Sebastian Wilczek

The effect of the driving frequency on the confinement of beam electrons and plasma density in low-pressure capacitive discharges

The effect of changing the driving frequency on the plasma density and the electron dynamics in a capacitive radio-frequency argon plasma operated at low pressures of a few Pa is investigated by Particle in Cell/Monte Carlo Collisions simulations and analytical modeling. In contrast to previous assumptions the plasma density does not follow a quadratic dependence on the driving frequency in this non-local collisionless regime. Instead, a step-like increase at a distinct driving frequency is observed. Based on the analytical power balance model, in combination with a detailed analysis of the electron kinetics, the density jump is found to be caused by an electron heating mode transition from the classical

Kinetic interpretation of resonance phenomena in low pressure capacitively coupled radio frequency plasmas

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Hysteresis effects and confinement of beam electrons in capacitive discharges

-mode into a low density resonant heating mode characterized by the generation of two energetic electron beams at each electrode per sheath expansion phase. These electron beams propagate through the bulk without collisions and interact with the opposing sheath. In the low density mode, the second beam is found to hit the opposing sheath during its collapse. Consequently, a high number of energetic electrons is lost at the electrodes resulting in a poor confinement of beam electrons in contrast to the classical

Nonlinear electron resonance heating in asymmetric capacitive discharges

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Kinetic simulation of mode transitions and hysteresis effects in low pressure capacitive discharges

-mode observed at higher driving frequencies. Based on the analytical model this modulated confinement quality and the related modulation of the energy lost per electron lost at the electrodes is demonstrated to cause the step-like change of the plasma density. The effects of a variation of the electrode gap, the neutral gas pressure, the electron sticking and secondary electron emission coefficients of the electrodes on this step-like increase of the plasma density are analyzed based on the simulation results.

Disparity between current and voltage driven capacitively coupled radio frequency discharges

The kinetic origin of resonance phenomena in capacitively coupled radio frequency plasmas is discovered based on particle-based numerical simulations. The analysis of the spatio-temporal distributions of plasma parameters such as the densities of hot and cold electrons, as well as the conduction and displacement currents reveals the mechanism of the formation of multiple electron beams during sheath expansion. The interplay between highly energetic beam electrons and low energetic bulk electrons is identified as the physical origin of the excitation of harmonics in the current.

Spatio-temporal analysis of the electron power absorption in electropositive capacitive RF plasmas based on moments of the Boltzmann equation

Summary form only given. In low-pressure capacitive discharges the radio-frequency modulated plasma sheaths generate a number of highly energetic beam electrons traversing the discharge gap. These electrons are important for sustaining the plasma via ionization. In this work, we investigate the dynamics of these electron beams as well as their effect on the plasma by means of Particle-In-Cell simulations for different process parameters (driving frequency, gap size, pressure). Especially at low pressures (large electron mean free path λm and small gap sizes Lgap (λm/Lgap>1), the interaction of electron beams with the opposing sheath becomes important1. Under a certain combination of parameters, electron beams generated at one electrode can approach the other electrode, when the local sheath length is minimum. These energetic electrons can overcome the sheath potential at this time and can be lost at this electrode. In that case, the plasma density decreases abruptly. Varying the process parameters (e.g., increasing or decreasing the driving frequency) indicates a hysteresis at this abrupt transition. In order to explain this hysteresis, the electron dynamics is investigated on a nanosecond timescale. From these results it is shown that the interaction of beam and bulk electrons is the governing mechanism.

The effect of realistic heavy particle induced secondary electron emission coefficients on the electron power absorption dynamics in single- and dual-frequency capacitively coupled plasmas

Summary form only given. In low-pressure capacitive discharges the concept of Nonlinear Electron Resonance Heating (NERH) becomes important to enhance Ohmic dissipation. Particularly in geometrically asymmetric capacitive discharges (generation of a DC self-bias), the nonlinearities of the boundary plasma sheaths lead to a strongly non-sinusoidal radio frequency current. The Fourier spectra of such a current can indicate harmonics which are in resonance with the Plasma Series Resonance (PSR). The scenario of PSR was investigated by different models (e.g. zero-dimensional, spatially resolved), which assume that the bulk current is carried by the electron current and the sheath current by the displacement current. Although these models are able to resolve the nonlinear behavior between bulk and sheath a detailed kinetic picture is missing. In this work, we discuss the particle dynamics in the regime of NERH on a nanosecond timescale by means of a self-consistent kinetic simulation. We use a 1d3v spherical Particle-In-Cell code in order to simulate an asymmetric discharge. It is shown that the excitation of harmonics is connected to the generation of multiple electron beams accelerated by the expanding plasma sheath. Furthermore, the interaction of these beams with bulk electrons leads to significant plasma oscillations and thus, to a moderate displacement current in the center of the discharge. These kinetic effects should be taken into account for future models in order to understand the comprehensive electron heating in capacitive discharges.

Kinetic Investigation of Ideal Multipole Resonance Probe

At very low gas pressures around 1 Pa the electron heating in capacitive radio frequency discharges is dominated by stochastic heating. In this regime electrons are accelerated by the oscillating sheaths, traverse through the plasma bulk and interact with the opposite sheath. Depending on the driving frequency the energetic electrons can enter the sheaths at different phases. These are i) the collapsing phase when the electrons are decelerated, ii) the expanding phase when they are accelerated, and iii) the instant of time, when the sheath width has its minimum and energetic electrons may reach the electrode and be lost. This work analyzes the resulting complex discharge dynamics by means of Particle-In-Cell simulation. It is shown that at certain frequencies the discharge switches abruptly from a low-density mode in a high-density mode. The inverse transition is also abrupt, but shows a significant hysteresis. This phenomenon is explained by the complex interaction of the bulk and the sheath.