Analysis of island dynamics in epitaxial growth of thin films

Russel E. Caflisch, Bo Li

Research output: Contribution to journalArticlepeer-review


This work is concerned with analysis and refinement for a class of island dynamics models for epitaxial growth of crystalline thin films. An island dynamics model consists of evolution equations for step edges (or island boundaries), coupled with a diffusion equation for the adatom density, on an epitaxial surface. The island dynamics model with irreversible aggregation is confirmed to be mathematically ill-posed, with a growth rate that is approximately linear for large wavenumbers. By including a kinetic model for the structure and evolution of step edges, the island dynamics model is made mathematically well-posed. In the limit of small edge Peclet number, the edge kinetics model reduces to a set of boundary conditions, involving line tension and one-dimensional surface diffusion, for the adatom density. Finally, in the infinitely fast terrace diffusion limit, a simplified model of one-dimensional surface diffusion and kink convection is derived and found to be linearly stable.

Original languageEnglish (US)
Pages (from-to)150-171
Number of pages22
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2003


  • Adatom diffusion
  • Epitaxial growth
  • Island dynamics
  • Line tension
  • Linear stability
  • Normal velocity
  • Step edges
  • Step-edge kinetics
  • Surface diffusion

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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