Developing quantitative, multiscale models for microgravity crystal growth

Annals of the New York Academy of Sciences

Volumn 1077, Issue , 2006, Pages 124-145

  Derby, Jeffrey J ^a   Kwon, Yong Il ^a   Pandy, Arun ^a   Sonda, Paul ^a   Yeckel, Andrew ^a   Jung, Thomas ^b   Müller, Georg ^b  

^a University of Minnesota   (United States)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

3d models; Convection; Crystal growth; Finite element methods; Furnace heat transfer; Heat transfer; Mass transfer; Mathematical model; Microgravity; Multiscale models; Numerical model; Segregation; Transient analysis

Indexed keywords

CONFERENCE PAPER; CRYSTALLIZATION; KINETICS; MATHEMATICAL MODEL; MICROGRAVITY; MOLECULAR MODEL; PREDICTION; QUANTITATIVE ANALYSIS; THERMODYNAMICS;

EID: 33845619019     PISSN: 00778923     EISSN: 17496632     Source Type: Book Series    
DOI: 10.1196/annals.1362.063     Document Type: Conference Paper

References (102)

1. HURLE, D.T.J. 2002. The origins of the International Crystal Growth Conferences, the International Organisation for Crystal Growth and the Journal of Crystal Growth. J. Crystal Growth 243: 1-7.
2. RINDONE, G.E., Ed. 1982. Materials Processing in the Reduced Gravity Environment of Space. Elsevier/North-Holland, New York.
3. WALTER, H.U., Ed. 1987. Fluid Sciences and Materials Science in Space. Springer, Berlin.
4. WILCOX, W.R. & L.L. REGEL. 2001. Microgravity effects on materials processing: A review. In: Proceedings of the 7th European Conference on Advanced Materials and Processes. Associazione Italiana di Metallurgia, Milano.
5. BENZ, K.W. & P. DOLD. 2002. Crystal growth under microgravity: present results and future prospects towards the International Space Station. J. Crystal Growth 237-239: 1638-1645.
6. WITT, A.F., H.C. GATOS, M. LICHTENSTEIGER, et al. 1975. Crystal growth and steady-state segregation under zero gravity: In Sb. J. Electrochem. Soc. 122: 276.
7. WITT, A.F., H.C. GATOS, M. LICHTENSTEIGER, et al. 1978. Quantitative analysis of the effects of destabilizing versus thermal gradients on crystal growth and segregation: Ga-Doped Ge. J. Electrochem. Soc. 125: 1832.
8. CROUCH, R.K., A.L. FRIPP, W.J. DEBNAN, et al. 1987. Results from a compound semiconductor crystal growth experiment in a low gravity environment. In Proceedings of the 1st International SAMPE Electronic Conference, 330. Santa Clara, CA.
9. BLY, J.M., M.L. KAFOREY, D.H. MATTHIESEN & A. CHAIT. 1997. Interface shape and growth rate analysis of Se/GaAs bulk crystals grown in the NASA crystal growth furnace (CGF). J. Crystal Growth 174: 220-225.
10. D.H. MATTHIESEN. 1994. The study of dopant segregation behavior during the growth of GaAs in microgravity. In Joint Launch + One Year Science Review. NASA Conference Publication 3272: 223.
11. GILLIES, D.C., S.L. LEHOCZY, F.R. SZOFRAM, et al. 2002. Effect of residual accelerations during microgravity directional solidification of mercury cadmium telluride on the USMP-2 mission. J. Crystal Growth 174: 101-107.
12. LEHOCZKY, S. et al. 1994. Crystal growth of selected II-VI semiconducting alloys by directional solidification. In Joint Launch + One Year Science Review. NASA Conference Publication 3272: 163-222.
13. CHANG, C.J. & R.A. BROWN. 1983. Radial segregation induced by natural convection and melt/solid interface shape in vertical Bridgman growth. J. Crystal Growth 63: 343-364.
14. BROWN, R.A. 1988. Theory of transport processes in single crystal growth from the melt. AIChE J. 34: 881.
15. BURTON, J.A., R.C. PRIM & W.P. SCHLICHTER. 1953. The distribution of solute in crystals grown from the melt. Theoretical J. Chem. Phys. 21: 1987-1991.
