Kinetic modeling of low temperature epitaxy growth of SiGe using disilane and digermane

Article abstract of DOI:10.1149/2.jes113689

Low temperature epitaxy (LTE) in Chemical Vapor Deposition (CVD) refers to 350-650°C interval. This temperature range is critical for this process since the thermal and lattice mismatch (or strain relaxation) issues diminish in advanced BiCMOS processing. The modeling of the epitaxy process is a vital task to increase the understanding the growth process and to design any desired device structure. In this study, an empirical model for Si₂H ₆/Ge₂H₆-based LTE of SiGe is developed and compared with experimental work. The model can predict the number of free sites on Si surface, growth rate of Si and SiGe, and the Ge content at low temperatures. A good agreement between the model and the experimental data is obtained.

Full text of DOI:10.1149/2.jes113689

H478
Journal of The Electrochemical Society, 159 (5) H478-H481 (2012)
0013-4651/2012/159(5)/H478/4/$28.00 © The Electrochemical Society
Kinetic Modeling of Low Temperature Epitaxy Growth of SiGe
Using Disilane and Digermane
*
M. Kolahdouz,a,z A. Salemi, M. Moeen, M. Ostling, and H. H. Radamson
¨
School of Information and Communication Technology, KTH (Royal Institute of Technology), Kista 16640, Sweden
Low temperature epitaxy (LTE) in Chemical Vapor Deposition (CVD) refers to 350–650◦C interval. This temperature range is critical
for this process since the thermal and lattice mismatch (or strain relaxation) issues diminish in advanced BiCMOS processing. The
modeling of the epitaxy process is a vital task to increase the understanding the growth process and to design any desired device
structure. In this study, an empirical model for Si2H6/Ge2H6-based LTE of SiGe is developed and compared with experimental work.
The model can predict the number of free sites on Si surface, growth rate of Si and SiGe, and the Ge content at low temperatures. A
good agreement between the model and the experimental data is obtained.
© 2012 The Electrochemical Society. [DOI: 10.1149/2.jes113689] All rights reserved.
Manuscript submitted December 28, 2011; revised manuscript received January 30, 2012. Published February 16, 2012.
SiGe epitaxy growth has always been an important step in de-
(HRXRD). These data were obtained from simulation of the rock-
ing curves by using the Takagi-Taupin equations.
vice processing in both micro–1–3 and opto–electronics4 due to the
strain engineering and bandgap narrowing in SiGe/Si heterojunctions.
Recently, new application of SiGe/Si heterostructures for infra-red
detectors5,6 and thermoelectrical devices7,8 converts them to an attrac-
tive system for many industrial applications. For these applications,
low temperature epitaxy (LTE) in CVD (350–650◦C) has attracted
attention because of the fact that the vulnerable parts of CMOS and
BiCMOS structures are preserved at this thermal budget. This eases
the prioritizing of different steps in the processing flow. Achieving a
very high quality epitaxial SiGe is crucial for these applications.
Plenty of experimental results have been presented on the issues
regarding integration of LTE SiGe layers for different applications;9–12
meanwhile, remarkably fewer reports are available about the modeling
of the epitaxy process.13–15 Another important point is that at low tem-
peratures (below 600◦C), the traditional precursors e.g. silane (SiH4)
and dichlorosilane (SiH2Cl2) are not applicable. This is because of
higher activation energy required for breaking Si–H (or Si–Cl) bonds
in traditional sources, e.g. SiH4 and SiH2Cl2, compared to Si-Si in dis-
ilane (Si2H6) and trisilane (Si3H8). Nowadays, higher order hydrides
gas sources are mainly used for epitaxy growth at temperature range
below 550◦C. A similar argument may apply here for germane (GeH4)
and digermane (Ge2H6) as germanium gas sources. In this case, high
quality SiGe layers can be grown at low temperatures, however, the
price issue may come forward for the epitaxy process.
Results and Discussion
In a CVD reactor the wafers are placed on a SiC susceptor which
is mounted inside a quartz chamber. A series of halogen lamps are
located on the top and down of the quartz in order to warm up the
susceptor. The heat radiation is absorbed mainly by the susceptor
and the substrate temperature is established. The kinetics of CVD
growth can physically be described by classical boundary layer theory
assuming a laminar gas flow over the wafer.16 Figure 1 illustrates a
schematic view of the gas kinetics.
