Modeling and bulk crystal growth processes: What is to be learned?

AIP Conference Proceedings

Volumn 1270, Issue , 2010, Pages 221-246

  Derby, Jeffrey J ^a  

^a University of Minnesota   (United States)

Author keywords

Continuum transport; fluid mechanics; heat transfer; morphological instability; segregation; solidification

Indexed keywords

EID: 77955643547     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.3476228     Document Type: Conference Paper

References (86)

1. G.E.P. Box and N.R. Draper, Empirical Model-Building and Response Surfaces, p. 424,Wiley, 1987.
2. R. Aris, "The mere notion of a model," Mathematical Modelling, 1 (1980) 1-12.
3. R. Aris, "Ut Simulacrum, Poesis," New Literary History, 20 (1988-89) 323-340.
4. Karlin, Samuel, 11th R A Fisher Memorial Lecture, Royal Society 20, April 1983.
5. R.B. Bird, W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, John Wiley, New York, 1960.
6. J.S. Szmyd and K. Suzuki, editors. Modelling of Transport Phenomena in Crystal Growth, volume 6 of Developments in Heat Transfer, WIT Press, Southampton, England, 2000.
7. R.A. Brown, "Theory of transport processes in single crystal growth from the melt," AIChE J. 34, 881 (1988).
8. J.J. Derby, "Theoretical modeling of Czochralski crystal growth," MRS Bulletin XIII(10), 29-35 (1988).
9. J.J. Derby. "Macroscopic transport processes during the growth of single crystals from the melt," In J.P. van der Eerden and O.S.L. Bruinsma, editors, Science and Technology of Crystal Growth, page p. 97. Kluwer Academic Publishers, Dordecht, The Netherlands, 1995.
10. G. Müller and A. Ostrogorsky, "Convection in melt growth," In D.T.J. Hurle, editor, Bulk Crystal Growth, Growth Mechanisms and Dynamics, Handbook of Crystal Growth Vol. 2b, page 708. North-Holland, Amsterdam, 1994.
11. A. Yeckel and J.J. Derby, "Computational simulations of the growth of crystals from liquids," In H.J. Scheel and T. Fukuda, editors, Crystal Growth Technology, chapter 6. John Wiley & Sons, West Sussex, UK, 2003.
12. V. I. Polezhaev, "Modeling of technologically important hydrodynamics and heat/mass transfer processes during crystal growth," In H.J. Scheel and T. Fukuda, editors, Crystal Growth Technology, chapter 8. John Wiley & Sons, West Sussex, UK, 2003.
13. K. Kakimoto, "Heat and mass transfer under magnetic fields," In H.J. Scheel and T. Fukuda, editors, Crystal Growth Technology, chapter 7. John Wiley & Sons, West Sussex, UK, 2003.
14. C.W. Lan, "Recent progress of crystal growth modeling and growth control," Chem. Engng. Science, 59, 1437-1457 (2004).
15. J.J. Derby and A. Yeckel, "Modeling of Crystal Growth Processes," in: Crystal Growth - From Fundamentals to Technology, Eds. G. Müller, J.-J. Métois, and P. Rudolph, Elsevier, Amsterdam (2004) pp. 143-167.
16. A. Yeckel and J.J. Derby, "Computer modelling of bulk crystal growth," in: Bulk Crystal Growth of Electronic, Optical, and Optoelectronic Materials, Ed. P. Capper, John Wiley & Sons, West Sussex, UK, pp. 73-119 (2005).
17. J.J. Derby, "Crystal Growth: Crystal growth, bulk (Theory and Models)," in: Encyclopedia of Condensed Matter Physics, Eds. F. Bassani, J. Liedl, and P.Wyder, Academic Press, pp. 274-282 (2005).
18. J.J. Derby, Y.-I. Kwon, A. Pandy, P. Sonda, A. Yeckel, T. Jung, and G. Müller, "Developing Quantitative, Multi-Scale Models For Microgravity Crystal Growth," Ann. N.Y. Acad. Sci. 1077, 124-145 (2006).
19. Y.I. Kwon, B. Dai, and J.J. Derby, "Assessing the dynamics of liquid-phase solution growth via step growth models: From BCF to FEM," Progress in Crystal Growth and Characterization of Materials 53, 167-206 (2007).
