A numerical model of silane pyrolysis in a gas-solids fluidized bed

A numerical model of silane pyrolysis in a gas-solids fluidized bed C. Guenther Fluent Incorporated, Morgantown, WV T. O Brien National Energy Technology Laboratory, Morgantown, WV M. Syamlal Fluent Incorporated, Morgantown, WV Abstract Recent experiments have shown that silane pyrolysis in a gas-solids fluidized bed may be an attractive way to produce ultra-pure silicon. Such a process would possess the general advantages of fluidized bed technology, namely, good contacting, thermal homogeneity, thorough mixing of particles, easy solids handling, and low pressure drop. Such a fluidized bed reactor is simulated using the two-fluid hydrodynamic model MFIX (Multiphase Flow with Interphase exchanges; www.mfix.org), developed at the National Energy Technology Laboratory. Using MFIX three-dimensional simulations of silane pyrolysis are performed. The chemistry is described by a simple set of homogeneous and heterogeneous reactions. Results are compared to available experimental data where silicon deposition rates on a bed of alumina particles were measured as a function of temperature, bed height, and fluidization velocity. Keywords: ultra-pure silicon; silane pyrolysis; fluidized bed; two-fluid model; reactive fluidized bed This research was supported by the DOE-OIT Chemical Industries of the Future, administered through Oak Ridge Institute for Science and Education under the direction of Dr.Thomas O Brien. Correspondence to: Fluent Inc., 3647 Collins Ferry Road, Morgantown, WV 26505, E-Mail: cpg@fluent.com 1

1 Introduction Although silicon is the second most abundant element in the Earth s crust, exceeded only by oxygen, it is quite reactive and is only found naturally in an oxidized form, silicon dioxide (as crystalline or amorphous minerals) or in the more abundant and wide-spread silicates. To produce commercial silicon (Si), silicon dioxide (SiO 2 ) is reduced by reaction with coke in large electric furnaces to produce an impure elemental product. This metallurgical grade Si requires further refinement to meet industrial needs, especially the demand for ultra-pure silicon in the microelectronic and solar industries. The conventional Siemens process for the production of ultra-pure silicon involves the reduction of silicon tetrachloride (SiCl 4 ) or trichlorosilane (SiHCl 3 ) by hydrogen (H 2 ). The product, silicon, is deposited on hot (T 1150 o C) filaments. Despite the popularity of this approach there are several obvious disadvantages, that include batch operation, high energy requirements, and harsh byproducts. Alternative approaches, using fluidized bed technology, have been suggested by [1]-[4]. In these approaches silane (SiH 4 ) is pyrolyzed in a fluidized bed and silicon is deposited onto the surface of bed particles. Some of the advantages of this process over the traditional route are lower energy consumption, easy solids handling, continuous operation, and the absence of harsh byproducts. Currently, as with all fluidized bed processes, there are no well established methods for scale-up. The design of fluidized bed reactors is usually based on a collection of empirical correlations which quantify concepts such as the minimum fluidization velocity, bed expansion, and bubble properties. These correlations were derived from many man-years of experimental study of fluidized beds ([5]-[6]). However, it is still difficult to integrate this information into a comprehensive model of fluidized beds because of the inability to predict these quantities accurately and to analyze their interactions. This becomes especially difficult for models which attempt to predict, not only bed dynamics, but also heat transfer and chemical reactions. Recently, [7] and [8] modified several of the classical fluidization models found in the literature to include the variation of gas flow-rate due to chemical reactions. However, these new models only considered mass transfer between a single spherical bubble and the emulsion phase, neglecting the more complex features inherent to fluidized beds such as complex mixing, bubbles splitting and coalescing, and gas-solids circulation rates and patterns. Bubbles (regions with very few particles), significantly affect reactor performance; the motion of these voids maintains uniform bed temperature and promotes mixing, although this allows reactant bypassing. So, it is essential for models of fluidized bed processes to accurately predict bubble characteristics and transient behavior. In this paper an alternative method for simulating fluidized bed reactors is presented using the two-fluid hydrodynamic model MFIX (Multiphase Flow with Interphase exchanges; www.mfix.org) developed at the National Energy Technology Laboratory [9]. The idea of describing fluidized beds with two-fluid hydrodynamic models has existed 2

