An integral equation method for epitaxial step-flow growth simulations

Jingfang Huang*, Ming-Chih Lai, Yang Xiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper, we describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equations (DAEs), and the time dependent potentials are evaluated efficiently using fast convolution algorithms. The numerical solver is applied to the BCF model for the epitaxial step-flow growth of crystals, for which the solutions are calculated accurately instead of using quasi-static approximations. Numerical results in 1 + 1 dimensions are compared with available results in the literature.

Original languageEnglish
Pages (from-to)724-743
Number of pages20
JournalJournal of Computational Physics
Volume216
Issue number2
DOIs
StatePublished - 10 Aug 2006

Keywords

  • Diffusion equation
  • Epitaxial step-flow
  • Fast algorithms
  • Integral equation
  • Jump conditions
  • Potential theory
  • Spectral deferred correction

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