
Observing the movement of a molybdenum marker, Af
folter et ai. 14,15 found an atomic transport ratio of about 13: 1
in favor of Pt diffusion. However, these researchers report a
ratio of between 1.; I and 1:3 in favor ofSi diffusion in samples
in which PtzSi growth was induced by ion mixing. They sug
gest that the presence of the marker could suppress silicon
motion, and argue that both species might move during ther
mal annealing. Our results of the 8i* tracer experiment,
where no foreign marker is present, refute these thoughts.
Another idea postulated is that the systematic deviation
from the pure Pt diffusion line observed for the thermal an
nealing data could be attributed to the amorphous nature of
the Si film. Yet we believe this to be rather the effect of im
purities imbedded during silicon preparation. This view is
supported by the observation of reduced reaction rates, an
effect which is expected to have its origin in the sensitivity of
Pt2Si growth to impurities.4,5
Impurities may also have played a role in the earHer
studies of Po ate et al.27 who reported silicon to be the diffus
ing species during PtzSi formation. This conclusion was de
rived from the simultaneous observation of the relative
movement of the Pt2SilPt and PtSilPtzSi interfaces. It is
clear that impurities played a major role in their investiga
tion as the simultaneous growth of both platinum sUicides is
only observed in contaminated systems.4
We are thus able to conclude that PtzSi growth occurs
by platinum diffusion. No information regarding the actual
235 J. AppL Phys., Vol. 67, No. i, i January 1990 mechanism of Pt diffusion could be extracted from our ex
periments. For clues in this respect we can turn to a detailed
investigation of platinum silicide microstructure on un
doped and on heavily As-doped poly-Si. g From the observa
tion of Kirkendali voids at the Pt2SilPt interface, Wittmer et
al. II proposed that Pt atoms are the dominant diffusing spe
cies during this reaction. The voids were thought to originate
from a large flux of vacancies in the reverse direction of the
flux of Pt atoms from the Pt layer through the silicide
towards the substrate silicon. These vacancies condense at
the siHcide/Pt interface forming the observed void network.
\I, CONCLUSION
We have shown that platinum is the diffusing species
during PtzSi formation. Results of our inert marker and ra
dioactive silicon tracer experiments support Pt-diffusion
based interpretations of dopant and impurity behavior as
investigated by other researchers, However, the experiments
conducted in this study only provide information on the dif
fusing species and do not anow us to characterize the trans
port processes involved in the reaction. The proposed mech
anism of Pt vacancy diffusion awaits further confirmation.
Experiments to this end using radioactive platinum isotopes
are currently under investigation in our laboratory.
ACKNOWLEDGMENT
The authors wish to thank the Foundation for Research
Development for their financial assistance and Johnson
Matthey (Pty) Ltd. for donating the platinum used in this
study.
'P. B. Gnate, Mater. Res. Soc. Symp. Proc. 10, 371 (1982).
2M. Kimata, M. Denda, N. Yutani, S. Iwade, and N. Tsubouchi, IEEE 1.
Saiid-State Circuits SC-22, 1124 (1987).
3C. Canali, e Catellani, M. Prudenziati, W. H. Wadlin, and C. A. Evans,
Jr., AppL Phys. Lett. 31,43 (1977).
·C. A. Crider, J. M. Poate, 1. E. Rowe, and T. T. Sheng, J. Appl. Phya. 52,
2860 (1981).
SF. Nava, S. Valeri, G. Majni, A. Cembali, G. Pignatel, and Go Queirolo, J.
Appl. Phys. 52, 6641 (1981).
6J._S. Song, and C.-A. Chang, J. Vae. Sci. Technol. A 5,1717 (1987).
'K, T. Ho, M-A. Nicolet, and L Wieluilski, Thin Solid Films 104, 243
(1983).
BM. Wittmer, J. T. Wetzel, and P. A. Psaras, Philos. Mag. B 54, 359
( 1986).
9R. Pretorius, W. Strydom, J. Wo Mayer, and C. Comrie, Phys. Rev. B 22,
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we_A, Chang, J. App\. Phys. 59, 3116 (1986).
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18,207 (1983).
I2R. Pretorius, C. L. Ramiller, and M-A. Nicolet, Nne!. Instrum. Methods
149,629 (1978).
13R. Pretorius, J. Electrochem. Soc. US, 107 (l98l).
14x. A. Zhao, K. Affolter, and M-A. Nicolet, Mater. Res. Soc. Symp, Fmc.
45,165 (1985).
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(1985).
16K. N. Tn, AppL Phys. Lett. 27, 221 (1975).
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edited by J. M. Poate, K. N. Tu, and J. W. Mayer (Wiley, New York.
1978), Chap. 10.
Wandt etal, 235
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:3218L. R. Doolittle, Nne!. lnstrum, Methods Phys. Res. B 9, 344 ( 1985).
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Lett. 30. 501 (1977).
2°C._D. Lien, J. App!. Phys. 57, 4554 (1985).
21M_A. Nicolet and S. S. Lan, in VL51 Electronics: lvliCl'ostructure Science,
edited by N. G. Einspruch and G. B. Larrabee (Academic, New York,
1983), Vol. 6, p. 360.
236 J. Appi. Phys., Vol. 67, NO.1, 1 January i 990 22M. Bartur and M-A. Nicolet, J. App\. Phys. 54, 5404 (1983).
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Wandt etal. 236
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137.207.120.173 On: Fri, 21 Nov 2014 20:55:32 |
1.38446.pdf | AIP Conference Proceedings 190, 450 (1989); https://doi.org/10.1063/1.38446 190, 450
© 1989 American Institute of Physics.Central current drive by
synchrotron radiation in a
tokamak reactor
Cite as: AIP Conference Proceedings 190, 450 (1989); https://
doi.org/10.1063/1.38446
Published Online: 16 June 2008
R. L. Meyer , I. Fidone , and G. Giruzzi
450
CENTRAL CURRENT DRIVE BY SYNCHROTRON RADIATION IN A TOKAMAK REACTOR
R.L. MEYER, I. FIDONE, G.GIRUZZI, LPMI, U.A. CNRS 835,
Universit6 de Nancy I, FRANCE and DRFC - CADARACHE, FRANCE
Abstract
Current drive by synchrotron radiation is considered. The general
formula for computing the generated current for a given asymmetric spec-
tral distribution is presented. Preliminary numerical results on the cur-
rent drive efficiency and radial profile are also shown.
I. INTRODUCTION
In a hot plasma (Te = 50 Kev) tokamak reactor, it is very tempting to
use a small fraction of the synchrotron radiation with a non-zero paral-
lel momentum for steady-state current drive I. Conceptual devices in which
the centrally located synchrotron driven current acts as a seed for the
bootstrap effect were discussed recently2'3,using crude estimates of the
radiated power and generated current. In order to assess the potential of
synchrotron radiation as a current driver, we have undertaken an extensive
and accurate study of the problem using the current drive efficiency of
Fidone at al 4 and Trubnikov's 5 theory of synchrotron radiation. While the
difficulty of achieving a wall configuration capable to create an asymme-
tric radiation spectrum with net nonzero momentum is recognized, here the
intention is to identify the role of the plasma and radiation parameters
which determine the driven current.
II. CURRENT DRIVE EFFICIENCY
A wave of frequency w and parallel refractive index Nli generates
a toroidal current in a Maxwellian target plasma through momentum transfer
and asymmetric resistivity 5 (the latter is in general predominant). The
figure of merit is given by 4
1 + ay [1 + Tor(~o)]
AJIAP = ~ GC~q,a) = e p Nil (i + ay) r ° ~(r o) ' (13
where p = mc2/T , a = W/Wc~, AJ and AP are in units nee(Te/m)~ and n e T e
(4~e 4 neJk/m~ Te~/2), respectively, y is the solution of the equation
shy - y = i/a (i - N~),
Zo = (i + aY)/[l + 2 aY + a 2 (I - N~) (2 - chy + y2)]~,
~(y) = (y _ i)3/2/(y + i)~ (y2 _ 2yRny - i)
® 1989 American Institute of Physics
451
r(T) = [2 .},2(.{ + 2) Rny - (4]" - 1) (./.2 _ 1)]/T(T2 _ 1) (T 2 - 2T~n/" - 1),
and we assume the ion charge Z = i. Equation (i) with e = 1 is valid for
sufficiently high values of w/w c and ~. In fact, e is a siowly varying
function of w/w c and ~ and a rigorous numerical computation of Eq.(1)
shows that for Te = 50 KeV and w/w > 5, e = 1.2. In order to compute the
C
spatial profil and the total current generated by synchrotron radiation,
it is necessary to evaluate AP for a given asymmetric wall configuration
and given values of Nil, ~ and plasma parameters. Note that AP is the frac-
tion of the reflected radiation with a nonzero average value of Nil and
AP = 0 for <Nll> = 0. From Eq.(1)
AJ (mc2/4~e3nedO G (NIl ,a) AS ° ro = 2k"(~) exp (-2 ~RK"d~'), where
K"(~) = K"Vg/Vg, K is the imaginary part of the wave propagation vector,
is the abscissa along the ray path, Vg is the group velocity, ASois the
energy flux, and the ordinary units are restored. K"is obtained from the
relevant dispersion relation. Using Eq. (I) we obtain
AI/AW = (mc2/4~e 3 neA ) 2, fardr GAp /(2~R) 2~ fa rd~ AP =
o o
(mc2/4~e 3 ne#~l ~adr G(NII ,=) p(r) /2~R fa dr p(r),
o o
where a and R are the minor and major radii of the torus of circular cross
section, p(r) = p (~(r)), and p(1) = 2 K"(~) exp (-f~ 2K"d~'). For a homo-
o
geneous plasma
AIIAW = (mc2/4~e 3 ne2i) G (Nll,a) = (~) 1.56 G CA/W), where R and n are
e
expressed in meters and 1020 m -3, respectively. For w/w c = 9, Nil= 0.5-0.7,
T e = 50 Kev (]l= 20), ~I/~W = (0.3/neR)(A/W). We now compare this result
with the corresponding for realistic profiles of he, Te, and B.
III. NUMERICAL RESULTS FOR AN INHOMOGENOUS PLASMA
We now present some preliminary results on the radial profile of the
generated current ~J and the global efficiency ~I/~W for given values of 8
and w. These results show that the generated current is located in the
plasma core and characterized by relatively high values of the current
drive efficiency. We consider a Tokamak device with a = 1.5 m, R = 4 m and
B(0) = 60 KG. The density and temperature profiles are given by n (r) =
n e (0) (i - r2/a2), T e (r) = T e (0) (i - r2/a2)3/~ - where ne(0) =el014cm-3
452
and Te(0) = 50 KeY. Values of p(r) versus r for the X - mode in the equa-
torial plane for w/w (o) = 7 and 9 = 60 = , 70 ° are shown in Fig.l. It ap-
c
pears that the main part of the power deposition as well as of the genera-
ted current lie within r = 50 cm. Similar results are obtained for diffe-
rent values of w/w (o) > 5. Note that for e = 60 =, the ray crosses the
C
plasma axis twice. In Fig.2, we present the total wave power absorbed in a
single transit n = fa p(r)dr versus w/~ (o) for the parameters of Fig.l In
o c
general, strong absorption occurs for w/w (o) <8 and 8> 50 ° . Note however c
that weakly absorbed waves at w/w (o) > 8 are relatively more important c
for current generation since the maximum of the intensity occurs at high
values of W/Wc(O). Figure 3 shows AI/AW versus W/We(O) for the parameters
of Fig.2 for e = 40 ° , 60 °, and 70 °. It appears t~at the values of AI/AW
are in general significantly smaller than the homogeneous case
(= 0.07 A/W) except for 8 = 60 ° and w/w c (o) > 9. The temperature depen-
dence of AI/AW for 8 = 60 ° is presented in Fig.4. It is found that the
current drive efficiency is a slowly increating function of T (o). e
REFERENCES
1 - J.M. DAWSON and P.KKAW, Phys. Rev. Lett 48,1730 (1982)
2 - J. JOHNER and I. FIDONE, in 12th Int. Conf. on Plasma Physics and
Contr. Nuel. Fusion Research, Nice (1988), paper IAEA - CN -
50/G-3-5.
3 - K. YOSHIKAWA et al, in 12th Int. Conf. on Plasma Physics and Contr.
Nucl. Fusion Research, Nice (1988), paper IAEA - CN - 50/G-3-4
4 - I. FIDONE, G. GRANATA, and J. JOHNER, Phys.Fluids 32, 2300 (1988)
5 - B.A Trubnikov, in Reviews of Plasma Physics, edited by M.A Leonto-
vich, Consultants Bureau, New-York, Vol 2, 345 (1979)
453
$
(cs'll
-~50 o .?o ° o.8
0A
Fig. I p(r) vs for the x-mode in the equatorial plane
0.0"/
0.06
O.OS
Q.Oh
0.03
0.02
0.01
0.00 0-00 '~
0 • 60" ~|/~W
tAtvl
O~r.O"
O.Oa,
0.02
Fig. 3 Current drive efficiency, Fig. 4 Current drive efficiency for 0" 60"
vs~O/~O e (o) for the parameters of Fig.! and T (o) - 40,SO,ar~ 60 KeY
|
1.1141481.pdf | A computercontrolled xray imaging scanner using a kinestatic charge detector
Douglas J. Wagenaar, Frank A. DiBianca, Charles R. Tenney, Joseph E. Vance, Mark S. C. Reed, Donald W.
Wilson, Apostolos Dollas, David L. McDaniel, Paul Granfors, and Scott Petrick
Citation: Review of Scientific Instruments 61, 701 (1990); doi: 10.1063/1.1141481
View online: http://dx.doi.org/10.1063/1.1141481
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/61/2?ver=pdfcov
Published by the AIP Publishing
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Computercontrolled xray microbeam—Method, history, and sample results
J. Acoust. Soc. Am. 71, S31 (1982); 10.1121/1.2019333
Tonguepellet tracking by a computercontrolled xray microbeam system
J. Acoust. Soc. Am. 57, 1516 (1975); 10.1121/1.380593
Observation of the tongue movement by computercontrolled xray microbeam
J. Acoust. Soc. Am. 57, S2 (1975); 10.1121/1.1995163
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11A computer-controlled x-ray imaging scanner using a kinestatic
charge detector
DouglasJ. Wagenaar, Frank A. DiBianca, Charles R. Tenney, Joseph E. Vance,
Mark S. C. Reed, Donald W. Wilson, and Apostolos Doliasa)
Curriculum in Biomedical Engineering and Department 0/ Radiology. University o/North Carolina, Chapel
Hill, North Carolina 27599
David L. McDaniel, Paul Granfors, and Scott Petrick
General Electric Medical Systems Group. Milwaukee, Wisconsin 53201
(Received 9 August 1989; accepted for pUblication 5 October 1989)
A prototype scanning imaging system which employs a kinestatic charge detector (KCD) and is
under the control of a V AXstation II/GPX computer is described. The operating principles and
advantages of the KCD method are reviewed. The detector is a 256-channel ionization drift
chamber which creates a two-dimensional x-ray projection image by scanning the detector past
the object ofinterest. The details of the drift chamber design, the signal collection electrodes
(channels), and the Frisch grid geometry are given. Also described are the scanning gantry
design, computer-controlled drive motor circuit, and safety features. The data acquisition system
for the capture of a 1 M byte digital image is presented. This includes amplification, filtration,
analog-to-digital conversion, data buffering, and transfer to the V AXstation II computer. The
image processing and display techniques specific to the KCD are outlined and the first two
dimensional image taken with this system is presented.
INTRODUCTION
The use of digital imaging techniques in diagnostic radiology
is growing due in part to advances in computed tomography
(CT) and magnetic resonance imaging (MRI). In addition
to these popular modalities, considerable effort has been de
voted to replacing conventional film-screen systems with an
electronic x-ray imager for projection radiography. Exam
ples of such devices are photostimulable phosphor screens, I
selenium charge plates,2 and scintillating fiber-optic strands
coupled to CCD arrays.3 Also among these devices is the
kinestatic charge detector4-6 (KCD). There are many ad
vantages to digital approaches to radiography, including ( 1)
the ability to enhance the image computationally through
temporal or energy subtraction, (2) an expanded display of
detector dynamic range due to the ability to set a window
about a given intensity level, (3) fast image acquisition and
display, and (4) convenient storage, transmission, and dis
play of archived images through computer networks. Also,
electronic detectors can improve on diagnostic image quality
by providing better spatial and contrast resolution and re
ducing the radiation scattered from the patient which con
tributes to the image.
The KCD is used in a strip-beam scanning geometry.
This geometry limits the x~ray beam illuminating the patient
to a width on the order of 1.0 cm. The x-ray beam has the
normal breadth of a chest radiograph, about 40 cm. This
geometry has the advantage of limiting the scattered radi
ation from the patient to very low angle, coherent, or certain
configurations of multiple scattering. Most of the scattered
radiation will not encounter the relatively small active area
of the detector.
The concept of kinestatic charge detection can be de-scribed concisely by referring to Fig. 1. Figure 1 (a) shows
that the KCD consists of a uniform x-ray detection volume
and a signal collection volume. The number of signal collec
tors, n, can be as high as 4000 for a 40-cm detector with 0.1-
mm collector spacing. The scan and charge drift velocities
are shown to be in opposite directions. Figure 1 (b) shows
that a uniform electric field, imposed within the active re
gion of the detector, causes ions created by x-ray interactions
to drift at a constant velocity 7 toward the signal collectors.
Figure 1 (c) demonstrates the KCD principie by concentrat
ing on a single x-ray projection line. The detector is scanned
at a speed equal to that of the drift of the ions. Recall that the
detector and the ions move in opposite directions. At time t [,
two ion clouds are formed. At time t2, these two clouds have
drifted toward the signal collectors and three more clouds
have been created by x rays along the same projection line.
Scanning the detector at the same speed as the ion drift has
allowed the ion clouds from I, to remain on the same x-ray
projection line at time [2' After t3, the ions which have accu
mulated during the scan enter the collection volume and
their electronic signals are used to produce a digital image.
The word "kinestatic" comes from the fact that the ions
are moving in the detector frame of reference, but are static
with respect to the set of all projection lines through the
patient. The ions are thus integrated over the time required
for the active volume ofthe detector to scan past a particular
projection line. The detection volume contains "virtual" de
tectors whose width w in the drift direction is determined by
the sampling time t, and the kinestatic speed vas follows:
w=vt,. (1)
Typical values of 100 cm/s for v and 100 Jis/sample for t,
701 Rev. Sci. Instrum. 61 (2), February 1990 0034-6743/90/02070101 1 $02.00 @ 1990 American Institute of Physics 701
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11(0)
\
(b) ... 0-2 n·1 n X-Ray Deleclion
Volume
Signal Collection
Volume
EieClric Field
\Si9OOI Conlribution
FIG. 1. (a) The x-ray detection volume isa uniform gas located immediately
above the signal collection volume. The scan and ion drift directions are
shown to be opposite. (b) A constant electric field causes ions created by x
ray interactions to drift toward the signal collectors. (e) As the detector
scans upward, ions are integrated with little loss of spatial resolution and
enter the collector region after t,.
yield a width of 0.1 mm. A 1.0-cm wide detector thus con
tains 100 lines of these "virtual" detectors. This is a major
advantage of the KCD when compared to slit-or single-line
beam detectorsX which contain only one line of detectors in
the drift direction. Without the integration of ions over sev
eral millimeters in these detectors, x-ray tube heat loading
becomes prohibitive. Furthermore, there is a loss in quan
tum detection efficiency (QDE) because the focal spot pen
umbra must be collimated at the detector to maintain resolu
tion. Increasing the width of a single line detector reduces
tube loading and penumbra problems, but introduces unac
ceptable reduction in the spatial resolution in the drift direc
tion. Having up to 100 lines of virtual detectors in the KCD
is a compromise which maintains acceptable drift-direction
spatial resolution, while also reducing x-ray tube loading
and patient scatter acceptance.
It is necessary to consider exposure times and total x-ray
dose when discussing a new radiographic technique. A com
parison between a KCD and a lanthanum screen with a 12:1
antiscatter grid has been performed using an x-ray Monte
Carlo computer simulation.9 For equal image signal-to
noise ratios (SNRs), the patient dose required by the KeD
is 3-5 times lower than the film-screen system. This is pri
marily due to the KCD's high detective quantum efficiency,
i.e., the square of the ratio of detected SNR to incident SNR.
The low scatter-to-primary ratio in the strip-beam KCD is
included in the calculation of detective quantum efficiency.
The local exposure time was calculated to be about half that
102 Rev. SCi.lnstrum., Vol. 61, No.2, February 1990 of the film-screen. However, total exposure time for patient
thicknesses exceeding 25 em of water were found to be as
high as 3.6 s, and maximum tube charge (mA s) concerns
must be addressed in these situations.
A 256-channel prototype KCD imaging scanner has
been installed in the X-ray Instrumentation Research Labo
ratory at the University of North Carolina at Chapel Hill.
Since the 256 channels span only 3.9 em, the device is rc
ferred to as the small-field-of-view (SFOV) detector. The
SFOV system is intended to test the KeD concept and
evaluate two-dimensional medical images. Comparisons of
KCD images will be made with both conventional film
screen systems and the alternative digital radiographic tech
niques mentioned earlier. The following is an overview of the
SFOV prototype, describing the design and operation of all
components of the imaging system.
t DETECTOR
A. Chamber and subcomponents
The SFOV KCD is a pressure vessel made of 6061 alu
minum alloy. The outer dimensions of the rectangular detec
tor are: 10.5 cm (drift or scan direction) by 33.7 em (trans
verse) by 17.8 cm (x ray). The chamber was designed to
safely contain pressures up to 40 atm, and a pressure relief
valve is set to prevent the pressure from exceeding this value.
Pressure is monitored by using a Barksdale Controls Divi
sion (Los Angeles, CA) Model No. 30241-l1CG-04 pres
sure transducer. The detection gas enters the vessel through
a Pyronetics (Denver, CO) Model No. 1832-3 fill and drain
valve. This valve has a male 0.125 in. AN connector to the
HIGH VOLT AGE PLATE
FINGER BOARD
FRISCH GRID
INCIDENT
X-RAYS
FIG. 2. A schematic representation of the major components of the kincsta
tic charge detector. The grid is suspended 0.5 mm from the finger surface,
and the stainless steel HV plate is 5.0 mm from the grid.
X-ray imaging scanner 702
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11laboratory's gas handling system. A female cap is placed
over this valve once the detector is charged in order to pre
vent gas loss through the valve itself.
Figure 2 is a schematic diagram of the three major sub
components within the pressure chamber. A Frisch gridlO is
necessary to separate the signal collection volume from the
x-ray detection volume. Without the grid, ions within the
detection volume will contribute to the signal sensed by the
channel electrodes (fingers) during their entire drift time.
The grid shields the fingers from the drifting ions by inter
cepting their electric field lines. The separation between the
grid and the finger plate is set at 0.5 mm, and the high voltage
plate-to-grid distance is 5.0 mm. Table I shows the typical
range of field parameters for the SFOV detector operating
with xenon between 20 and 25 atm. The voltages are positive
and therefore electrons and negative ions (impurities) are
drawn to the HV plate while Xe f-and other positive ions are
collected by the KCD fingers. Single-channel KCD experi
ments and calculations have shown6 that good spatial reso
lution and quantum detection efficiency performance can be
achieved simultaneously using xenon in this pressure range.
The typical kinestatic speed in a constant electric field
Ed can be calculated using the foHowing'l :
u = ,urEd (PI/PP)' (2)
where f1r is the reduced mobility of the medium (0.4
cm2/V s for xenon12), pp is the density of the medium at
pressure P, and P 1 is the density at atmospheric pressure. If
Ed = 5000 V jcm and PP/Pl = 20.0, then the kinestatic
speed is 100 cm/s. Speeds of this magnitUde are easily and
safely achieved in a clinical setting.
A photograph of the finger plate is shown in Fig. 3. This
plate was manufactured by Augat Microtec (Newbury
Park, CA). The fingers are 50-pm-thick nickel plated onto a
O.16-cm polyimide insulator base plate. The finger length is
7.5 cm. The 256 channels were specified to have a 6-mil
(0.15 mm) center-to-center spacing which spans 3.90 cm
total. The width of each finger was specified to be 4.5 mils
(0.11 mm). The fingers fan out to span 25.5 cm to facilitate
access to the finger leads.
The Frisch grid was designed to span the fingers with
support on both sides of the fingers, as shown schematically
in Fig. 2. The grid is a ceramic plate with a thickness of 0.4
mm. A hexagonal honeycomb pattern on O.36-mm centers is
etched through for ion transmission. Electric fields within
the etched openings and on both sides of the grid are defined
by layers of Ni of 50-,um thickness plated onto both sides of
the ceramic substrate. The potential at the Ni layer closer to
TABLE I. Typical field parameters for tbe small-ficld-of:view (SFOV) Kin
estatic Charge Detector. The field ratio E,.I Ed is assumed to be 4.0. The
grid potential V is the voltage on the finger-plate side oftbe grid and is equal
toO.57 V" where V, is the potential applied to the HV-plateside of the grid.
Grid HV plate Drift field Collector
potential potential Ed fieldE,
(V) (V) (V/cm) (V/cm)
Minimum 300 1050 1500 6 000
Maximum 1200 420(} 6000 24000
703 Rev. Sci. !nstrum., Vol. 61, No.2, February 1990 FlG. 3. Photograph of the finger plate in use in the small-tield-of-view
(SFOV) KCD. The fingers fan out to facilitate connection ufthe signals to
tbe preamplifiers. The finger terminals are used to connect the signal leads
to the feed-through hoard as discussed in tbe text. The terminal and fanned
out path of one of the central fingers have been highlighted.
the HV plate, Vg, is set by connection to an external power
supply. The potential at the Ni layer closer to the fInger
board is fixed to be 0.57 Vii by a voltage divider employing
5.34-and 3.97-Mn resistors. The Ni layer on the finger
board side is positioned 0.5 mm from the finger board. The
electric field in the signal collection region is given by
E, = O.S7V g/O.05 cm = 11.40 VJcm. (3)
The potential on the HV plate is set 10 give a Held ratio which
obeys the relation
(4)
assuring 100% ion transmission through the grid for the
SFOV detector (see Table I). The threshold value in Eg. (4)
is determined by the geometry of the grid design (e.g., wire
thickness and number of wires per unit length in a wire-mesh
grid) and the electrode separation distances within the de
tector.13 The grid-finger plate distance is set to be small
enough so that the ion transit time in this region does not
contribute significantly to the detector spatial resolution. A
field ratio less than the threshold value will result in signal
loss from ions terminating on the grid rather than proceed
ing through the grid openings. The field ratio is selected to be
only slightly higher than the threshold value. This is donc to
avoid signal multiplication due to electron avalanching near
the grid, and field nonuniformities in the vicinity ofthe grid
which cause a loss in spatial resolution.
The detector signal leads, having been fanned out on the
X-ray imaging scanner 703
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11rear of the finger plate (see Fig. 3), are jumpered with Ni
wire a distance of approximately 1 em to the feed-through
board which serves as a sealing surface between the two
halves of the detector chamber. This board has grounded
copper layers on either side to shield the outgoing signals
from eiectromagnetic noise.
A Pb-slit collimator (0.32-mm thickness) is attached to
the front of the detector. This slit can be opened to expose the
entire drift and collector regions or closed to expose a specif
ic volume of interest only. The collimation used for the pres
ent study extends 2.0 mm into the drift region from the grid.
The x-ray entrance window in the chamber is 4.0 mm thick,
and the front of the finger board is 2.0 mm from the x-ray
window's inner surface. The fingers begin 1.0 mm from the
front of the finger board. The "dead" volume, i.e., the x-ray
detection volume which does not contribute ions to the fin
ger leads, extends 3.0 mm into the xenon volume. For the
first images, no attempt has been made to fill this volume
with material which is less x-ray attenuating than xenon. In
addition, no electric field shaping electrodes have been in
corporated in the front window region in this prototype de
tector. This leads to further losses in both quantum detection
efficiency and spatial resolution which are avoided in later
detector designs.
B. Alignment
Alignment of the detector is important in order to en
sure optimal spatial resolution performance in the KCD.
