Reaction of Si with HCl to form chlorosilanes time dependent nature and reaction model

Article abstract of DOI:10.1149/1.1737386

We propose a chemical vapor deposition (CVD) process with closed gas recycling for making low-cost, crystalline silicon thin films for solar cells, which connects chlorosilane synthesis from Si and HCl with Si thin-film growth by CVD from chlorosilanes. In this work we studied the formation of chlorosilanes by the reaction of Si with HCl at temperatures ranging from 623 to 723 K. The reaction rate is time dependent, and many pores are formed on the surface of particles after reaction. These pores are active sites for chemical reactions, and the reaction rates increase with increasing pore area. The rate can be correlated with the conversion ratio of Si, and the temporal evolution of the reaction rate can be explained by a reaction model called the shrinking-core model with growing pores. By using this model, we estimated the reaction rates per unit area of activated surfaces and converted them into a rate equation that can be used for the reactor design. The incubation time of the reaction can be shortened by pretreating the Si particles in a fluidized bed, which probably creates defects in the native oxide layers on the particles, which in turn become reactive sites.

Full text of DOI:10.1149/1.1737386

Journal of The Electrochemical Society, 151 ͑6͒ C399-C404 ͑2004͒
C399
0
013-4651/2004/151͑6͒/C399/6/$7.00 © The Electrochemical Society, Inc.
Reaction of Si with HCl to Form Chlorosilanes
Time Dependent Nature and Reaction Model
z
Suguru Noda, Katsuaki Tanabe, Takashi Yahiro, Toshio Osawa,
and Hiroshi Komiyama
Department of Chemical System Engineering, School of Engineering, The University of Tokyo,
Tokyo 113-8656, Japan
We propose a chemical vapor deposition ͑CVD͒ process with closed gas recycling for making low-cost, crystalline silicon thin
films for solar cells, which connects chlorosilane synthesis from Si and HCl with Si thin-film growth by CVD from chlorosilanes.
In this work we studied the formation of chlorosilanes by the reaction of Si with HCl at temperatures ranging from 623 to 723 K.
The reaction rate is time dependent, and many pores are formed on the surface of particles after reaction. These pores are active
sites for chemical reactions, and the reaction rates increase with increasing pore area. The rate can be correlated with the
conversion ratio of Si, and the temporal evolution of the reaction rate can be explained by a reaction model called the shrinking-
core model with growing pores. By using this model, we estimated the reaction rates per unit area of activated surfaces and
converted them into a rate equation that can be used for the reactor design. The incubation time of the reaction can be shortened
by pretreating the Si particles in a fluidized bed, which probably creates defects in the native oxide layers on the particles, which
in turn become reactive sites.
©
2004 The Electrochemical Society. ͓DOI: 10.1149/1.1737386͔ All rights reserved.
Manuscript submitted April 26, 2003; revised manuscript received January 2, 2004. Available electronically May 4, 2004.
Crystalline Si solar cells are commonly used because of their
high efficiency, stability, and relatively low production costs. For
such solar cells to be widely used, however, continued production
cost reductions are still needed. Because Si substrates account for
about half of the module costs, new low-cost production processes
are needed for forming the Si photovoltaic layer. Si substrates are
currently made by slicing Si ingots, each of which constitutes about
that available by using substrates cut from ingots. To design a CVD
process with closed gas recycling, kinetic information on the reac-
tants is needed because the reactions are controlled kinetically espe-
cially in thin-film growth in CVD reactors, and also because it is
needed to properly model the complicated interaction between the
two reactors of chlorosilane production and Si-CVD. Because the
Siemens process is well-established and is controlled thermody-
namically rather than kinetically, little information is available in the
open literature on the kinetics of this reaction system. Therefore, we
investigated the reaction kinetics both for chlorosilane synthesis and
for Si deposition. We report the former reaction in this paper.
