Asymptotic properties of step bunching in epitaxial growth with elasticity effects

In epitaxial thin film growth, elasticity effects often lead to self-organizing pattern formation which can be important in the fabrication of nanostructures. We discuss an elasticity model that takes into account of the lattice misfit between the substrate and the film, and the broken-bond effect due to surface steps. The former is an attractive while the latter is a repulsive interaction. It is found that uniform step train is unstable and will evolve into structures consisting of macroscopic step bunches. For the case of vicinal surface which consists of a sequence of monotonically decreasing steps, using a variational formulation, we analyze the properties of these bunches, notably their energy scaling and bunch width. We emphasize on a discrete model but continuum description will also be discussed. This is joint work with Tao Luo and Yang Xiang.