Capture numbers and island size distributions in models of submonolayer surface growth

Abstract

The capture numbers entering the rate equations (RE) for submonolayer film growth are determined from extensive kinetic Monte Carlo (KMC) simulations for simple representative growth models yielding point, compact, and fractal island morphologies. The full dependence of the capture numbers sigma(s)(Theta, Gamma) on island size s and on both the coverage Theta and the Gamma = D/F ratio between the adatom diffusion coefficient D and deposition rate F is determined. Based on this information, the RE are solved to give the RE island size distribution (RE-ISD), as quantified by the number n(s) (Theta, Gamma) of islands of size s per unit area. The RE-ISDs are shown to agree well with the corresponding KMC-ISDs for all island morphologies. For compact morphologies, however, this agreement is only present for coverages smaller than Theta similar or equal to 5% due to a significantly increased coalescence rate compared to fractal morphologies. As found earlier, the scaled KMC-ISDs n(s)(s) over bar (2)/Theta as a function of scaled island size x = s/(s) over bar approach, for fixed Theta, a limiting curve f(infinity)(x, Theta) for Gamma -> infinity. Our findings provide evidence that the limiting curve is independent of Theta for point islands, while the results for compact and fractal island morphologies indicate a dependence on Theta.