DYNAMIC SCALING OF THE ISLAND-SIZE DISTRIBUTION AND PERCOLATION IN A MODEL OF SUBMONOLAYER MOLECULAR-BEAM EPITAXY

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