Continuum limit of a step flow model of epitaxial growth

R. V. Kohn, T. S. Lo, N. K. Yip

Research output: Contribution to journalConference articlepeer-review


We examine a class of step flow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent continuum model for the evolution of the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reflecting the microscopic physics of nucleation. We investigate this boundary condition by numerical simulation of the step flow dynamics using a simple nucleation law. Our results reveal the presence of special structures in the profile near a peak; we discuss the relationship between these structures and the continuum equation. We further address the importance of evaporation for matching the local behaviour near the peak to the solution of the continuum equation.

Original languageEnglish (US)
Pages (from-to)285-291
Number of pages7
JournalMaterials Research Society Symposium - Proceedings
StatePublished - 2002
EventCurrent Issues in Heteroepitaxial Growth Stress Relaxation and Self Assembly - Boston, MA, United States
Duration: Nov 26 2001Nov 29 2001

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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