Influence of temperature and of structure of antimony substrate on gallium diffusion into the GaSb semiconductor compound

Article abstract of DOI:10.1016/S0925-8388(00)01032-X

The diffusion coefficient of Ga electrodeposits on Sb electrodeposited thin films, either amorphous or crystalline, was investigated to determine the influence of the morphology and structure of the antimony substrates on the diffusion and reaction process. The Ga/Sb bilayer was studied by SEM-EDS and X-ray diffraction before and after heating at temperatures of 50, 75 and 100 °C. The formation of the GaSb semiconductor compound was particularly considered and the activation energy and frequency factor of the process was determined. At these temperatures, Ga was at least partially molten and the diffusion coefficient showed that the geometrical factor was prevailing over the structural one. For example, at 75 °C, the values of the diffusion coefficient were 1.5×10^-17 and 6.3×10^-17 m² s^-1 for the amorphous and crystalline antimony, respectively. On the contrary, at 20 °C, a temperature at which Ga is in the solid state, the structural factor prevailed over the geometrical one and values were obtained lower by around three orders of magnitude. The prevailing influence at 20 °C was identical to that previously observed for In diffusion into amorphous and crystalline Sb with InSb formation. The experimental results, both at low and high temperatures, are discussed also taking the behaviour of the In-Sb system into account.

Full text of DOI:10.1016/S0925-8388(00)01032-X

Journal of Alloys and Compounds 313 (2000) 161–167
L
www.elsevier.com/locate/jallcom
Influence of temperature and of structure of antimony substrate on gallium
diffusion into the GaSb semiconductor compound
1
*
Valentin M. Kozlov , Luisa Peraldo Bicelli
Dipartimento di Chimica Fisica Applicata del Politecnico, Centro di Studio sui Processi Elettrodici del CNR, Via Mancinelli, 7, 20131 Milano, Italy
Received 10 April 2000; accepted 16 May 2000
Abstract
The diffusion coefficient of Ga electrodeposits on Sb electrodeposited thin films, either amorphous or crystalline, was investigated to
determine the influence of the morphology and structure of the antimony substrates on the diffusion and reaction process. The Ga/Sb
bilayer was studied by SEM–EDS and X-ray diffraction before and after heating at temperatures of 50, 75 and 1008C. The formation of
the GaSb semiconductor compound was particularly considered and the activation energy and frequency factor of the process was
determined. At these temperatures, Ga was at least partially molten and the diffusion coefficient showed that the geometrical factor was
21
2
17
217
2
prevailing over the structural one. For example, at 758C, the values of the diffusion coefficient were 1.5310
and 6.3310
m s
for the amorphous and crystalline antimony, respectively. On the contrary, at 208C, a temperature at which Ga is in the solid state, the
structural factor prevailed over the geometrical one and values were obtained lower by around three orders of magnitude. The prevailing
influence at 208C was identical to that previously observed for In diffusion into amorphous and crystalline Sb with InSb formation. The
experimental results, both at low and high temperatures, are discussed also taking the behaviour of the In–Sb system into account.

2000 Elsevier Science B .V . All rights reserved.
Keywords: Diffusion coefficient; Molten and solid gallium; Amorphous antimony; Crystalline antimony; GaSb semiconductor compound
1
. Introduction
depends on temperature. However, in addition to the
thermal factor, other factors may influence the kinetics of
the process: among them not only the structural factor
(particularly the structure of the first electrodeposited
metal), but also the geometrical one, mainly connected to
the surface area of the different phases in contact.
In a previous paper [4], we examined the influence of
the morphology and structure of Sb substrates on the
diffusion and reaction process at constant temperatures of
an electrodeposited In overlayer. The Sb substrates, either
amorphous or crystalline, were also prepared by elec-
trodeposition. It appeared that the structural factor pre-
vailed over the geometrical factor. The aim of this paper is
to investigate the influence of the same factors on the
diffusion coefficient of Ga into Sb with formation of the
GaSb semiconductor compound. For this purpose, Sb and
Ga films were electrodeposited in sequence, and then
heated. To our knowledge, an analysis of this type has
never been performed before.
