Power absorption in electrically asymmetric dual frequency capacitive radio frequency discharges

Abstract

The symmetry of capacitive radio frequency discharges can be controlled via the electrical asymmetry effect by driving one electrode with a fundamental frequency and its second harmonic. In such electrically asymmetric discharges, the mean ion energies at both electrodes are controlled separately from the ion flux by tuning the phase angle between the harmonics at fixed voltage amplitudes. Here, the question why the ion flux is nearly independent of is answered by investigating the power absorbed by the electrons P e as a function of and time experimentally, by a particle in cell simulation, and an analytical model. The dynamics of P e is understood by the model and is found to be strongly affected by the choice of. However, on time average, P e is nearly constant, independently of. Thus, the ion flux remains approximately constant. In addition, it is shown that the absolute value of the individual voltages across the powered and grounded electrode sheath vary linearly with the dc self-bias. However, their sum remains constant. This yields, in combination with the constancy of the ion flux, a constant power absorbed by the ions and, in conclusion, a total power absorption that is independent of .

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

“…At both low and high pressure, the mean electron power stays rather constant as a function of θ. A slight decrease is found around θ ≈ 45 • , which is due to the weak dependence of the normalized total charge, q t , on θ [32]. Therefore, the density of positive ions, which are mainly produced by collisions between fast electrons and the neutral background gas molecules, depends only weakly on θ.…”

“…Again, Q 0 is the normalization constant of q(t) introduced above. This directly leads to the power absorbed by the plasma electrons, P e (t) [32]. We find P e (t) = [j 2 e (t)/σ]A p L b by using the bulk length L b and conductivity σ ∝n b [1] for a given pressure.…”

“…is of particular interest, since the constancy of P e as a function of θ apparently is the reason for the bulk densities and the ion fluxes to remain almost constant, independently of θ [24,32]. Here, P e,0 = 2φ 0 ε 0 en sp A p L b /σ depends on the ratio of the positive ion density in the powered electrode sheath and the electron density in the plasma bulk.…”

“…The analytical approximation of P e , which holds under all conditions investigated here, has been studied in detail before [32].…”

“…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.…”