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 ${\ensuremath{\sigma}}_{s}(\ensuremath{\Theta},\ensuremath{\Gamma})$ on island size $s$ and on both the coverage $\ensuremath{\Theta}$ and the $\ensuremath{\Gamma}=D/F$ 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 ${n}_{s}(\ensuremath{\Theta},\ensuremath{\Gamma})$ 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 $\ensuremath{\Theta}\ensuremath{\simeq}5%$ due to a significantly increased coalescence rate compared to fractal morphologies. As found earlier, the scaled KMC-ISDs ${n}_{s}{\overline{s}}^{2}/\ensuremath{\Theta}$ as a function of scaled island size $x=s/\overline{s}$ approach, for fixed $\ensuremath{\Theta}$, a limiting curve ${f}_{\ensuremath{\infty}}(x,\ensuremath{\Theta})$ for $\ensuremath{\Gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our findings provide evidence that the limiting curve is independent of $\ensuremath{\Theta}$ for point islands, while the results for compact and fractal island morphologies indicate a dependence on $\ensuremath{\Theta}$.