Numerical Simulation of Solidification Behavior and Grain Structure for Multi-Crystalline Silicon Casting and its Experimental Verification


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The quality of multi-crystalline silicon ingot from casting process by heat exchange method (HEM) is significantly affected by the cooling condition and the design of the hot-zone. The shape of the liquid-solid interface has great impact on the direction and orientation of grain growth and the occurrence of defects such as dislocations, impurities segregation, and residual thermal stresses. In this study, the temperature variation/distribution of crystallization process of silicon ingot is investigated through numerical simulation and compared with experimental measurements. In HEM system, the temperature variation/distribution is affected by the adiabatic condition of the furnace and temperature curves of the heaters in the furnace. Incorporated with the Cellular Automaton (CA) method and residual thermal stress computation, the grain structures are also simulated. The different slices of the practical silicon ingot are then compared with the results of grain growth simulation to verify the accuracy of the numerical system. With the numerical system validated, various designs and operating conditions can then be numerically evaluated to obtain the optimal design and operation.



Edited by:

T. Chandra, M. Ionescu and D. Mantovani




J. Y. Liu et al., "Numerical Simulation of Solidification Behavior and Grain Structure for Multi-Crystalline Silicon Casting and its Experimental Verification", Advanced Materials Research, Vol. 409, pp. 401-406, 2012

Online since:

November 2011




[1] Ch. -A. Gandin and M. Rappaz, A 3D Cellular Automaton algorithm for the prediction of dendritic grain growth, Acta Metallurgica et Materialia, Vol. 45, No. 5, pp.2187-2195(1997).


[2] Ch. A. Gandin, J. L. Desbiolles, M. Rappaz, and Ph. Thevoz, A Three-Dimensional CellularAutomaton–Finite Element Model for the Prediction of Solidification Grain Structures, Metallurgical and Materials Transactions A, Vol. 30A, pp.3153-3165 (1999).


[3] Bei Wu, Nathan Stoddard, Ronghui Ma, Roger Clark, Bulk multicrystalline silicon growth for photovoltaic (PV) application, Journal of Crystal Growth, Vol. 310 , p.2178–2184(2008).


[4] Jiuan Wei, HuiZhang, LiliZheng, ChenleiWang, BoZhao, Modeling and improvement of silicon ingot directional solidification for industrial production systems , Solar Energy Materials & Solar Cells, Vol. 93 , p.1531–1539(2009).


[5] Hiroaki Miyazawa, Lijun Liu, Sho Hisamatsu, Koichi Kakimoto, Numerical analysis of the influence of tilt of crucibles on interface shape and fields of temperature and velocity in the unidirectional solidification process , Journal of Crystal Growth, Vol. 310 , p.1034–1039(2008).


[6] Bei Wu, Sam Scott, Nathan Stoddard, Roger Clark, Adi Sholapurwalla, Simulation of silicon casting process for photovoltaic (pv) application, The Minerals, Metals & Materials Society.

[7] Jung Min Kim, Young Kwan Kim, Growth and characterization of 240 kg multicrystalline silicon ingot grown by directional solidification, Solar Energy Materials & Solar Cells, Vol. 81 , p.217–224(2004).


[8] K. Arafune, T. Sasaki, F. Wakabayashi, Y. Terada, Y. Ohshita, M. Yamaguchi, Study on defects and impurities in cast-grown polycrystalline silicon substrates for solar cells, Physica B, Vol. 376–377, p.236–239(2006).


[9] D. Franke, T. Rettelbach, C. Haβler, W. Koch, A. Muller, Silicon ingot casting: process development by numerical simulations, Solar Energy Materials & Solar Cells , Vol. 72 , p.83–92(2002).