Z. Donkó

PIC simulations of the separate control of ion flux and energy in CCRF discharges via the electrical asymmetry effect

Recently a novel approach for achieving separate control of ion flux and energy in capacitively coupled radio frequency (CCRF) discharges based on the electrical asymmetry effect (EAE) was proposed (Heil et al 2008 J. Phys. D: Appl. Phys. 41 165202). If the applied, temporally symmetric voltage waveform contains an even harmonic of the fundamental frequency, the sheaths in front of the two electrodes are necessarily asymmetric. A dc self-bias develops and is a function of the phase angle between the driving voltages. By tuning the phase, precise and convenient control of the ion energy can be achieved while the ion flux stays constant. This effect works even in geometrically symmetric discharges and the role of the two electrodes can be reversed electrically. In this work the EAE is verified using a particle in cell simulation of a geometrically symmetric dual-frequency CCRF discharge operated at 13.56 and 27.12MHz. The self-bias is a nearly linear function of the phase angle. It is shown explicitly that the ion flux stays constant within ±5%, while the self-bias reaches values of up to 80% of the applied voltage amplitude and the maximum ion energy is changed by a factor of 3 for a set of low pressure discharge conditions investigated. The EAE is investigated at different pressures and electrode gaps. As geometrically symmetric discharges can be made electrically asymmetric via the EAE, the plasma series resonance effect is observed for the first time in simulations of a geometrically symmetric discharge. (Some figures in this article are in colour only in the electronic version)

Simulation benchmarks for low-pressure plasmas: Capacitive discharges

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, which 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 the 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.

Particle simulation methods for studies of low-pressure plasma sources

This paper illustrates the application of particle simulation methods for the description of low-pressure discharges: Townsend discharges, cathode fall dominated dc glows and capacitively coupled radiofrequency discharges. The spatially and/or temporally varying electric field and the presence of boundaries (e.g. electrodes) in these plasma sources induce a non-hydrodynamic (or non-equilibrium) transport of some types of charged species, particularly of electrons. Particle-based methods provide, even under non-equilibrium conditions, a correct method of mathematical description of the particle transport and the determination of the distribution functions, which are crucial quantities in discharge modeling.

The electrical asymmetry effect in multi-frequency capacitively coupled radio frequency discharges

The electrical asymmetry effect (EAE) in geometrically symmetric capacitively coupled radio frequency discharges operated at multiple consecutive harmonics is investigated by a particle-in-cell (PIC) simulation and an analytical model. The model is based on the original EAE model, which is extended by taking into account the floating potentials, the voltage drop across the plasma bulk, and the symmetry parameter resulting from the PIC simulation. Compared with electrically asymmetric dual-frequency discharges we find that (i) a significantly stronger dc self-bias can be generated electrically and that (ii) the mean ion energies at the electrodes can be controlled separately from the ion flux over a broader range by tuning the phase shifts between the individual voltage harmonics. A recipe for the optimization of the applied voltage waveform to generate the strongest possible dc self-bias electrically and to obtain maximum control of the ion energy via the EAE is presented.

The electrical asymmetry effect in capacitively coupled radio-frequency discharges

We present an analytical model to describe capacitively coupled radio-frequency (CCRF) discharges and the electrical asymmetry effect (EAE) based on the non-linearity of the boundary sheaths. The model describes various discharge types, e.g. single and multi-frequency as well as geometrically symmetric and asymmetric discharges. It yields simple analytical expressions for important plasma parameters such as the dc self-bias, the uncompensated charge in both sheaths, the discharge current and the power dissipated to electrons. Based on the model results the EAE is understood. This effect allows control of the symmetry of CCRF discharges driven by multiple consecutive harmonics of a fundamental frequency electrically by tuning the individual phase shifts between the driving frequencies. This novel class of capacitive radio-frequency (RF) discharges has various advantages: (i) A variable dc self-bias can be generated as a function of the phase shifts between the driving frequencies. In this way, the symmetry of the sheaths in geometrically symmetric discharges can be broken and controlled for the first time. (ii) Almost ideal separate control of ion energy and flux at the electrodes can be realized in contrast to classical dual-frequency discharges driven by two substantially different frequencies. (iii) Non-linear self-excited plasma series resonance oscillations of the RF current can be switched on and off electrically even in geometrically symmetric discharges. Here, the basics of the EAE are introduced and its main applications are discussed based on experimental, simulation, and modeling results.

