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 Citations (Scopus)

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
StatePublished - 1998

Fingerprint

Asymptotic analysis
Chemical Vapor Deposition
Asymptotic Analysis
Chemical vapor deposition
Semiconductor materials
Semiconductor Manufacturing
Perturbation Analysis
Singular Perturbation
Adsorption
Diffusion equation
Model
Wafer
Replacement
Preprocessing
Semiconductors
Boundary conditions
Gases

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

  • Mathematics(all)
  • Applied Mathematics

Cite this

An Asymptotic Analysis for A Model of Chemical Vapor Deposition on A Microstructured Surface. / Gobbert, Matthias K.; Ringhofer, Christian.

In: SIAM Journal on Applied Mathematics, Vol. 58, No. 3, 1998, p. 737-752.

Research output: Contribution to journalArticle

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