The process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach

TL;DR

This paper critically examines the mean-field theory for nucleation during multilayer epitaxial growth, revealing its inaccuracies and overestimations, and sets the stage for a more precise subsequent analysis.

Contribution

It demonstrates the failure of mean-field theory in modeling nucleation, quantifies the overestimation factor, and relates it to random walk properties of adatoms.

Findings

Mean-field theory overestimates nucleation rate by a factor N.

N depends on terrace size and step-edge barriers.

Spatial distribution of nucleation events differs from mean-field predictions.

Abstract

The formation of stable dimers on top of terraces during epitaxial growth is investigated in detail. In this paper we focus on mean-field theory, the standard approach to study nucleation. Such theory is shown to be unsuitable for the present problem, because it is equivalent to considering adatoms as independent diffusing particles. This leads to an overestimate of the correct nucleation rate by a factor N, which has a direct physical meaning: in average, a visited lattice site is visited N times by a diffusing adatom. The dependence of N on the size of the terrace and on the strength of step-edge barriers is derived from well known results for random walks. The spatial distribution of nucleation events is shown to be different from the mean-field prediction, for the same physical reason. In the following paper we develop an exact treatment of the problem.