Surface-diffusion-driven kinetic growth on one-dimensional substrates

Abstract

Motivated by the physics of molecular-beam epitaxial (MBE) growth, we present a detailed numerical study of the dynamic scaling behavior of two atomistic solid-on-solid kinetic growth models in (1+1) dimensions in the presence of surface diffusion under a strong chemical bonding environment. Our goal is to relate stochastic molecular-beam epitaxial growth models with the existing statistical-mechanical-driven dynamical growth models. In the first model, which is the usual stochastic MBE growth model, diffusion of surface atoms follows an Arrhenius activation behavior. The effective growth exponents ${\mathrm{\ensuremath{\alpha}}}_{\mathit{e}\mathit{f}\mathit{f}}$ and ${\mathrm{\ensuremath{\beta}}}_{\mathit{e}\mathit{f}\mathit{f}}$, calculated as functions of the temperature, show a crossover from random deposition (\ensuremath{\beta}=0.5) to \ensuremath{\beta}\ensuremath{\approxeq}0.375 and \ensuremath{\alpha}\ensuremath{\approxeq}1.5 at intermediate temperatures, and then to \ensuremath{\beta}\ensuremath{\approxeq}0 and \ensuremath{\alpha}\ensuremath{\approxeq}0 at high temperatures. In the second model, which is a manifestly nonequilibrium dynamical model, newly arrived atoms instantaneously migrate to the nearest kink sites, with probability ${\mathit{p}}_{1}$, and within a diffusion length l. After finding a kink site they are allowed to break two bonds and make a nearest-neighbor hop with probability ${\mathit{p}}_{2}$. Here we see a behavior qualitatively similar to that in the first model, but, additionally, for ${\mathit{p}}_{2}$\ensuremath{\ne}0, a crossover to the Edwards-Wilkinson universality is observed. Surface morphologies produced by these models are presented with a detailed discussion of the scaling exponents, finite-size effects, and conditions for smooth growth.