Extensive information on the distribution of islands formed during submonolayer deposition is provided by the joint probability distribution (JPD) for island sizes, s, and capture zone areas, A. A key ingredient determining the form of the JPD is the impact of each nucleation event on existing capture zone areas. Combining a realistic characterization of such spatial aspects of nucleation with a factorization ansatz for the JPD, we provide a concise rate equation formulation for the variation with island size of both the capture zone area and the island density.
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Evans, J.W., Li, M. & Bartelt, M.C. Rate Equation Theory for Island Sizes and Capture Zone Areas in Submonolayer Deposition: Realistic Treatment of Spatial Aspects of Nucleation. MRS Online Proceedings Library 749, 22 (2002). https://doi.org/10.1557/PROC-749-W2.2