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Anomalous Dimension and Spatial Correlations in a Point-Island Model

Ji Li·A. G. Rojo·Leonard M. Sander
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Abstract

We examine the island size distribution function and spatial correlation function of a model for island growth in the submonolayer regime in both 1 and 2 dimensions. In our model the islands do not grow in shape, and a fixed number of adatoms are added, nucleate, and are trapped at islands as they diffuse. We study the cases of various critical island sizes $i$ for nucleation as a function of initial coverage. We found anomalous scaling of the island size distribution for large $i$ . Using scaling, random walk theory, a version of mean-field theory we obtain a closed form for the spatial correlation function. Our analytic results are verified by Monte Carlo simulations.

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Ji Li, A. G. Rojo, Leonard M. Sander. 1996-06-13. Anomalous Dimension and Spatial Correlations in a Point-Island Model. https://doi.org/10.1103/physrevlett.78.1747

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