Most studies related to Reaction 1 have been oriented towards
1000 ␮m thickness of the ingot, including the thickness required for
cutting. Using such a thick layer of silicon is one source of the
relatively high costs of these solar cells. Substituting Si substrates
with Si thin films is a promising approach for cost reduction and
several processes so-called layer transfer processes have been devel-
oped to produce either monocrystalline or large-grained polycrystal-
Si-wafer cleaning processes that typically operate at temperatures,
1
3-11
line Si thin films. Because the higher deposition temperature of
T Ͼ 1300 K,
and few studies have been made at temperatures
1
12
active Si layers tends to produce higher open-circuit cell voltage, Si
near 800 K, where Reaction 1 is thermodynamically favored, as
shown in Fig. 2. The main products of Reaction 1 are trichlorosilane
chemical vapor deposition ͑Si-CVD͒ from chlorosilanes at high tem-
peratures is suitable for photovoltaic layer formation.
1
3,14
(
SiHCl ) and silicontetrachloride (SiCl ),
and copper is useful
3
4
3
,15,16
In CVD thin film growth, to maintain high film uniformity, the
reactant conversion ratio is usually kept low and the residual gases
are discarded because they may contain particulates and contami-
nants. This low conversion efficiency of high-purity Si results in
relatively high production costs. To overcome this problem, we pro-
pose a CVD process with closed gas recycling, in which the outlet
gases of the CVD reactor are recycled to the reactor to synthesize
chlorosilanes from metallurgical-grade Si ͑MG-Si͒ particles and HCl
as a catalyst
to drive Reaction 1. But this information is insuf-
ficient for designing the reaction system.
In this work, we experimentally investigated the reaction of HCl
with Si particles to form chlorosilanes by using a fluidized-bed re-
actor at temperatures ranging from 623 to 723 K. A model called the
shrinking-core model with growing core was also developed to ex-
plain the time-dependent nature of this reaction and also to extract
the reaction rate of active Si surfaces.
2
gas ͑Fig. 1͒. The reactions for this process can be expressed as
Experimental
MG-Si ϩ xHCl → SiH4ϪxCl ϩ ͑x Ϫ 2͒H
͓1͔
͓2͔
x
2
The fluidized-bed reactor was made of a silica glass tube with an
outer diameter of 24 mm, an inner diameter of 22 mm, and a height
SiH4ϪxCl ϩ ͑x Ϫ 2͒H → SOG-Si ϩ xHCl
x
2
which are reversible, and the direction can be controlled mainly by
temperature, as shown in Fig. 2. In this process, MG-Si powder is
converted into solar-grade Si ͑SOG-Si͒ thin films, with high Si-
reactant-to-film conversion efficiency and minimum consumption of
H and Cl.
This reaction system is similar to the Siemens process, which is
one of the standard processes for synthesizing high-purity Si from
MG-Si. In the Siemens process, however, chlorosilanes are decom-
posed near equilibrium conditions to thicken polycrystalline Si seed
rods, which are then used to form Si ingots. By changing the form of
Si products from rods to thin films, we can obtain areas of Si pho-
tovoltaic layers that are more than an order of magnitude larger than
z
E-mail: noda@chemsys.t.u-tokyo.ac.jp
Figure 1. Conceptual view of the CVD process with closed gas recycling.
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C400
Journal of The Electrochemical Society, 151 ͑6͒ C399-C404 ͑2004͒
Figure 2. Thermodynamic equilibrium composition of an Si/H/Cl system vs.
temperature.
of 250 mm. The temperature was controlled by using an external
cylindrical heater 200 mm high. We filled the reactor with 0.08 g of
Si particles and 19.92 g of silica particles, both of which had sieve
diameters between 90 and 150 ␮m. We investigated the reaction of
both MG-Si ͑98 wt %͒ and high-purity Si ͑99.9 wt %͒ particles, and
the reaction rates were almost the same for these two types of Si
particles. Most of the results reported here are for MG-Si particles,
however, for the experiment examining the effect of pretreatment,
we used high-purity Si particles ͑Fig. 3͒. Silica was used as a flu-
idization medium. The porosity of the fluidized bed was 0.56. To dry
the particles and to remove organic impurities from the surface of
the particles, either H or He was run through the reactor for 0 to
2
150 min at T ϭ 673 or 773 K and a gas flow rate, Q ϭ 100 or 300
sccm. The particles were in the fixed-bed condition ͑i.e., nonfluid-
ized͒ for Q ϭ 100 sccm, whereas they were in the fluidized-bed
condition for Q ϭ 300 sccm. After this pretreatment, the gas was
switched to a HCl/H mixed gas, and the reaction was started. The
2
4
reaction conditions were pressure, P ϭ 9.0 ϫ 10 Pa, T ϭ 623,
6
73, or 723 K, Q ϭ 300 sccm, and the concentration of HCl,
CHCl ϭ 1.0, 3.3, or 10 vol %. The fraction of each gas was mea-
sured at the exit of the reactor by using gas chromatography, and the
reaction rate was calculated as the conversion rate of Si to chlorosi-
lanes. To satisfy the differential reactor assumption, the reaction
conditions were set to keep the conversion ratio of HCl low.
