Geometry-based simulation (GBS) algorithms for island nucleation and growth during sub-monolayer deposition

Versatile geometry-based simulation (GBS) algorithms are developed to describe the formation of two-dimensional islands during sub-monolayer film growth. These GBS algorithms avoid an explicit treatment of the diffusion of deposited atoms across terraces, the process which mediates both island nucleation and growth. Treatment of terrace diffusion is a computationally expensive component of either conventional atomistic kinetic Monte Carlo (KMC) simulations, or of coarse-grained continuum formulations of island edge evolution. Our GBS approach characterizes island growth in terms of simply constructed “capture zones” surrounding each island, an old concept which was recently refined and made quantitatively precise. However, in addition, GBS implements simple but realistic geometric rules to incorporate crucial spatial aspects of the island nucleation process, specifically nucleation nearby capture zone boundaries. By detailed comparison of predictions of results from GBS with conventional atomistic KMC simulations, we show that this approach correctly predicts island size distributions as well as subtle spatial correlations in island locations. Perhaps, just as importantly, refinement of the prescription of island nucleation is readily achieved in GBS, thus elucidating the effects of this prescription on the resulting island distribution. Finally, we emphasize that GBS is particularly effective for highly reversible island formation where atomistic KMC simulation becomes inefficient.