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

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 αeff and βeff, calculated as functions of the temperature, show a crossover from random deposition ({β}=0.5) to {β}{}0.375 and {α}{}1.5 at intermediate temperatures, and then to {β}{}0 and {α}{}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 p₁, 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 p₂. Here we see a behavior qualitatively similar to that in the first model, but, additionally, for p₂{≠}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.