Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth

TL;DR

This paper analytically derives the asymptotic capture-number and island-size distributions for one-dimensional irreversible submonolayer growth, showing good agreement with kinetic Monte Carlo simulations and confirming the self-averaging property of capture zones.

Contribution

It provides the first analytical expressions for the asymptotic capture-number distribution and island-size distribution in one-dimensional growth, validated by simulations.

Findings

Analytical asymptotic CND matches KMC results.

Asymptotic ISD is non-divergent and agrees with simulations.

Self-averaging property of capture zones holds exactly asymptotically.

Abstract

Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett. {\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate analytically the asymptotic scaled capture-number distribution (CND) for one-dimensional irreversible submonolayer growth of point islands. The predicted asymptotic CND is in reasonably good agreement with kinetic Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic} scaled island-size distribution (ISD). We then show that a slight modification of our analytical form leads to an analytic expression for the asymptotic CND and a resulting asymptotic ISD which are in excellent agreement with KMC simulations. We also show that in the asymptotic limit the self-averaging property of the capture zones holds exactly while the asymptotic scaled gap distribution is equal to the scaled CND.