FLUID FLOW AND TRANSPORT PHENOMENA
Chinese Journal of Chemical Engineering, 19(1) 1—9 (2011)
Effect of Boundary Layers on Polycrystalline Silicon Chemical Vapor Deposition in a Trichlorosilane and Hydrogen System*
ZHANG Pan (张攀)1, W ANG Weiwen (王伟文)2, CHENG Guanghui (陈光辉)2 and LI Jianlong (李建隆)2,**
1 Institute of Electronmechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, China
2 Institute of Chemical Engineering, Qingdao University of Science and Technology, Qingdao 266042, China
Abstract This paper presents the numerical investigation of the effects of momentum, thermal and species bound-ary layers on the characteristics of polycrystalline silicon deposition by comparing the deposition rates in three chemical vapor deposition (CVD) reactors. A two-dimensional model for the gas flow, heat transfer, and mass trans-fer was coupled to the gas-phase reaction and surface reaction mech
anism for the deposition of polycrystalline sili-con from trichlorosilane (TCS)-hydrogen system. The model was verified by comparing the simulated growth rate with the experimental and numerical data in the open literature. Computed results in the reactors indicate that the deposition characteristics are closely related to the momentum, thermal and mass boundary layer thickness. To yield higher deposition rate, there should be higher concentration of TCS gas on the substrate, and there should also be thinner boundary layer of HCl gas so that HCl gas could be pushed away from the surface of the substrate immediately.
Keywords boundary layer, polycrystalline silicon, numerical simulation, mass diffusion
1  INTRODUCTION
Chemical vapor deposition (CVD) is a synthesis process of the deposition of a solid on a heated surface from a chemical reaction in the vapor phase. With CVD, it is possible to produce most metals, many nonmetal-lic elements such as carbon and silicon as well as a large number of compounds including carbides, ni-trides, oxides and many others. The CVD technology integrates several scientific and engineering disci-plines including thermodynamics, plasma physics, kinetics, fluid dynamics, and of course chemistry. In order to understand the complex transport phenomena, various types of reactor
configurations such as hori-zontal reactor [1], impinging jet and rotating disk re-actor [2], pancake reactor [3], and vortex enhanced reactor [4] have been investigated. The effects of many factors on the deposition characteristics of a CVD re-actor were also discussed, such as the choice of pre-cursor gases and carrier gas [5], their respective flow rates [6], the total pressure in the reactor [7], the sub-strate temperature [8, 9], the substrate position [10], the substrate geometry [11, 12], the substrate rotation rate [13], and the tilted substrate [14, 15].
Many researchers paid more attention to the ef-fects of the macroscopical structure of the reactors, but the effects of the boundary layer characteristics at the substrate in the deposition process were less ad-dressed in the CVD reactor. The rate-limiting step of a CVD reactor is generally determined either by the surface reaction kinetics or by mass transport [16-18]. When the process is limited by mass-transport phe-nomena, the controlling factors are the diffusion rate of the reactant through the boundary layer and the diffusion out of the gaseous by-products through this layer. Thus the boundary layer characteristics have vital effect on the CVD of polycrystalline silicon.
It has been recognized that numerical models based on computational fluid dynamics (CFD), accounting for the interaction between gas flow, heat and mass transfer and chemical reactions, can be of great help in the optimization of CVD equipment and processes. Besides, CVD numerical models
may provide funda-mental insights into the underlying physico-chemical processes. In last few decades, many numerical stud-ies of CVD processes have been performed, which can be roughly divided into tow categories: (1) CVD re-actor studies (as those mentioned above), in combina-tion with rather simple descriptions of the CVD chem-istry; (2) CVD chemistry studies [19-22], in combina-tion with simple 0-dimensional (0-D) or 1 dimensional (1D) hydrodynamic models. Recent years, enabled by the ever increasing computer performance, it has be-come possible to combine detailed descriptions of transport phenomena and reaction chemistry into a single computational model [23]. But for the trichloro-silane (TCS)-hydrogen system, it is still a challenge.