Due to the frictional force between the gas steam and the stationary
susceptor/substrate, a stagnant boundary layer is established during
the gas flow (see Figure 1). Beyond this boundary layer, the gas
is assumed to be well-mixed and moving at a constant speed. Gas
molecules, which have diffused through the gas boundary layer, are
pulled down due to the pressure gradient between the surface and
the boundary layer. They are attracted toward the dangling bonds and
are then consumed. The vertical diffusion path of the gas molecules
was 10–15 mm for the total pressure of 20–40 torr in an Epsilon
2000 CVD reactor.17
There are a series of publications about the physics behind the
epitaxy growth of SiGe layers using the CVD technique.18–20 In this
process, the impinging reactant molecules on the Si surface are incor-
porated to the dangling bonds. By applying the Maxwell distribution
function in unit time, the number of the reactant molecules (ꢀ) which
interact with a unit area of the substrate with kinetic energy above EA
can be estimated:
In this study, an empirical model for LTE of SiGe in a reduced
pressure chemical vapor deposition (RPCVD) using disilane (Si2H6)
and digermane (Ge2H6) is established. The model can predict the
number of free sites on Si surface, growth rate of Si and SiGe, and
the Ge content at low temperature. The model demonstrates a decent
correspondence with the experimental data.
ꢀ
ꢁ
NR
EA
ꢀ =
(EA + kB T ) exp
−
[1]
1
2
kB T
(2πmRkB T )
Experimental
The epitaxial layers were grown on blanket Si(100) substrates in
an ASM Epsilon 2000 RPCVD reactor at temperature range between
400 to 600◦C. Disilane (Si2H6) and 10% digermane (Ge2H6) in H2
were used as Si and Ge sources, respectively.
Different partial pressures of Si2H6 (PSi2H6) and Ge2H6 (PGe2H6
)
were chosen to verify the validity of the model. The hydrogen partial
pressure has been considered as an important point for the thermody-
namics and gas kinetics in the reactor. This parameter has been altered
to achieve different partial pressures of the precursors.
The Ge content and the layer thickness of deposited SiGe lay-
ers were measured directly by high resolution X-ray diffraction
Figure 1. Schematically illustration of how classical boundary layer forms
from laminar gas stream flowing over the wafer in non-selective epitaxy growth
(NSEG) during the CVD process. Black arrows in this figure demonstrate the
diffused molecules path to reach the dangling bonds. Si substrate is placed
inside the susceptor.
* Electrochemical Society Active Member.
a Present address: Department of Electrical and Computer Engineering, Nano-
Electronic Laboratory, University of Tehran, Tehran, Iran.
z E-mail: mkes@kth.se
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Journal of The Electrochemical Society, 159 (5) H478-H481 (2012)
H479
Figure 2. Surface coverage of hydrogen as a function of temperature.
Figure 3. Growth rate of Si for two disilane partial pressure (60 and
100 mtorr) as a function of temperature.
where NR is the number of reactant molecules in a unit volume of
the gas phase and mR is the mass of a reactant molecule and EA is
deposition activation energy. kB and T are respectively Boltzmann
constant and temperature. The deposition of Si layers on a Si surface
is notably the simplest case of epitaxy growth. The main contributing
specie in this case is the SiH2 radical which has a unity sticking
coefficient on the dangling bonds according to the previous reports.21
The growth rate for Si deposition can be calculated as follows:
However, epitaxy is a non-equilibrium process in which the above
expression must be thus modified. Desorption of hydrogen is the lim-
itation of the growth rate at low temperature. Basically, the deposition
in LTE is limited by the availability of free surface sites. Our model
in this work empirically calculates the surface coverage of hydrogen
which is illustrated in Figure 2. Figure 2 shows that 50% of all sur-
face sites are blocked with hydrogen at around 314◦C. According to
our calculations, 2 to 20% of the silicon sites are occupied in the
temperature range chosen for this study (from 400 to 600◦C).
Figure 3 depicts the Si growth rate model for two different disilane
partial pressure (60 and 100 mtorr) as a function of temperature.
The experimental results are also added to proof the correctness of
the calculations. The nice feature in this plot is that the growth rate
increases linearly with increasing the disilane partial pressure. This
is due to the independency of the hydrogen surface coverage on the
disilane partial pressure. Since hydrogen is the carrier gas with very
high input levels in this process (slm range), changing the precursor
flow (sccm range) does not affect the hydrogen amount inside the
chamber.