On the reliability of low-pressure dc glow discharge modelling

Modelling approaches used for the description of the cathode region of dc glow discharges are reviewed, with the focus on hybrid models which combine the fluid description of positive ions and bulk electrons with the kinetic simulation of fast electrons. The reliability of the calculated discharge characteristics is analysed by testing the different assumptions of the models and the sensitivity of the calculated characteristics on the input data. The applicability of the particle-in-cell technique (complemented with Monte Carlo simulation of collision processes) for the simulation of dc glow discharges is also discussed.

Different modes of electron heating in dual-frequency capacitively coupled radio frequency discharges

A systematic study of different modes of electron heating in dual-frequency capacitively coupled radio frequency (CCRF) discharges is performed using a particle-in-cell simulation. Spatio-temporal distributions of the total excitation/ionization rates under variation of gas pressure, applied frequencies and gas species are discussed. Some results are compared qualitatively with an experiment (phase resolved optical emission spectroscopy) operated under conditions similar to a parameter set used in the simulation. Different modes of electron heating are identified and compared with α- and γ-mode operation of single-frequency CCRF discharges. In this context the frequency coupling and its relation to the ion density profile in the sheath are discussed and quantified. In light gases the ion density in the sheath is time modulated. This temporal modulation is well described by an analytical model and is found to affect the excitation dynamics via the frequency coupling. It is shown that the frequency coupling strongly affects the generation of beams of highly energetic electrons by the expanding sheath and field reversals caused by the collapsing sheath. The role of secondary electrons at intermediate and high pressures is clarified and the transition from α- to γ-mode operation is discussed. Depending on the gas and the corresponding cross sections for excitation/ionization the excitation does not generally probe the ionization as is usually assumed.

Self-excited nonlinear plasma series resonance oscillations in geometrically symmetric capacitively coupled radio frequency discharges

At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies.

Phase resolved optical emission spectroscopy: a non-intrusive diagnostic to study electron dynamics in capacitive radio frequency discharges

Various types of capacitively coupled radio frequency (CCRF) discharges are frequently used for different applications ranging from chip and solar cell manufacturing to the creation of biocompatible surfaces. In many of these discharges electron heating and electron dynamics are not fully understood. A powerful diagnostic to study electron dynamics in CCRF discharges is phase resolved optical emission spectroscopy (PROES). It is non-intrusive and provides access to the dynamics of highly energetic electrons, which sustain the discharge via ionization, with high spatial and temporal resolution within the RF period. Based on a time dependent model of the excitation dynamics of specifically chosen rare gas levels PROES provides access to plasma parameters such as the electron temperature, electron density and electron energy distribution function (EEDF). In this work the method of PROES is reviewed and some examples of its application are discussed. First, the generation of highly energetic electron beams by the expanding sheath in geometrically symmetric as well as asymmetric discharges and their effect on the EEDF are investigated. Second, the physical nature of the frequency coupling in dual frequency discharges operated at substantially different frequencies is discussed. Third, the generation of electric field reversals during sheath collapse in single and dual frequency discharges is analysed. Then excitation dynamics in an electrically asymmetric novel type of dual frequency discharge is studied. Finally, limitations of PROES are discussed.

Optimization of the electrical asymmetry effect in dual-frequency capacitively coupled radio frequency discharges: Experiment, simulation, and model

An electrical asymmetry in capacitive rf discharges with a symmetrical electrode configuration can be induced by driving the discharge with a fundamental frequency and its second harmonic. For equal amplitudes of the applied voltage waveforms, it has been demonstrated by modeling, simulation, and experiments that this electrical asymmetry effect (EAE) leads to the generation of a variable dc self-bias that depends almost linearly on the phase angle between the driving voltage signals. Here, the dependence of the dc self-bias generated by the EAE on the choice of the voltage amplitudes, i.e., the ratio A of high to low frequency amplitude, is investigated experimentally as well as by using an analytical model and a particle-in-cell simulation. It is found that (i) the strongest electrical asymmetry is induced for A<1 at pressures ranging from 6 to 100 Pa and that (ii) around this optimum voltage ratio the dc self-bias normalized to the sum of both voltage amplitudes is fairly insensitive to changes of A. T...