Modeling of poly-crystalline silicon ingot crystallization during casting and theoretical suggestion for ingot quality improvement

Abstract

Finite element (FE) and cellular automaton (CA) models are used in order to predict the microstructure of Poly-Crystalline Silicon (PC-Si) ingots during casting in a directional solidification furnace. During solidification, the 3D-FE model is used to simulate thermal field inside the furnace, while the nucleation and growth of PC-Si are simulated by the modified version of CA model. In this model both nucleation at silicon-crucible interface and nucleation of equiaxed grains on impurities are modeled. The origin of impurity is considered SiC particles when carbon segregates during the solidification and precipitates as SiC particles if carbon solubility limit is reached. The model is evaluated with experimental data for different parameters, such as: the temperature profile at the top and bottom of the PC-Si, grain size, and the height of solidified silicon during solidification. A one-dimensional form of grain growth is observed at the crucible-silicon interface, while a more two-dimensional form of growth is predicted at higher silicon height. The microstructure of PC-Si shows that the grain size increases as a function of PC-Si ingot height. The effects of the cooling rate and competitive growth on the final microstructure of PC-Si are also investigated. The results show that less nucleation sites are formed at the bottom of the crucible with a slower cooling rate, which leads to a larger grain size. Furthermore, the grains at the crucible side walls tend grow inward at a lower cooling rate, which can significantly change the microstructure of PC-Si. This study shows that the competitive growth phenomena plays an important role in the final microstructure of silicon ingots. A simulated model is proposed which shows that by changing the density and location of nucleation sites it is possible to achieve more effective control on final PC-Si micro structure. This simulation helps to explain the crystal behavior observed in ingots cast under different conditions.