SHARP INTERFACE MODELS FOR SOLID STATE DEWETTING AND THEIR APPLICATIONS

Abstract

Solid-state dewetting is a ubiquitous physical phenomenon occurring in the solid-solid-vapor system. The solid thin film on the substrate is typically unstable and exhibits complex morphological evolutions, including hole formation, edge retraction, rim pinch-off and so on. In this thesis, we develop mathematical models and efficient numerical schemes for simulating the solid-state dewetting, and the problem is approached in both 2D and 3D via the Cahn-Hoffman $\boldsymbol{\xi}$-vector formulation. The sharp interface models are rigorously derived based on the thermodynamic variation, which include the surface diffusion flow and moving contact line. The governing equations for the model belong to fourth order geometric partial differential equations with proper boundary conditions such that the total volume is conserved and total surface energy is dissipative. Besides, a semi-implicit parametric finite element method is proposed for solving the models efficiently. Numerical examples are presented to show consistent morphological evolutions observed in physical experiments.