Moving boundary computation of the float-zone process

International Journal for Numerical Methods in Engineering

Volumn 40, Issue 7, 1997, Pages 1231-1261

  Rao, Madhukar M ^a   Shyy, Wei ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Crystal growth; Float zone; Moving boundary; Solidification; Thermocapillary transport

Indexed keywords

BOUNDARY CONDITIONS; CAPILLARY FLOW; FINITE VOLUME METHOD; INTERFACES (MATERIALS); NATURAL CONVECTION; NAVIER STOKES EQUATIONS; TEMPERATURE DISTRIBUTION;

FLOAT ZONE PROCESS; FREE SURFACE SHAPE; MELT CRYSTAL INTERFACE; MOVING BOUNDARY METHOD; THERMOCAPILLARY CONVECTION;

CRYSTAL GROWTH FROM MELT;

EID: 0031120949     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19970415)40:7<1231::AID-NME112>3.0.CO;2-F     Document Type: Article

References (26)

1. W. Shyy and M. M. Rao, 'Calculation of meniscus shapes and transport processes in float zone', Int. J. Heat Mass Transfer, 38, 2281-2295 (1995).
2. N. Kobayashi, 'Computer simulation of the steady flow in a cylindrical floating Zone under low gravity', J. Crystal Growth, 66, 63-72(1984).
3. N. Kobayashi, 'Steady convection caused by the temperature inhomogeneity in a cylindrical floating zone', Japan. J. Appl. Phys., 27, 20-24 (1988).
4. G. W. Young and A. Chait, 'Surface tension driven heat, mass and momentum transport in a two-dimensional float zone', J. Crystal Growth, 106, 445-466 (1990).
5. G. P. Neitzel, J. R. Hyer and D. F. Jankowski, 'Thermocapillary convection in a model float-zone', AIAA Paper No. 90-0406 (1990).
6. C.-F. Chu and J.-C. Chen, 'Numerical computation of fluid flow of floating-zone crystal growth of molybdenum', Int. J. Heat Mass Transfer, 38, 1841-1853 (1995).
7. J. L. Duranceau and R. A, Brown, 'Thermal-capillary analysis of small-scale floating zones', J. Crystal Growth, 75, 367-389 (1986).
8. C. W. Lan and S. Kou, 'Thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity', J. Crystal Growth, 102, 1043-1058 (1990).
9. C. W. Lan and S. Kou, 'Heat transfer, fluid flow and interface shapes in floating-zone crystal growth', J. Crystal Growth, 108, 351-366 (1991).
10. C. W. Lan and S. Kou, 'Shortened floating zone crystal growth under normal gravity', J. Crystal Growth, 119, 281-291 (1992).
11. Y. T. Chan and S. K. Choi, 'Numerical simulations of inductive-heated float-zone growth', J. Appl. Phys., 72, 3741-3749 (1992).
12. Y. T. Chan, 'Crystal growth', in M. Meyyappan (ed.), Computational Modeling in Semiconductor Processing, Artech House, Boston (1995).
13. A. Mühlbauer, A. Muiznieks, J. Virbulis, A. Lüdge and H, Riemann, Interface shape, heat transfer and fluid flow in the floating zone growth of large silicon crystals with the needle-eye technique', J. Crystal Growth, 151, 66-79 (1995).
14. C. W. Lan and S, Kou, 'Effect of rotation on radial dopant segregation in microgravhy floating-zone crystal growth', J. Crystal Growth, 133, 309-321 (1993).
15. C. W. Lan, 'Newton's method for solving heat transfer, fluid flow and interface shapes in a floating molten zone', Int. j. numer. methods fluids, 19, 41-65(1994).
16. H. Chen, M. Z. Saghir, D, H. H. Quon and S. Chehab, 'Numerical study on transient convection in float zone induced by g-jitiers', J. Crystal Growth, 142, 362-372 (1994).
17. R. N, Grugel, X. F. Shen, A. V. Anilkumar and T. G, Wang, 'The influence of vibration on microstructural uniformity during floating-zone crystal growth', J. Crystal Growth, 142, 209-214 (1994).
18. W. R. Hu, J. Z. Sbu, R. Zhou and Z. M. Tang, 'Influence of liquid bridge volume on the onset of oscillation in floating zone convection. I. Experiments', J. Crystal Growth, 142, 379-384 (1994).
19. Z. M. Tang and W. R. Hu, 'Influence of liquid bridge volume on the onset of oscillation in floating zone convection. II. Numerical simulation', J. Crystal Growth, 142, 385-391 (1994).
20. J. Lee, D.-J. Lee and J. H. Lee, 'On the mechanism of oscillation in a simulated floating zone', J. Crystal Growth, 152, 341-346 (1995).
21. A. Yeckel, A. G. Salinger and J. J. Derby, 'Theoretical analysis and design considerations for float-zone refinement of electronic grade silicon sheets', J. Crystal Growth, 152, 51-64 (1995).
22. M. Levenstam, G. Amberg, T. Carlberg and M. Andersson, 'Experimental and numerical studies of thermocapillary convection in a floating zone like configuration', J. Crystal Growth, 158, 224-230 (1996).
23. W. Shyy and M. M. Rao, 'Enthalpy based formulations for phase change problems with application to g-jitter', AIAA Paper No. 93-2831, also Microgravhy Sci. Technol, 7, 441-491 (1994).
24. W. Shyy, Computational Modeling for Fluid Flow and Interfacial Transport, Elsevier, Amsterdam (1994).
25. W. Shyy, H. S. Udaykumar, M. M. Rao and R. W. Smith, Computational Fluid Dynamics with Moving Boundaries, Taylor & Francis, Washington, D. C. (1996).
26. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Washington, D. C. (1980).