Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas

Abstract

The self-excitation of Plasma Series Resonance (PSR) oscillations plays an important role in the electron heating dynamics in Capacitively Coupled Radio Frequency (CCRF) plasmas. In a combined approach of PIC/MCC simulations and a theoretical model based on an equivalent circuit, we investigate the self-excitation of PSR oscillations and their effect on the electron heating in geometrically symmetric CCRF plasmas driven by multiple consecutive harmonics. The discharge symmetry is controlled via the Electrical Asymmetry Effect, i.e. by varying the total number of harmonics and tuning the phase shifts between them. It is demonstrated that PSR oscillations will be self-excited under both symmetric and asymmetric conditions, if (i) the charge-voltage relation of the plasma sheaths deviates from a simple quadratic behavior and if (ii) the inductance of the plasma bulk exhibits a temporal modulation. These two effects have been neglected up to now, but we show that they must be included in the model in order to properly describe the nonlinear series resonance circuit and reproduce the self-excitation of PSR oscillations, which are observed in the electron current density resulting from simulations of geometrically symmetric CCRF plasmas. Furthermore, the effect of the PSR self-excitation on the discharge current and the plasma properties, such as the potential profile, is illustrated by applying Fourier analysis. High frequency oscillations in the entire spectrum between the applied frequencies and the local electron plasma frequency are observed. As a consequence, the electron heating is strongly enhanced by the presence of PSR oscillations. A complex electron heating dynamics is found during the expansion phase of the sheath, which is fully collapsed, when the PSR is initially self-excited. The Nonlinear Electron Resonance Heating associated with the PSR oscillations causes a spatial asymmetry in the electron heating. By discussing the resulting ionization profile in the non-local regime of low-pressure CCRF plasmas, we examine why the ion flux at both electrodes remains approximately constant, independently of the phase shifts.

The role of surface quenching of the singlet delta molecule in a capacitively coupled oxygen discharge

“…At the higher pressure of 50 mTorr the EEPF still curves outward for the highest quenching coefficients (as there is DA-heating present) but it transitions to curve inward (bi-Maxwellian) for the lowest quenching coefficients. The bi-Maxwellian shape of the EEPF in CCPs is commonly associated with predominant sheath 10 heating (α-mode). The low energy electron population represents electrons confined in the bulk plasma by an ambipolar potential, which are only weakly heated by the rf field, while the high energy population participates in the sheath heating.…”

“…This electron heating process is referred to as * tumi@hi.is electron bounce resonance heating (BRH) and can occur for certain combinations of driving frequency and electrode gap [3][4][5][6][7]. The sheath motion and thus the stochastic heating can also be enhanced by self-excited non-linear plasma series resonance (PSR) oscillations [8][9][10][11]. Collisionless electron heating via sheath oscillations is commonly referred to as the α-mode [12].…”

On electron heating in a low pressure capacitively coupled oxygen discharge

“…This effect is referred to as electron bounce resonance heating (BRH) [3]. The sheath motion and thus the stochastic heating can also be enhanced by selfexcited non-linear plasma series resonance (PSR) oscil- * tumi@hi.is lations [4][5][6][7][8]. At higher pressures some of the power is deposited by ohmic heating in the bulk plasma due to collisional momentum transfer between the oscillating electrons and the neutrals.…”

Evolution of electron temperature in inductively coupled plasma

“…The evolution in T e is interesting because it was well known that T e will either remain constant or slightly decrease with n e in the single-step or multi-step ionization global model. 1, 16 One possible explanation for this trend in T e may be the dramatic evolution of the EEPF through the electron heating effect 11,21,[30][31][32][33][34][35][36][37] or electronelectron collisions. 17,26,38,39 However, our experiment was conducted in plasmas having nearly Maxwellian EEPFs.…”