NUMERICAL MODEL OF A FLUIDIZED BED REACTOR FOR POLYCRYSTALLINE SILICON PRODUCTION-ESTIMATION OF CVD AND FINES FORMATION

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1 NUMERICAL MODEL OF A FLUIDIZED BED REACTOR FOR POLYCRYSTALLINE SILICON PRODUCTION-ESTIMATION OF CVD AND FINES FORMATION T. Kimura, T. Kojima To cite this version: T. Kimura, T. Kojima. NUMERICAL MODEL OF A FLUIDIZED BED REACTOR FOR POLY- CRYSTALLINE SILICON PRODUCTION-ESTIMATION OF CVD AND FINES FORMATION. Journal de Physique IV Colloque, 1991, 02 (C2), pp.c2-103-c < /jp4: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1991 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE IV C2-103 COllOqUe cz, suppl. au Journal de Physique 11, Vol 1, septembre 1991 NUMERICAL MODEL OF A FLUIDIZED BED REACTOR FOR POLYCRYSTALLINE SILICON PRODUCTION-ESTIMATION OF CVD AND FINES FORMATION T. KIMURA and T. KOJIMA Department of Industrial Chemistry, Seikei University, Kichijojikita-machi, Musashino-shi, Tokyo 180, Japan Abstru- A numerical model of a fluidized bed reactor was developed for estimating rates of CVD and fines formation in polycrystalline silicon production from monosilane. In the model, Kunii-Levenspiel fluidized bed model and reaction kinetics were combined. The model predicts both the homogeneous decomposition to give fine powder and the heterogeneous CVD on seed silicon particles. The relative and quantitative contributions of both reactions were elucidated in fluidized bed bubbling zone including both bubble and emulsion phases. The present model also predicts the effects of operational conditions on the rates. The numerical values were compared with experimental data by ourselves and Hsu et al. The results indicated that fines mainly form in the bubble phase. Polycrystalline silicon for electronic use has been produced via Siemens bell-jar reactor by hydrogen reduction of trichlorosilane. The fluidized bed process by monosilane pyrolysis is an alternative to the conventional one and has several merits i.e., (1) high purity of produced silicon, (2) no hydrochloric gas, (3) lower reaction temperature, (4) high productivity of continuous operation. However, several significant problems have been pointed out: by-product of fines, clogging phenomena of defluidization by particle agglomeration, impurities of hydrogen and other elements in the product and so on. Especially in the fluidized bed CVD process for polysilicon production from monosilane, the elutriation and entrainment of the fine powders formed by the gas phase homogeneous reaction, and the quality or the morphology of the produced silicon were also found to be critical problems. The fine powder is easily contaminated in the course of the transportation, is difficult to handle in the later processes and possibly damages the quality of produced silicon by adhesion on its surface. It is essential for commercialization and scale up of this process to predict the effects of these phenomena quantitatively. Several models have been presented to simulate the rate of monosilane decomposition including both homogeneous nucleation and heterogeneous deposition in a fluidized bed reactor. Hsu et al. 111 estimated the fraction of fines formation as kf/(kf+ks) where kf is the fines formation rate of Hogness et al. 121 and ks is the heterogeneous deposition rate of Iya et al However, the estimated value (around 80% of silicon in feed) was much higher than the experimental data (around 10%) and they could not explain the effect of inlet silane concentration on the fraction of fines elutriation (Fine powders carried away from the fluidized bed by gases). Lai et al. /4/ developed an ideal backmixed model and a fluidized bed bubbling reactor model for silane pyrolysis and applied to the silicon production process. Both models accounted for the homogeneous and heterogeneous rates of silane decomposition 12.31, nucleation, growth and coagulation of fines, and scavenging of fines by large particles. In these Article published online by EDP Sciences and available at

3 C2-104 JOURNAL DE PHYSIQUE IV models, they distinguished between the bubble phase, emulsion phase and grid zone. They pointed out the significance of good gas-solid contacting in the grid zone for suppression of fines formation. However, these models did not consider local behavior of gas and solids in the grid zone. Li et al. 151 presented a modified bubble assemblage model and simulated the monosilane decomposition in a fluidized bed reactor. In their model, a bubble-cloud-emulsion mass transfer mechanism was considered and the reaction rates of Hogness et al. 121 and Iya et al. 131 were also employed. However, they could not explain the effect of inlet silane fraction on fines elutriation experimentally presented by Hsu et al Summarising the previous activities on modelling of the fluidized bed CVD of polysilicon, the problems to be solved are (1) to explain the dependence of fines elutriation on silane concentration