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Numerical Flow Simulation III pp 49–76Cite as

High Performance Computer Codes and their Application to Optimize Crystal Growth Processes, III

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Summary

The rapid development on the information technology market implies a growing demand in quantity and quality of semiconductor and optical crystalline material. For the correlated process development and optimization, numerical simulation is playing an essential role, with the necessity for further improvement of numerical techniques and capacities. The collaborative work presented in this paper numerically deals with important issues in the field of crystal growth like global simulation of bulk crystal growth and vapor phase epitaxy, phase transition problems, as well as new methods for high performance three-dimensional flow simulation. The different numerical codes applied were developed in a complementary way to cover a wide range of aspects important for crystal growth.

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References

  1. 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, M. Schäfer: “High Performance Computer Codes and their Application to Optimize Crystal Growth Processes”. In E. H. Hirschel (ed.), Numerical Flow Simulation I, Notes on Numerical Fluid Mechanics vol. 66, Vieweg, 1998, pp.115–143.

    Google Scholar 

  2. A. Degenhardt, P. Droll, M. El Ganaoui, L. Kadinski, M. Kurz, A. Lamazouade, D. Morvan, I. Raspo, E. Serre, P. Bontoux, E Durst, G. Müller, M. Schafer: ”High Performance Computer Codes and their Application to Optimize Crystal Growth Processes, II”. In E. H. Hirschel (ed.), Numerical Simulation of Flows II, L. N. Physics, Springer, 2001, pp.69–97.

    Google Scholar 

  3. G. Müller: “Melt growth of semiconductors”. Materials Science Forum 276–277, 1998, pp. 87–108.

    Article  Google Scholar 

  4. S. R. Idelsohn, M. A. Storti, L. A. Crivelli: “Numerical methods in phase-change problems”. Archives of Computational Methods in Engineering 1, 1994, pp. 49–74.

    Article  MathSciNet  Google Scholar 

  5. Y. Stry, M. Hainke, T. Jung: “Comparison of linear and quadratic shape functions for a hybride control-volume finite element method”. Submitted to Int. J. Num. Meth. Heat Fluid Flow.

    Google Scholar 

  6. M. Hortmann, M. Perié, G. Scheuerer: “Finite volume multigrid prediction of laminar natural convection: bench-mark solutions”. Int. J. Numer. Meth. Fluids 11, 1990, pp. 189–207.

    Article  MATH  Google Scholar 

  7. P. Spelluci, Numerische Verfahren der nichtlinearen Optimierung, Birkhäuser Verlag, 1993.

    Book  Google Scholar 

  8. M. Metzger, Optimal Control of Industrial Crystal Growth Processes, PhD thesis, University Erlangen-Nürnberg, 2000.

    Google Scholar 

  9. M. Metzger, R. Backofen: “Optimal temperature profiles for annealing of GaAscrystals”. J. Crystal Growth 220, 2000, 6–15.

    Article  Google Scholar 

  10. M. Metzger: “Optimal control of crystal growth processes”. J. Crystal Growth 230, 2001, 210–216.

    Article  Google Scholar 

  11. P. Droll, M. Schäfer, E. Serre, P. Bontoux: “An implicit pseudospectrl multi-domain method for the simulation of incompressible flows”. Submitted to Int. J. for Num. Meth. in Fluids.

    Google Scholar 

  12. J. H. Bramble, J. E. Pasciak, A. H. Schatz: “The construction of preconditioners for elliptic problems by substructuring I”. Mathematics of Computation 47,1986, pp. 103–134.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Haldenwang, G. Labrosse, S. Abboudi, M. Deville: “Chebyshev 3d spectral and 2d pseudospectral solvers for the Helmholtz equation”. J. of Comp. Physics 55, 1984, pp. 115–128.

    Article  MATH  MathSciNet  Google Scholar 

  14. S. Hugues, A. Randriamampianina: “An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations”. Int. J. for Num. Meth. in Fluids 28, 1998, pp. 501–521.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Van Kan: “A second-order accurate pressure-correction scheme for viscous incompressible flow” SIAM. J. Sci. Stat. Comp. 7, 1986, pp. 870–891.

    Article  MATH  Google Scholar 

  16. P. M. Gresho: “On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix, part 1: Theory”. Int. J. Numer. Meth. Fluids 11, 1990, pp. 587–620.

    Article  MATH  MathSciNet  Google Scholar 

  17. S. Turek: “Efficient solvers for incompressible flow problems”. Vol. 5 of Lecture Notes in Computational Science and Engineering, Springer, Berlin, 1999.

    Google Scholar 

  18. M. Schäfer, S. Turek: “Benchmark computations of laminar flow around a cylinder”. In E. H. Hirschel et al. (ed.), Flow Simulation with High-Performance Computers II, Notes on Numerical Fluid Mechanics, 1996, pp. 547–566.

