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

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.

arXiv comment19 pages, 3 figures. To appear in Phys. Rev. E

References in corpus (6)

• Instabilities in crystal growth by atomic or molecular beams
• Island nucleation in the presence of step edge barriers: Theory and applications
• Nucleation on top of islands in epitaxial growth
• Spatio-temporal distribution of nucleation events during crystal growth
• Scaling regimes for second layer nucleation
• The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions

Cited by in corpus (4)

• Lonely adatoms in space
• The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions
• Impact of anisotropic interactions on non-equilibrium cluster growth at surfaces
• Irreversible nucleation in molecular beam epitaxy: From theory to experiments