DOI QR코드

DOI QR Code

Numerical analysis of steady and transient processes in a directional solidification system

  • Lin, Ting-Kang (Department of Mechanical Engineering, National Chiao Tung University) ;
  • Lin, Chung-Hao (Department of Mechanical Engineering, National Chiao Tung University) ;
  • Chen, Ching-Yao (Department of Mechanical Engineering, National Chiao Tung University)
  • Received : 2015.06.26
  • Accepted : 2015.12.15
  • Published : 2016.12.25

Abstract

Manufactures of multi-crystalline silicon ingots by means of the directional solidification system (DSS) is important to the solar photovoltaic (PV) cell industry. The quality of the ingots, including the grain size and morphology, is highly related to the shape of the crystal-melt interface during the crystal growth process. We performed numerical simulations to analyze the thermo-fluid field and the shape of the crystal-melt interface both for steady conditions and transient processes. The steady simulations are first validated and then applied to improve the hot zone design in the furnace. The numerical results reveal that, an additional guiding plate weakens the strength of vortex and improves the desired profile of the crystal-melt interface. Based on the steady solutions at an early stage, detailed transient processes of crystal growth can be simulated. Accuracy of the results is supported by comparing the evolutions of crystal heights with the experimental measurements. The excellent agreements demonstrate the applicability of the present numerical methods in simulating a practical and complex system of directional solidification system.

