Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon

Journal of Crystal Growth

Volumn 205, Issue 1, 1999, Pages 71-91

  Lipchin, Aleksey ^a   Brown, Robert A ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; COMPUTER SIMULATION; CRYSTAL GROWTH FROM MELT; FINITE VOLUME METHOD; HEAT CONVECTION; OXYGEN; REYNOLDS NUMBER; TEMPERATURE; TURBULENCE;

LARGE SCALE CZOCHRALSKI CRYSTAL GROWTH; OXYGEN SEGREGATION; TURBULENT MODELS;

SEMICONDUCTING SILICON;

EID: 0032598206     PISSN: 00220248     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0248(99)00242-0     Document Type: Article

References (52)

1. Kim K.M. Solid State Technol. 39(11):1996;70.
2. T. Abe, Silicon materials science and technology, Electrochemical Society Proceedings, Vol. 98-1, 1998, p. 157.
3. Derby J.J., Brown R.A. J. Crystal Growth. 74:1986;605.
4. Derby J.J., Brown R.A. J. Crystal Growth. 75:1986;227.
5. Crowley A.B. IMA J. Appl. Math. 30:1983;173.
6. Dupret F., Ryckmans Y., Wouters P., Crochet M.J. J. Crystal Growth. 79:1986;84.
7. Bornside D.E., Kinney T.A., Brown R.A., Kim G. Int. J. Numer. Meth. Eng. 30:1990;133.
8. Brown R.A. A.I.Ch.E. J. 34:1988;881.
9. Dupret F., Van den Bogaert N. Hurle D.T.J. Handbook of Crystal Growth, Vol. 2B, Modelling Bridgman and Czochralski Growth. 1994;North-Holland, Amsterdam. (Chapter 15).
10. Sackinger P.A., Brown R.A., Derby J.J. Int. J. Numer. Meth. Fluids. 9:1989;453.
11. Ristorcelli J.R., Lumley J.L. J. Crystal Growth. 116:1992;447.
12. Kinney T.A., Bornside D.E., Brown R.A., Kim K.M. J. Crystal Growth. 126:1993;413.
13. Kim K.M., Langlois W.E. J. Electrochem. Soc. 138:1991;1850.
14. Kim K.M., Smetana P. J. Appl. Phys. 58:1985;2731.
15. Kim K.M., Smetana P. J. Electrochem. Soc. 133:1986;1682.
16. A. Seidl, G. Müller, E. Dornberger, E. Tomzig, B. Rexer, W. von Ammon, Silicon materials science and technology, Electrochemical Society Proceedings, Vol. 98-1, 1998, p. 417.
17. Tennekes H., Lumley J.L. A First Course in Turbulence. 1974;MIT Press, Cambridge, MA.
18. D.C. Wilcox, Turbulence Modeling for CFD, DCW Industries, La Canãda, CA, 1994.
19. Derby J.J., Brown R.A. J. Crystal Growth. 87:1987;251.
20. Iacovides H., Launder B.E. Int. J. Heat Fluid Flow. 16:1995;454.
21. Iacovides H., Launder B.E., Li H.-Y. Int. J. Heat Fluid Flow. 17:1996;22.
22. Hanjalić K., Vasić S. Int. J. Heat Mass Transfer. 36(14):1993;3603.
23. Patel V.C., Rodi W., Scheuerer G. AIAA J. 23(9):1985;1308.
24. Jones W.P., Launder B.E. Int. J. Heat Mass Transfer. 15:1972;301.
25. Henkes R.A.W.M., Hoogendoorn C.J. Henkes R.A.W.M., Hoogendoorn C.J. Turbulent Natural Convection in Enclosures. A Computational and Experimental Benchmark Study. 1993;64 EETI, Paris.
26. T. Zhang, F. Ladeinde, H. Zhang, V. Prasad, Proceedings of the 1996 31st ASME National Heat Transfer Conference. Part 1. August 3-6 1996, Vol. 323, no. 1, p. 17.
27. Kobayashi S. J. Crystal Growth. 99:1990;692.
28. Kobayashi S., Miyahara S., Fujiwara T., Kubo T., Fujiwara H. J. Crystal Growth. 109:1991;149.
29. Chung H.-T., Lee S.-Ch., Yoon J. J. Crystal Growth. 163:1996;249.
30. Kinney T.A., Brown R.A. J. Crystal Growth. 132:1993;551.
31. Launder B.E., Sharma B.I. Lett. Heat Mass Transfer. 1:1974;131.
32. Ristorcelli J.R., Lumley J.L. J. Crystal Growth. 129:1993;249.
33. Henkes R.A.W.M., Hoogendoorn C.J. Int. J. Heat Mass Transfer. 32(1):1989;157.
34. Ferziger J.H., Perić M. Computational Methods for Fluid Dynamics. 1996;Springer, Berlin.
35. Langlois W.E. Ann. Rev. Fluid Mech. 17:1985;191.
36. Xiao Q., Derby J.J. J. Crystal Growth. 129:1993;593.
37. Anselmo A., Prasad V., Koziol J., Gupta K.P. J. Crystal Growth. 134:1993;116.
38. Wheeler A.A. J. Crystal Growth. 102:1990;691.
39. W. Rodi, Turbulence Models and their Application in Hydraulics, a State of the Art Review, International Association for Hydraulic Research, Delft, The Netherlands, 1980.
40. E. Nobile, in: R.A.W.M. Henkes, C.J. Hoogendoorn (Eds.), Turbulent Natural Convection in Enclosures, a Computational and Experimental Benchmark Study, EETI, Paris, 1993, p. 214.
41. K. Hanjalić, Proceedings of 10th International Heat Transfer Conference, Brighton, UK, 1994, Vol. 1, p. 1.
42. Henkes R.A.W.M., Van Der Vlugt F.F., Hoogendoorn C.J. Int. J. Heat Mass Transfer. 34(2):1991;377.
43. Henkes R.A.W.M., Hoogendoorn C.J. Henkes R.A.W.M., Hoogendoorn C.J. Turbulent Natural Convection in Enclosures, a Computational and Experimental Benchmark Study. 1993;185 EETI, Paris.
44. Kuyper R.A., Van der Meer Th.H., Hoogendoorn C.J., Henkes R.A.W.M. Int. J. Heat Mass Transfer. 36(11):1993;2899.
45. Henkes R.A.W.M., Hoogendoorn C.J. Numer. Heat Transfer Pt. B. 28:1995;59.
46. Ince N.Z., Launder B.E. Int. J. Heat Mass Transfer. 10(2):1989;110.
47. Vasić S., Hanjalić K. Henkes R.A.W.M., Hoogendoorn C.J. Turbulent Natural Convection in Enclosures, a Computational and Experimental Benchmark Study. 1993;133 EETI, Paris.
48. Wolfshtein M. Int. J. Heat Mass Transfer. 12:1969;301.
49. Kim C.-J., Ro S.T. Numer. Heat Transfer Pt. B. 28:1995;385.
50. T. Mori, R.A. Brown, private communication, 1996.
51. A. Lipchin, R.A. Brown, Computational technology for fluid/thermal/chemical system and industrial applications, Proceedings of the 1998 Joint ASME/JSME Pressure Vessels and Piping Conference, July 26-30, 1998, San Diego, CA.
52. T. Mori, T.R. Sinno, R.A. Brown, K.M. Kim, Abstracts of the 193rd Meeting of The Electrochemical Society, May 3-8, 1998, San Diego, CA, p. 496.