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

We propose a sharp interface model for simulating solid-state dewetting where the surface energy is (weakly) anisotropic. The morphology evolution of thin films is governed by surface diffusion and contact line migration. The mathematical model is based on an energy variational approach. Anisotropic surface energies lead to multiple solutions of the contact angle equation at contact points. Introduction of a finite contact point mobility is both physically based and leads to robust, unambiguous determination of the contact angles. 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, Young's angle $θ_i$, anisotropy strength and crystal symmetry, and film crystal orientation relative to the substrate normal. We find that the contact point retraction rate can be well described by a power-law, $l \sim t^n$. Our results demonstrate that the exponent $n$ is not universal -- it is sensitive to the Young's angle $θ_i$ (and insensitive to anisotropy). 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 leave 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 break-up into multiple islands, (ii) enhances hole healing, and (iii) leads to finite island size even under some conditions where the Young's angle $θ_i$ suggests that the film wets the substrate.