Because the reaction rate was time-dependent, we analyzed Si
particles after the reaction. In these experiments, 5.0 g of Si particles
were fed into the reactor without silica particles, and their conver-
sion ratio was calculated from the ratio of the amount of the chlo-
rosilanes produced to the amount of the Si particles initially fed.
Optical microscopy ͑OM͒ was used for measuring the size distribu-
tion of the particles, and scanning electron microscopy ͑SEM͒ was
used for determining the surface morphology of the particles. The
surface area of the unreacted and reacted Si particles were measured
Figure 3. Reaction rate of Si particles at HCl concentration, CHCl
ϭ 3.3 vol %, and T ϭ 673 K. The reaction rate was time dependent and
did not correlate well with reaction time, t ͑a͒, but correlated well with Si
conversion ratio, c ͑b͒.
r
hydrofluoric acid (HF ). The wafers were placed in a silica-glass
aq
tube-reactor and then reacted with a HCl/H2 mixed gas for 5 h.
4
The operating conditions were P ϭ 9.0 ϫ 10 Pa, T ϭ 673 K,
Q ϭ 300 sccm, and CHCl ϭ 3.3 vol %. The surface of these wafers
was also observed by OM after the reaction.
Results and Discussion
Time-dependent reaction rate and pretreatment of Si par-
ticles.—The main reaction products were SiHCl3 and SiCl4 , and
SiCl concentrations were less than 1 vol % of the SiHCl concen-
trations. Typical reaction rates are shown in Fig. 3a, which indicate
that the reaction rates were time dependent and that their repeatabil-
by using Brunauer-Emmett-Teller ͑BET͒ N adsorption.
2
In addition, Si wafers with and without native oxide layers were
used in the reaction to investigate the influence of the native oxide
layer on the reaction between HCl and Si. Si wafers without native
oxide layers were prepared by pretreating the Si wafers with 5 vol %
4
3
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Journal of The Electrochemical Society, 151 ͑6͒ C399-C404 ͑2004͒
C401
Figure 4. OM images of Si particles for Si conversion ratios, c ϭ (a) 0
r
͑before reaction͒, ͑b͒ 0.1, ͑c͒ 0.3, and ͑d͒ 0.75.
Figure 6. Images of Si surfaces after reaction. ͑a͒ SEM image of particles
for Si conversion ratio, c ϭ 0.1, ͑b͒ OM images of Si wafers with ͑b͒ and
r
without ͑c͒ native oxide layers after reaction at HCl concentration, CHCl
ϭ 3.3 vol %, and T ϭ 673 K for 5 h.
ity was poor between runs made using the same operating condi-
tions. However, once the reaction began, the time dependence of the
reaction-rate was repeatable. Figure 3b shows the reaction rates vs.
conversion ratio of Si particles, c . cr was calculated from the
r
implies that native oxide layers prevent Si particles from reacting,
except at the breaks in the oxide layers. Apparently chemically re-
active areas on the particles are formed during pretreatment in the
fluidized state when the native oxide layers are probably eroded by
collisions with the particles. Thus, in addition to removing water and
organic compounds, the pretreatment enhances the reactivity of the
particles.
amount of the chlorosilane produced and the amount of the Si par-
ticles initially fed. Because some particles were blown out of the
reactor during the reaction by becoming small enough to be sus-
pended in the flowing gas, c did not increase to 1. Figure 3b clearly
r
shows that the reaction rate is well correlated with cr .
