The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions

TL;DR

This paper provides exact solutions for irreversible dimer nucleation during epitaxial growth in one and two dimensions, revealing significant differences from mean-field estimates especially at moderate step-edge barriers.

Contribution

It introduces an exact analytical approach transforming the nucleation problem into a first passage problem for a random walker, applicable in all step-edge barrier regimes.

Findings

Spatial distribution of nucleation events differs from mean-field predictions

Exact nucleation rate including numerical prefactors is computed

Differences are most pronounced at moderate step-edge barriers

Abstract

We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.