A $\theta$-$L$ Approach for Solving Solid-State Dewetting Problems

Abstract

We propose a $\theta$-$L$ approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies. The sharp-interface model is governed by surface diffusion and contact line migration. For solving the model, traditional numerical methods usually suffer from the severe stability constraint and/or the mesh distribution trouble. In the $\theta$-$L$ approach, we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables (i.e., the tangential angle $\theta$ and the total length $L$ of the interface curve), so that it not only could reduce the stiffness resulted from the surface tension, but also could ensure the mesh equidistribution property during the evolution. Furthermore, it can achieve second-order accuracy when implemented by a semi-implicit linear finite element method. Numerical results are reported to demonstrate that the proposed $\theta$-$L$ approach is efficient and accurate.