Electron energy distribution functions in radio-frequency collision dominated nitrogen discharges

Abstract

Electron energy distribution functions (EEDFS) in RF collision dominated N₂ discharges have been calculated by solving the time-dependent Boltzmann equation including elastic, inelastic and superelastic collisions. The results have been obtained at different field amplitudes E₀/ rho ₀ (100/ rho ₀-1 Torr^-1), at different frequencies omega / rho ₀ ( pi *10⁶08 s^-1 Torr ^-1) and different concentrations of excited (vibrational and electronic) states. It has been found that the presence of excited states strongly modified the modulation of the tail of EEDFS with strong consequences on the collision frequencies of processes having high energy thresholds. The role of field frequency is studied for the understanding of both the temporal behaviour of EEDFS and the averaged (over the period) values of EEDFS and of macroscopic quantities. The authors obtain that at fixed E₀/ rho ₀ the increase of frequency decreases the tail of EEDFS, strongly reducing the collision frequency of the ionisation process. Finally the importance of the time-dependent solution of the Boltzmann equation is tested by comparing the present results with the corresponding ones obtained by using the effective field approximation. Differences up to several orders of magnitude are obtained in this comparison, the differences being reduced at high E₀/ rho ₀, high omega / rho ₀ and large concentrations of excited states.