Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase
Influence of strains that appear in GaSb/InAs heterosystem on heteroepitaxial layer planarity is considered. It is shown that minimal supercooling of solution-melt at the saturation temperature of gallium antimonide in gallium melt 450 ºC is 7.8 ºС for [111] and 5.8 ºС for [100] growth directions. C...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2006
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| Цитувати: | Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase / S.V. Shutov, Ye.A. Baganov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 1. — С. 84-87. — Бібліогр.: 17 назв. — англ. |
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irk-123456789-1215792017-06-15T03:05:35Z Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase Shutov, S.V. Baganov, Ye.A. Influence of strains that appear in GaSb/InAs heterosystem on heteroepitaxial layer planarity is considered. It is shown that minimal supercooling of solution-melt at the saturation temperature of gallium antimonide in gallium melt 450 ºC is 7.8 ºС for [111] and 5.8 ºС for [100] growth directions. Calculated are the minimal growth rate 22 nm/s that is necessary for prevention of distortion appearance of epitaxial layer surface caused by elastic strains and the critical thicknesses of misfit dislocation formation – 50 and 54 nm for the [100] and [111] growth directions, respectively. It is shown experimentally that the lack of minimal supercooling leads to the island growth mode. 2006 Article Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase / S.V. Shutov, Ye.A. Baganov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 1. — С. 84-87. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 81.05.Ea, 81.15.Lm http://dspace.nbuv.gov.ua/handle/123456789/121579 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Influence of strains that appear in GaSb/InAs heterosystem on heteroepitaxial layer planarity is considered. It is shown that minimal supercooling of solution-melt at the saturation temperature of gallium antimonide in gallium melt 450 ºC is 7.8 ºС for [111] and 5.8 ºС for [100] growth directions. Calculated are the minimal growth rate 22 nm/s that is necessary for prevention of distortion appearance of epitaxial layer surface caused by elastic strains and the critical thicknesses of misfit dislocation formation – 50 and 54 nm for the [100] and [111] growth directions, respectively. It is shown experimentally that the lack of minimal supercooling leads to the island growth mode. |
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Article |
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Shutov, S.V. Baganov, Ye.A. |
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Shutov, S.V. Baganov, Ye.A. Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Shutov, S.V. Baganov, Ye.A. |
| author_sort |
Shutov, S.V. |
| title |
Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase |
| title_short |
Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase |
| title_full |
Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase |
| title_fullStr |
Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase |
| title_full_unstemmed |
Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase |
| title_sort |
elastic strains influence during gasb/inas heteroepitaxy from liquid phase |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2006 |
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http://dspace.nbuv.gov.ua/handle/123456789/121579 |
| citation_txt |
Elastic strains influence during GaSb/InAs heteroepitaxy from liquid phase / S.V. Shutov, Ye.A. Baganov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 1. — С. 84-87. — Бібліогр.: 17 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT shutovsv elasticstrainsinfluenceduringgasbinasheteroepitaxyfromliquidphase AT baganovyea elasticstrainsinfluenceduringgasbinasheteroepitaxyfromliquidphase |
| first_indexed |
2025-07-08T20:09:25Z |
| last_indexed |
2025-07-08T20:09:25Z |
| _version_ |
1837110779163181056 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 84-87.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
84
PACS 81.05.Ea, 81.15.Lm
Elastic strains influence during GaSb/InAs heteroepitaxy
from liquid phase
S.V. Shutov1, Ye.A. Baganov2
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: shutov_sv@mail.ru, phone/fax: +380 (552) 515457
2Kherson National Technical University, 24, Berislavskoye shosse, 73008 Kherson, Ukraine
E-mail: ewgb@newmail.ru, phone: +380 (552) 326922
Abstract. Influence of strains that appear in GaSb/InAs heterosystem on heteroepitaxial
layer planarity is considered. It is shown that minimal supercooling of solution-melt at
the saturation temperature of gallium antimonide in gallium melt 450 ºC is 7.8 ºС for
[111] and 5.8 ºС for [100] growth directions. Calculated are the minimal growth rate
22 nm/s that is necessary for prevention of distortion appearance of epitaxial layer
surface caused by elastic strains and the critical thicknesses of misfit dislocation
formation – 50 and 54 nm for the [100] and [111] growth directions, respectively. It is
shown experimentally that the lack of minimal supercooling leads to the island growth
mode.
Keywords: liquid phase epitaxy, strain, growth rate, GaSb, InAs.
Manuscript received 30.11.05; accepted for publication 15.12.05.
1. Introduction
Recently the properties of type-II broken gap
heterojunction based on InAs and GaSb are widely used
for different optoelectronic devices manufacturing [1].
