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

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.

12 pages, uses equation.sty

References in corpus (3)

• Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior
• Spacing distribution functions for the one-dimensional point-island model with irreversible attachment
• Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models

Cited by in corpus (6)

• Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications
• Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models
• Crossover in the scaling of island size and capture zone distributions
• Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling
• Distributional fixed-point equations for island nucleation in one dimension: The inverse problem
• Deposition, diffusion, and nucleation on an interval