Island coarsening in one-dimensional models with partially and completely reversible aggregation

TL;DR

This study uses simulations to analyze how island size distributions evolve in one-dimensional models with reversible aggregation, revealing distinct behaviors based on the reversibility constraints and providing insights into the effects of detachment rates.

Contribution

It extends previous work by comparing partially and fully reversible models, identifying crossover behaviors, and deriving relationships between island size and detachment parameters.

Findings

Peaked island size distributions transition to exponential decay over time in fully reversible models.

Crossover time scales as i^3/ε in partially reversible models.

Mean island size at saturation depends on critical size i and detachment rate ε.

Abstract

Using computer simulations and scaling ideas, we study one-dimensional models of diffusion, aggregation and detachment of particles from islands in the post-deposition regime, i. e. without flux. The diffusion of isolated particles takes place with unit rate, aggregation occurs immediately upon contact with another particle or island, and detachment from an island occurs with rate epsilon = exp(-E/kT), where E is the related energy barrier. In the partially reversible model, dissociation is limited to islands of size larger than a critical value i, while in the completely reversible model there is no restriction to that process (infinite i). Extending previous simulation results for the completely reversible case, we observe that a peaked island size distribution in the intermediate time regime, in which the mean island size is increasing, crosses over to the theoretically predicted exponentially decreasing distribution at long times. It contrasts with the partially reversible model, in which peaked distributions are obtained until the long time frozen state, which is attained with a crossover time $\tau \sim \frac{i^3}{\epsilon}$. The mean island size at saturation varies as $S_{sat}\approx 2i+C\epsilon$ (C constant), while the completely reversible case shows an Ahrrenius dependence of the mean island size, $S\sim \epsilon^{-1/2}$. Thus, for different coverages, the effect of the critical size i on the geometric features is much stronger than that of epsilon, which may be used to infer the relevance of size-dependent detachment rates in real systems and other models.