When the particles were fluidized with H2 for 120 min at T
ϭ 773 K before the reaction, incubation time became negligible,
and the time evolution of reaction rates became repeatable as shown
in Fig. 9. We selected this procedure as the standard pretreatment
condition of Si particles for the following experiments.
Figure 7a shows the change of the surface area of Si particles as
a function of c . The broken line represents the change for a shrink-
r
ing particle where the reaction occurs over the entire particle surface
͑shrinking-core model͒, and the solid line indicates fitting of the
measured data with the model we developed, which is explained in
the next section. The increase of the surface area at the beginning of
the reaction results from the increasing roughness of Si particles
Structural change of Si particles during reaction.—Typical OM
images are shown in Fig. 4, and the measured size distributions are
shown in Fig. 5. They indicate that the particle size decreases as the
reaction proceeds. Many particles below the lower cut point of the
sieve diameter ͑90 ␮m͒ existed in the nonreacted Si particles, but
their influence on the reaction was negligible because their total
surface area was insignificant compared to the total surface area of
the particles. Most of these particles disappeared in the regime cr
Ͻ 0.1, which indicates that they reacted and disappeared early in
the reaction process.
Figure 6a shows a typical SEM image of Si particles, which
indicates that the reaction proceeds locally to form many pores.
Because these pores were observed on the surfaces of both MG-Si
and high-purity Si particles after reaction, contamination should not
be the cause for the formation of these pores. Another possibility
causing this uneven surface morphology is in the native oxide layers
on the surface of Si particles. To determine the influence of native
oxide layers on the reaction with HCl, we made experiments using
two kinds of Si wafers instead of Si particles. One wafer had its
native oxide layer removed by etching it with HFaq before reaction,
and the other wafer was used without this etching pretreatment. As a
result, as shown in Fig. 6b, the reaction occurred over the entire
͑Fig. 6a͒. A form factor, f, is defined as the ratio of the measured
value of the BET surface area to the value calculated by using the
shrinking-core model. Initially f ϭ 1, and Fig. 7b shows that f in-
creased with increasing cr and approached 5.
Reaction model.—We formulated a reaction model to explain the
dependence of the surface area and the reaction rate on c , by con-
r
sidering the effect of the Si particle shrinking and its surface rough-
ness increasing. Figure 8 shows a schematic of the morphological
change of Si particles in our model. In the model we assumed that
the Si particles are spheres all of the same size, and that each par-
ticle initially has N active points, which are breaks in the native
oxide layers from which the reaction starts. We further assumed that
the reaction proceeds isotropically at a constant rate R ͑m/s͒. The
s
new surfaces generated by the reaction become active surfaces and
spread. After multiple active surfaces meet and overlap each other,
the entire surface becomes activated, and the particles shrink, main-
taining a similar shape during shrinkage.
The increase of the etched, outer surface area by the reaction,
2
⌬
S ͑m ͒, can be represented as
e
surface of the HF -etched wafer, but as shown in Fig. 6c, etch-pits
aq
appeared on the unetched wafer. The production of such etch-pits
results from surface reactions at a limited number of active points on
the surface where there are probably breaks in the oxide layer. This
S0 Ϫ Se
2
⌬
S ϭ N ϫ ⌬͓␲͑R t͒ ͔ ϫ
͓3͔
e
s
S0
Figure 5. Si particle size distribution
for Si conversion ratios, c ϭ (a) 0
r
͑
before reaction͒ ͑500 particles mea-
sured͒, ͑b͒ 0.1 ͑300 particles mea-
sured͒, ͑c͒ 0.3 ͑250 particles mea-
sured͒, and ͑d͒ 0.75 ͑100 particles
measured͒.
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C402
Journal of The Electrochemical Society, 151 ͑6͒ C399-C404 ͑2004͒
Figure 8. Schematic image of the morphological change of Si particles in
our model. ͑a͒ Si particle shrinks and ͑b͒ pores grow on the surface as the
reaction proceeds.
shrinks with time. We incorporated the effect of the change of the
2
outer surface area of Si particles, S ͑m ͒, including both etched and
nonetched regions, by substituting S for S in the left side of Eq. 5.
