Continuum models for surface growth

TL;DR

This paper provides an overview of continuum PDE models for homoepitaxial surface growth, discussing their derivation, applications, and limitations, with examples on mound coarsening and growth transition phenomena.

Contribution

It introduces heuristic derivation methods for continuum models based on physical symmetries and illustrates their application to surface growth phenomena.

Findings

Continuum models can describe large-scale surface growth behaviors.

They effectively model mound coarsening and growth mode transitions.

Discussion of strengths and limitations guides future modeling efforts.

Abstract

As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the physical process (mass conservation, crystal symmetry, ...) which determines their {\em structure}. Two examples of applications are given, one for large scale properties, one including crystal lattice discreteness. These are: (i) a simplified model for {\em mound coarsening} and (ii) for the transition from {\em layer-by-layer} to {\em rough growth}. Virtues and shortcomings of this approach is discussed in a concluding section.