The effect of Ge atoms on growth rate was considered by adding
the digermane to the source gases. Four different partial pressures
for Ge (0.5, 3, 4 and 4.9 mtorr) were used and the activation ener-
gies were calculated through the Arrhenius plots. To eliminate effects
of other parameter, the disilane partial pressure was kept constant at
60 mtorr. Figure 4 illustrates the calculated activation energies vs. di-
germane/disilane partial pressure ratio. The results show that increas-
ing Ge2H6 partial pressure decreases the total deposition activation
energy. All values in this chart are less than activation energy calcu-
lated for Si deposition (1.56 0.07 eV in this figure). The presence of
ꢀ
(1 − θH(Si)
)
PSi
H
2
6
RSi
=
= β
1
2
N0
N0
(2πmSi kB T )
H
6
2
ꢀ
ꢁ
ꢀ
ꢁ
ESi
ESi
H
2
H
6
2
6
×
+ 1 exp
−
[2]
kB T
kB T
where β, θ, P, m, N0 and E are respectively: unit-less constant; surface
coverage of hydrogen; partial pressure of disilane; molecular mass of
disilane; number of atoms in a unit volume of the substrate layer; and
activation energy needed for deposition. Activation energy of 1.56 eV
was extracted practically for disilane deposition from the Arrhenius
plot. The parameter β in above equation is called tooling factor which
should not be considered as a fitting parameter. It presents the vertical
diffusion of the molecules downwards and it obeys the Fick’s law. In
other words, β parameter has a physical meaning and is dependent
on the reactor geometry and the distribution of gases in the reactor
chamber. This parameter alters by the gas injectors.
The surface coverage of an adsorbed gas, which is temperature
dependent, can be obtained through the Langmuir isotherm. For Si
deposition at low temperature from disilane, the dominant reactions
occur through a series of H dissociation but ultimately the following
chemical reactions and adsorption can be written:22
Si2H6(g) + → SiH2 + SiH4(g)
[R1]
SiH4(g) + → SiH2 + H2(g)
SiH2 + → SiH + H
[R2]
[R3]
where _ is a dangling bond. The Langmuir isotherm for an equilibrium
case can be written as:
θ2H
B (T ) =
[3]
PH (1 − θH )2
where B(T) is the reaction constant and P is the hydrogen partial
pressure which is close to 1. Therefore, this reaction constant can be
rewritten as:
θ2H
(1 − θH )2
Figure 4. Activation energy of deposition vs. Ge2H6/Si2H6 partial pressure
ratio.
B (T ) =
[4]
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H480
Journal of The Electrochemical Society, 159 (5) H478-H481 (2012)
Ge atoms on the surface enhances the growth rate for two reasons;
first, they require lower activation energy for deposition than do Si
(0.29 eV for Ge compared to 1.56 eV for Si); and second, the des-
orption energy of H from these atoms is also lower than Si23 which
makes them favorable desorption sites for undesired hydrogen atoms
on the surface. Thus, Si atom binding becomes easier in the presence
of Ge atoms.
For the modeling of LTE of SiGe, a phenomenological considera-
tion was taken into account. This means that the total growth rate was
assumed as a sum of the growth rates from different sources contribut-
ing in the epitaxy process. The total growth rate can thus be given by:
RT = RSi + RGe + RSi/Ge + RGe/Si
[5]
where RSi/Ge (RGe/Si) relates to the Si (Ge) deposition in the presence
of Ge (Si) atoms on the surface. Since Ge atoms on the surface mainly
contribute to provide free sites, the term RGe/Si is negligible in this
equation. This means that the RSi/Ge is a result of RGe. Thus, they can
be merged and Eq. 5 is simplified as:
Figure 6. Inverse Ge content (x−1) as a function of the inverse partial pressure
ratio of digermane and disilane.
Substitution of Eqs. 7 and 8 in Eq. 10 gives:
RT = RSi + RGe + mRGe = RSi + (1 + m) RGe
[6]
1
A PGe
2
m in this equation is called substitution coefficient.24 “m” is related to
be the number of silyl groups which have been substituted for hydro-
gen atoms in digermane molecules by a chemical gas reaction. Thus,
an individual molecule of the hypothetical digermane intermediate
transports not only a germanium atom from the gas to the surface but
also “m” silicon atoms which will be incorporated in the epitaxial
layer. Eq. 2 represents the growth rate of Si in the epitaxy process
which can simply be shown as:
H
6
−1
= (1 + m) +
(
)
[11]
x
B PSi
2
H
6
The inverse germanium content (x−1) versus the inverse partial
pressure ratio of digermane and disilane is ploted in Figure 6. In this
figure, the straight lines show that the experimental data are fairly
in decent agreement with Eq. 11. The ordinate intercept of each line
correlates to the inverse maximum amounts of relative Ge contents
possible at the corresponding temperature.25 Accoring to this figure,
at 500, 525, 550 and 575◦C, the maximum Ge contents will be 49, 40,
37 and 33%, respectively.