since the early 60 s ([10]-[12]). The resulting equations set forth by these researchers are very difficult to solve, and numerical solutions that predict bubbles came much later ([13]-[19]). These studies, as well as the majority of other numerical investigations, were restricted to two-dimensions because of computational costs. Three-dimensional studies using two-fluid models are rarely found in the literature and the few that do generally use very low-order spatial discretization techniques such as first-order upwinding (FOU) to improve convergence. Unfortunately, this type of approach is typically unsatisfactory because of the large amount of numerical diffusion inherent to FOU [19]. One of the primary objectives of this paper is to demonstrate the importance of conducting highorder three-dimensional simulations especially when chemical reactions are present and explicit tracking of species concentrations is required. This paper begins with details of the physical models and numerical techniques used in the simulations. Grid independence is established which is essential to ensure the bed hydrodynamics predicted by MFIX is the true solution of the governing equations. With grid independent simulation results, a global reaction kinetics scheme [3] and a more detailed scheme [4], are compared with experimental data of [4] where silicon deposition rates on a bed of alumina particles were measured as a function of temperature, bed height, and fluidization velocity. 2 Mathematical Model 2.1 Two-Fluid Model Two-fluid hydrodynamic models, also referred to as Eulerian-Eulerian models, treat the fluid and solids as two continuous and fully interpenetrating phases. This approach results in mass, momentum, and energy balance equations for both the gas and solids phases. For isothermal conditions, the continuity, momentum balance, and species balance equations for two phases (gas and solids) with chemical reactions are given below. Gas-phase continuity Solids-phase continuity Gas-phase momentum ε g ρ g v t g ε g ρ t g ε s ρ t s ε g ρ g v g ε s ρ s v s N g R gn (1) n 1 N s R sn (2) n 1 ε g ρ g v g v g ε g P g τ g F gs v s v g 3

ε g ρ gg R 0 ξ 0 v s ξ0 v g (3) Solids-phase momentum ε t s ρ sv s ε s ρ sv sv s ε s P g S s F gs v s v g ε s ρ sg R 0 ξ 0 v g ξ0 v s (4) Species balance ε t m ρ m X mn ε m ρ m X mnv m R mn (5) where m g s for the gas(solids) phase and ξ 0 1 ξ 0 and ξ 0 1 if R 0 0; else ξ 0 0. The eight dependent hydrodynamic variables in 3D: void fraction ε g (the solids fraction ε s 1 ε g ), pressure P g, and six velocity components are found by using MFIX to numerically solve the coupled non-linear partial differential equations (1)-(5). The number of species mass fractions (X mn ) tracked are given in Section 4.1. Constitutive relations, needed to close the system (1)-(4), can be found in [9]. 3 Numerical Procedure The governing set of partial differential equations (1)-(5) are solved on the computational domain with a finite number of cells or control volumes [20]. Nodal points are located at cell centers where scalars (pressure, voidage, etc.) are stored. Velocities are defined at cell faces by using a staggered grid [21]. The finite volume method integrates the equations over each cell which, for a general property φ, produces a discretized set of equations of the form a P φ P a nb φ nb nb S P (6) where the P is the nodal point and the subscript nb represent contributions from surrounding cell faces. The partial elimination algorithm [22] is used to uncouple the discretized momentum equations due to the gas-solids drag. Using an extension of SIMPLE [21], a sequential iterative procedure is used to solve (6) and a solids volume fraction correction equation [20] adjust velocities in order to satisfy conservation of mass in both phases. One of the key features of the finite volume method is the need to calculate convective fluxes at cell faces. Recent investigations [19] have shown that this step is crucial for accurately predicting bubble dynamics. To summarize this important point, [19] used the universal limiter [23] and deferred correction [24] to implement high-order approximation of cell face contributions. The universal limiter prevents non-physical numerical oscillations; the deferred correction method retains the desirable stability properties of a low order method, in this paper first-order upwinding (FOU), to form the algebraic system 4