Figure 4 shows the three degrees of freedom relevant to the
KCD. The finger board is shown schematically in this figure.
The origin afthe coordinate system is defined to be the point
located at the front of the center finger. Figure 4(a) is the
crucial alignment of the finger board with the x-y plane. Any
nonzero value for the angle a will mean a depth-dependent
arrival time for ions which ideally should encounter the grid
simultaneously. Angle a is minimized by examining the sig
nal from a single channel as the detector scans a narrow
(~O.2 mm) tungsten slit aligned in the x direction. The
detector is stepped through several values of a in the neigh
borhood of zero and the full width at half maximum
(FWHM) of the signal from x rays through the slit is plot
ted. The detector is considered aligned in the a direction
where the FWHM of the peak is a minimum.
Figure 4(b) is referred to as alignment in the transverse
direction since misalignment in this direction mainly effects
the transverse spatial resolution. The fingers ideally should
be parallel to the y direction. Any x component in the finger
board position will allow an effective crosstalk between
neighboring fingers. X rays interacting very near the front
edge of the finger plate will create ions which drift to the
correct fingers. At depth d in the y dimension, however, ions
which are created deeper within the detector will be collect
ed by a finger located a distance
lld=dsin/3 (5)
from the correct finger. Ions created at the maximum depth
of7.5 em in the SFOV will be a distance d = 0.15 mm (the
SFOV center-to-center finger spacing) from the correct fin
ger if the detector is misaligned by 0.115°, For the same ion
704 Rev. Sci. Instrum., Vol. 61, No.2, February 1990 DIRECTION
OF SCIIN z
X-RAY
FOCAL SPOT (a) (b)
(c)
FIG. 4. The three rotational degrees offreedom important to detector align
ment. The finger board is depicted as comb-shaped with nine fingers. The
correct orientation is shown in (a).
depth, a misalignment of {:J by as little as 1.0° will result in a
lld of 1.3 mm or displaced by nearly nine channels.
The detector is aligned in the fJ direction by positioning
the narrow slit in the z direction. The detector is stepped
through a set of possible {3 angles in the neighborhood of
zero. For each scan a plot is made of all detector signals at
the same sampling time location taken from the two-dimen
sional image. The peak resulting from the slit is centered on
one channel, and contributions to the peak from other chan
nels indicate the degree of misalignment. When the FWHM
of this peak is minimized, the detector has been aligned in
this direction (fJ has been minimized) .
The least significant of the three detector alignment di
rections is shown in Fig. 4 (c). The effect of a nonzero y can
be seen if an object with a right angle has one side aligned
with the scan direction. The object will appear to have an
angle of 90-y in the resulting image. In addition, the spatial
resolution in the drift direction of the image will be dimin
ished because the component of their drift speed in the z
direction is not the kinestatic value v but rather v cos y. A
misalignment of as much as go will result in less than a 1 %
scan versus drift speed mismatch (cos 8° = 0.9903 ). In or
der to align the detector, an object with a right angle is
aligned with the scan direction by stepping through object
orientations until one side of the angle is contained in a mini
mum number of channels. The detector is then stepped
through y values centered on zero until the other side of the
object's right angle is contained in a minimum number of
time samples. The SFOV detector's alignment and support
apparatus allows for movement in each of the three direc
tions, although with a small degree of coupling to the other
directions (Le., the directions are not completely indepen
dent). Therefore, a second pass is made to ensure optimum
system alignment.
C. Detector response
For clinical x-ray technic factors and xenon at 25 atm,
the ion current passing through the grid was measured to be
X-ray imaging scanner 704
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11as high as 50 nA. Given a noise level of 5 pA, this corn:
sponds to a dynamic range of 104 Detector linearity was
investigated by measuring the detector output signal for the
rnA values available from a General Electric MSI 1250 x-ray
generator for a beam energy of 120 k V p. The mA values were
25, 50, 100, 200, 300, and 400. The correlation coefficient of
an unwcighted linear fit to the output voltage levels was
found to be 0.995. Detector nonlinearities are expected to be
encountered at high ion density in an ionization chamber
because the effects of recombination and space charge repul
sion increase with density. Corrections for these effectsl4
can be performed by digital image processing routines.
Thc detector uniformity in the drift direction should be
extremely high, since the detection medium is a homoge
neous gas. In the transverse direction, nonuniformities will
result from geometrical differences between the ilngers.
These effects are small and easily corrected through chan
nel-to-channel computer normalization. Dynamic range,
linearity, and uniformity contributions from amplification
and digitization electronics are discussed in Sec. III.
II. SCANNING GANTRY
A. Scanning arm and drive motor
The SFOV KCD imaging prototype is located in the X
ray Instrumentation Research Laboratory of the Universily
of North Carolina. Figure 5 is a schematic diagram of the
layout of this facility. Two GE Maxiray 100 x-ray tubes arc
controlled from aGE MSI 1250 x-ray generator. The room
FIG. 5. Layout of the ONe X-ray Instrumentation Research Laboratory.
Stationary-detector (single channel) experiments are performed in the
room at the top; the gantry ancl associated ekctronics are located in the
larger room at the bottom.
705 Rev. Sci.lnstrum., Vol. 61, No.2, February 199() at the top of Fig. 5 is a stationary-detector work area. The
physical properties of individual KeD channels can be stud
ied by moving bar patterns and other phantoms at kinestatic
speed between the x-ray source and a stationary detector.
The detector can be kept aligned and connected to the near
by gas transfer station (GTS). This enables the experiment
er to study the effects of changing gas pressure and detection
media without altering the position or other parameters of
the study.
The SFOV KCD is positioned on the scanning gantry
shown in the bottom room of Fig. 5. The detector can also be
connected to the GTS via a flexible stainless steel hose (al
though not during a scan). The alignment of the detector is
again unaffected by the charging or draining of the detector.
The sl:anning gantry is depicted in greater detail in Figo 6.
The detector and prepaticnt collimator are shown to be at
tached to an arm which is supported at its pivot point. The
arm subtends approximately 60° between the two side sup
port beams. A steel arch (not shown) at a radius of 198.1 em
and an arc length of 228.2 em is located beneath the patient
catwalk. A steel cable (0.635 em diam) is stretched across
this arch and wraps twice around a helical screw on the drive
motor's shaft. A photograph of this arrangement is shown in
Fig. 7. The motor is attached to the side of the scan arm and
its axis is vertical. The motor is a model R404-N de servo
motor (Contraves Goerz Corp., Pittsburgh, PA). The de
tails of the control of this motor will appear later in this
section. The x-ray tube is positioned on a vertical post cen
tered on the pivot point. The rotation axis of the tube anode
is aligned with the rotation axis of the arm, and the tube's
focal spot is direl:tly above the pivot point. The prepatient
collimator consists oftwo 4.76 X 50.8 crne Pb sheets of 0.32-
em thickness. Each of these Pb sheets is sandwiched between
two O.16-cm brass sheets for added mechanical strength.
The collimator edges have been machined at a 2° angle for x
ray beam acceptance. The center of the Pb sheet is positioned
COLLIMATOR
\, ',,-KCD
SCANN!NG
GANTRY
Fl(;. 6. Schematic diagram of the SFOV KeD scanning gantry. The x-ray
beam is collimated before entering the patient. The detector and culJimator
are mounted on the scanning arm (beneath the patient platform), which
pivots beneath the x-ray tuhe's focal spot.
X-ray imaging scanner 705
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11FIG. 7. Photograph of the drive motor of the KeD scanning gantry. A steel
cable is wound around the helical drive shaft. Also shown are two of the
position sensors described in the text.
120 cm from the x-ray focal spot. The front edge of the signal
collection fingers is 184.6 cm from the x-ray focal spot.
B. Computer control
The SFOV imaging prototype is under the control of a
DEC V AXstation II/GPX computer (Digital Equipment
Corporation, Marlboro, MA). This microcomputer will
henceforth be referred to as the f1. V AX. Figure 8 is a block
diagram of the KeD imaging system. The It V AX is shown
controlling the gantry movement system, the x-ray expo
sure, and the data capture and storage subsystems. After the
image has been stored, the image is available to view on the
image display console shown in Fig. 8. Figure 9 shows the
computer control scheme in more detail. The DEC AXVll-C
analog interface is used to output (through a digital-to-ana
log converter) an analog signal corresponding to a desired
X-RAY
SYSTEM
GANTRY
MOVEMENT
SYSTEM DETECTOR
AND
CAS
MULTIBUS
DATA
BUFFER
FIG. 8. Block diagram of the computer-controlled x-ray imaging scanner.
Thc,uVAX"at"''' II/GPX coordinates scanner motion, x-ray exposure, and
data acquisition_ It also processes and displays the image on a high resolu
tion monitor.
706 Rev. Sci. Instrum., Vol. 61, No.2, February 1990 VELOCITY I
PROFILE I
I
X-RAY
SYSTEM
FIG. 'l. Block diagram of the computer hardware used to interface with the
scanner components. Analog signals define (output) and check (input) the
velocity profile_ Digital signals monitor position and status in addition to
triggering x-ray exposure, data capture, and (ifneccssary) emergency stop.
velocity profile stored in the flY AX memory. The profile can
be readily altered by editing the f1. V AX program which gen
erates its shape. The acceleration segments of the velocity
profile contain half the period of a sine wave with a zero
slope at the endpoints. A slope of zero in the velocity means
an acceleration of zero where the acceleration segments con
nect with the two constant-velocity segments (zero and kin
estatie). Minimizing the impulse from sudden accelerations
is important to prevent the excitation of oscillation modes in
the suspended Frisch grid within the detector. An oscillating
grid will produce micro phonic noise in the detector signals.
The return arrow in Fig. 9 from the gantry system to the
analog I/O hardware of the flVAX represents the analog
tachometer signal from the motor. This signal is proportion
al to the motor speed. It is sampled at a rate of 100 Hz by the
AXVU-C analog-to-digital converter. The tachometer signal
is plotted along with the desired velocity profile immediately
after the scan is completed.
As shown in Fig. 9, the DEC DRVll-J digital I/O board
is interfaced with all subsystems of the imaging scanner. Op
tical isolators (Opto-22, Huntington Beach, CA) are used
for both digital input and output to isolate electrical grounds
and to protect the computer from voltage surges. A series of
five photoelectric position sensors (Skan-a-matic Corp., El
bridge, NY) are positioned along the steel arch described in
the above text. A reflective surface is attached beneath the
scanning arm and a 5-V transition is made when the reflec
tive surface encounters a position sensor. These signals are
used to monitor the position and velocity of the arm during
the scan. The first sensor defines the "home position" or the
beginning of the scan. Home position is at the extreme right
of Fig. 6. The scanning routine in the p VAX cannot begin
until this sensor signal is read by the DRVll-J digital inter
face. Before scanning motion begins, a 5-V signal is output
from the DRVll-J which turns on the x-ray tube rotor. The
ROTOR READY signal from the generator is input
through the DR VU-J to alert the computer that the rotor has
reached its operating speed. The second sensor is the "X
RAY ON" sensor. The X-RAYON sensor is positioned
such that, when it is triggered, the kinestatic speed has been
reached for all available speeds (up to 125 cm/s). The signal
from this sensor interrupts the velocity profile routine
X-ray imaging scanner 706
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11(which at this point is outputting a constant voltage) and
triggers another signal which turns on the x-ray exposure.
The "Data Acquisition System (DAS) ON" sensor is locat
ed a few centimeters from the X-RAY ON sensor. This dis
tance allows the x-ray output to stabilize. The arm triggers
the DAS ON sensor, which interrupts the velocity profile
routine again, this time to begin the acquisiton of the x-ray
image data (see Sec. III). The fourth sensor turns off the x
ray exposure (if the exposure time is set to be greater than
the scan time) and the rotor. It also begins the deceleration
portion oftlle velocity profile. The fifth sensor is used to stop
the scanning arm and return it to home position where it is
stopped until the next scan.
C. Safety features
Personnel and equipment are protected from unexpect
ed gantry motion by the following means: The power to the
motor controller is single phase 480 V ac. This input line
must first go through a relay which is open only when the
120-V ac coil is energized. The 120-V ac power to this power
relay is available only if a second relay has 24 V de across its
coil. This 24-V dc circuit is referred to as the "safety circuit."
Any failure of this circuit to provide 24 V dc will result in a
loss of power to the motor. In addition to the 120 Vac, the
24-V dc relay controls the contacts to a third relay. This
relay must be energized in order for the armature leads to be
connected to the servo controller. When the safety circuit is
broken, the armature leads are shorted and the motor is dy
namically braked by its permanent magnet.
The safety circuit can be opened by four independent
methods. The first is a pair of micros witches located beyond
the home (1 st) and return (5th) position sensors. These
microswitches open the safety circuit when the arm leaves its
normal travel boundaries. The second is a manual emergen
cy stop switch which is thrown by the system operator when
necessary. The third is controlled by an output channel of
the DRVll-J digital interface in the ,uVAX. This allows the
f.1 V AX software to stop the scan if abnormal conditions are
sensed by the ,u VAX. For example, the DEC KWVll-C real
time clock is started at the beginning of the scan and the time
is recorded when each position sensor is triggered. Because
the velocity profile and the positions of the sensors are
known, a tight window can be placed on the expected values
for the arrival times at the sensors. Ifthe time interval is too
short between sensors (the scan speed is too high), then the
/-l V AX software can stop the scanning arm through the
DRVll-J. This DRVll-J bit can be accessed only while the
scan control program is running. It is "normally open" at all
other times. Finally, an external circuit has been installed
which monitors the tachometer signal using differentia! am
plifiers. An upper voltage limit is set by a potentiometer at
tached to + 15 V dc and the tachometer is compared with
this limit. The same circuit is used for negative (reverse scan
direction) voltages. If the tachometer voltage is outside the
boundaries set by the operator ( 125 cm/ s for forward and 10
cm/ s for reverse), then a Darlington driver is made to open
the safety circuit and the scanning arm is stopped.
707 Rev. ScLlnstrum., Vol. 61, No.2, February 1990 III. DATA ACQUISITION ELECTRONICS
A. Preamplification
In an ideal kinestatic charge detector, a plane of ions
arrives at the grid containing the transverse-direction image
information for one particular drift-direction position with
in the patienL The flow of charges across the grid during a
scan represents an input surface-current density (charge per
unit area). Only the ions drifting between the grid and the
finger plate will be sensed by the fingers if one assumes per
fect grid shielding from ions in the drift region. A charge Q
in the collection volume produces an induced surface charge
density 0" on the surrounding conductor surfaces such thatlS
Q= -SO"dA, (6)
where A is the area of the conductors surrounding the
charge. The value of 0" at a given point on a conductor in
creases as Q is brought closer to that point.
The total surface charge density O"T (t) for one finger is
created by the superposition of 0" for all charges within the
collection volume during the scan. Both the influx of ions
through the grid and the drift of ions within the collection
volume contribute to 0" T (t) for each finger. The presence of
(}' T (t) on the finger surface leaves a residual opposite charge
--O"T (t)Af• whereAf is the active finger surface area within
the finger volume. The finger current i is defined to be
(7)
The finger current i is transmitted to the current-to-voltage
preamplifier circuit shown in Fig. 10. Since positive ions are
being used in the SFOV KeD (see Sec. I), Qis positive and it
follows from Eq. (7) that i is positive. Assuming no current
enters the inverting input of the operational amplifier in Fig.
10 (i.e., ideal components are assumed), the transfer func
tion is
(8)
I I ...-----111 !--c---'
FIG. 10. The operational amplifier current-to· voltage circuit employed hy
the SFOV detector. The diodes ensure that voltages with a magnitude
greater thlln the diode's conduction voltage, ahout 0.5 V for a silicon P'lI
junction, do not exist on the input to the op-amp.
X-ray imaging scanner 707
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11wherefis the frequency in Hz.
The SFOV preamplifier of Fig. 10 has feedback resis
tance R of 12.4 Mfl and capacitance C of2 pF. The feedback
resistor determines the current-tn-voltage conversion factor
since, at low frequencies:
Vo = -iR. (9)
It should be noted that Vo will take on negative values since i
is positive when positive ions are being collected. As stated in
Sec. I C, the currents in the SFOV are assumed to be between
5 pA and 50 nA. For 50 nA the output voltage is -0.62 V.
The op-amp used is the OP Am low-noise precision op-amp
by Burr-Brown (Tucson, AZ). Op-amp instabilities due to
high gain and internal phase shifts are reduced by the feed
back capacitor.16 The 3-dB frequency of this preamplificr
circuit is
f= l/21TRC = 6.42 kHz. ( 10)
The linearity of this FET op-amp circuit is excellent due to
the low bias current (l-pA maximum) and input offset vol
tage (250-fl V maximum) and the use of a high-quality feed
back resistor (Caddock Tetrinox film resistor, 0.01% resis
tance tolerance).
There are four preamplifier boards which contain 64
circuits each. These are 9U Eurocards which are held in a
rack mounted to the feed-through board (see Sec. n. Each
board has two 3-row X 32-pin sockets which fit into corre
sponding plugs mounted directly to the feed-through board.
The outer pins are grounded on the feed-through board for
added shielding from radiative noise; only the center row is
used for KCD signals. Each of the four preamplifier boards
has six output ports. Ribbon cables connect these ports to the
Data Acquisition System (DAS) located about 0.4 m from
the detector. Four cables carry ten output signals and two
carry 12 signals. Each cable supplies ± 15 V dc power to the
preamplifier board from the DAS power supplies.
B. Data acquisition system
The 256 detector voltage signals are input to a 288-chan
nel Data Acquisition System designed by Analogic Corp. of
Peabody, MA. First the signals are filtered by eight 36-chan
nel filter cards. A low-pass two-pole Butterworth filter with
a 3 dB frequency of 12.5 kHz is used. The input signal range
is + 0.024 to -9.582 V dco The dcgain of the filter is 1.041.
The filtered analog signals are connected to 1-of-9 multi
plexers on each of the filter cards (four per card) . Each l-of-
9 multiplexer output is connected to an input of a 1-of-4
multiplexer located on the converter cards. One of the l-of-4
multiplexer inputs is used for data and another is used to
introduce a zero-level value for test purposes and auto-zero
ing. There are eight converter cards and each one has two 1-
of-4 multiplexers. Each of the 1-of-4 multiplexer outputs is
connected to a corresponding floating point amplifier. This
amplifier can automatically select a gain of 1, 8, or 64 de
pending upon the magnitude of the input signal. This assures
that the signals will be digitized to a broader resolution range
( i8-bit effective range) than is possible with the 12-bit con
verter alone. Each of the 16 floating point amplifier outputs
is connected to an analog-to-digital converter (O-W-V
708 Rev. SCi.lnstrum., Vol. 61, No.2, February 1990 range) which samples every 2 fLs. Every 2 fLs, 16 different
detector signals are sampled. The AID converter digitizes
the analog voltage level into a 12-bit binary value. The gain
information for each digitized sample is carried in the two
bits directly above the 12-bit mantissa. The linearity of the
DAS is defined in terms of a deviation from the expected
voltage. The deviation is specified to be no larger than
± 0.1 % of the expected voltage plus 1 LSB, where LSB is
the least significant bit and depends upon the voltage range
of the signal (see above) .
The digitized data are sent to the "I/O Card" of the
DASo This card adds two parity to the two gain bits and the
12-bit mantissa from the converter cards to create a 16-bit
data word. The I/O card arranges the data into two output
data channels, A and B, each of which outputs eight data
words every 2 fls. After every four data words on both A and
B the I/O card inserts a "SYNC" word. A "Control Card" is
necessary to handle the timing of the filter and converter
cards and to control the functioning of the I/O card. Digi
tized data on channels A and B are connected from the I/O
card to the "DAS Driver Board". This board utilizes 74S240
tristate inverting buffers to prepare the signals for a trans
mission distance of about 9 m.
Every 2-flS data channel A outputs data words from
eight detector channels plus two SYNC words. This gives a
'transfer rate r for data channel A of
r = _1_0_w_o-=r...:.d_s...:.X-=--2_b...:Y:...:t_es...:./_w_o_r_d
2fLs
= 10 M bytes/so ( 11 )
The total data rate from the DAS is therefore 20 Mbytes/s.
Each channel is sampled by the DAS every 40 ps, corre
sponding to a frequency of 25 kHz with a Nyquist frequency
of 12.5 kHz (recall the 3-dB frequency of the DAS filter is
12.5 kHz). The output lines of the preamplifier boards are
connected in such a way that the output of the DAS has the
correct spatial arrangement. That is, data channel A outputs
the eight detector channels located at the top of the finger
board and channel B outputs the following eight during the
first 2 f.ls. This sequence continues until the eight channels
located at the bottom of the finger board are output from
channel R
C. Multibus data buffer
Since the KCD image is taken by moving the detector at
a constant (kinestatic) velocity, the data stream leaving the
DAS cannot be interrupted without loss of image informa
tion. The data are buffered using the multibus-based data
buffer subsystem shown in Fig. 11. Multibus 17 is a standard
bus structure for microcomputer systems. Figure 11 shows
that five multibus boards are used to buffer the data stream.
They are (1) an 8086 microprocessor-based single board
computer (SBC), (2) a parallel communications board
which interfaces the multibus with the fl VAX, (3) the 1-
Mbyte dynamic random access memory (DRAM) board,
and the coupling of (4) the UNC interface (UNC I1F) with
(5) the DAS lIF. These latter two boards act together to put
image data and memory addresses onto the multibus for
X-ray imaging scanner 708
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11MUlT!SUS
--=:=k'j DAS UNC I iNTERFACE INTERFACE i]---'_ ~. "]=-
1 MEl ECOMMUNICATIOJS I~O~tJ' BUFFER BOARD iPROCESSOR
, MEMORY L BOAR °
HIGH -SPE-E-O'-'-- ~/'
(£AS DRIVER]
l~t
~REAMPS
~~TECTOR PARALLEL LINK ./S£RIAL \.,.INE
..--_--'-_-,.Lt/,~~~2)
DM2~N~~~~tCE I l
DEC jJVAX J'
HOST SYSTEM _.
FIG, 11, The multibus-based subsystem used to buffer the 20 M byte/s data
stream from the DAS, Thc DAS and UNe lIF boards assert data and ad
dresses. respectively, to the multibus for storage in the 1 M byte DRAM
board. DMA transfer takes plact' between the multibtls and the flV AX
memory through the high speed parallel link.
storage in the memory board. The two boards are linked
through an external (to the muItibus) 50-pin ribbon cable in
order to share signals. The operation of these two boards in
the multibus subsystem will be discussed in the following
paragraphs.
Two assembly language programs are loaded into the
memory of the 8086 SBC (Matrox Electronic Systems, Que
bec, Canada). This is done through the serial port (see Fig.
11) at the beginning of each scanning session. The first pro
gram is used to initialize the UNC l/F for data acquisition.
This entails programming the AD2940 address generators
(Advanced Micro Devices, Sunnyvale, CA), supplying the
DAS IIF with the scan speed, clearing the memory board
and disabling on-board memory refresh, and issuing a GET
READY signal which allows the UNC and DAS I/F combi
nation to control the multibus and acquire data when the
DRVU-J DAS ON signal is given (see Sec. II). The second
8086 code is run to program the communications board to
transfer the contents of the memory board to the /-L V AX. The
communications board is aCOM-l (Matrox) DRll-W com
patible parallel port which functions as a multibus to Q-bus
(the p V AX microcomputer bus) interface.
The memory board (Zitel Corporation, San Jose, CA)
has dynamic memory which must be periodically refreshed
(128 refreshes are required every 2 ms). This would require
an interruption in the constant data stream entering the
memory board and data would be lost during the refresh
period. The UNC IIF is designed to disable on-board auto
matic refresh during the scan and to restart the automatic
refresh upon completion of the data acquisition. During data
acquisition, the memory is refreshed by accessing different
rows of the memory board. Writing a data word refreshes an
of the data stored in the row to which the data word was
written.
As mentioned previously, the scan speed must be writ
ten to the DAS lIF. This is to ensure that the correct dimen
sional scaling takes place in the scan direction. Recall that
the finger-to-finger spacing is 0.152 mm. The I-Mbyte mem-
709 Rev. ScLlnstrum., Vol. 61, No.2, February 1990
•••••••••• -••• -.-•• -••••••••••• , •••• <;<; •••• ' ••• ;.:'7':.:.:.;.;.-;-.;.;.;.:.- .•••••••.•••••••••••••• ' ••••••••• r ••••••••• _._.; ••• ; •••• ~ •• ,;" •• -•••••••• o; •• '.' ....... _ ••• r •• ; •• ' ••••• ., .... . ory board can store 2048 samples of the 2-byte data words
from the 256 channels. The pixel length of 0.152 mm gives a
constant scan length 31.1 em (2048 X 0.0 152 cm2). Since the
DAS samples each finger every 40/-Ls, only the speeds shown
in Table II can be used to achieve square pixels in the final
image. Of course, any speed not in Table II can also be used
and square pixels can be calculated through interpolation
(provided that the kinestatic requirement is stilI met). The
DAS IIF can sum from three to seven samples, inclusively,
for each detector channel. This means the sampling times are
slowed to between 120 and 280 ps. The "scan time required"
column of Table II is useful for setting the x-ray generator
exposure time to the minimum required. The DAS lIF ac
cepts the data from the DAS driver board through optical
isolators on each data bit line. The SYNC data words arc
used to identify the position within the data stream and then
discarded. The gain bits are used to shift the location of the
12 bits of data resolution on a 16·bit word. For example, a
high signal from the detector would occupy the 12 most sig
nificant bits, a low signal the 12 least significant bits. The
parity bits are used to check the parity of the incoming data
and errors are indicated on an LED display on the DAS lIF.
The DAS IfF multiplexes the data channels A and B onto
the multibus (eight channels from A, eight channels from
B). A signal (DATA READY-DAS) is issued to the UNC
lIF when a data word is being put on the multibus. The DAS
IIF continues to operate this way until the DONE signal is
received from the UNC lIF. The DONE signal is generated
by the address generators once they have generated 0.5 M
addresses. These addresses are asserted from the UNC liP
onto the multibus address lines synchronously with the data
from the DAS lIF. After the memory board has been loaded
with the image data, the DONE signal is used to initiate on
board memory refresh. The scanning arm is allowed to come
to a halt before the transfer from the multibus memory to the
p V AX is initiated. This transfer is direct memory access
(DMA) from the COM-l communications board to the
DRVlI-W A parallel interface located in the f.l VAX.
IV. IMAGE DISPLAY
Arrangement of the data to create a CRT image is
straightforward since the order of the data leaving the DAS
corresponds to the physical location of the detector fingers.
A DEC VR290 high-resolution color monitor with eight bits
TABLE n. Kinestatic speeds necessary to produce square pixels. The DAS
sampling time is 40,ts. The desired pixel size is 0.152><0.152 mm2, The
kinestatic speed is determined by dividing the effective sampling time into
the pixel length.
Number of Effective Kinestatic Scan time
DASsamples sampling time speed required
(,tS) (em/s) (5 )
3 120 126.7 0.25
4 160 95.0 0.33
5 200 76.0 0.41
6 240 63.3 0.49
7 280 54.3 0.57
X-ray imaging scanner 709
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11of gray shades is used to display the x-ray image. The moni
tor is 1084 (horizontal) by 864 (vertical) pixels. The image
is displayed using 256 vertical pixels by 992 horizontal pix
els. Therefore, slightly less than half of the 2048 samples can
be displayed at one time. The user can specify which segment
of the complete image he wishes to view. Because the x-ray
intensity falls exponentially as a function of increasing ab
sorber thickness, the natural logarithm of the data is taken.
This linearizes the relationship between signal level and ab
sorber thickness. The values are then mapped into the set of
256 discrete gray levels. The contrast of the image can be
magnified by mapping selected subsets (windows) of the
signal range into the set of 256 gray levels.
A "blank" image with no object between the x-ray
source and the KCD will produce an image with horizontal
streaks due to unequal signal levels in each channel. The
unequal signal levels result from geometrical variations in
the electrodes and channel-ta-channel electronic differences
in the preamplifier circuits and the DAS input channels. The
256 circuits show a standard deviation of 0.65% of the full
scale when the x -ray beam is blocked by a lead absorber. This
is a measure of the range of dc offsets for the 256 channels.