Semiconducting III–V compounds having the zinc-
blende (cubic) structure with tetrahedrally coordinated
atoms and strong covalent bonds are of great interest and
find important applications in several fields of modern
microelectronics because of their use in the production of,
e.g. advanced optoelectronic devices, mid-IR detectors,
solar cells and sensors. A method for their preparation is
the sequential electrodeposition of the two metals followed
by a heat treatment which, normally, allows to obtain the
third phase, i.e. the semiconducting compound, as for
example, GaSb [1], InSb [2] and InAs [3]. The most
important process taking place during the heterogeneous
reaction is solid-state diffusion.
As well acknowledged, the growth of a new phase
during the diffusion process with chemical reaction mainly
*
Corresponding author. Tel.: 139-02-2399-3142; fax: 139-02-2399-
180.
E1 -mail address: luisa.bicelli@polimi.it (L. Peraldo Bicelli).
On leave from Department of Physics, National Metallurgical
Academy of Ukraine, Dniepropetrovsk, Ukraine.
As to literature data, an electrochemical method for the
preparation of GaSb polycrystalline films was investigated
3
[1] involving the sequential deposition of Sb and Ga films
(from an acid and an alkaline solution, respectively)
0
925-8388/00/$ – see front matter
 2000 Elsevier Science B .V . All rights reserved.
PII: S0925-8388(00)01032-X

1
62
V.M. Kozlov, L. Peraldo Bicelli / Journal of Alloys and Compounds 313 (2000) 161–167
followed by a mild thermal annealing under inert atmos-
phere, generally at 1008C for 4 h. The proposed electro-
chemical route permitted to prepare thin GaSb films from
aqueous solutions although difficulties in the control of the
Ga layer thickness, and thus of GaSb stoichiometry, were
met owing to hydrogen evolution simultaneously occurring
with Ga electrodeposition. The alternative approach based
on the simultaneous deposition of Sb and Ga was unsuc-
cessful. The same authors also studied the synthesis of thin
films of the ternary compounds Ga In12xSb [2] and
x
GaAs Sb
[5]. More recently, McChesney et al. [6]
x
12x
investigated the electrodeposition of GaSb from aqueous
electrolytes containing SbCl3 and either Ga (SO ) or
2
4 3
GaCl , at a pH lower than 1. Thin film mixtures of GaSb
3
and Sb were produced, the stoichiometric control being
limited by the concurrent evolution of hydrogen and SbH3.
GaSb was also deposited from a non-aqueous (glycerol)
medium in one electrochemical step [7]. The electrodepo-
sition of the pure metals is well documented in the
literature both for Ga [8–11] and Sb [12].
Fig. 1. Coulombic efficiency as a function of the current density during
Ga electrodeposition on Sb.
hydrogen evolution always paralleled Ga deposition, not-
withstanding the rather high alkalinity of the electrolyte to
improve the current efficiency. Fig. 1 shows the depen-
dence of the current efficiency on the current density; the
2
. Experimental
2
2
The Fe substrate was a disk of 14 mm diameter
optimal values for Ga deposition are 40–50 mA cm . The
deposited Ga quantity was determined by weighing the
sample with an accuracy of 60.002 mg. The deposition
time was 2 and 4 min and the thus-obtained Ga deposits
had a mass of either 0.5 to 0.7 or 1.5 to 1.8 mg which
corresponded to an average thickness from 0.75 to 1 and
from 2.25 to 2.70 mm, respectively. They are in the
following called thin and thick deposits, respectively. Both
of them were employed to perform the SEM analysis while
the thin ones, only, were used for X-ray diffraction
investigation. Ga electrodeposition on the Sb deposits with
the different structures was rather easy and the adhesion to
the underlying Sb perfect.