In this study, a two-dimensional model for the gas flow, heat transfer, and mass transfer was coupled to the detailed mechanism of gas-phase reaction and surface reaction for the deposition of polycrystalline silicon from TCS-hydrogen system. The model was used to study the boundary layer characteristics in three CVD reactors with a flat substrate, a tilted sub-strate and an additional rib placed on the upper wall, respectively, and investigate the effects of the bound-ary layer characteristics on the polycrystalline silicon
Received 2010-06-11, accepted 2010-11-16.
* Supported by the Natural Science Foundation of Shandong Province of China (ZR2009BM011), and the Doctor Foundation of Shandong Province of China (BS2010NJ005).
** To whom correspondence should be addressed. E-mail: jlong_li@hotmail
Chin. J. Chem. Eng., Vol. 19, No. 1, February 2011
2 deposition rate, and the uniformity of the deposited polycrystalline silicon in the TCS-H 2 system. 2  PHYSICAL MODEL 2.1  Reactor geometry
In view of computational costs, a two-dimensional (2-D) model coupled with gas phase reaction and sur-face reaction is considered for three CVD reactors illustrated in Fig. 1. The overall geometry of the model in Fig. 1 (a) is identical to that employed by Habuka et al  [24]. In Fig. 1 (b), the substrate is tilted with an angle of 7°. In the third reactor in Fig. 1 (c), an additional rib is placed on the center of the upper wall. The dimension of the rib is 6 mm (width) ×10 mm (height). The three reactors have same overall dimensions, and the same conditions otherwise are
imposed on them.
(a) A flat reactor
(b) A tilted reactor
(c) A rib reactor
Figure 1  Geometry and internal structure of studied re-actors
A mixture of TCS and H 2 enters the reactors at the top left corner and exits through the lower right corner. The substrate surface is held at a fixed tem-perature. The gases react in the reactors depositing the desired solid silicon film on the surface of the sub-strate. Finally, the reactant and product gases leave the reactors through the outlet, which is fixed at atmos-pheric pressure. 2.2  Transport models
As the deposition rate are strongly influenced by the complex transport phenomena of reacting mixtures in the CVD reactor, detailed computational modeling of the gas flow, temperature distribution and species transport in the reactor is of vital importance. The model of the three CVD reactors involves four pri-mary governing equations: mass conservation (or con-tinuity), momentum conservation, energy conservation, and species conservation. It describes the turbulent flow of an incompressible gas with properties that depend on the local temperature. With the above as-sumption, the governing equations can be expressed as follows:
Continuity equation:
()0i i
u t x ρρ∂∂+=∂∂            (1) Momentum equation:
()()ij i i j i i j i j
p u u u g F t x x x τ
ρρρ∂∂∂∂+=−+++∂∂∂∂  (2) Energy equation:
()()()eff eff
i i j j j ij h j i
i E u E p t x T k h J u S x x ρρτ′′′∂∂
⎡⎤++=⎣⎦∂∂∂
∂⎛⎞
−++⎜⎟∂∂⎝
⎠
∑    (3) where k eff  is the effective thermal conductivity coeffi-cient (including the molecular and turbulent thermal conductivity). The effect of heat transfer by radiation on the substrate temperature is ignored. Since the concentrations of TCS and HCl are low, the effects of radiation heat on these gases are also assumed to be negligible. The last term on the right-hand side de-scribes the consumption and production of heat due to the chemical reactions. Although for most CVD sys-tems, especially when the reactants are highly diluted in an inert carrier gas, the heat of reactions has a neg-ligible influence on the gas temperature distribution, the source term is accounted for in the simulation.  Mass equation:
()()i i i i i Y Y R S t
ρρ∂
+∇⋅=−∇++∂v J    (4) where J i  is the diffusion flux of species i . For thermal CVD, the relevant driving forces for diffusion are the
Chin. J. Chem. Eng., Vol. 19, No. 1, February 20113
concentration and temperature gradients. Since the mass fractions of all species must sum up to unity, this equation is solved for all species except the carrier gas H2. At steady-state, the transport of the reagent species to the substrate surface is balanced by the surface re-action rate. The deposition reaction is considered as a boundary condition on the species transport equation.
