Kinetic model for a step edge in epitaxial growth

Russel E. Caflisch, W. E. Weinan, Mark F. Gyure, Barry Merriman, Christian Ratsch

Research output: Contribution to journalArticlepeer-review


A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the density of kinks and “edge adatoms” along the step edge. Equilibrium and kinetic steady states, corresponding to zero and nonzero deposition flux, respectively, 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-dimensional islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.

Original languageEnglish (US)
Pages (from-to)6879-6887
Number of pages9
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number6
StatePublished - 1999

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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