and (2) to elucidate where the fines are produced. One of the clues for the first problem is that the previous kinetic expressions /2,31 were first order ones and do not include the effects of concentration of hydrogen used as diluent in the fluidized bed CVD process. In a previous study 161, we conducted the kinetic experiments to formulate both homogeneous and heterogeneous reaction rates considering inhibition effects of hydrogen and monosilane on the rates. In another previous paper 171, we have developed a fluidized bed grid zone model considering local behavior of gas and solids to elucidate the contribution of the grid zone. The model was applied to the silicon production process to estimate the fines formation rate in the fluidized bed grid zone. The results of this model showed that the contribution of fines formation in the grid zone including the jet region, which Lai et al. suggested plays an important role, was negligibly small compared with the experimental data by Hsu et al. 1 Additionally, the numerical results for the possibility of the clogging explained well the experimental results including the effects of bed temperature, inlet silane fraction, gas velocity and structure of gas injector. In this study, the Kunii-Levenspiel fluidized reactor model 181 was applied to monosilane pyrolysis. In the proposed model, the rates of fine powder production and silicon deposition on the seed silicon particle were estimated using own our kinetic equations 161. Numerical results on the fines formation were compared with experimental data by Hsu et al. /I/ and by ourselves /lo/. Relative and quantitative contribution of both reactions was elucidated. We also discuss the effects of operational conditions on the rates of these reactions in the fluidized bed bubbling zone, i.e., effect of bed temperature, inlet silane concentration and gas velocity. 2-. Fluidized bed reactor model 2.1- Outline of the fluidized bed reactor model bed height ow nuba emulsion bubble phase phase \ 168 Fig. 1 Concept of the fluidized bed reactor model. Recently, Kunii and Levenspiei /8/ proposed their improved fluidized bed reactor models for various fluidization conditions. Considering the present operational conditions, an intermediate particles model for Geldart B particle (dp = mm) 191 was selected for our

4 reactor modeling. An outline of their model employed in this study is shown in Fig. 1. In the model, the fluidized bed consists of two regions, bubble and emulsion, interacting with each other through one interchange coefficient of gas, Kbe, and several assumptions are employed as follows. The wake and cloud region is neglected. Bubble size distribution is ignored. In the emulsion phase, gas ascends at the minimum fluidization velocity, umf. In the bubble phase, bubble gas ascends at the velocity of ub*. The bubble diameter is kept invariant through the bed and is treated as a fitting parameter. The volume fraction of bubble in the bed is kept constant as 6 and that of emulsion, as (1-6). Gases ascend as plug flow in each phase and is exchanged at the rate of gas interchange coefficient Kbe. disappearance in bubble = (reaction in bubble) + (transfer to the emulsion) disappearance in emulsion = (reaction in emulsion) - (transfer from the bubble) and for first order reaction -6uba dcsb - 6ybKrC~b+6Kh(Csb-C~e) (1) dz -(1-6)umf- dcse = (1-6)(1-w)KrCse - 6Kbe(CSb-Cse) (2) dz In the Kunii and Levenspiel model 181, the rise velocity of an isolated bubble relative to the surrounding bed solids was calculated from ubr = 0.711m (3) The rise velocity of bubble gas, not just the bubble, was ub* = ub +umf (4> The fraction of bed consisting of bubble was calculated from 6 =- UO - Umf ub The interchange coefficient of gas between bubble and the emulsion was calculated from Kbe = 4.5 (y] The volume of solids dispersed in the bubble/volume of bubble was given as 'yb = The minimum fluidization velocity was given by Wen and Yu /11/ as Thus (5) (6) (7) Viscosity of mixed gas was given by Wilke 1121 as YlP1 + Y2P2 + Y3P3 P= ~1+~2$1,2+~3$1,3 ~2+~1@2,1+~3$2,3 ~3+~143,1+~2$3,2 Where +i,j was calculated as [I+ (pilc~~)'~~ $i,j = (~fli)~'~]~ [8 (~+MJM~)]~" In the present model, the above mentioned Kunii and Levenspiel model 181 was applied and modified as follows. The bubble diameter was assumed to be a half of the bed diameter. In the fluidized bed, monosilane decomposed as SiI& + Si (fines or deposit) + 2H2 (1 1) The reaction rate of monosilane pyrolysis in the fluidized bed was given after Furusawa et al. 161 as dx, kso kvo (1- X) dt l+khph+ksps (3)(l-x)+m V where kso = 2.15X108e-1.915~16/R~ (13) KH = (14) Ks = 7.6x10"e329mT (15) kvo = 2. 14x1013e mT (16) Kv = 0.50 (17) In the reaction rate expression, complex parts in eq. (12) were replaced as RKS and RKV, as follows. (12)

