Stress-Driven Surface Instabilities in Epitaxial Thin Films

Heteroepitaxial thin films are essential components in many technological applications including optical, electronic and other functional devices. These films are also becoming important in the coating technologies for high-temperature materials applications. Typical heteroepitaxial systems involve one or more solid phases deposited on support structure called the substrate. Often the lattice and thermal mismatch in these systems results in significant elastic strains that, under the appropriate temperature conditions, drive mass transport by diffusion. Surface diffusion in these systems is usually a dominant mass transport mechanism that leads to morphological evolution of the surface. This evolution is called stress-driven morphological growth, and it has received much attention by materials modelers. In the current work, the problem of stress-driven morphological evolution in strained thin films is revisited; we develop a generalized formulation of this problem in the non-linear regime based upon a curvilinear coordinate formalism and finite element solution of the elastic sub-problem. This combination of methods facilitates the analysis of the onset of the instability and the early stage temporal evolution of the film surface. We apply our numerical scheme to surface wave, dot, pit, and ring morphologies and demonstrate the effects of model parameters on the incipient instabilities.