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

Schüngel, Edmund; Brandt, Steven; Korolov, Ihor; Derzsi, Aranka; Schulze, Julian

doi:10.1063/1.4918702

Cited by 25 publications

(23 citation statements)

References 39 publications

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“…[42]. Moreover, recent investigations have indicated that the PSR oscillations can occur in symmetric (ε = 1) CCRF plasmas, as well [102].…”

Section: Modelmentioning

confidence: 95%

“…Following Kirchhoff's rule for closed loops, the voltage balance of a CCRF discharge is obtained as [19,52,77,84,102]…”

Section: Modelmentioning

confidence: 99%

“…Then, it will be explained how the electron current and the electron heating are determined. Following Kirchhoff's rule for closed loops, the voltage balance of a CCRF discharge is obtained as [19,52,77,84,102]…”

Section: Modelmentioning

confidence: 99%

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Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas

Schüngel

Brandt

Korolov

et al. 2015

Plasma Sources Sci. Technol.

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The self-excitation of Plasma Series Resonance (PSR) oscillations plays an important role in the electron heating dynamics in Capacitively Coupled Radio Frequency (CCRF) plasmas. In a combined approach of PIC/MCC simulations and a theoretical model based on an equivalent circuit, we investigate the self-excitation of PSR oscillations and their effect on the electron heating in geometrically symmetric CCRF plasmas driven by multiple consecutive harmonics. The discharge symmetry is controlled via the Electrical Asymmetry Effect, i.e. by varying the total number of harmonics and tuning the phase shifts between them. It is demonstrated that PSR oscillations will be self-excited under both symmetric and asymmetric conditions, if (i) the charge-voltage relation of the plasma sheaths deviates from a simple quadratic behavior and if (ii) the inductance of the plasma bulk exhibits a temporal modulation. These two effects have been neglected up to now, but we show that they must be included in the model in order to properly describe the nonlinear series resonance circuit and reproduce the self-excitation of PSR oscillations, which are observed in the electron current density resulting from simulations of geometrically symmetric CCRF plasmas. Furthermore, the effect of the PSR self-excitation on the discharge current and the plasma properties, such as the potential profile, is illustrated by applying Fourier analysis. High frequency oscillations in the entire spectrum between the applied frequencies and the local electron plasma frequency are observed. As a consequence, the electron heating is strongly enhanced by the presence of PSR oscillations. A complex electron heating dynamics is found during the expansion phase of the sheath, which is fully collapsed, when the PSR is initially self-excited. The Nonlinear Electron Resonance Heating associated with the PSR oscillations causes a spatial asymmetry in the electron heating. By discussing the resulting ionization profile in the non-local regime of low-pressure CCRF plasmas, we examine why the ion flux at both electrodes remains approximately constant, independently of the phase shifts.

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“…[42]. Moreover, recent investigations have indicated that the PSR oscillations can occur in symmetric (ε = 1) CCRF plasmas, as well [102].…”

Section: Modelmentioning

confidence: 95%

“…Following Kirchhoff's rule for closed loops, the voltage balance of a CCRF discharge is obtained as [19,52,77,84,102]…”

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas

Schüngel

Brandt

Korolov

et al. 2015

Plasma Sources Sci. Technol.

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“…Further, the approximation of a quadratic charge voltage relation of the sheaths is used here. An analytical treatment would not be possible, if the cubic correction was included. The time dependent normalized charge in the grounded electrode sheath is found as

q_{s g} true(t true) = q_{t o t} - q_{s p} true(t true) = \frac{q_{t o t} - \sqrt{ϵ q_{t o t}^{2} - true(1 - ϵ true) \frac{η + ϕ_{\sim} true(t true)}{ϕ_{t o t}}}}{1 - ϵ} .

