Brian Heil

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)

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.

Electric field reversals in the sheath region of capacitively coupled radio frequency discharges at different pressures

Electric field reversals in single and dual-frequency capacitively coupled radio frequency discharges are investigated in the collisionless (1Pa) and the collisonal (65Pa) regimes. Phase resolved optical emission spectroscopy is used to measure the excitation of the neutral background gas caused by the field reversal during sheath collapse. The collisionless regime is investigated experimentally in asymmetric neon and hydrogen single frequency discharges operated at 13.56MHz in a GEC reference cell. The collisional regime is investigated experimentally in a symmetric industrial dual-frequency discharge operated at 1.937 and 27.118MHz. The resulting spatio-temporal excitation profiles are compared with the results of a fluid sheath model in the single frequency case and a particle-in-cell/Monte Carlo simulation in the dual-frequency case. The results show that field reversals occur in both regimes. An analytical model gives an insight into the mechanisms causing the reversal of the electric field. In the dual-frequency case a qualitative comparison between the electric fields resulting from the PIC simulation and from the analytical model is performed. The field reversal seems to be caused by different mechanisms in the respective regimes. In the collisionless case it is caused by electron inertia, whereas in the collisional regime it is caused by a combination of the low mobility of electrons due to collisions and electron inertia. Finally, the field reversal during the sheath collapse seems to be a general source for energy gain of electrons in both single and dual-frequency discharges. (Some figures in this article are in colour only in the electronic version)

The Electrical Asymmetry Efiect - A novel and simple method for separate control of ion energy and ∞ux in capacitively coupled RF discharges

If a temporally symmetric voltage waveform is applied to a capacitively coupled radio frequency (CCRF) discharge, that contains one or more even harmonics of the fundamental frequency, the sheaths in front of the two electrodes will necessarily be asymmetric even in a geometrically symmetric discharge. Optimally this is achieved with a dual-frequency discharge driven at a phase locked fundamental frequency and its second harmonic, e.g. 13.56 MHz and 27.12 MHz. An analytical model, a hybrid ∞uid/Monte-Carlo kinetic model as well as a Particle in Cell (PIC) simulation show that this Electrical Asymmetry Efiect (EAE) leads to the generation of a DC self bias as a function of the phase between the applied voltage harmonics in geometrically symmetric as well as asymmetric discharges. The DC self bias depends almost linearly on the phase angle and the role of the electrodes (powered and grounded) can be reversed. At low pressures the EAE is self-amplifying due to the conservation of ion ∞ux in the sheaths. By tuning the phase, precise and convenient control of the ion energy at the electrodes can be achieved, while the ion ∞ux remains constant. The maximum ion energy can typically be changed by a factor of about three at both electrodes. At the same time the ion ∞ux is constant within §5%.

Numerical Modeling of Electron Beams Accelerated by the Radio Frequency Boundary Sheath

The stochastic heating of electrons by the radio frequency boundary sheath in capacitively coupled plasmas is not completely understood or at least agreed upon by researchers. To aid in understanding this phenomena, a conceptually simple simulation of electron heating is presented. A fluid model is used to calculate the electric fields in the discharge, and a Monte Carlo simulation is used to calculate electron distribution functions. The plots of the density of energetic electrons are presented in this paper. They show electron beams that have been accelerated by the sheath.

Kinetic two-dimensional modeling of inductively coupled plasmas based on a hybrid kinetic approach

In this paper, we present a two-dimensional (2-D) kinetic model for low-pressure inductively coupled discharges. The kinetic treatment of the plasma electrons is based on a hybrid kinetic scheme in which the range of electron energies is divided into two subdomains. In the low energy range the electron distribution function is determined from the traditional nonlocal approximation. In the high energy part the complete spatially dependent Boltzmann equation is solved. The scheme provides computational efficiency and enables inclusion of electron-electron collisions which are important in low-pressure high-density plasmas. The self-consistent scheme is complemented by a 2-D fluid model for the ions and the solution of the complex wave equation for the RF electric field. Results of this model are compared to experimental results. Good agreement in terms of plasma density and potential profiles is observed. In particular, the model is capable of reproducing the transition from on-axis to off-axis peaked density profiles as observed in experiments which underlines the significant improvements compared to models purely based on the traditional nonlocal approximation.

Electron Beams in Capacitively Coupled Radio-Frequency Discharges

The generation of electron beams by the expanding sheath is observed experimentally in asymmetric single-frequency capacitively coupled radio-frequency discharges using phase-resolved optical-emission spectroscopy. Depending on the discharge geometry and conditions, such beams can propagate through the entire discharge and are reflected at the opposing plasma boundary. They are closely related to stochastic heating, and their generation is enhanced by the plasma-series-resonance effect. Confinement of these energetic electrons can lead to an effective heating of the plasma.

A hybrid, one-dimensional model of capacitively coupled radio-frequency discharges

A one-dimensional, numerical model was developed to aid in the investigation of electron dynamics in the plasma boundary sheath of RF discharges. It incorporates several different modules. A fluid based plasma boundary sheath model and an accompanying equivalent circuit model are first used to calculate the time-dependent electric field due to displacement current and charged particle densities in the sheath. The electric fields calculated in this model are then combined with the Ohmic electric field or the field due to conduction current and joined to a simplified model of the plasma bulk. This combination is then used in a Monte Carlo simulation to calculate the electron energy distribution function. This model includes stochastic and Ohmic heating of electrons. The model reproduces experimentally measured electron energy probability functions over a broad range of pressures.

The gain and loss of energy by electrons in the RF-CCP sheath

The exact mechanism for the heating of electrons in the sheath of radio frequency capacitively coupled plasma (RF-CCP) discharges is poorly understood. A hybrid one-dimensional model of a RF-CCP discharge is used to study this problem by tracking electron trajectories and electron energy change in the RF-CCP sheath. This study shows that the Ohmic electric field, the field due to conduction current, can have an effect on electron heating in the plasma sheath. Both the ambipolar and the Ohmic electric field can repel low energy electrons and reduce their interaction with the changing electric field in the sheath region. A comparison is made between the more realistic Brinkmann fluid sheath model and a hard wall approximation. For energetic electrons, the hard wall approximation accurately models electron heating. However, the hard wall approximation does not accurately model the heating of lower energy electrons or allow for electron losses to the electrode. A comparison is also made between the electron energy probability function calculated using a Monte Carlo simulation with and without the effects of the sheath.