Island size distributions in submonolayer growth: successful prediction by mean field theory with coverage dependent capture numbers

TL;DR

This paper demonstrates that mean-field rate equations, incorporating coverage-dependent capture numbers, can accurately predict island size distributions in submonolayer growth, validated by kinetic Monte Carlo simulations.

Contribution

It introduces a comprehensive mean-field approach that accounts for nonlinear capture number dependence on island size and coverage, improving prediction accuracy.

Findings

Mean-field equations with coverage-dependent capture numbers match simulation results.

Nonlinear dependence of capture numbers on island size is crucial for accurate predictions.

Analytical solutions are challenging due to the nonlinearity in capture numbers.

Abstract

We show that mean-field rate equations for submonolayer growth can successfully predict island size distributions in the pre-coalescence regime if the full dependence of capture numbers on both the island size and the coverage is taken into account. This is demonstrated by extensive Kinetic Monte Carlo simulations for a growth kinetics with hit and stick aggregation. A detailed analysis of the capture numbers reveals a nonlinear dependence on the island size for small islands. This nonlinearity turns out to be crucial for the successful prediction of the island size distribution and renders an analytical treatment based on a continuum limit of the mean-field rate equations difficult.