3D numerical study of coupled crystallization and carbon segregation during multi-crystalline silicon ingot solidification

During the solidification of silicon ingot, the carbon concentration may play a critical role with regard to the final silicon microstructure. If the carbon concentration passes the solubility limit, SiC particles precipitate and it is possible the grain structure changes from columnar to equiaxed grains. Furthermore, carbon atoms are confined inside these equiaxed grains during solidification, which may decrease the carbon concentration inside the liquid silicon, and the equiaxed grains then become columnar again. Therefore, both solidification and carbon concentration will impact each other. A 3D multiscale model is developed to simulate the microstructural evolution of Multi-Crystalline Silicon (mc-Si) ingots coupled with the carbon concentration during the casting process. Our microstructural model is based on the simulation of nucleation and crystal growth. Besides modelling the nucleation due to silicon-crucible interaction, this model can successfully represent the occurrence of equiaxed grains observed ahead of a planar faceted interface due to carbon segregation during solidification. In addition, by coupling concentration and crystallization, the transition from columnar to equiaxed growth and equiaxed to columnar growth can be modeled. Several comparisons are made between the mc-Si ingot's microstructure obtained by our model and the experimental data in order to evaluate our model. These comparisons show good agreement between our model and the experimental data.