Scaling of island size and capture zone distributions in submonolayer growth

Abstract

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 $\mathrm{exp}(\ensuremath{-}{s}^{\ensuremath{\gamma}})$, with $\ensuremath{\gamma}=4$, $\ensuremath{\approx}$$2.4$, and $2$ for point, fractal, and square islands, respectively. A scaling approach explains the values of $\ensuremath{\gamma}$ from the Gaussian decay of CZDs and the efficiency of islands to capture diffusing adatoms.