0
By using the shrinking-core model, S can be expressed as
2
/3
V
S ϭ ͩ ͪ S0
͓6͔
V
0
3
3
where V0 ͑m ͒ and V ͑m ͒ are the volumes of the unreacted and
reacted Si particles, respectively. The conversion ratio of Si particles
can be expressed as
V
cr ϭ 1 Ϫ
͓7͔
V0
Because the volume change occurs due to reaction on activated sur-
faces, it can be expressed as
⌬
V
S d͑R t͒
a s
cr ϭ Ϫ
ϭ
͵
͓8͔
V0
V0
By substituting Eq. 6 and 7 into Eq. 5, the activated surface area can
be expressed as
Sa
S0
␲NRs2
ϭ fЈ
ͫ
1 Ϫ exp
ͩ
Ϫ
t2
ͪ
ͬ
͑1 Ϫ cr͒2/3
͓9͔
S0
Figure 7. Comparison of experimental and modeling results for the morpho-
logical change of Si particles. ͑a͒ Surface area experimentally obtained ͑open
circles͒, that calculated by using the shrinking-core model ͑broken line͒, and
that calculated by using our model ͑solid line͒. ͑b͒ Form factor experimen-
tally obtained ͑open circle͒, that used in the shrinking-core model ͑broken
line͒, and that calculated by using our model ͑solid line͒.
From Eq. 8 and 9, S and c can be calculated numerically. The total
a
r
surface area of Si particles, Sall , can be calculated as
Sall ϭ S Ϫ S ϩ S ϭ S ϩ ͑ fЈ Ϫ 1͒S
e
͓10͔
e
a
and is shown in Fig. 7b. Figure 7 indicates that the changes of both
Sall and f with c is well reproduced by this model. Equation 9
become simple for large t as
r
2
where t ͑s͒ is time, S0 ͑m ͒ is the initial outer surface area of Si
particles before reaction, and (S Ϫ S )/S is the modification co-
efficient resulting from the overlapping of active surfaces. The time
evolution of the area of the inactive surface lost can be expressed as
S → fЈ͑1 Ϫ c ͒2/3S ͑t → ϱ͒
0
e
0
͓11͔
a
r
0
which is the same as the product of fЈ times the surface area from
the shrinking core model. Thus, the two form factors become the
Se
S0
␲NR 2
s
ϭ 1 Ϫ exp
ͩ
Ϫ
t2
ͪ
͓4͔
same at high Si conversion ratios, i.e., fЈ ϭ f for c → 1. For a
S0
r
hemispherical active surface, fЈ ϭ 2, however, for reacting Si par-
ticles, Fig. 7b indicates that fЈ ϭ 5. In the following discussion,
We introduce a form factor, fЈ ͑dimensionless͒, which is the ratio of
therefore, we use fЈ ϭ 5. Because R can be estimated from the
the activated surface area generated to the inactive surface area lost.
s
2
measured overall reaction rate and from the BET surface area at
high Si conversion ratios, where the entire surface becomes acti-
vated, Eq. 9 has only a single fitting parameter, N.
Figure 9 shows measured reaction rates ͑dots͒ and the fitted re-
sults from our model ͑lines͒ vs. t for 1.0 р CHCl р 10 vol % and
23 р T р 723 K. For the fitted results, N ϭ 1000 and the final
conversion ratio of Si particles, crf ϭ 0.8. Note that because of the
loss of small particles from the fluidized-bed reactor, crf Ͻ 1. The
The time evolution of the active surface area, S ͑m ͒, can be ex-
a
pressed as
Sa
S0
␲NR 2
s
ϭ fЈ
ͫ
1 Ϫ exp
ͩ
Ϫ
t2
ͪ
ͬ
͓5͔
S0
6
The ratio of the activated surface area to the outer surface area
should be expressed with Eq. 5, however, the outer surface itself
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Journal of The Electrochemical Society, 151 ͑6͒ C399-C404 ͑2004͒
C403
Figure 9. Measured ͑dots͒ and calcu-
lated ͑lines͒ reaction rates of Si par-
ticles vs. reaction time, t, for HCl con-
centration, CHCl ϭ 1.0 ͑c͒, 3.3 ͑a, d, f͒,
and 10 ͑b, e, g͒ vol % at T ϭ 723 ͑a,
b͒, 673 ͑c, d, e͒, and 623 ͑f, g͒ K. The
symbols show the results of different
experimental runs. The experimental
results were well represented by our
model for ͑a͒, ͑c͒, ͑e͒, ͑f͒, and ͑g͒,
whereas the correlation of the fitted re-
sults was poor for ͑b͒ and ͑d͒.
