Anisotropic step stiffness from a kinetic model of epitaxial growth

Dionisios Margetis, Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review


Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson-type formula and the associated step stiffness as a function of the step edge orientation angle, Θ. Basic ingredients of the model are (i) the diffusion of point defects ("adatoms") on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a meanfield approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, β̃(Θ), is determined via perturbations of the kinetic steady state for small edge Péclet number P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, β̃ is found to satisfy β̃ = O(Θ-1) for O(P 1/3) > Θ ⇒ 1, which is in agreement with independent, equilibrium-based calculations.

Original languageEnglish (US)
Pages (from-to)242-273
Number of pages32
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2008


  • Adatoms
  • Edge-atoms
  • Ehrlich-Schwoebel barrier
  • Epitaxial growth
  • Gibbs-Thomson formula
  • Island dynamics
  • Kinetic steady state
  • Line tension
  • Step edge
  • Step edge kinetics
  • Step permeability
  • Step stiffness
  • Surface diffusion

ASJC Scopus subject areas

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


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