Phase-field modeling of stress-induced surface instabilities in heteroepitaxial thin films

Abstract

A phase-field model for investigating the surface morphological evolution of a film is developed, taking into account the surface energies of film and substrate, the interfacial energy between the film and substrate, and the elastic energy associated with the lattice mismatch between the film and substrate. Using the lattice mismatch and the surface energies for the Ge∕Si heteroepitaxial system, the morphology of islands and the formation of a wetting layer are investigated using two-dimensional simulations. The results show that the wetting angle increases continuously with the increase in the lattice mismatch, and the surface angle of the island on wetting layer varies with the island size. It is demonstrated that the anisotropy of elastic interactions alone is not sufficient to cause surface angle discontinuity or faceting that is observed in experiments.