MODELING PLASMA DISCHARGES AT HIGH ELECTRONEGATIVITY

Macroscopic models for the equilibrium of a three-component electroneg ative gas discharge are developed. Assuming the electrons and the nega tive ions to be in Boltzmann equilibrium, a positive ion ambipolar dif fusion equation is derived. Such a discharge can consist of an electro negative core and may have electropositive edge regions, but the elect ropositive regions become small for the highly electronegative plasma considered here. In the parameter range for which the negative ions ar e Boltzmann, the electron density in the core is nearly uniform, allow ing the nonlinear diffusion equation to be solved in terms of elliptic integrals. If the loss of positive ions to the walls dominates the re combination loss, a simpler parabolic solution can be obtained. If rec ombination loss dominates the loss to the walls, the assumption that t he negative ions are in Boltzmann equilibrium is not justified, requir ing coupled differential equations for positive and negative ions. Thr ee parameter ranges are distinguished corresponding to a range in whic h a parabolic approximation is appropriate, a range for which the reco mbination significantly modifies the ion profiles, but the electron pr ofile is essentially flat, and a range where the electron density vari ation influences the solution. The more complete solution of the coupl ed ion equations with the electrons in Boltzmann equilibrium, but not at constant density, is numerically obtained and compared with the mor e approximate solutions. The theoretical considerations are illustrate d using a plane parallel discharge with chlorine feedstock gas of p = 30, 300 and 2000 mTorr and n(eO) = 10(10) cm(-3), corresponding to the three parameter regimes. A heuristic model is constructed which gives reasonably accurate values of the plasma parameters in regimes for wh ich the parabolic profile is not adequate.