Nonlinear dynamics of dual frequency capacitive discharges: a global model matched to an experiment

Abstract

The dynamics of dual frequency capacitively coupled plasmas (2f-CCPs) is investigated using an approach that integrates theoretical insight and experimental data. Basis of the analysis is a recently published model which casts the high-frequency behavior of asymmetric 2f-CCPs in terms of a nonlinear second-order differential equation, or equivalently, a lumped element equivalent circuit (Mussenbrock et al 2006 Phys. Plasmas 13 083501). The model comprises a nonlinear capacitor (the electrode boundary sheath), a lossy inductance (electron inertia and Ohmic losses in the bulk), a blocking capacitor and two ideal voltage sources in series (the 2f excitation). In contrast to Mussenbrock et al (2006 Phys. Plasmas 13 083501) which conducted a general parameter study, the current work bases the choice of its model parameters on the data obtained by an actual 2f-CCP experiment conducted by Semmler et al (2007 Plasma Sources Sci. Technol. 16 839, and 2008 private communication). A good quantitative correspondence is obtained. The analysis shows that the system is governed by a nonlinear interaction of the applied RF with the inner dynamics of the discharge, particularly with the collective oscillation mode known as the plasma series resonance (PSR). With respect to the power dissipation, two distinct paths can be identified which contribute in approximately equal parts. The first path is non-resonant and corresponds to the traditional picture of 2f-CCPs; the second path is resonant and identical with the mechanism of nonlinear electron resonance heating (NERH) proposed by Phys. Plasmas 13 083501, 2006. The results change the understanding of 2f-CCPs considerably.

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

“…Of course, the amplitude of these PSR oscillations is very small compared to the total current amplitude due to the relatively small asymmetry. This is different from the "classical" scenario of the PSR self-excited in geometrically asymmetric discharges [65,[86][87][88][89][90][91], where usually ε 1 and NERH (Nonlinear Electron Resonance Heating) gives a large contribution in the electron heating [65,87,92]. Due to the symmetry parameter ε shown in Fig.…”

“…The self-excitation of the plasma series resonance (PSR) is an important issue in asymmetric capacitive discharges operated at low pressures, because it enhances the electron heating [65,67,[73][74][75][76][86][87][88][89][90][91][92]. Due to Eq.…”

Making a geometrically asymmetric capacitive rf discharge electrically symmetric

“…In spherical geometries, this is an inherent mechanism of the discharge to reduce its asymmetry, which has important consequences for, e.g., electron heating due to a reduction of nonlinear electron resonance heating. [15][16][17][18] In conclusion, we have found a method to reduce the asymmetry of geometrically asymmetric discharges electrically via the electrical asymmetry effect. By tuning the phase shift between two consecutive driving harmonics, the absolute value of the dc self-bias voltage can be substantially reduced and the mean ion energies at both electrodes can be made similar.…”

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

“…This might explain the discrepancy between the theoretical and the measured current waveforms observed in previous studies. 4,14,23 Different from these investigations of geometrically asymmetric discharges, 043512-3 Figure 4 shows that the PSR is self-excited at the times of the collapse of both the powered and the grounded electrode sheath.…”