After Ga deposition on Sb, the samples were heated at
50, 75 and 1008C in a vacuum furnace for a predetermined
time. No losses of Ga were expected, owing to its low
vapour pressure, the Ga boiling point being 19838C. In any
case, the weight of the samples was tested after the heating
treatment and the values obtained were in the range of the
balance accuracy.
previously polished with silicon carbide paper. Before Sb
deposition, the Fe surface was etched in a solution of 5%
NH OH in ethyl alcohol. The electrochemical cell with a
thermostatic water jacket was in pyrex. Sb galvanostatic
electrodeposition was performed from an aqueous solution
of the following composition: 0.3 M SbCl 11.6 M
H SO 11.7 M HCl. Two different optimal conditions
were selected to prepare either amorphous or crystalline Sb
deposits, i.e. the current density was 40 A m 2 and
temperature 228C in the former case and 440 A m and
4
3
2
4
2
2
2
5
08C, respectively, in the latter. Instead, the deposition
time was the same: 20 min, so, the thickness of the
crystalline deposit was 33 mm and that of the amorphous
deposit 3 mm, only. In addition to amorphous Sb (a-Sb)
and crystalline (c-Sb) deposits, crystalline deposits ob-
tained by heating a-Sb for 3 h at 1108C to induce complete
crystallization (ca-Sb) were also considered.
Ga was deposited at 208C in a similar but smaller cell,
Ga salts being very expensive and pollutant. Conditions of
5
08C are recommended in the literature to obtain the
X-ray diffraction of the Sb sublayer and analysis of the
Ga–Sb deposits were performed by a Philips diffractome-
ter PW3020 instrument, making use of Cu Ka radiation.
The registration conditions were the same for all deposits.
They were 0.028 step size and 1 s time per step in the 2u
registration range from 22 to 328 and from 39 to 518C.
Scanning electron microscopy (SEM) and X-ray energy
dispersive analysis (EDS) measurements were carried out
using a Stereoscan 360, Cambridge Instrument and an
AN1000-Link, while the surface profile of the Sb deposits
was investigated by a UBM laser profilometer. For more
details, see Ref. [4].
highest coulombic efficiency [11] and a fairly homoge-
neous coverage of many substrates, such as Sb [1].
However, Ga with a melting point of 29.88C is molten at
5
08C, and deposits are produced consisting, for example,
of a large number of microscopic droplets regularly
distributed and adherent to the substrate, as in the case of
an As–Sb alloy, or of drops which detach from the
electrode, as in the case of a Ti substrate [5]. Therefore, Ga
was deposited in galvanostatic conditions at the lower
temperature of 20–228C from the aqueous solution 0.6 M
GaCl (99.9% Fluka)15 M KOH. As expected, intensive
3

V.M. Kozlov, L. Peraldo Bicelli / Journal of Alloys and Compounds 313 (2000) 161–167
163
3
. Results
(more than 2 mm) Ga(a-Sb) and Ga(c-Sb) deposits, respec-
tively. Both of them presented an inhomogeneous dis-
tribution of Ga which formed large as well as small
crystals, as clearly evidenced by the corresponding Ga dot
map. In the case of the Ga(a-Sb) and Ga(ca-Sb) deposits,
the two different crystal fractions had an average diagonal
size of 50 to 60 and 3 to 5 mm, respectively. In conclusion,
the Ga deposits were not compact and the majority of the
Sb surface was covered with isolated crystals. A similar
type of morphology was shown by the Ga(c-Sb) deposits,
but the size of their second crystal fraction was smaller,
around 1 to 2 mm. In this case, the isolated Ga crystals
nearly completely filled the numerous hollows and inter-
stices of the irregular surface of the c-Sb underlayer,
tending to support the hypothesis of electrolyte penetration
and subsequent electrocrystallization in situ.
3
.1. Surface morphology
The influence of the heating time at a constant tempera-
ture of 758C on the morphology of the Ga deposits on
either amorphous or crystalline Sb, Ga(a-Sb) and Ga(c-Sb),
respectively, was investigated.
Before Ga deposition, the a-Sb deposits presented a
much smaller surface roughness than the c-Sb ones, and
showed typical spherical particles, whereas the c-Sb de-
posits were covered with regularly shaped crystals. More-
over, the ca-Sb deposits, obtained by crystallization of
a-Sb, had a very smooth morphology similar to that of the
original amorphous material [4]. This basically different
morphology was more or less observed even after Ga
deposition, as shown in Fig. 2a and b relevant to the thick
During the annealing treatment, the small Ga crystals
Fig. 2. SEM micrographs (a) and (b) of Ga deposits on amorphous and crystalline Sb, respectively, before and (c) and (d) after heating at 758C for 75 min.

