SOLID-ON-SOLID MODELS OF MOLECULAR-BEAM EPITAXY

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 p articles is not allowed and surface diffusion is driven by a Hamiltoni an 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 ar e repelled from step edges by so-called Schwoebel barriers: (i) Positi ve Schwoebel barriers lead to unstable growth and the formation of pyr amidlike structures. (ii) Negative Schwoebel barriers result in surfac e roughness that scales only logarithmically with separation or system size. This class is described at large length scales by the Edwards-W ilkinson equation. The atypical case of no Schwoebel barrier occurs on ly if there is a special symmetry in the diffusion process. This scena rio 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, t here are only two generic universality classes. These results are disc ussed in terms of a general Langevin equation and related to recent ex periments.