A new sharp-interface model for simulating solid-state dewetting problems

Solid-state dewetting is a ubiquitous phenomenon in materials science, and it describes the agglomeration of solid thin films into arrays of isolated particles on a substrate. In recent years, solid-state dewetting has found wide applications in modern technology, and much efforts have been devoted to understanding this important phenomenon. One of the effective tools for modeling and simulations of solid-state dewetting was the sharp-interface model proposed by my group [see Phys. Rev. B, 91:045303, 2015; SIAM J. Appl. Math., 80:1654, 2020]. However, these sharp-interface models belong to free boundary problems, which explicitly include surface diffusion and contact line migration. It is very difficult to design efficient numerical algorithms for solving the sharp-interface models. On the other hand, lots of pinch-off events will occur when a long island film evolves by solid-state dewetting, but the previous sharp-interface models can not automatically handle with topological events. In order to tackle these difficulties, we propose a new sharp-interface model with the thickness-dependent surface energy for simulating solid-state dewetting by removing the singularity of the triple point among the film, vapor and substrate phases. The new model is only needed to solve in a fixed domain, and it can automatically capture “topological events”. Numerical results demonstrate the high performance of the new model.