2.3  Chemical reaction
The knowledge of the detailed gas phase and surface chemistry involved in the deposition process is of fundamental importance. During the last years a great effort was devoted to the comprehension of the reactions involved in silicon deposition. We adopted TCS chemistry primarily because of the broad appli-cation of polycrystalline silicon [25-27]. TCS decom-position kinetics was compiled by Ho et al. [28], who pointed out that SiCl2 has a high desorption rate and thus assumed TCS as the most important precursor. Valente et al. [29] analyzed the kinetics of the HCl and SiCl2 adsorption and deposition, updating the original mechanism in Ref. [28]. The overall mechanism is taken from the literature and summarized in Table 1.
Table 1 The mechanisms of the chemical reactions and surface reactions in trichlorosilane and hydrogen system (G: gas-phase reaction, F: surface reaction)
No. Reaction lg AβE a Ref.
G1 TCS SiCl2+HCl 14.69
0.0
308582[28]
G2 SiH2Cl2SiCl2+H2 13.92
0.0
324074[28]
G3 SiCl2H2HSiCl+HCl 14.94
0.0
66155[28]
G4 Si2Cl5H SiCl4+HSiCl 13.7
0.0
218980[28]
G5 Si2Cl5H SiCl3H+SiCl2 13.9
0.0
188415[28]
G6 Si2Cl6SiCl4+SiCl2 14.2
0.0
200976[28]
F1 TCS+4σ→SiCl*+H*+2Cl* 8.05 0.5 −15911[30]
F2 SiH2Cl2+4σ→SiCl*+2H*+Cl* 8.58 0.5 −15911[30]
F3 SiCl4+4σ→SiCl*+3Cl* 9.84
0.5
−2814[29]
F4 3SiCl*→SiCl2+Cl*+2Si(s)+2σ 24.20 0.0 280529[29]
F5 2Cl*+Si(s)→SiCl2+2σ 24.2
0.0
280529[29]
F6 H2+2σ→2H* 11.36
0.5
72226[29]
The decomposition of TCS and SiH2Cl2 are con-sidered as the most important reactions in the gas-phase reaction mechanism. About the surface chemistry, three adsorbed species were considered: H*, Cl* and SiCl* [29]. All gaseous species adsorb dissociatively on the surface leading to the formation of
adsorbed hydrogen and chlorine, and SiCl* through reactions.
2.4 Turbulent model and numerical method
Reynolds numbers in CVD reactors are usually quite low, and as a consequence the gas flow is as-sumed to be laminar [15, 31, 32]. But these low Rey-nolds numbers in combination with quite large tem-perature difference (up to 1000 K) can lead to signifi-cant interactions between forced and free convection in the CVD equipment. The mixed convection can be an important factor influencing heat, mass transfer and chemistry. van Santen et al. [33] found that turbulence can increases the heat flux, which offer the possibility for a high deposition rate. Thus, the low-Reynolds- number k-ε turbulent model was used to simulate the turbulent transport [22].
The governing equations coupled with the bound-ary conditions have been solved using a commercially available software package FLUENT, which is based on the finite volume method (FVM) to discretize the non-linear partial differential equations of the model, and the segregated solution algorithm has been se-lected. For the pressure-velocity coupling, the SIM-PLE (Semi-Implicit Method for Pressure-Linked Equa-tions) method was used.
The geometry and the mesh are created using GAMBIT 2.2 starting from its primitives (shown in Fig. 1)
. Numerical tests are carried out using 2300, 4800 and 6600 cells to evaluate the effect of mesh size on the calculated results. Comparison of 4800 cells velocities estimates with 6600 cells estimates showed a mean relative difference of 0.87% and a root mean square difference of 2.8%. The computational grid is defined by hexahedral cells, non-uniformly distributed, with a total of 4800 cells.
Compared to the solution of the hydrodynamics problem, the solution of the accompanying chemical reactions is not a trivial task because it gives the im-portant chemical source terms in the aforementioned governing equations. Especially for the surface reac-tion in the study, the transport process (diffusion) that carries species to and from the surface may be com-parable in rate to that of reaction at the surface. Transport and reaction have to be solved simultane-ously as a set of nonlinear algebraic equations at each node on the reacting surface. The numerical stiffness of the multi-dimensional multi-species transport cou-pled detailed CVD chemistry models leads to poor convergence, excessive computation time, and unreli-able predictions.