20. J.J. Derby, J.R. Chelikowsky, T. Sinno, B. Dai, Y.-I. Kwon, L. Lun, A. Pandy, and A. Yeckel, "Large- Scale Numerical Modeling of Melt and Solution Crystal Growth," in: Perspectives on Inorganic, Organic and Biological Crystal Growth: From Fundamentals to Applications: 13th International Summer School on Crystal Growth, Eds. M. Skowronski, J.J. DeYoreo, and C.A. Wang, AIP Conference Proceedings 916, Melville, New York, 139-158 (2007).
21. F. Dupret, J.J. Derby, K. Kakimoto, G. Müller, N. Van Den Bogaert, and A.A. Wheeler, editors, Proceedings of the Second International Workshop on Modelling in Crystal Growth, volume 180 of J. Crystal Growth. Elsevier, 1997.
22. A. Yeckel, V. Prasad, and J.J. Derby, editors, Proceedings of the Third International Workshop on Modeling in Crystal Growth, volume 230 of J. Crystal Growth. Elsevier, 2000.
23. C.W. Lan, N. Imaishi and K. Kakimoto, editors, Proceedings of the Fourth International Workshop on Modelling in Crystal Growth, volume 226 of J. Crystal Growth. Elsevier, 2004.
24. J. Friedrich and G. Müller, editors, Proceedings of the Fifth International Workshop on Modelling in Crystal Growth, volume 303 of J. Crystal Growth. Elsevier, 2007.
25. C. Lynch, J.J. Derby, R. Bhatt, C. Caneau, S. Dost, A. Yeckel, editors, Proceedings of the 6th International Workshop on Modeling in Crystal Growth, volume 312 of J. Crystal Growth, Elsevier, 2007, pp. 1397-1467.
26. M.C. Flemings, Solidification Processing (McGraw-Hill, New York, 1974).
27. E. Scheil, "Bemerkungen zur schichtkristallbildung," Z. Mettalk. 34, 70-72 (1942).
28. W.A. Tiller, K.A. Jackson, J.W. Rutter, and B. Chalmers, "The redistribution of solute atoms during the solidification of metals," Acta Metall. 1, 428 (1953).
29. V.G. Smith, W.A. Tiller, and J.W. Rutter, "A mathematical analysis of solute redistribution during solidification," Can. J. Phys. 33 723 (1955).
30. K.A. Jackson, "Constitutional supercooling surface roughening," Journal of Crystal Growth 264 (2004) 519-529.
31. J. A. Burton, R. C. Prim, and W. P. Slichter, "The distribution of solute in crystals grown from the melt. Part I. Theoretical," J. Chem. Phys., 21, 1987-1991 (1953).
32. D.T.J. Hurle and P. Rudolph, "A brief history of defect formation, segregation, faceting, and twinning in melt-grown semiconductors," Journal of Crystal Growth 264 (2004) 550-564.
33. W. R. Wilcox, "Validity of the stagnant-film approximation for mass transfer in crystal growth and dissolution," Mat. Res. Bull., 4, 265-274 (1969).
34. F. Rosenberger and G. Müller, "Interfacial transport in crystal growth, a parametric comparison of convective effects," J. Crystal Growth, 65, 91-104 (1983).
35. R.A. Brown and D.H. Kim, "Modeling of directional solidification: From Scheil to detailed numerical simulation," J. Crystal Growth, 109, 50-65 (1991).
36. W.W. Mullins and R.F. Sekerka, "Stability of a planar interface during solidification of a dilute binary alloy," J. Appl. Phys. 35, 444 (1964).
37. R.F. Sekerka, Morphological stability, J. Cryst. Growth 3, 71 (1968).
38. Z. Bi, "Directional Solidification of a Binary Alloy Using the Phase Field Model," Doctoral Thesis, Carnegie Mellon University, Pittsburgh 2001.
39. Z. Bi, R. F. Sekerka, "Phase field modeling of shallow cells during directional solidification of a binary alloy," J. Crystal Growth 237-239, 138-143 (2002).
40. K.A. Jackson, "Mechanism of growth," in: Liquid Metals and Solidification, Am. Soc.Metals (1958) 174-186.
41. W. K. Burton and N. Cabrera, "Crystal growth and surface structure: Part I," Discussions Faraday Soc., 5, 33, (1949).
42. F.C. Frank, "The influence of dislocations on crystal growth," Discussions Faraday Soc., 5, 48, (1949).
43. W. K. Burton, N. Cabrera, and F. C. Frank, "The growth of crystals and the equilibrium structure of their surfaces," Phil. Trans. Roy. Soc. London, 243, 299-358, (1951).
44. N. Cabrera and M.M. Levine, "XLV. On the dislocation theory of evaporation of crystals," Phil. Mag. 1 (1956), 450-458.
