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.

Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We therefore claim that the results of these simulations represent strong benchmarks, that can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models.We discuss an example of this kind in an appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena. * Electronic address: miles.turner@dcu.ie 2

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.

Technological processing plasmas are frequently operated at relatively low gas pressure (<10Pa). A characteristic feature of this regime is that collisions of the electrons with the atoms or molecules of the neutral background are relatively rare, and the so-called collisional or Ohmic heating ceases to be an effective mechanism of energy deposition into the plasma. Experiments indicate that at low pressure an alternative mechanism of electron heating exists which can sustain the plasma. Despite 30years of intense research, the exact nature of this “anomalous” heating mechanism is still under discussion. The two standard models are known as “stochastic heating” and “pressure heating,” respectively. This work proposes a third explanation of anomalous electron heating and suggests that, in the last analysis, all three mechanisms may contribute to the observed effect.