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

Tak Shing Lo, Robert 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

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continuum modeling
Epitaxial Growth
Adatoms
Coarsening
Epitaxial growth
adatoms
Slope
Continuum
slopes
Modeling
Hamilton-Jacobi equation
Predict
Nonlinear Diffusion Equation
Hamilton-Jacobi Equation
partial differential equations
Partial differential equations
Partial differential equation
Model

Keywords

  • Ehrlich-Schwoebel barrier
  • Epitaxial growth
  • Slope selection

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

A new approach to the continuum modeling of epitaxial growth : Slope selection, coarsening, and the role of the uphill current. / Lo, Tak Shing; Kohn, Robert.

In: Physica D: Nonlinear Phenomena, Vol. 161, No. 3-4, 15.01.2002, p. 237-257.

Research output: Contribution to journalArticle

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