Investigation of Ion and Electron Kinetic Phenomena in Capacitively Coupled Radio-Frequency Plasma Sheaths: A Simulation Study

Stochastic heating is an important phenomenon in low-pressure radio-frequency (RF) capacitive discharges. Recent theoretical work on this problem using several different approaches has produced results that are broadly in agreement in-so-far as scaling with the discharge parameters is concerned, but there remains some disagreement in detail concerning the absolute size of the effect. Here we report a simulation study for single and dual frequency capacitive discharges with two main aims. In the case of single frequency discharge, this work investigates the dependence of stochastic heating on various discharge parameters by scaling of these parameters with the help of particle-in-cell (PIC) simulation. This research work produces a relatively extensive set of simulation data that may be used to validate theories over a wide range of parameters. The analytical models are satisfactory for intermediate current density amplitude ˜ J0 (or control parameter H) and in agreement with PIC results. However in extreme cases new physical effects appear (like field reversal, electron trapping, reflection of ions etc.) and the simulation results deviate from existing analytical models. The dependence of stochastic heating on applied frequency is also investigated. The second aim is to study any evidence of wave emission with a frequency near the electron plasma frequency at the sheath edge. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expansion phase of the sheath. Trapping of electronsnear to this field reversal region is observed. Calculation shows that these waves are electron plasma waves. In the dual frequency case, this research has produced a relatively extensive set of simulation data and shown that the dual-frequency analytical model is in agreement for wide range of parameters. However, in extreme cases, new phenomena like the presence of strong field reversal and the reflection of ions appear and the simulation results deviate from the analytical model. A further aim is the investigation of the presence of strong wave phenomena during the expanding and collapsing phase of the low frequency sheath. The characteristics of waves in the dual-frequency case is entirely different from the single-frequency case. The presence of electron trapping near to the field reversal regions is also observed at multiple times of an RF period. The frequency of these waves are calculated and to be of the order of the plasma frequency

Flux and energy asymmetry in a low pressure capacitively coupled plasma discharge excited by sawtooth-like waveform -- a harmonic study

Control over plasma asymmetry in a low-pressure capacitively coupled plasma (CCP) discharges is vital for many plasma processing applications. In this article, using the particle-in-cell simulation technique, we investigated the asymmetry generation by a temporally asymmetric waveform (sawtooth-like) in collisionless CCP discharge. A study by varying the number of harmonics (N) contained in the sawtooth waveform is performed. The simulation resultspredict a non-linear increase in the plasma density and ion flux with N i.e., it first decreases, reaching a minimum value for a critical value of N, and then increases almost linearly with afurther rise in N. The ionization asymmetry increases with N, and higher harmonics on the instantaneous sheath position are observed for higher values of N. These higher harmonics generate multiple ionization beams that are generated near the expanding sheath edge and are responsible for an enhanced plasma density for higher values of N. The ion energy distribution function (IEDF) depicts a bi-modal shape for different values of N. A strong DC self-bias is observed on the powered electrode, and its value with respect to the plasma potential decreases with an increase in N due to which corresponding ion energy on the powered electrode decreases. The simulation results conclude that by changing the number of harmonics of a sawtooth-like in collisionless CCP discharges, the ion flux asymmetry is not generated, whereas sheath symmetry could be significantly affected and therefore a systematic variation in the ion energy asymmetry is observed. Due to an increase in the higher harmonic contents in the sawtooth waveform with N, a transition from broad bi-modal to narrow-shaped IEDFs is found

A systematic investigation of electric field nonlinearity and field reversal in low pressure capacitive discharges driven by sawtooth-like waveforms

Understanding electron and ion heating phenomenon in capacitively coupled radio-frequency plasma discharges is vital for many plasma processing applications. In this article, using particle-in-cell simulation technique we investigate the collisionless argon discharge excited by temporally asymmetric sawtooth-like waveform. In particular, a systematic study of the electric field nonlinearity and field reversal phenomenon by varying the number of harmonics and its effect on electron and ion heating is performed. The simulation results predict higher harmonics generation and multiple field reversal regions formation with an increasing number of harmonics along with the local charge separation and significant displacement current outside sheath region. The field reversal strength is greater during the expanding phase of the sheath edge in comparison to its collapsing phase causing significant ion cooling. The observed behavior is associated with the electron fluid compression/rarefaction and electron inertia during expanding and collapsing phase respectively

Simulation study of wave phenomena from the sheath region in single frequency capacitively coupled plasma discharges; field reversals and ion reflection