16. SCHEIL, E. 1942. Bemerkungen zur schichtkristallbildung. Z. Metallk. 34: 70-72.
17. TILLER, W.A., K.A. JACKSON, J.W. RUTTER & B. CHALMERS. 1953. The redistribution of solute atoms during the solidification of metals. Acta Met. 1: 428.
18. SMITH, V.G., W.A. TILLER & J.W. RUTTER. 1955. A mathematical analysis of solute redistribution during solidification. Can. J. Phys. 33: 723.
19. WILCOX, W.R. 1969. Validity of the stagnant-film approximation for mass transfer in crystal growth and dissolution. Mat. Res. Bull. 4: 265.
20. ROSENBERGER, F. & G. MÜLLER. 1983. Interfacial transport in crystal growth, a parametric comparison of convective effects. J. Crystal Growth 65: 91.
21. BROWN, R.A. & D.H. KIM. 1991. Modeling of directional solidification: from Scheil to detailed numerical simulation. J. Crystal Growth 109: 50.
22. MÜLLER, G. & A. OSTRAGORSKY. 1994. Convection in melt growth. In Handbook of Crystal Growth. D.T.J. Hurle, Ed. North-Holland. Amsterdam.
23. MÜLLER, G. 2003. Modeling of crystal growth from the melt. In Computational Modelling and Simulations of Materials. P. Vincenzini and A. Lami, Eds.: 267-278. Techna Srl.
24. LAN, C.W. 2004. Recent progress of crystal growth modeling and growth control. Chem. Eng. Sci. 59: 1437-1457.
25. YECKEL, A. & J.J. DERBY. 2005. Computer modelling of bulk crystal growth. Bulk Crystal Growth of Electronic, Optical, and Optoelectronic Materials. P. Capper, Ed.: 73-119. John Wiley & Sons, West Sussex, UK.
26. POLEZAHEV, V.I. & A.I. FEDYOSHKIN. 1980. Izv. Akad. Nauk SSR. Mekh. Zhidkosti i Gaza 3: 11.
27. POLEZAHEV, V.I., A.P. LEBEDEV & S.A. NIKITIN. 1984. In Proceedings of the 5th European Symposium on Materials Science under Microgravity, p. 237. Schloss Elmau, ESA SP-222.
28. KAMOTANI, Y., A. PRASAD & S. OSTRACH. 1981. Thermal convection in an enclosure due to vibrations aboard a spacecraft. AIAA J. 19: 511.
29. HEISS, T., S. SCHNEIDER & J. STRAUB. 1987. In Proceedings of the 6th European Symposium on Materials Science under Microgravity Conditions, p. 517. Bordeaux, ESA SP-256.
30. SCHNEIDER, S. & J. STRAUB. 1989. Influence of Prandtl number on laminar natural convection in a cylinder caused by g-jitter. J. Crystal Growth 97: 235.
31. MCFADDEN, G.B. & S.R. CORIELL. 1988. Solutal convection during directional solidification. In Proceedings of the AIAA/ASME/SIAM/APS 1st National Fluid Dynamics Congress, p. 1572. Cincinnati, OH.
32. GRIFFIN, P.R. & S. MOTKEF. 1989. Influence of nonsteady gravity on natural convection during microgravity solidification of semiconductors. Part I. J. Appl. Microgravity Tech. 2: 121.
33. GRIFFIN, P.R. & S. MOTKEF. 1989. Influence of nonsteady gravity on natural convection during microgravity solidification of semiconductors. Part II. J. Appl. Microgravity Tech. 2: 128.
34. BIRINGEN, S. & G. DANABASOGLU. 1990. Computation of convective flow with gravity modulation in rectangular cavities. J. Thermophysics Heat Transfer 4: 357.
35. BAUMGARTL, J. & G. MÜLLER. 1996. The use of magnetic fields for damping the action of gravity fluctuations (g-jitter) during crystal growth under microgravity. J. Crystal Growth 169: 582.
36. LI, B.Q. & H.C. DE GROH. 2003. Three-dimensional gravity-jitter- induced melt flow and solidification in magnetic fields. J. Thermophys. Heat Transfer 17: 498-508.
37. MONTI, R. 1990. Gravity jitters: effects on typical fluid science experiments. In Low Gravity Fluid Dynamics and Transport Phenomena. J.N. Koster & R.L. Sani, Eds. AIAA Astronaut. Aeronout. 130: 275.
