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 ${\mathit{E}}_{\mathit{N}}$. The total island density is observed to saturate before coalescence becomes important. In this regime, the density of adatoms ${\mathit{N}}_1$∼${\mathit{FTHETA}}^{\mathrm{-}\mathit{r}}$ ${\mathit{gerR}}^{\mathrm{-}\mathrm{\omega }}$ while the density of islands composed of s>1 atoms ${\mathit{N}}_{\mathit{s}}$∼FTHETA〈s${\mathrm{〉}}^{\mathrm{-}2}$g(s/〈s〉) where the average island size 〈s〉∼${\mathit{FTHETAgerR}}^{\mathit{x}}$. The exponents r, ω, and χ vary smoothly with ${\mathit{E}}_{\mathit{N}}$.