Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior

Details Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior

2006-12-18

arxiv.org/abs/cond-mat/0612471v2

Phys. Rev. Lett. 99, 226102 [4pp.] (2007)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures, originally submitted to Phys. Rev. Lett. on Dec. 15, 2006; revised version v2 tightens and focuses the pre

Scientific paper

10.1103/PhysRevLett.99.226102

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory sheds light on the result.

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