Multiscale modeling for epitaxial growth

Russel E. Caflisch

Research output: Contribution to conferencePaperpeer-review


Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale models that use continuum coarse-graining in the lateral direction, but retain atomistic discreteness in the growth direction. Establishing connections between the various length and time scales in these models is a principal goal of mathematical materials science. Progress towards this goal is described here, including the derivation of surface diffusion, line tension and continuum equations from atomistic, kinetic models.

Original languageEnglish (US)
Number of pages14
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006


Other25th International Congress of Mathematicians, ICM 2006


  • Adatom diffusion
  • Epitaxial growth
  • Gibbs-Thomson
  • Island dynamics
  • Kinetic Monte Carlo
  • Line tension
  • Renormalization group
  • Step edge
  • Step stiffness
  • Surface diffusion

ASJC Scopus subject areas

  • General Mathematics


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