The slopes of output signal versus plastic absorber (Lexan)
thickness curves show a standard deviation of 1.7% for the
256 channels. A program has been written to remove these
channel-to-channel variations hy using the measured rc
sponse of each channel to the same x-ray input (i.c., varying
thicknesses of Lexan). The channel-to-channel variations
are removed by mapping the corresponding number of x rays
(determined from the signal level) from each finger's curve
to the gray levels. A check of this method is the blank image,
which produces the same gray level for all the channels for
each time sample. Circuit components were chosen to pro
vide long-term stability. For example, the feedback resistors
in the preamplifier circuits have a nominal stability of 0.01 %
per 1000 h. Nevertheless, periodic recalibration (perhaps
every three months) of the channel-to-channel variations is
being scheduled for the SFOV system.
The time dimension also contains artifacts which can be
removed from the KeD image. Changes in x-ray output
with time are recorded by every channel at the same time.
Periodic changes due to the kVp ripple and imperfections in
the rotation or surface of the x-ray tube's anode will appear
as equally spaced vertical bands in the image. These time
dependent artifacts can be removed through normalization
to a "monitor" signal which corresponds only to the x-ray
tube output and does not show any time-dependent structure
due to attenuation within the object. A separate x-ray pho
ton detector can be placed between the object and the x-ray
tube, but the charge integration response of the KCD will be
somewhat cumbersome to calculate using the output ora CsI
scintillator, for example. Even an ion chamber placed before
the object would have to match the geometry and response of
the imaging KCD closely in order for this method to work
effectively.
Leaving several channels of the dctector exposed to un
attenuated beam allows for the simplest removal of time
dependent x-ray fluctuations. After the channel-to-channe1
variations havc been removed, ten channel signals from the
710 Rev. Sci. Instrum., Vol. 61, No.2, February 1990 FIG. 12. Kinestatic charge detector image of the index finger of one of the
authors (FAD). Each of the 256 vertical traces is the signal from one detec
tor channel; each horizontal trace is a different time sample.
open end of the K CD (top or bottom of the finger board in
Fig. 2) arc summed to give an average time-dependent nor
malization curve. This average is subtracted from (or divid
ed into) the remaining data to produce the normalized im
age. Methods using Fourier analysis of the x-ray ripple and
anode contributions are being investigated at the time of this
writing. These methods, if successful, should effectively re
move time-dependent artifacts without the limitation of re
quiring one side of the detector be exposed to unattenuated
beam.
Figure 12 is a photograph of one of the first images to be
processed at the University of North Carolina. It shows the
index finger of one of the authors. The x-ray technic factors
were 120 kVp, 400 rnA (1.2-mm focal spot), and O. 7-s expo
sure time. The slowest sampling rate of 280 lis/pixel was
used, corresponding to a scan speed of 54.3 cm/s. An observ
er study is planned to compare the performance of the SFOV
with that of conventional film-screen radiography using a
contrast phantom.
ACKNOWLEDGMENTS
The authors wish to express their appreciation to Eliot
Mayer, Dennis Knack, and William Allen for their help in
data acquisition electronics, Willi Hempel for the design of
the scanning gantry, Bin Liu, Harold Cox, and Raymond
Bingham for assistance in equipment assembly, and Gerry
Cohen for procuring the x-ray generator and tubes. Special
thanks are expressed to Walt Robb and Gary Keyes for sup-
X-ray imaging scanner 710
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128.248.155.225 On: Sun, 23 Nov 2014 10:52:11porting this project from its conception. Funding for this
project was provided by General Electric Medical Systems
Group (Milwaukee, WI), and by PHS Grant No. l-ROl
CA-44411-01, awarded by the National Cancer Institute,
DHHS.
aj Present address: Department of Electrical Engineering, Duke University,
Durham, NC 27706.
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X-ray imaging scanner 711
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1.101643.pdf | Orientationdependent metalorganic vapor phase epitaxy regrowth on GaInAsP/InP
laser structures
F. Fidorra, P. Harde, H. Venghaus, and D. Grützmacher
Citation: Applied Physics Letters 55, 1321 (1989); doi: 10.1063/1.101643
View online: http://dx.doi.org/10.1063/1.101643
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/55/13?ver=pdfcov
Published by the AIP Publishing
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F. Fidorra, P. Harde, and H. Venghaus
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GalnAsPllnP lasers made by Imv-pressure metalorganic vapor phase epitaxy regrowth on
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horizontal resolution using the checkerboard matrix gate technique yield unexpected results
for structures with stripes parallel to the (0 T 1 > direction: phosphorus is found in the nominal
GalnAs layer, its distribution is strongly inhomogeneous. Zn diffused into the GalnAs layer
exhibits also pronounced spatial variations. Unwanted P outdiffnsion and anomalous Zn
diffusion are a ttributed to reduced crystalline perfection of the InP above (011) oriented laser
stripes.
Epitaxial regrowth on patterned semiconductor sur
faces is an important technique for the realization of mono
lithic optoelectronic integrated circuits (OEICs). It is
known from investigations on AIGaAs/GaAs \-'1 and to a
limited extent on hlP-based structures 10,11 that low-pressure
metalorganic vapor phase epitaxy (LPMOVPE) and molec
ular beam epitaxy (MBE) regrowth are strongly dependent
on the orientation of the structures to be overgrown. Similar
ly, GalnAsP/lnP buried ridge structure (DRS) lasers ex
hibit yield and performance dependent on laser stripe orien
tation, and we have made a detailed comparative
investigation of lasers with stripes parallel to the (011) and
<oT 1) directions within a (100) surface. The former orienta
tion is the one generally chosen, while the latter offers addi
tiona! flexibility necessary for the design of high perfor
mance, higher complexity OEICs,12,13
The lasers investigated have a cross section as shown in
Fig. 1. In a first, liquid phase epitaxial (LPE) step the !l
buffer and the quaternary layers are grown. The latter are
then structured into stripes of 1.6 f-lm width and 200 11m
separation by a combination of reactive ion etchingl4 and
wet chemical etching with a mixture ofH.>Cl1 and Het
The sidewalls of the ridges are not perpendicular to the
semiconductor surface (as drawn in the schematic represen
tation of Fig. 1), but are oblique, and the angle of inclination
is different for the two orientations investigated [cf. Figs.
2(a) and 2(b) J. Lasers with stripe orientation parallel to the
< 011) or <aT 1) direction will be designated type A or type H,
respectively. In a second, LPMOVPE step the laser stripes
are covered by a p-type IuP layer of 1.2 ,urn thickness and a
D.S-flm-thick p-GaInAs capping layer.
Typical scanning electron microscope (SEM) pictures
of cross sections of the laser stripe region are shown in Figs.
2(a) and 2(b). FortypeA lasers the InP layer grown on top
of the GalnAsP layers has almost constant thickness, while
the thickness of the InP layer is particularly enhanced above
the laser stripe in case of the type B laser. The top GaIn As layers, which are missing in Fig. 2, since they are dissolved
by the wet chemical etchant used to decorate the facets of the
GaInAs!' stripes, have a constant thickness everywhere, in
dependent from the shape of the InP layer below.
Lasers of type A and B exhibit strong differences with
respect to threshold current Itll' quantum efficiency, ana
yield. These resuhs are in agreement with observations re
ported by Razeghi et al. lion similar structures. For lasers of
type A we observed I'll ,,20 mA (30 rnA) for 50% (90%) of
the lasers compared to Ie" ,,20 rnA (30 rnA, 60 rnA) for
0.6% (20%.40%) of the lasers of type E as wen as 55%
completely failing lasers of the latter type.
Three-dimensional secondary-ion mass spectroscopy
(SIMS) promes were taken using an ATOMIKA 6500 ion
microprobe operating in dynamic mode and applying the
checkerboard matrix gate technique. Horizontal resolution
was 1.6XL6.um2 (or3.2><3.2Ilm2). The total size of the
area evaluated: 25 X 25 12m2 (50 X 50 11m2); the size of the
etched crater was: 50 X 50 11m2 (100 X 100 12m2).
SIMS measurements on stnlctures of type A provided
results as expected, i.e., showed the constituent components
of the GalnAs, InP, and GalnAsP layers with appropriate
relative intensities and homogeneous horizontal distribu
tion.
:,c=r=?==:~~~~r- p+-Ir.GaAs: Zn
p -lnP: 211
/ZK--P -!nGaAsI? (1.3 j.Lml
i -InGa.AsP (1.5I!ml
-T'----- n -lnP:Sn
FIG. 1. Cross section and composition of constituent layers of the BRS laser
(schematic). 1.3 pm and L51tm indicates fundamcntal band gap ofrespec
live quaternary compound. Grid Oll top surfilce visualizes resolution of spa
tially resolved SIMS.
1321 AppL Phys, Lett 55 (13), 25 September 1989 0003-6951/89/391321-03$01,00 @ 1989 American Institute of Physics 1321
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140.254.87.149 On: Sat, 20 Dec 2014 15:41:40FIG. 2. SEM pictures showing cross sections of overgrown laser stripes.
Top GalnAs layer missing. (a) Laser stripe parallel to (011 >; (b) parallel
to (011) direction.
On the other hand, measurements on structures of type
B revealed, most surprisingly, a considerable amount of
phosphorus above the laser stripes in the nominal GalnAs
layer. Phosphorus has a depth distribution as shown in Fig. 3
with a strong concentration increase as the GalnAs/lnP in
terface is approached. In the perpendicular direction the P
concentration falls off rapidly with increasing distance from
the ridge. The In distribution exhibits a corresponding in
crease, while the Ga concentration goes down simultaneous
ly. The correlated changes of Ga, In, and P concentrations
are in such a way as to reduce the lattice mismatch which
would result from incorporation ofP into GalnAs which has
the proper stoichiometry of ternary material lattice matched
to InP. The total relative change of the In and the Ga aU over
the ternary GalnAs layer is estimated to be of the order of 5-
10%.
In a second series of SIMS measurements we deter
mined concentration profiles of the Zn diffused into the
104
CI) (al "'-103
--c;;
-<-d
102 <.... .-
C
::::l
0 w
10
o 0.5 o 0.5
Depth I ~m
FIG. 3. Count rate of the SIMS phosphorus signal on the BRS laser struc
ture, measured above laser stripe (dash-dotted) and far from the stripe (full
line). (a) Laser stripe parallel to <011); (b) parallel to {OIl) direction,
1322 Appl. Phys. Lett., Vol. 55, No. 13,25 September 1989 GaIn As to form the p contact. For lasers of type A we find a
homogeneous Zn distribution all over the GalnAs layer. The
results are strongly different for lasers of type B. Zn is no
longer evenly distributed within the GainAs layer, but its
concentration is significantly reduced above the (011) ori
ented laser stripe; the width of the region with low( er) Zn
concentration is of the order of SO pm.
A second difference is related to the morphology of the
crater eroded during the SIMS experiment: the ridge of type
A, which can be seen after the second epitaxial step already
(cf. Fig. 2), is preserved during the SIMS measurement, i.e.,
a ridge of approximately the same height and width as ob
served initially can be discerned at the bottom of the crater
(cf. Fig. 4), and whether the investigation is made prior to or
after the Zn diffusion does not make any difference. The
same holds for structures of type B if SIMS is performed
before Zn diffusion. However, if type B structures are inves
tigated after Zn diffusion, no ridges can be seen after the
SIMS measurement but the area of the former ridge and its
vicinity exhibits contiguous hollows instead. The width of
the region of more pronounced erosion is of the order of 50
p.m, i.e., corresponds to the width of the GaIn As layer with
reduced Zn concentration.
The results are interpreted as follows: We attribute the
presence of phosphorus in the nominal GalnAs top layer to a
low crystalline perfection of the MOVPE-grown InP layer
above the (011) oriented laser stripes, where the reduced
crystallinity enhances the diffusion velocity in the InP. This
interpretation is in accordance with recent investigations by
Sartorius et ai.,15 who studied the thermal degradation of
InP and have shown that P has a strong tendency to migrate
along (extended) defects from the bulk to the semiconduc
tor surface during high-temperature processes. The ob
served correlated concentration changes of P, In, and Ga
suggest that P out diffusion occurs essentially during growth
of the GalnAs layer (at a temperature of 630°C). The as
sumption P might be incorporated into the top GalnAs layer
as a consequence of reactor contamination can be rejected
readily, since structures of types A and B were grown simul
taneously, and structures A do not show any P in the ternary
layer.
Low Zn concentration in the GaIn As layer above the
(a)
-2 l Ilm
-3
::t~~
o 100
FIG. 4. Bottom of crater eroded during SIMS measurement. (a) Laser
stripe parallel (011) with/without Zn diffusion, and along (011) without
Zn diffusion. (b) Laser stripe parallel <011); SIMS performed after Zn dif
fusion.
Fidorra et al. 1322
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140.254.87.149 On: Sat, 20 Dec 2014 15:41:40laser stripe of type B samples is due to an enhanced Zn ditfu~
sion into the InP, and this is another consequence of the low
crystalline perfection of the MOVPE-regrown InP already
inferred from the anomalous phosphorus distribution. An
increased Zn concentration in the loP below the GalnAs
with reduced Zn content could not directly be proven since
the overall Zn signal was too low while the InP was moni
tored. The Zn diffusing into the region of already lowered
crystalline perfection then induces drastic further changes:
the crystallinity is impaired so strongly that the sputter rate
rises substantially which could not be observed without Zn
diffusion. The apparent weakening of the crystal lattice is
attributed to mechanisms similar to those responsible for
impurity-induced disorder observed in multiquantum well
structures. 16
It is interesting to note that a prerequisite for the strong
Zn-induced changes to occur is the presence of a modest
reduction in crystalline perfection, so that minor irregulari
ties give rise to subsequent strong effects, while Zn has no
apparent detrimenta1 consequences in more regularly grown
regions of a wafer (cf. laser structures of type A ).
On the basis of the SIMS analysis the high threshold
current and the low overall yield observed on type B lasers
can be understood easily. The reduced Zn concentration in
the GalnAs above the laser stripe increases the contact resis
tance and the particularly low Zn concentration above the
active area favors current flow beside the laser stripe, Thus, a
large proportion of the laser current does not lead to minor
ity-carrier injection into the active area, and as a conse
quence the threshold current is high or lasing action does not
start at all.
In conclusion, the three-dimensional SIMS analysis has
elucidated various interdependent mechanisms (impaired
regrowth and reduced crystallinity, constituent interdiffu
sion or outdiffusion, and anomalous dopant diffusion),
1323 Appl. Phys. Lett., Vol. 55, No. 13,25 September 1989 which may occur under certain circumstances and lead to
unsatisfactory device behavior. Information of the kind re
ported here is the basis for the replacement of processes with
unwanted orientational dependence by more favorable ones,
which is a prerequisite for the design of complex high perfor
mance integrated optics devices.
IJ. S. Smith, P. L. Derry, S. Margalit, and A. Y~.riv, AppL Phys. Lett. 47,
712 (1985).
LK. Kamon, M. Shimazli, K. Kimura, M, Mihara, and M. Ishii, J. Cryst.
Growth 77,297 (1986).
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(1986),
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(1987).
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Ishii,], App!. Phys. 62, 764 (1987).
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165 (\988).
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8R. P. Meier, E. van Gieson, W. Walter, C. Harder, M. Krahl, and D.
Bimberg, AppL Phys. Lett. 5~, 433 (1989).
9H. P. Meier. E. vall Gieson, P. W. Epperlein, C. Harder, W. Walter, M.
Krahl, and D. Bimberg, J. Cryst. Growth 95, 66 (1989).
Wc. Blaauw, A. Szaplonczay, K. Fox, and B. Emmerstorfer, J. Cryst.
Growth 77,326 (1986).
I'M. Razeghi, M. Krakowski, R. mondeau, K. Kazmierski, P. Hirtz, J.
Riccia,di, B. de Cremoux, and J. P. Duchemin, Conference Digest of 10th
IEEE International Semiconductor Laser Conference, Oct. 14-17, Kan
azawa, Japan, i 986, p. 52.
12M. Schlak, H. P. Nolting, p, Albrecht, W. Diildissen, D. Franke, U. Nig·
gebriigge, and F Schmitt, Electron. Lett. 22, 883 (1986),
"Y. Tahmad, X. Jiang, S. Ami, F. Koyama, and Y. Suematsll, Jpn. J. Appl.
Phys. 24, L 399 (1985).
'·'H. Schmid, Proceedings of the 6th IntematloMl Conference Oil Ion and
Plasma Assisted Techllology, Brighton, United Kingdom, 1987 (CEP
Consultants, Edinburgh, 1987), p. 98,
';B. Sartorius, M. Schlak, M. Rosenzweig, and K. Piirschke, J. Appl. Phys.
63,4677 (1988).
'oW. D. Laidig, N. Holonyak, Jr., M. D. Camras, K. Hess, J. J. Coleman, P.
D. Dapkus, and J. Bardeen, Appl. Phys. Lett. 38, 776 (1981).
Fidorra et sl. 1323
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1.866409.pdf | Thermally driven convective cells and tokamak edge turbulence
D. R. Thayer and P. H. Diamond
Citation: Physics of Fluids (1958-1988) 30, 3724 (1987); doi: 10.1063/1.866409
View online: http://dx.doi.org/10.1063/1.866409
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1.343810.pdf | Range profiles of Hg+, Hg2 +, and Hg3 + in polymer polyvinylalcohol
KeMing Wang, BoRong Shi, JiTian Liu, XiangDong Liu, and KeJun Yao
Citation: Journal of Applied Physics 66, 4577 (1989); doi: 10.1063/1.343810
View online: http://dx.doi.org/10.1063/1.343810
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130.133.66.132 On: Wed, 26 Nov 2014 17:40:29Range profiles of Hg+, Hg2+, and Hg3+ in polymer polyvinylalcohol
Ke-Ming Wang
China Center of Advanced Science and Technology (World Laboratory), P.o. Box 8730, Beijing, China and
Department of Physics, Shandong University, Jinan, Shandong, China
So-Rang Shi, Ji-Tian Uu, and Xiang-Dong Liu
Department of Physics, Shandong University, Jinan, Shandong, China
Ke-Jun Yao
Department of Chemistly, Shan dong University, Jinan, Shan dong, China
(Received 24 March 1989; accepted for publication 28 June 1989)
Depth profiles of Hg+, Hg2+, and Hg3 , implanted in polymer polyvinylaIcohol at energies
from 50 to 600 ke V are measured by 2.1-Me V 4He2 + Rutherford backscattering. Based on
Biersack's angular diffusion model, a computer program is written for comparison with the
experimental values. The result shows that the measured projected range is in good agreement
with the calculated value for first-order treatment. The experimentally determined range
straggling is still higher than the calculated value after considering the second~order energy
loss. The Monte Carlo simulation shows that the Hg profile is not described by an ionization or
nuclear damage profile, but rather is described by a classical predicted implantation profile.
I. INTRODUCTION
Ion beams are widely used for modifying electrical, opti
cal, and mechanical properties of solids. The investigation of
ion-bombardment effects on polymers have received in~
creased attention during the last few years.1-6 It is known
that energetic ion irradiation of polymers results in both
structural changes and stoichiometric modification accom
panied by emission of volatile components as a consequence
of bond breaking. These modifications result in changes of
mechanical, optical, and electrical properties. For example,
high~energy ion~beam irradiation of polymer film results in a
decrease in resistivity. Resistivity decreases of 14 orders of
magnitude have been observed. 7
One of the less-studied aspects of the ion-implanted
polymers is related to the characterization of the concentra
tion profile of the implanted species. Despite the fact that
mean projected range (Rp) and range straggling (/!>.Rp) of
implanted ions must be known in many important applica
tions, very few experimental profiles have been published.
The Lindhard-Scharff-Schi0H (LSS) procedure and Monte
Carlo simulation can be used to calculate the implanted-ion
distribution parameters into polymers. The main purpose of
this work is to study mean projected range and range strag
gling of Hg +, Hg2+, and Hg31 implanted at energies from
50 to 600 keY into polymer polyvinyl alcohol (PVA) by 2.1
MeV4He2+ Rutherford backscattering (RBS). Experimen
tal results have been compared to our calculation based on
the Biersack's angular diffusion model and Monte Carlo
simulation.
II, EXPERIMENT
Thin films of polymer PV A were spun on clean glass and
baked for 1 hat 120"C. The nominal composition ofPVA is
(C2H40) n' The density of PV A was measured and taken to
be 1.25 g/cm3, Thin films ofPV A were implanted with doses
of I X 1015 ions/em2 and 5 X 1014 ions/cm2 at energies from 50 to 600 keY, respectively. Implantations above 200 keY
were carried out using doubly~charged Hg2+ and triply
charged Hg3 +. The problem with charging of the sample
was almost eliminated by placing a metal mask in immediate
contact with the sample. All implantations were performed
at room temperature and current density was less than 0.5
pA/cm2 to avoid excessive heating of the sample. In order to
ensure uniformity over the implanted area, a two-directional
electrostatic scanning system was used. A neutral trap was
also employed.
The mean projected range and range straggling were
measured by a 1.I-MeV 4He2+ beam at normal incidence
and with a scattering angle of 165°. When the implant distri
bution in depth is Gaussian, the depth profile can be de
scribed by the projected range and range straggling which is
the standard deviation of the Gaussian distribution in depth.
The range straggling has been obtained from the measured
FWHM after performing the deconvolution process. In or
der to determine the Hg surface position, we have used gold
film for calibration. To enhance the depth resolution, a
glancing angle measurement was performed at low-energy
implantation of Hg ions. For most of the samples, two RBS
energy spectra were taken, one for normal incidence, the
second at an angle of 50° between the direction of the He ion
beam and the surface normal. In the latter arrangement the
depth resolution was improved by a factor of 2. The error in
the profile measurement was estimated from the stability of
the PV A energy edge of the spectrum which was determined
by ± 3 channels. Each channel was equal to 50 A for normal
incidence. The ion implantation was performed on a 400 ke V
ion implanter made at Shandong University. The RBS mea
surement was carried out at the 2 X 1.7-MV tandem accel~
erator of Shan dong University.
III. RESULTS AND DISCUSSION
It is known that the theoretical calculation of the range
profile of ions in a polyatomic target is complicated, espe-
4577 J. Appl. Phys. 66 (10), 15 November 1989 0021-8979/89/224577-04$02.40 @ 1989 American Institute of Physics 4577
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130.133.66.132 On: Wed, 26 Nov 2014 17:40:29cially for a polymer. A number of physical and chemical
phenomena occur under ion irradiation. Some effects such as
target compaction, chemical decomposition, cross linking,
and formation of free radicals will take place. These pro
cesses may influence the final distribution of implanted ions
in the polymer. It is reported that light ions (OLi, lOB) distri
bute neither according to their calculated range nor to their
nuclear damage distribution, but according to their ioniza
tion distribution after ion implantation into organic poly
mers.1! For heavy ions, such as Bi, the final distribution in
AZlll photoresist can be described by classical theoretical
prediction.9
The theory of Lindhard-Scharff-Schi0tt, known as LSS
theory, widely used for calculation of low-velocity ion
ranges in solids, was originally developed for monoatomic
targets. 10 Johnson and Gibbons had used the LSS procedure
to calculate the mean projected range and range straggling
for ions implanted in polyatomic targets. A Monte Carlo
simulation is also widely used for calculating the range pro
file of ions in polyatomic targets. II In the present work, an
efficient method based on Biersack's angular diffusion mod
el12•13 has been developed for calculating the mean projected
range and range straggling of heavy ions in polyatomic tar
gets, which differs from the LSS procedure and Monte Carlo
simulation. Our calculation is given in detail elsewhere. 14
Biersack's model attempts to base range theory on weU
known stopping powers and energy straggling, Thus avoid
ing uncertainties in prescribing the differential cross section.
The important input quantities in the present calculation are
reliable nuclear and total stopping cross sections as func
tions of energy. During the present calculation, the nuclear
stopping cross section Sn proposed by Wilson, Haggmark,
and Biersack (WHB) and implemented by Ziegler has been
used. 15 To obtain the total stopping cross section, we have to
know the electronic stopping cross section S,. We have used
the electronic stopping cross-section formula by Vargas
Aburto and co-workers. 16.17 In order to improve the preci
sion of projected range and range straggling, it is necessary
to consider higher-energy loss moments in nuclear stopping,
such as the second moment in nuclear energy loss. Low
energy ions that are slowed down mainly by elastic collisions
lose their energy in relatively large portions. Electronic
straggling is of minor influence in low-energy ranges. It con
tributes to the projected range straggling only at high ener
gy, e.g., for E,> I MeV for light ions. Therefore, in the pres
ent calculation, the second moment in electronic energy loss
may be neglected as in the LSS calculation. The second mo
ment in nuclear energy loss can be obtained from Ref. IS. A
survey of tests concerning Bragg's rule of stopping power
additivity is updated. A general failure of simple additivity is
well established, but magnitudes of effects are still subjected
to uncertainty. 19 In the present calculation, we assume that
Bragg's rule is valid. This is the idea contained in the princi
ple of additivity of stopping cross sections, which states that
the energy loss in a polymer composed of various atomic
species is the sum of losses in the constituent elements,
weighted according to their abundance in the polymer. Fig
ure 1 shows the calculated nuclear stopping cross section S n'
electronic stopping cross section Se' and total stopping cross
4578 J. Appl. Phys., Vol. 66, No. 10,15 November 1989 ""' C\l E :3 St; u
::>
..JI -, 5n a 2 ....
'" -+' /-)5. IJl
1) c 1 fG
c:
III
GI
!.Il
10° 101 HjZ 103
ENERG'r'CIc aIJ)
PIG. 1. Nuclear stopping cross section SM , electronic stopping cross section
S" and total stopping cross section Sf as a function of energy E for Hg ions
incident on polymer PV A. The normal composition (C2H40) M is used for
calculation.
section SI as a function of energy E for Hg ions incident on
the polymer PV A. One ofthe purposes ofthe present work is
to compare the experimental projected range and range
straggling of Hg ions in polymer PV A with calculated val
ues. Figure 2 compares the mean projected range (Rp) and
range straggling (tlRp ) between the measured and calculat
ed values for Hg ions implanted at energies from 50 to 600
keV in polymer PV A. The solid line represents results of the
present calculation. The result indicates that there is a good
agreement between the measured projected ranges and our
calculated values in this case. The maximum difference in
the mean projected range between experimental and theo
retical values is less than 19%. For higher energies from 150
to 600 keY, there is an overall good agreement (less than
10%) between experimental and present calculated values.
As for range straggling, the experimentally determined data
show a much larger straggling than the theoretical calcula
tion for first-order treatment. Although a marked improve
ment in the range straggling is obtained after including the
second-order energy loss in the Biersack model, the mea-
u.I 104
0.9 i ~ .. Il!
103
~ a: ~ .. ' I.I.i
102 ~.a <t...-
Il:..., oz w ....
H.li I-...J
~ UUi
!!j~ Oil! I:r: .... !l..(Jl 01 HI
10° iOA 102 103 10" ENERGYCkulJ)
FIG. 2. Comparison of experimental and calculated projected range and
range straggling of Hg ions implanted at energies from 50 to 600 keY in
polymer PV A, The solid lines represent the calculated values based on the
angular diffusion model.
Wang eta!, 4578
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130.133.66.132 On: Wed, 26 Nov 2014 17:40:29sured range straggling is still higher than the calculated val
ue. For comparison, a Monte Carlo code is also used to cal
culate the implanted-ion distribution parameters into
polymer PV A. Table I lists the experimental values of mean
projected range and range straggling as a function of the
implanted energy together with the present calculation and
the transport of ion in matter (TRIM) prediction. In the
experimental range determination as well as the theoretical
calculation, we have taken the density ofPVA film to be 1.25
g/cm2. The nominal composition of polymer PYA is
(C2H40)n. It is recognized that the relative difference
between the theoretical and experimental Rp and tlRp val
ues is dependent of the assumed polymer PYA density. The
implantation profile for Hg3+ implanted at 600 keY into
polymer PV A is depicted in Fig. 3 together with the TRIM
prediction. The dose is 5 X 1014 ionslcm2• The measured dis
tribution shows similarity with the range distribution calcu
lated by TRIM simulation.
