Exclusion zone model of islands spatial distribution in molecular beam epitaxy

A simple model of islands spatial distribution based on the statistical nuc leation model combined with a forbidden for nucleation zone is proposed. Is lands nucleate at random points of uncovered substrate with a constant rate and then grow in a hemisphere at a constant velocity. Around each growing island there exists an exclusion zone of some width L within which nucleati on is forbidden, while outside this zone islands continue to germinate in a usual spatially random fashion, By this model formulas for the probability that an arbitrarily chosen surface region at any given time moment t will be either empty or contain just one island, W-0(t) and W-1(t), respectively , are derived. Calculations with this formula shows that a simple introduct ion of the forbidden zone leads to some ordering degree in a spatial distri bution of islands, similar to that observed in experiments, and provides a good quantitative coincidence with experiment at reasonable values of the m odel parameter L. (C) 2000 Elsevier Science B.V. All rights reserved.