A fundamental problem in technological plasmas has been how to control the ion energy and the ion flux (plasma density) independently of one another. A simple, but previously overlooked asymmetry effect is reported that should allow a high degree of control of the ion energy. The idea is that when a temporally symmetric, multi-frequency voltage waveform containing one or more even harmonics is applied to a discharge, even a geometrically symmetric one, the two sheaths are necessarily asymmetric. To balance the charged particle fluxes, a dc self-bias develops. Optimally, this is achieved with a dual frequency discharge that uses the phase locked fundamental and its second harmonic. The resulting dc self-bias and hence the ion energy are a nearly linear function of the phase angle between the two applied RF voltages. This works even for geometrically symmetric discharges, and the roles of the two electrodes can be reversed using the phase. This means that the technique can be used to increase or decrease the ion energy striking a substrate while leaving the applied RF voltage and frequency and thereby the discharge parameters effectively unchanged.

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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.

In low-pressure capacitive radio frequency discharges, two mechanisms of electron heating are dominant: (i) Ohmic heating due to collisions of electrons with neutrals of the background gas and (ii) stochastic heating due to momentum transfer from the oscillating boundary sheath. In this work we show by means of a nonlinear global model that the self-excitation of the plasma series resonance which arises in asymmetric capacitive discharges due to nonlinear interaction of plasma bulk and sheath significantly affects both Ohmic heating and stochastic heating. We observe that the series resonance effect increases the dissipation by factors of 2-5. We conclude that the nonlinear plasma dynamics should be taken into account in order to describe quantitatively correct electron heating in asymmetric capacitive radio frequency discharges.