Thermal strain analysis considering in-plane anisotropy for sputtered AlN on c- and a-plane sapphire under high-temperature annealing

High-temperature annealing of sputtered AlN (Sp-AlN) using a face-to-face configuration is a novel technique that has attracted considerable attention because it can reduce the threading dislocation density of Sp-AlN to 107 cm−2. However, drawbacks such as cracking, residual stress, and wafer curvature remain because of a high annealing temperature of 1700 °C. We previously developed a thermal strain analysis model that uses an elastic multilayer system to describe the elastic behavior of Sp-AlN on sapphire under high-temperature annealing. In this study, we expand this model to consider in-plane anisotropy. By performing thermal strain analysis of the curvature, strain, stress, and strain energy of c-plane AlN grown on c- and a-plane sapphire, our calculation successfully approximates the experimental results, even for an in-plane anisotropic structure. The proposed model is, therefore, useful for quantitative evaluation of the residual strain and can contribute to strain engineering of AlGaN-based deep-ultraviolet light-emitting diodes.