given by (6). In this paper high-order cell face fluxes were approximated using the Superbee method. Superbee was chosen because of its superior performance over other second order methods [19]. To capture the resolution of a higher order method an additional source term is added The additional source term is given by a P φ P a nb φ nb S P S DC (7) nb S DC! ε m ρ m" f v m" f φ LO # φ HO " f A f (8) where A f is the area of the cell face f and the subscript m g(s) for the gas(solids) phase. Equation (7) is derived by adding and subtracting FOU convection terms to the higher order convection terms. The difference between the higher order convection terms and the FOU convection terms are combined to form the source term S DC. The added FOU convection term appears implicitly in the coefficients a P and a nb. Since the added and subtracted FOU convection term cancel out, at convergence there is no net contribution to equation (7) from φ LO. Therefore, at convergence the discretization used in equation (7) is purely higher order. 4 Experimental and Numerical Results The reaction vessel used in the experiments is a 5.3 cm (ID), 63 cm long, stainless steel cylinder, surmounted by a 11.2 sloping transition section, joined to a 17.7 cm tall expansion zone [4]. A mixture of silane (SiH 4 ) and nitrogen (N 2 ) is introduced into the reactor through a stainless steel perforated plate distributor. Gases exit the reactor through a 2 cm (ID) tube in the center of the top plate. In the experiments of [4], alumina particles (Al 2 O 3 ) were employed as seed particles, rather than ultra-pure silicon particles, claiming that this change in the nature of the seed particles did not affect the deposition process. The average size of the particles is 82 µm with a density of 3.9 g/cm 3 and a minimum fluidization velocity of 1.3 cm/s. 4.1 Chemical Model In this paper two chemical schemes have been implemented to describe the chemistry of the pyrolysis of silane. The first is a global scheme corresponding to the following overall reaction SiH 4 $ Si+2H 2 where two gas species (SiH 4, H 2 ), and two solids species, (Si, Al 2 O 3 ), were tracked using (5). Reaction mechanisms for the kinetics can be found in [3]. In addition to this global 5

mechanism, a more detailed description of the chemistry was considered, initiated by the reversible, homogeneous reaction SiH 4 % SiH 2 +H 2. The highly reactive silylene (SiH 2 ) can participate in a series of reactions to form higher order silanes. In this paper we only consider the homogeneous reaction to form disilane (Si 2 H 6 ) SiH 2 +SiH 4 % Si 2 H 6. Heterogeneous decomposition of SiH 4 and SiH 2 is described by the irreversible reactions; SiH 4 & Si(s)+2H 2, SiH 2 & Si(s)+H 2. For these reactions four gas species (SiH 4, H 2, SiH 2, and Si 2 H 6 ), and two solid species (Si, Al 2 O 3 ), were tracked. Details of this reaction mechanisms can be found in [3] and [4]. 4.2 Grid Independence and MFIX Results In order to establish grid independent solutions several simulations were performed neglecting chemical reactions. The number of cells was kept constant in the radial and axial directions with 25 and 80 cells respectively, which has been determined to be grid independent in two-dimensions. Beginning with a 2-dimensional simulation with symmetry, the number of cells was incrementally increased in the azimuthal or z-direction. To demonstrate the importance of using high-order methods, a single simulation using first-order upwinding (FOU) was included. For this simulation 24 cells in the z-direction were used. Simulations were run for 3.6 seconds and time averaged over the final 2.6 seconds of each run. Because of the chaotic nature of fluidized beds we use the term grid independence as a qualitative measure for determining when grid independent average bed behavior has been reached rather than a point to point convergence criteria. Figure 1 shows the axial profiles of the solids volume fraction averaged over both time and the radial direction. Clearly, a qualitative change in the bed expansion occurs when the resolution of the higher-order simulations are increased from 4 to 12 z-cells. However, the FOU over predicts the bed expansion despite the increased resolution in the z-direction. According to this measure the calculation has converged with 12 z-cells using the higher order method. Voidage profiles are shown in Figures 2 and 3 as a function of radial position, averaged over different horizontal sections of the bed. Again, a qualitative change in the profiles is clear as the grid is refined from 4 z-cells to 12 z-cells and grid independence is reached with 24 z-cells. In the transient results voids or bubbles which form at the bottom of the bed migrate towards the center of the reactor as they travel upwards. 6