…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

A Simple Model for Ion Flux‐Energy Distribution Functions in Capacitively Coupled Radio‐Frequency Plasmas Driven by Arbitrary Voltage Waveforms

Schüngel

Schulze

2016

Plasma Processes & Polymers

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The ion flux‐energy distribution function (IFEDF) is of crucial importance for surface processing applications of capacitively coupled radio‐frequency (CCRF) plasmas. Here, we propose a model that allows for the determination of the IFEDF in such plasmas for various gases and pressures in both symmetric and asymmetric configurations. A simplified ion density profile and a quadratic charge voltage relation for the plasma sheaths are assumed in the model, of which the performance is evaluated for single‐ as well as multi‐frequency voltage waveforms. The IFEDFs predicted by this model are compared to those obtained from PIC/MCC simulations and retarding field energy analyzer measurements. Furthermore, the development of the IFEDF shape and the ion dynamics in the plasma sheath region are discussed in detail based on the spatially and temporally resolved model data.

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“…Based on the PIC/MCC approach, a wide variety of phenomena and effects have been investigated during the past decades in various plasma sources [33], e.g., the breakdown of the gases and the formation of the plasma [34,35], the energy and/or angular distributions of ions at boundary surfaces [36][37][38][39][40][41], the operation of Hall thrusters [42][43][44], electron heating and heating mode transitions [45][46][47] (termed more correctly as electron power absorption and power absorption mode transitions in more recent literature [1,48,49]), the formation of striations [50], plasma series resonance oscillations [51,52], electron dynamics in the afterglow [53], as well as the effects of ioninduced [54], and electron-induced [55,56] secondary electrons on the plasma characteristics, the physics of fast-pulsed discharges [57] and atmospheric-pressure plasma jets [58]. Most of these investigations have found that the Electron Energy Probability Function (EEPF) in these plasmas is highly non-Maxwellian, which confirms the need for kinetic simulations.…”

Section: Introductionmentioning

confidence: 99%

eduPIC: an introductory particle based code for radio-frequency plasma simulation

Donko,

Derzsi,

Vass

et al. 2021

Preprint

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Particle based simulations are indispensable tools for numerical studies of charged particle swarms and low-temperature plasma sources. The main advantage of such approaches is that they do not require any assumptions regarding the shape of the particle Velocity/Energy Distribution Function (VDF/EDF), but provide these basic quantities of kinetic theory as a result of the computations. Additionally, they can provide, e.g., transport coefficients, under arbitrary time and space dependence of the electric/magnetic fields. For the self-consistent description of various plasma sources operated in the low-pressure (nonlocal, kinetic) regime, the Particle-In-Cell simulation approach, combined with the Monte Carlo treatment of collision processes (PIC/MCC), has become an important tool during the past decades. In particular, for Radio-Frequency (RF) Capacitively Coupled Plasma (CCP) systems PIC/MCC is perhaps the primary simulation tool these days. This approach is able to describe discharges over a wide range of operating conditions, and has largely contributed to the understanding of the physics of CCPs operating in various gases and their mixtures, in chambers with simple and complicated geometries, driven by single-and multi-frequency (tailored) waveforms. PIC/MCC simulation codes have been developed and maintained by many research groups, some of these codes are available to the community as freeware resources. While this computational approach has already been present for a number of decades, the rapid evolution of the computing infrastructure makes it increasingly more popular and accessible, as simulations of simple systems can be executed now on personal computers or laptops. During the past few years we have experienced an increasing interest in lectures and courses dealing with the basics of particle simulations, including the PIC/MCC technique. In a response to this, this paper (i) provides a tutorial on the physical basis and the algorithms of the PIC/MCC technique and (ii) presents a basic (spatially one-dimensional) electrostatic PIC/MCC simulation code, whose source is made freely available in various programming languages. We share the code in C/C++ versions, as well as in a version written in Rust, which is a rapidly emerging computational language. Our code intends to be a "starting tool" for those who are interested in learning the details of the PIC/MCC technique and would like to develop the "skeleton" code further, for their research purposes. Following the description of the physical basis and the algorithms used in the code, a few examples of results obtained with this code for single-and dual-frequency CCPs in argon are also given.

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

Cited by 25 publications

References 39 publications

Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas

Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas

A Simple Model for Ion Flux‐Energy Distribution Functions in Capacitively Coupled Radio‐Frequency Plasmas Driven by Arbitrary Voltage Waveforms

eduPIC: an introductory particle based code for radio-frequency plasma simulation

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