45. S. Brandon and J.J. Derby, "Heat transfer in vertical Bridgman growth of oxides: Effects of conduction, convection, and internal radiation," J. Crystal Growth 121, 473-494 (1992).
46. S. Brandon and J.J. Derby, "A finite element method for conduction, internal radiation, and solidification in a finite axisymmetric enclosure," Int. J. Num. Meth. Heat Fluid Flow, 2:299, 1992.
47. A. A. Chernov, "The spiral growth of crystals," Soviet Physics Uspekhi, 4, 116-148, (1961).
48. G. H. Gilmer, R. Ghez, and N. Cabrera, "An analysis of combined surface and volume diffusion processes in crystal growth," J. Crystal Growth, 8, 79-93 (1971).
49. J. P. van der Eerden, "The advance velocity of steps under the influence of volume surface diffusion, by direct and indirect incorporation of growth units," J. Crystal Growth, 56, 174-188 (1982).
50. H. C. Jeong and E. D.Williams, "Steps on surfaces: experiment and theory," Surface Science Reports, 34, 171-294 (1999).
51. J. Krug, "Introduction to step dynamics and step instabilities," in Multiscale Modeling in Epitaxial Growth, A. Voigt, editor. Birkhauser, 69-96 (2005).
52. T. Michely and J. Krug, Islands, mounds, and atoms : patterns and processes in crystal growth far from equilibrium, Springer, Heidelberg, 2004.
53. S. R. Coriell, B. T. Murray, A. A. Chernov, and G. B. McFadden, "Step bunching on a vicinal face of a crystal growing in a flowing solution," J. of Crystal Growth, 169, 773-785 (1996).
54. S. R. Coriell, A. A. Chernov, B. T. Murray, and G. B. McFadden, "Step bunching: generalized kinetics," J. Crystal Growth, 183, 669-682 (1998).
55. B. Dai, Finite element modeling solution crystal growth at a meso-scale, Ph.D. thesis, University of Minnesota, 2005.
56. Winn, D. and Doherty, M. F., "Modeling Crystal Shapes of Organic Materials Grown from Solution," AIChE J. 46, 1348 (2000). (Pubitemid 30602676)
57. E. van Veenendaal, A. J. Nijdam and J. van Suchtelen, "Simulation of crystal shape evolution in two dimensions," J. Crystal Growth 235 603-618 (2002).
58. R.F. Sekerka, "Equilibrium and growth shapes of crystals: how do they differ and why should we care?" Cryst. Res. Technol. 40 291-306 (2005).
59. James, R. B., Schlesinger, T. E., Lund, J. C., and Schieber, M., "Cd1 xZnxTe spectrometers for gamma and X-ray applications," in [Semiconductors for Room Temperature Nuclear Detector Applications], an R. B. James, T. E. S., ed., Semiconductors and Semimetals 43, 335-381, Academic Press Inc, San Diego, CA (1995).
60. James, R. B. and Siffert, P., "Room Temperature semiconductor detectors: Proceedings of the 11th international workshop on room Temperature semiconductor x- and gamma-ray detectors and associated electronics," in [Nuclear Instruments and Methods in Physics Research A], James, R. B. and Siffert, P., eds., 458 (2001).
61. Szeles, C. and Driver, M. C., "Growth and properties of semi-insulating CdZnTe for radiation detector applications," SPIE Proceedings 3445, 2-9 (1998).
62. Szeles, C., "Advances in the crystal growth and device fabrication technology of CdZnTe room temperature radiation detectors," IEEE Transactions on Nuclear Science 51, 1242-1249 (2004).
63. Szeles, C., Cameron, S., Soldner, S., Ndap, J.-O., and Reed, M., "Development of the high-pressure electro-dynamic gradient crystal-growth technology for semi-insulating CdZnTe growth for radiation detector applications," J. Electron. Mater 33, 742-752 (2004).
64. Rudolph, P., "Fundamental studies on bridgman growth of CdTe," Progress in Crystal Growth and Characterization of Materials 29, 275-381 (1994).
65. Rudolph, P., "Melt growth of II-VI compound single crystals," in [Recent Development of Bulk Crystal Growth], Isshiki, M., ed., Research Signpost, Trivandrum, India (1998).
