Space-averaged kinetic analysis of stochastically heated electropositive and electronegative rf capacitive discharges

In low pressure capacitive rf plasma discharges, stochastic sheath heating, combined with potentials that exclude low energy electrons from reaching the sheath, produce an electron energy probability function (EEPF) which approximates a two-temperature Maxwellian, as seen in both experiments and numerical simulations. We have used the fundamental kinetic equation to derive a space- and time-averaged kinetic equation to analytically calculate this EEPF. In this paper, we improve over our model for stochastic heating by allowing the stochastic heating to be gradually turned on over a range of electron energy, instead of abruptly. A complete set of equilibrium conditions are used so that all the unknown parameters can be solved self-consistently. The theory is applied to both argon and oxygen discharges, and the results agree well with particle-in-cell (PIC) simulations and experiments. For electronegative oxygen discharges, the equilibrium equations for the two ion species are coupled with the electron kinetic equation. The spatial diffusion profiles and the EEPF both agree well with PIC simulations.