Logarithmic Clustering in Submonolayer Epitaxial Growth

Abstract

We investigate submonolayer epitaxial growth with a fixed monomer flux and irreversible aggregation of adatom islands due to their effective diffusion. When the diffusivity D_k of an island of mass k is proportional to k^{-μ}, a Smoluchowski rate equation approach predicts steady behavior for 0<μ<1, with the concentration c_k of islands of mass k varying as k^{-(3-μ)/2}. For μ>1, continuous evolution occurs in which c_k(t)~(\ln t)^{-(2k-1)μ/2}, while the total island density increases as N(t)~(\ln t)^{μ/2}. Monte Carlo simulations support these predictions.

4 pages, 2 figures

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