Fast modelling of low-pressure radio-frequency collisional capacitively coupled discharge and investigation of the formation of a non-Maxwellian electron distribution function

Abstract

The principles of fast modelling (FM) of a low-pressure radio-frequency capacitively coupled discharge are presented. They are based on averaging over fast electron and ion motions and on eliminating a small spatial scale, the Debye radius. As a result, the solution of a self-consistent system of the electron kinetic equation, Poisson and ion continuity equations takes approximately 10 min on a 486 PC. The calculation of discharge parameters has been performed for a wide range of current and pressure. The comparison with full-scale Monte Carlo calculations and experimental data has been performed. The performed comparisons demonstrate that the developed method of fast modelling has a good accuracy for calculating the global parameters such as central plasma density, applied voltage, sheath thickness, ionization rate, etc, and the profiles of plasma density and the electric fields. The accuracy of the electron distribution function (EDF) calculation is high when the EDF form is not enriched by slow electrons, and seems satisfactory in the case of a strongly peaked EDF. The results are in qualitatively good agreement with the experiment. The quantitative agreement is mainly within a factor of two. This discrepancy can be attributed to the fact that the EDF form is very sensitive to the details of plasma description, e.g. small variation of cross-sections results in considerable changes in the EDF. The mechanism of non-Maxwellian EDF formation due to non-locality effects has been analysed. The evolution of the low-pressure radio-frequency collisional capacitively coupled discharge with current and pressure variation has been investigated.

Revisiting the Anomalous rf Field Penetration into a Warm Plasma

“…In the opposite limit, n c > 4n h , the electron acoustic waves do not exist [24]. In capacitively-coupled discharges, the electron population does stratify into two populations of cold and hot electrons, as has been observed in experiments [27] and simulation studies [25,26]. Cold electrons trapped by the plasma potential in the discharge center do not interact with the large electric fields in the sheath region and have low temperature.…”

“…Cold electrons trapped by the plasma potential in the discharge center do not interact with the large electric fields in the sheath region and have low temperature. Moreover, because of the nonlinear evolution of plasma profiles, the cold electron density is much larger than the hot electron density [25]. Therefore, weakly-damped electron acoustic waves do not exist in the plasma of capacitively-coupled discharges.…”

Landau Damping and Anomalous Skin Effect in Low-pressure Gas Discharges: Self-consistent Treatment of Collisionless Heating

“…The "nonlocal" approach is the opposite case to the "local" description of a plasma, where f 0 (r, v) can be assumed to be a function of only the kinetic energy and the local rf electric field f 0 [mv 2 /2, E(r)] whereas gradients of the local rf electric field and the influence of the ambipolar electric field are neglected. The nonlocal approach has been successfully applied to the self-consistent kinetic modelling of various low-pressure discharges: the capacitively coupled plasmas [28][29][30][31], the inductively coupled plasmas [32][33][34][35], the dc discharges [36,37], the afterglow [38], and the surface-wave discharges [39]. Additional references can be found in reviews [40][41][42].…”

“…The cold electrons, which are trapped in the discharge center, do not reach periphery plasma regions where an intensive rf electric field is located and, as a result, these electrons are not heated by the rf electric field. The coupling between the EEDF shape and collisionless heating may result in a new nonlinear phenomenon: an explosive generation of the cold electrons [28].…”

Effect of electron energy distribution function on power deposition and plasma density in an inductively coupled discharge at very low pressures

“…This method has been successfully employed in the study of non-Maxwellian EEDFs in lowpressure RF capacitive discharges as well [24,25]. These approaches use the so-called quasi-linear theory [27,28], applied when the electron drift velocity is smaller than their thermal velocity, which is typical for low temperature discharges.…”