Anomalous Dimension and Spatial Correlations in a Point-Island Model

TL;DR

This paper investigates the size distribution and spatial correlations of islands in a model of submonolayer growth, revealing anomalous scaling behaviors and providing analytical and simulation results.

Contribution

It introduces a model where islands do not change shape and analyzes the effects of critical island size on growth dynamics using scaling and mean-field theories.

Findings

Discovered anomalous scaling of island size distribution for large critical sizes

Derived a closed-form expression for spatial correlation functions

Validated analytical results with Monte Carlo simulations

Abstract

We examine the island size distribution function and spatial correlation function of a model for island growth in the submonolayer regime in both 1 and 2 dimensions. In our model the islands do not grow in shape, and a fixed number of adatoms are added, nucleate, and are trapped at islands as they diffuse. We study the cases of various critical island sizes $i$ for nucleation as a function of initial coverage. We found anomalous scaling of the island size distribution for large $i$ . Using scaling, random walk theory, a version of mean-field theory we obtain a closed form for the spatial correlation function. Our analytic results are verified by Monte Carlo simulations.