Self-excited nonlinear plasma series resonance oscillations in geometrically symmetric capacitively coupled radio frequency discharges

Abstract

At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies.

Control of plasma properties in capacitively coupled oxygen discharges via the electrical asymmetry effect

“…In this way, the density profiles of the charged species can be shifted away from the discharge center towards the powered or grounded electrode. However, this shift is quite small under these conditions compared to the scenario of even lower pressures discussed in argon [28] and oxygen [36] before. In addition, it is found that the bulk length L b , which we define as the difference between the electrode gap and the sum of the maximum sheath extension at both electrodes,…”

“…2, the nonlinearities of the plasma sheaths do not cancel if ε = 1 and resonance oscillations occur. In general, it does not matter whether this asymmetry is induced geometrically (A p = A g ) or electrically (φ ∼,max = −φ ∼,min ) [28]. It should be noted that the discharge symmetry is characterized by ε and not by the value ofη [37]; even though we could define an electrical symmetry byη = 0, this would not necessarily mean that the densities are symmetric with respect to the discharge center, which would imply ε = 1 in the case of a geometrically symmetric discharge.…”

“…However, it is known that the coupling of both frequencies [9][10][11][12][13][14][15][16][17][18][19] and the effect of secondary electrons [8,[20][21][22] places a strong limitation to realize this goal. A rather new approach was recently proposed to control the ion properties via the Electrical Asymmetry Effect (EAE) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]: By applying a voltage waveform, that contains a fundamental frequency and (at least) one even harmonic, the symmetry of the discharge can be changed by tuning the phase angle between the driving harmonics. This in turn allows controling basic properties of the plasma, such as the dc self-bias, the position of the plasma bulk, and the ion energy at both electrodes while maintaining an almost constant ion flux.…”

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

“…Donko et al 17 have shown that the PSR is self-excited in geometrically symmetric, electrically asymmetric discharges operated at a fundamental frequency (13.56 MHz) and its second harmonic (27.12 MHz). The control of the discharge asymmetry via the EAE, i.e., by tuning the relative phase between the applied harmonics, translates into a convenient control of the DC self-bias, mean sheath voltages, and mean ion energy at the electrodes independently of the ion flux.…”

“…Another way of inducing an asymmetry is via the Electrical Asymmetry Effect (EAE), [17][18][19][20][21][22][23][24][25][26] i.e., by using a driving voltage waveform with unequal absolute values of the global maximum and minimum. Donko et al 17 have shown that the PSR is self-excited in geometrically symmetric, electrically asymmetric discharges operated at a fundamental frequency (13.56 MHz) and its second harmonic (27.12 MHz).…”