Hydrodynamic Model of Plasma-Sheath for RF Discharges with and without Collision

Abstract

We present a numerical model for two-species bounded plasma discharge with a time varying potential at 0.1 torr pressure in collisional and collisionless regimes. The plasma-wall problem is modeled using hydrodynamic equations coupled with the Poisson equation. The model is based on a robust finite element algorithm utilized to overcome the stiffness of the plasma-wall equations. Appropriate flux boundary conditions with directions are imposed at both electrodes. Typical discharge characteristics including electron gas flooding at electrode, sheath heating, sheath evolution with time and electric double layer are predicted. The spatial and temporal evolution of charge density, electric field and total current are documented. Numerical limitations are also highlighted from the theoretical derivation of algorithm amplification factor and phase velocity. Nomenclature x (z)Spatial co-ordinate, cm t (τ)Time co-ordinate, s n (N) ** Number density, cm -3