Exclusion zone model of islands spatial distribution in molecular beam epitaxy

A simple model of islands spatial distribution based on the statistical nucleation model combined with a forbidden for nucleation zone is proposed. Islands 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 nucleation 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 introduction of the forbidden zone leads to some ordering degree in a spatial distribution of islands, similar to that observed in experiments, and provides a good quantitative coincidence with experiment at reasonable values of the model parameter L.