Dynamic Scaling of the Island-Size Distribution and Percolation in a Model of Sub-Monolayer Molecular Beam Epitaxy
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ABSTRACT The results of a detailed study of the scaling and percolation behavior of the submonolayer in a model of molecular beam epitaxy are presented. In our model adatoms are randomly deposited on a square lattice and then allowed to diffuse. Whenever an adatom encounters another adatom or an island, it is attached to them and becomes immobile. We have found and studied four distinct scaling regimes, corresponding to a low-coverage (nucleation) regime, intermediate-coverage regime, an aggregation regime, and coalescence and percolation regime. At low coverage the islands have a dendritic structure such as seen in Au/Ru(0001) while at higher coverages they become compact. The scaling of the cluster fractal dimension, island density, monomer density, island size distribution, and structure factor and pair-correlation function are studied as a function of the coverage 9 and the ratio R = DIF of the diffusion rate to the deposition rate.
INTRODUCTION Recent experimental work using scanning tunneling microscopy (STM) as well as diffraction techniques has enabled the detailed study of the submonolayer island morphology, density, and size distribution for a variety of systems ranging from homoepitaxial systems [1-4] to heteroepitaxial systems such as Pb/Cu(001) [5], and Au/Ru(0001) [6]. In addition, a variety of experiments have been performed (1,3-4) which attempt to measure the parameters of surface diffusion (activation energy for example) by measuring the scaling of the island density as function of temperature at low coverage. If one assumes that for fixed coverage 9, the island density N(6) scales as N = C 1 (D/F)-x where D is the diffusion rate in unit of hops per unit time and F is the deposition rate in units of monolayers deposited per unit time, then the exponent X may be experimentally determined by studying the variation of N with F. Once X is known the activation energy Ea for diffusion may be determined from the dependence of the island density as a function of temperature, while if the constant of proportionality C1 is known the absolute diffusion rate may be determined. Thus, the knowledge of the scaling behavior of the island density and distribution for simple models of island formation both in the very-early-time and the aggregation regime may be used to determine important physical quantities in epitaxial growth. In this work [7] we investigate the evolution, growth, and scaling of islands in a minimal model of molecular beam epitaxy (without island relaxation and for which the critical cluster size is 2) from very low coverage through the coalescence and percolation regimes. In our model, adatoms (monomers) are deposited randomly on a square lattice 167 Mat. Res. Soc. Symp. Proc. Vol. 317. ©1994 Materials Research Society
with deposition rate F (in units of atoms per site per unit time) and then diffuse with diffusion rate D (nearest-neighbor hops per adatom per unit time). Whenever an adatom encounters another adatom as its nearest neighbor, both atoms are 'frozen' (stop diffusing) and form a
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