Observation of nonlinear sheath oscillations in symmetric capacitive discharges at low pressures

Abstract

The mechanism of nonlinear oscillations in symmetric capacitively coupled plasmas is studied by the particle-in-cell/Monte Carlo collisions approach. A physical origin of this nonlinear phenomenon is identified by spatiotemporal kinetic analysis of electron dynamics. It is found that multi-beams of high-energy electrons are stimulated at the sheath expansion phase, following with reversed electric field filaments. The instantaneous absence of the quasi-neutrality in the vicinity of the sheaths is responsible for the observed phenomenon. In addition, a simple theoretical model is introduced to qualitatively illustrate the numerical findings. Our simulations demonstrate that the frequency and intensity of this nonlinearity are very sensitive to the plasma density, sheath velocity, and sheath thickness. More nonlinear oscillations could be stimulated at the condition of high density and high sheath velocity, while a large sheath thickness normally induces large-amplitude oscillations. A simple relation of pressure and gap distance for nonlinear sheath oscillations has been built.

Modulation of uniform magnetic field on electron dynamics in low‐pressure capacitively coupled plasmas

“…Figure 2 presents the spatiotemporal plots of the fast electron (electron with energy above 30 eV) densities (left column), which is obtained by counting the number of electrons that have energy above 30 eV in 1000 RF cycles at the same grid, as well as electric fields (center column) and the mean energy (calculated by ½mV 2 ) of all electrons (right column) within one rf period as a function of magnetic fields at a fixed rf frequency of 54.24 MHz. It is clearly visible that dual beams of fast electrons are generated during one sheath expansion in panel a1, which corresponds to the nonlinear sheath oscillations reported in Reference [17]. As the sheath expands so fast that the electrons are heated into fast electrons and penetrate into bulk plasma (generating the first beam), leaving a small ion-rich region with a positive space charge near the sheath edge (displayed in Reference [17]), which induces a reversed electric field filament [in panel a2].…”

“…It is clearly visible that dual beams of fast electrons are generated during one sheath expansion in panel a1, which corresponds to the nonlinear sheath oscillations reported in Reference [17]. As the sheath expands so fast that the electrons are heated into fast electrons and penetrate into bulk plasma (generating the first beam), leaving a small ion-rich region with a positive space charge near the sheath edge (displayed in Reference [17]), which induces a reversed electric field filament [in panel a2]. This electric field filament is in the opposite direction with the electric field in the sheath, which damps the sheath expansion for a short time.…”

“…The simulation results are based on one-dimensional PIC/ MCC simulation code, which considers one spatial coordinate and three-dimension in velocity space, offering complete kinetic information, including the momentum transfer from the oscillating sheaths. The code has been verified in References [15][16][17]. The schematic of the reactor is shown in Figure 1.…”

High energy electrons induced by nonlinear effect in synchronized dual-level radio frequency pulsing capacitively coupled plasmas

“…In the case of modulated HF parameter σ = 0, more and strong filamentary electric field reversals appear in figure 5(b1), which corresponds to the nonlinear behaviors revealed in figure 2(a1). As well explained in [24,[26][27][28][29][30][31], when the high energy electron beams are stimulated by the oscillating sheath at the expansion phase, a positive charge (positive ion-rich) region will be left behind, i.e. a charge separation is induced, which could further cause the reversed electric field.…”

Collisionless magnetized sheath resonance heating induced by a transverse magnetic field in low-pressure capacitive rf discharges

“…resonance heating occurs, at which the power deposition and plasma density will be markedly enhanced. Besides, two other types of resonance heating have been found in capacitive discharges, including nonlinear electron resonance heating in symmetric discharges [16][17][18] and the self-excitation of the plasma series resonance in asymmetric discharges [19][20][21][22]. Each resonance mode has attracted enormous interest due to its complex inherent physical mechanisms and significant power deposition, as well as the impressively high plasma density.…”