Solid-on-solid models of molecular-beam epitaxy.

Abstract

We discuss a number of solid-on-solid models that contain the two most important features of molecular-beam epitaxy: a flux of particles and relaxation of the growing film by surface diffusion. Evaporation of particles is not allowed and surface diffusion is driven by a Hamiltonian containing short-range interactions. In the absence of deposition, the correct equilibrium phase is recovered. We find that there are two generic situations depending on whether or not diffusing particles are repelled from step edges by so-called Schwoebel barriers: (i) Positive Schwoebel barriers lead to unstable growth and the formation of pyramidlike structures. (ii) Negative Schwoebel barriers result in surface roughness that scales only logarithmically with separation or system size. This class is described at large length scales by the Edwards-Wilkinson equation. The atypical case of no Schwoebel barrier occurs only if there is a special symmetry in the diffusion process. This scenario is present regardless of whether surface diffusion is implemented through an Arrhenius process or through Metropolis-type hopping rates. We conclude that, at least in the context of solid-on-solid models, there are only two generic universality classes. These results are discussed in terms of a general Langevin equation and related to recent experiments.