RENORMALIZATION OF ATOMISTIC GROWTH MODELS

Abstract

We review a general procedure for the multiscale analysis of atomistic lattice models of fluctuating interfaces driven by the deposition of new material. Beginning with a lattice Langevin formulation of site fluctuations, stochastic differential equations are derived by regularizing the lattice transition rules. Subsequent coarse graining is accomplished by applying the renormalization group, which yields trajectories from initial conditions determined by the regularized atomistic models. These trajectories correspond to hierarchies of continuum equations that describe the original lattice models over expanding length and time scales as the extent of coarse graining increases. This provides a systematic method for the derivation of continuum equations from the transition rules of lattice models appropriate for any length and time scales, and thereby establishes a quantitative link between atomistic transition rules and the collective behavior of the system. The results obtained with this method are confirmed by all available kinetic Monte Carlo simulations and, in some cases, have provided new interpretations of previous experimental observations. In this review, we first discuss the elements of our multiscale method in general terms, and then illustrate their implementation for specific growth models.