It is seen that the Hg distribution is not described by
ionization or nuclear damage profiles, as is the case for light
ions reported by Fink et ai" 8 but rather by the theoretically
predicted implantation profile. To demonstrate the applica
bility and reliability of the present calculation, we have made
a comparison between the calculated value and the experi
mental value of Rp and ARp. Guimaraes et al.9 have used
Rutherford backscattering to determine the range param
eters ofBi + implanted into AZl11 photoresist film at ener
gies from 10 to 400 keY. The nominal composition of the
AZlll photoresist is (CSHg02)n. Figure 4 shows the com
parison between the experimental values and our calculated
values of mean projected range and range straggling for Bi +
implanted at energies from 10 to 400 keVin AZ 111 photore
sist. Experimental data, TRIM results, and our calculated
values are listed in Table II. For comparison, we have also
plotted in Fig, 4 our calculated results of the mean projected
range and range straggling for Bi + implanted into AZ 111
photoresist film. The maximum difference between the ex
perimental and our calculated values for mean projected
range is less than 14% at energies from 50 to 400 keY. The
range straggling is obtained after considering the second
order energy loss.
TABLE I. Experimental TRIM, and our calculated projected range (Rp)
and range straggling (t:..R p ) for Hg ions implanted into polymer PV A. The
range straggling for ARp of the present calculation is obtained based on the
second-order treatment by Biersack's model.
Projected range (Rp) (ft.) Range straggling (.6.R p) 0 .. )
Energy
(keV) Expt. TRIM Our calc. Expt. TRIM OUf calc.
50 425 412 498 93 58 72
100 606 647 756 153 96 102
150 811 834 990 202 113 127
200 1096 1002 1193 244 133 147
300 1534- 1365 1595 270 193 184
350 1792 1562 1760 322 2lJ 198
400 1810 1687 1945 347 258 214-
600 2690 2335 2630 418 316 267
4579 J. Appi. Phys., Vol. 66, No. iO, 15 November 1989 i!
1\1
Q ....
:K 'J
lI'I ,..
Z
:l
0
u
asCI
(s)
u
... ..... m
E u
'" '+Xl.o'i-UI I
0
I-
G: '-' « ;)
Ii,
Il
(bl .:
'.
" "
"
,'. ." . ,
", , .
" .
qeo
CHANNELS
p ....... <>".,,,,, ..
'"'
-<I:
"-
:> 120
W
v
Z
Q eo
H
!-
<C
N
H '+0
Z a
H 2~
0 c:
?o-
III
WI
Z (t
"-
'"' Z
1 S
"-
!!::'
W
III x:
::I z
FIG. 3. (a) Experimental depth profile of 600-keV Hg ions implanted into
polymer PV A. The dose is 5 >< 101• ions/cm2• Each channel equals 50 A.
(b) The predicted range profile (P), damage (V) and ionization (I) pro
files by TRIM for 6OO-keV Hg ions in polymer PYA.
I.!.l 10
L!I Z «
'" 103
0 z
<I:
~" 102 z-a: <I: ~
0.:
o~ w ... 101 t;d w'"' .,« 0'"' !!<I-1L<Il
10° Hf
FIG. 4. Comparison of experimental and calculated projected range and
range straggling of Bi ions implanted at energies from 10 to 400 keY into
AZlll photoresist (C,H802)". The solid lines represent the calculated val
ues based on Biersack's angular diffusion model. The line for aRp is ob
tained after including the second-order energy loss. The experimental data
come from Ref. 9.
Wang sf al. 4579
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130.133.66.132 On: Wed, 26 Nov 2014 17:40:29TABLE II. Experimental, TRIM, and our calculated projected range (R p )
and range straggling (fiRp) for Bi j implanted intoAZlll photoresist film.
The experimental data come from Ref. 9.
Projected range (Rp) (A) Range straggling (t:.R p) C4.)
Energy ._---
(keV) Expt, TRIM Our calc. Expt. TRIM Our calc.
10 180 160 215 31 23 33
20 240 240 304- 36 34 45
30 310 300 378 50 42 55
50 450 400 500 72 58 70
70 500 520 611 100 70 83
100 750 650 754 140 80 98
200 1200 1020 1176 260 150 141
400 2200 1780 1891 450 260 204
iV,SUMMARY
The mean projected range and range straggling of an Hg
ion (Hg +, Hg2 -;-, and Hg3 +) implanted at energies from 50
to 600 keVin polymer PV A have been measured by 2.1-MeV
4He2+ Rutherford backscattering. Based on Biersack's an
gular diffusion model, a computer program was written to
calculate the mean projected range and range straggling. In
the calculation, the nuclear stopping cross section Sn pro
posed by WHB and implemented by Ziegler and the elec
tronic stopping cross section Se by Vargas-Aburto and co
workers have been used. In the present calculation, we
assume that Bragg's rule is valid in this case of a low-Z com
pound. The results show that the measured projected range
is in good agreement with calculated values. As for range
straggling, the measured value is much larger than one ob
tained from the first-order treatment for heavy ions implant
ed in PV A. After including the second-order energy loss, a
marked improvement in the range straggling is obtained, but
the experimentally determined values are still higher than
the calculated values. The TRIM simulation is also made for
comparison with our experimental data. It is observed that
the Hg distribution in polymer PV A is not described by ion1-
4580 J. Appl. Phys., Vol. 66, No, 10, 15 November 1989 zation or nuclear damage profile, but is described rather by
the classical predicted implantation profile. Also, the pres
ent calculation is compared to the work by Guimaraes et al.
It is found that the range profile of Mg+, HgH, and Hg3+
implanted into polymer PV A has nearly the same behavior
as that of Hi + implanted into AZ 111 photoresist.
ACKNOWLEDGMENT
The authors would like to thank Lu Ju-Xin for ion im
plantation.
IA M. Guzman, J. D. Carlson, J. E, Bares, and P. P. Pronko, Nue!. In
strum. Methods Phys. Res. Sec. n ? /8, 468 (1985).
'1. Adesida, Nue!. lnstrum. Methods 209/210,79 (1983).
31. Bello. G. Carter, K. F. Knott, L. Haworth, G, A. Stephens, and G.
Farrell, Radiat. Eff. 89, 189 (1985).
4'1'. Venkatesan, Nuc!. lnstrum. Methods Phys. Res. Sec. B 7/8, 461
(1985).
5'f. M. Hall, A. Wagner, and L. F. Thompson, J. AppL Phys. 53, 3997
( 1982).
6L. Calcagno and G. Fati, Nuc!. lnstrum. Methods Phys. Res. Sec. B 19/
211,895 (1987),
7S. R. Forrest, M. L. Kaplan, P. H. Schmidt, T. Venkatesan, and A. J.
Lovinge, AppL Phys. Lett. 41, 708 (1982).
8D. Fink. l. P. Biersack, J. T. Chen, M. Stadcle, K. Tjan, M. Behar, e. A.
Olivieri, and F. C. Zawislak, 1. App!. Phys. 58, 668 (1985).
'J R. n. Guimaraes, L. Amaral, M. Behar, F. e. Zawislak, and D. Fink, J.
App!. Phys. 63, 2502 (1988).
IOJ. Linclhard, M. Scharff, and H, E. Schi0tt, K. Dan. Vidensk, Selsk. Mat.
Fys. Medd. 33,14 (1963).
IIJ. P. Biersack and L. G. Haggmark, Nuc!. lnstrum. Methods 174, 257
(1980).
12J. P. Biersaek, Nue!. lnstrum. Methods 182/183,199 (1981).
13J. P. Biersack, Z, l'hys, A 305, 9S (1982).
14Wang Ke-Ming, Lin Xi-liu, Wang Yi-hua, Shi Bo·Rong, and Liu Ji-Tian,
J, App!. Phys. 64 3341 (1988).
ISU. Littmark and J. F. Ziegler, Handbook of Range Distribution of Energet
ic Tons in All Elements (Pergamon, New York, 1978), Vol. 6.
l0e. Vargas-Aburto, S, A. Cruz, and E. C. Montengro, Radiat. Elf. 80, 23
(1984).
liE, C. Montengro, S. A. Cruz, and e. Vargas-Aburto, Phys. Lett. 92A, 195
(1982).
IRW. D. Wilson, L. G. Haggmark, and J. P. Biersack, Phys, Rev. B 15, 2458
(1977).
19D, I. Thwaites, Nue!. lustrum. Methods Phys. Res. Sec. H2?, 293 (1987),
Wang eta!. 4580
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1.457397.pdf | Improved phase diagram of nitrogen up to 85 kbar
W. L Vos and J. A. Schouten
Citation: The Journal of Chemical Physics 91, 6302 (1989); doi: 10.1063/1.457397
View online: http://dx.doi.org/10.1063/1.457397
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128.189.203.83 On: Fri, 12 Dec 2014 07:26:48Improved phase diagram of nitrogen up to 85 kbar
w. L Vos and J. A. Schouten
Van der Waals Laboratory. University of Amsterdam. Valckenierstraat 67,
1018 XE Amsterdam. The Netherlands'
(Received 9 February 1989; accepted 4 August 1989)
A quasi-isochoric scanning method has been used to study the phase diagram of nitrogen from
150 to 550 K and up to 85 kbar in a diamond anvil cell in order to make a comparison with
previous measurements of the binary phase diagram He-N2.1t has been confirmed that there is
only one solid-solid-fluid triple point in N2 up to 85 kbar. However, both the t>-{3 transition
line and the melting line have shifted appreciably towards lower pressures. The present
experiment shows that, as a result of this, the triple point is located at 555 ± 5 K and 80 ± 2
kbar, which is 20% lower in pressure than previous data.
I. INTRODUCTION
In order to investigate fluid-fluid demixing at high pres
sures in simple molecular systems, a study of the binary mix
ture helium-nitrogen was undertaken in our laboratory. It
was found that the fluid-fluid equilibria persist up to at least
100 kbar.1 The most remarkable feature, however, was the
occurrence of two quadruple points along the three-phase
line solid-fluid-fluid at 34 and 58 kbar. A quadruple point in
a binary mixture is related to a triple point in a pure sub
stance. On the basis of the known phase diagram of nitrogen,
only one quadruple point could be expected, since only one
solid-solid-fluid triple point was known2 with which it
could be related. Therefore, van den Bergh and Schouten
proposed that there might be a second triple point along the
melting line of nitrogen at a lower pressure than the one
already known.3 In that case, the upper quadruple point in
the mixture would be related to the known triple point ofN2
and the quadruple point at 34 kbar would be connected to
the second triple point. Another possibility could be that the
lower quadruple point is connected to the known triple point
of N2 and that the quadruple point at 58 kbar is related to a
triple point at higher pressure. Therefore it is worthwhile to
study the phase diagram of nitrogen, because either it shows
a new triple point along the melting line below 100 kbar or by
comparing the 8-{3 line with the three-phase line of the mix
ture, one can deduce if gaseous helium dissolves in solid ni
trogen.
In spite of its simple molecular structure, nitrogen
shows a very rich phase diagram (see Fig. 1). At zero pres
sure and low temperature it exists in a cubic and ordered
structure with space group4 Pa3, known as a-N2• Between
35.6 K and the melting point at 63.1 K it exhibits a hexagon
al disordered structure, {3-N 2 with space groupS P 63/mmc.
Pressurizing a-N2 to about 4 kbar yields6 r-N2' which is
also an ordered phase with tetragonal space group7
P42/mnm. On further pressurizing, one obtains €-N2 at
about 20 kbar.8 This is an ordered rhombohedral phase with
space group9 R 3c. At still higher pressures of about 200
kbar,8 it reveals another phase whose structure is possibly
rhombohedral with space group9 R 3c.
At room temperature, fluid nitrogen freezes at 24 kbarlO
into 11 {3-N2. At 48 kbar, a transition occurs 12 t08-N2, a cubic
disordered phase with space group13,14 Pm3n. Pressurizing of 8-N2 yields phase transitions at 200,660, and 1000 kbar to
other, yet unidentified, phases. IS Previous investigators re
port that the 8-{3 phase line and the melting line intersect at
578 K and 99 kbar to yield the ,8--8-fluid triple point.2
II. EXPERIMENTAL
The diamond anvil cell (DAC) which was used in this
experiment has been described in detail in an earlier paper. 16
The usual ruby technique is used to determine the pressure in
situ. The pressure coefficient is taken as 0.0366 nmlkbar.17
Heating was accomplished through an electrical coil wound
on a "cold" finger projecting from a copper ring surrounding
the cell.
The temperature dependence of the ruby lines was not
taken from literature data, but has been determined experi
mentally before and after each run at about ten tempera
tures. The average of the measurements before and after
each run was used. The temperature dependence, which may
120
kbor
p
100 f
80
60
40
20
o 100 -T
300 fluid
CD Zinn et 01-
a Chong ot 01..
1041110 ot 01 ..
Zinn et 01.
<:> Olinger.linn.t 01.
A Mills et 01.
500 K 700
FlO. l.~T diagram of nitrogen. D Triple point Zinn et al. <t Triple point
this work. -Melting curve Eq. (I).
6302 J. Chern. Phys. 91 (10).15 November 1989 0021·9606/89/226302-04$02.10 © 1989 American Institute of Physics
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128.189.203.83 On: Fri, 12 Dec 2014 07:26:48W. L. Vos and J. A. Schouten: Phase diagram of nitrogen 6303
differ for different ruby chips, cannot be conveniently repre
sented here by a simple analytical expression, and will be
discussed in a future publication. 18 The ruby was illuminat
ed with an Ar or a Heed laser at a beam power of about 10
m W to prevent heating. We estimate the error in pressure to
be ± 0.3 kbar below room temperature and up to ± 1 kbar
at the highest temperatures. The gas used was of research
grade quality with a purity better than 99.999%.
The sample space was loaded by mounting the DAC in a
high pressure vessel and pressurizing it with nitrogen. 19 The
cell was closed at a pressure of a few kilobars and placed in
the main frame for further pressurizing the sample. The ex
periment was performed with a stainless steel 301 gasket in
the DAC. The temperature was measured with a calibrated
platinum resistance thermometer. Moreover, corrections
were made for gradients within the cell, yielding a total un
certainty of less than 0.5 K.
Two experimental methods were applied:
(a) visual observation, in which case a phase transition
can generally be detected by a change in color, structure or
refractive index,
(b) isochoric scanning,20 where the temperature of the
DAC is varied under nearly isochoric conditions and a
first-order phase transition manifests itself as a discontinuity
in pressure if there is a measurable volume change. In a typi
cal scan, we heated in steps of 1 K and after each step we
waited 15 min before measuring the pressure. In order to
check if equilibrium conditions were reached, we lowered
the temperature while maintaining a two-phase equilibrium
and scanned again. We observed then that the results repro-
54
kbar
53
52
33
32 II-I! transition
p
i
~
~
~ ~ ~b:IJ:.
~~.
I! -fluid transition
-T
31 L-______ -L ______ ~~ ______ ~
340 350 360 K 370
FIG. 2. p-Tscans of the 6-P transition and the melting line. The pressure
jump ofthe melting line is about 1/3 that calculated from PVT data for an
isochoric transition. duced. We were not able to detect any phase transition in
nitrogen when using visual observation. This is due to the
fact that N2 forms clear and colorless crystals IS and that the
view through the sample was disturbed by some small pieces
of ruby.
The isochoric scanning method worked out very well as
can be seen in Fig. 2, which shows very pronounced pressure
jumps of about 1 kbar for the ~{3 and P-ftuid transitions. In
fact, we do not observe a discontinuous jump but a sharp
increase of the slope of the p-Tplot. The p-Tplot follows the
phase line, because the transition takes place gradually, so
that there is a range of temperatures where the two phases
coexist. The investigation of the phase lines was hampered
by three factors:
( 1 ) At high temperatures, the ruby lines broaden so that
above 500 K only one line was resolved by us, which in
creases the scatter of the data points along a p-T scan. This
problem was tackled by taking more points along a scan.
(2) On some occasions the pressure decreased on heat
ing probably due to a rearrangement in the experimental
setup. This shortens the trajectory in the p-T plane where
two phases coexist and, thus, diminishes the pressure jump.
This difficulty was overcome by slightly turning the pressing
nut to eliminate the tolerance in the main frame without
increasing the pressure.
(3) Sometimes, the sample superheated or supercooled.
This is described below in more detail.
III. RESULTS AND DISCUSSION
Some typical examples of p-T plots for the 8-{3 transi
tion and the melting line are shown in Fig. 2. We have a large
number of data points, but for an overview only the mid
points of the p-T scans have been listed in Table I. It is
evident from Fig. 1 that the melting line and the ~{3 transi
tion line agree with previous data at low temperatures 10.2 1,22
but deviate considerably from the previous data above room
temperature. We found the 8-{3-ftuid triple point at 555 ± 5
K and 80 ± 2 kbar, which is considerably lower than the
values2 of 578 ± 10 K and 99 ± 5 kbar reported previously.
Note that if the temperature of the triple point is taken as 560
K, the pressure should be taken as 82 kbar. Similarly, 550 K
should correspond to 78 kbar. Our value for the temperature
at the H transition at 84 kbar is in reasonable agreement
with previous experiments,9 but due to the steepness of the
E-O transition line, any possible pressure deviations are not
visible.
TABLE I. Experimental data for the phase transitions in nitrogen.
6-ftuid
p-ftuid (metastable) 6-P H
T (K) p (kbar) T (K) p (kbar) T (K) p (kbar) T (K) P (kbar)
303.0 24.7 504.8 70.2 166.2 29.2 164.7 84.0
353.4 32.5 513.9 72.3 293 ± 7 45.7
412.4 44.7 533.5 76.2 319 ±4 49.3
449.9 53.5 350.3 53.0
489.3 62.8 423.9 62.7
511.0 69.0 478 ± 7 70.1
J. Chern. Phys., Vol. 91, No.1 0, 15 November 1989
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128.189.203.83 On: Fri, 12 Dec 2014 07:26:486304 W. L. Vos and J. A. Schouten: Phase diagram of nitrogen
The dashed melting line in Fig. 1 represents the tabulat
ed values from Young et al.23 These authors have smoothed
the experimental data of Zinn et al.2 Only one experimental
point of Zinn et al. (at 450 K and 63 kbar) has been plotted
in the interval from 20 to 100 kbar, since this is the only point
that has been given numerically. Note the relatively large
deviation of this point from the dashed melting line.
Our results for the P-ftuid melting line, together with
the low pressure results of Cheng et al.21 and Mills et al., 10
can be fitted to a smooth curve (full line in Fig. 1). A Simon
Glatzel equation yields:
P(kbar) = 0.54910* 1O-3*T(K) 1.8835 -1.1 (1)
with a standard deviation of ± 0.3 kbar.
The position of the melting line was determined from p
T scans with increasing temperature. At decreasing tem
perature undercooling of the sample of about 30 to 40 K
occurred. This undercooling manifests itself in a p-T scan as
a sudden drop in pressure, while on raising the temperature a
smooth increase in pressure was always observed as in Fig. 2.
The pressure jumps on melting were always 1 kbar or more,
so that the transition could be easily detected.
Only two experimental points have been plotted on the
dashed 0-{3 transition line in Fig. 1: one point given by
Olinger13 and one point reported by Zinn et aF We are
unaware of any other tabulated values. The 0-{3 transition
showed both undercooling and overheating. This is shown in
Fig. 3. In run 1, the temperature was decreased during the p
Tscan and a sudden jump occurred at 419 K. Apparently the
whole sample changed from P-N2 to 8-N2 at this tempera
ture. On raising the temperature in run 2, the reverse process
occurred at 440 K. The third run, performed at increasing
64 Metastable transition
63
62
61
64 Partly stable and
p
63 i
62 metastable transition
./$>~~
~<;)
<;) 0 Run 1 Cooling
f ~~ % [!) Run 2 Heating
<;) Run 3 Heating
-T
61 ~ ____ ~ ____ ~~ ____ ~ ____ ~~
410 430 K 450
FIG. 3. p-Tscans of the 8-/3 transition near 63 kbar. 85
kbor
80
75
70
65
500 520 540 560 K 580
FIG. 4.p-T diagram in the vicinity ofthe8-{3-ftuid triple point. Curve I is
the {3-ftuid transition line given by Eq. (I), line 2 is a linear fit through the
8-ftuid points, curve 3 is a quadratic fit though the 8-/3 points and line 4 is a
linear fit through the 8-/3 points. The circles are some of the 70 experimen
tal points determined for the metastable 8-ftuid transition.
temperature, shows that the pressure jumps slightly at 423
K, subsequently increases smoothly and then remains nearly
constant. We interpret this as follows: at first the sample
overheats, then part of it suddenly transforms from the 8
phase to the {3 phase. From then on, the 8 phase is in equilib
rium with the {3 phase and the transition proceeds until the 8
phase has completely disappeared. On another occasion we
observed that the 0-{3 transition occurred at the same tem
perature and pressure at decreasing as well as increasing
temperature. We conclude from this behavior that the sys
tem shows only metastability and no hysteresis as reported
previously.22 The data points at which metastability oc
curred are marked with an error bar in Fig. 1 to show the
difference between the heating and the cooling transition
temperature. The pressure jump for the 8-{3 transition re
mains about 1 kbar over the whole temperature range.
Close to the triple point only one transition was ob
served on heating instead of the two transitions 0-{3 and P
fluid. This is most likely to be the metastable O-fluid transi
tion because, as mentioned before, the 8 phase showed over
heating with respect to the {3 phase and because the experi
mental points do not coincide with an extrapolation of the 0-
{3 or the P-fluid line (see Fig. 4). Moreover the pressure
jump on this metastable O-fluid transition is more than 2
kbar, which is consistent with the sum of the jumps for the 0-
{3 and P-fluid transitions.
The triple point was estimated from extrapolations of
the Simon-Glatzel equation and linear and quadratic ex
trapolations of the 0-{3 and metastable 8-fluid data, see Fig.
4. It should be noted that, close to a triple point, a melting
line does not obey a Simon-Glatzel equation, but deviates to
higher pressure.2 Therefore 80 kbar was chosen as the most
probable value for the triple point pressure. The E-8 points
were taken from Mills et al.9 and this work. A pressure jump
of about 0.8 kbar was observed at the E-8 transition.
J. Chem. Phys., Vol. 91, No.1 0, 15 November 1989
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128.189.203.83 On: Fri, 12 Dec 2014 07:26:48W. L. Vos and J. A. Schouten: Phase diagram of nitrogen 6305
A possible explanation for the discrepancy with pre
vious data is probably the temperature induced shift in the
ruby lines. Our shifts were measured with the same pieces of
ruby used in the experiment. Zinn et al.2 used a value of
0.0068 nm/K, that was probably taken from the literature.24
However, in the literature a number of temperature shifts
have been reported,25 which may result in discrepancies of
more than 1 kbar per 100 K increase from room tempera
ture.
Another possible reason for the discrepancy may be
temperature gradients in the DAC. The temperature differ
ence between the diamonds and the thermometer was mea
sured with a differential thermocouple. One lead was put
near the gasket on one of the diamonds and the other next to
the thermometer. Care was taken to provide a good thermal
contact between the thermocouples and the surrounding
parts of the DAC. The maximum difference was -0.4 K at
150 K to + 0.3 Kat 530 K, for which corrections were
applied. In the report of Zinn et al. an error of up to 10 K
below 600 K was suggested. A third possible reason which
they do not mention may be laser heating of the ruby. In our
experiment, care was taken to avoid this effect.
In a theoretical article by LeSar,26 the error in the pres
sure measurements of Zinn et al.2 was estimated to be ± 5
kbar. As mentioned before, in our work the error is probably
less than 1 kbar.
The slight discrepancy with the data of Olinger13 is
caused by his use of the NaF scale instead of the ruby scale.
We do not consider sample impurity to be a possibility,
since the data agree at room temperature. Addition of all
possible discrepancies results in a total of 13 kbar at 550 K,
which is larger than the actual discrepancy of 11 kbar.
IV. CONCLUSION
Accurate measurements of the N2 phase diagram con
firm that, up to 85 kbar, there is only one solid-solid-fluid
triple point. The results concerning the position of the 8-{3
and ,B-fluid transition lines at high pressures obtained from
this work differ considerably from the results obtained by
other investigators. In particular, the coordinates of the tri
ple point have shifted from 578 K and 99 kbar to 555 K and
80 kbar. A comparison with the data for the binary mixture
He-N2 will be presented in a separate paper. 27 ACKNOWLEDGMENTS
The authors wish to thank Mr. T. van Lieshout and Mr.
F. C. J. van Anrooij for technical assistance during the mea
surements and Mrs. J. Batson for reading the manuscript.
IL. c. van den Bergh and J. A. Schouten, Chern. Phys. Lett. 145, 471
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(1988).
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(1986).
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Schiferl, Solid State Commun. 32, 131 (1979).
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Phys. Rev. Lett. 55, 1464 (1985).
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Instrum.54, 1209 (1983).
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46,2774 (1975).
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L307 (1979).
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Uppsala, 1982).
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( 1975).
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(1984).
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Schiferl, S. Kinkead, R. C. Hanson, and D.A. Pinnick, Phys. Rev. B 35,
3533 (1987).
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(1973).
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Yamaoka, O. Shimomura, and O. Fukunaga, Proc. Jpn. Acad. Ser. B 56,
103 (1980); S. L. Wunder and P. E. Schoen, J. Appl. Phys. 52, 3772
(1981 ).
20R. LeSar, J. Chern. Phys. 86, 4138 (1987).
27W. L. Vos and J. A. Schouten (to be published).
J. Chem. Phys., Vol. 91, No.1 0, 15 November 1989
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1.100815.pdf | Superconducting phonon spectroscopy using a lowtemperature scanning tunneling
microscope
H. G. LeDuc, W. J. Kaiser, B. D. Hunt, L. D. Bell, R. C. Jaklevic, and M. G. Youngquist
Citation: Applied Physics Letters 54, 946 (1989); doi: 10.1063/1.100815
View online: http://dx.doi.org/10.1063/1.100815
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131.111.185.72 On: Sun, 14 Dec 2014 09:08:10Superconductlng phonon spectroscopy using a low~temperature
scanning tunneling microscope
H. G. LeDuc, W. J. Kaiser, B. D. Hunt, and L. D. Bell
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
R. C. Jaklevic
Ford Motor Company, Dearborn, Michigan 48121-2053
M. G. Youngquist
California Institute of Technology, Pasadena, California 91125
(Received 29 September 1988; accepted for publication 15 December 1988)
We report the fIrst observation of phonon density of states effects ina superconductor using a
low-temperature scanning tunneling microscope (STM). The phonon effects were observed
using a STM spectroscopy method to measure dltlinneliIlg / d V vs V for the tunnel junction
formed by the Au STM probe and a superconducting Pb sample.
The scanning tunneling microscope (STM), since its
invention,l has evolved into a sophisticated tool for direct
imaging of many surfaces with atomic resolution. More re
cently, the STM has emerged as a powerful spectroscopic
tool with the potential for observation of surface and subsur
face electronic properties also with very high spatial resolu
tion. The large field of conventional tunneling spectroscopy
on macroscopic tunnel junctions is credited with many fun
damental observations. Measurements involving macro
scopic tunnel junctions, however, are limited by the spatial
averaging over the junction area and potential insulator bar
rier induced alteration ofthe system under study. Due to the
local nature of the tunnel current in a STM experiment, one
can hope to study macroscopically nonideal samples such as
polycrystalline thin films and measure properties of funda
mental as well as technological importance.