38. ALEXANDER, J.I.D., J. OUAZZANI & F. ROSENBERGER. 1989. Analysis of the low-gravity tolerance of Bridgman-Stockbarger crystal growth. Part I. Steady and impulse accelerations. J. Crystal Growth 97: 285-302.
39. ALEXANDER, J.I.D., S. AMIROUDINE, J. OUAZZANI & F. ROSENBERGER. 1991. Analysis of low gravity tolerance of Bridgman-Stockbarger crystal growth. Part II. Steady and impulse accelerations. J. Crystal Growth 113: 21-302.
40. GARANDET, J.P., S. CORRE, S. GAVOILLE, J.J. FAVIER & J.I.D. ALEXANDER. 1996. On the effect of gravity perturbations on composition profiles during Bridgman crystal growth in space. J. Crystal Growth 165: 471-481.
41. SHYY, W. & M.M. RAO. 1994. Enthalpy-based formulations for phase-change problems with applications to g-jitters. Microgravity Sci. Technol. 7: 41-49.
42. NAUMANN, R.J. 1994. Modeling flows and solute redistribution resulting from small transverse accelerations in Bridgman growth. J. Crystal Growth 142: 142.
43. NAUMANN, R.J. 1996. Stabilizing/destabilizing effects of axial accelerations in Bridgman growth. J. Crystal Growth 165: 129-146.
44. DUFFAR, T. & J.-P. GARANDET. 2000. Gravity driven disturbances during Bridgman crystal growth in space. Acta Astronaut. 47: 317-323.
45. LAN, C.W. & C.Y. TU. 2002. Three-dimensional analysis of flow and segregation control by slow rotation for Bridgman crystal growth in microgravity. J. Crystal Growth 237-239: 1881-1885.
46. VOLLER, V. & F. PORTÉ-AGEL. 2002. Moore's law and numerical modeling. J. Comput. Phys. 179: 698-703.
47. DERBY, J., R. BROWN, F. GEYLING, et al. Finite element analysis of a thermal-capillary model for liquid-encapsulated Czochralski growth. 1985. J. Electrochem. Soc. 132: 470-482.
48. SACKINGER, P., R. BROWN & J. DERBY. 1989. A finite element method for analysis of fluid flow, heat transfer, and free interfaces in Czochralski crystal growth. Int. J. Numer. Methods Fluids 9: 453-492.
49. XIAO, Q. & J. DERBY. 1995. Three-dimensional melt flows in Czochralski oxide growth: high-resolution, massively parallel, finite element computations. J. Crystal Growth 152: 169-181.
50. YECKEL, A., J. SMITH & J. DERBY. 1997. Parallel finite element calculation of flow in a three-dimensional lid-driven cavity using the CM-5 and T3D. Int. J. Numer. Methods Fluids 24: 1-13.
51. MAROUDAS, D. 2003. AIChE Annual Meeting San Francisco, CA, November 16-21.
52. KUPPURAO, S., S. BRANDON & J.J. DERBY. 1995. Modeling the vertical Bridgman growth of cadmium zinc telluride I. Quasi-steady analysis of heat transfer and convection. J. Crystal Growth. 155: 93-102.
53. KUPPURAO, S., S. BRANDON & J.J. DERBY. 1995. Modeling the vertical Bridgman growth of cadmium zinc telluride II. Transient analysis of zinc segregation. J. Crystal Growth. 155: 103-111.
54. DERBY, J.J. & A. YECKEL. 2004. Modeling of crystal growth processes. In Crystal Growth - From Fundamentals to Technology. G. Müller, J.-J. Métois & P. Rudolph, Eds.: 143-167. Elsevier, Amsterdam.
55. HUGHES, T.J.R. 1987. The Finite Element Method. Prentice-Hall, Inc. Englewood Cliffs, NJ.
56. DAHLQUIST, G. & A. BJÖRCK. 1974. Numerical Methods. Prentice-Hall. Englewood Cliffs, NJ..
57. SONDA, P., A. YECKEL, P. DAOUTIDIS & J.J. DERBY. 2003. Improved radial segregation via the destabilizing vertical Bridgman configuration. J. Crystal Growth 260: 263-276.
58. SONDA, P., A. YECKEL, P. DAOUTIDIS & J.J. DERBY. 2005. Hopf bifurcation and solution multiplicity in a model for destabilized Bridgman crystal growth. Chem. Eng. Sci. 60: 1323-1336.
59. CHRISTODOULOU, K., S. KISTLER & P. SCHUNK. 1997. In Liquid Film Coating. S. Kistler & P. Schweizer, Eds.: 297. Chapman and Hall, London.
