Coarsening of Surface Structures in Unstable Epitaxial Growth

TL;DR

This paper investigates the late-stage coarsening behavior of surface structures in unstable epitaxial growth using continuum models, deriving scaling laws and analyzing the dynamics of mound formation.

Contribution

It introduces a continuum framework with a slope-dependent current to derive scaling relations and predicts multiscaling versus conventional scaling in surface growth.

Findings

Lateral size of mounds scales as t^{1/z} with z ≥ 4

Mean-field approximation predicts multiscaling behavior

Numerical solutions show consistent z=4 scaling

Abstract

We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is observed. For the lateral size of mounds we obtain $\xi \sim t^{1/z}$ with $z \geq 4$. An analytic treatment within a self-consistent mean-field approximation predicts multiscaling of the height-height correlation function, while the direct numerical solution of the continuum equation shows conventional scaling with z=4, independent of the shape of the surface current.