Historically, tunneling spectroscopy has been the most
sensitive probe ofthe superconducting state. Observation of
the superconductor energy gap by current-voltage (1-V)
spectroscopy using the STM has been reported.2 4 In this
letter we report, for the first time, the application of the STM
to the observation of superconductor phonon density of
states effects in conductance-voltage (dl/dV-V) spectrosco
py. Conductance spectroscopy has been important in the
study of superconductors. In the case of a normal metal
insulator-superconductor (NIS) tunnel junction, the nor
malized conductance as a function of bias voltage,
o-(eV) = G"s(eV)/Gnn (eV) whereG" andG,,,, are the tun
neling conductance with the S electrode in the supercon
ducting and normal states respectively, is a nearly exact rep
resentation of the superconductor excitation density of
states. Small structures in the excitation density of states
deviating from the predictions of the Bardeen-Cooper
Schrieffer (BCS) theory5 were first observed by Giaever6
using conductance-voltage spectroscopy with macroscopic
area tunnel junction~. The deviations are strongest in super
conductors such as Pb, and were used to establish the valid
ity of the strong coupling modifications of the theory of su
perconductivity culminating in the theory of Eliashberg.7
This structure has been shown to arise from the energy de
pendence of the phonon mediated electron-electron cou
pling responsible for the superconducting state. The devia-tions from BCS behavior in Pb observed in
conductance-voltage spectroscopy are weak; the phonon
structure is resolved as a change in conductance of only a few
percent of the total conductance. Therefore, the observation
of phonons represents a difficult measurement for low-tem
perature STM where the tunnel current and conductance
signals are reduced by a factor of greater than 10° compared
to conventional macroscopic area tunnel junctions.
Our STM system has been described previously.4 The
basic design is similar to one used for room-temperature
STM studies8 with modification for use in low-temperature
STM of superconductors. For phonon spectroscopy the tun
nel voltage range of interest is 0.0-20.0 mY. The need to
maintain large tunnel resistances in STM spectroscopy has
been discussed previously.4 Tunneling resistance for these
measurements was maintained in the 1 X 107-1 X 109 n
range, Under these conditions the tunneling currents are
typically in the range of 20-2000 pA. Two basic require
ments for the feedback and spectroscopy method are (1)
small voltage control and (2) direct dl/dV measurement.
To meet these requirements techniques used in macroscopic
tunneling spectroscopy were employed, two tunnel voltage
modulation signals at separate frequencies (to and It ) are
applied simultaneously to the STM tunnel junction. The tip
sample separation control is achieved, using techniques sim
ilar to those employed in Ref. 2, by measuring the amplitude
of the current signal at the lower frequency fo with a lock-in
amplifier and maintaining this amplitude at a constant value
using a feedback circuit. Using this method, the J-V spectra
can be measured by monitoring the tunnel voltage and cur
rent without interrupting feedback control. The dI /dV-V
spectra were measured using standard analog derivative
techniques by phase sensitively detecting the modulated cur
rent at the higher modulation frequency h using a second
lock-in amplifier. To avoid distortions due to slew rate limi
tations of the second lock-in, it is important to keep.hJ as low
as possible while maintaining stable tunneling. In the experi
ments reported here j~ = 10-20 Hz. 1-V spectra were mea
sured as a function of tunneling resistance and have been
shown to be independent of tunneling resistance for resis
tances of 107 n or greater. The sweep frequency j~ was also
varied to check for distortions due to insufficient electronic
946 Appl. Phys. lett. 54 (10), 6 March 1989 0003-6951/89/100946-03$01.00 @ 1989 American Institute of PhysiCS 946
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131.111.185.72 On: Sun, 14 Dec 2014 09:08:10bandwidth. In this regard, the preamplifier incorporated
into our STM design is critical. The spectra were acquired by
a signal averager to improve the signal to noise ratio.
The superconducting materials were thin films deposit
ed on silicon. The Ph samples were thermally evaporated
from 99.999% pure metal in a liquid-nitrogen trapped diffu
sion-pumped vacuum chamber. The NbN was deposited by
reactive de magnetron sputtering from a high-purity Nb tar
get in an argon-nitrogen atmosphere in a high vacuum
chamber under conditions used for making NbN-based tun
nel junctions.9
A topogram of NbN taken at 4.2 K using the low-tem
perature STM is shown in Fig. 1. The surface reveals a sin
gle-crystal grain with a sequence of two atom layer high
steps. T opograms such as this can be rescanned over periods
of many hours with minimal drift in the scan window. This
stability is required in the derivative spectroscopy experi
ments where extensive signal averaging is need to enhance
the signal-to-noise ratio.
Shown in Fig. 2 is an electron tunneling J-V spectrum
for NbN taken with a STM at 4.2 K. The data exhibit NIS
character with the characteristic superconductor energy gap
clearly defined. The sman conductance region followed by a
sharp rise in the current at one half the gap voltage and an
asymptotic approach to the normal-state tunneling charac
teristic clearly distinguishes NIS tunneling from other tun
neling J-V characteristics. The theoretical J-V data can be
numerically calculated using an elementary tunneling for
malism and BeS density of states. 10 Using a single parameter
/J, and approximating the normal conductance from the data
gives b. = 2.58 meV, which is in the range expected for
NbN.11•12
An I-V spectra obtained by electron tunneling into Ph at
4.2 K using the low-temperature STM is shown in Fig. 3,
The slight hysteresis in the STM spectrum is a result of the
bidirectional voltage sweep and the resulting tip-sample dis
placement current, A fit yields b. = 1.28 meV for this data.
Using the normalized temperature dependence of the energy
gap measured by Adler13 and our fit data at 4.2 K we have
" 20 A/div
FIG. I. STM topogram of a sputter-deposited NbN thin film obtained at
4.2K.
947 Appl. Phys. Lett., Vol. 54, No, 10,6 March 1989 VOLTAGE (mV)
FIG. 2. Electron tunneli,tg cmrent-vohage and conductance-voltage spec
tra of a NbN thin film measured by STM at 4.2 K. The points are STM data
while the line represents it theoretical fit.
calculated a zero temperature gap parameter l!.() = 1.36 me V
which is within the range observed for Pb.14 The smaller
energy gap of Pb relative to NbN leads to clearly observable
changes in the character of this spectrum from that ofNbN
shown in Fig. 2. The energy gap difference is reflected in the
smaller extent of the lower conductance region. In addition,
although the subgap current is dominated by the thermal
broadening in the normal metal (the energy gap ofPb at 4.2
K is large compared to k T), the extent of the smearing as a
fraction of the energy gap leads to a less dramatic 1-V nonlin
earity.
For NIS tunneling in macroscopic tunnel junctions, the
phonon effects occur for voltage bias above one half of the
superconductor energy gap and the major structure in the
conductance is observed below 13 meV in Ph. It can be seen
from the Pb I-V curve in Fig. 3 that the deviations from
linearity above the gap are smaIl and derivative spectroscopy
is, therefore, required to resolve them. Conductance mea
surements over the voltage range of interest are shown in
Fig. 4 along with that measured using a macroscopic
Pbl AIOxl Al tunnel junction 15 for comparison. \6 There is
good qualitative agreement between the experimental STM
and macroscopic tunnel junction curves. The conductance
voltage spectra measured by STM covering th.e supercon
ductor gap voltage range for a NbN thin film are shown in
Fig. 2. Phonon density of states effects in NbN are weaker
and broader and they were not observed with our STM.
Recently it has been suggested that multiparticle tunnel
ingl7 which is predicted to give rise to excess subgap tunnel
ing current might be operative in STM experiments per-
VOLTAGE (mV)
FIG. 3. Electron tunneling J-V spectra ofa Ph thin film measuredby STM at
4.2 K (upper curve) and a theoretical fit displaced for clarity (lower
cllfve).
LeDuc eta!. 947
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131.111.185.72 On: Sun, 14 Dec 2014 09:08:101.35
5
$ 1.25 W
U
Z « 1.15 I-U
:J
0 1.05 Z
0 ... :'~">.... ! .... -
" -- .... .. ~ .......
U
0.95 C 5 10 15
VOLTAGE (mV)
FIG. 4. Tunneling conductance-voltage spectra obtained at 4.2 K for a Ph
thin film. The upper curve is measured by STM electron tunneling and the
lower measured on a macroscopic Pbl AlO'; AI tunnel jUllction. The ar
rows indicate features associated with the transverse (left arrow) and longi
tudinal (right arrow) peaks in the phonon density of states.
formed at low tunneling resistance, 18 Careful observation of
the J-V characteristics in the gap region of NbN did not
reveal any excess tunneling current. The BCS-based fit 10 to
the NbN J-V spectrum in Fig. 2 does not include multiparti
de tunneling, yet accounts for the measured subgap currents
within experimental error.
In the course of our experiments, we have observed var
iations in the superconductor energy gap in 1-V measure
ments of Pb thin films from region to region on the same
sample and from sample to sample. One possible explanation
for this observation is the known gap anisotropy of Pb19
combined with the polycrystalline nature of the deposited
films and the local nature of the STM tunnel probe. Experi
mental zero temperature gap parameter values (~o) report
ed in the literature for single-crystal samples vary from 1.18
to 1.40 meV.19 This range includes variations due to direc
tion-dependent gap anisotropy and variations due to multi
ple energy gap superconductivity arising from different
sheets of the Fermi surface. These gap variations are masked
in macroscopic tunnel junctions fabricated with polycrystal
line films due to spatial averaging, which again highlights
the potential ofSTM to measure fundamental properties on
samples which are macroscopically nonideal. such as poly
crystalline thin-film samples.
The observation of phonon effects in superconductors
represents a measurement of conductance to a minimum of
one part in one hundred. This measurement demonstrates
that, in principle, variations in phonon effects could be spa
tially imaged with a STM. However, measurement of low
noise spectra with small currents requires extensive signal
averaging and limits the spatial resolution with which these
variations could be observed in an experiment of reasonable
duration. The advantages ofSTM for conductance spectros
copy may lie in the formation of a microscopic, neariy ideal
tunnel junction on samples which are macroscopically noni-
948 Appl. Phys. Lett., Vol. 54, No.1 0.6 March 1989 deal such as polycrystalline thin films. Thus local properties
of samples can be measured at selected points of the sample
surface,
In summary, we have developed techniques for simulta
neous tip-sample separation control and 1-V and d/ /dV-V
measurement. Using these techniques we have made the first
observation of phonon density of states spectrum in a super
conductor using a STM. We have measured electron tunnel
ing 1-V characteristics for NbN and Pb. We have observed
variations in the superconductor energy gap in 1-V measure
ments of Pb thin films. One possible explanation for this
observation is gap anisotropy observed for Pb combined
with the polycrystaHine nature of the deposited films and the
local nature of the STM tunnel probe. In addition, our /-V
measurements on NbN and Pb films under typical STM con
ditions showed no evidence for multipartic1e tunneling ef
fects.
This work was performed at the Jet Propulsion Labora
tory, California Institute of Technology, as part of the Cen
ter for Space Microelectronics Technology and was spon
sored by the Strategic Defence Initiative Organiza
tion/Innovative Science and Technology through an
agreement with the National Aeronautics and Space Ad
ministration (NASA).
'G. Binnig and H. Rohrer, IBM Res. Develop. 30, 355 (1985).
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IEEE Trans. Magn. MAG-17, 509 (]985).
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!SR. C. Jaklcvic (unpUblished),
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dilation along the voltage axis to remove experimental voltage offsets.
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Principles o/Electron Tunneling Spectroscopy (Oxford University, New
York,1985).
LeDuc eta!. 948
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1.344093.pdf | Silicon nitride films prepared using a SiH4/NH3 microwave multipolar plasma
Pierre Boher, Jacques Schneider, Monique Renaud, Yves Hily, and Joop Bruines
Citation: Journal of Applied Physics 66, 3410 (1989); doi: 10.1063/1.344093
View online: http://dx.doi.org/10.1063/1.344093
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/66/7?ver=pdfcov
Published by the AIP Publishing
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129.120.242.61 On: Fri, 28 Nov 2014 11:14:39Silicon nitride fUms prepared using a SiH4/NH3 microwave multipolar plasma
Pierre Boher, Jacques Schneider, Monique Renaud, Yves Hily, and Joop Bruinesa)
Laboratoires d'Electronique et de Physique appliquee (LEP),b) 3 Avenue Descartes, BP15, 94451 Limeil-
Brevannes Cedex, France
(Received 13 March 1989; accepted for publication 15 May 1989)
Silicon nitride films have been prepared at room temperature using a microwave multipolar
plasma chemical vapor deposition system. In situ kinetic ellipsometry during deposition and
ex situ measurements such as infrared absorption or spectroscopic ellipsometry have been used
to investigate the dependence of film composition and properties on the flow ratio SiH4fNH3
and on the total pressure, Depending on the silane partial pressure, the films contain a variable
amount of oxygen or amorphous silicon which directly affects the electrical properties.
Silicon nitride thin films play an important role in inte
grated circuits technology for the fabrication of insulating
intcrlayers and to achieve passivating films. On III-V com
pounds, these films must be prepared without plasma bom
bardment and at low temperature ( < 300 ·C). In this context,
different methods such as plasma-enhanced chemical vapor
deposition enhanced by a rf discharge (PECVD), I light ex
citation chemical vapor deposition (photo CVD) 2 or micro
wave discharge,:l have been developed.
Since the first work of Limpaecher and Mackenzie,4
multipolar plasmas excited by electron emission from a hot
filament have attracted a lot of attention because of their
capacity to provide large plasma densities (up to 1011
cm -3), without high energetic ions. For this reason, we have
devc10ped an ultrahigh vacuum system using this type of
plasma. A process which includes a native oxide removal, a
native nitridation, and a silicon nitride deposition has been
optimized and applied to the passivation of GaAs (Ref. 5)
and GafnAs (Ref. 6). Metal insulator semiconductor fieid
effect transistors (MISFET) without current drift and with
good transconductances have been manufactured.7 All the
details on the deposition of silicon nitride in this system have
already been reported elsewhere.s
In order to solve contamination and lifetime problems
related to the use of a hot cathode and at the same time to
take advantage of the multipolar configuration, we have
constructed a new multipolar system with a microwave exci
tation of the plasma. The plasma discharge at 2.45 GHz is
produced by coupling a quartz tube through an iris located
on the large side of a rectangular waveguide in which the
wave is propagating. A quartz tube connected to the top of
the chamber enters the guide through this iris and allows the
plasma excitation. The same type of excitation has been de
veloped previously by Burke and Pomoe and applied to the
etchinglO and to the epitaxyll of silicon. The permanent
magnets are located inside the chamber in order to have a
more efficient magnetic confinement. To minimize the sur
face bombardment during the deposition, the sample is elec
trically isolated and the distance between the plasma excita
tion and the sample is fixed to 15 cm. The large diameter of
a) Permanent address: Philips Research Laboratories, NL-5600 JA Eindho
ven, The Netherlands.
b) Laboratories d'Eleetronique et de Physique Applique: a Member of the
Philips Research Organization. the chamber (25 cm) allows us to obtain a good homogene
ity of the films on 2-in. wafers. SiH4 (diluted at 10% into
argon) and pure NH3 are used as reactant gases and mass
flow meters control precisely the composition of the plasma.
The total pressure during the deposition is measured with a
capacitive manometer. All the depositions have been made
on ( 100) silicon substrates undoped (300 n) for IR absorp
tion, and doped n + (15 mn) for electrical measurements.
Before introduction in the plasma system, the samples are
cleaned by a standard procedure (HF diluted at 5% in water
for 20 s). AuTi dots with a diameter of200jlm are deposited
on n + -type samples to perform the electrical measurements
of the dielectric films.
A kinetic real-time ellipsometry measurement during
deposition is made using a helium-neon laser ( 1.96 e V). The
sample is also ex situ characterized by spectroscopic ellipso
metry (1.6-5.4eV range) before and after deposition, and by
infrared absorption measurements (200-4000 cm -1 range).
The kinetic and spectroscopic ellipsometers used in this
work have been described previously.s The infrared absorp
tion spectra are recorded with a Perkin Elmer 983 system.
The contribution of the silicon nitride film itself is obtained
making a spectral difference between a reference sample and
each dielectric film.
In Table I, we report the plasma conditions used to de
posit eight films on silicon substrates and some characteris
tics obtained by ellipsometry, infrared absorption, and elec
trical measurements. All samples were prepared at room
temperature and the applied power level was kept constant
(600 W). The kinetic ellipsometry trajectories were fitted to
obtain the optical refractive index and the thickness of each
film. The results are reported in Table I together with the
Si02 (or a-Si) percentages determined by spectroscopic el
lipsometry. The Si-N absorption peak position and some
electrical results (breakdown voltage EB and resistivity pat
106 V fcm) are also reported.
For the samples numbered 1-4, we changed only the
flux ratio rj = SiH4/NH3• First, notice the rapid variation of
the optical index which increases from 1.75 for rf = 25% up
to 2.21 for rf = 100%. This variation is clear from the begin
ning of the kinetic ellipsometry trajectories. In Fig. 1 we
report the trajectories for flow ratios of 25%, 50%, 75%,
and 100%. The curves corresponding to the flow ratio 50%
and 75% are nearlv the same. A theoretical network ob
tained by varying th~ thickness (0-500 A) and the refractive
3410 J. Appl. Phys, 66 (7),1 October 1989 0021-8979/89/193410-03$02.40 @ 1989 American Institute of Physics 3410
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129.120.242.61 On: Fri, 28 Nov 2014 11:14:39TABLE I. Plasma conditions and physical and electrical properties of dielectric films deposited on silicon substrates. All deposits were made at room
temperature for a power level of 600 W. Refractive indices were determined by in siru kinetic ellipsometry. Thickness and SiOz or a-Si amounts were
determined by spectroscopic ellipsometry. The resistivity p is measured at 106 V/crn (4-5 means between 4 and 5).
Plasma conditions Ellipsometry IR Electrical properties
absorption -----,
Sample Pressure SiH4fNtf\ Thickness Deposition Refractive 3i02 Si-N E" p
No. (mTorr) (%) (nm) rate index (%) (em ') 106 V fcm (1010 n cm)
I 18 25 127 41.0
2 18 50 117 46.8
3 17 75 123 51.6
4 17 100 89 37.2
5 30 75 115 60.6
6 50 75 115 60,5
7 65 75 110 64.7
8 77 75 124 69.2
index ( 1. 50-2. 50), has also been indicated. The deposits are
wel! fitted by one single refractive index value and then the
composition of the film does not change during deposition.
This observation is confirmed for layers thicker than = 1000
A. The kinetic trajectory turns back on itself indicating the
deposition of a perfectly transparent film. The position of
infrared absorption peak corresponding to the Si-N stretch
ing model (around 850 cm -I) 12 is also shifted to the lower
values when the flux ratio is increased (cf. Table 0. We
already observed this effect for filament-enhanced PECVD
SiN films and attributed it to the occurrence of another peak
corresponding to a Si-O stretching mode at a higher wave
length number.s This assumption is confirmed by an ex situ
spectroscopic ellipsometry analysis. Si02 content of the
films varies from 56% for r = 25 % to 31 % for r = 50%.
When the flux ratio is higher than 75% the film becomes
absorbing which is probably due to a non-neglectable amor
phous silicon content (7% for fr = 100% by spectroscopic
ellipsometry assuming no Si02 in the film) (cf. Table I). The
1.0
008 Prusure 18m Torr
2.50
POWER LEVEL 60l)W
006
0.1,
0.2
<l (Ul
vi " -002 w
-0.4 SiLICON 1.75
1.88
1.89
2.21
1.99
2.02
2.00
1.96
-0.6 +++ 50% ind 15%
••• 100% 57 883 3-4 0.5
31 R60 4-5 300
35 856 3 600
7 824 2-3 0.5
(a-SO
24 845 3 300
18 834 3-4 2000
21 840 3 300
27 850 4 80-4000
presence of amorphous silicon is also observed by the kinetic
ellipsometry measurements. The trajectory obtained for a
thick film ( > 1000 A) does not reproduce exactly that ob
tained at the beginning of the deposit, indicating little absor
bance of the film. The presence of amorphous silicon is also
confirmed by the infrared absorption measurements on sam
ples 1-4. In Fig. 2 we report the corresponding absorption
spectra in the range of 200-4000 em -I, The N-H stretch
ing bonds and bending modes (between 3300-3400 em-I
and around 1200 cm!, respectively) 12 are clearly present
for r = 25% but disappear when r = 100% and are replaced
by the Si~H stretching mode (2150-2200 cm -') 12 which is
characteristic for amorphous silicon. Moreover, the conduc~
tivity pat 106 V jcm drops under 5 X 109 n em in this case.
These results are easily explained in terms of a defi
ciency of excess of ammonia. When the flux ratio is low
( < 25%), there is an excess ofNH3 and some N-H bonds
remain in the film. On the contrary, when the fiux ratio is
high ( > 100%) there is a lack of amonia and some Si--H
FIG. 1. Kinetic ellipsometry trajectories
measured in situ at 1.96 eV during the begin
ning of the deposit of films 1-4 on silicon
substrates. The flow ratio wa, changed from
25% to 100%. The simulation is obtained
assuming a perfectly transparent film
(k = 0) and varying the refractive index
from 1.5 to 2.5 and the thickness furm 0 up
to 500 A.
~1.0 '-_-4~_...L- __ .l.-_---L __ -'-__ ..A.....-_..........l __ """"" __ -'-_--'
0.10 0.15 0.20 Q.25 tUG 0.35 0.40 (j,ltS (l.50 0.55 0.60
TAN lV
3411 J. Appl. Phys., Vol. 66, No.7, 1 October 1989 Boheretal. 3411
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129.120.242.61 On: Fri, 28 Nov 2014 11:14:39NH SiH NH SiO SiN
4000 2000 lZ00 400
WAVELENGTH NUMBER (em -1 )
FIG. 2. Infrared absorption spectra of four films (samples 1-4) obtained by
varying only the flux ratio. The thicknesses of the four films are in the 100
nm range. The approximate theoretical position of the different bending
and strckhing modes and the precise position of the Si-N stretching mode
obtained for the four films are indicated.
bonds remain in the film to form amorphous silicon.
In the second series of four samples we fixed the flux
ratio at 75% and changed the total pressure in the chamber
from 30 to 77 mTorr. This fiux ratio value was chosen be
cause it provides a refractive index not far from the theoreti
cal value for a pure Si3N4 film (1.9 to 2.0 for conventional
thermal CVD films 13), and also bec:ause the film is quasi-free
of amorphous silicon (cf. Fig. 3) and has interesting electri
cal properties (cf. Table I). The refractive index reaches a
maximum value of 2.02 for a pressure of 50 mTorr which
corresponds to a Si02 percentage of 18% determined by
spectroscopic ellipsometry. The position of the Si-N stretch
ing mode absorption peak is also minimalll.t 834 cm I and
not far from the position for a pure Si3N.~ film. 14 The best
electrical properties are also obtained for this pressure value
(breakdown voltage E B around 3 X 106 V / cm and electrical
conductivity pat 106 V / cm up to 2 X 10 t1 n cm). This effect
ofthe total pressure on the properties of the dielectric films is
completely different from that generally notices for PECVD
systems.15 Indeed, the total pressure does not drastically
change the deposition conditions in the latter case but rather
the plasma density and the bombardment of the substrate,
3412 J. Appl. Phys., Vol. 66, No.7, 1 October 1989 thus no optimum appears. In contrast, in our system, a com
promise must be found between the diffusion of the plasma
in the multipolar chamber (which decreases with the pres
sure) and the plasma density (which increases with the pres
sure). 50 mTorr certainly corresponds to a medium plasma
diffusion with an optimized plasma density.
In conclusion, silicon nitride films with an interesting
electrical quality have been prepared at room temperature
using a microwave multipolar plasma system. The physical
and electrical properties of these films have been optimized
varying the flux ratio SiH4/NH3 and the total pressure in the
chamber. The density variations of the films have been at
tributed to the presence ofSiOz in the films at low silane flux
and by the deposition of amorphous silicon at higher silane
flux. The improvement of other plasma conditions such as
power level or substrate temperature are in progress. Ruth
erford backscattering and elastic recoil detection measure
ments will also be applied to the samples in order to measure
precisely the amounts of oxygen and hydrogen in the films.
The authors would like to express their gratitude to G.
Martin for his active contribution to adjust the plasma sys
tem, E. Boucherez for the fabrication of test structures, and
J. Michel for assistance in the spectroscopic ellipsometry
measurements.
'M. Maeda and Y. Arita. J. AppL Phys. 10, 53 (1982).
'V. Numasawa, K. Yamazaki, and K. Hamano, Jpn. J. App!. Phys. 22,
U92 (1983).
'I. Kato, K. Noguchi, and K. Nurnada, J. App!. Phys. 62,492 (1987).
4K. Limpaccher and K. R. Mackenzie, Rev. Sci. lnstrum. 44, 926 (1973).
'1'. Boher, F. Pasqualini, J. Schneider, and Y. Hily, Colioque International
our les Plasmas et la Grevwe, CIPG '87, Antihes, France, 1987, edited by
the Societe Francaise du Vide (Societe Francaise du Vide, 1987), No, 237,
p.120.
"P. Boher, M. Remmd, J. M. Lopez-Villegas, J. Schneider, and J. P. Chane,
App!. Surf. Sci. 30, 100 (I9H7).
7M. Renaud, P. Boher, J. Schneider, and J. Barrier, Electron. Lett. 24, 750
(1988) .
xP. Boher, M. Renaud, L. J. Van Ijzendoorn, J. Barrier, and Y. Hily, J.
Appl. Phys. 63,1464 (1988).
oR. Burke and e. Pornol. Solid State Techno!. 67 (1988).
HIe. Pomo!. B. Mahi, B. Petit, Y. Arnal, and J. Pelletier, J. Vac. Sci. Tech
no!. B 4, 1 (1986).
"R. Burke, M. Guillermet, L. Vallier, and E. Voisin, 4th InternationalSym
posium on Dry Etching and Plasma Deposition, Antibes, France, 1987,
edited by the Societe Francaise du Vide, Le Vide, les Couches Minces 237,
11 (1957).
"R J. Stein, J. Electron. Mater. 5,161 (1976).
"R. Dun, P. Pan, F. R. White, and R. W. Douse, J. Electrochem. Soc. 128,
1555 (1981).
14J. Rernmerie and H. E. Maes, Proceedings of the Symposium on Silicon
Nitride and Silicon Dioxide Thin Insulating Films, 87-10,189 (1987).
ISH. DUll, P. Pan, R. White, and R. W. Douse. J. Eleetrocnem. Soc. 12,
1555 (1981).
Bcher etal. 3412
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1.459187.pdf | The Jahn–Teller instability of fivefold degenerate states in icosahedral molecules
A. Ceulemans and P. W. Fowler
Citation: The Journal of Chemical Physics 93, 1221 (1990); doi: 10.1063/1.459187
View online: http://dx.doi.org/10.1063/1.459187
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129.105.215.146 On: Fri, 19 Dec 2014 15:54:11The Jahn-Teller instability of fivefold degenerate states in icosahedral
molecules
A. Ceulemans
Department of Chemistry, University of Leuven, Celestijnenlaan 2ooP, B-3030 Leuven, Belgium
P. W. Fowler
Department of Chemistry, University of Exeter, Stocker Road, Exeter EX 4 4QD, England
(Received 14 February 1990; accepted 3 April 1990)
The linear H ® (g E9 2h) Jahn-Teller problem, relevant to the instability of icosahedral
molecules in fivefold degenerate states, is analyzed in detail for the first time. The method of
the isostationary function is used to identify all the extrema of the corresponding potential
energy surface. Depending on one single mode-splitting parameter, two different coupling
regimes are possible, favoring either pentagonal or trigonal minima. The saddle points on
interconversion paths between equivalent minima are identified and the topology of the low
energy regions of the surface is detennined. The results are found to be in agreement with the
epikernel principle. In addition the symmetry characteristics of the principal warping tenn
under the SO( 5) symmetry group of electronic space are assigned.
