The electrical asymmetry effect in multi-frequency capacitively coupled radio frequency discharges

Abstract

The electrical asymmetry effect (EAE) in geometrically symmetric capacitively coupled radio frequency discharges operated at multiple consecutive harmonics is investigated by a particle-in-cell (PIC) simulation and an analytical model. The model is based on the original EAE model, which is extended by taking into account the floating potentials, the voltage drop across the plasma bulk, and the symmetry parameter resulting from the PIC simulation. Compared with electrically asymmetric dual-frequency discharges we find that (i) a significantly stronger dc self-bias can be generated electrically and that (ii) the mean ion energies at the electrodes can be controlled separately from the ion flux over a broader range by tuning the phase shifts between the individual voltage harmonics. A recipe for the optimization of the applied voltage waveform to generate the strongest possible dc self-bias electrically and to obtain maximum control of the ion energy via the EAE is presented.

Slope and amplitude asymmetry effects on low frequency capacitively coupled carbon tetrafluoride plasmas

“…It is worth noting that the variation of the DC self-bias with H is not as linear as in argon. 21 Indeed, for H lower than 0.5p, it only slightly increases with H, whereas it increases more significantly for H between 0.5p and p. Overall, the range over which the DC self-bias can be controlled is significantly larger than that observed previously in the case of argon, 10,12,20 or in CF 4 25 (although only two frequencies have been used in the latter case).…”

“…(1). 20 The phase shift H can be varied to control the amplitude asymmetry from a maximum (H ¼ 0) to a minimum (H ¼ p). Such waveforms, with N ¼ 4, are shown in Fig.…”

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.…”

On the self-excitation mechanisms of plasma series resonance oscillations in single- and multi-frequency capacitive discharges

“…The range of this control can be extended by using multiple consecutive harmonics. [27][28][29][30] Moreover, an asymmetry can be caused by applying a temporally asymmetric sawtooth waveform due to the difference in the upward and downward slopes. 31,32 An asymmetry was believed to be a necessary requirement for the self-excitation of PSR oscillations, 16 because the nonlinearity of the sheaths will cancel in a symmetric discharge if they are modelled by a quadratic charge-voltage relation.…”

“…(1) are optimized to provide the greatest control range of the DC self-bias as a function of the phase shifts. 27 In this work, we use h 1 ¼ h 3 ¼ 0 and h 2 ¼ h 4 ¼ p=2, so that the absolute values of the maximum and the minimum of / $ ðuÞ are equal. Hence, the resulting profiles of the density and potential averaged over the RF period are approximately symmetric around the discharge center; there is only a slight disturbance in the symmetry of the discharge due to the weak asymmetry of the applied multifrequency voltage waveform in time.…”