Stress-induced surface instability of an elastic layer

Abstract

The surface evolution of an elastic layer subjected to a far-field uniform tensile stress is analyzed by using a linear perturbation theory. The atomic transport mechanism controlling the surface evolution is the gradient of chemical potential associated with elastic strain energy and surface curvature. The critical spatial frequency of unstable surface perturbations is a function of the thickness of the elastic layer, surface energy, Young’s modulus of the elastic layer, and the applied tensile stress. For thin films, the critical spatial frequency is inversely proportional to the square root of the film thickness and proportional to the applied stress, while it is proportional to the square of the applied stress and independent of the layer thickness for thick films.