60. DE SANTOS, J. 1991. Two-phase cocurrent downflow through constructed passages. Ph.D. Thesis, University of Minnesota, available through University Microfilms, Inc. (www.umi.com).
61. CHRISTODOULOU, K. & L.E. SCRIVEN. 1992. J. Comput. Phys. 99: 39.
62. YECKEL, A. & J.J. DERBY. 2005. A parallel, finite element method for computing three-dimensional moving boundaries in crystal growth problems. In preparation.
63. CROUZEIX, M. & P.-A. RAVIAR. 1973. Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, RAIRO, Série Analyse Numérique 7: 33-75.
64. BERTRAND, F., M.R. GADBOIS & P.A. TANGUY. 1992. Tetrahedral elements for fluid flow. Int. J. Number Methods Eng. 33: 1251-1267.
65. BALAY, S., K. BUSCHELMAN, W.D. GROPP, et al. 2001. PETSc. Available at http://www.mcs.anl.gov/petsc.
66. SONDA, P., Y.-I. KWON, A. YECKEL & J.J. DERBY. 2005. Computing three-dimensional, incompressible flows in melt crystal growth systems using a new, higher-order, mixed-formulation, Galerkin finite element method. The Third M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, June 14-17.
67. ETHIER, C.R. & D.A. STEINMAN. 1994. Exact fully 3D Navier-Stokes solutions for benchmarking. Int. J. Number Methods Fluids 19: 369-375.
68. SONDA, P., Y.-I. KWON, A. YECKEL & J.J. DERBY. 2005. Computing three-dimensional, incompressible flows using a higher-order, mixed Galerkin finite element method. To be submitted.
69. KASSAB, A.J. & M.H. ALIABADI, Eds. 2001. Advances in Boundary Elements: Coupled Field Problems. Computational Mechanics. Boston.
70. MORAND, H. & R. OHAYON. 1995. Fluid-Structure Interaction. John Wiley & Sons. Chichester.
71. DOWELL, E. & K.C. HALL. 2001. Modeling of fluid-structure interaction. Annu. Rev. Fluid Mech. 33: 445-490.
72. BELYTSCHKO, T. & R. MULLEN. 1981. Two-dimensional fluid-structure impact computations with regularization. Comput. Methods Appl. Mech. Eng. 27: 139-154.
73. DONEA, J., S. GIULIANI & J.P. HALLEUX. 1982. An arbitrary Lagrangian-Eulerian finite element method for transient fluid-structure interaction. Comput. Methods Appl. Mech. Eng. 33: 689-723.
74. BATHE, K.-J., H. ZHANG & M.H. WANG. 1995. Finite element analysis of incompressible and compressible fluid flows with free surfaces and structural interactions. Comput. Struct. 56: 193-213
75. MOURO, M. & P. Le TALLEC. 2001. Fluid structure interaction with large structural displacements. Comput. Methods Appl. Mech. Eng. 190: 3039-3067.
76. MORTON, S.A., R.B. MELVILLE & M.R. VISBAL. 1998. Accuracy and coupling issues of aeroelastic Navier Stokes solutions on deforming meshes. J. Aircr. 35: 798-805.
77. PIPERNO, S., C. FARHAT & B. LARROUTURO. 1995. Partitioned procedures for the transient solution of coupled aeroelastic problems. Comput. Methods Appl. Mech. Eng. 124: 79-112.
78. DUBINI, G., R. PIETRABISSI & F.M. MONTEVECCHI. 1995. Fluid-structure interaction in bio-fluid mechanics. Med. Eng. Phys. 17: 609-617.
79. ARGYRIS, J.I., S. DOLTSINIS, P. PIMENTA & H. WÜSTENBERG. 1982. Thermomechanical response of solids at high strains natural approach. Comput. Methods Appl. Mech. Eng. 32: 3-57.
80. ZIENKIEWICZ, O.C., D.K. PAUL & A.H.C. CHAN. 1988. Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. Int. J. Number Methods Eng. 26: 1039-1055.
81. DIVO, E., E. STEINTHORSSON, F. RODRIGUEZ, et al. 2003. Glenn-HT/BEM Conjugate Heat Transfer Solver for Large-Scale Turbomachinery Models. NASA/CR2003-212195.
82. DIVO, E., E. STEINTHORSSON, A.J. KASSAB & R. BIALECKI. 2002. An iterative BEM/FVM protocol for steady-state multi-dimensional conjugate heat transfer in compressible flows. Eng. Anal. Bound. Eleme. 26: 447-454.