1
64
V.M. Kozlov, L. Peraldo Bicelli / Journal of Alloys and Compounds 313 (2000) 161–167
were most probably the first to melt while increasing the
heating time caused the large crystals to melt too, starting
from their borders. For example, after heating the deposits
for 75 min at 758C, SEM analysis showed on the same
sample surface both large crystals which had not yet
melted and other ones which had already melted. Exam-
ples of SEM micrographs of the latter case for Ga(a-Sb)
and Ga(c-Sb) deposits are reported in Fig. 2c and d,
respectively, where the molten and recrystallized region is
clearly evident.
Another point worth noting, is the presence of small
rounded Ga crystals similar to droplets on the surface of
the heated Ga(c-Sb) deposits. More probably, they were
the result of the melting process of part of the small Ga
crystals, their coalescence in the liquid phase and re-
crystallization.
hexagonal coordinates and Miller indices. These peaks
were completely absent in the case of the amorphous
deposits. Indeed, a characteristic broad band between 2u5
24 to 368 and minor bands at higher diffraction angles
were observed. Both materials also presented the main
peak of the Fe substrate at 44.7 (h110j).
After Ga deposition on both Sb substrates, the peaks
typical of othorhombic Ga were also observed. The most
intense ones (in order of decreasing intensity) are: the peak
at 2u530.248 due to the h111j planes; at 45.408 (h113j);
39.828 (h020j); 46.368 (h211j) having a relative intensity of
100; 85; 60; 56, respectively [16]. By heating the samples,
e.g. at 758C for 60 min, a dramatic change of the X-ray
diffraction spectrum was noted. The intensity of the Ga
peaks strongly decreased and some of them practically
disappeared, while the peaks due to GaSb became visible.
In particular, a new peak, the third most intense of GaSb at
49.558 (h311j), with a relative intensity of 45 [16], was
rather especially evident. The most intense peak of GaSb at
25.288 (h111j) and the second most intense one at 41.86
(h220j), whose relative intensities are 100 and 65, respec-
tively, overlapped some of the Sb peaks and were more
clearly seen to increase in the case of the Ga(a-Sb)
deposits.
The decreased and increased intensity of the Ga and
GaSb peaks, respectively, could be related to Ga diffusion
into Sb and to the formation and growth of crystalline
GaSb initially occurring at the Ga/Sb interface, and,
subsequently, at the GaSb/Sb one. Indeed, we assumed
that Ga, only, diffused, owing to its much higher mobility
than Sb, as also evidenced by its much lower melting point
(29.88C) in comparison to that of Sb (630.618C).
The behaviour of the Ga(a-Sb) deposits was similar to
that of the Ga(c-Sb) ones submitted to the same thermal
treatment for the same time, but, the comparison of the
change in intensity of the corresponding Ga and GaSb
peaks showed the kinetics of the process to be slower in
the former than in the latter case. Of course, the deposits
on a-Sb had to be carefully heated to avoid the transition
from the amorphous to the crystalline phase during the
diffusion and reaction process. As to this aspect, specific
research was carried out on a-Sb crystallization at various
temperatures to determine the maximum possible anneal-
ing time [17].
To determine the Ga diffusion coefficient, we utilized
the thin Ga deposits because their morphology was practi-
cally the same after the heating treatment. However, since
Ga partially melted and was submitted to X-ray diffraction
investigation after recrystallization, we preferred to follow
a different approach than in our previous research on In
diffusion into Sb [4,18]. First of all, each sample was
heated only once; secondly, instead of considering the
decrease with time of the intensity of the main Ga
diffraction peak, we considered that of the sum of the
intensities of the first seven diffraction peaks. In this way,
possible changes occurring in the peak intensities not due
3
.2. X-ray results
The SEM results of the thick Ga deposits showed that
the majority of the surface of the Sb underlayer, either
a-Sb, ca-Sb or c-Sb, was irregularly covered with large,
isolated Ga crystals which melted, at least partially, during
the thermal treatment. Therefore, it may be expected that
the overall area of the Ga–Sb interface continuously
changes during the Ga diffusion process, thus changing the
value of the active surface area for Ga diffusion into the
forming GaSb compound. So, for the Ga–Sb system, a
deviation had to be observed from the usual square-root
law between the Ga moles removed by diffusion from the
unit surface area, mrem, and the diffusion time, t , accord-
1
1
/ 2
ing to Schmalzried’s equation: mrem proportional to t1
13–15]. In these conditions, it is practically not possible
[
to quantitatively control the Ga diffusion process. So, to
achieve a significant value of the Ga diffusion coefficient,
it was necessary to modify the electrolysis conditions to
obtain deposits with a homogeneous morphology, first of
all excluding the formation of the large crystals. The most
simple but efficient method we found was to decrease the
deposition time of Ga in order to reduce the deposited
mass to 0.5–0.7 mg. Indeed, thin Ga deposits, with an
average thickness not higher than 1 mm, practically
presented the small crystals, only, which were homoge-
neously distributed on the a-Sb and c-Sb surface. After the
thermal treatment of such thin Ga deposits, no substantial
changes in their morphology were observed, but those of
Ga(c-Sb) showed an increased number of the small drop-
let-shaped crystals with heating time.
