Julian Schulze

Control of plasma properties in capacitively coupled oxygen discharges via the electrical asymmetry effect

Using a combined experimental, numerical and analytical approach, we investigate the control of plasma properties via the electrical asymmetry effect (EAE) in a capacitively coupled oxygen discharge. In particular, we present the first experimental investigation of the EAE in electronegative discharges. A dual-frequency voltage source of 13.56 MHz and 27.12 MHz is applied to the powered electrode and the discharge symmetry is controlled by adjusting the phase angle θ between the two harmonics. It is found that the bulk position and density profiles of positive ions, negative ions, and electrons have a clear dependence on θ, while the peak densities and the electronegativity stay rather constant, largely due to the fact that the time-averaged power absorption by electrons is almost independent of θ. This indicates that the ion flux towards the powered electrode remains almost constant. Meanwhile, the dc self-bias and, consequently, the sheath widths and potential profile can be effectively tuned by varying θ. This enables a flexible control of the ion bombarding energy at the electrode. Therefore, our work proves the effectiveness of the EAE to realize separate control of ion flux and ion energy in electronegative discharges. At low pressure, the strength of resonance oscillations, which are found in the current of asymmetric discharges, can be controlled with θ.

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)

Frequency coupling in dual frequency capacitively coupled radio-frequency plasmas

An industrial, confined, dual frequency, capacitively coupled, radio-frequency plasma etch reactor (Exelan®, Lam Research) has been modified for spatially resolved optical measurements. Space and phase resolved optical emission spectroscopy yields insight into the dynamics of the discharge. A strong coupling of the two frequencies is observed in the emission profiles. Consequently, the ionization dynamics, probed through excitation, is determined by both frequencies. The control of plasma density by the high frequency is, therefore, also influenced by the low frequency. Hence, separate control of plasma density and ion energy is rather complex.

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.

Stochastic heating in asymmetric capacitively coupled RF discharges

Electron dynamics in a strongly asymmetric capacitively coupled radio-frequency (RF) discharge at low pressures is investigated by a combination of various diagnostics, analytical models and simulations. Electric fields in the sheath are measured phase and space resolved using fluorescence dip spectroscopy in krypton. The results are compared with a fluid sheath model. Experimentally obtained input parameters are used for the model. The excitation caused by beam-like highly energetic electrons is measured by phase resolved optical emission spectroscopy (PROES) and compared with the results of a hybrid Monte Carlo model based on the electric field resulting from the sheath model. The plasma itself is characterized by Langmuir probe measurements in terms of electron density, electron mean energy and electron energy distribution function (EEDF). The RF voltage and the current to the chamber wall are measured in parallel. At low pressures the plasma series resonance (PSR) effect is observed. It leads to high frequency oscillations of the current (non-sinusoidal RF current waveforms) and, consequently, to a faster sheath expansion. The measured current is compared with an analytical PSR model. Another analytical model using experimentally obtained input parameters determines the influence of beams of highly energetic electrons on the time averaged isotropic EEDF as measured by Langmuir probes. The main result is the observation of beams of highly energetic electrons during the sheath expansion phase, that are enhanced by the PSR effect. The paper shows that the nature of stochastic heating is closely related to electron beams and the PSR effect.

Electron beams in asymmetric capacitively coupled radio frequency discharges at low pressures

The generation of directed energetic electrons by the expanding sheath is observed in asymmetric capacitively coupled radio frequency discharges at low pressures (≤ 1 Pa) in different gases. The phenomenon of such electron beams is investigated by a combination of experimental diagnostics, an analytical model and simulations. At sufficiently low pressures multiple reflections of electron beams at the plasma boundaries are observed. An analytical model shows how these beams lead to an enhanced high energy tail of the electron energy distribution function. Thus, stochastic heating is closely related to electron beams.

Space and phase resolved plasma parameters in an industrial dual-frequency capacitively coupled radio-frequency discharge

The dynamics of high energetic electrons (11.7 eV) in a modified industrial confined dual-frequency capacitively coupled RF discharge (Exelan, Lam Research Inc.), operated at 1.937 MHz and 27.118 MHz, is investigated by means of phase resolved optical emission spectroscopy. Operating in a He–O2 plasma with small rare gas admixtures the emission is measured, with one-dimensional spatial resolution along the discharge axis. Both the low and high frequency RF cycle are resolved. The diagnostic is based on time dependent measurements of the population densities of specifically chosen excited rare gas states. A time dependent model, based on rate equations, describes the dynamics of the population densities of these levels. Based on this model and the comparison of the excitation of various rare gas states, with different excitation thresholds, time and space resolved electron temperature, propagation velocity and qualitative electron density as well as electron energy distribution functions are determined. This information leads to a better understanding of the dual-frequency sheath dynamics and shows, that separate control of ion energy and electron density is limited. (Some figures in this article are in colour only in the electronic version)

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.

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.