Porous Media Based Modeling of parallel Plate PE-CVD Apparatus: Approximation to the Experiments with $SiC$ and $TiC$.

Juergen Geiser , M. Arab

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 30 pp.

MSC 2000

35K25 General theory of higher-order, parabolic equations

35K20 Boundary value problems for second-order, parabolic equations

Abstract
The numerous technical applications in deposit metal plates with new materials like $SiC$ and $TiC$ has an advantage to overcome the leaking corrosive behavior and have additional a good electrical behavior. Here we present an application of a porous media to model a homogenized deposition with a parallel plate PE-CVD apparatus. Special geometries of parallel Anodes and cathodes helps to obtain at least a laminar flow field. By the way the delicate arrangement of the anode and cathode has to be simulated. The flux of the precursors are important to simulate to the porous media given as the plasma background. Here we can optimize the transport to the delicate geometry respecting the flux field in the permeable layers. To derive a mathematical model, we deal with a model for the transport and kinetics of the different species. Underlying physical experiments help to approximate the parameters of the numerical model. We introduce a multi regression method to approximate the physical to the mathematical parameters. We present results of some numerical simulations and help to foresee some effects to find on optimal deposition process.