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

Abstract

The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current 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.

Authors:
; ;  [1]; ; ;  [2]
  1. Department of Physics, West Virginia University, Morgantown, West Virginia 26506-6315 (United States)
  2. Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, 1121 Budapest, Konkoly-Thege Miklós Str. 29-33 (Hungary)
Publication Date:
OSTI Identifier:
22408373
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASYMMETRY; COLLISIONS; COMPUTERIZED SIMULATION; ELECTRIC DISCHARGES; ELECTRIC POTENTIAL; ELECTRONS; EQUIVALENT CIRCUITS; EXCITATION; LANGMUIR FREQUENCY; MONTE CARLO METHOD; OSCILLATIONS; PLASMA SHEATH; PRESSURE RANGE KILO PA; RADIOWAVE RADIATION; RESONANCE; TIME DEPENDENCE

Citation Formats

Schüngel, Edmund, Brandt, Steven, Schulze, Julian, Korolov, Ihor, Derzsi, Aranka, and Donkó, Zoltán. On the self-excitation mechanisms of plasma series resonance oscillations in single- and multi-frequency capacitive discharges. United States: N. p., 2015. Web. doi:10.1063/1.4918702.
Schüngel, Edmund, Brandt, Steven, Schulze, Julian, Korolov, Ihor, Derzsi, Aranka, & Donkó, Zoltán. On the self-excitation mechanisms of plasma series resonance oscillations in single- and multi-frequency capacitive discharges. United States. doi:10.1063/1.4918702.
Schüngel, Edmund, Brandt, Steven, Schulze, Julian, Korolov, Ihor, Derzsi, Aranka, and Donkó, Zoltán. 2015. "On the self-excitation mechanisms of plasma series resonance oscillations in single- and multi-frequency capacitive discharges". United States. doi:10.1063/1.4918702.
@article{osti_22408373,
title = {On the self-excitation mechanisms of plasma series resonance oscillations in single- and multi-frequency capacitive discharges},
author = {Schüngel, Edmund and Brandt, Steven and Schulze, Julian and Korolov, Ihor and Derzsi, Aranka and Donkó, Zoltán},
abstractNote = {The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current 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.},
doi = {10.1063/1.4918702},
journal = {Physics of Plasmas},
number = 4,
volume = 22,
place = {United States},
year = 2015,
month = 4
}
  • At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies.
  • Self-excited plasma series resonances (PSR) are observed in capacitve discharges as high-frequency oscillations superimposed on the normal rf current. This high-frequency contribution to the current is generated by a series resonance between the capacitive sheath and the inductive and ohmic bulk of the plasma. The nonlinearity of the sheath leads to a complex dynamic. The effect is applied, e.g., as a diagnostic technique in commercial etch reactors where analysis is performed by a numerical model. Here a simple analytical investigation is introduced. In order to solve the nonlinear equations analytically, a series of approximation is necessary. Nevertheless, the basic physicsmore » is conserved and excellent agreement with numerical solutions is found. The model provides explicit and simple formula for the current waveform and the spectral range of the oscillations. In particular, the dependence on the discharge parameters is shown. Further, the model gives insight into an additional dissipation channel opened by the high-frequency oscillations. With decreasing pressure, the ohmic resistance of the bulk decreases as well, while the amplitude of the PSR oscillations grows. This results in substantially higher power dissipation that exceeds the contribution of classical stochastic heating.« less
  • Spatial structures of the electron density and temperature in ring-shaped hollow cathode capacitive rf plasma with a single narrow trench of 2 mm width have been investigated at various trench depths of D = 5, 8, 10, 12, and 15 mm. It is found that the plasma density is increased in the presence of the trench and that the radial profile of the plasma density has a peak around the narrow hollow trench near the cathode. The density becomes uniform further away from the cathode at all trench depths, whereas the electron temperature distribution remains almost uniform. The measured radial profiles of the plasmamore » density are in good agreement with a theoretical diffusion model for all the trench depths, which explains the local density increase by a local enhancement of the electron heating. Under the conditions investigated, the trench of 10 mm depth is found to result in the highest plasma density at various axial and radial positions. The results show that the radial uniformity of the plasma density at various axial positions can be improved by using structured electrodes of distinct depths rather than planar electrodes.« less
  • The flow of electron and ion conduction currents across a nonlinear capacitive sheath to the electrode surface self-consistently sets the dc bias voltage across the sheath. We incorporate these currents into a model of a homogeneous capacitive sheath in order to determine the enhancement of the Ohmic and stochastic heating due to self-excitation of the nonlinear series resonance in an asymmetric capacitive discharge. At lower pressures, the series resonance can enhance both the Ohmic and stochastic heating by factors of 2-4, with the Ohmic heating tending to zero as the pressure decreases. The model was checked, for a particular setmore » of parameters, by a particle-in-cell (PIC) simulation using the homogeneous sheath approximation, giving good agreement. With a self-consistent Child-law sheath, the PIC simulation showed increased heating, as expected, whether the series resonance is important or not.« less