Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

Abstract

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density $p_n^{XY}(x,y)$, which represents the probability density to have nucleation at position $x$ within a gap of size $y$. Our proposed functional form for $p_n^{XY}(x,y)$ describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

12 pages, 9 figures

References in corpus (1)

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

Cited by in corpus (10)

• Correlations between Optical Properties and Voronoi-Cell Area of Quantum Dots
• Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications
• Voronoi Cell Patterns: theoretical model and applications
• Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models
• 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
• Mean-Field Approximation for Spacing Distribution Functions in Classical Systems
• Distributional fixed-point equations for island nucleation in one dimension: The inverse problem
• Deposition, diffusion, and nucleation on an interval