Electron heating modes and frequency coupling effects in dual-frequency capacitive CF4 plasmas

Two types of capacitive dual-frequency discharges, used in plasma processing applications to achieve the separate control of the ion flux, Гi, and the mean ion energy, , at the electrodes, operated in CF4, are investigated by particle-in-cell simulations: (i) In classical dual-frequency discharges, driven by significantly different frequencies (1.937 MHz + 27.12 MHz), and Гi are controlled by the voltage amplitudes of the low-frequency and high-frequeny components, ΦLF and ΦHF, respectively. (ii) In electrically asymmetric (EA) discharges, operated at a fundamental frequency and its second harmonic (13.56 MHz + 27.12 MHz), ΦLF and ΦHF control Гi, whereas the phase shift between the driving frequencies, θ, is varied to adjust . We focus on the effect of changing the control parameter for on the electron heating and ionization dynamics and on Гi. We find that in both types of dual-frequency strongly electronegative discharges, changing the control parameter results in a complex effect on the electron heating and ionization dynamics: in classical dual-frequency discharges, besides the frequency coupling affecting the sheath expansion heating, additional frequency coupling mechanisms influence the electron heating in the plasma bulk and at the collapsing sheath edge; in EA dual-frequency discharges the electron heating in the bulk results in asymmetric ionization dynamics for values of θ around 45°, i.e., in the case of a symmetric applie

On the self-excitation mechanisms of Plasma Series Resonance oscillations in single- and multi-frequency capacitive discharges

The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current of low pressure capacitive radio frequency (RF) discharges. This resonance leads to high frequency oscillations of the charge in the sheaths and enhances electron heating. Up to now, the phenomenon has only been observed in asymmetric discharges. There, the nonlinearity in the voltage balance, which is necessary for the self-excitation of resonance oscillations with frequencies above the applied frequencies, is caused predominantly by the quadratic contribution to the charge-voltage relation of the plasma sheaths. Using PIC/MCC simulations of single- and multi- frequency capacitive discharges and an equivalent circuit model, we demonstrate that other mechanisms such as a cubic contribution to the charge-voltage relation of the plasma sheaths and the time dependent bulk electron plasma frequency can cause the self-excitation of PSR oscillations, as well. These mechanisms have been neglected in previous models, but are important for the theoretical description of the current in symmetric or weakly asymmetric discharges

Electron heating modes and frequency coupling effects in dual-frequency capacitive CF4 plasmas

Two types of capacitive dual-frequency discharges, used in plasma processing applications to achieve the separate control of the ion flux, Гi, and the mean ion energy, , at the electrodes, operated in CF , i4 are investigated by particle-in-cell simulations: (i) In classical dual-frequency discharges, driven by significantly different frequencies (1.937 MHz + 27.12 MHz), and Гi are controlled by the voltage amplitudes of the low-frequency and high-frequeny components, ΦLF and ΦHF, respectively. (ii) In electrically asymmetric (EA) discharges, operated at a fundamental frequency and its second harmonic (13.56 MHz + 27.12 MHz), ΦLF and ΦHF control Гi, whereas the phase shift between the driving frequencies, θ, is varied to adjust . We focus on the effect of changing the control parameter for on the electron heating and ionization dynamics and on Гi. We find that in both types of dual-frequency strongly electronegative discharges, changing the control parameter results in a complex effect on the electron heating and ionization dynamics: in classical dual-frequency discharges, besides the frequency coupling affecting the sheath expansion heating, additional frequency coupling mechanisms influence the electron heating in the plasma bulk and at the collapsing sheath edge; in EA dual-frequency discharges the electron heating in the bulk results in asymmetric ionization dynamics for values of θ around 45°, i.e., in the case of a symmetric applied voltage waveform, that affects the dc self-bias generation

On the self-excitation mechanisms of plasma series resonance oscillations in single- and multi-frequency capacitive discharges

The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the cur- rent of low pressure capacitive radio frequency discharges. This resonance leads to high frequency oscillations of the charge in the sheaths and enhances electron heating. Up to now, the phenomenon has only been observed in asymmetric discharges. There, the nonlinearity in the voltage balance, which is necessary for the self-excitation of resonance oscillations with frequencies above the applied frequencies, is caused predominantly by the quadratic contribution to the charge-voltage relation of the plasma sheaths. Using Particle In Cell/Monte Carlo collision simulations of single- and multi-frequency capacitive discharges and an equivalent circuit model, we demonstrate that other mechanisms, such as a cubic contribution to the charge-voltage relation of the plasma sheaths and the time dependent bulk electron plasma frequency, can cause the self-excitation of PSR oscillations, as well. These mechanisms have been neglected in previous models, but are important for the theoretical description of the current in symmetric or weakly asymmetric discharges

Frequency-dependent electron power absorption mode transitions in capacitively coupled argon-oxygen plasmas

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulations are performed to investigate the excitation dynamics in low-pressure capacitively coupled plasmas (CCPs) in argon-oxygen mixtures. The system used for this study is a geometrically symmetric CCP reactor operated in a fixed mixture gas composition, at fixed pressure and voltage amplitude, with a wide range of driving RF frequencies (2$~$MHz$~\le f \le~15~$MHz). The measured and calculated spatio-temporal distributions of the electron impact excitation rates from the Ar ground state to the Ar$~\rm{2p_1}$ state (with a wavelength of 750.4~nm) show good qualitative agreement. The distributions show significant frequency dependence, which is generally considered to be predictive of transitions in the dominant discharge operating mode. Three frequency ranges can be distinguished, showing distinctly different excitation characteristics: (i) in the low frequency range ($f \le~3~$MHz), excitation is strong at the sheaths and weak in the bulk region; (ii) at intermediate frequencies (3.5$~$MHz$~\le f \le~5~$MHz), the excitation rate in the bulk region is enhanced and shows striation formation; (iii) above 6$~$MHz, excitation in the bulk gradually decreases with increasing frequency. Boltzmann term analysis was performed to quantify the frequency dependent contributions of the Ohmic and ambipolar terms to the electron power absorption.Comment: arXiv admin note: text overlap with arXiv:2205.0644

Nonlocal dynamics of secondary electrons in capacitively coupled radio frequency discharges

In capacitively coupled radio frequency (CCRF) discharges, the interaction of the plasma and the surface boundaries is linked to a variety of highly relevant phenomena for technological processes. One possible plasma-surface interaction is the generation of secondary electrons (SEs), which significantly influence the discharge when accelerated in the sheath electric field. However, SEs, in particular electron-induced SEs (\updelta-electrons), are frequently neglected in theory and simulations. Due to the relatively high threshold energy for the effective generation of \updelta-electrons at surfaces, their dynamics are closely connected and entangled with the dynamics of the ion-induced SEs (\upgamma-electrons). Thus, a fundamental understanding of the electron dynamics has to be achieved on a nanosecond timescale, and the effects of the different electron groups have to be segregated. This work utilizes $1d3v$ Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulations of a symmetric discharge in the low-pressure regime ($p\,=\, 1\,\rm{Pa}$) with the inclusion of realistic electron-surface interactions for silicon dioxide. A diagnostic framework is introduced that segregates the electrons into three groups ("bulk-electrons", "\upgamma-electrons", and "\updelta-electrons") in order to analyze and discuss their dynamics. A variation of the electrode gap size $L_\mathrm{gap}$ is then presented as a control tool to alter the dynamics of the discharge significantly. It is demonstrated that this control results in two different regimes of low and high plasma density, respectively. The fundamental electron dynamics of both regimes are explained, which requires a complete analysis starting at global parameters (e.g., densities) down to single electron trajectories