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

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.

arXiv comment5 pages, 4 figures, originally submitted to Phys. Rev. Lett. on Dec. 15, 2006; revised version v2 tightens and focuses the presentation, emphasizes the importance of universal features of fluctuations, corrects an error for d=1, replaces 2 of the figures

References in corpus (8)

• Random Matrix Theories in Quantum Physics: Common Concepts
• A Random Matrix Approach to Cross-Correlations in Financial Data
• Submonolayer Epitaxy Without A Critical Nucleus
• The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles
• How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: the case of InAs/GaAs(001)
• Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances
• Modelling gap-size distribution of parked cars using random-matrix theory
• Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth

Cited by in corpus (25)

• Nucleation and growth of thin films of rod--like conjugated molecules
• Colloquium: Cluster growth on surfaces - densities, size distributions and morphologies
• Capture numbers and islands size distributions in models of submonolayer surface growth
• Effect of impurities on pentacene island nucleation
• Spacing distribution functions for the one-dimensional point-island model with irreversible attachment
• Island size distributions in submonolayer growth: successful prediction by mean field theory with coverage dependent capture numbers
• Scaling in reversible submonolayer deposition
• Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications
• Correlations between Optical Properties and Voronoi-Cell Area of Quantum Dots
• Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models
• 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
• 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
• Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using multi-state lattice model
• Dynamics of curved interfaces
• On the statistics of area size in two-dimensional thick Voronoi Diagrams
• Reentrant behavior of the density vs temperature of indium islands on GaAs(111)A
• Rigorous derivation of the rate equations for the epitaxial growth
• Water Nucleation via Transient Bonds to Oxygen Functionalized Graphite
• Mean-Field Approximation for Spacing Distribution Functions in Classical Systems
• Point island dynamics under fixed rate deposition
• Size Distribution and Its Scaling Behavior of InAlAs/AlGaAs Quantum Dots Grown on GaAs by Molecular Beam Epitaxy
• Distributional fixed-point equations for island nucleation in one dimension: The inverse problem
• Deposition, diffusion, and nucleation on an interval