Saturation and scaling of epitaxial island densities

The aggregation of adatoms into 2D islands is studied as a function of coverage FTHETA and the ratio of surface diffusion rate to deposition rate gerR=D/F by Monte Carlo simulations of a model of epitaxial growth that permits atoms to detach from island edges at a rate determined by a pair bond energy E_N. The total island density is observed to saturate before coalescence becomes important. In this regime, the density of adatoms N₁∼FTHETA^-rgerR^-ω while the density of islands composed of s>1 atoms N_s∼FTHETA〈s〉^-2g(s/〈s〉) where the average island size 〈s〉∼FTHETAgerR^x. The exponents r, ω, and χ vary smoothly with E_N.