Constitutive Relations for Modeling Single Crystal GaN at Elevated Temperatures

Abstract

Thermal–mechanical constitutive relations for bulk, single-crystal, wurtzite gallium nitride (GaN) at elevated temperatures, suitable for modeling crystal growth processes, are presented. A crystal plasticity model that considers slip and the evolution of mobile and immobile dislocation densities on the prismatic and basal slip systems is developed. The experimental stress–strain data from Yonenaga and Motoki (2001, “Yield Strength and Dislocation Mobility in Plastically Deformed Bulk Single-Crystal GaN,” J. Appl. Phys., 90(12), pp. 6539–6541) for GaN is analyzed in detail and used to define model parameters for prismatic slip. The sensitivity to the model parameters is discussed and ranges for parameters are given. Estimates for basal slip are also provided.