data in Fig. 9a, c, e, f, and g are well reproduced by the model,
except for the short time region of Fig. 9a and c, where the HCl
conversion ratio approached 1, and therefore the differential reactor
assumption is no longer valid. The reaction rates at the full HCl
conversion are 0.74, 2.5, and 7.4 mol-Si/min for CHCl ϭ 1.0, 3.3,
and 10 vol %, respectively. For Fig. 9b and d, however, the model
results do not agree with the experimental results. The reaction rate
began decreasing at relatively low Si conversion ratios. One possible
cause of the decreased reaction rate is that either a small amount of
oxygen or water impurities reacted with Si surfaces to form oxide
layers, inhibiting the reaction of Si surfaces with HCl.
The surface area of the 0.08 g of Si particles in Fig. 9 is
3 ϫ 10 Ϫ 9 ϫ 10 m for the 0-0.7 conversion ratio, which is
Ϫ4
Ϫ4
2
estimated from the surface area of the 5 g Si particles in Fig. 7. The
Ϫ6
Ϫ5
feeding rate of reactant HCl is 2 ϫ 10 Ϫ 2 ϫ 10 mol/s, and
therefore the characteristic time constant for monolayer adsorption
can be estimated at around 1 ms. The characteristic time constant of
Si consumption is around 10 min, and therefore the adsorption of
HCl proves to be in the steady state at each moment of the reaction.
SiHCl and H should be the major species desorbing from Si
3
2
surfaces because no other species like Cl nor SiCl are thermody-
2
2
namically stable under these conditions. If this reaction is of
Because the model agreed well with many of the measured data
shown in Fig. 9, we conclude that this model reasonably represents
the mechanism of the reaction of Si with HCl.
¨
Langmuir-type, it can be expressed as
HCl͑g͒ ϩ 2s ꢀ H͑s͒ ϩ Cl͑s͒
͓12͔
͓13͔
͓14͔
Reaction rate.—We discuss the underlying mechanism for the
reaction rate, R , in this section. To simplify the discussion, SiCl is
H͑s͒ ϩ 3Cl͑s͒ ϩ Si͑b͒ ꢀ SiHCl ͑g͒ ϩ 4s
3
s
4
ignored, whose production rate is less than one-hundredth of
2H͑s͒ ꢀ H ͑g͒ ϩ 2s
2
SiHCl . We assumed that the reaction rate of Si, which is the same
3
as the production rate of SiHCl , is proportional to the area of
where ͑g͒, ͑s͒, and ͑b͒ denote the gas-phase, surface, and bulk spe-
cies, respectively, and s denotes vacant sites of Si surfaces. Under
steady-state conditions, these three reactions should be in balance. If
Reaction 12 is the rate-determining step, the overall reaction rate
should have a reaction order of 1 on HCl concentration, however,
the reaction order was around 0.5, and therefore, Reaction 12 proves
not to be the rate-determining step. It is reasonable that the desorp-
tion reaction, i.e., either Reactions 13 or 14, is the rate-determining
step because the reaction order can be less than 1 under desorption-
limited conditions. Reaction 14 has been studied extensively.1
3
activated Si surfaces in our model. Actually, our model reproduced
the BET surface area as well as the production rate of chlorosilanes
by using a constant value for the reaction rate of the activated sur-
faces, R , and thus it is considered that this assumption is reason-
s
able.
As for the dependence of the reaction rate on the HCl concen-
tration, the reaction order appears to be smaller than 1 because the
maximum reaction rates in Fig. 9 do not increase linearly with the
HCl concentrations. In the model of Fig. 9, we used a reaction rate
with a reaction order of 0.5 on HCl concentration and an activation
energy of 60 kJ/mol. This reaction rate appears to reproduce the data
well. The origin of this reaction rate is discussed next.
