Dynamic scaling of the island-size distribution and percolation in a model of submonolayer molecular-beam epitaxy

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Abstract
The results of a detailed study of the evolution, scaling, and percolation of islands in a model of submonolayer molecular-beam epitaxy appropriate for the case of dendritic island growth are presented. The scaling of the island density, monomer density, island-size distribution, structure factor, and pair-correlation function are studied as a function of the coverage θ and the ratio R=D/F of the diffusion rate D to the deposition rate F. Our results span the full range of coverage starting from very low coverage all the way through the coalescence and percolation regimes. For small coverages the islands are fractal while at higher coverages they become compact, similar to what has been observed in Au/Ru(0001). For large R, four distinct scaling regimes are found: a low-coverage nucleation regime, an intermediate-coverage regime, an aggregation regime in which the island density remains constant, and a coalescence and percolation regime. The scaling behavior in the first three regimes is compared with results obtained using a generalized rate-equation approach. An anomalous fractal scaling form for the structure factor in the aggregation regime is also derived. The dependence of the percolation threshold on R is also studied and found to show interesting nonmonotonic behavior.