Computational Studies of an Asymmetric rf Plasma using Particle-in-cell Techniques

Abstract

A one-dimensional, electrostatic Particle-in-cell code in spherical geometry has been used to simulate low pressure, asymmetric, rf discharges. The simulation consists of two concentric, spherical electrodes, between which a plasma is generated. The inner electrode is connected to a voltage source through an external circuit, which can include a variable capacitor and resistor; the outer electrode is grounded. Electrons and ions are modelled explicitly by the simulation, and neutrals are included implicitly as a background gas pressure. Ion and electron motion is included and both species can make binary collisions with the neutrals. The simulation uses realistic ion masses and collision cross-sections for each species. Electrons make ionisation, excitation and elastic scattering collisions; while ions can undergo charge exchange and elastic scattering collisions.

The plasma is generated by operating the voltage source at a given voltage and frequency. An analytic model is derived for the sheath and bulk regions, based on a kinetic description of the plasma, in order to provide a comparison to the simulation. Results from the model are found to be in good agreement with those from the simulation for an atomic hydrogen discharge. The effects of changing the applied voltage and frequency, the background gas pressure and the radii of the electrodes on the steady-state parameters and structure of the plasma are examined and some scaling laws determined. The effects of changing the ratio of the electrode areas on the voltage distribution in the plasma is studied in detail and dependence is found to disagree with predictions from other theoretical and numerical models. Heating of the electrons through interaction with the moving sheath edge has previously been determined to be the main mechanism sustaining low pressure, planar discharge models, and this effect is investigated for the asymmetric system. The relative distribution of power into ions and electrons is also determined. Ion energy and angular distributions at the electrodes are found to be dependent on both potential variation and ion collisions in the sheath.

A detailed Monte Carlo model of differential argon ion-neutral collision cross-sections was determined and used in the PIC code to simulate an argon discharge. Ion energy and angular distributions at the electrode, determined from the simulations, were found to be in good agreement with published experimental data.