Solid-state dewetting of axisymmetric thin film on axisymmetric curved-surface substrates: modeling and simulation

TL;DR

This paper develops a mathematical model and numerical methods for simulating the solid-state dewetting of axisymmetric thin films on curved substrates, ensuring energy stability and volume conservation, and explores related phenomena through numerical examples.

Contribution

It introduces a novel symmetrized variational formulation and structure-preserving algorithms for axisymmetric dewetting on curved surfaces, with extensive numerical validation.

Findings

Numerical schemes are proven to be energy-stable and volume-conserving.

Simulation results reveal phenomena like particle migration, pinch-off, and edge retraction.

The methods demonstrate convergence and robustness in complex geometries.

Abstract

In this work, we consider the solid-state dewetting of an axisymmetric thin film on a curved-surface substrate, with the assumption that the substrate morphology is also axisymmetric. Under the assumptions of axisymmetry, the surface evolution problem on a curved-surface substrate can be reduced to a curve evolution problem on a static curved substrate. Based on the thermodynamic variation of the anisotropic surface energy, we thoroughly derive a sharp-interface model that is governed by anisotropic surface diffusion, along with appropriate boundary conditions. The continuum system satisfies the laws of energy decay and volume conservation, which motivates the design of a structure-preserving numerical algorithm for simulating the mathematical model. By introducing a symmetrized surface energy matrix, we derive a novel symmetrized variational formulation. Then, by carefully discretizing the boundary terms of the variational formulation, we establish an unconditionally energy-stable parametric finite element approximation of the axisymmetric system. By applying an ingenious correction method, we further develop another structure-preserving method that can preserve both the energy stability and volume conservation properties. Finally, we present extensive numerical examples to demonstrate the convergence and structure-preserving properties of our proposed numerical scheme. Additionally, several interesting phenomena are explored, including the migration of 'small' particles on a curved-surface substrate generated by curves with positive or negative curvature, pinch-off events, and edge retraction.