Kinetic model for a step edge in epitaxial growth

A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the den sity of kinks and "edge adatoms" along the step edge. Equilibrium and kinet ic steady states, corresponding to zero and nonzero deposition flux, respec tively, are derived for a periodic sequence of step edges. The theoretical results are compared to results from kinetic Monte Carlo (KMC) simulations of a simple solid-on-solid model, and excellent agreement is obtained. This theory provides a starting point for modeling the growth of two-dimensiona l islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.