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Numerical Simulation of Physical Vapour Transport Crystal Growth Processes by a Finite Volume Solution Algorithm

  • M. Selder
  • L. Kadinski
  • F. Durst
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 21)

Abstract

A mathematical model for the numerical simulation of physical vapour transport (PVT) crystal growth processes is presented in this paper. The model is based on the two-dimensional conservation equations for mass, momentum, energy and chemical species. Radiative heat transfer and species generation/consumption by heterogeneous chemical reactions are taken into account. The equations are solved by a finite volume algorithm on block-structured grids using the multi-grid technique to speed up convergence. The efficiency of the method is demonstrated. Results on the simulation of the SiC bulk growth process are given, and physical phenomena involved in the growth process are discussed

Keywords

Radiative Heat Transfer Grid Level Crystal Growth Process Multigrid Solver Species Mass Fraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P.A. Ivanov, V.E. Chelnokov: Recent developments in SiC single-crystal electronics. Semicond. Sci. Technol. 7 (1992) 863–880Google Scholar
  2. 2.
    Y.M. Tairov, V.F. Tsvetkov: Investigation of growth processes of ingots of silicon carbide single crystals. J. Crystal Growth 43(2) (1978) 209CrossRefGoogle Scholar
  3. 3.
    M. Selder, L. Kadinski, Y. Makarov, F. Durst, P. Wellmann, T. Straubinger, D. Hofmann, S. Karpov, M. Ramm: Global numerical simulation of heat and mass transfer for SiC bulk crystal growth by PVT. J. Crystal Growth 211 (2000) 333–338CrossRefGoogle Scholar
  4. 4.
    M. Selder, L. Kadinski, F. Durst, T. Straubinger, P. Wellmann, D. Hofmann: Numerical simulation of thermal stress formation during PVT-growth of SiC bulk crystals. Mat. Sci. Forum 353–356 (2001) 65–68CrossRefGoogle Scholar
  5. 5.
    D. Hofmann, R. Eckstein, M. Kölbl, Y. Makarov, E Schmitt, A. Winnacker, R. Rupp. R. Stein, J. Völkl: SiC bulk growth by physical vapour transport and its global modeling. J. Crystal Growth 174 (1997) 669–674Google Scholar
  6. 6.
    E. Schmitt, M. Rasp, A.D. Weber, M. Kölbl, R. Eckstein, L. Kadinski, M. Selder: Defect reduction in sublimation grown silicon carbide crystals by adjustment of thermal boundary conditions. Mat. Sci. Forum 353–356 (2001) 15–20CrossRefGoogle Scholar
  7. 7.
    F. Durst, L. Kadinski, M. Perie, M. Schäfer: Numerical study of transport phenomena in MOCVD reactors using a finite volume multigrid solver. J. Crystal Growth 125 (1992) 612–626CrossRefGoogle Scholar
  8. 8.
    F. Durst, L. Kadinski, M. Schäfer: A multigrid solver for fluid flow and mass transfer coupled with grey-body surface radiation for the numerical simulation of chemical vapor deposition. J. Crystal Growth 146 (1995) 202–208CrossRefGoogle Scholar
  9. 9.
    D.W. Greenwell, B.L. Markham, F. Rosenberger: Numerical maodeling of diffusive physical vapor trnsport in cylindrical ampoules. J. Crystal Growth 51 (1981) 413–425CrossRefGoogle Scholar
  10. 10.
    J.P. Garandet: Thermal stress in vertical gradient freeze furnace. J. Crystal Growth 96 (1989) 680–684CrossRefGoogle Scholar
  11. 11.
    J. P. Hirth, J. Lothe: Theory of Dislocations. Wiley, New York (1982)Google Scholar
  12. 12.
    J.H. Ferziger, M. Perié: Computational Methods for Fluid Dynamics. Springer Verlag, Berlin (1999)zbMATHCrossRefGoogle Scholar
  13. 13.
    S.V. Patanker, D.B. Spalding: A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat and Mass Transfer 15 (1972) 1787CrossRefGoogle Scholar
  14. 14.
    H.L. Stone: Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J. Numerical Analysis 5 (1968) 530–558zbMATHCrossRefGoogle Scholar
  15. 15.
    F. Dupret, P. Nicodeme, Y. Ryckmans, P. Wouters: Global modelling of heat transfer in crystal growth furnaces. Int. J. Heat Mass Transfer 33 (1990) 1849–1871zbMATHCrossRefGoogle Scholar
  16. 16.
    M. Selder, L. Kadinski, F. Durst, D. Hofmann: Global modeling of the SiC sublimation growth process: Prediction of thermoelastic stress and control of growth conditions. J. Crystal Growth 226 (2001) 501–510CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. Selder
    • 1
  • L. Kadinski
    • 1
  • F. Durst
    • 1
  1. 1.Institute of Fluid MechanicsUniversity of ErlangenNürnbergErlangenGermany

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