I. INTRODUCTION
In this paper we discuss the general structural proper
ties of the adiabatic Jahn-Teller (JT) surface near a fivefold
degenerate instability point of icosahedral symmetry. The
literature on the Jahn-Teller effect contains very few refer
ences to this problem. I Khlopin et al. have previously stud
ied a partial solution,2 and some group theoretical aspects
have been discussed by Pooler3,4 and by Judd.s Here we will
consider a more general treatment based on the method of
the isostationary function.6 Recently the same method has
been used to solve the related problem of the Jahn-Teller
instability in a fourfold degenerate icosahedral state.7
II. ICOSAHEDRAL STRUCTURES
The icosahedral point group, long regarded as some
thing of a mathematical curiosity,8,9 is increasing in practi
cal importance in chemistry as further examples of mole
cules with this symmetry are discovered. Salts of the
icosahedral closo-dodecaborane anion [B12H12 ]2-have
been known since the early 1960s \0 and the nature of the
electronic structure and bonding in the isolated ion was un
derstood even earlier. I I The B12 cage is a structural compo
nent in allotropes of boron, 12 though as in the borane salts it
usually occupies a cubic site and may suffer consequent
small distortions from ideal icosahedral symmetry. 13 Dode
cahedral C20 H2o was first synthesized in 1982 in the culmi
nation of a project stretching over many years and various
derivatives which retain the C20 core are known,I4 Al
though the groups [ and [h are themselves noncrystallogra
phic, there is intense theoretical and experimental research
activity on the possibility that quasiperiodic structures based
on local icosahedral symmetry may be realized in metallic
alloys. 15 The near-tetrahedral bond angles in the dodecahe
dral cage lend it credibility as a possible structure for clusters
of water molecules,16 and a hypothetical C~o+ carbon cluster
has been discussed in connection with theories of aromati
city. 17 The most recent surge of interest in all things icosahe
dral was undoubtedly started by the claiml8 that laser va
porization of graphite produces a long-lived C60 cluster, and
the hypothesis that this molecule should take the shape of
the Archimedean truncated icosahedron, a polyhedron in
which all 60 vertices are equivalent and which has full [h
symmetry. Although aspects of the interpretation of the ex
perimental observations have been challenged,19,20 the C60
hypothesis has survived theoretical investigation by meth
ods ranging from graph theory21 to all-electron ab initio cal
culation,22,23 and support for it is accumulating from experi
ments on radical scavenging,24 photofragmentation,2s UV
spectroscopy,26 x-ray microscopy of soot particles,27 and
flame studies. 28
The consensus from the many theoretical treatments is
that t-icosahedral C60 would at least be a local minimum on
the potential hypersurface for 60 carbon atoms and would
have a closed electronic shell with a fivefold degenerate Hu
HOMO and a large "band gap" retaining much of the 1T
stabilization energy of planar graphite.
In the original experiments by Kroto et ai., 18 the vapori
zation products are ionized by a second laser and then passed
through a mass spectrometer system. The species actually
detected is thus C6t; , which, with its h : electronic configura
tion, is a candidate for the Jahn-Teller distortion of the type
discussed in the present paper. Its apparent resistance to
photofragmentation has led Smalley and others29,30 to sug
gest that C6t; may be abundant in the interstellar medium. In
contrast to neutral C60, the cation is predicted to have a
relatively rich optical spectrum and it has been proposed as a
possible carrier of the mysterious diffuse interstellar
lines.18,31 The plausibility of such suggestions depends in
part on the assumption that Jahn-Teller distortion from
ideal icosahedral symmetry will be small, since loss of a sin
gle electron should not strongly perturb a framework of 90
C-C bonds (60 single + 30 double). Evaluation of this as
sumption would require a detailed discussion of the modes of
JT distortion and a knowledge of the vibrational force field.
Calculations of model force fields for neutral C60 have been
J. Chern. Phys. 93 (2),15 July 1990 0021-9606/90/141221-14$03.00 @ 1990 American Institute of Physics 1221
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129.105.215.146 On: Fri, 19 Dec 2014 15:54:111222 A. Ceulemans and P. W. Fowler: Icosahedral molecules
published by several groups,32-34 and the theory of the rovi
brational spectra of exactly icosahedral molecules has been
developed by Harter and Weeks.35,36 The present paper pro
vides an analytical treatment of JT distortion in the general
case of a fivefold degenerate state of an icosahedral molecule.
III. THE ICOSAHEDRAL SYMMETRY GROUP
The finite symmetry group of the present problem is the
icosahedral group Ih• Without loss of generality the problem
can be treated equally well in the subgroup of proper rota
tions l Figure 1 shows the numbering of the symmetry oper
ations on in a Cartesian frame. Our conventions are strictly
in line with the recommendations of Boyle and Parker. 37
These authors have specified a standard choice of irreducible
representations, based on the subductional chain I ~ T ~D2' In
this chain the generator elements of the tetrahedral sub
group T were the C(j ~,4,3 and ~ 1,2 symmetry axes. Of particu
lar interest are the fourfold and fivefold degenerate represen
tations, denoted, respectively, as G and H. The
corresponding canonical components are labeled Ga, Gx,
Gy, Gz and HO, HE, Ht, H'T/, Ht. Transformation matrices
for the G representation may be found in Refs. 7 and 37. The
defining matrices for the H representation are listed in Ap
pendix A.
A complete set of Clebsch-Gordan (CG) coupling co
efficients for the Boyle and Parker symmetry basis has been
published recently. 38 In this respect it must be noted that the
icosahedral group is nonsimply reducible.39 This means that
the Kronecker products of two irreducible representations
of [ may contain an irreducible representation more than
once. A case in point is the symmetrized square of the H
representation, denoted as [H] 2. As Eq. (1) shows, this
square contains the H representation twice. Accordingly
two independent
x
9
FIG. 1. Icosahedral symmetry group in a Cartesian reference frame, ac
cording to the conventions of Boyle and Parker (Ref. 37). Various useful
generator elements of icosahedral subgroups are indicated. [H]2 =A + G+2H (1)
sets of H XH = H coupling coefficients can be constructed.
These sets can be defined only within unitary equivalence. In
the present publication we will comply with the definitions
in Ref. 38. The corresponding sets will be labeled as
(Hh1IHh2Hh3)a and (Hh11Hh2Hh3 )b' where a and bare
multiplicity labels. A complete table of CG coupling coeffi
cients is a valuable tool with many applications in group
theory and we have found the tables in Ref. 38 particularly
useful in our work on JT surfaces. So far, at least, no errors
have been detected and we recommend them to anyone
working on icosahedra.
IV. THE H4D(ge2h) INSTABILITY
According to the JT theorem a fivefold degenerate state
of an icosahedral molecule will be unstable under distortion
al coordinates that transform like the nontotally symmetric
representations in [H F. From Eq. (1) these representa
tions are readily identified as G and H. The corresponding JT
instability is usually denoted as H ® (g $ 2h), where lower
case symmetry labels are used for the active modes. A linear
model of this instability contains only linear distorting
forces, proportional to force elements F, and harmonic re
storing forces, proportional to force constants K. For a dis
tortion along a G-type coordinate, say QGg, the matrix ele
ments, which describe the distorting force, are as follows:
Wij(QGg) = QGgFG(HiIGgHj). (2)
In this expression the bracket denotes a CG coefficient,
which is symmetric under exchange of the electronic compo
nent labels i and j. Coupling to the H modes is special, be
cause of their multiple occurrence in the Kronecker product
ofEq. (1). In fact two independent Fconstants will be need
ed to describe the linear distorting forces along a QHh coordi
nate:
Wij (QHh) = QHh [ FHa (HiIHhHj) a
+ F Hb (HiIHhHj) b ]. (3)
Explicit expressions for the W matrices are listed in Appen
dix B. Combination of these expressions with the harmonic
restoring potentials for all active coordinates yields the adia
batic JT surface Ek (Q) with five sheets:
EdQ) =..l L KA Q~A + Ek (Q), k = 1,2,3,4,5, (4)
2 AA
where E k (Q) is the k th root of the secular equation
IlL Wij (QAA) -Ek (Q)8ijll = O. (5)
AA
In this equation the summation index A runs over all active
modes. In principle both G and H representations can give
rise to multimode coupling. However, as long as one oper
ates in a linear model, the multimode problem will have ex
actly the same symmetry characteristics as the so-called sin
gle-mode approximation, with only one vibrational mode of
each symmetry type. 1
For this reason we will restrict our treatment of the
H ® (g $ 2h) problem to a nine-dimensional coordinate
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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129.105.215.146 On: Fri, 19 Dec 2014 15:54:11A. Ceulemans and P. W. Fowler: Icosahedral molecules 1223
space, consisting of one G mode with components
{QGa,QGx,QGy,QGz}, and one H mode with components
{QH9,QHE,Q HS,QH1/,QH,}. The spatial origin corresponds to
the icosahedral point at zero energy.
It is important to realize that the presence of only one H
mode in this coordinate space does not remove the nonsimp
ly reducible character of the problem. Indeed the multiplic
ity aspect of the coupling to H modes is retained via the
presence of two independent coupling parameters, FHa and
F Hb' In this respect three different JT stabilization energies
can be defined:
EJGT = _~ F~
2 K ' G
EJT __ ~ F~a
Ha -5 K '
H
E~b = _~ F~b.
5 KH
V. EXTREMAL STRUCTURE OF THE JT SURFACE (6)
In this section we analyze the structure of the adiabatic
JT surface, using the method of the isostationary function.6
Previous applications of this method were restricted to sim
ply reducible instabilities.7•40 However as the present exam
ple will show, the method can also be extended to cases
which exhibit a product multiplicity.
A. The stationary conditions
An eigenvector IHa) ofthe secular equation can be de
scribed by five parameters, say 0, E, S, 1/, ;, that specify the
direction cosines between IHa) and the five standard com
ponents of the electronic basis set. Hence one has
with IHa) = 0 IHO) + EIHE) + slHs)
+ 1/IH1/) +; IH;)
02+C+S2+1/2+;2= 1. (7)
The five-dimensional parameter space also will be referred to
as the electronic space, as opposed to the nine-dimensional
QAA space, which is the coordinate space. In view of the
normalization condition in Eq. (7) a real eigenvector is rep
resented by a point on the unit hypersphere in electronic
space.
Following Oepik and Pryce,41 the energy associated
with IHa) is obtained by inserting the eigenvector coeffi
cients in the secular equation. This yields
(8) By minimizing this expression in coordinate space one ob
tains extremal coordinates, IIQAA II, that are functions of the
five electronic parameters:
(9)
Using the W matrices from Appendix B, Eq. (9) can be
made explicit in the following way:
J. Chern. Phys .• Vol. 93, No.2, 15 July 1990
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129.105.215.146 On: Fri, 19 Dec 2014 15:54:111224 A. Ceulemans and P. W. Fowler: Icosahedral molecules
The IIQA'" II functions represent the so-called stationary co
ordinates of Oepik and Pryce. They constitute the first step
in the construction of the isostationary function.
B. The isostationary function
The isostationary function (liE II> is obtained by insert
ing the stationary coordinates in the energy expression for
(E>a [seeEq. (8)]:
(11 )
In this way one obtains a function in electronic space, which
can be shown to exhibit the same extremal structure as the
actual JT surface in coordinate space.6 This equivalence has
a practical interest, since it allows the extremal points of a
nine-dimensional surface to be obtained by minimizing a
simple function in a reduced space of only five dimensions.
Upon appropriate substitutions of the foregoing equations,
theisostationary function (liE II> of the quintuplet instability
problem reduces to the following form:
with
EO= (4E~T + 5E~ + 5E~b)/14,
E I = 5( 4EIJ' + 5E~ -9E~b )/56,
/'= iz«()2 + C)2 + j(52'Y/2 + 52{;2 + 'Y/2{;2) (12)
--ih,()E(52 -'Y/2) + ~«()2 _ C)(2{;2 -52 -'Y/2) -j.
As can be seen from Eq. (12) the isostationary function42
consists of two terms. The first term (EO) represents the
average JT stabilization energy of the problem [cf. Eq. (6)].
The second term contains a function /. that depends on the
I orientation of the eigenvector in electronic space. This term
is weighted by a parameter E I, which is proportional to the
difference between 9E~b and 4EIJ' + 5E~. If E I vanishes,
the isostationary function is seen to remain constant. This
implies the existence of an equipotential minimal energy
trough on the JT surface. For E I ¥= 0, the stationary points of
(liE II>, and hence of the JT surface, may be found by mini
mizing the /,polynomial. The results will be described in the
next paragraph.
c. Location of the extremal pOints
The function /,is a fully symmetrized polynomial of
rank 4, which can be shown to be invariant under the opera
tions on. Other interesting group theoretical properties of I
will be discussed in Sec. VII B.
Minimization of the isostationary function in the space
of the electronic coordinates, subject to the eigenvector nor
malization condition, was performed using the method of
Lagrange multipliers. A computer-assisted search yielded
five different classes of critical points. These classes were
labeled a, /3, y, Il, and vand are listed in Table I. Since /is an
even function, all solutions occur in pairs of antipodal
points. Each class corresponds to an orbit of equivalent an
tipodal pairs that are mapped onto each other under the
symmetry operations of the icosahedral group.
The Il and v orbits are exceptional in that they are both
composed of continuous critical loci, rather than of discrete
critical points. It can readily be shown that these loci are
great circles of the unit hypersphere in the five-dimensional
parameter space. In all there are 15 of these circles, forming
2 separate orbits under the operators of I.
The symmetry of a critical point is the group of all sym
metry operations on which either leave this point invariant
or turn it into its antipode. Such an invariance group is also
referred to as the stabilizer of a critical point. The stabilizers
of the a, /3, and r orbits are [])s, [])3' and [])2' respectively.
When considering the stabilizers of the great circles in the Il
and v orbits one must include those symmetry operations
that merely rotate the circle about its own axes of revolution.
As an example the effect of the Crfi ~.4.3 operation on the first
element of the Il orbit is to displace all its points43 over an
angle of 21T/3:
Crfi ~.4.3 (cos tp,sin tp,O,O,O) = [ -~ cos tp -v'3 sin tp, v'3 cos tp -~ sin tp,O,O,O] 222 2
= [cos( tp + 2;) ,sin( 'P + 2;) ,0,0,0].
Hence Crfi ~.4.3 stabilizes this circle as a whole. In this way it
can easily be shown that the stabilizer of the elements in the
Il orbit is the group 'f, while the stabilizer of the v orbit is [])3'
In each case the dimension of an orbit equals the quotient of
the orders of the parent and stabilizing groups. Hence one
has dim a = dim I1dim [])s = 6,
dim /3 = dim lI/dim [])3 = 10,
dim y = dim lI/dim [])2 = 15,
dimll = dim I1dim 'f = 5,
dim v = dim lI/dim [])3 = 10.
J. Chern. Phys., Vol. 93, No.2, 15 July 1990 (13)
(14)
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TABLE I. Extremal eigenvectors· of the isostationary function for the H ® (g al 2h) problem.
a:D,
I -(vJ,l, ± ,/6,0,0)
{fO I V3 (0,0,1,1,1) (0,0,1,0,0)
I -(vJ, -1,0, ± ,/6,0)
{fO I V3 (0,0, -1,1,1) (0,0,0,1,0)
I -(0,v2,0,0, ± vJ)
,f5 I V3 (0,0,1, -1,1) (0,0,0,0,1)
I V3 (0,0,1,1, -I) I -(l,vJ,v2,O, ± v2)
.J8
I -(I, -vJ, ± v2,0,0)
,/6 I -(l,vJ, -v2,0, ± v2)
.J8
I -(l,vJ,O, ± v2,0)
,/6 I -(I, -vJ,O,v2, ± v2)
.J8
I V3 (v2,0,0,0, ± I) I -(I, -vJ,O, -v2, ± v2)
.J8
I "2 (v2,0,1, ± 1,0)
I "2 (v2,0, -I, ± 1,0)
Jl:T (great circ\esb ) v:D3 (great circlesb )
(cos lP,sin 11',0,0,0) ( O,cos 11', ± ~ sin 11', ~ sin 11',0 )
-cosm -smm --cos m--cosm -cos m (I I . I I + I )
2 T' 2 T' v2 T' v2 T' v2 T (vJ 1 ° 1. I.) 2 cos 11', "2 cos 11', ,± V2 sm 11', V2 sm II'
-cosm -smm -cosm- --cosm -cosm (I I. I I + I )
2 T' 2 T' v2 T' v2 T' v2 T (vJ 1 1 . ° 1 . ) -cos 11', - -cos 11', ± -sm 11', ,-sm II' 2 2 v'2 v2
-cosm -smm -cosm --cosm --cosm (I I. I I + I )
2 T' 2 T' v2 T' v2 T' v2 T (1 1. 1 1 1) "2 cos 11', "2 sm 11', V2 cos II' -, V2 cos II' + , V2 cos II'
-cosm -smm --cosm- --cosm --cosm (I I. 1 1 + 1 )
2 T' 2 T' v2 T' v2 T' v2 T -cosm -smm --cosm- --cosm -cosm (1 1. 1 1 + 1 )
2 T' 2 T' v2 T' v2 T' v2 T
-cosm -smm --cosm- -cosm --cosm (1 1. 1 1 + 1 )
2 T' 2 T' v2 T' v2 T' v2 T
-cosm -smm -cosm ---cosm --cosm (I 1. 1 1 + 1 )
2 T' 2 T' v2 T' v2 T' v2 T
• Eigenvectors are denoted as «(J,E,S, 1l,t) rows. Only one eigenvector of each antipodal pair ± «(J,E,S, 1l,t) is listed.
b The solutions of the Jl and v sets are one-dimensional continua, which correspond to great circles of the unit hypersphere. The angular variable II' parameter
izes points on a great circle; II' ± are defined as II' ± 211"13.
Finally, the nature of an extremum may be found by evaluat
ing the Hessian matrix for displacements on the surface of
the unit sphere in parameter space. As in our previous work
on the quadruplet instability,7 these matrix elements can
most conveniently be calculated using hyperspherical polar
coordinates. The corresponding surface tensor is developed
in Appendix C. The Hessian eigenvalues are shown in Table
II. Since all critical points in a given orbit are equivalent,
TABLE II. Symmetry, energy, and nature of the four stationary orbits.
Orbit dim Symmetry / Eneru
a 6 D, -4/5 EJT
Hb
f3 10 D3 +4/9 (4E~ + 5E~ )/9 they will all be characterized by the same curvature. Table II
shows that pentagonal and trigonal extrema are either mini
ma or maxima, depending on the sign of the difference pa
rameter El, defined earlier [see Eq. (12)]. On the other
hand, the D2 points of the r orbit are always saddle points.
The extremal nature of the p, and v orbits is less straightfor
ward. Although there are no symmetry operations that in
terconvert elements of these orbits, their energies appear to
Hessian eigenvaluesb
28/5,28/5,28/5,28/5
-28/9, -28/9, -28/9, -28/9
r 15 D2 -1/3 (4E~ + 5E~ + 15E~b)/24 -14/3,14/3,14/3,14/3
Jl 5 T f + 1/4 (12E~ + 15E~ + 5E~b )/32
v 10 D3 c
• The JT stabilization energies are defined in Eq. (6).
b All values are to be multiplied by the parameter E', defined in Eq. (12).
C Points on the great circles always have one zero eigenvalue. The other three eigenvalues are found to vary with the angle 11', defined in Table I (cf. Sec. VI B).
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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be identical. In fact they intersect each other in points of ][)2
symmetry (but not members of the r orbit). In these points
three out of four Hessian eigenvalues are found to vanish.
This indicates that in these points three rings (one of fL, and
two of v) are linked together. Away from these intersection
points only one zero eigenvalue remains, corresponding to a
movement along the great circles. For a more detailed analy
sis of the extremal nature of these loci we refer to Sec. VI B.
As we have pointed out before, the I'function in elec
tronic parameter space is isostationary with the adiabatic JT
potential in coordinate space. The coordinate images of the
critical eigenvector points in Table I may immediately be
obtained by inserting the appropriate eigenvector coeffi
cients in the stationary conditions of Eq. (10). Evidently
two antipodal eigenvectors with opposite signs will be
mapped onto one and the same coordinate point. In this
mapping, extremal nature and symmetry characteristics of
the critical solutions are retained. Hence we may conclude
from our analysis of the isostationary function that the
H ® (g $ 2h) instability will be characterized by minima of
pentagonal or trigonal symmetry, depending on the sign of
the E I parameter. In Sec. VI a more detailed description of
these minima will be presented.
VI. DESCRIPTION OF THE PENTAGONAL AND
TRIGONAL MINIMA
The method of the isostationary function predicts the
existence of pentagonal and trigonal turning points on the
H ® (g $ 2h) surface. A detailed description of these points
can easily be obtained by inserting eigenfunctions of the ap
propriate ][)s or D3 symmetries in the secular equation.
A. The Ds minima
In Ds the orbital quintet transforms as Al + EI + E2·
The pentagonal eigenfunctions44 of the subgroup with 1ff ~.12
and '1ff ~.8 generators are given in Eq. (15):
IHAI (Z'2» =_1_ (v'3IHO) -IHE) +$Jln-,,»,
JW
IHEI (y'z'» =_1_ (~5 +$IHt) +~5 -$IH~», JW ..
IHEI (x'z'» = _1_ ( _ 3 -$ IHO)
JW 2
+ v'3(1 + $) IHE) + v'1IH7]») (15) 2 '
IHE2(x'y'» =_1_ (-~5 -$jHt)
JW
+~5 +$IH~»,
IHE2 (X,2 _ y'2» = _1_ (3 + $ IHO)
JW 2
_ v'3( 1; $) IHE) _ v'1IH7]») .
In this equation Z,2, y' z', ... refer to the transformational prop-erties of the real d orbitals in a primed coordinate system,
with z' along the 1ff ~.12 axis and y' coincident with y. Note
that the A I eigenfunction corresponds to an element of the a
orbit in Table I. In coordinate space the distortions that con
serve][)s symmetry will be found along the coordinates that
are totally symmetric under][)s . There are no such directions
in the QG space, since G transforms in Ds asEI + E2. On the
other hand, the H mode yields one totally symmetric compo
nent, exactly as the electronic state itself. For the 1ff ~.12 based
subgroup this coordinate is given by
1
QHa = I1i\ (v'3QH9 -QHE + $JQH7/)'
,,10 (16)
Figure 2 (a) illustrates the splitting of the fivefold degener
acy under the Ds distortion. The corresponding energies45
are specified in Eq. (17):
(.)
(b) E(At> = -~FHbQHa +J.KHQ~a, $ 2
E(EI) = (-J.FHQ +_I-FHb)QHa +J.KHQ~a,
2 2$ 2
(17)
E(E2) = (J.FHQ +_I-FHb)QHa +J.KHQ~a.
2 2$ 2
..
FIG. 2. Splitting of the fivefold electronic degeneracy under a pentagonal
(a) and trigonal (b) distortion coordinate. The corresponding energy func
tions are given in Eqs. (17) and (24). In (a) FHb is taken to be equal to
..j5FHu• ---
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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The minimal energy of the A I potential is E ~b' as indicated
in Table II. A prerequisite for this minimum to be an abso
lute pentagonal minimum is that the nondegenerate A I com
ponent will be more stabilized than the EI and E2 compo
nents. Otherwise one would obtain a pentagonal ground
state, which is likely to undergo further symmetry lowering
distortions. Hence, in order to test the consistency of the
solutions in Table II, it is worthwhile to examine under what
conditions the EI or E2 potentials in Fig. 2(a) may drop
below the minimum of the A I potential. As can be seen from
Eq. (17) a degenerate pentagonal ground state will be ob
tained if the absolute values of the force elements obey the
following inequality:
(18)
or
Substitution of this inequality in the expression for the E I
parameter yields
EI-S(4EJT+5EJT -9EJT)<0 -36 0 Ha Hb . (19)
The minimal energy of the degenerate ground state is given
by the lower of the two minima for EI and E2 states, i.e.,
The lower bound of this energy cim be found by combining
Eqs. (18) and (20):
- JT E(EI or E2) > §E Ha' (21)
From these results one may conclude that the degenerate
pentagonal ground state only exists for negative values of
E I, i.e., in the region of existence of the trigonal minima, and
that its minimal energy will be above the energies of the D3
solutions given in Table II. This confirms the previous result
that the ][)s and][)3 turning points are true minima, respec
tively, for E I > 0 and E I < O. Finally we recall that there are
six equivalent pentagonal minima, which form the a orbit
(cf. Table I). It can easily be shown that all these minima are
equidistant in coordinate space. The distribution of the Ds
turning points can thus be represented by the fully connected
six-vertex graph. Such a graph has 15 edges or "pathways"
between equivalent minima. The corresponding saddle
points are readily identified as the][)2 solutions in the rorbit,
each r point lying at an equal distance from two a points.
B. The D3 minima
Symmetry does not offer a unique description of the tri
gonal eigenfunctions, since the orbital quintet reduces to
A I + 2E in ][)3' A convenient set of trigonal components,
that are adapted to the subgroup of the <if ~.4,3 and <if i,8 gener
ators, are given in Eq. (22): IHAI) = ~ (IHs) + IH7J) + IH,»,
IH lEu) =.!. (v'JIHO) + IHE) -,/6IH7J) 4
+ ,/6IH,»,
IH lEv) =.!. ( -IHO) + v'JIHE) + 2v1IHs) 4
-v1IH7J) -v'2IH,»,
IH2Eu) = ! (v'JIHO) -3IHE) + 2:; IHs)
v1 v'2) -V3IH7J) -V3IH,) ,
IH2Ev) =.!. (3IHO) 4
+ v'JIHE) + v1IH7J) -v1IH, ) ). (22)
In this equation the labels IE and 2E are introduced to de
note a particular separation of the two E representations.
The component labels u and v denote components that are,
respectively, symmetric and antisymmetric with respect to
<ifi,8. TheAI component is included in Table I as one of the
elements of the p orbit.
Contrary to the ][)s case, there are two distortional co
ordinates that are invariant under D3, one in Qo space and
one in QH space. For the <if ~,4.3 based subgroup these coordi
nates are given by
The QO/3 and QH/3 modes in Eq. (23) subtend a two-dimen
sional space of trigonal configurations. The IT surface in this
space consists ofthree sheets corresponding to the three tri
gonal levels of the quintet state. Figure 2(b) illustrates a
cross section of this surface along the QO/3 coordinate. The
potential functions are specified in Eq. (24):
E(AI) = -j(FoQo/3 + FHaQH(3) + !KoQ~/3 + !KHQ~/3'
E± (E) =t(FoQo/3 +FHaQH(3)
± [q,FHaQH/3 -r"FoQO(3)2 + !F~bQ~/3] 112
(24)
The two E levels in Eq. (24) correspond to the upper and
lower root of the interaction matrix between the IE and 2E
functions, given in Table III.
The minimal energy of the A I component corresponds
to ;E!i + aE ~a' as indicated in Table II. As for the Ds case,
the trigonal turning points can only be true minima if the
nondegenerate component is the actual trigonal ground
state. This is easily confirmed for the special cases, where one
of the three IT stabilization energies equals zero. A general
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TABLE III. Interaction matrix between the two trigonal E levels" as a func
tion of the trigonal distortion modes QGP and QHP'
IBIEr)
(BIEri !(FGQGp+FHaQHP)
-?,.FGQGP + !FHQQHP
+ !KGQ~p + !KHQ~P
(B2Erl WHbQHP IB2Er)
!(FGQGP +FHaQHP)
+ ?,.FGQGP -!FHaQHP
+ !KGQ~p + !KHQ~P
"The IE and 2E functions are given in Eq. (22); l' = U, v.
analysis seems far more difficult though, because of the
square-root terms in Eq. (24). Distance calculations on the
distribution of the ten trigonal minima in coordinate space
reveal that each minimum is surrounded by three minima at
distance rA, and six at distance rB, as specified in Eq. (25):
r. =~ F~ +~ F:;'a
A 27 K 27 K2 ' G H
~ =~ F~ +~ F:;'a .
B 27 K~ 27 K:;' (25)
Accordingly in the local D3 symmetry of a given turning
point, the adjacent minima form 2 suborbits of dimensions 3
and 6. The fact that there are only three elements in the
suborbit at distance r A indicates that these elements and the
center of the orbit must have a ~ 2 axis in common. This
implies that they can be reached along pathways of C2 sym
metry. In contrast the six elements of the suborbit at distance
rB are not stabilized by symmetry elements of the orbital
center. Therefore, they must be lying along directions of C1
symmetry. Since all 10 minima are equivalent, there will be
15 pathways ofC2 symmetry vs 300fCI symmetry.
In order to check whether all these pathways are al
lowed, we must find all corresponding transition states.
