Capture zone area distributions for homogeneous nucleation and growth of islands during deposition

The size distribution of islands formed by homogeneous nucleation and growth during deposition is known to encode information about the nucleation mechanism. The same was recently proposed for the distribution, g(A), of areas, A, of capture zones (CZ) surrounding islands [1], where most atoms landing within a CZ aggregate with the associated island. We have developed a precise theory for g(A) whose evolution is driven by the nucleation of new islands [2]. g(A) has a complicated form controlled by details of the spatial aspects of nucleation. However, it is reasonably approximated by a Generalized Gamma distribution, g(A) $\sim $ A$^{\beta }$ exp[-cA$^{n}$]. For compact 2D islands, one has n $\sim $ 1.5, and $\beta \quad \sim $ 3(i+2)/2 for critical size i. Here, $\beta $ follows from analysis of the creation of new small capture zones between nearby pairs of islands, and n from analysis of the likelihood that a new CZ overlaps an existing large CZ. \\[4pt] [1] Pimpinelli {\&} Einstein, PRL 99 (2007) 226102; 104 (2010) 149602;\\[0pt] [2] Li, Han {\&} Evans, PRL 104 (2010) 149601.