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

Dennis Ziegler, Thomas Mussenbrock, Ralf Peter Brinkmann

PSST Volume 17, Number 4


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 Mussenbrock et al (2006 Phys. Plasmas 13 083501, 2006 Appl. Phys. Lett. 88 151503). The results change the understanding of 2f-CCPs considerably.

[DOI]

Tags: capacitively coupled plasmas, differential equation, dual frequency, electron inertia, inductance, lumped element, nonlinear, nonlinear capacitor, nonlinear electron resonance heating (NERH), Ohmic losses, plasma series resonance (PSR), power dissipation, quivalent circuit, second-order