Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-07-16
Phys. Rev. E 66, 031605 (2002)
Physics
Condensed Matter
Statistical Mechanics
19 pages, 3 figures. To appear in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.66.031605
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.
Castellano Claudio
Politi Paolo
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