A homogenization technique for the Boltzmann equation for low pressure chemical vapor deposition

Matthias K. Gobbert, Christian Ringhofer

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Abstract

We present a homogenization technique for rarefied gas flow over a microstractured surface consisting of patterns of periodic features. The length scale of the model domain is comparable to the mean free path of the molecules, while the scale of the surface patterns is much smaller. The flow is modeled by a system of linear Boltzmann equations with a diffusive boundary condition at the patterned surface. The resulting homogenized boundary condition holds at a virtual flat surface and incorporates the microscopic geometry information about the surface structure on the macroscopic level. Numerical results validate the approach. The setup models low pressure chemical vapor deposition processes in the manufacturing of integrated circuits.

Original languageEnglish (US)
Pages (from-to)196-215
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume64
Issue number1
DOIs
StatePublished - Oct 1 2003

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Keywords

  • Boltzmann equation
  • Boundary homogenization
  • Chemical vapor deposition
  • Microstructured surface
  • Rarefied gas dynamics

ASJC Scopus subject areas

  • Applied Mathematics

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