Logarithmic Clustering in Submonolayer Epitaxial Growth

TL;DR

This paper studies submonolayer epitaxial growth with a focus on how island diffusivity affects aggregation, revealing different steady and evolving behaviors depending on the diffusivity exponent, supported by theoretical and simulation results.

Contribution

It introduces a rate equation model for island growth with diffusivity proportional to k^{-ermu}, predicting distinct behaviors for different ermu values, supported by Monte Carlo simulations.

Findings

For 0<ermu<1, steady state with c_k  k^{-(3-ermu)/2}

For ermu>1, continuous growth with c_k(t)  ( t)^{-(2k-1)ermu/2}

Total island density N(t)  ( t)^{ermu/2}

Abstract

We investigate submonolayer epitaxial growth with a fixed monomer flux and irreversible aggregation of adatom islands due to their effective diffusion. When the diffusivity D_k of an island of mass k is proportional to k^{-\mu}, a Smoluchowski rate equation approach 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, continuous evolution occurs in which c_k(t)~(\ln t)^{-(2k-1)\mu/2}, while the total island density increases as N(t)~(\ln t)^{\mu/2}. Monte Carlo simulations support these predictions.