Sharp interface model for solid-state dewetting problems with weakly anisotropic surface energies

Abstract

Based on an energy variational approach, we propose a sharp interface model for simulating solid-state dewetting of thin films with (weakly) anisotropic surface energies. The morphology evolution of thin films is governed by surface diffusion and contact line migration. For the contact line migration, we introduce a relaxation kinetics with a finite contact line mobility by energy gradient flow method. We implement the mathematical model in an explicit finite-difference scheme with cubic spline interpolation for evolving marker points. Following validation of the mathematical and numerical approaches, we simulate the evolution of thin-film islands, semi-infinite films, and films with holes as a function of film dimensions, isotropic Young angle θi, anisotropy strength and crystal symmetry, and film crystal orientation relative to the substrate normal. We find that in addition to classical wetting (where holes in a film heal) and dewetting (where holes in a film grow), we observe cases where a hole through the film heals but leaves a finite-size hole/bubble between the continuous film and substrate or where the hole heals leaving a continuous film that is not bonded to the substrate. Surface energy anisotropy (i) increases the instability that leads to island breakup into multiple islands, (ii) enhances hole healing, and (iii) leads to finite island size even under some conditions where the isotropic Young angle θi suggests that the film wets the substrate. The numerical results presented in the paper capture many of the complexities associated with solid-state dewetting experiments.