Surface roughness evolution in a solid-on-solid model of epitaxial   growth
  The paper presents results from kinetic Monte Carlo simulations of kinetic surface roughening using an important and experimentally relevant model of epitaxial growth -- the solid-on-solid model with Arrhenius dynamics. A restriction on diffusing adatoms is included allowing hopping down only at steps of height one monolayer in order to avoid possibly unrealistic events of jumping from arbitrarily high steps. Simulation results and precise analytic expressions representing the time evolution of surface roughness do not depend on the substrate size and clearly put forward the conclusion that for any basic set of parameters the model approaches in asymptotic limit the usual random deposition process with growth exponent $\beta=1/2$. At high temperatures, it is preceded by a long transient regime characterized by a smooth surface covered with porous pillars and described by a power law with $\beta=3/4$. 
Petar P. Petrov and Daniela Gogova
cond-mat.mtrl-sci