Capture-zone distribution in one-dimensional sub-monolayer film growth: a fragmentation theory approach

TL;DR

This paper develops a fragmentation theory approach to analyze the distribution of capture zones during one-dimensional monolayer film growth, providing asymptotic forms that differ from the Generalised Wigner Surmise, and discusses the reasons for these differences.

Contribution

It introduces a fragmentation theory method to derive capture zone distribution asymptotics for one-dimensional island growth, contrasting with existing models.

Findings

Derived small and large size asymptotics for CZD

Identified discrepancies with the Generalised Wigner Surmise

Discussed assumptions affecting the distribution forms

Abstract

The distribution of capture zones formed during the nucleation and growth of point islands on a one-dimensional substrate during monomer deposition is considered for general critical island size $i$. A fragmentation theory approach yields the small and (for $i=0$) large size asymptotics for the capture zone distribution (CZD) under the assumption of no neighbour-neighbour gap size correlation. These CZD asymptotic forms are different to those of the Generalised Wigner Surmise which has recently been proposed for island nucleation and growth models, and we discuss the reasons for the discrepancies.