Linear theory of unstable growth on rough surfaces

TL;DR

This paper develops a linear continuum theory to analyze unstable growth on rough surfaces, identifying key length scales and predicting surface width evolution, with applications to experimental data on InAs buffer layers.

Contribution

It introduces a linear theoretical framework for surface roughness evolution considering multiple length scales, and compares predictions with experimental observations.

Findings

Surface width W(t) exhibits a minimum at a specific coverage.

Linear theory captures overall roughness features but shows deviations indicating nonlinear effects.

The theory relates surface roughness dynamics to substrate roughness, terrace size, and Ehrlich-Schwoebel length.

Abstract

Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width W(t) is governed by three length scales: The characteristic scale $l_0$ of the substrate roughness, the terrace size $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$. If $l_{ES} \ll l_D$ (weak step edge barriers) and $l_0 \ll l_m \sim l_D \sqrt{l_D/l_{ES}}$, then W(t) displays a minimum at a coverage $\theta_{\rm min} \sim (l_D/l_{ES})^2$, where the initial surface width is reduced by a factor $l_0/l_m$. The r\^{o}le of deposition and diffusion noise is analyzed. The results are applied to recent experiments on the growth of InAs buffer layers [M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall features of the observed roughness evolution are captured by the linear theory, but the detailed time dependence shows distinct deviations which suggest a significant influence of nonlinearities.