In order to chemically characterize the deposits, the
X-ray diffractograms of the Sb deposits were preliminarily
recorded. The diffraction peaks typical of rhombohedral Sb
were shown by the crystalline deposits. In agreement with
the ASTM cards [16], the most intense peaks are at
2
u528.698 due to the h012j planes; at 40.078 (h104j) and
4
5
1.958 (h110j), their relative intensities being 100, 70 and
6, respectively. They are described with reference to the

V.M. Kozlov, L. Peraldo Bicelli / Journal of Alloys and Compounds 313 (2000) 161–167
165
Table 1
to GaSb formation but, for example, to changes in the
deposit texture, were expected to be taken into account and
averaged, thus permitting us to obtain significant intensity
values.
Gallium diffusion coefficient at various temperatures for the amorphous,
D(a), and crystalline, D(c), Sb substrates. Activation energy, Q, and
frequency factor, D , for the diffusion and reaction process at high
temperatures (50 to 1008C)
0
2
21
2
21
t (8C)
D(a) (m
s
)
D(c) (m s )
2
20
17
220
3
.3. Ga diffusion coefficient
20
(2.0560.5)310
(0.6560.14)310
2
217
217
5
7
1
0
5
00
(0.1360.04)3120
(1.660.5)310
(6.361.6)310
17
(1.560.5)310
(6.361.4)310
To determine the Ga diffusion coefficient, we followed
217
217
(75615)310
the method, previously described [18], based on Schmal-
zried’s theory [13–15] for solid-state diffusion with chemi-
cal reaction. We assumed that a local thermodynamic
equilibrium was established within the reaction layer and
at the interphases, and that the Ga activity within the GaSb
layer was practically constant. This allowed us to consider
an average Ga diffusion coefficient, D. This last condition
was fulfilled since the standard Gibbs free energy of
2
1
Q (kJ mol
)
7864
(6.261.1)310
7664
(2.960.3)310
2
21
26
25
D
(m
s
)
0
talline GaSb from both crystalline Ga and Sb, since the
values for a-Sb were not known. The influence of this
approximation on the D values was considered to be
negligible. The determination from electrochemical data of
the free energy of formation of a-Sb from c-Sb [17]
showed this to be the case. The values obtained are
reported in Table 1 together with their standard deviations.
The dependence of the diffusion coefficient from the
annealing temperature followed an Arrhenius-type equa-
tion, as shown in Fig. 3, where the results for the Ga–Sb
system are shown together with those previously obtained
for the In–Sb system [4], which will be discussed in the
following.
formation of GaSb from the elements, DG 8, equal to
f
2
1
2
2
38.9 kJ mol2 [19], is sufficiently high, i.e. higher than
1
100 kJ mol
.
Resuming the theoretical treatment (see Ref. [18]), two
equations may be taken into account. Indeed, the already
introduced Ga quantity removed by diffusion from the unit
surface area, mrem, is proportional to both:
(a) the deposited Ga quantity, again on the unit surface
area, mdep, (known from experimental data) times the
relative decrease (oI 2 oI )/oI of the sum of the
0
1
0
intensities of the first seven Ga peaks. oI and oI are
From the linear dependence of the logarithm of D from
the reverse of the absolute temperature, both the activation
energy, Q, and the frequency factor, D , were determined
for Ga diffusion into crystalline GaSb on the two Sb
substrates. These values are also collected in Table 1.