Capacitively coupled radio-frequency discharges have great significance for indus- trial applications. Collisionless electron heating in such discharges is important, and sometimes is the dominant mechanism. This heating is usually understood to orig- inate in a stochastic interaction between electrons and the electric fields. However, other mechanisms may also be important. There is evidence of wave emission with a frequency near the electron plasma frequency, i.e. ωpe , from the sheath region in collisionless capacitive radio-frequency (RF) discharges. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped in a few centimeters during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expanding phase of the sheath. Trapping of electrons near to this field reversal region is observed. The amplitude of the wave increases with increasing RF current density amplitude J˜0 until some maximum is reached, beyond which the wave diminishes and a new regime appears. In this new regime, the density of the bulk plasma suddenly increases because of ion reflection which occurs due to presence of strong field reversal near sheath region. Our calcu- lation shows that these waves are electron plasma waves. These phenomena occur under extreme conditions (i.e. higher J˜0 than in typical experiments) for sinusoidal current waveforms, but similar effects may occur with non-sinusoidal pulsed wave- forms for conditions of experimental interest, because the rate of change of current is a relevant parameter. The effect of electron elastic collisions on plasma waves is also investigated

Discharge characteristics of a low-pressure geometrically asymmetric cylindrical capacitively coupled plasma with an axisymmetric magnetic field

We investigate the discharge characteristics of a low-pressure geometrically asymmetric cylindrical capacitively coupled plasma discharge with an axisymmetric magnetic field generating an EXB drift in the azimuthal direction. Vital discharge parameters, including electron density, electron temperature, DC self-bias, and Electron Energy distribution function (EEDF), are studied experimentally for varying magnetic field strength (B). A transition in the discharge asymmetry is observed along with a range of magnetic fields where the discharge is highly efficient with lower electron temperature. Outside this range of magnetic field, the plasma density drops, followed by an increase in the electron temperature. The observed behavior is attributed to the transition from geometrical asymmetry to magnetic field-associated symmetry due to reduced radial losses and plasma confinement in the peripheral region. In this region, the DC self-bias increases almost linearly from a large negative value to nearly zero, i.e., the discharge becomes symmetric. The EEDF undergoes a transition from bi-Maxwellian for unmagnetized to Maxwellian at intermediate B and finally becomes a weakly bi-Maxwellian at higher values of B. The above transitions present a novel way to independently control the ion energy and ion flux in a cylindrical CCP system using an axisymmetric magnetic field with an enhanced plasma density and lower electron temperature operation that is beneficial for plasma processing applications

Ion energy distribution function in very high frequency capacitive discharges excited by saw-tooth waveform

Tailoring the ion energy distribution function (IEDF) is vital for advanced plasma processing applications. Capacitively coupled plasma (CCP) discharges excited using a non-sinusoidal waveform have shown its capability to control IEDF through the generation of plasma asymmetry and DC self-bias. In this paper, we performed a particle-in-cell simulation study to investigate the IEDF in a symmetric capacitive discharge excited by a saw-tooth-like current waveform at a very high frequency. At a constant driving frequency of 27.12 MHz, the simulation results predict that the ion energy asymmetry in the discharge scales with the discharge current amplitude. A transition from a single narrow ion energy peak to a bi-modal type IEDF is observed with an increase in the current density amplitude. Further studies at a constant current density and varying the fundamental excitation frequency show that the ion energy asymmetry enhances with a reduction in the driving frequency. Increase in the plasma asymmetry and significant DC self-bias at a lower driving frequency is observed to be one of the principal factors responsible for the observed asymmetry in the ion energy peaks. An investigation of DC self-bias and plasma potential confirms that the powered electrode energy peak corresponds to the DC self-bias with respect to the plasma potential, and the grounded electrode peak corresponds to the plasma potential. These results suggest that although lower driving frequency is beneficial for generating the discharge asymmetry and large DC self-bias, a narrow low energy IEDF is plausible in very high frequency driven CCP systems

The effect of intermediate frequency on sheath dynamics in collisionless current driven triple frequency capacitive plasmas

The CCP (Capacitively Coupled Plasma) discharge featuring operation in current driven triple frequency configuration has analytically been investigated and the outcome is verified by utilising 1D3V particle-in-cell (PIC) simulation code. In this analysis the role of middle frequency component of the applied signal has precisely been explored. The discharge parameters are seen to be sensitive to the ratio of the chosen middle frequency to lower and higher frequencies for fixed amplitudes of the three frequency components. On the basis of analysis and PIC simulation results, the middle frequency component is demonstrated to act as additional control over sheath potential, electron sheath heating and ion energy distribution function (iedf) of the plasma discharge. For the electron sheath heating, effect of the middle frequency is seen to be pronounced as it approaches to the lower frequency component. On the other hand for the iedf, the control is more sensitive as the middle frequency approaches towards higher frequency. The PIC estimate for the electron sheath heating is found to be in reasonably good agreement with the analytical prediction based on Kaganovich formulation