A sharp-interface model and its numerical approximation for solid-state dewetting with axisymmetric geometry

TL;DR

This paper develops a sharp-interface model for solid-state dewetting with axisymmetric geometry, deriving governing equations from thermodynamic principles and solving them numerically to analyze morphological evolution.

Contribution

It introduces a rigorous derivation of the sharp-interface model for axisymmetric solid-state dewetting and proposes an efficient finite element method for its numerical approximation.

Findings

Demonstrates morphological evolution during dewetting

Validates the model with numerical simulations

Shows energy dissipation and volume conservation

Abstract

Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric curve evolution partial differential equations, with proper boundary conditions such that the total volume of the system is conserved and the total energy is dissipative during the time evolution. We propose a variational formulation for the sharp-interface model and then apply the parametric finite element method for solving it efficiently. Extensive numerical simulation results are presented lastly to demonstrate the morphological characteristics for solid-state dewetting.