    Chapter  Google Scholar 

  19. M. P. Escudier: “Observations of the flow produced in a cylindrical container by a rotating end wall”. Exps. Fluids 2, 1984, pp. 179–186.

    Article  Google Scholar 

  20. A. Spohn, M. Mory, E. J. Hopfinger: “Experiments on vortex breakdowm in a confined flow generated by a rotatin disc”. J. Fluid Mech. 370, 1998,pp. 73–99.

    Article  MATH  Google Scholar 

  21. K. Fujimara, H. S. Koyama H., J. M. Hyun: “Time dependent vortex breakdown in a cylinder with a rotating lid”. ASME J. Fluids Engrg. 119, 1997, pp. 450–453.

    Article  Google Scholar 

  22. O. Daube, J. N. Sorensen: “Simulation numérique de l’écoulement périodique axisymétrique dans une cavité cylindrique”. C. R. Acad. Sci. Série II b 308, 1989, pp. 463–469.

    MATH  Google Scholar 

  23. J. N. Sorensen, E. A. Christensen: “Direct numerical simulation of rotating fluid flow in a closed cylinder”. Phys. of Fluids 7, 1995, pp. 764–778.

    Article  Google Scholar 

  24. J. L. Stevens, J. M. Lopez, B. J. Cantwell: “Oscillatory flow states in an enclosed cylinder with a rotating endwall”. J. Fluid Mech. 389, 1999, pp. 101–118.

    Article  MATH  Google Scholar 

  25. F. Sotiroupolos, Y. Ventikos: “The three-dimensional structure of confined swirling flows with vortex breakdown”. J. Fluid Mech. 426, 2001, pp. 155–175.

    Article  Google Scholar 

  26. J. C. E Pereira, J. M. M. Sousa: “Confined vortex breakdown generated by a rotating cone”. J. Fluid Mech. 385, 1999, pp. 287–323.

    Article  MATH  MathSciNet  Google Scholar 

  27. H. M. Blackburn, J. M. Lopez: “Symmetry breaking of the flow in a cylinder by a rotating end wall”. Phys. of Fluids 12, 2000, pp. 2698–2701.

    Article  Google Scholar 

  28. E. Serre, J. P. Pulicani: “A 3D pseudospectral method for convection in a rotating cylinder”. Computers and Fluids 30, 2001, pp. 491–519.

    Article  MATH  MathSciNet  Google Scholar 

  29. P. R. Fenstermacher, H. L. Swirmey, J. P. Gollub J.P: “Dynamical instabilities and the transition to chaotic Taylor vortex flow”. J. Fluid Mech. 94, 1979, pp. 103–128.

    Article  Google Scholar 

  30. C. D. Andereck, S. S. Liu, H. L. Swinney: “Flow regimes in a circular Couette system with independently rotating cylinders”. J Fluid Mech. 164, 1986, pp. 155–183.

    Article  Google Scholar 

  31. C. L. Street, M. Y. Hussaini: “A numerical simulation of the appearance of chaos in finite-length Taylor-Couette flow”. Appl. Numer.Math. 7, 1991, pp. 41–71.

    Article  Google Scholar 

  32. E. Serre, E. Crespo Del Arco, P. Bontoux: “Annular and spiral patterns in flows between rotating and stationary discs” J. Fluid Mech. 434, 2001, pp. 65–100.

    Article  MATH  MathSciNet  Google Scholar 

  33. V. R. Voller, C. Prakash: “A fixed grid numerical modelling methodology for convectiondiffusion mushy region phase-change problems”. Int. J. Heat Mass Transfer 30, 1987, pp. 1709–1719.

    Article  Google Scholar 

  34. W. D. Bennon, E P. Incropera: “A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems: 1 model formulation”. Int. J. Heat Mass Transfer 30, 1987, 2161–2170.

    Article  MATH  Google Scholar 

  35. G. H. Yeoh, G. de Vahl Davis, E. Leonardi, H. C. de Groh III, M. Yao: “A numerical and experimental study of natural convection and interface shape in crystal growth”. J. of Crystal Growth 173, 1997, pp. 492–502.

    Article  Google Scholar 

  36. J. E. Simpson, H. C. De Groh III, S. V. Garimella: “Directional solidification of pure succinonitrile and a Succinonitrile-Acetone alloy”. NASA/TM-1999–209381, 1999.

    Google Scholar 

  37. M. Cruchaga, M. El Ganaoui: “Numerical simulation of the natural convection in a horizontal bridgman apparatus using finite elements finite volumes approximations”. Under preparation, 2001.

    Google Scholar 

  38. C. Beckermann, R. Viskanta: “Effect of solid supercooling on natural convection melting of a pure metal”. J. Heat Transfer 111, 1989, pp. 416–424.

    Article  Google Scholar 

  39. K. H. Winters: “Oscillatory convection in liquid metals in a horizontal temperature gradient”. Int. J. Numer. Meth. Eng. 25, 1988, pp. 401–414.

