Session ET2: Capacitively Coupled Plasmas I

Gaining greater control and understanding of processing plasmas through Tailored Voltage Waveforms

The use of multiple harmonics of an RF frequency to generate the exciting voltage waveform for a capacitively coupled plasma has in recent years become a rich and diverse field of research. Initially proposed, observed, and named as the Electrical Asymmetry Effect by the Bochum group, the use of such Tailored Voltage Waveforms to sustain a plasma has gone beyond asymmetrizing the ion bombardment energy and flux to the electrodes. It is now clear that one can gain control over such plasma features as localization of ionization events and composition of species flux by using more counterintuitive waveforms. In this talk, progress in this field in three areas is discussed: (1) identification of new TVW's that give rise to more complex asymmetries (namely ``slope-asymmetric'' waveforms), (2) identifying applications of TVW's in plasma processing and metrology, and finally, (3) solving the technical challenges of using the technique in an industrially feasible way. The talk will focus on work done at the LPICM and LPP CNRS laboratories at the Ecole Polytechnique, but in collaboration with a number of partners from other institutes.   

Control of electron heating and ion energy distributions in capacitive plasmas by voltage waveform tailoring based on a novel power supply and impedance matching

We present a novel RF power supply and impedance matching to drive technological plasmas with customized voltage waveforms. By adjusting the individual phases and amplitudes of multiple consecutive harmonics any voltage waveform can be realized as a customized finite Fourier series. This RF supply system is easily adaptable to any technological plasma for industrial applications and allows the commercial utilization of process optimization based on voltage waveform tailoring for the first time. Here, this system is tested on a capacitive discharge based on three consecutive harmonics of 13.56 MHz in argon. The effect of changing the shape of the driving voltage waveform on the electron heating and sheath dynamics is investigated by Phase Resolved Optical Emission Spectroscopy (PROES) for different electrode gaps, pressures, and applied voltages. At low pressure the results are correlated with ion energy distribution functions measured at both electrodes. Tuning the phases between the applied harmonics results in an electrical control of the DC self-bias and the mean ion energy. A comparison with the reference case of a dual-frequency discharge reveals that using more than two consecutive harmonics significantly enlarges the control range of the mean ion energy.   

Control of electron heating dynamics and DC self bias in electronegative capacitive CF$_{4}$ plasmas by voltage waveform tailoring

The effect of tailoring the driving voltage waveform on the electron heating dynamics and the generation of a DC self bias in multi-frequency capacitive CF$_{4}$ plasmas is investigated by a combination of Phase Resolved Optical Emission Spectroscopy, voltage measurements, and kinetic PIC/MCC simulations. One electrode is driven by up to 5 consecutive harmonics of different fundamental frequencies (3 MHz - 13.56 MHz). By adjusting the harmonics' phases and amplitudes different waveforms (peaks, valleys, sawtooths) are realized and found to strongly affect the spatio-temporal excitation dynamics and the electrical generation of a DC self bias via the Electrical Asymmetry Effect. For a given waveform, increasing the pressure induces an electron heating mode transition from the $\alpha $- to the Drift-Ambipolar mode due to an increase of the electronegativity. For sawtooth waveforms, the ionization induced asymmetry and the polarity of the DC self bias are found to be reversed at high pressures compared to electropositive gases. At high frequencies the simulations show that the discharge can be split into two halves of different electronegativity, which can be controlled by tailoring the driving voltage waveform.   

Student Award Finalist: Comparison of the effect of sawtooth-like voltage waveforms on discharge dynamics of Ar, H$_{2}$, and CF$_{4}$ plasmas

The use of Tailored Voltage Waveforms to excite a plasma has been previously shown to efficiently control the ion energy (through the Electrical Asymmetry Effect) by varying the ``amplitude'' asymmetry of the waveform. In this work, the effect of a ``slope'' asymmetry of the waveform is investigated by using sawtooth-like waveforms. When a discharge is excited with such a waveform, one sheath expands rapidly and contracts slowly, while the reverse occurs at the other sheath. While using such waveforms, different discharge gases are compared, namely Ar (as an electropositive gas), H2 (as a light gas), and CF4 (as an electronegative gas). For each gas, phase resolved optical emission spectroscopy measurements are compared with PIC simulations, showing excellent agreement. The dynamics of the excitation rates are very different for the different gases and are shown to be correlated with the dominant heating mechanisms. It is shown that the asymmetry obtained with sawtooth-like voltage waveforms can be very large, and can even be reversed, depending on the gas used.   

