Crossover in the scaling of island size and capture zone distributions

TL;DR

This study investigates how island size and capture zone distributions in irreversible growth models change with coverage and diffusion rates, revealing a crossover from PE theory predictions to exponential decay behaviors.

Contribution

It demonstrates the conditions under which the Pimpinelli and Einstein theory applies and identifies a crossover to exponential decay regimes in island growth models.

Findings

Crossover from PE Gaussian tail to exponential decay in CZD at high coverage and low R.

ISD also shifts from Gaussian or faster decay to exponential decay.

Deviations from PE predictions occur near certain coverages due to island coalescence.

Abstract

Simulations of irreversible growth of extended (fractal and square) islands with critical island sizes i=1 and 2 are performed in broad ranges of coverage \theta and diffusion-to-deposition ratios R in order to investigate scaling of island size and capture zone area distributions (ISD, CZD). Large \theta and small R lead to a crossover from the CZD predicted by the theory of Pimpinelli and Einstein (PE), with Gaussian right tail, to CZD with simple exponential decays. The corresponding ISD also cross over from Gaussian or faster decays to simple exponential ones. For fractal islands, these features are explained by changes in the island growth kinetics, from a competition for capture of diffusing adatoms (PE scaling) to aggregation of adatoms with effectively irrelevant diffusion, which is characteristic of random sequential adsorption (RSA) without surface diffusion. This interpretation is confirmed by studying the crossover with similar CZ areas (of order 100 sites) in a model with freezing of diffusing adatoms that corresponds to i=0. For square islands, deviations from PE predictions appear for coverages near \theta=0.2 and are mainly related to island coalescence. Our results show that the range of applicability of the PE theory is narrow, thus observing the predicted Gaussian tail of CZD may be difficult in real systems.