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Cited by 22Low-Pressure Plasma Processing and DiagnosticsMagnetic confinement fusion researchVacuum and Plasma Arcs

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Electron dynamics in planar radio frequency magnetron plasmas: II. Heating and energization mechanisms studied via a 2d3v particle-in-cell/Monte Carlo code

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Eremin, D, Berger, B, Engel, D, Kallähn, J, Köhn, K, Krüger, D, Xu, L, Oberberg, M, Wölfel, C, Lunze, J, Awakowicz, P, Schulze, J, Brinkmann, R P·2023·Plasma Sources Science and Technology
DOI 10.1088/1361-6595/acc47f
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Abstract

The present work investigates electron transport and heating mechanisms using an (r, z) particle-in-cell simulation of a typical rf-driven axisymmetric magnetron discharge with a conducting target. Due to a strong geometric asymmetry and a blocking capacitor, the discharge features a large negative self-bias conducive to sputtering applications. Employing decomposition of the electron transport parallel and perpendicular to the magnetic field lines, it is shown that for the considered magnetic field topology the electron current flows through different channels in the (r, z) plane: a ‘transverse’ one, which involves current flow through the electrons’ magnetic confinement region (EMCR) above the racetrack, and two ‘longitudinal’ ones, where electrons’ guiding centers move along the magnetic field lines. Electrons gain energy from the electric field along these channels following various mechanisms, which are rather distinct from those sustaining dc-powered magnetrons. The longitudinal power absorption involves mirror-effect heating (MEH), nonlinear electron resonance heating, magnetized bounce heating (MBH), and the heating by the ambipolar field at the sheath-presheath interface. The MEH and MBH represent two new mechanisms missing from the previous literature. The MEH is caused by a reversed electric field needed to overcome the mirror force generated in a nonuniform magnetic field to ensure sufficient flux of electrons to the powered electrode, and the MBH is related to a possibility for an electron to undergo multiple reflections from the expanding sheath in the longitudinal channels connected by the arc-like magnetic field. The electron heating in the transverse channel is caused mostly by the essentially collisionless Hall heating in the EMCR above the racetrack, generating a strong E × B azimuthal drift velocity. The latter mechanism results in an efficient electron energization, i.e. energy transfer from the electric field to electrons in the inelastic range. Since the main electron population energized by this mechanism remains confined within the discharge for a long time, its contribution to the ionization processes is dominant.

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  • Non-linear effects such as the generation of higher harmonics, parametric decay instabilities, non-linear wave-particle interaction including particle trapping effects, and non-linear skin-effect can be important but require evolving the EM fields in the time domain.

    “Non-linear effects, such as the generation of higher harmonics, parametric decay instabilities, non-linear wave-particle interaction including particle trapping effects, non-linear skin-effect (see, e.g., Refs.131-136) can be important but require evolving the EM fields in the time domain.”

    From Plasma propulsion modeling with particle-based algorithms (2023) · cites this paper as [136]

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Metadata

Authors
Eremin, D., Berger, B., Engel, D., Kallähn, J., Köhn, K., Krüger, D., Xu, L., Oberberg, M., Wölfel, C., Lunze, J., Awakowicz, P., Schulze, J., & Brinkmann, R. P.
Affiliations
Ruhr University Bochum (DE)
Corresponding author
Eremin, D
ORCID
Venue
Plasma Sources Science and Technology
Publisher
IOP Publishing
Published
2023-04-01
Volume
32
Issue
4
Pages
045008
ISSN
  • 0963-0252 (ISSN-L)
  • 1361-6595
DOI
10.1088/1361-6595/acc47f
OpenAlex
W4324319948
Cited by
22
References
1
Citations by year
2026: 7 · 2025: 2 · 2024: 7 · 2023: 6
FWCI
1.64
Type
journal article
Language
en
Open access
Licence
Locations
  • Plasma Sources Science and Technology (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
Deutsche Forschungsgemeinschaft (417888799 and SFB-TR 87)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Low-Pressure Plasma Processing and Diagnostics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Magnetic confinement fusion research
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Vacuum and Plasma Arcs
Keywords
electron transport, electron heating, magnetron discharge, electron energization, ambipolar field, electron confinement, magnetic field topology, sputtering, particle-in-cell/Monte Carlo simulation

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