On the importance of dislocation flow in continuum plasticity models for semiconductor materials

Crystalline defects, such as dislocations, may have a strong negative influence on the performance and quality of electronic devices. Modelling the defect evolution of such systems helps to understand where defects occur, how they evolve and interact, Modelling also might allow to avoid - or at least to reduce - the number of line defects in such materials. A widely used continuum model for predicting the evolution of dislocation density in semiconductors is the Alexander-Haasen (AH) model (Alexander and Haasen, Solid state physics, 1969) which describes the evolution of dislocation density through a local dislocation multiplication law; the motion of dislocations, i.e. dislocation flow, is not considered. Within this work, the underlying assumptions for the validity of the AH model are studied and compared to a more complex continuum model of dislocation dynamics (CDD) which explicitly considers dislocation fluxes. We use a simplified 2D scenario of a 4H-SiC crystal at the end of the growth as a benchmark system. Our comparisons show that considering the motion of dislocations can have a significant influence on the evolution and final distribution of dislocation density, which may strongly limit the applicability of the AH model. Based on the CDD model, we then investigate the cooling process and study the effect of the cooling rate on the resulting dislocation microstructure.