Scaling of island size and capture zone distributions in submonolayer growth

Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming the Pimpinelli-Einstein approach for large CZs/large island dynamics. The ISDs decay as exp(-s(gamma)), with gamma = 4, approximate to 2.4, and 2 for point, fractal, and square islands, respectively. A scaling approach explains the values of gamma from the Gaussian decay of CZDs and the efficiency of islands to capture diffusing adatoms.