Sharp interface limits of an anisotropic phase field model for solid-state dewetting

Abstract

We propose a phase field model for solid state dewetting where the surface energy is weakly anisotropic. The evolution is based on the Cahn-Hilliard equation with degenerate mobility and a free boundary condition at the film-substrate contact line. We derive the corresponding sharp interface limit via matched asymptotic analysis involving multiple inner layers. The resulting sharp interface model is consistent with the pure surface diffusion model. In addition, we show that the natural boundary conditions, as indicated from the first variation of the total free energy, imply a contact angle condition for the dewetting front, which, in the isotropic case, is consistent with the well-known Young's equation.