Keywords

References

  1. Black, A., Medina, J., Pineiro, A. and Dieguez, E. (2012), "Optimizing seeded casting of mono-like silicon crystals through numerical simulation", J. Cryst. Grow., 353(1), 12-16. https://doi.org/10.1016/j.jcrysgro.2012.04.033
  2. Chen, J.C., Teng, Y.Y., Wun, W.T., Lu, C.W., Chen, H.I., Chen, C.Y. and Lan, W.C. (2011), "Numerical simulation of oxygen transport during the CZ silicon crystal growth process", J. Cryst. Grow., 318(1), 318-323. https://doi.org/10.1016/j.jcrysgro.2010.11.145
  3. Chen, L. and Dai, B. (2012), "Optimization of power consumption on silicon directional solidification system by using numerical simulations", J. Cryst. Grow., 354(1), 86-92. https://doi.org/10.1016/j.jcrysgro.2012.06.010
  4. Devulapalli, B. and Kulkarni, M.S. (2009), "Modeling multi-crystalline silicon growth in directional solidification systems", ECS Trans., 18(1), 1023-1029.
  5. Demina, S.E. and Kalaev, V.V. (2011), "3D unsteady computer modeling of industrial scale Ky and Cz sapphire crystal growth", J. Cryst. Grow., 320(1), 23-27. https://doi.org/10.1016/j.jcrysgro.2011.01.101
  6. Fujiwara, K., Pan, W. and Sawada, K. (2006), "Directional growth method to obtain high quality polycrystalline silicon from its melt", J. Cryst. Grow., 292(2), 282-285. https://doi.org/10.1016/j.jcrysgro.2006.04.016
  7. Kuliev, A.T., Durnev, N.V. and Kalaev, V.V. (2007), "Analysis of 3D unsteady melt flow and crystallization front geometry during a casting process for silicon solar cells", J. Cryst. Grow., 303(1), 236-240. https://doi.org/10.1016/j.jcrysgro.2006.12.050
  8. Lin, C.H., Chen, P.W. and Chen, C.Y. (2011), "Simulations of silicon Cz growth in a cusp magnetic field", Magnetohydr., 47(1), 17-28.
  9. Li, Z.Y., Liu, L., Ma, W.C. and Kakimoto, K. (2011a), "Effects of argon flow on heat transfer in a directional solidification process for silicon solar cells", J. Cryst. Grow., 318(1), 298-303. https://doi.org/10.1016/j.jcrysgro.2010.11.040
  10. Li, Z.Y., Liu, L., Ma, W.C. and Kakimoto, K. (2011b), "Effects of argon flow on impurities transport in a directional solidification furnace for silicon solar cells", J. Cryst. Grow., 318(1), 304-312. https://doi.org/10.1016/j.jcrysgro.2010.11.030
  11. Miyazawa, H., Liu, L. and Kakimoto, K. (2008), "Numerical analysis of influence of crucible shape on interface shape in a unidirectional solidification process", J. Cryst. Grow., 310(6), 1142-1147. https://doi.org/10.1016/j.jcrysgro.2007.12.056
  12. Miyazawa, H., Liu, L. and Kakimoto, K. (2009), "Numerical investigation of the influence of material property of a crucible on interface shape in a unidirectional solidification process", Cryst. Grow. Des., 9(1), 267-272. https://doi.org/10.1021/cg800435d
  13. Newman, R.C. (1996), "Light impurities and their interactions in silicon", Mater. Sci. Eng.: B, 36(1-3), 1-12. https://doi.org/10.1016/0921-5107(95)01271-0
  14. Noghabi, O.A., M'Hamdi, M. and Jomaa, M. (2011), "Effect of crystal and crucible rotations on the interface shape of Czochralski grown silicon single crystals", J. Cryst. Grow., 318(1), 173-177. https://doi.org/10.1016/j.jcrysgro.2010.11.113
  15. Nakano, S., Gao, B. and Kakimoto, K. (2013), "Relationship between oxygen impurity distribution in multi-crystalline solar cell silicon and the use of top and side heaters during manufacture", J. Cryst. Grow., 375, 62-66. https://doi.org/10.1016/j.jcrysgro.2013.04.001
  16. Noghabi, O.A., Jomaa, M. and M'hamdi, M. (2013), "Analysis of W-shape melt/crystal interface formation in Czochralski silicon crystal growth", J. Cryst. Grow., 362, 77-82. https://doi.org/10.1016/j.jcrysgro.2011.10.062
  17. Shimura, F. (1989), "Semiconductor silicon crystal technology", Academic Press, San Diego, U.S.A.
  18. Shur, J.W., Kang, B.K., Moon, S.J., So, W.W. and Yoon, D.H. (2011), "Growth of multi-crystalline silicon ingot by improved directional solidification process based on numerical simulation", Sol. Energy Mater. Sol. Cell., 95(12), 3159-3164. https://doi.org/10.1016/j.solmat.2011.04.020
  19. STR Group (2012), Private Communications.
  20. Teng, Y.Y., Chen, J.C., Lu, C.W. and Chen, C.Y. (2010), "The carbon distribution in multi-crystalline silicon ingots grown using the directional solidification process", J. Cryst. Grow., 312(8), 1282-1290. https://doi.org/10.1016/j.jcrysgro.2009.11.020
  21. Teng, Y.Y., Chen, J.C., Lu, C.W., Chen, H.I., Hsu, C. and Chen, C.Y. (2011), "Effects of the furnace pressure on oxygen and silicon oxide distributions during the growth of multi-crystalline silicon ingots by the directional solidification process", J. Cryst. Grow., 318(1), 224-229. https://doi.org/10.1016/j.jcrysgro.2010.11.110
  22. Teng, Y.Y. (2011), "Investigation of thermal-fluid and impurity concentration distributions for growing the solar multi-crystalline Si ingots", Ph.D. Dissertation, National Central University, Taiwan.
  23. Teng, Y.Y., Chen, J.C., Huang, C.C., Lu, C.W., Wun, W.T. and Chen, C.Y. (2012), "Numerical investigation of the effect of heat shield shape on the oxygen impurity distribution at the crystal-melt interface during the process of Czochralski silicon crystal growth", J. Cryst. Grow., 352(1), 167-172. https://doi.org/10.1016/j.jcrysgro.2011.12.070
  24. Teng, Y.Y., Chen, J.C., Lu, C.W. and Chen, C.Y. (2012), "Numerical investigation of oxygen impurity distribution during multi-crystalline silicon crystal growth using a gas flow guidance device", J. Cryst. Grow., 360(1), 12-17. https://doi.org/10.1016/j.jcrysgro.2011.12.064
  25. Teng, Y.Y., Chen, J.C., Huang, B.S. and Chang, C.H. (2014), "Numerical simulation of impurity transport under the effect of a gas flow guidance device during the growth of multi-crystalline silicon ingots by the directional solidification process", J. Cryst. Grow., 385(1), 1-8. https://doi.org/10.1016/j.jcrysgro.2013.01.040
  26. Zhang, Z.Q., Huang, Q., Huang, Z.F., Li, B.W. and Chen, X. (2011), "Analysis of microcrystal formation in DS-silicon ingot", Sci. China: Technol. Sci., 54(6), 1475-1480. https://doi.org/10.1007/s11431-010-4271-2

Cited by

  1. Application of artificial neural network to optimize sensor positions for accurate monitoring: an example with thermocouples in a crystal growth furnace vol.12, pp.12, 2016, https://doi.org/10.7567/1882-0786/ab52a9