Scaling of island size and capture zone distributions in submonolayer growth

TL;DR

This paper investigates how island size and capture zone distributions behave in submonolayer growth, confirming theoretical models and revealing how different island shapes influence decay behaviors.

Contribution

It provides a numerical analysis of ISDs and CZDs across various island shapes and sizes, validating the Pimpinelli-Einstein approach for large capture zones.

Findings

CZDs scaled by variance match Wigner surmise

ISD decay follows exp(-s^x) with shape-dependent x values

Scaling explains decay exponents from CZD Gaussian decay

Abstract

Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming the Pimpinelli-Einstein approach for large CZs / large island dynamics. The ISD decay as exp(-s^x), with x=4, x approx 2.4 and 2 for point, fractal, and square islands, respectively. A scaling approach explains the values of x from the Gaussian decay of CZD and the efficiency of islands to capture diffusing adatoms.