Thus, computationally efficient methods are needed for simulating CVD reacting flows. Different numerical methods have been developed to solve these nonlinear equations introduced by the chemistry [34, 35]. Available approaches include direct integra-tion (DI) in the FLUENT package, and DI is computa-tionally expensive in CVD simulation.
The in-situ-adaptive tabulation (ISA T) method [36], which is an effective preconditioning technique, was used to implement detailed chemical kinetics. Since the chemical source term is computationally costly, a pre-computed chemical look-up table is calculated and stored for a set of representative initial conditions in the composition space. Then, numerical interpolation is used to find the values based on the neighboring points, replacing DI operation in the simulation.
Chin. J. Chem. Eng., Vol. 19, No. 1, February 2011
4 The turbulence-chemistry interactions were com-puted by Eddy-Dissipation- Concept (EDC) model [37]. The results presented in this paper were obtained using the second order scheme for spatial discretization of the momentum equations and species transports equations. For pressure, linear discretization was used. A con-vergence criterion of 1×10−6 was used for continuity, momentum, energy and species transport equations. 2.
5  Boundary condition and gas properties
At the inlet, the velocity distribution is consid-ered uniform; the gas feed is assumed to be uniform at 3
00 K. The mass fraction of the species in the inlet mixture is specified. A no-slip and an adiabatic or a temperature condition is imposed on the side walls, respectively as shown in Fig. 1 (a), and the substrate boundary is set to a constant temperature. A thermal conductivity of 204 W·m −1·K −1 was applied for the susceptors.
Some reasonable simplifying assumptions have been made to reduce the complexity of the numerical problem: the gases, being highly diluted in hydrogen, obey the ideal gas law and Newton’s law of viscosity; the gaseous mixture behaves as continuum under steady state conditions; pressure variations in the en-ergy equation are neglected as the Mach number is very small.
The viscosity and thermal conductivity of the gas species may be calculated from the kinetic theory. The coefficients of the specific heat capacity polynomial and the Lennard-Jones parameters (the characteristic energy and the collision diameter) were taken from Ref. [38].
Mixture gas density is estimated based on the ideal gas law [39, 40]:
i
i
i
Y p RT m ρ=∑
(5) The full multi-component diffusion model is used to calculate the ordinary diffusion, because the mass fraction of the hydrogen reagent species is too large for it to be considered dilute. 3  RESULTS AND DISCUSSION 3.1  Model validation
In order to ascertain proper functioning of the model, the operation conditions and boundary condi-tions applied by Habuka et al . [24] were used, so that the computed results can be compared with those ob-tained previously for the flat reactor [Fig. 1 (a)] [41].
The comparison between the average growth rates obtained from various models at the flat substrate is presented in Fig. 2. It can be derived that the model predicts the growth rate. More detailed can be seen in Ref. [42]
.
Figure 2  Growth rates obtained from the model presented and those presented in the literature  (T s =1389 K, p =0.1 MPa) △ the present model; × Habuk calculated in Ref. [24]; ○ Habuk measured in Ref.
[24];  Coso calculated in Ref. [41]
3.2  Velocity boundary layer
Some work [12, 32, 43, 44] revealed that the tilted susceptor can produce a greater deposition rate and a more uniform distribution of material than a non-tilted susceptor. Cheng and Hsiao [12] also concluded that the deposition rate can be improved if a rib was placed at the center of the susceptor. So we have selected the three reactors (shown in Fig. 1) to detect the effects of the various boundary layers on polycrystalline silicon CVD in the TCS-H 2 system. The follow results are obtained with the same boundary conditions at the three reactors, which were employed that an inlet ve-locity of 0.67 m·s −1, an inlet TCS mole concentration of 0.05, inlet temperature of 300 K, surface tempera-ture of the substrate of 1398 K and the atmospheric pressure (as applied in [24]).