Height (cm) 60 40 20 2-D FOU 4 z-cells 12 z-cells 24 z-cells 36 z-cells 0 0 0.25 0.5 0.75 1 Solids Volume Fraction Figure 1: Axial Profile of the Solids Volume Fraction. 7

' ' 0.68 0.68 0.64 0.64 Voidage 0.6 Voidage 0.6 0.56 0.56 0.52 0.52 Figure 2: Radial Voidage Profiles Averaged Over Time and the Heights 2-10 cm and 10-20 cm. This behavior is shown in Figures 2 and 3. On the other hand, the 2-D simulation and FOU both predict very different qualitative behavior i( e(, higher voidage away from the center of the bed and significant under prediction of the solids concentration at the wall in the lower regions of the bed. The results using MFIX to model silane pyrolysis in a gas-solids fluidized bed are presented using the Superbee method with 24 cells in the z-direction. Due to the limited space available only the results of run S5 will be shown. Figures 4 and 5 show the gas phase mass fractions for run S5 using the detailed chemistry scheme. These results have been time-averaged and, since the chemical reactions are mainly confined to the lower region of the reactor, results have been averaged over the bottom 10 centimeters of the bed. Figures 4 and 5 also include the results of both a 2-D simulation with symmetry and FOU with 24 z-cells. Experimental conditions and outlet concentrations of H 2 predicted by the high-order three-dimensional simulations for runs S2-S14 are summarized in Table 1. RUN T( o C) M po (g) H o (cm) y o (%) U o /U m f ȳ H2 (%) MFIX ȳ H2 (%) S2 606.8 1338.6 30.6 5.0 5.47 9.52 9.0 S5 609.3 1358.1 33.2 14.0 6.07 24.5 23.6 S12 596.1 2046.0 48.0 25.0 6.85 40.0 39.0 S14 598.4 1315.7 30.5 9.29 17.06 17.0 17.0 Table 1: Experimental conditions and MFIX results. 8

' ) ' * 0.68 0.72 0.64 0.67 Voidage 0.6 Voidage 0.62 0.56 0.57 0.52 0.52 Figure 3: Radial Voidage Profiles Averaged Over Time and the Heights 20-30 cm and 30-34 cm. 0.035 0.018 Mass Fraction SiH4 0.025 0.015 Mass Fraction H2 0.014 0.01 0.005 0.006 Figure 4: Radial Mass Fraction Profiles of SiH 4 and H 2. 9

) ) 3e-07 0.0055 Mass Fraction SiH2 2e-07 Mass Fraction Si2H6 0.0045 0.0035 0.0025 0.0015 5e-08 0.0005 Figure 5: Radial Mass Fraction Profiles of SiH 2 and Si 2 H 6. Similar high-order three-dimensional simulations were conducted using the global chemistry scheme. These results showed very little difference in the mass fraction of SiH 4 and H 2, as well as, outlet concentrations of H 2. Hence, these results are not shown. The fact that very little difference was observed between the global and detailed schemes suggests that the dominate reaction mechanism is certainly due to the heterogeneous reaction. Finally, when the effects of the chemistry (global or detailed) were included, CPU times increased by roughly a factor of 10 with the detailed scheme being only slightly more expensive than the global scheme. 5 Conclusion This investigation has demonstrated that two-fluid models can be used to accurately model silane pyrolysis in a gas-solids fluidized bed. The results showed excellent agreement with experimental outlet concentrations of hydrogen and established that either a global or detailed chemistry scheme can be used with similar accuracy and computational effort. Many researchers still continue to perform two-dimensional simulations with symmetry and/or three-dimensional FOU simulations because of the obvious reduction in CPU times. However, this investigation has demonstrated that these techniques can predict qualitatively different bed dynamics and species concentrations compared to those calculated using high-order three-dimensional simulations. 10

