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

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

2002-07-16

arxiv.org/abs/cond-mat/0207404v1

Phys. Rev. E 66, 031606 (2002)

Physics

Condensed Matter

Statistical Mechanics

22 pages, 10 figures. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.66.031606

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.

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