Lattice Gas Models and Kinetic Monte Carlo Simulations of Epitaxial Growth

  • Michael Biehl
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 149)


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.


Crystal growth Lattice gas Kinetic Monte Carlo vicinal surfaces 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Michael Biehl
    • 1
  1. 1.Institute for Mathematics and Computing ScienceUniversity GroningenGroningenThe Netherlands

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