5 JOURNAL DE PHYSIQUE 1V RKS = kso I+KHPH+KsPs In the K-L model. K-Cn was diked as and From eqs. (12) to (21), the following equation was obtained - dt = cs@ = (RK~(~)+RKV](~-X)C~~ where cs = CsoU - X) Therefore, Kr in the bubble phase was given as follows Kr=-l!%=.-%!%=& VsCs dt VsCs dt VFs = -!LvsCs (RK~(Q)+RKV]CS= -($)+RKV] finally, K~ = ~ R K Sl Yb - ~ *+RKV] b d ~ In the emulsion phase, Kr was also exdressed as. Gas composition and flow rate in the bed vary with height. Especially in the emulsion phase, the value of u/umf is increased by gas volume increment. Furthermore, the reaction rate constants, Kr in both phases vary with height. Therefore, in the present numerical model, the stepwise calculation from the first slice of the bottom to the nth slice of the top of the bed was conducted, while the temperature distribution in the bed was neglected and that in bubble and emulsion was assumed to be same. The surplus gas more than 1 umf in the einulsion phase was assumed to be introduced to the bubble in the next slice. The rate constants, the values of Kr in both phases at the top of (n-l)th layer were employed for the calculation in the nth layer Outline of computational algorithm The computational simulation was conducted according to the following procedure. 1. Input of reaction parameters, e.g., flow rate of gases, bed temperature, diameter of reactor, number of slice, etc. 2. Calculation of physical properties of gases as functions of gas composition for a given temperature. 3. Calculation of fluidization condition, i.e., umf, as a representative value for the entire bed, using inlet gas condition. 4. Iteration from the first slice (bottom) to the last slice (top) in the bed. 4.1 Calculation of umf and gas interchange between bubble and emulsion phases. 4.2 Calculation of local homogeneous and heterogeneous reaction rates in bubble and emulsion. 4.3 Calculation of accumulated values of fines formation and silicon deposition for each phase. 5. Output of results.

6 3.- Results and Discussion Output of the present numerical calculation. Molar fractions of monosilane converted into fines by homogeneous reaction and deposit on particle surface in bubble phase are denoted as Xbf and Xbd and in emulsion phase, as Xef and Xed, respectively. Thus the sum of Xbf+Xbd+Xef+Xed equals to the total monosilane conversion in the bubbling bed. In the following section, the numerical results are shown and compared with the experimental data by Hsu et al. /I/ and those by ourselves 191. Furthermore, present results are compared with the numerical results of monosilane conversion to fines, Xgf in the grid zone /7/. It has already been reported /7/ that the contribution of fines formation in jet is extremely small compared with that in annulus in the grid zone Comparison of numerical results with Experimental results on fines elutriation by Hsu et al. 1. I. I - I. Hsu et al. Gin. 923K Numerical 2in. 973K 0 Hsu et al. 2in. 973K Numerical 0 - _-_----- : ---IT Inlet silane concentration I%] Fig. 2 Comparison of numerical results with experimental data on fines elutriation; effects of inlet silane concentration. I.,.,.,. Bed temperature [K] Fig. 3 Comparison of numerical results with experimental data on fines elutriation; effects of bed temperature. The numerical results on the respective sums of the fractions of fines formation in bubble and emulsion, Xbf+Xef, calculated for the reaction in the bubbling zone under the same condition as that in the experiment by Hsu et al. /I/ were compared with their experimental results on fines elutriation. The effects of inlet silane concentration and of bed temperature are shown in Figs. 2 and 3, respectively. Total monosilane conversion calculated by the model was almost 100% and 85% for the reactor diameter of 2in. and 6in., respectively. At higher concentration of silane, i.e., under the industrially realistic condition, numerical results of fines formation coincide well with experimental fines elutriation data by Hsu et al As shown in Fig. 2, the experimental tendency of increase of fines elutriation with increasing silane concentration is well explained by the present model. This tendency has not been predicted in the other models. Furthermore the experimental value is qualitatively closed to the predicted value.neverthe1ess at low concentrations of silane, numerical results are much higher than experimental data. It is possibly explained by the phenomena that at the low concentration of silane, fines formation rate was low and those formed easily adhere to silicon particles. The effects of bed temperature of monosilane conversion are shown in Fig. 3. The numerical results of the monosilane conversion to fine powder increase with increasing bed temperature. These tendencies agree with experimental results. At lower bed temperatures (below 973 K), the numerical results are in good agreement with the experimental data. However, at higher bed temperatures (above 973 K), the numerical results are much higher than the experimental data. It is also considered that formed fines were possibly scavenged by silicon particles.