The deposition rates along the three substrates are shown in Fig. 3. The average deposition rates at tilted substrate and at the substrate in the rib reactor reach 8.0 and 10.4 µm·min −1, which are 1.5 and 1.9 times that at the flat substrate, respectively. The polysilicon deposition rate along the flat substrate is large firstly and then becomes smaller. For the tilted substrate and the substrate in the rib reactor, the varia-tion trend of deposition rate is similar to that at the flat substrate. And there is a hump at the c
enter at the sub-strate in the rib reactor. The growth rates at the tail section of the substrates are all decreasing, and that at tilted substrate sharply decrease. Generally, this dif-ference in deposition rate is mostly considered due to a change in the velocity boundary layer thickness along the substrate [16, 45, 46]. The nominal boundary layer is thin at the beginning and increases along the substrate (qualitatively shown as Fig. 4), and it is the most thinnest at the center of the substrate with addi-tional rib, that leads to a difference in the deposition rate as shown in Fig. 3.
And the velocity boundary layer characteristics can not explain the change of the deposition rate at the beginning and at the tail section of the substrates, but also not explain that the deposition rates at the tilted substrate and at the substrate with additional rib are
Chin. J. Chem. Eng., Vol. 19, No. 1, February 2011 5
higher than that at the flat substrate. 3.3  Profiles of Nu  number
reaction rateIt has been shown that the distribution of the lo-cal heat flux on the susceptor can be closely related to
the growth rate and the uniformity of the deposition in the CVD reactor [12, 44]. Therefore, the local heat flux, in terms of Nusselt number (Nu ), on the heated sub-strate is calculated to identify the effects of the sub-strate tilting and the additional rib on the heat flux and the uniformity of deposition. Fig. 5 shows the com-
parison of the isotherm at the three CVD reactors. It
can be seen that the tilted substrate and the additional rib result in thinner boundary layer and higher t
em-perature gradient. The retardation of the growth ther-mal boundary layer and the increase of temperature gradient could yield an increased average heat flux. The computed Nusselt number distributions along the three substrates are shown in Fig. 6. It can be seen that the Nusselt numbers are large at the frontier and small at the tail section. This non-uniformity is due to the heat dissipation through the substrate, and the tem-perature decrease sharply along the substrates. This phenomenon can explain that the deposition rates are low at the frontier and the tail section.
We conclude that there is a similar trend between the deposition rate and the local heat flux along the substrate [Figs. 3 and 6 (b)]. The Nusselt numbers at the tail section of the substrate in the rib reactor are less than those at the same section of the tilted sub-strate. The deposition rate also has the same trend.
Comparisons of the computed results for the tilted substrate reveal that the converging channels is in favor of an increase of heat transfer as compared to a flat substrate. Moreover, this geometry can effec-tively improve the uniformity of heat flux distribution and deposition rate on the substrate. The uniformity of heat flux distribution at the substrate in the rib reactor is worse. But the addition of the rib enhances the heat flux on the substrate. The mean Nesselt numbers at the tilted substrate and at the substrate with rib are 90.2, 102.1, which are 1.99 and 2.25 times that at the flat substrate, respectively.
The local heat transfer on the substrate is taken as a qualitative measure of the depo-sition rate, and the enhancement of heat transfer rate could lead to the improvement of deposition rate [12]. The results are consistent with the theory. 3.4  Mass transfer
However, this kind of understanding is not com-prehensive enough. For these CVD systems, the diffu-sion rates of the reactant through the boundary layer and the diffusion out through this layer of the gaseous by-products have primary effect on the deposition progress. Habuka et al . [47] considered that transport of TCS molecules to the substrate surface plays a dominant role in the silicon epitaxial growth in the TCS-H 2 system and concluded that the dominant chlorosilane species in the system is TCS gas, whereas HCl gas is a major product in a TCS-H 2 system.
In order to investigate the mass boundary layers of the above main species, we defined the seven equi-distant lines (named as a, b, c, d, e, f and g in Fig. 1) in the three reactors, respectively, which are from sub-strate to the upper wall, and perpendicular to the sub-strates. The molar concentration distributions of the two substances in the three reactors are shown in Figs. 7 and 8, respectively.
Figure 7 plots the molar concentration of TCS
against the vertical position above the substrates. It
Figure 3  Comparison of polysilicon deposition rates along the substrate  ☆ flat; ■ rib; △
tilted
(a) Flat reactor
(b) Tilted reactor
(c) Rib reactor
Figure 4  Velocity distributions in the three CVD reactors

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