A 2-DIMENSIONAL FLUID MODEL FOR AN ARGON RF DISCHARGE

A fluid model for an argon rf discharge in a cylindrical discharge cha mber is presented. The model contains the particle balances for electr ons and ions and the electron energy balance. A nonzero autobias volta ge is obtained by imposing the condition that the time-averaged curren t toward the powered and grounded electrode is zero. Particle densitie s and ionization profiles peak strongly in front of the smaller, power ed electrode. There electric fields are stronger and the electron curr ent density is higher, resulting in more ohmic heating and therefore h igher ionization rates. The radial uniformity of the plasma in front o f the powered electrode gives a homogeneous ion flux toward this elect rode. The asymmetric character of the profiles of the cylindrical geom etry is in clean contrast with the essentially one-dimensional infinit e parallel-plate geometry, which is fully symmetric with respect to th e center of the discharge and has a zero dc autobias voltage. A compar ison with results of a one-dimensional model shows that the average io n density, the average ion flux, and the average ionization rate in th e cylindrical reactor are comparable to those in a parallel-plate reac tor. The numerical treatment of the time evolution of the transport eq uations and Poisson's equation needs an implicit method to avoid numer ical instabilities. The resulting system of discretized equations is s olved by a multigrid technique. The spatial discretization uses the Sh arfetter-Gummel scheme.