4. Time-Dependent Viscoplastic Model for Dislocation Generation During the Cooling Process in the Silicon Ingot

Silicon growth is a process in which a silicon ingot is solidified from the melted and then cooled to the room temperature through the control of multi-heater. Dislocation densities are generated in the ingot by excessed thermal stresses caused by the nonuniform temperature field in the ingot. The generation of the dislocation density is considered as s a process of viscoplastic deformation. A three dimensional transient finite element model based on the Haasen viscoplastic constitutive model (HAS) is developed to evaluate the dislocation densities generated in silicon ingots grown by directional solidification process. The stress fields and dislocation densities generated in silicon ingots are the two major parameters for the evaluation of ingot quality. These two results calculated by HAS model are compared with those obtained from CRSS model. The result demonstrates that HAS model is more accurate than CRSS model for the calculation of dislocation densities and stresses during the cooling process of silicon ingot because of the consideration of time-dependent viscoplastic deformation in HAS model.