New Epitaxial Thin Film Models and numerical approximation

TL;DR

This paper introduces a new continuum model for epitaxial thin film growth featuring a convex-concave structure, providing rigorous analysis and stable numerical schemes, and demonstrating consistent morphological instability results with existing models.

Contribution

The paper presents a novel epitaxial thin film growth model with a convex-concave structure and develops unconditionally stable numerical methods for it.

Findings

The new model captures essential morphological states in thin film growth.

Numerical experiments show good agreement with existing models.

The model allows for easier implementation of stable numerical schemes.

Abstract

This paper concerns new continuum phenomenological model for epitaxial thin film growth with three different forms of the Ehrlich-Schwoebel current. Two of these forms were first proposed by Politi and Villain [1996] and then studied by Evans, Thiel and Bartelt [2006]. The other one is completely new. Following the techniques used in Li and Liu [2003], we present rigorous analysis of the well-posedness, regularity and time stability for the new model. We also studied both the global and the local behavior of the surface roughness in the growth process. The new model differs from other known models in that it features a linear convex part and a nonlinear concave part, and thus by using a convex-concave time splitting scheme, one can naturally build unconditionally stable semi-implicit numerical discretizations with linear implicit parts, which is much easier to implement than conventional models requiring nonlinear implicit parts. Despite this fundamental difference in the model, numerical experiments show that the nonlinear morphological instability of the new model agrees well with results of other models published in Li and Liu [2003], which indicates that the new model correctly captures the essential morphological states in the thin film growth process.