An Asymptotic Analysis for A Model of Chemical Vapor Deposition on A Microstructured Surface

Matthias K. Gobbert, Christian Ringhofer

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

We consider a model for chemical vapor deposition, the process of adsorption of gas onto a surface together with the associated deposition of a chemical reactant on the surface. The surface has a microscopic structure which, in the context of semiconductor manufacturing, arises from a preprocessing of the semiconductor wafer. Using singular perturbation analysis, a boundary condition for the corresponding diffusion equation is derived, which allows for the replacement of the microstructured surface by a flat boundary. The asymptotic analysis is numerically verified with a simple test example.

Original languageEnglish (US)
Pages (from-to)737-752
Number of pages16
JournalSIAM Journal on Applied Mathematics
Volume58
Issue number3
DOIs
StatePublished - Jan 1 1998

Keywords

  • Asymptotic analysis
  • Chemically reacting flows
  • Homogenization
  • Mass transfer
  • Microstructured surfaces
  • Partial differential equations
  • Singular perturbation
  • Time-dependent initial-boundary value problem

ASJC Scopus subject areas

  • Applied Mathematics

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