7-19
Interestingly, H desorption rate at high H coverage is in the first
2
1
7,18
order of H coverage for Si͑100͒ surface,
second order for Si͑111͒ surface. From their results, the desorption
whereas it is in the
1
8
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C404
Journal of The Electrochemical Society, 151 ͑6͒ C399-C404 ͑2004͒
rate can be estimated at 5 ϫ 10Ϫ4 Ϫ 5 ϫ 10Ϫ2 ML/s at 685-790 K
at the full H coverage for both ͑100͒ and ͑111͒ surfaces. On the
Acknowledgments
The authors thank Professor Fumio Okada for his helpful discus-
sion and comments. This study was partially supported by the In-
dustrial Technology Research Grant Program, 00B64024c, of the
New Energy and Industrial Technology Development Organization
of Japan, and by the Grant-in-Aid for Scientific Research ͑A͒,
15206086, 2003, of the Ministry of Education, Culture, Sports, Sci-
ence and Technology, Japan.
other hand, the reaction rate was 0.18 р R р 1.4 nm/s, which cor-
s
responds to several ML/s. The small desorption rate of H implies
2
that the H desorption is the rate-determining step, however, it is too
2
small to account for the observed reaction rate. One possible reason
is the difference in the Si surface structure. The surface was atomi-
cally smooth in Ref. 17 and 18, whereas it was rough in this work.
As for the activation energy, it was 190-250 kJ/mol for H desorp-
2
The University of Tokyo assisted in meeting the publication costs of this
article.
tion in Ref. 17 and 18, whereas it was about 60 kJ/mol for R in Fig.
s
9. This large difference in activation energy might also be caused by
the difference in the Si surface structure, but we lack information to
determine which is the rate-determining step, Reactions 13 or 14.
List of Symbols
The mechanism of H desorption is still unclear, even for the atomi-
2
19
cally smooth surfaces of monocrystalline Si.
CHCl HCl concentration, vol %
cHCl
HCl concentration, mol/m
We summarize the overall production rate of SiHCl below. The
3
3
3
reaction rate per unit reactor volume, Rtotal (mol/m /s), can be ex-
cr conversion ratio of Si particles
pressed as
crf final conversion ratio in the model
f
ratio of actual surface area of Si particles to that calculated by using the
shrinking-core model
␳
SV
Rtotal
ϭ
Rs
͓15͔
f
Ј
ratio of generated area of the activated surface to area of inactive surface
lost
M
k
reaction rate constant, m2.5/mol0.5/s
atomic weight of Si, kg/mol
3
3
where ␳ ϭ 2.33 ϫ 10 (kg/m ) is the density of crystalline Si,
M
N
P
2
3
number of active points on each Si particle
gas pressure, Pa
SV (m /m ) is the activated surface area of Si per unit reactor vol-
Ϫ3
ume, and M ϭ 28.09 ϫ 10 (kg/mol) is the atomic weight of Si.
The reaction rate used in the model of Fig. 9 was
Q
R
total flow rate of reactant gases, sccm
gas constant, J/mol/K
Rs reaction rate of activated Si surfaces, m/s
Rtotal reaction rate per unit reactor volume, mol/m /s
0
.5
R ϭ kc
͓16͔
3
s
HCI
2
S
S0
outer surface area of Si particles, m
initial surface area of Si particles, m
where cHCl (mol/m ) is the HCl concentration and k ͑m2.5/mol0.5/s͒
3
2
2
Sa area of activated surface of Si particles, m
is a rate constant expressed as
Sall overall surface area of reacted Si particles, m2
Se area of etched outer surface of Si particles, m
SV activated surface area of Si particles per unit reactor volume, m /m
2
6
0͑kJ/mol͒
k ϭ 2.5 ϫ 10Ϫ5͑m2.5/mol0.5/s͒exp
Ϫ
͓17͔
2
3
ͫ
ͬ
RT
t(s), t ͑min͒
reaction time
T
V
temperature, K
the volume of the reacted Si particles, m
3
where R ϭ 8.314 (J/mol/K) is the gas constant. These equations
can be used to estimate the production rate of SiHCl at 623 р T
р 723 K and 0.15 р cHCl р 1.8 mol/m .
3
V0 the volume of the unreacted Si particles, m
␳
3
density of crystalline Si, kg/m
3
3
References
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͑
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2
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1
66 ͑1991͒.
1
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