Crack formation in surface layers with strain gradients

Abstract

Abstract The problem of crack formation in surface layers where a linear profile of elastic strain prevails through the thickness of a layer is investigated. Such strain gradients can be generated, for example, in graded alloy semiconductor layers or due to specific stress relaxation mechanisms in lattice mismatched layers or previously unanticipated dislocation-related strain gradients. The operation of the relaxation mechanisms related to threading dislocation inclination and leading to the strain gradients in nominally compressed Al x Ga1 – x N layers grown on buffer layers with smaller lattice constants is discussed. A fracture mechanics model is developed for the calculation of the stress intensity factor of mode I cracks initiated at the surface of the layer exhibiting a linear strain dependence. The critical layer thickness for crack formation in such a gradient elastic field has been found in the framework of this fracture mechanics model. Results of the modeling are compared with experimental observations of crack onset in nominally compressed layers of Al x Ga1−x N semiconductors. Good agreement between the model predictions and the experimental data is found.