Coupled Thermal Solidification Process Simulation of Sapphire Growth

Thermal distribution during the sapphire growth process determines to a great extent the thermal stresses and dislocation density in sapphire. In this work, thermal and defect simulations of sapphire growth in a simplified single-boule furnace are presented. The heat transfer in the furnace is modeled via ANSYS Fluent® by considering conduction, convection and radiation effects. A dislocation density-based crystal plasticity model is applied for the numerical simulation of dislocation evolution during the crystal growth of sapphire. The physical models are validated by using a temporal series of measurements in the real furnace geometry, which capture the crystal–melt interface position during the technological growth process. The growth rate and the shape of the crystal growth front are analyzed for different side and top heater powers which result in different thermal distributions in the furnace. It is found that the cooling flux at the crucible bottom wall determines to a great extent the growth profile in the first half of the growth stage. Only toward the end of the growth stage, different top and side power distributions induce different growth front shapes. The effect of the convexity of the growth surface on the generation of dislocation defects is investigated by the crystal plasticity model. The results of simulations show that the convexity of the growth surface has a significant effect on the generation of dislocations.