Self-excitation of the plasma series resonance in radio-frequency discharges: An analytical description

Self-excited plasma series resonances (PSR) are observed in capacitve discharges as high-frequency oscillations superimposed on the normal rf current. This high-frequency contribution to the current is generated by a series resonance between the capacitive sheath and the inductive and ohmic bulk of the plasma. The nonlinearity of the sheath leads to a complex dynamic. The effect is applied, e.g., as a diagnostic technique in commercial etch reactors where analysis is performed by a numerical model. Here a simple analytical investigation is introduced. In order to solve the nonlinear equations analytically, a series of approximation is necessary. Nevertheless, the basic physics is conserved and excellent agreement with numerical solutions is found. The model provides explicit and simple formula for the current waveform and the spectral range of the oscillations. In particular, the dependence on the discharge parameters is shown. Further, the model gives insight into an additional dissipation channel opened by the high-frequency oscillations. With decreasing pressure, the ohmic resistance of the bulk decreases as well, while the amplitude of the PSR oscillations grows. This results in substantially higher power dissipation that exceeds the contribution of classical stochastic heating.