Analytical and Numerical Modeling of Surface Morphologies in Thin Films

Abstract

ABSTRACTExperimental studies have shown that strains due to thermal expansion mismatch between a film and its substrate can produce very large stresses in the film that can lead to the formation of holes and hillocks. Based on a phenomenological description of the evolution of a solid surface under both capillary and stress driving forces and for surface and grain boundary self-diffusion, this article provides, for the first time, analytical and numerical solutions for surface profiles of model geometries in polycrystalline thin films. The results can explain a variety of surface morphologies commonly observed experimentally and are discussed to give some practical insights on how to control the growth of holes and hillocks in thin films.