Lattice Gas Models and Kinetic Monte Carlo Simulations of Epitaxial Growth

A brief introduction is given to Kinetic Monte Carlo (KMC) simulations of epitaxial crystal growth. Molecular Beam Epitaxy (MBE) serves as the prototype example for growth far from equilibrium. However, many of the aspects discussed here would carry over to other techniques as well. A variety of approaches to the modeling and simulation of epitaxial growth have been applied. They range from the detailed quantum mechanics treatment of microscopic processes to the coarse grained description in terms of stochastic differential equations or other continuum approaches. Here, the focus is on discrete representations such as lattice gas and Solid-On-Solid (SOS) models. The basic ideas of the corresponding Kinetic Monte Carlo methods are presented. Strengths and weaknesses become apparent in the discussion of several levels of simplification that are possible in this context. Mathematics Subject Classification (2000). Primary 82B24; Secondary 82B80.