Nonlinear standing wave excitation by series resonance-enhanced harmonics in low pressure capacitive discharges

It is well known that standing waves having radially center-high rf voltage profiles exist in high frequency capacitive discharges. It is also known that in radially uniform discharges, the capacitive sheath nonlinearities excite strong nonlinear series resonance harmonics that enhance the electron power deposition. In this work, we consider the coupling of the series resonance-enhanced harmonics to the standing waves. A one-dimensional, asymmetric radial transmission line model is developed incorporating the wave and nonlinear sheath physics and a self-consistent dc potential. The resulting coupled pde equation set is solved numerically to determine the discharge voltages and currents. A 10 mT argon base case is chosen with plasma density $2\times10^{16}$ m$^{-3}$, gap width 2 cm and conducting electrode radius 15 cm, driven by a high frequency 500 V source with source resistance 0.5 ohms. We find that nearby resonances lead to an enhanced ratio of 4.5 of the electron power per unit area on axis, compared to the average. The radial dependence of electron power with frequency shows significant variations, with the central enhancement and sharpness of the spatial resonances depending in a complicated way on the harmonic structure.   

Non-Linear Electron Resonance Heating in CCRF Discharges: A Kinetic Interpretation

In this work, the physical origin of non-linear electron resonance heating in capacitively coupled radio frequency discharges is investigated using Particle-in-Cell/Monte Carlo Collisions simulations. A detailed kinetic description of the electron dynamics is used to explain the mechanism of the excitation of harmonics in the rf current. It is shown that, especially at low pressures, highly energetic electrons are accelerated by the modulated plasma sheath and leave behind a positive space charge close to the sheath edge. Consequently, cold bulk electrons are attracted back towards this electron depleted zone. After a short time interval (defined by the local plasma frequency), bulk electrons reach the expanding sheath phase, are reflected, and gain energy forming a new energetic electron beam. Since such electron beams represent the major part of the conduction current, this mechanism leads to harmonics in the rf current. Finally, the question ``In which way current continuity is ensured at all the times?'' is answered.   

Electron Heating Mode Transitions in Nitrogen (13.56 and 40.68) MHz RF-CCPs

Capacitively coupled radio frequency plasmas (RF-CCPs) are commonly used in plasma material processing. Parametrical structure of the plasma determines the demands of processing applications. For example; high density plasmas in gamma mode are mostly preferred for etching applications while stabile plasmas in gamma mode are usually used in sputtering applications. For this reason, characterization of the plasma is very essential before surface modification of the materials. In this work, analysis of electron heating mode transition in high frequency (40.68 MHz) RF-CCP was deeply investigated. The plasma was generated in a home-made (500 x 400 mm$^{2})$ stainless steel cylindrical reactor in which two identical (200 mm in diameter) electrodes were placed with 40 mm interval. In addition, L-type automatic matching network system was connected to the 40.68 MHz RF generator to get high accuracy. Moreover, the pure (99.995 {\%}) nitrogen was used as an activation gas on account of having an appreciable impression in plasma processing applications. Furthermore, diagnostic measurements of the plasma were done by using the Impedans Langmuir single and double probe systems. It was found that two transition points; $\alpha $-$\gamma $ (pressure dependent) and $\gamma $-$\alpha $ (RF power dependent) were observed in both medium and high RF-CCPs. As a result, the $\alpha $-$\gamma $ pressure transition increased, whereas the $\gamma $-$\alpha $ power transition remained constant by changing the RF frequency sources.   

Electron Heating in Capacitively Coupled RF Discharges Investigated with the Smooth Step Model

Electron heating in radio-frequency driven capacitively coupled plasmas is studied on the basis of the recently proposed \textit{Smooth Step Model} [R.P.~Brinkmann, \textit{Plasma~Sources Sci.~Technol.} (2015)]. This algebraic model provides an expression for the electric field in a RF modulated plasma sheath transition which yields i) the space charge field in the sheath, ii) the generalized Ohmic and ambipolar field in the plasma, and iii) a smooth interpolation for the rapid transition in between. It was derived via an expansion of an electron fluid model in terms of two smallness parameters, the ratios $\epsilon =\lambda_{\rm D}/l$ of the Debye length $\lambda_{\rm D}$ to the minimum gradient length $l$ and $\eta=\omega_{\rm RF}/\omega_{\rm pe}$ of the RF frequency $\omega_{\rm RF}$ to the electron plasma frequency $\omega_{\rm pe}$. The explicit field formula provided by the Smooth Step Model enables semi-analytic expressions for the phased-resolved and the phase-averaged dissipated power. Comparison with other models of electron heating is made.