A new approach to the continuum modeling of epitaxial growth: Slope selection, coarsening, and the role of the uphill current

Tak Shing Lo, Robert V. Kohn

Research output: Contribution to journalArticle

Abstract

We develop a new approach to the macroscopic modeling of epitaxial growth, focusing on the slope selection and coarsening observed in spiral-mode growth. Our model distinguishes between the surface height and the surface adatom density. These quantities evolve by a coupled pair of partial differential equations: a Hamilton-Jacobi equation for the height, coupled to a nonlinear diffusion equation for the adatom density. The influence of the Ehrlich-Schwoebel barrier is included through an "uphill current" in the equation for adatom density. Our model predicts slope selection and coarsening - thus it offers a possible mechanism for these effects. The model predicts, in particular, that the coarsening rate depends mainly on the strength of the Ehrlich-Schwoebel barrier.

Original languageEnglish (US)
Pages (from-to)237-257
Number of pages21
JournalPhysica D: Nonlinear Phenomena
Volume161
Issue number3-4
DOIs
StatePublished - Jan 15 2002

Keywords

  • Ehrlich-Schwoebel barrier
  • Epitaxial growth
  • Slope selection

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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