From the energy values in Table II, it is clear that if these
transition states exist, they must be situated on the great
circles of the I" and v orbits. An extremal analysis of the
(cos q;, sin q;, 0, 0, 0) circle in the I" orbit yields the following
set off our Hessian eigenvalues, in units of -1.fE I:
[ O,sin (q; + ~) sin (q; -~) ,cos q; sin( q; + ~),
-COSq;Sin(q;- ~)].
As mentioned before, the zero root corresponds to the move
ment along the circle. Likewise, for q; = 1T16 + n1T/3, one
finds three zero roots, corresponding to the intersections of
the ring with two rings of the v orbit. Outside these points,
the Hessian has, for E 1 < 0, exactly one negative eigenvalue.
This indicates that on a surface with trigonal minima the
great circles can act as transition regions. The points of
steepest descent are found for q; = n1T/3, and have eigenval
ues (0, -114, 112, 112) in units ofa -ZjE I. There are 15 antipodal pairs of such points in the I" orbit indicating that
they have D2 symmetry. The I" orbit thus provides the re
quired transition states of the C2 interconversion paths be
tween equivalent trigonal minima.
A similar analysis can be carried out for the [0,
cos q;,( 1Iv'1)sin q;,( 1Iv'1)sin q;,0] great circle as a represen
tative of the v orbit. In this case the Hessian eigenvalues, in
units of -1.fE I, read
[ O,sin (q; + ;) sin q;,cos( q; + ~) sin( q; + ;),
-cos(q; + ~)sinq; J.
Quite remarkably, these values are identical with the results
for the I" orbit, except for an irrelevant angular phase shift of
30·. The great circles in the I" and v orbits thus are not only at
the same energy, but in addition also have the same Hessian
eigenvalues. The difference is that the critical points on the v
orbit are oflower symmetry, C2 instead ofD2, and thus form
an orbit of 30 equivalent antipodal pairs. This makes them
eligible as transition states for the C1 paths between trigonal
minima.
In conclusion both types of interconversion paths be
tween the ten equivalent trigonal minima are allowed. The
graph which represents the C2 interconversion paths is iden
tical to the ten-vertex Petersen graph for the interconversion
paths between the trigonal minima in the G ® (g ED h) cou
pling case.7 The graph for the C1 path is its complement, as
shown in Fig. 3. The sum of the two is the fully connected
ten-vertex graph of all possible tunneling processes between
ten equivalent potential wells. Interestingly, both subgraphs
also occur in the description of isomerization modes in a
trigonal bipyramid.46 The topology of the paths connecting
the D3 minima is also encountered in the study of the four
dimensional simplex or pentahedroid. Backhouse and
Gard47 give the vertices of the regular figure as
A: (4/$,0,0,0),
B:( -1/$, -1, + 1, + 1),
C:( -1/$, + 1, -1, + 1),
D:( -1/$, + 1, + 1, -1),
E:( -11$, -1, -1, -1)
which corresponds to an edge length of 2v'1. Taking subsets
of vertices it is easily seen that this polyhedron has five ver
tices, ten edges, ten equilateral triangular faces, and five reg
ular tetrahedral volumes. The ten face centers have coordi
nates
(213$, ± 213,0,0),
(213$,0, ± 213,0),
(213$,0,0, ± 213),
( -11$, ± 1/3, ± 1/3, + 1/3),
( -11$, + 1/3, ± 113, -1/3)
and so the edge dual of the pentahedroid (formed by joining
nearest-neighbor face centers) has 30 sides of length 2l"1/3
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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lal
b:t1 paths
Ibl
FIG. 3. Topology of the JT surface in the case of trigonal minima, belonging
to the P orbit. The ten vertices of the graphs represent the ten equivalent
trigonal minima. The 15 edges in (a) refer to C2 isomerization paths over
D2 transition states belonging to orbit f.l. The 30 edges in (b) refer to C,
isomerization paths over C2 transition states belonging to orbit v. Each
graph is the complement of the other.
and has the topology of the complement of the Petersen
graph, the same as the (;1 paths between our [)3 minima [see
Fig. 3 (b) ]. Conversely, if we join not nearest but furthest
neighbors we produce a figure with 15 edges of length 4/3 and the topology of the (;2 paths, i.e., the Petersen graph [see
Fig. 3(a)].
VII. DISCUSSION
A. The epikernel principle
An epikernel is an intermediate subgroup in the decom
position scheme of a given point group. The epikernels are
uniquely defined by the irreducible representations of the
symmetry lowering process. In the case of a J ahn-Teller dis
tortion along modes of G and H symmetry, the maximal
epikernels correspond? to the maximal subgroups T, Os,
and D3. According to the epikernel principle, 40 stable mini
ma on the JT surface are to be found with structures of the
maximal epikernel symmetries. The T epikernel is forbid
den, since it splits the electronic manifold into two degener
ate components, E + T2, which remain JT active. The re
maining Ds and D3 epikernels are indeed found to
characterize the minima of the JT surface, in agreement with
the general principle.
Quite interestingly the 03 minima do not depend on the
F Hb constant, while the Ds minima do not depend on the FHa
constant. Hence our initial choice of two independent sets of
H X H = H coupling coefficients, with associated constants
FHa and F Hb' exactly coincides with the separation of tri
gonal and pentagonal coupling schemes. In spite of its com
plexity, the H ® (g fB 2h) JT problem essentially may be
looked upon as a two-mode problem, with two alternative
epikernel orbits. As such it resembles the icosahedral
G ® (g fB h) problem,7 based on T and D3 epikernels, or the
cubic T® (efB t2) problem,40,48 based on D4 and 03 epiker
nels. In each case the crucial parameter which controls the
structure of the surface is the energy splitting between the
two alternative epikernels.
B. 50(5) symmetry
As indicated in Eq. (7) real components of the elec
tronic H state may be described by five directional cosines,
specifying a point on a five-dimensional unit hypersphere.
The rotational symmetry group of this sphere is the group
SO( 5). In this group the five electronic components of H
transform as the fundamental vector representation (1,0).
This correspondence forins the basis for an embedding49 on
in SO(5). Judd has offereds a terse account of the SO(5)
properties, which allow derivation of the relevant branching
rules. Table IV lists the results for representations up to the
fourth rank.
The square of the electronic representation yields
(1,0) X (1,0) = [(0,0) + (2,0)] + {(1,1)}. (26)
The nonscalar part of the symmetrized square is the (2,0)
representation, which subduces4 the coordinate representa
tions G + 2H. The appropriate coupling is described in Eq.
(10).
The isostationary function (liE II) is defined in elec
tronic space and therefore can be characterized by SO( 5)
symmetry species. The trivial case occurs for the mode split
ting parameter E 1 equal to zero. In this case (liE II) is a scalar
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TABLE IV. Decomwsition ofirreducible representations of SOC 5) to irre-
ducible representations of I.
Rank SO(5) dim
0 (0,0) 1 A
1 ( I,D) 5 H
2 (2,0) 14 G+2H
0,1) 10 T1+T2+G
3 (3,0) 30 2A + TI + T2 + 3G + 2H
(2,1) 35 2TI +2T2 +2G+3H
4 (4,0) 55 A + 2TI + 2T2 + 3G + 6!l
(3,1) 81 A + 5T1 + 5T2 + 5G + 6H
(2,2) 35 2A + TI + T2 + 3G + 3H
constant E 0 [see Eq. (12) ]. The corresponding adiabatic1T
surface will exhibit an equipotential minimal energy trough,
with four degrees of freedom. This trough incorporates the
rotational invariance of the hypersphere since a change in
direction of the eigenvector component is related to an equi
potential displacement on the bottom of the trough. How
ever, if there is a splitting between the pentagonal and tri
gonal modes (E ) =1= 0 ), the surface of the trough will become
warped. In this case (liE II) acquires the tensorial properties
of the warping function /. As has been demonstrated else
where,6 I'must belong to the fully symmetrized irreducible
representation 50 of rank 4. This representation can be found
by trace reductionS) of the fully symmetrized fourth rank
representation [4] of the covering group U( 5). One has
U(5) -+SO(5),
[4]-+(0,0) + (2,0) + (4,0). (27)
Removal of the (0,0) and (2,0) representations, respective
ly, of rank zero and two, yields (4,0) as the representation of
the warping function. More specifically I'corresponds to the
unique icosahedral invariant of ( 4,0), as indicated in Table
IV. Furthermore (4,0) may be generated by taking the sym
metrized direct square of the coordinate representation
(2,0):
(2,0) X (2,0) = [(0,0) + (2,0) + (2,2) + (4,0)]
+ {(1,l) + (3,l)}. (28)
Note that I'is a hyperspherical harmonic and as such must
be an eigenfunction of the five-dimensional surface Lapla
cian operator V2, specified in Eq. (C4). This operator is re
lated52,53 to the generalized angular momentum operator
'y2:
5 j-I
- V2 = 'y2 = L L .Yt (29)
j=2 i= I
with components
.Y .. =i(X. 3.....-x. 3.....). IJ Ja. 'a. Xi Xj (30)
In this equation the coordinates Xi and Xj stand for the 0, E, S,
1}, ; variables of Eq. (7). For a (1,0) representation, one
readily proves
'y2(1,Q) = 1(1 + 3) (1,0). (31 )
Hence one has for the (4,0) representation of the warping
function V2(4,0) = -28(4,0). (32)
It is indeed verified that the trace of the Hessian matrix is
equal to -28 /. at least for all the points in the stationary
orbits. (See Table II.)
C. The H. h problem
Khlopin, Polinger, and Bersuker2 have studied the cou
pling of the icosahedral quintet with the fivefold degenerate
H mode, using the coupling coefficients published by Gold
ing.54 Their treatment can be denoted as a H ® h problem,
since only one of the two independent sets of H X H = H
coupling coefficients was taken into account. In order to re
late this formalism to our results, we may, for instance, com
pare the expressions for the orbital splitting under the penta
gonal distortion mode55 QHa, as defined in Eq. (16). The
equivalent of our Eq. (17) in the formalism of Ref. 2 reads
E(A) = 2VQHa + !KHQ1a'
E(EI) = -2VQHa + !KHQ1a, (33)
E(E2) = VQHa +!KHQ1a'
Upon comparison of the two formalisms one obtains
FHb 1 1 V= ---=-F Ha +--FHb $ 2 2$
or
(34)
The coupling scheme of Khlopin et al.2 thus corresponds to
the exceptional case with 5E~ = 9E~ and E:J' = O. This
means that the mode splitting parameter E I vanishes as well.
Under these conditions the trigonal and pentagonal turning
points are degenerate but in addition the A I and E) states of
the pentagonal structures are both found to be ground states,
respectively, at QHa = -2V IKH and QHa = 2V IKH, and
similarly for the A I and E states along the trigonal mode
QHP' defined in Eq. (23). In fact the H®h IT surface as a
whole is found to exhibit SO(3) symmetry.2 Pooler has
briefly discussed the high-symmetry effects in this special
solution.4 However, a precise description of the embedding
of this symmetry group in the SO( 5) group of electronic
space is still lacking.
ACKNOWLEDGMENTS
A. C. is indebted to the Belgian National Science Foun
dation (NFWO) and the Belgian Government (Program
matie van het Wetenschapsbeleid) for financial support.
APPENDIX A: TRANSFORMATIONAL MATRICES FOR
THE H REPRESENTATION
Boyle and Parker37 have listed the transformational
matrices of the H representations under Ctf ~,12, Ctf ~.4'3, and
Ctf i,2 operations of I, as specified in Fig. 1. For convenience
these matrices are repeated here, together with the matrices
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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129.105.215.146 On: Fri, 19 Dec 2014 15:54:11A. Ceulemans and P. W. Fowler: Icosahedral molecules 1231
for the twofold symmetry axes ee? and ee? In this way the
generators of all the subgroups of I are made available:
ee ~.4.3, C(J j.2 .... T,
ee ~.12, ee ~.8 .... lOs,
ee ~.4.3, ee ~.8 .... lO3 ,
C(J j.2, ee ~.8 .... lO2 .
It is important to keep in mind that the 0 and E components
of H do not denote components that transform like the real d
functions d:? and d x2 _ y>' but refer to linear combinations of
these:37•38
-1/4 -..[3/4 1/.J8 1/.,fi -1/.J8
-..[3/4 1/4 -~3/8 0 -M
D( C(J ~.12) = -1/.J8 ~3/8 0 1/2 1/2
1/.,fi 0 -1/2 1/2 0
1/.J8 M 1/2 0 -1/2
0 0 0 0 1 0
0 1 0 0 0 0 1
D(eej·2) = 0 0 -1 0 0 , D(ee~·8) = 0 0
0 0 0 -1 0 0 0
0 0 0 0 0 0
-1/4 -..[3/4 1/.J8 -1/.,fi 1/../8
-..[3/4 1/4 -M 0 M
D(ee~·8) = 1/../8 -~3/8 0 1/2 1/2
-1/.,fi 0 1/2 1/2 0
1/.J8 ~3/8 1/2 0 1/2 Hz2 = .J+ HO -.J+ HE,
Hx2
-T = .J+ HO + .J+ HE. (A2)
As before we prefer a row vector notation for the transfor
mation matrices, in the following way:
!!II (HO,HE,Hs,Hll,Ht)
= (HO,HE,HS,Hll,Ht)(D(!!II». (A3)
The D (!!II) matrices in Eq. (A3) are transposed, as com
pared to the matrices of Boyle and Parker. Following this
convention, one has
-1/2 -..[3/2 0 0 0
..[3/2 -1/2 0 0 0
, D(ee~·4.3) = 0 0 0 0 1 ,
0 0 1 0 0
0 0 0 0
0 0 0
0 0 0
-1 0 0
0 0
0 0 -1
APPENDIX B: THE LINEAR FORCE ELEMENTS OF THE JT HAMILTONIAN
The linear force elements are arranged in W(QAA) matrices, operating in the (HO,HE,Hs,Hll,Ht) electronic basis.
Matrix elements are obtained from the expressions in Eqs. (2) and (3), using the CG coefficients of Ref 38:
3 0 0 0 0 0 0 -1 0 0
0 3 0 0 0 0 0 ..[3 0 0
W(Q ) = QGaFG 0 0 -2 0 0 W(QGx) = $QGxFG -1 ..[3 0 0 0 , ,
Ga 2J6 0 0 0 -2 0 4..j3 0 0 0 0 .,fi
0 0 0 0 -2 0 0 0 .,fi 0
0 0 0 -1 0 0 0 0 0 2
0 0 0 -..[3 0
$QGzFG 0 0 0 0 0
W(QGY) = $QGyFG 0 0 0 0 .,fi W(QGz) = 0 0 0 .,fi 0 , ,
4..j3 -1 -..[3 0 0 0 4..j3 0 0 .,fi 0 0
0 0 .,fi 0 0 2 0 0 0 0
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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3 0 0 0 0 0 0 0 0
0 -3 0 0 0 1 0 0 0 0
W(QHO) = QHOFHa 0 0 -1 0 0 + QHOFHb 0 0 ..[3 0 0
2./6 0 0 0 -1 0 2.J2 0 0 0 -..[3 0
0 0 0 0 2 0 0 0 0 0
0 -3 0 0 0 0 0 0 0
-3 0 0 0 0 0 -1 ·0 0 0
W(QHE) = QHEFHa 0 0 ..[3 0 0 + QHEFHb 0 0 0 0
2./6 0 0 0 -..[3 0 2.J2 0 0 0 1 0
0 0 0 0 0 0 0 0 0 -2
0 0 -1 0 0 0 0 ..[3 0 0
0 0 ..[3 0 0 0 0 0 0
W(QHs) = QHsFHa -1 ..[3 0 0 0 + QHsFHb ..[3 1 0 0 0 2./6 2.J2 ,
0 0 0 0 -2.J2 0 0 0 0 0
0 0 0 -2.J2 0 0 0 0 0 0
0 0 0 -I 0 0 0 0 -..[3 0
0 0 0 -..[3 0 0 0 0 1 0
W(QH'1) = QH'1FHa 0 0 0 0 -2.J2 + QH'1FHb 0 0 0 0 0
2./6 2.J2 ,
-I -..[3 0 0 0 -..[3 0 0 0
0 0 -2.J2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 -I
W(QH~) = QH~FHa 0 0 0 -.J2 0 + QH,FHb 0 0 0 0 0
./6 0 0 -.J2 0 0 .J2 0 0 0 0 0
0 0 0 0 0 -I 0 0 0
APPENDIX C: HESSIAN OPERATOR IN HYPERSPHERICAL POLAR COORDINATES
The e, E,5, 1], t coordinates of the parameter space may be transformed to hyperspherical polar coordinates, following the
general method of Louck:52
5 = r cos a sin /3 sin r sin 8, 1] = r sin a sin /3 sin r sin 8,
t = r cos /3 sin r sin 8, e = r cos r sin 8,
E=rcos8
with
The gradient operator in these coordinates is given by
(a 1 a 1 a 1 a 1 a) v = er ar ,e.s -; a8 ,ey r sin 8 ar ,ep r sin r sin 8 a/3 ,ea r sin /3 sin r sin 8 aa . (CI)
(C2)
Here the e's represent the unit vectors in the polar coordinate system. The Hessian operator for displacements on the surface
of the unit hypersphere can be derived according to the method described by Stone. 53 One obtains a symmetrical 4 X 4 tensor
operator of the following form:
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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129.105.215.146 On: Fri, 19 Dec 2014 15:54:11A. Ceulemans and P. W. Fowler: Icosahedral molecules 1233
VVlr= 1 = cot8 a
sin 8 ay
1 a2 +--sin 8 a8ay
cot 8 a
sin y sin 8 a{3
+ 1 a2
sin y sin 8 a8a{3
cot 8 a cot8 a
sin 8 ay
1 a2 +--sin 8 a8ay
cot8~ a8
1 a2 +---sin28 ay
coty a
sin y sin2 8 a{3
+ a2
sin ysin2 8 aya{3
coty cot 8 a cot 8 a
sin y sin 8 ap sin p sin y sin 8 aa
1 a2
+ sin y sin 8 a8ap 1 a2
-?-sin p sin y sin 8 a8aa
coty a coty a
sin y sin2 8 ap sin p sin ysin2 8 aa
a2 +----sin y sin2 8 ayap 1 a2 + --sin {3 sin y sin2 8 ayaa
cot{3 a
sin {3 sin2 y sin2 8 aa
+---sin2 y sin2 8 ap 2 1 a2 + --sin{3 sin2 ysin2 8 a{3iJa
a cotP a
sin {3 sin y sin 8 aa sin {3 sin y sin28 aa sin {3 sin2 y sin2 8 aa cot8~+ coty ~
a8 sin28 ay
+ a2 1 a2
+ --1 a2 + --+ cot{3 a --sin {3 sin y sin 8 a8aa sin {3 sin y sin2 8 ayaa sin {3 sin2 Y sin2 8 a{3iJa sin2y sin2 8 a{3
The trace of this tensor corresponds to the surface Laplacian in five-dimensional space:
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2' R. E. Smalley, "Down-to-earth Studies of Carbon Clusters," NASA Con
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J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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38 P. W. Fowler and A. Ceulemans, Mol. Phys. 54, 767 (1985).
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125 (1989).
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42 Notice that (liE II) does not contain cross terms in F HQ F Hb. This is a con
sequence of orthogonality of the two sets of H X H = H Clebsch-Gordan
coefficients.
43 Notice that the transformation of the vectorin Eq. (13) is contrary to the
displacement of the corresponding component functions, as described in
Appendix A. See S. L. Altmann, Rotations, Quaternions and Double
Groups (Clarendon, Oxford, 1986), p. 40.
«The pentagonal eigenfunctions in Eq. (15) are obtained in a straightfor
ward way by rotating the real d functions about the y axis over the azi
muthal angle 8 of the <tf~.12 axis (cos 28= lI,j5), keeping in mind the
conventions ofEq. (A2).
4S The energies in Eq. (17) are found by using Eq. (11) with a D5 electronic ket and constraining the W matrices to pentagonal symmetry (i.e., put
ting QHO = ~3/IOQHa,Q", = -~lI1OQHa, QHt = 0,
QH~ = ~6/IOQHa' and QH, = 0 in the definitions of Appendix B).
46 J. Brocas, M. Gielen, and R. Willem, The Permutational Approach to Dy-
namic Stereochemistry (McGraw-Hill, New York, 1983), pp. 646-647.
47N. B. Backhouse and P. Gard, J. Phys. A 7,2101 (1974).
48M. C. M. O'Brien, Phys. Rev.lS7, 407 (1969).
49 The embedding on in SO( 4) is discussed in Ref. 7. See also Ref. 47.
so For the rotational group in n dimensions, SO( n), the fully symmetrized
representation of rank 4 can be shown to have dimension
n(n2 -l)(n + 6)/2.3.4.
51 See Ref. 9, p. 401.
S2 J. D. Louck, J. Mol. Spectrosc. 4, 298 (1960).
53 A. J. Stone, Mol. Phys. 41, 1339 (1980).
54R. M. Golding, Mol. Phys. 26, 661 (1973).
S5 In Ref. 2 the pentagonal distortion coordinate is denoted by Q •.
J. Chern. Phys., Vol. 93, No.2, 15 July 1990
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1.344200.pdf | Thermal stability of Be, Mg, and Znimplanted layers in GaAs for hightemperature
deviceprocessing technology
A. C. T. Tang, B. J. Sealy, and A. A. Rezazadeh
Citation: Journal of Applied Physics 66, 2759 (1989); doi: 10.1063/1.344200
View online: http://dx.doi.org/10.1063/1.344200
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/66/6?ver=pdfcov
Published by the AIP Publishing
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153.106.93.40 On: Wed, 10 Dec 2014 18:46:07Thermal stability of Be .. , Mg ... , and In'''implanted layers in GaAs
for high .. temperature device .. processing technology
A. c, T, Tanga) and 8, J. Sealy
Department of Electronic and Electrical Engineering. University of Surrey. Guilford. Surrey GU2 5XH,
United Kingdom
A. A. Rezazadeh
GEe Hirst Research Centre, East Lane, Wembley, Middlesex HA9 7Pp, United Kingdom
(Received 14 April 1989; accepted for pUblication 17 April 1989)
Results on the thermal stability of active acceptor layers in GaAs formed by Be, Mg, and Zn
implantation are reported. Following rapid thermal annealing at 635 ·C/35 sand 800 ·C/lS s,
the sheet carrier concentration is observed to remain constant after subsequent heat treatment
below 600 ·C for times Up to 6 h. At and above this temperature, however, various changes are
observed for different implants. These changes in the sheet electrical properties are observed to
be reversible in the case of the Zn-implanted samples, where almost complete carrier recovery
is observed after the samples were rapid thermal annealed at 800 ·C/15 s after a long thermal
anneal at 600 ·C for 6 h.
There has been considerable interest in the use of rapid
thermal annealing to activate implanted layers in GaAs and
many reviews have been published. 1.2 In order to assess de
vice performance after various thermal processing stages at
elevated temperatures, there is the need to investigate the
thermal stability of implanted layers, Davies et al.3 reported
that GaAs samples implanted with Si to doses 1.5 and
4 X lO'4/cm2 at 200 keV, followed by rapid thermal anneal
ing at 1080 ·C for 1 5, were stable up to 600 ·C for subsequent
annealing periods of 10 min. Apart from this report, how
ever, the topic of thermal stability has received little atten
tion. We report here the first results on the thermal stability
of active acceptor implanted layers in GaAs.
Undoped semi-insulating GaAs of (100) orientation
was implanted at room temperature with Be, Mg, and Zn
ions to doses of 5 and 2.5 X lO'4/cm2 at energies of 40, 100,
and 260 keY, respectively. The implant doses and energies
were chosen to generate, approximately, the same projected
range and peak atomic concentration as predicted by the
projected range algorithms (PRAL).4 Approximately 1000
A of silicon nitride was deposited pyrolytically at 635 ·C for
35 s. A double-graphite strip heater was used to rapid ther
mal anneal the samples at 800 ·C/IS s. Both the "as-capped"
and the rapid-thermal-annealed (RTA) samples were sub
sequently heat treated in the temperature range of 100-
600 ·C for times up to 6 h. Following annealing, sheet hole
concentration and mobility were measured by the van der
Pauw technique using indium contacts. The carrier and mo
bility profiles were obtained by performing differential Hall
measurements. A solution of H202:H2S04:H20 of ratio
1: 1: 125 was used as the etchent. Table I is a summary of the
sheet carrier concentration Ns' sheet mobility /l-s' and sheet
resistivity R SH of the samples fonowing rapid thermal an
nealing.
From the data given in Table I, it can be seen that a
a) Present address: Cavendisll Laboratory, University of Cambridge, Ma
dingley Road, Cambridge cm OHE, UK. considerable amount of activity is achieved for an threee
implants after a low-temperature RTA. After RTA at
800 ·C/1S s, the Be-implanted samples showed no signifi
cant change in activity when compared to the "as-capped"
samples. However, the Zn-and Mg-implanted samples in
creased from 60% and 20% to 90% and 30%, respectively,
Figure I shows the isothermal annealing results of the
"as-capped" samples following annealing at 600 ·C for times
up to 6 h. No changes in the N, values are observed for all
three implants at temperatures below 6oo·C after for an
nealing times up to 6 h. At 600 ·C, however the IV, values of
both the Be and Mg implants decrease with time; but, in
contrast, the value for the Zn implants increase with time.
That is, the activities decreased from 46% to 32% for the Be
implants and from 20% to 7% for the Mg implants after
subsequent heat treatments at 600 ·C for 6 h. The activity of
the Zn implants, however, increased from 40% to 64%. A
slight increase in the mobility values for all three species
occurred over the 6-h annealing period.
For the RTA samples (800 ·e/15 s), isothermal anneal
ing results in a decrease in IV, for all three implants as shown
in Fig. 2. The activity of the Zn implants has decreased from
90% to 60%, whereas the Be and Mg implants have de
creased from 44% and 31 % to 30% and 22%, respectively.
The sheet mobility values again increase with the long time
anneal; in particular for the Zn implants, the mobility has
increased from 60 to 103 cm2/V s.
Some electrical profiles of the Be implants are given in
Fig. 3, The "as-capped" sample profile is very similar in
shape to the theoretical profile predicted by PRAL and has a
peak hole concentration of about 1Q19/cm3. However, this
profile changes after a subsequent anneal performed at
6OO·C for 6 h, The hole concentration increases near the
surface and decreases throughout most of the profile, This
behavior could well be related to the in-and out-diffusion of
Be atoms. From these observations, it is suggested that the
decrease in the electrical activity is due to the loss of Be
atoms into the encapsulant which has been previously re
ported by Barrett et a/.6
2759 J. Appl. Phys, 66 (6), 15 September 1989 0021-8979/89/182759-03$02040 © i 989 American Institute of Physics 2759
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153.106.93.40 On: Wed, 10 Dec 2014 18:46:07TABLE I. Sheet values for various ions after rapid thermal annealing. (The sheet values are given as an average of five samples with plus and minus one
standard deviation.)
Annealing Be 40 keY Mg 100keV Zn 260 keV
condition Ions (5xlOI4cm' ') (5XI014cm-') (2.5XlO"cm .,)
As-capped n, (cm-') (2.3 J 0.1) 1014 (1 ±0.llIOI4 (It 0.1) 1014
(RTAat ,u,(cm'/Vs) 115 ± 10 90 ± 5 4O±4
635·C 35 s) RSH (H/sq) 238 J: 40 667 ± 30 1574±: 80
% activity 46 ± 2 20 ± 2 40t 4
Plus n\(cm--2) (2.2 ± 0.1) 1014 (!.5 + 0.1) 1014 (2.2 :t 0.1) 1014
(800'C/15 s) /1,. (cm'/V 5) 107.= 10 100 ±: 12 92± 15
RSH (!l/sq) 275 ±.40 400 ± 20 320 ± 35
% activity 44 ± 2 30± 2 88 J-4
It is interesting to note that the Zn activity has increased
(after RTA at 635 ·C/35 s) or decreased (after RTA
800 °C/15 s) to around 60% after a subsequent anneal per
formed at 600 ·C for 6 h. This suggests that an equilibrium
has been achieved between zinc interstitials (which are inac
tive) and zinc atoms on gallium sites after the long-time
anneaL The following equation represents the likely reaction
that occurs:
60()"C/6 h
Znj + Voa ~ Znoa + hole.