At present, the basic methods used for obtaining
GaSb/InAs are molecular beam epitaxy (MBE) and me-
tal organic chemical vapour deposition (MOCVD) [2, 3].
Most close to equilibrium growth conditions are
provided with methods of liquid phase epitaxy (LPE) [4].
At the same time, there are several specific problems in
the course of obtaining GaSb/InAs with the LPE methods.
One of the problems is related with interaction between
the substrate and liquid phase with non-equilibrium
composition. It leads to substrate erosion, non-planarity
and uncontrolled composition of the epitaxial layer [5, 6].
Such problem can be solved by LPE from an initially
supercooled liquid phase [6]. The second type of problems
is connected with availability of elastic strains in the
GaSb/InAs heterostructure owing to lattice constants
mismatch (0.74 % at the epitaxy temperature 450 ºС).
The availability of elastic strains in the epitaxial
layer, when it grows isomorphously until appearance of
misfit dislocations, imposes a requirement on minimal
solution-melt supercooling ΔТmin due to increasing the
solid phase chemical potential. When ΔТ values of
supercooling are smaller than ΔТmin the epitaxial layer
grows in accordance with the Stranski-Krastanov
mechanism [7]. As a result, layer planarity can be
broken, to avoid the epitaxial layer non-planarity the
supercooling that is sufficient for suppression of
Stranski-Krastanov growth mechanism must take place
until the layer thickness reaches a critical value of misfit
dislocation formation. The elastic strains are driving
forces for surface distortion of epitaxial layer, too [8, 9].
Process of suppression of such distortion development
can be provided due to the sufficient epitaxial layer
growth rates.
In this connection, the aim of this work is calculation
of minimal supercooling ΔТmin and necessary growth
rate for optimization of GaSb growth on InAs substrate
from liquid phase as well as providing continuous
character of the epitaxial layer and its planarity.
2. Calculation model and results
GaSb/InAs heteroepitaxial layer critical thickness
calculated using the Matthews and Blakeslee method
[10] is significantly less than the experimental ones [11-
13]. That is why, to determine the epitaxial layer critical
thickness, used was a two-dimensional simulation of
elastic strains and deformation energy distribution in the
strained structure with an available network of misfit
dislocations.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 84-87.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
85
Substrate
Intermediate layer
Epitaxial layer
у
х
Fig. 1. Initial GaSb/InAs heterostructure for simulation.
Simulation by the finite-element method was based
on the Van-der-Merwe heteroepitaxial layer growth
model [14]. But use of any adequate forces model on the
substrate-epitaxial layer interface (such as the Peierls-
Nabarro potential) leads to nonlinear or transcendent
combined equations in the course of simulation. To
solve this system the intermediate layer was introduced.
The initial structure for simulation (Fig. 1) consisted of
the unstrained epitaxial layer, unstrained substrate and
strained intermediate layer, one side of which was fitted
to the substrate lattice parameter and other one – to the
unstrained epitaxial layer lattice parameter. Physical
properties of this intermediate layer were defined by
averaging those of the substrate and epitaxial layer.
From [14], an atom located at the central line of
symmetry can be considered as horizontally undisplaced.
The misfit dislocation appears when the displacement
between the substrate and layer atoms reaches a half of
the lattice parameter.
As a critical epitaxial layer thickness, we assumed
such thickness value that provides the equality of
energies between two-dimensional strained epitaxial
layers without dislocations and that with misfit
dislocations. The energy of the elastically strained two-
dimensional epitaxial layer is determined as follows:
h
aa
aaEU
F
sl
slxx
−−
=
)1(2
1
2
2
μ
, (1)
where Е, μ, Uxx are Young’s modulus, Poisson’s ratio
and epitaxial layer strain, respectively; al, as are the
lattice parameters of the epitaxial layer and substrate,
respectively, h is the epitaxial layer thickness. The factor
alas/(al – as) is the misfit dislocation period [14]. The
obtained critical thickness (Fig. 2) is 50 nm for growth
on (100) InAs substrate and 54 nm in the case of (111)
substrate orientation. These values are in a good
agreement with the experimental results from [12] based
on X-ray scattering analysis of misfit dislocation density.
