Influence of Island Diffusion on Submonolayer Epitaxial Growth

TL;DR

This paper analyzes how island diffusion affects submonolayer epitaxial growth, revealing different growth regimes and distribution behaviors depending on island mobility and substrate dimensionality.

Contribution

It introduces a comprehensive theoretical framework accounting for island diffusion effects and extends the analysis to various substrate dimensions.

Findings

Steady behavior for diffusivity exponent 0<=mu<1 with specific island size distribution.

Logarithmic growth of island density for mu>=1 in mean-field approximation.

Dimensionality influences growth dynamics, with 2D showing only logarithmic corrections.

Abstract

We investigate the kinetics of submonolayer epitaxial growth which is driven by a fixed flux of monomers onto a substrate. Adatoms diffuse on the surface, leading to irreversible aggregation of islands. We also account for the effective diffusion of islands, which originates from hopping processes of their constituent adatoms, on the kinetics. When the diffusivity of an island of mass k scales as k^{-mu}, the (mean-field) Smoluchowski rate equations predicts steady behavior for 0<=mu<1, with the concentration c_k of islands of mass k varying as k^{-(3-mu)/2}. For mu>=1, a quasi-static approximation to the rate equations predicts slow continuous evolution in which the island density increases as ln t^{mu/2}. A more refined matched asymptotic expansion reveals unusual multiple-scale mass dependence for the island size distribution. Our theory also describes basic features of epitaxial growth in a more faithful model of growing circular islands. For epitaxial growth in an initial population of monomers and no external flux, a scaling approach predicts power-law island growth and a mass distribution with a behavior distinct from that of the non-zero flux system. Finally, we extend our results to one- and two-dimensional substrates. The physically-relevant latter case exhibits only logarithmic corrections compared to the mean-field predictions.