Semiconductor Film Grown on a Circular Substrate: Predictive Modeling of Lattice-Misfit Stresses

An effective and physically meaningful analytical predictive model is developed for the evaluation the lattice-misfit stresses (LMS) in a semiconductor film grown on a circular substrate (wafer). The two-dimensional (plane-stress) theory-of-elasticity approximation (TEA) is employed in the analysis. The addressed stresses include the interfacial shearing stress, responsible for the occurrence and growth of dislocations, as well as for possible delaminations and the cohesive strength of a buffering material, if any. Normal radial and circumferential (tangential) stresses acting in the film cross-sections and responsible for its short- and long-term strength (fracture toughness) are also addressed. The analysis is geared to the GaN technology.