Scaling of Heteroepitaxial Island Sizes

TL;DR

This study uses Monte Carlo simulations to explore how lattice misfit influences island size distribution during heteroepitaxial growth, revealing strain-driven island dissolution and a specific scaling law for island densities.

Contribution

It introduces a detailed atomistic simulation analysis of heteroepitaxial island size distribution and highlights differences from rate equation models.

Findings

Misfit promotes island dissolution into smaller, strain-relieving islands.

Island size distribution follows a specific scaling law involving average size.

Rate equation theory predicts qualitatively different behavior than simulations.

Abstract

Monte Carlo simulations of an atomistic solid-on-solid model are used to study the effect of lattice misfit on the distribution of two-dimensional islands sizes as a function of coverage $\Theta$ in the submonolayer aggregation regime of epitaxial growth. Misfit promotes the detachment of atoms from the perimeter of large pseudomorphic islands and thus favors their dissolution into smaller islands that relieve strain more efficiently. The number density of islands composed of $s$ atoms exhibits scaling in the form \mbox{$N_s(\Theta) \sim \Theta / \langle s \rangle^2 \, g(s/\langle s \rangle$)} where $\langle s \rangle$ is the average island size. Unlike the case of homoepitaxy, a rate equation theory based on this observation leads to qualitatively different behavior than observed in the simulations.