Modeling of island formation during submonolayer deposition: A stochastic geometry-based simulation approach

Homogeneous nucleation and growth of two-dimensional islands during submonolayer deposition has been analyzed extensively by kinetic Monte Carlo (KMC) simulation of atomistic models and more recently by Burton-Cabrera-Frank-type continuum formulations for diffusion and aggregation of the deposited adatoms. Here, we develop an alternative geometry-based simulation (GBS) approach. This approach replaces an explicit treatment of adatom diffusion ( either within an atomistic or continuum framework) with a formulation based on the stochastic geometry of "depletion zones" or "capture zones" surrounding islands. We consider models with a prescribed critical size, i, above which islands are stable. For canonical models with small i, we show that prediction of the nucleation rate and island density by GBS (or any other multiscale approach) requires precise description of adatom capture by critical clusters, for which we extend existing theory. We also present results for the island size distribution including the regime of large i where KMC simulation becomes inefficient and where the initial transient regime of the growing adatom population becomes protracted and thus more important. Finally, we discuss extension of the GBS approach to treat island coalescence and multilayer growth, and to a variety of other nucleation mechanisms.