66. V.V. Godlevsky,J.J. Derby and J.R. Chelikowsky, "Ab Initio Molecular Dynamics Simulations of Liquid CdTe and GaAs: Semiconducting versus Metallic Behavior," Phys. Rev. Lett. 81, 4959-4962 (1998).
67. A. Yeckel, F.P. Doty, and J.J. Derby, "Effect of steady crucible rotation on segregation in highpressure vertical Bridgman growth of cadmium zinc telluride," J. Crystal Growth 203, 87-102 (1999).
68. V.V. Godlevsky, M. Jain, J.J. Derby, and J.R. Chelikowsky, "First principles calculations of liquid CdTe at temperatures above and below the melting point," Phys. Rev. B 60, 8640-8649 (1999).
69. A. Yeckel and J.J. Derby, "Effect of accelerated crucible rotation on melt composition in highpressure vertical Bridgman growth of cadmium zinc telluride," J. Crystal Growth 209, 734-750 (2000).
70. A. Yeckel and J.J. Derby, "Buoyant and rotational flows in small-scale vertical Bridgman growth of cadmium zinc telluride using accelerated crucible rotation," J. Crystal Growth 233, 599-608 (2001).
71. A. Yeckel, G. Compère, A. Pandy, and J.J. Derby, "Three-dimensional imperfections in a model vertical Bridgman growth system for cadmium zinc telluride," J. Crystal Growth 263, 629-644 (2004).
72. P. Sonda, A. Yeckel, P. Daoutidis, and J.J. Derby, "Development of model-based control for Bridgman crystal growth," J. Crystal Growth 266, 182-189 (2004).
73. A. Yeckel and J.J. Derby, "Feasibility study of cadmium zinc telluride growth using a submerged heater in a Bridgman system," J. Electronic Materials 33, 488-497 (2004).
74. E. Ko, M. Alemany, J.J. Derby, and J.R. Chelikowsky, "Ab initio simulations of non-stoichiometric CdxTe1 x liquids," J. Chem. Phys. 123, 084508 (2005).
75. A. Pandy, A. Yeckel, M. Reed, C. Szeles, M. Hainke, G. Müller, and J.J. Derby, "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 (2005).
76. L. Lun, A. Yeckel, C. Szeles, M. Reed, P. Daoutidis, and J.J. Derby, "On the effects of furnace gradients on interface shape during the growth of cadmium zinc telluride in EDG furnaces," J. Crystal Growth 290, 35-43 (2006).
77. L. Lun, A. Yeckel, P. Daoutidis, and J.J. Derby, "Decreasing lateral segregation in cadmium zinc telluride via ampoule tilting during vertical Bridgman growth," J. Crystal Growth 291, 348-357 (2006).
78. D. Gasperino, M. Bliss, K. Jones, K. Lynn, and J.J. Derby, "On crucible effects during the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace," J. Crystal Growth 311, 2327-2335 (2009).
79. M. Kurz, A. Pusztai, and G. Müller, "Development of a new powerfull computer code CrysVUN++ especially designed for fast simulation of bulk crystal growth processes," J. Crystal Growth 198, 101 (1999).
80. R. Backofen, M. Kurz, and G. Müller, "Process modelling of the industrial VGF crystal growth process using the software package CrysVUN++," J. Crystal Growth 199, 210 (2000).
81. A. Yeckel and R. T. Goodwin, Cats2D (Crystallization and Transport Simulator), User Manual, Unpublished (available at http://www.msi.umn.edu/ ~yeckel/cats2d.html), 2003.
82. A. Yeckel, A. Pandy, and J.J. Derby, "Fixed-point convergence of modular, steady-state heat transfer models coupling multiple scales and phenomena for melt crystal growth," Int. J. Numer. Meth. Engng. 67, 1768-1789 (2006).
83. J.J. Derby, L. Lun, and A. Yeckel, "Strategies for the coupling of global and local crystal growth models," J. Crystal Growth 303, 114-123 (2007).
84. A. Yeckel, L. Lun, and J.J. Derby, "An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications," J. Comp. Phys. 228, 8566-8588 (2009).
85. A. Yeckel, L. Lun, and J.J. Derby, "Multi-scale crystal growth computations via an approximate block Newton method," J. Crystal Growth 312, 1463-1467 (2010).
86. N. Zhang, A. Yeckel, and J.J. Derby, "An analysis of zinc distribution during electrodynamic gradient freeze growth of cadmium zinc telluride," J. Crystal Growth, submitted (2010).