According to Eq. 11, “m” can be obtained from the ordinate in-
tercepts given in Figure 6. It can also be extracted by multiplying the
slopes of corresponding temperatures in Figs. 5 and 6. This may be ex-
plained by comparing Eqs. 9 and 11. Table I summarizes the results.
The average, which is shown on the last column, is more reliable.
Table I just shows the integers by rounding the average numerical
values.
RSi = APSi
[7]
H
6
2
where A includes all other parameters in Eq. 2. Similar equation can
also be given for Ge growth rate:
RGe = B PGe
[8]
H
6
2
Thus, substituting Eqs. 7 and 8 in Eq. 6 leads to the following expres-
sion:
RT − RSi
(1 + m) RGe
B PGe
A PSi
H
2
6
=
= (1 + m)
[9]
RSi
RSi
According to this table, “m” in this temperature range is two which
means each Ge atom is contributing in deposition of two Si atoms.
Thus, using Eqs. 2 and 6, the total growth rate of SiGe epitaxy growth
can be expressed by:
H
6
2
Using this equation, the relative Ge-related growth rate can be plotted
as a function of the ratio of the partial pressures of digermane and
disilane. Figure 5 illustrates the results of the calculations. In this
figure, the relative Ge-related growth rate is plotted for 4 different
temperatures.
There are different ways of explaining the substitution
coefficeient.25 In this case, for calculating the Ge content (x) the
following simple assumption can be considered:
ꢂ
ꢃ
1 − θH(Si)
PSi
H
2
6
RT = β
1
2
ꢂ
ꢃ
N0
2πmSi kB T
H
2
6
ꢀ
ꢁ
ꢀ
ꢁ
ESi
ESi
H
6
H
6
2
2
×
+ 1 exp
−
kB T
kB T
1
RT
RSi + (1 + m) RGe
ꢂ
ꢃ
=
=
[10]
1 − θH(Si)
PGe
H
x
RGe
RGe
2
6
+ χ(1 + m)
1
2
ꢂ
ꢃ
N0
2πmGe kB T
H
2
6
ꢀ
ꢁ
ꢀ
ꢁ
EGe
EGe
H
2
H
6
2
6
×
+ 1 exp
−
[12]
kB T
kB T
where χ is a unit-less tooling factor which is dependent on the
gas property and the reactor geometry. It should be emphessized
here that Ge deposition occurs mostly through series of Ge2H6
Table I. M estimation.
Temp.
x
−1(0)-1
tanαtanβ-1
m
500
525
550
575
1.04
1.47
1.69
1.97
2.4435191
2.1532922
2.4016827
1.452974
2
2
2
2
Figure 5. Relative germane-related growth rate of SiGe as a function of the
ratio of the partial pressures of digermane and disilane.
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Journal of The Electrochemical Society, 159 (5) H478-H481 (2012)
H481
temperature, Ge content increases. If an epitaxy growth process con-
tinues long enough that the epi-film reaches the critical thickness, it
begins to relax.26
This can be seen in this figure at temperatures below 773 K. At
these temperatures by using 4.9 mtorr Ge2H6, the experimental result
is located below the model lines. This is because the thickness of SiGe
layer (e.g. 818 Å at 773 K) exceeds the critical thickness. It is worth
mentioning here that 37% as shown in this figure is not the highest
limit for the Ge content. Layers with even higher Ge contents can be
grown using these sources but with a thickness which is located in the
meta-stable growth region.
Conclusions
An empirical model for Si2H6/Ge2H6-based epitaxy growth of
SiGe at LTE was presented. The growth rate of Si and SiGe was
calculated by considering the number of free sites and impinging
atoms to the surface at a certain temperature. The activation energy
for the chemical reactions were estimated from the experimental data.
The Ge content in epi-layers was also calculated and compared with
the experimental data. A good agreement between the model and
experimental data was found.
Figure 7. Growth rate of SiGe vs. temperature for different digermane partial
pressures (3, 4, and 4.9 mtorr); disilane partial pressure was 60 mtorr.
dissociations and adsorption of GeH2 radicals on the surface. R1, R2
and R3 can also be written using digermane parameters. Finally, the
experimental and calculated results from Eq. 12 are shown in Figure 7.
Four different temperatures and three different GeH4 partial pres-
sures have been used to prove the sanity of the model. This figure
shows a fairly good concurrence between the model and experimental
data.
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H
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= α
[13]
1 − x
H
6
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Figure 8. Ge content (%) of the SiGe layers vs. the growth temperature
for different digermane partial pressure (3, 4, and 4.9 mtorr); disilane partial
pressure was 60 mtorr.
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