Electron dynamics in planar radio frequency magnetron plasmas: I. The mechanism of Hall heating and the µ-mode

Abstract

The electron dynamics and the mechanisms of power absorption in radio-frequency (RF) driven,
magnetically enhanced capacitively coupled plasmas (MECCPs) at low pressure are investigated.
The device in focus is a geometrically asymmetric cylindrical magnetron with a radially nonuniform
magnetic field in axial direction and an electric field in radial direction. The dynamics is studied
analytically using the cold plasma model and a single-particle formalism, and numerically with the
inhouse energy and charge conserving particle-in-cell/Monte Carlo collisions code ECCOPIC1S-M.
It is found that the dynamics differs significantly from that of an unmagnetized reference discharge.
In the magnetized region in front of the powered electrode, an enhanced electric field arises during
sheath expansion and a reversed electric field during sheath collapse. Both fields are needed to
ensure discharge sustaining electron transport against the confining effect of the magnetic field.
The corresponding azimuthal E×B-drift can accelerate electrons into the inelastic energy range
which gives rise to a new mechanism of RF power dissipation. It is related to the Hall current and
is different in nature from Ohmic heating, as which it has been classified in previous literature.
The new heating is expected to be dominant in many magnetized capacitively coupled discharges.
It is proposed to term it the “μ-mode” to separate it from other heating modes.

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

“…In the present work we simulate the discharge behavior for a single set of typical parameters in a more complicated 2D (r, z) geometry of a planar magnetron with a realistic magnetic field topology. Many aspects remain similar to [33]. In particular, we find that the dominant heating mechanism is still caused by the Hall heating in the electrons' magnetic confinement region (EMCR) above the racetrack, where electrons are confined by the magnetic field across, and by the electrostatic sheath potential or by the mirror effect along the magnetic field lines.…”

“…Comparing these equations to the ones given in [33], one can see that now equations of motion additionally govern the z coordinate in the configuration and velocity spaces and include the B z component of the magnetic field. The magnetic field does not influence the particle motion along the magnetic field lines, whereas it inhibits the transport across them leading to the effects described in [33].…”

“…First, in [33] we argue that in magnetized CCRF discharges operated at low pressures the electron energization occurs via an efficient and essentially collisionless Hall mechanism. It consists in generation of a strong time-dependent E × B azimuthal drift through strong time-dependent electric fields, shifting a large number of electrons into the inelastic energy range (see the reference for more details).…”

“…It is a two-dimensional electrostatic member of the in-house developed ECCOPIC code family based on the fully implicit energy-conserving particle-in-cell (ECPIC) method. The latter was originally introduced by [39,40] and is then adapted to bounded plasmas in [33,41]. As has been recently shown in [42], this algorithm is robust against excitation of the finite grid instability even if the cell size exceeds the Debye length and the time step is greater than the plasma period.…”

“…This work is a part of a companion paper series (see also [33,34]) aimed at deepening the understanding of electron heating/energization mechanisms in electropositive rfMS discharges with a conducting target.…”