7 JOURNAL DE PHYSIQUE IV 3.3- Comparison of numerical result with experimental data by ourselves; effects of operational conditions on the monosilane conversion. Comparison of numerical results with our experimental data on total conversion calculated from monosilane concentration in exit stream is shown in Fig. 4. Detail of our experimental I I A Run018 CI Run 022 r Run 128 A Run 204A o Run 209A - Numerical R018 I I I K [K -'I Fig. 4 Comparison of numerical results with experimental data; effects of temperature on monosilane conversion. conditions and results were mentioned in the accompanying paper /lo/. The slope of the numerical line is almost same as that of the line correlating the experimental data, while the numerical values on conversion are smaller than those of experimental data. To explain the discrepancy in the values in Fig. 4, further improvement may be necessary. The most essential one is to consider the deposition of silicon on the formed fine in the bubble phase Relative importance of fines formation in bubble; effect of operational conditions on local conversions to fines. and deposition. Xbd;conversion to deposit in bubble Xbf;conversion to fines in bubble Xed;conversion to deposit in emulsion Xef;conversion to fines in emulsion Xgf;total conversion in grid Inlet silane concentration [%] Fig. 5 Numerical results on conversion in fluidized bed; effects of inlet silane concentration. Standard conditions employed for the numerical calculation were the same as those employed in the previous paper /7/ in which the relative importance of fines formation in the grid zone of a fluidized bed was discussed. The outline is as follows: (1) diameter of the reactor; 0.05 m, (2) gas velocity u/umf; 6, (3) void fraction in emulsion phase Emf; 0.5, (4) diameter of seed silicon particle; mm, (5) particle density; 2330 kg/m3,(6) bed temperature; 923 K, (7) inlet silane concentration; 20%. The numerical results on conversions are shown in Figs. 5,6 and 7. Fig. 5 shows the effect of inlet silane concentration on the monosilane conversions. It is clearly seen that the monosilane

8 conversion to deposit on the seed silicone particle in the emulsion phase is gradually suppressed by the increase in silane concentration. This result is caused by the inhibition effect of monosilane in eq. (12). i.e., the value of KS at 923 K, 0.553, is much larger than KH of Fig. 5 suggests that an increase in the inlet silane concentration causes the increase of the levels of fine powder in the bubble and emulsion. This result is explained by the reduction of inhibition effects of hydrogen with increasing the monosilane concentration. It is also found that fines mainly form in the bubble phase and heterogeneous deposition mainly occurs on the seed silicon particle in the emulsion phase. The fines foimation rate in the grid 171 is found negligibly small compared with that in bubble. In summary, it was found that the fines mainly form in the bubble. The effect of bed temperature on the conversion in the fluidized bed is shown in Fig. 6. The level of conversion to fine powder increases with increasing bed temperature, as shown in Fig. 3. On the contrary, the level of conversion to deposition on the particles in the emulsion phase decreases with increasing bed temperature higher than 973 K. The relative importance of Xbf to Xef increases with increasing bed temperature. These results are explained as follows. At high temperature, the conversion of the monosilane is almost 100% and homogeneous nucleation and heterogeneous deposition are competitive reactions. Activation energy of the fines formation rate is higher than the heterogeneous deposition rate. Furthermore, the gas interchange coefficient, Kt,,, is almost kept constant with temperature change. Thus the level of fines formation fraction in the