800°C/lS ,
Since the RT A cycle at 800 "C/IS s involves the quench
ing of the samples, this has resulted in an excess of zinc atoms
being incorporated into the crystal lattice. A long-time an
neal at 600 °C for 6 h has enabled the process of deactivation
of the zinc atoms to occur. Hence, an equilibrium has been
achieved between the zinc interstitials and the zinc atoms on
gallium sites. In the case of the beryllium- and magnesium
implanted samples, the reactions are observed to be irrevers
ible. Further experiments7 have shown that out-diffusion
~.--.- .. ----
Zn
Tlt1E I HOURSi
FIG, 1. Time dependence of the electrical activity at 600"C aftt>,r silicon
nitride deposition at 635 "C/35 s.
2760 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 has occurred. Hence, the implanted atoms are not available
in the sample for activation.
The electrical profiels of the zinc-implanted samples are
given in Fig. 4. For the sample that has been RT A at 800 ·C;
15 s, a double peak is observed in the profile with the mini
mum carrier concentration occurring near the projected
range and the profile tail extending to a depth of about 3000
A. A possible explanation for the double peak is that crystal
regrowth is imperfect at the region of maximum disorder
which is near the projected range. This has resulted in a
lower activation of zinc atoms in this region,
For the sample that underwent a subsequent heat treat
ment at 600°C for 6 h, the profile is observed to be flat with
an average carrier concentration of 5 X lOl8/cm3• The
change in shape of the profile may be associated with the
diffusion and annealing out of residual defects. These defects
are now spread homogeneously around the implanted region
after this long-time anneal.
A further R T A at 800 "C/IS s results in the profile being
modified to become gaussian in shape with a peak carrier
\-.-~-'-.-~------
'oo~
~~
801
"--l &___. I e___ Z I &. ______ .. n
>-6°1 ---..
~ ~
~ :t~=:=:==:=:=--= 8< :
Mg
o -,-- , r---,--o I 2 3 4 6
TIME I HOUR$i
FIG. 2. Time dependence of the electrical activity at 600 'c after rapid ther
mal annealing at 800 "C/lS s.
Tang, Sealy, and Rezazadeh 2760
T
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153.106.93.40 On: Wed, 10 Dec 2014 18:46:07" 1
.~
w
0
~
FIG. 3. Electrical profiles of Be implants after silicon nitride deposition at
635 ·C/3S ~ (open circles) and further annealed at 600·C for 6 h (closed
circles). B'~ dose and energy: 5 X IO"'/em", 40 keY.
concentration of 1019/cm3 at around the projected range.
Also, the profile has not broadened significantly. This resul
tant profile arises from the reactivation of zinc atoms in the
implanted region which now has improved crystallinity.
The thermal stability of Be-, Mg-, and Zn-implanted
layers in GaAs has been investigated using both R T A and
long-term furnace anneals. This is of great impmtance since
it is found from this work that the electrical properties can
change significantly during subsequent high-temperature
processing in, for example, implant activation and molecu
lar-beam epitaxy growth at elevated temperatures. The sheet
electrical properties are observed to remain constant up to
600 QC At and above this temperature, the electrical proper
ties change significantly. These changes are observed to be
reversihle for the zinc-implanted samples but irreversible in
the beryllium- and magnesium-implanted samples.
2761 J. Appl. Phys., Vol. 66, No.6, 15 September 1989 '"§
z
'2
! ,. z
~
" z
0 u
'"
~
4:
U
Q ••
DEPTH (r'C-)
FIG. 4. Electrical profiles ofZn implants after silicon nitride deposition and
various annealing conditions. Zn dosc and cnergy: 2.5 /. 10'"/cm2, 260 keY.
(a) 800 'C/IS S; (b) 800 'C/lS H· 600 "C/6 h; and (c) 800 "e/15
s -+ 600 'C/6 h -+ 800 'C/IS s.
The authors gratefully acknowledge the staff of the D.
R. Chick accelerator laboratory for assistance with the im
plants. This work was supported in parts by ESPRIT Project
No. 971, Technology for GaAs/ AIGaAs Heterojunction Bi
polar Integrated Circuits. One of the authors (A.C.T.T.)
was supported by a GEe studentship.
'D. E. Davies, N uet. lnstrum. Methods Phys. Res. B 7/8. 387 (I %5).
"B. J. Scaly, Microeli:;ctron . .I. 13,21 (1982).
'D. E. Davies, P. J. McNally, T. G. Ryan, K. J. Soda, and J. J. Comer, inst.
Phys. Conf. SeT. 65, 619 (1982).
"J. P. Biersack, Nucl. instrum. Methods Phy~. Res. 1821183, 199 (1981).
'R. Gwiiliam. R. Bensalem, 13. J. Scaly, and K. G. Stephens.l'hysica 129B,
440 (1985).
"N. J. Barrett, D. C. Bartle, R. Nicholls, and J. D. Grange, Inst. Phys. Conf.
Ser. 74, 77 (1984).
7 A. c. T. Tang, Ph.D. thesis, University of Surrey, UK, 1988.
Tang, Sealy, and Rezazadeh 2761
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1.338436.pdf | Hall effect in heavy fermion compounds (abstract)
P. M. Levy and A. Fert
Citation: Journal of Applied Physics 61, 4397 (1987); doi: 10.1063/1.338436
View online: http://dx.doi.org/10.1063/1.338436
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/61/8?ver=pdfcov
Published by the AIP Publishing
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Magnetism and superconductivity in heavyfermion compounds (abstract)
J. Appl. Phys. 75, 6747 (1994); 10.1063/1.356871
Narrow bands and magnetic properties of heavy fermions (abstract)
J. Appl. Phys. 63, 3422 (1988); 10.1063/1.340754
Coherence in heavy fermion compounds: Effect of impurities
J. Appl. Phys. 61, 3391 (1987); 10.1063/1.338782
Coherentstate Hall effect in the heavy fermions CeCu6 and U2PtC2 (abstract)
J. Appl. Phys. 61, 4397 (1987); 10.1063/1.338435
Heavy fermions in Kondo lattice compounds (invited)
J. Appl. Phys. 57, 3054 (1985); 10.1063/1.335212
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137.189.170.231 On: Mon, 22 Dec 2014 06:15:11Coherent~state Han effect in the heavy fermions CeCus and U2PtC2 (abstract)
T. Penney, F. P. Milliken, and F. Holtzberg
IBM T. J. Watson Research Center, P. O. Box 218, Yorktown Heights, New York 10598
Z. Fisk
Los Alamos National Laboratory, Los Alamos, New Mexico 87545
G. P. Meisner
General Motors Research Laboratories, Warren, Michigan 48090
The Hall effect is found to set the scale for coherence in the normal state of CeCu" and U2PtC2•
CeCu6 is a nonmagnetic, nonsuperconducting heavy fermion system. 1-4 Its resistivity at high
temperature is like that of a collection of incoherent Kondo scatterers. At low temperature the
resistivity smoothly decreases to a very small value, indicating that scattering has become
coherent. The Hall effect has two strong extrema in its temperature dependence which define a
high-temperature incoherent scattering region, a transition region, and a low temperature
coherent region. Although U2PtC2 is superconducting below 1.5 K,5 the Hall results in the
normal state show two extrema similar to those of CeCu6. However, these features are scaled
to higher temperatures, consistent with the smaller low-temperature electronic specific heat
and higher Fermi temperature.
Work at Los Alamos supported by the U. S. Dept. of Energy.
'H. R. Ott et ai., Solid State Comrnun. 53, 235 (1985)0
"Y. Onuki etal., j, Phys, Soc. Jpn. 54, 2804 (1985).
'J, Ftouquet eta!', J. Magn, Magn. Mater. 52, 85 (1985).
'T. Penney et al., J. Magn. Magn. Mater. 54-57, 370 (1986); Phys. Rev. B 34, 5959 (1986).
5G. p, Meisner et al., l'hys. Rev. Lett. 53, 1829 (1984).
HaU effect in heavy fermion compounds (abstract)
P. M. Levy
Department of Physic5~ New York University, New York, New York 10003
A. Fert
Laboratoire de Physique des Solides, Universite de Paris-Sud 91405 Orsay, France
As a result of a recent analysis of data on the Hall effect in heavy fermion compounds I we
evaluated the higher-order resonant scattering contributions to the skew scattering of
conduction electrons. In the single-site approximation we have calculated the t matrix elements
for skew scattering correct to fourth order in the Anderson mixing interaction, i.e., we have
neglected pair correlation effects. By including this fourth-order correction in our calculation
of the Han resistivity we find it is positive at high temperatures which is in agreement with
data on heavy fermion compounds. Prior calculations of this scattering in these compounds
were limited to second order in the mixing interaction above TK• and predicted a negative Hall
constant at high temperatures.2 By using a phase shift analysis of the skew scattering we have
extended our calculation to the incoherent (single-site) strong coupling regime. In the
temperature ranges we considered the Hall resistivity is proportional to the product of the
resistivity and magnetic susceptibility. This is in agreement with data on heavy fermion
compounds.
'M. Hadzic-Lcroux, A. Harnzic, A. Fert, P. Haen, F. Lapierre, and O. Laborde, Europhys. Lett. 1, 579 (1986).
2P. Coleman, P. W. Anderson, and T. V. Ramakrishnan, Phys. Rev. Lett. 55,414 (1985).
4397 J. Appl. Phys. 61 (8), 15 April 1987 0021-8979/87/084397 -01 $02.40 © i 987 American Institute of Physics 4397
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1.339123.pdf | Electron spin resonance investigation of ion beam modified amorphous hydrogenated
(diamondlike) carbon
M. E. Adel, R. Kalish, and S. Prawer
Citation: Journal of Applied Physics 62, 4096 (1987); doi: 10.1063/1.339123
View online: http://dx.doi.org/10.1063/1.339123
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/62/10?ver=pdfcov
Published by the AIP Publishing
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Characteristics of electron spin resonance in hydrogenated amorphous siliconcarbon/hydrogenated amorphous
silicon heterojunctions
Appl. Phys. Lett. 54, 807 (1989); 10.1063/1.100853
Effects of heavy ion irradiation on amorphous hydrogenated (diamondlike) carbon films
J. Appl. Phys. 61, 4492 (1987); 10.1063/1.338410
Electron spectroscopy of ion beam and hydrocarbon plasma generated diamondlike carbon films
J. Vac. Sci. Technol. 18, 226 (1981); 10.1116/1.570729
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142.244.5.147 On: Thu, 27 Nov 2014 01:50:12Eiectron spin resonance investigation of ion beam modified amorphous
hydrogenated (diamondUke) carbon
M. E. Adet and R. Kalish
Physics Department and Solid State Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel
S. Prawer
CSIRO Division of Materials Science and Technology, Locked Bag 33, Clayton, Victoria, 3168, Australia
(Received 6 Apri11987; accepted for publication 21 July 1987)
Electron spin resonance (ESR) measurements on diamondlike carbon films show that the as
grown material possesses a very high (2.5 X 1020 cm -3) concentration of dangling bonds.
Upon irradiation with 50-keV C+ carbon ions, the number of ESR active centers increases by a
factor of 3.5 and the linewidth narrows, but no shift in the g value is observed, and the resonant
peak remains Lorentzian. These effects are concomitant with the previously observed dramatic
decrease in the electrical resistivity (4--5 orders of magnitude). The ESR results verify that no
graphitelike islands have formed as a result of the irradiation. The likely conduction
mechanism is via hopping in band tail states, the number of which increases as a result of the
ion impact.
INTRODUCTION
Diamondlike carbon (DLC) films consist of an amor
phous carbon network with both Sp2 (graphitelike) and Sp3
(diamondlike) bonds. 1 As is the case for amorphous silicon
and germanium, hydrogenation results in a marked increase
in the resistivity accompanied by a widening of the optical
band gap, both of which are presumably caused by the passi
vation of dangling bonds. 2
Recently, we have reported the large decrease in resis
tivity and reduction in the band gap which accompanies ion
beam irradiation ofDLC films.3•4 The decrease in resistivity
with increasing ion dose was found to be correlated with a
loss of hydrogen from the films. However, Raman measure
ments showed that the hydrogen loss was not accompanied
by the growth of graphite crystaUites4 to within the sensitiv
ity limit of this technique which is about 20 A.5 The results of
temperature-dependent conductivity measurements of irra
diated specimens could be explained by assuming that the
ion irradiation and the accompanying loss of hydrogen lead
to a smearing out of the band tails and anincrease in. the ...
number of gap sbttes. However, no direct measure of the
dangling bond density was made and the effectiveness ofhy
drogen in passivating dangling bonds remained an open
question.
As is well known, electron spin resonance (ESR) can
provide a measure of the total number of unpaired spins in
the sample under study and, if the affected. volume is known,
the average dangling bond density can be estimated.6 Here
in, we report ESR measurements on DLC samples irradiated
with 50-keV carbon ions over a range of doses in which dra
matic changes in the conductivity have been observed by us.3
The results of this work enabl.ed us to correlate the large
increase in conductivity with an increase in the spin density
and a narrowing of the ESR linewidth.
In contrast to previous studies 7 in which the rote of hy
drogen was studied in specimens prepared with varying
amounts of incorporated hydrogen, we report the effects of
hydrogen removal by ion irradiation. While this has the ad-vantage of obtaining data from specimens originating from a
single deposition, it must be noted that ion impact is expect
ed to cause damage which may result in an increase in dan
gling bond density additional to that caused by the loss of
hydrogen.
EXPERiMENT AND RESULTS
DLC films 2500 ± 100 A thick were grown on single
crystal substrates by extracting ions from a glow discharge of
CzH2, CO2, and Ar gases.8 The fiJ.ms were grown under con
ditions identical to those used in our previous study3.4 to
enable direct comparison between the ESR results reported
herein and the previously reported dose dependence of the
electrical conductivity and hydrogen content of the ion beam
irradiated films.
Small samples (3X3 mm2), all cut from the same de
posited Si wafer, were implanted with 50-keV C+ ions at 370
K with doses ranging from 2X 1014 to 1 X 1017 cm-2• The
implantation conditions and charge colJ!ection arrangement
were identical to those used previously:3.4 The: dmlef; were
chosen so as to cover the region in which major changes in
the film properties have been observed. Carbon ions at the
chosen energy affect the D LC film to a depth of about 1. 500
A so that the Si substrate remains unaffected by the ion
beam. Since undamaged crystalline Si exhibits no ESR sig
nal, the substrate is not expected to contribute to the mea
sured number of spins.
The ESR measurements were carried out at room tem
perature using a Varian E4 spectrometer at a microwave
frequency of 9.5 GHz (X band). Only derivative spectra
were recorded. The number of spins in a given specimen was
determined from the expression9
Ns = KY'(Hpp )2lHmod,
where Y' is the peak-to-peak amplitude of the derivative
spectrum, Hpp is the peak-to-peak linewidth, Hmod is the
static magnetic field moduJ.ation amplitude, and K is a con
stant depending on the line shape. K was evaluated by cali-
4096 J. Appl. Phys. 62 (10),15 November 1967 0021-6979/67/224096-04$02.40 @ 1967 American Institute of Physics 4096
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142.244.5.147 On: Thu, 27 Nov 2014 01:50:12bration to a standard sample of CVD deposited a-Si:F with a
known number of spins. The g value was obtained by cali
brating the spectrometer to a standard diphenyl-picrylhy
drazyl (DPPH) sample with its well-knowng of2.0036. For
evaluation of Ns' H mod was maintained at a constant value of
0.8 G for aU samples studied, whereas for the determination
of the linewidth, care was taken to ensure that Hmod was
always a factor of 5 smaller than H pp'
The affected volume was estimated from the known di
mensions of the irradiated area and the estimated 1500 A
thickness of the ion beam modified layer.4 The contribution
from the woo-A DLC layer which lies beneath the ion beam
modified region was subtracted from the measured total
number of spins to obtain the spin density in the ion beam
modified volume.
A set of representative derivative spectra is shown in
Fig. 1. The slight horizontal displacement of the curves with
respect to each other does not reflect any significant change
in the g value but rather is due to minor variations in the
sample position within the resonant cavity. The resonance
linewidth and spin density obtained from these data are plot
ted in Fig. 2 together with the dose dependence of the resis
tivity and hydrogen content as reported in Ref. 3. The close
correlation between the dose dependence of the resistivity
and hydrogen content [Fig. 2(a)], resonance linewidth
[Fig. 2(b)], and spin density [Fig. 2(c)] is clearly evident.
The scatter in the calculated spin density (Fig. 2(c)] was
mainly due to uncertainties inherent in the subtraction of the
spin contribution attributable to the unaffected DLC layer
and variations in the Q of the cavity for different sized sam
ples. Obviously, there is much less error in the determination
of the linewidth, as this is directly measured from the spec
tra.
DISCUSSION
The unpaired spin density of the as-grown material
(2X lQ2° cm-3) is very high compared to that reported for
a-Si:H and for DLC films grown by many other workers.2.1O
This is surprising in view of the large hydrogen contcnt of
our films (30 at. % or 4 X 1022 cm -3), which suggests that
most ofthe incorporated hydrogen is ineffective in passivat-
dI
dH ~:;.._""""===::::::=---
3390 3400
H (Gauss) 5x10'6C+cm- 2(X1 )
2xlO'6C+cm·2 (x5)
1.4 x 10'~C+cm'Z (x8) I
As depOSited (x50)
I
3410
FIG. 1. The ESR derivative spectra ofDLC films irradiated with varying
doses of 50-keV carbon ions. Note that the curves have been scaled by the
factors indicated in the figure.
4097 J. Appl. Phys., Vol. 62, No. 10,15 November 1987 --j --........ 0
AA AO ........ "\\
A A
"" 0
A \
A \
A \
't--~A
A
A
A
:~ A
3r-A
A
lJ.
~t--As grown -->
\==;.
\
\
0
"-'\.
"-'\..
"-0
lJ.
lJ.
AlJ.
lJ.AlJ. olJ.lJ. 0.6
611 3
-2
-1 o
0"<:
~ c: o u
c: .,
"" o o ~ " >-J:
-o
10" 5f-
on on " o t?
8: J:
<l
,;;-
'E
u o
'" 52
~
1:';;; c: ., o 4 _1_ --____ -1---1 __ ,
'\ 3-\
\
t
\ 2 ,
'\ 'l---1---1----4--"
lf-
81- / J r -1-T --!-J
6f- / rf
4 I
t------J_ --r /
2
I I
1015 10'6
C+ ( ions cm-2)
FIG. 2. Variation with 50-keV C+ ion dose of (a) resistivity and hydrogen
content (from Ref. 3), (b) ESR resonance linewidth. and (c) spin density.
ing dangling bonds. It is noteworthy that the comparatively
large spin density of our films is consistent with the fact that
they display resistivities lower than those reported by some
other workers.
For doses up to 7X 1014 C+ cm-2, the ESR linewidth
and the spin density remain essentially unchanged from
their as-grown values. This is remarkable in view of the fact
that such a number of impinging ions is expected to generate
about 1021 vacancies cm-3 (Ref. 11), presumably together
with a comparable number of additional dangling bonds.
The absence of an observed increase in the spin density de
spite the considerable damage produced by the ion beam
may indicate that the incorporated hydrogen is effective in
passivating the newly created dangling bonds. Considering
the small average separation of spins (about 15 A) at these
densities, a likely mechanism for this passivation is that free
mobile hydrogen atoms generated by the collision cascade
are trapped by a dangling bond and passivate it before they
come to rest.
This dynamic passivation may find support in the gra-
Adel, Kalish, and Prawer 4097
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142.244.5.147 On: Thu, 27 Nov 2014 01:50:12dual initial resistivity increase observed at irradiation doses
up to 7 X 1014 ions/cm2, at which short-range hydrogen dif
fusion occurs, but significant effusion has yet to commence.
A hint of such a mechanism is also suggested by the slight
increase in linewidth at these low doses.
For doses above 1 X 1016 cm-2, the spin density again
remains constant despite the damage produced by the ion
beam. In this region, insufficient hydrogen remains in the
film for effective dynamic passivation of dangling bonds (as
suggested above) to occur. Rather, we believe that the satu
ration value of 8 X HtO spins cm -3 is the intrinsic maximum
spin density of the material and reflects the point at which a
dynamic equilibrium is reached between ion beam induced
dangling bond generation and their annihilation due to the
proximity of dangling bonds to each other.
It is clear from Fig. 2 that the dramatic decrease in the
resistivity in the dose range 1015_1016 cm -2 is directly corre
lated with an increase in the number of spins and a narrow
ing of the ESR linewidth. Importantly, this dose range also
corresponds to that in which most of the hydrogen is lost
from the film. Hence, in this region it is likely that newly
created dangling bonds cannot be passivated due to the lack
of hydrogen. This implies a minimum hydrogen concentra
tion requirement for passivation to occur.
Figure 1 shows that regardless of ion dose, the reson
ances remain centered about the same magnetic field
strength, i.e., the g value remains constant. The functional
form of the resonance curve may be revealed by integrating
the measured differential spectrum. The dotted line in Fig. 3
shows the result of such an integration for a DLC film irra
diated with a dose of 1 X 1015 C+ cm -2, and is representative
of the ]jne shape obtained from all the measured spectra. It
should be noted that the curve is highly symmetric and fol
lows a Lorentzian rather than a Gaussian line shape.
The ESR signal from graphite displays very marked an
isotropy (g varies from 2.0026 to 2.0495) (Ref. 12), so that
the presence of graphite crystallites would be expected to
cause a shift in the measured g value and a skewness in the
10
? 8
'c
::l
>-
~ 6-
:0 o
.~ 4,-
c
~ c
~
2 G(:I.J~:~;{m
Lc",,'~,,:,,:~
E .p~:r:""efl\al
~
!
I
I
/ ",r
--.-::.::: .. ~~'
3390 3400 3410
H ( Gauss)
FIG. 3. Numerically integrated spectrum of the ESR derivative spectrum of
a DLC film irradiated with 1 X lO'~ C+ em" 2, together with Gaussian and
Lorentzian curves adjusted to fit the full width at half maximum and peak
height of the experimental curve.
4096 J. Appl. Phys., Vol. 62. No. 10.15 November 1987 measured line shape. Since the measured peak remains sym
metric (Fig. 3) and no shift in g value is observable (Fig. 1)
as a function of ion dose, it may be concluded that graphite
microcrystallites have not formed as a result of the irradia
tion. This conclusion is in accordance with that drawn from
our previous Raman spectroscopy studies of ion beam irra
diated DLC films.4 It should be noted that the measured g
value is consistent with that obtained from crushed diamond
powder,13 where the ESR signal is attributable to dangling
bonds on the exposed diamond surfaces.
The Lorentzian (rather than Gaussian) line shape (Fig.
3) is indicative of exchange (or motional) narrowing. The
existence of significant exchange coupling between the
spinsl4 is hardly surprising considering their smal.! average
separation (about 15 A) observed for the as-grown materia!'
The narrowing of the line as a function of dose [Fig. 2 (b) 1 is
consistent with an increase in the exchange coupling as the
average separation decreases.
The spin density increases by a factor of about 3.5 over
the dose range studied [Fig. 2 (c)]. It is noteworthy that
such a modest increase in the spin density can account for
changes in the resistivity of 4-5 orders of magnitude. Similar
effects have been reported for a-Si:H, where an increase in
dangling bond density of a factor of about 7 corresponds to a
resistivity decrease by a factor of 104 (Ref. 2).
~ With regard to the conduction mechanism, the two
most likely possibilities which should be considered are hop
ping conducthity between midgap states and hopping con
ductivity betw'e~n hand tail states. For conduction due to
carriers hopping bet\wen localized states at the Fermi ener
gy, dear predictions for the temperature dependence of the
cOllductivity exist. 15 At high temperatures, the conduction
process is expected to be therm.ally activated, hence a plot of
In (J" vs liT should yield a straight line with a slope which
c{wresponds to the hopping activation energy. At lower tem
peratures, hopping conductivity about the Fermi energy is
predicted to be of variable range nature for which the
expected temperature dependence is of the form
In a c-:::: A -BT -1/4. Previous tempenl.ture-dependent con
ductivity measurements carried out by us on DLe samples
implanted over the relevant range of doses (see Fig. 8 of Ref.
4) show an increase in the activation energy with tempera
ture. However, for the temperature range considered
( 1. 50 < T < 500 K), In a( T) does not foHow either the liT
nor the T -1/4 functional dependence expected. for hopping
of carriers between midgap states. Furthermore, the ob
served 4-5 orders of magnitude increase in conductivity in
duced by the irradiation cannot possibly be accounted for by
the increase in dangling bond. density within the framework
of the hopping cond.uctivity between midgap states.
The alternative explanation for the radiation-induced
conductivity rise is due to band-gap shrinkage. In this case,
variable range hopping of carriers excited into localized
states at the band edges is responsibl.e for the conductivity, as
has also been suggested by other authors. 16 The conductivity
in this case is given by
a=aOexp[ -(ECbe -E/+ W)/kT].
Ecbe is the energy at the conduction-band edge and W is the
Adel, Kalish. and Prawer 4098
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142.244.5.147 On: Thu, 27 Nov 2014 01:50:12activation energy for hopping between tail states and is not
expected to be a sensitive function of energy below the mobil
ity edge.15 As the irradiation progresses, the dangling bond
density rises, leading to an increase in the short-range disor
der. This, in turn, introduces new localized states below the
mobility edge (in the case of electrons), thus smearing out
the band tails. A reduction in the optical band gap of the
order of 0.6 eV upon irradiation has indeed been observed by
US.3•4 If each band edge shifts towards midgap by about half
of this reduction [i.e., (Ecbe2 -Ecbel ) = 0.3 eV], then a
large increase in occupation of these states is expected. The
relative conductivity increase associated with this is expect
ed to be
0'210'1 = exp ( -(ECbe2 -Ef + W)lkT] 1
exp [ -(Ecbel -Ef + W)lkT]
= exp L -(Ecbe2 -Ecbel ) IkT ] ,
where it has been assumed that both 0'0 (Refs. 4 and 16) and
W remain constant with irradiation dose. At the irradiation
temperature of 370 K, the term in the exponent is about 9.
The expected increase in conductivity of e9 ;:::; 104 is in agree
ment with the measured relative increase of 2X 1~, thus
supporting the explanation that the conductivity in irradiat
ed DLC is caused by carriers hopping between band tail
states.
CONCLUSION
The results of this study may be summarized as follows:
(i) DLC carbon films irradiated with doses of up to
7 X 1014 C+ cm -2 display no changes in the spin density or
resonant linewidth, despite the considerable damage pro
duced by the ion beam. It is speculated that the dangling
bonds generated by the ion beam are dynamically passivated
by the excess hydrogen incorporated in the as-grown film.
(ii) Films irradiated in the dose range
7 X 1014 -1 X 1016 C+ em -2 show a narrowing of the reso
nant linewidth and an increase in the spin density. Since in
this dose range hydrogen is effusing from the fi1m, the
changes in the ESR signal may be attributed to the net cre
ation of dangling bonds which could not be passivated due to
the deficiency of hydrogen.
(iii) The effusion of hydrogen from the film has been
shown to be only indirectly responsible for the major con-
4099 J. Appl. Phys .• Vol. 62, No.1 0, 15 November 1987 ductivity increase. The dangling bond density increase in
duced by the irradiation leads to a smearing out of the band
tails, increasing the number of tail states participating in
hopping conductivity.
(iv) The symmetry of the resonant curve and the con
stancy of the g value show that no microcrystalline growth
has taken place as a result of the irradiation.
(v) For doses exceeding 1 X 1016 C+ cm-2, the dan
gling bond density saturates and an equilibrium is estab
lished between defect generation and annihilation by recom
bination.
ACKNOWLEDGMENTS
This work was supported in part by the Fund for Basic
Research, administered by the Israel Academy of Science
and Humanities. One of us (SP) gratefully acknowledges
the award of a CSIRO postdoctoral fellowship and the hos
pitality extended by the Solid State Institute of the Technion.
The authors would like to thank K. Weiser, J. Pilbrow, and
E. Ehrenfreud for very useful discussions. Weare also grate
ful to B. Silver of the Technion Chemistry Department for
use of the ESR spectrometer.
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