Scaling relation of domain competition on (2+1)-dimensional ballistic deposition model with surface diffusion

Abstract

During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing. The number density of active domains ρ decreases as the height h increases. A simple scaling argument leads to a scaling law of θ ∼ h−γ with a coarsening exponent γ = d/z, where d is the dimension of the substrate surface and z the dynamic exponent of a growth front. This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional (d = 2) surface, even when an isolated deposited particle diffuses on a crystal surface.