0
1
the sums of the intensities of the first seven Ga peaks
immediately after electrodeposition and after heating,
respectively;
0
(
b) the square root of D times the heating (diffusion)
time, t , divided by the heating temperature, T.
1
By equating the two relationships, it results that
2
[(
O
I0 2
O
I1)/
O
I ] 5 const 3 t
(1)
0
1
where the proportionality constant is equal to
2
2
dep
const 5 [22 3 D 3 DG 8 3 (r/M) ]/[RT 3 m
]
f
with R, r and M being the gas constant, the GaSb mass
2
3
density (5595 kg m ) and molar mass (0.19147 kg
2
1
mol ), respectively.
The sum of the intensities of the seven Ga peaks
regularly decreased directly proportional to the square root
of the heating time at the same temperature. So, according
to Eq. (1), it was possible to determine the Ga diffusion
coefficient from such intensity decrease. For each heating
temperature, 50, 75 and 1008C, five different samples were
investigated, determining five values of the Ga diffusion
coefficient from which the average value, at the considered
temperature, was estimated. To perform the calculations,
we used the standard free energy of formation of crys-
Fig. 3. Dependence of the logarithm of the diffusion coefficient of Ga
(upper two curves) and of In (lower three curves) on the reverse of the
absolute temperature (Arrhenius plot) for Ga and In deposits on amor-
phous Sb (curves labelled a), crystalline Sb (c) and crystalline Sb obtained
from a bath containing the surface-active addition agent Trilon B (ct),
respectively.

1
66
V.M. Kozlov, L. Peraldo Bicelli / Journal of Alloys and Compounds 313 (2000) 161–167
4
. Discussion
values at high temperatures. By inspection, two observa-
tions are straightforward: (i) the values of the diffusion
coefficients at room temperature being by around three
orders of magnitude lower and (ii) the inversion of values,
D(c-Sb) being now lower than D(a-Sb), in spite of the
larger surface area for diffusion of the c-Sb samples.
The former observation supports previous considera-
tions, whereas the latter confirms that the structural factor
prevails over the geometrical one except when Ga is in the
molten state. A prevailing structural factor over the
geometrical one has already been observed for In diffusion
into a-Sb and c-Sb substrates at temperatures from 40 to
1408C, that is below the In melting point (Fig. 3). This
result was explained by the structural disorder in amor-
phous Sb [4]. Indeed, the interatomic distances were found
to be generally larger (e.g. Ref. [21]) and the density lower
(e.g. Ref. [22]) than those in rhombohedral c-Sb, where the
Sb atoms are incorporated into two-dimensional networks
of puckered sixfold rings forming typical layers. In par-
ticular, the structural characterization by X-ray diffraction
of our electrodeposited materials evidenced a higher
structural disorder and a more open structure of a-Sb than
c-Sb, the average distance between the layers being 27%
higher [17]. So, structural data are in agreement with the
more favourable conditions for diffusion in amorphous Sb.
Fig. 3 compares the behaviour of the Ga–Sb system to
that of the In–Sb system. The curve of the latter system
labelled with ct refers to a crystalline Sb substrate obtained
from a bath also containing the organic compound Trilon
B, a special addition agent selectively adsorbed on the In
deposit surface. The two crystalline Sb substrates had the
same structure and practically the same morphology but
the effective area for In diffusion was smaller for the ct-Sb
than for the c-Sb substrate and, therefore, as expected, the
value of the In diffusion coefficient was lower, too: D(ct-
Sb),D(c-Sb), as shown in Fig. 3.
As shown in Table 1 and in Fig. 3, Ga diffusion and
formation of GaSb depend on the Sb substrate, whether
amorphous or crystalline. In addition to their different
structure, the morphology of these two deposits is also
completely different. While the surface of c-Sb is covered
with homogeneously distributed very large crystallites
(
15–20 mm average size) that of a-Sb shows typical
spheroidal particles (about 2 mm average size). Further-
more, the maximum individual roughness depth, deter-
mined from the surface profile analysis, is 10.0 and 2.6
mm, respectively [4]. So, the diffusion coefficient is higher
for Ga deposits on c-Sb substrates whose effective surface
area for diffusion is larger than that of a-Sb substrates, and
the geometrical factor seems to prevail over the structural
one.
