7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Particle-based simulations of rotating spokes in radio frequency magnetrondischarges
L. Xu,1 Haoming Sun,2 Denis Eremin,3 Sathya Ganta,4 Igor Kaganovich,5Kallol Bera,4 and Shahid Rauf 41

2Department of Physical Science and Technology, Soochow University, China
École polytechnique fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), Switzerland
3Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Germany
4Applied Materials, Inc., USA
5Princeton Plasma Physics Laboratory, USAe-mail (speaker):liangxu@suda.edu.cn

Magnetron sputtering represents an advanced
technique widely used in the industrial material
processing, particularly, the high-quality thin films
manufacturing. Azimuthal spokes is a ubiquitous
oscillation mode in magnetron discharge plasmas, aswell as in other typical E×B plasma sources, such as Hall
thrusters and Penning discharges. The spoke modesignificantly affects the dynamics of electrons and ionsand its fundamental understanding is hereby ofsignificant importance in the operation and control ofmagnetron sputtering discharges. Although spokes in
direct current and pulsed magnetrons were studied
extensively, their presence and the underlying physics
are little studied in radio frequency (RF) driven
magnetron discharge, which is an important technique
for the deposition of both insulating and conducting
films. The first experimental evidence of the rotating
spoke in RF magnetron discharges was recently reported,but its formation and physics is not elucidated by far. In
this work, the rotating spoke mode experimentallyobserved in RF magnetron discharges was successfully
reproduced by means of 2D axial-azimuthal fully kinetic
Particle-in-cell/Monto Carlo collision approach. The
spoke rotates in the -E×B direction with the velocity 5km/s, consistent with the experimental observation. The
underlying physics of prominent spoke features in RF
magnetron discharge: the potential hump and theRF-modulated ionization, were observed and elucidated
to uncover the driving mechanism behind the spoke[1, 2]
formation.
The analysis of the computational results,aided by the perturbation two-fluid theory, reveals thatthe cathode sheath electric field Ez triggers the gradientdrift instability (GDI), which is saturated with thedestruction of the GDI condition due to the deformationof the potential and the redistribution of the electrondensity. As a consequence, the potential hump region
forms with the presence of the azimuthal electric field Ey.
We found that in the linear stage, the instability mode
wavelength and the corresponding growth rate are ingood agreement with the prediction of the GDI linear
theory. It is further shown that the saturation level of Ey
is synchronized with and proportional to the cathodevoltage, leading to the RF-modulation of the spokeionization. Due to the gradient B drift induced electronenergy gain is proportional to the saturation level of Ey,
it is suggested that the spoke ionization may be
manipulated by the cathode voltage in DC or pulsed
magnetron discharges.
References[1] L. Xu, D. Eremin, and R. Brinkmann Plasma Sources
Science and Technology 30, 075013 (2021).
[2] L. Xu, H. M. Sun, D. Eremin, S. Ganta, I.
Kaganovich, K. Bera, and S. Rauf arXiv:2305.15941(2023)

Figure a) The layout of the 2D axial (z)-azimuthal (y) PIC/MCC model of the RF magnetron plasma. b) The voltage waveform
applied at the cathode. c) The 2D map of the RF period averaged ionization rate. d) The spatio (azimuthal)-temporal plot of theionization rate in the long duration at z=0.5 cm (note the ionization rate is RF period averaged). e) The contour 2D map of potential
in the steady state when cathode voltage is minimum (U=-180 V). f) The spatio (azimuthal)-temporal plot of the ionization rate in theduration of 20 RF periods at z=0.5 cm (here the ionization rate is transient instead of the RF period-averaged).