References [1] M. Dudukovic, 1983. Reactor models for cvd of silicon, JPL Publication, 83-13, 199-226. [2] G. Hsu, A. Morrison, N. Rohatgi, R. Lutwack, T. MacConnell, 1984. Fluidized bed silicon deposition, IEEE, 553-557. [3] T. Furusawa, T. Kojima, H. Hiroha, 1988. Chemical vapor deposition and homogeneous nucleation in monosilane pyrolysis within interparticle spaces, application of fines formation analysis to fluidized bed cvd, Chem. Engng. Sci., 43, 2037-2042. [4] B. Caussat, M. Hemati, J. Couderc, 1995. Silicon deposition from silane or disilane in a fluidized bed part 1: experimental study, Chem. Engng. Sci., 50, 3615-3624. [5] D. Geldart, 1986. Gas Fluidization Technology, John Wiley & Sons, New York. [6] D. Kuni and O. Levenspiel, 1976. Fluidization Engineering, John Wiley & Sons, New York. [7] B. Caussat, M. Hemati, J. Couderc, 1995. Silicon deposition from silane or disilane in a fluidized bed Part II: theoretical analysis and modeling, Chem. Engng. Sci., 50, 3615-3624. [8] B. Caussat, M. Hemati, J. Couderc, 1999. Local modeling of mass transfer with chemical reactions in a gas-solid fluidized bed. Application to the chemical vapor deposition of silicon from silanes, Powder Technol., 101, 43-55. [9] M. Syamlal, W. Rogers, and T. O Brien, 1993. MFIX documentation: theory guide, Technical Note, DOE/METC-95/1013. [10] J. Davidson, 1961. Symposium on Fluidization-Discussion, Trans. Inst. Chem. Eng., 39, 230-232. [11] R. Jackson, 1963. The mechanics of fluidized beds: Part 1; the stability of the state of uniform fluidization, Trans. Inst. Chem. Eng., 41, 13-21. [12] T. Anderson and R. Jackson, 1967. A fluid mechanical description of fluidized beds, I&EC Fundam., 6, 527-534. [13] D. Gidaspow, Y. Seo, B. Ettehadieh, 1983. Hydrodynamics of fluidization: experiments and theoretical bubble sizes in a two-dimensional bed with a jet, Chem. Eng. Comm., 22, 253-272. 11

[14] J. Bouillard, D. Gidaspow, and R. Lyczkowski, 1991. Hydrodynamics of fluidization: fast-bubble simulation in a two-dimensional fluidized bed, Powder Technol., 66, 107-118. [15] J. Kuipers, K. van Duin, F. van Beckup, and W. van Swaaij, 1993. Computer simulation of the hydrodynamics of a two-dimensional gas-fluidized bed, Computers Chem. Engng., 17, 839-858. [16] J. Sanyal and E. Cesmebasi, 1994. On the effect of various momentum transfer coefficient models on bubble dynamics in a rectangular gas fluidized bed, Chem. Engng. Sci., 49, 3955-3966. [17] A. Boemer, H. Qi, and U. Renz, 1997. Eulerian simulation of bubble formation at a jet in a two-dimensional fluidized bed, Int. J. Numer. Methods Eng., 23, 927-944. [18] M. Syamlal and T. O Brien, 1989. Computer Simulations of bubbles in a fluidized bed, AIChE Symposium Series on Fluidization and Fluid Particle Systems: Fundamentals and Applications, 85, 22-31. [19] C. Guenther and M. Syamlal, 2001. The effect of numerical diffusion on isolated bubbles in a gas-solid fluidized bed, Powder Technol., To Appear. [20] M. Syamlal, 1998. MFIX documentation, numerical technique, EG&G technical report, DE-AC21-95MC31346. [21] S. Patankar, 1980. Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York. [22] D. Spalding, 1980. Numerical computations of multiphase flow and heat transfer, recent advances in numerical methods in fluid mechanics, C. Taylor and K. Morton eds., Pineridge, Swansea, 139-168. [23] B. Leonard and S. Mokhtari, 1990. Beyond first-order upwinding: the ultra sharp alternative for non-oscillatory steady-state simulation of convection, Int. J. Numer. Methods Eng., 30, 729-766. [24] S. Rubin and P. Khosla, 1982. Polynomial interpolation method for viscous flow calculations, J. Comput. Phys., 27, 153-168. 12