Modeling of basal plane dislocations in single-crystal sapphire

The Alexander-Haasen model was originally used to model the multiplication of the mobile dislocations in crystalline silicon. Here, we extend this model for studying multiplication of basal plane dislocations (BPDs) in single-crystal sapphire. By fitting the Alexander-Haasen model to experimental data, we find that the model accurately describes the plastic deformation of sapphire caused by BPDs. The application of the Alexander-Haasen model to sapphire growth made it possible to minimize the dislocation density and residual stress in growing crystals by optimizing the furnace structure and operation conditions. We apply the Alexander-Haasen model to investigate the dynamical deformation of single-crystal sapphire during cooling process, and examine the effect of the cooling rate on the generation of BPDs and residual stress. Finally, we present the BPD distribution and discuss the main factor that influences the generation of BPDs