Ostwald ripening of two-dimensional homoepitaxial islands

Abstract

Ostwald ripening in homoepitaxy in the submonolayer regime is studied by means of numerical simulations based on a step flow model, which accounts for attachment-detachment kinetics at the island boundaries. Diffusion-limited ripening and the crossover to attachment-limited ripening is investigated. The simulations indicate that the coarsening kinetics of the average island radius is described by a ${t}^{a}$ power law, where $1∕3\ensuremath{\leqslant}a\ensuremath{\leqslant}1∕2$. Here $a$ takes the value $1∕3$, if the ripening is purely diffusion-limited (infinite attachment rate at the island boundaries), and increases with decreasing attachment rate, approaching the value $a=1∕2$ if the ripening becomes attachment-limited. For the diffusion-limited regime, the numerical simulations are shown to correspond with the predictions of the mean-field theory proposed by Yao et al., for both the scaling behavior of the average island size as well as the island size distribution in the late stage. Approaching the attachment-limited regime, the numerical results meet the predictions of the classical mean-field theory of Lifshitz, Slyozov, and Wagner for attachment-limited ripening. We also analyze the influence of anisotropic edge energies and edge diffusion.