A Coupled Equations Model for Epitaxial Growth on Textured Surfaces

TL;DR

This paper introduces a continuum model for epitaxial growth on textured surfaces, linking atomic processes to surface morphology changes with film thickness and temperature, and relates it to the KPZ equation.

Contribution

It presents a novel coupled equations model that captures complex surface shapes in epitaxial regrowth, integrating atomic scale processes into a continuum framework.

Findings

Model explains complex surface shapes observed in experiments.

Surface morphology depends on film thickness and temperature.

Reduces to a form of the KPZ equation in the long wavelength limit.

Abstract

We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in terms of a few simple atomic scale processes including adatom diffusion, step-edge attachment and detachment, and a net downhill migration of surface adatoms. The continuum model reduces to the linear part of the Kardar-Parisi-Zhang equation with a flux dependent smoothing coefficient in the long wavelength limit.