Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior

TL;DR

This paper introduces a simple, universal phenomenological model for the distribution of capture zones in island nucleation, linking it to fluctuation phenomena and substrate properties, validated by simulations and experiments.

Contribution

It proposes a generalized Wigner surmise-based expression for capture-zone distribution, connecting it to critical nucleus size and substrate dimensionality.

Findings

The model accurately fits kinetic Monte Carlo data.

The single parameter relates to critical nucleus size.

Experimental data supports the theoretical predictions.

Abstract

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory sheds light on the result.