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Two fluid models of RF glow discharges, the non-equilibrium and equilibrium, are compared. The non-equilibrium fluid model is obtained by interpolating between a kinetic and a three-moment non-equilibrium formulation of the Boltzmann equation. The three-moment non-equilibrium model is valid in the time scale of the energy moment relaxation time and all coefficients are based on the mean energy. The equilibrium model is a single-moment model in which equilibrium conditions are assumed and the mean energy and average velocity relax to the equilibrium. Consequently, the transport coefficients in the equilibrium model are obtained from formulae based on local electric field and background gas pressure. Self-consistent RF glow discharge simulations for helium gas are carried out based on these two models, and the differences between the non-equilibrium and equilibrium models are compared. Owing to the finite relaxation time in the non-equilibrium model, momentum and energy, which require time and space to change in space-time varying electric fields, cannot change as rapidly as in the equilibrium model. Consequently, the non-equilibrium model shows the transition between the alpha and gamma regimes, a higher plasma density and a reduced sheath width.

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For the first time, a two-dimensional self-consistent nonequilibrium fluid model is used in simulations of rf glow discharges to evaluate the quantitative effects of the radial and axial flow dynamics inside a cylindrically symmetric geometry. Electrons are modeled with a three-moment nonequilibrium model and ions are modeled with a nonequilibrium single-moment model which includes an ionic effective electric field. The nonuniform plasma density profiles and the radial sheath width variation with various gas pressures are discussed. These resulting radially nonuniform plasma density profiles are an important issue for plasma processing.

Self-consistent nonequilibrium fluid models of both the two-dimension (2D) and one-dimension (1D) are presented. In the 2D simulations, the models evaluate the quantitative effects of both radial and axial flow dynamics inside a cylindrically symmetric parallel-plate geometry. The 1D model assumes that the radius of the electrode is much larger than the electrode gap and the moment distributions are uniform along the radial direction. The models are based on the first three moments of the Boltzmann equation and Poisson’s equation. Radio frequency (rf) glow discharge simulations from those two fluid models are presented and compared in this study. The comparisons are presented in terms of plasma density, electric field, mean energy, and ionization rate. Results of the 1D fluid model are close to those at the center of the reactor from the 2D simulations. Nonuniform profiles along the radial direction are obtained from the 2D simulations due to the radial dynamics. Higher electron mean energy in the middle region of the radial sheath is observed. The maximum ionization rate is located in the radial sheath region and agrees with the experimental observation.