Minimal supercooling related with the necessity to
compensate the influence of elastic strains can be
defined from the equality of chemical potentials of solid
and liquid phases in the regular solution approach. When
considering ΔTmin << Т0 , one can obtain
( ) ,
)()(
)()(
ln
12
1
min0min0
00
0B
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
Δ−Δ−
=Ω
− TTCTT
TCT
Tk
EU xx
γ
γ
μ
(2)
where Ω is the atomic volume, kB is the Boltzmann
constant, Т0 is the temperature of solution-melt
saturation, С(Т), γ(Т) are the concentration and activity
coefficients of GaSb in gallium melt at the temperature
T. Based on dependence [15],
2
GaSbGaSb )1(ln xRT −= αγ , (3)
where R is the absolute gas constant, αGaSb, xGaSb are the
parameters of interphase interaction and mole fraction of
GaSb in gallium melt and assuming xGaSb<<1, Eqs (2),
(3) lead to the transcendent equation with respect to
ΔTmin:
( )
,
)()(
)(
)(
ln
12
1
min0
min0GaSb
0
0GaSb1
min0
0
0B
2
⎟
⎟
⎠
⎞
⎥
⎦
⎤
⎢
⎣
⎡
Δ−
Δ−
−+
⎜⎜
⎝
⎛
+
Δ−
=Ω
−
−
TT
TT
T
T
R
TTC
TC
Tk
EU xx
αα
μ
(4)
Using the approximation of antimony atomic fraction
dependence in gallium melt [16] on the temperature
close to the saturation one Т0 = 450 ºС, xSb =
= 1.01·10−9+100.0098Т and the parameter of interphase
interaction dependence αGaSb = (14738−21.48Т) J/mol
[15], it can be found from (4) that the minimal
supercooling temperatures are 7.8 and 5.8 ºС for (111)
and (100) orientations, respectively. These values are
quite reachable during the epitaxy of GaSb layers,
because the critical supercooling values of transition to
labile region for antimony solution in gallium melts is
about 12 ºС [17].
Let us consider the influence of mechanical strains
on growing epitaxial layer surface. In [8], the surface
distortions induced by mechanical strains are considered
with the harmonic approach. The highest rate of
amplitude increasing is
TkE
qDn m
m
B
34
38
0
2
0
2
27
α
σ
ω
Ω
= , (5)
where σ0 is the epitaxial layer strain, D is the adatom
diffusion coefficient, n0 is the density of surface defects,
α is the surface energy. Estimation of ωm value by (5)
shows that ωm = 0.4 s−1 (it was assumed that n0 =
1.46·1010 cm−2, α = 0.364 J/m2, D = 2.8·10−5 cm2/s, σ0 =
8.7·108 Pa). As a characteristic time of process the value
1/ωm can be used [8]. Hence, for suppression of
dislocations, it is necessary that the time of achieving the
critical thickness, which leads to relaxation of
considerable part of elastic strains due to misfit
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 84-87.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
86
Fig. 2. Dependences of energy of structures that contains misfit dislocation (curves 1) and elastically strained dislocation-free
epitaxial layer (curves 2) on the layer thickness, the layer being grown on the substrates with orientations (111) (a) and (100) (b).
dislocation formation, must be less than 1/ωm = 2.5 s,
hence, the growth rate must be higher than 22 nm/s.
3. Experiment
Calculated values of minimal supercooling and growth
rate were used for GaSb heteroepitaxy on the (111) InAs
substrate. The conditions for obtaining the planar layer
were as follows:
7.8 C 12 C,
(2.5 s) 55 nm.
T
h
⎧ ≤ Δ <
⎨
>⎩
o o
(6)
Morphology of epitaxial layers obtained by (6) and at
ΔT = 5 ºC are shown in Fig. 3a and b, respectively. In
Fig. 3a shown are the continuous heteroepitaxial layer
obtained under fulfiment of the conditions (6). The layer
roughness was less than 0.3 μm (layer thickness was
about 3 μm). The deviation from the conditions (6) led to
pronounced island growth that resulted in the non-planar
epitaxial layer surface (Fig. 3b).
Fig. 3. Morphology of GaSb/InAs (111) epitaxial layers
obtained: a) adhering the conditions (6); b) not adhering the
latter (6).
4. Conclusions
Thus, influence of strains during the initial growth stages
of GaSb/InAs heterostructure on epitaxial layer planarity
was considered. The availability of strains increases the
chemical potential in the solid phase. To compensate this
increase, it is necessary to provide the supercooling
temperature higher than 7.8 ºС for [111] and 5.8 ºС for
[100] growth directions. Also, the elastic strains can
cause distortion of epitaxial layer surface. To suppress
all distortion modes the minimal growth rate must be
22 nm/s.
Such growth conditions must be provided until the
epitaxial layer thickness reaches the critical thickness
value for misfit dislocation formation when elastic
strains considerably relax. The calculated critical
thicknesses are 50 nm for [100] and 54 nm for [111]
growth directions, respectively.
Experiment shows that adherence of calculated
growth conditions causes obtaining the unbroken GaSb
heteroepitaxial layer on the InAs substrate with a small
roughness. Using the insufficient supercooling leads to
an island growth mode.
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© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
87
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