Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models

Abstract

The nucleation and growth of point islands during submonolayer deposition on a one-dimensional substrate is simulated for critical island size $i=0,1,2,3$. The small and large size asymptotics for the gap size and capture zone distributions (GSD and CZD) are studied. Comparisons to theoretical predictions from fragmentation equation analyses are made, along with those from the recently proposed Generalised Wigner Surmise (GWS). We find that the simulation data can be fully understood in the framework provided by the fragmentation equations, whilst highlighting the theoretical areas that require further development. The GWS works well for the small-size CZD behaviour, but completely fails to describe the large-size CZD asymptotics of the one-dimensional system.

9 pages, 8 figures

References in corpus (5)

• 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
• Accelerated kinetic Monte Carlo algorithm for diffusion limited kinetics
• Scaling of island size and capture zone distributions in submonolayer growth
• Capture-zone distribution in one-dimensional sub-monolayer film growth: a fragmentation theory approach

Cited by in corpus (7)

• Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications
• Capture-zone distribution in one-dimensional sub-monolayer film growth: a fragmentation theory approach
• 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
• Rigorous derivation of the rate equations for the epitaxial growth
• Distributional fixed-point equations for island nucleation in one dimension: The inverse problem
• Deposition, diffusion, and nucleation on an interval