Modeling electronegative plasma discharges

A macroscopic analytic model for a three-component electronegative plasma has been developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is found. The electron density is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane rf driven oxygen plasma for two cases: (1) p=50 mTorr, ne0=2.4×1015 m−3, and (2) 10 mTorr, ne0=1.0×1016 m−3. In the simulation, for the low power case (1), the ratio of negative ion to electron density was found to be α0≊8, while in the higher power case α0≊1.3. Using an electron energy distribution that approximates the simulation distribution by a two-temperature Maxwellian, the analytic values of α0 are found to be close to, but somewhat larger than, the simulation values. The average electron temperature found self-cosistently in the model is close to that in the simulation. The results indicate the need for determining a two-temperature electron distribution self-consistently within the model.