bubble phase increases, and silicon deposition rate in the emulsion phase decreases, and Xef decrease with increasing bed temperature. The levels of fines formation rate in the jet is also found to be negligibly small compared with the total fines formation rate in the fluidized bed as indicated in Fig. 5. XW Xbf xed Xef Xsf Bed temperature [K] UIUmf [-I Fig. 6 Numerical results on conversion in Fig. 7 Numerical results on conversion in fluidized bed; effects of bed temperature. fluidized bed; effects of gas velocity. The effects of inlet gas velocity on levels of conversion in the fluidized bed are shown in Fig. 6. The numerical results show that the levels of conversion in the emulsion phase to fines, Xef, and to deposition, Xed decrease with increasing inlet gas velocity. On the other hand, the levels of silane conversion in the bubble phase increase with increasing inlet gas velocity. This tendency is explained by the increase in volume fraction of bubble phase, and constant umf in emulsion phase and gas interchange coefficient with increasing gas velocity. Thus reaction of the monosilane gas in the emulsion phase shows a relative decrease with increasing inlet gas velocity. Conclusion The Kunii-Levenspiel fluidized bed model has been applied to analysis of monosilane pyrolysis in a fluidized bed bubbling zone. The experimentally observed dependence of fines elutriation on not only bed temperature but also on inlet silane concentration have been explained by the proposed model. Numerical results suggest that fines mainly form in the bubble and not in the grid zone nor in the emulsion phase.

9 C2-110 JOURNAL DE PHYSIQUE IV Acknowledgement T. Kojima wish to express his thanks for Grants-in-Aid for Scientific Research by the Ministry of Education, Science and Culture, Japan. T. Kimura gratefully acknowledges Sasakawa Scientific Research Grant for this study from the Japan Science Society. Symbols Y z S Emf 0 Y I.I P Reference concentration [mol/l] effective bubble diameter [m] average particle diameter [m] acceleration of gravity [mls] first order reaction rate constant [s-l] gas interchange coefficient between bubble and emulsion [s-l] heterogeneous reaction rate constant [mls] homogeneous reaction rate constant [s-l] moles of monosilane gas [moll molecular weight [glmol] local hydrogen pressure [kpa] local monosilane pressure [kpa] gas constant [J/(mol K)] surface to voidege ratio [m-l] time [s] rise velocity of bubble gas [mls] bubble rise velocity in a bubbling fluidized bed [mls] rise velocity of bubble with respect to the emulsion [mls] minimum fluidization velocity [m/s] superficial gas velocity [mls] volume of solid [m3] volume of gas [m31 monosilane conversion, refer to Fig. 5 [-I mole fraction [-I height [m] volume fraction of bubble in the bed [-I volume fraction of bed at minimum fluidization [-] mixing factor of viscosity [-] volume of solids in bubble phase divided by the volume of bubble [-I viscosity [Pa s] density [kg/m31 I11 HSU G, HOGLE R., ROHATGI N. and MORRISON A., J. Electrochem. Soc.,l31 (1984) HOGNESS T, WILSON T. L. and JOHONSON W. C., J. Am. Chem. Soc., 58 (1936) IYA S. K., FLAGELLA R. N. and DIPAOLO F. S., J. Electrochem. Soc., 129 (1982) LA1 S., DUDUKOVIC M. P. and RAMACHANDRAN A., Chem. Eng. Sci., 41 (1986) LI K. Y., PENG S. H. and HO T. C., AIChE Symp. Ser (1989) FURUSAWA T., KOJIMA T. and HIROHA H., Chem. Eng. Sci., 43 (1988) 2037 /7/ KOJIMA T., KIMURA T. and MATSUKATA M., Chem. Eng. Sci., 45 (1990) KUNII D. and LEVENSPIEL 0.. Ind. Eng. Chem. Res., 29 (1990) 1226 /9/ KUNII D. and LEVENSPIEL 0.. "Fluidization Engineering", 2nd ed., Buttenvorth- Heinemann. (1991) KOJIMA T. and MORISAWA 0.. submitted to J. de Physiqe, (1991) 1111 WEN, C. Y., and W Y. H., Chem. Eng. Progr. Symp. Ser., 62 (1966) 100 I121 WILKE C. R., J. Chem. Phys., 18 (1950) 517