Numerical Modelling on Industrial Scale Multi-Crystalline Silicon Growth Process at Critical Prandtl Number for PV Applications

Abstract

Directional solidification (DS) is a very important technique for growing good quality multi-crystalline silicon at a large scale for photovoltaic (PV) solar cells. Time dependent numerical modelling of the temperature distribution, residual stress and dislocation density rate in multi-crystalline silicon ingots grown by directional solidification have been investigated for five growth stages using the finite volume method at the critical Prandtl number, Pr = 0.01. Impurity concentrations of O, C and SiC are calculated in the central region of grown crystal from bottom to top. The history of temperature distribution, stress generation, and dislocation multiplication are tracked in our modelling continuously considering the growth process from the beginning to the end of the solidification process. This paper reports an advanced understanding of the thermal and mechanical behaviour and generation of impurities in grown multi-crystalline ingots. The computational results show good agreement with experimental data for residual stress, dislocation density and impurities formation in grown ingots. From the obtained results, the crystal quality is evaluated under various solidification stages. We found that the above crystal properties undergo a sudden change at the final stage of the solidification process.