TY - JOUR
T1 - A homogenization technique for the Boltzmann equation for low pressure chemical vapor deposition
AU - Gobbert, Matthias K.
AU - Ringhofer, Christian
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003/10
Y1 - 2003/10
N2 - 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.
AB - 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.
KW - Boltzmann equation
KW - Boundary homogenization
KW - Chemical vapor deposition
KW - Microstructured surface
KW - Rarefied gas dynamics
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U2 - 10.1137/S0036139902393476
DO - 10.1137/S0036139902393476
M3 - Article
AN - SCOPUS:1842509222
VL - 64
SP - 196
EP - 215
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 1
ER -