    Article  MATH  Google Scholar 

  40. J. P. Pulicani, E. Crespo del Arco, A. Randriamampianina, P. Bontoux, R. Peyret: “Spectral simulations of oscillatory convection at low Prandtl number”. Int. J. Numer. Meth. Fluids 10, 1990, pp. 481–517.

    Article  MATH  Google Scholar 

  41. C. W. Lan, M. K. Chen, M. C. Liang: “Bifurcation and stability analyses of horizontal Bridgman crystal growth of a low Prandtl number material”. J. Crystal Growth 187, 1998, pp. 303–313.

    Article  Google Scholar 

  42. T. Nakano, Y. Nakano, Y. Schimogali: “Kinetic ellipsometry measurement of InGaP/GaAs hetero-interface formation in MOVPE”. J. Cryst. Growth 221, 2000, pp. 136–141.

    Article  Google Scholar 

  43. T. Ohori, M. Takechi, M. Suzuki, M. Takikawa, J. Komeno: J. Cryst. Growth 93, 1988, pp. 905.

    Article  Google Scholar 

  44. G. B. Stringfellow: “Organometallic Vapor-Phase Epitaxy: Theory and Practice”. 2nd ed., Academic Press, San Diego, 1999.

    Google Scholar 

  45. R. ‘A. Talalev, E. V. Yakovlev, S. Yu. Karpov, Yu. N. Makarov, O. Schoen, M. Hueken, G. Strauch, H. Juergensen: “Modeling of InGaN MOVPE in AIX 200 reactor and AIX 2000 HT planetary reactor”. MRS Internet J. Nitride Semicond. Res. 4, paper 5, 1999.

    Google Scholar 

  46. M. G. Jacko, S. J. W. Price: Can. J. Chem. 42, 1964, pp. 1198.

    Article  Google Scholar 

  47. M. G. Jacko, S. J. W. Price: Can. J. Chem. 41, 1963, pp. 1560.

    Article  Google Scholar 

  48. G. B. Stringfellow: In W.T. Tsang (ed.), Semiconductors and Semimetals 22A, Academic Press, Orlando, 1985, pp. 209–259.

    Google Scholar 

  49. P. Kurpas, E. Richter, M. Sato, E Brunner, D. Gutsche, M. Weyers: “MOVPE growth of GaInP/GaAs Hetero-Bipolar-Transistors using CBr4 as carbon dopant source”. J. Cryst. Growth 170, 1997, pp. 442–446.

    Article  Google Scholar 

  50. L. Kadinski, P. Kaufmann, C. Lindner, E. Durst: “3D block-structured grid algorithms for the numerical simulation of chemical vapor deposition in horizontal reactors”. Proc. 3rd Int. FORTWIHR Conf. on HPSEC, March 12–14, 2001, Erlangen, Germany. To be published in M. Breuer, F. Durst, C. Zenger (eds.), Lecture Notes in Computational Science and Engineering Computing 21, Springer, 2002.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fachgebiet Numerische Berechnungsverfahren im Maschinenbau, Technische Universität Darmstadt, Petersenstr. 30, 64287, Darmstadt, Germany

    P. Droll, K. Krastev & M. Schäfer

  2. Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstr. 4, 91058, Erlangen, Germany

    L. Kadinski, P. Kaufmann, E. Mešgić & E. Durst

  3. Kristallabor, Institut für Werkstoffwissenschaften VI, Universität Erlangen-Nürnberg, Martensstr. 7, 91058, Erlangen, Germany

    B. Fischer, M. Hainke, M. Metzger & G. Müller

  4. Sciences des Procédés Céramiques et Traitment de Surface (SPCTS), UMR 66 38 CNRS-Université de Limoges, 123 Albert Thomas, 87000, Limoges, France

    M. El Ganaoui

  5. Laboratoire Modélisation Simulation Numérique en Mécanique, CNRS, Université d’Aix-Marseille, IMT-Château-Gombert, 36 Rue Frédéric Joliout-Curie, 13451, Marseille cedex 20, France

    O. Czarny, I. Raspo, E. Serre & P. Bontoux

Authors
  1. O. Czarny
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  2. P. Droll
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  3. M. El Ganaoui
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  4. B. Fischer
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  5. M. Hainke
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  6. L. Kadinski
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  7. P. Kaufmann
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  9. E. Mešgić
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  10. M. Metzger
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  11. I. Raspo
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  14. E. Durst
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  15. G. Müller
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  16. M. Schäfer
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Editors and Affiliations

  1. Herzog-Heinrich-Weg 6, D-85604, Zorneding, Germany

    Ernst Heinrich Hirschel

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Czarny, O. et al. (2003). High Performance Computer Codes and their Application to Optimize Crystal Growth Processes, III. In: Hirschel, E.H. (eds) Numerical Flow Simulation III. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45693-3_4

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  • DOI: https://doi.org/10.1007/978-3-540-45693-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53653-3

  • Online ISBN: 978-3-540-45693-3

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