83. PATANKAR, S.V. 1878. A numerical method for conduction in composite materials, flow in irregular geometries and conjugate heat transfer. In Proceedings of the 6th International Heat Transfer Conference. NRC Canada, and Hemisphere Pub. Co., New York, Vol. 3, 297-302.
84. COMINI, G., O. SARO & M. MANZAN. 1993. A physical approach to finite element modeling of coupled conduction and convection, Vol. 24. In Numerical Heat Transfer, Part B.: 243-261.
85. SHYY, W. & J. BURKE. 1994. Study of Iterative Characteristics of Convective Diffusive and Conjugate Heat Transfer Problems, Vol. 26. In Numerical Heat Transfer, Part B.: 21-37.
86. HASSAN, B., D. KUNTZ & D.L. POTTER. 1998. Coupled Fluid/Thermal Prediction of Ablating Hypersonic Vehicles. AIAA Paper 98-0168.
87. SHYY, W. 2002. Multi-scale computation of heat transfer with moving boundaries. Int. J. Heat Fluid Flow 23: 278-287.
88. DUPRET, F., P. NICODÈME, Y. RYCKMANS, et al. 1990. Global modelling of heat transfer in crystal growth furnaces. Int. J. Heat Mass Transfer 33: 1849.
89. KURZ, M., A. PUSZTAI & G. MÜLLER. 1999. Development of a new powerful computer code CrysVUn++ especially designed for fast simulation of bulk crystal growth processes. J. Crystal Growth 198: 101.
90. BACKOFEN, R., M. KURZ & G. MÜLLER. Process modelling of the industrial VGF crystal growth process using the software package CrysVUn++. J. Crystal Growth 199: 210.
91. BAUMGARTL, J., A. BUNE, K. KOAI, et al. 1993. Global simulation of heat transport, including melt convection in a Czochralski crystal growth process - combined finite element/finite volume approach. Mat. Sci. Eng. A173: 913.
92. OUYANG, H. & W. SHYY. 1996. Multi-zone simulation of the Bridgman growth process of β-NiAl crystal. Int. J. Heat Mass Transfer 39: 2039-2051.
93. OUYANG, H. & W. SHYY. 1997. Numerical simulation of CdTe vertical Bridgman growth. J. Crystal Growth 173: 352-366.
94. TOMÁS, C.M. & V. MUŃOZ. 2001. CdTe crystal growth process by the Bridgman method: numerical simulation. J. Crystal Growth 222: 435-451.
95. VIRBULIS, J., Th. WETZEL, A. MUIZNIEKS, et al. 2001. Numerical investigation of silicon melt flow in large diameter CZ-crystal growth under the influence of steady and dynamic magnetic fields. J. Crystal Growth 230: 92-99.
96. LUKANIN, D.P., V.V. KALAEV, Yu. N. MAKAROV, et al. 2004. Advances in the simulation of heat transfer and prediction of the melt-crystal interface shape in silicon CZ growth. J. Crystal Growth 266: 20-27.
97. YECKEL, A., A. PANDY & J.J. DERBY. 2001. Representing realistic complexity in numerical models of crystal growth: coupling of global furnace modeling to three-dimensional flows. In Advances in Computational Heat Transfer II, Vol. 2, G. De Vahl Davis & E. Leonardi, Eds.: 1193-1200. Begell House, Inc. New York.
98. YECKEL, A., G. COMPERE, A. PANDY & J.J. DERBY. 2004. Three-dimensional imperfections in a model vertical Bridgman growth system cadmium zinc telluride. J. Crystal Growth 263: 629-644.
99. PANDY, A. 2004. Global modeling of bulk crystal growth of cadmium zinc telluride in industrial VB/VGF systems. PhD Thesis, University of Minnesota.
100. YECKEL, A. & R.T. GOODWIN III. 2003. Cats2D (Crystallization and Transport Simulator), User Manual. Unpublished. Available at http://www.msi.umn.edu/~yeckel/cats2d.html.
101. PANDY, A., A. YECKEL, M. REED, et al. 2005. Analysis of the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace via a self-consistent, multi-scale numerical model. J. Crystal Growth 276: 133-147.
102. YECKEL, A., A. PANDY, & J.J. DERBY. 2006. Fixed-point convergence of modular, steady-state heat transfer models coupling multiple scales and phenomena for melt crystal growth. Int. J. Number Methods Eng. In press.