To verify this hypothesis, a crystalline Sb deposit was
prepared by heating an a-Sb deposit up to its complete
crystallization. This so-called ca-Sb deposit presented the
same smooth morphology of the original amorphous
material but it was crystalline. After Ga deposition, the
SEM analysis of the Ga(ca-Sb) sample showed a morphol-
ogy strictly similar to that of Ga(a-Sb). The Ga diffusion
coefficient was estimated after heating at 758C for 2 and 3
2
18
2
21
h and was found to be around 2.3310
m s , i.e. it
was about one order of magnitude lower than D(a-Sb).
This showed the amorphous substrate to be more suitable
for promoting Ga diffusion than the crystalline one, when
the geometrical factor is the same.
The fact that the geometrical factor plays a primary role
in the case of Ga deposits, when the substrate surface
roughness is particularly high, as in c-Sb substrates, may
be explained considering that Ga is at least partly molten at
the experimented temperatures (50, 75 and 1008C), achiev-
ing a very good contact with the Sb surface. Here the
question arises whether it is possible to apply Schmal-
zried’s treatment when the diffusing species is in the
molten rather than in the solid state. Strictly speaking the
answer is no. However, comparing the essential points of
the theoretical treatment [20] with the Ga diffusion and
reaction process, it turns out that in this case, too, the
reaction product (crystalline GaSb) separates the two
reactants (molten Ga and solid Sb). Of course, owing to its
fluidity, liquid Ga can easily reach ‘fresh’ surface areas of
Sb, that is regions of the Sb surface not yet covered with
the reaction product, where the diffusion process occurs
more easily. This may explain why higher D values are
expected and observed in this case, i.e. when the surface
area is larger and Ga is in the molten state.
By extrapolation of the Arrhenius plot for the In–Sb
system, we determined the average In diffusion coefficient
at 208C, as the experimental values were limited to 408C.
2
20
220
The D values are 7.9310 , 0.44310
10
and 0.673
2
21
2
21
m s for the In diffusion process into crystalline
InSb on the a-Sb, c-Sb and ct-Sb substrates, respectively,
i.e. they are of the same order of magnitude as those of Ga
diffusion into crystalline GaSb on the a-Sb and c-Sb
substrates. The average diffusion coefficients at room
temperature of both Ga and In into Sb lie close to the
upper range usually considered for common metals and
2
50
220
2
21
semiconductors (10
to 10
m s [23]).
A further comparison worth doing is that between the
activation energy and the frequency factor for diffusion of
molten Ga and solid In, within practically the same
temperature range. The values for the Ga–Sb system are
reported in Table 1; those for the In–Sb one are: 5364 kJ
To analyse in more detail the influence of the Ga state,
whether liquid or solid, the Ga diffusion coefficient in both
a-Sb and c-Sb was investigated at 208C, too, notwithstand-
ing the time requested (several weeks) to perform the
measurements. These results are also reported in Table 1.
They dramatically evidence the difference with previous D
2
1
210
2
21
mol
and 2.0660.80310
m
s 2 , respectively, for
1
diffusion into a-Sb, and 6364 kJ mol and 8.2062.503
2
10
2
21
10
m s , respectively, for diffusion into c-Sb [4]. By

V.M. Kozlov, L. Peraldo Bicelli / Journal of Alloys and Compounds 313 (2000) 161–167
167
inspection, it appears that the higher values of the Ga
Acknowledgements
diffusion coefficient, when Ga is in the molten state, are
entirely due to the value of the frequency factor being by
around five orders of magnitude higher than that of In, as
the activation energy is higher, too. Since the frequency
factor represents the frequency of successful attempts to
overcome the energy barrier, the much higher values found
are in agreement with the higher mobility of molten Ga
and, thus, support previous considerations.
V.M. Kozlov kindly acknowledges the Cariplo Founda-
tion, ‘A. Volta’ Centre for Scientific Culture, for the
financial support. The research was funded in part by the
Ministero dell’ Universit a` e della Ricerca Scientifica e
Tecnologica.
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