Summary
The paper deals with the continuation of the development of high performance computer codes and their application to modelling of crystal growth processes started by the authors’ research groups and reported in [1]. The mathematical model is based on the continuity equation and the conservation equations for momentum and heat transfer combined with mass transfer including chemical reactions. The thermal radiation analysis assumes a non-participating medium and semi-transparent walls. The radiation heat transfer is coupled with convection and conduction. The heat conduction includes thermal solid/fluid interactions between the gas and solid parts of the computational domain. The results of thermal calculations are used for the analysis of thermal stresses. The models are implemented in finite volume (both, block-structured and unstructured on non-orthogonal grids), and spectral and coupled finite volume/spectral numerical solution procedures.
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P.Droll, M.El Ganaoui, L.Kadinski, M.Kurz, A.Lamazouade, O.Louchart, D.Morvan, M.Naamoune, A.Pusztai, I.Raspo, P.Bontoux, F.Durst, G.Müller, J.Ouazzani, and M.Schäfer. High Performance Computer Codes and their Application to Optimize Crystal Growth Processes. In Numerical Flow Simulation I, volume 66 of Notes on Numerical Fluid Mechanics, pages 115–143. Vieweg Verlag, 1998.
F. Durst, L. Kadinski, and M. Schäfer. A multigrid solver for fluid flow and mass transfer coupled with grey-body surface radiation for the numerical simulation of CVD processes. J. Crystal Growth, 146: 202–208, 1995.
L. Kadinski. Mathematische Modellierung and numerische Simulation von CVD-Prozessen in der Halbleitertechnik. PhD thesis, Friedrich-Alexander-Universit“at zu Erlangen, 1996.
Modest. Radiative Heat Transfer. McGraw-Hill, 1993.
Timoschenko and Goodier. Theory of elasticity. McGraw-Hill Book Company, Inc.
D. Lambropoulos J.: The isotropic assumption during czochralski growth of single semiconductors crystals. Journal of Crystal Growth, 84: 349–358, 1987.
F. Durst and M. Schäfer. A parallel blockstructured multigrid method for the prediction of incompressible flows. Int. J. for Num. Meth. in Fluids,22:549–565, 1996.
M. Kurz. Development of CrysVUN++, a software system for numerical modelling and control of industrial crystal growth processes. Ph. D. thesis, university of Erlangen, 1998.
P. Droll, M. Schäfer, O. Louchart, and P. Bontoux. Coupling of a finite-volume method with a pseudospectral method. ECCOMAS 98, Proceedings, 1 (2): 1240–1245, 1998.
S. Hugues and A. Randriamampianina. An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations. Int. J. for Num. Meth. in Fluids,1997.
M. Hortmann and M. Perié. Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions. Int. J. for Num. Meth. in Fluids,11:189–207, 1990.
P. Droll and M. Schäfer. An implicit pseudospectral method for the solution of the incompressible Navier-Stokes equations. Special Issue of CFD Journal, 9, to appear in 2000.
C. D. Dimitropoulos, B. J. Edwards, K.-S. Chae, and A. N. Beris. Efficient pseudospectral flow simulations in moderately complex geometries. J. of Comp. Physics, 144: 517–549, 1998.
Y. Saad and M.H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7: 856–869, 1986.
G.L.G. Sleijpen and D.R. Fokkema. BiCGSTAB(L) for linear matrices involving unsymmetric matrices with complex spectrum. ETNA, 1: 11, 1993.
E. Serre and J. P. Pulicani. A 3d pseudospectral method for rotating flows in a cylinder. Int. J. of Computers and Fluids,Paper in print.
O. Savas. Stability of bödewadt flow. J. of Fluid Mech., 183: 77–94, 1987.
H.P. Greenspan. The theory of rotating fluids. Cambridge University Press, 1972.
M.P. Escudier. Observations of the flow produced in a cylindrical container by a rotating endwall. Exp. in Fluids.,2:189–196, 1984.
R. Rupp, P. Lanig, J. Völkl,, and D. Stephani. First results on silicon carbide vapour phase epitaxy growth in a new type of vertical low pressure chemical vapor deposition reactor. J. Crystal Growth, 31: 41–146, 1995.
M. D. Allendorf and R. J. Kee. A model of silicon carbide chemical vapor deposition. J. Electrochem. Soc., 138: 841–852, 1991.
M. D. Allendorf. Equilibrium predictions of the role of organosilicon compounds in the chemical vapor deposition of silicon carbide. J. Electrochem. Soc., 140: 747–753, 1993.
P. Kaufmann and Yu. N. Makarov. Modelling of flow, heat transfer, mass transport during CVD of SiC in a vertical reactor. Technical report, LSTM, University Erlangen-Nürnberg, 1994. unpublished.
T. Weber. Die numerische Simulation reaktiver Strömungen als Basis zukünftiger Reaktormodellierungen. PhD thesis, Friedrich-Alexander-Universität zu Erlangen, 2000.
R. Rupp, P. Lanig, J. Völkl, and D. Stephani. Mater. Res. Soc. Symp. Proc, 423:253ff, 1996.
A.N. Vorobev, A.E. Komissarov, A.S. Segal, Yu.N. Makarov, S.Yu. Karpov, A.I. Zhmakin, and R. Rupp. Modeling analysis of gas phase nucleation in silicon carbide chemical vapor deposition. Mat. Sci Eng, B, 61–62: 176–178, 1999.
M. Kurz and G. Müller. Control of thermal conditions during crystal growth by inverse modelling. J. Crystal Growth.
El Ganaoui M. and Bontoux P. An homogeneisation method for solid-liquid phase change during directional solidification. ASME H.T.D., Numerical and Experimental methods in Heat Transfer, 361: 453–469, 1998.
M. El Ganaoui. Modélisation de la convection instationnaire en presence d’un front de solidification déformable. application à la croissance cristalline. Phd Thesis, 1997.
D. Morvan, M. El Ganaoui, and P. Bontoux. Numerical simulation of 2d crystal growth problems in a vertical bridgman-stockbarger furnace, latent heat effects and crystal-melt in interface morphology. Int. J. Heat Mass Transfer, 42: 573–579, 1999.
El Ganaoui M., Bontoux P., and et Morvan D. Capture d’un front de solidification en interaction avec un bain fondu instationnaire. C. R. Acad. Sciences Paris, t. 327 (Srie II b): 41–48, 1999.
Lamazouade A., El Ganaoui M., Morvan D, and et Bontoux P. Simulation numérique par une approche porosité enthalpie de la convection thermique et solutale dans une ampoule de bridgman. Int. J. of Thermal Sciences (Revue Générale de Thermique), 8 (N 38), 1999.
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Degenhardt, A. et al. (2001). High Performance Computer Codes and their Application to Optimize Crystal Growth Processes, II. In: Hirschel, E.H. (eds) Numerical Flow Simulation II. Notes on Numerical Fluid Mechanics (NNFM), vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44567-8_5
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DOI: https://doi.org/10.1007/978-3-540-44567-8_5
Publisher Name: Springer, Berlin, Heidelberg
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