Sheath Oscillations Research Articles

Particle-in-cell simulation of grid sheath oscillations in a double-plasma device

The oscillation process around a strongly negative grid in a double-plasma device is studied with one-dimensional particle-in-cell simulation. The code is an extension of PDP1, and its proper adaption to the present situation is described. For asymmetric operation of the double-plasma device, the formation of virtual anode oscillations (VAOs) is observed. The scaling law f/spl prop/n/sup 1/2/U/sub g//sup -/spl alpha//, which formerly was derived from the transit time through a static Child-Langmuir sheath, is now recovered with /spl alpha/=0.33 by self-consistent simulations. A group of ions, that is trapped in the sheath, leads to feedback stabilization of the VAO. The simulations show that ion bunches that have gained energy in the VAO process are periodically injected into the source plasma where they excite damped ion waves.

Collisional electron heating in a RF discharge

The question of how far the concept of reflection of electrons at the oscillating sheath can be applied to the collisional situation is investigated. A radiofrequency discharge between two parallel plates is considered. Model calculations on the basis of the transport equations result in two contributions to the collisional sheath oscillation heating. The first contribution represents heating in an expanding sheath and cooling in a contracting sheath due to reflection at the sheath edge. The second contribution describes Joule heating within the sheath range and is of the same order of magnitude as the corresponding bulk heating. In the experiment a 300 kHz discharge is operated by a non-sinusoidal voltage with a steep rise and fall to a plateau. Optical emission spectroscopy resolved in time and space is applied. Owing to the special voltage shape, emission caused by radiofrequency heating can be separated from emission caused by secondary electrons from the cathode. The experimental results confirm the predictions of the model.

Effect of RF-Biased Electrode on Microwave Plasma

The effect of an rf-biased electrode on a microwave plasma has been studied experimentally and compared with the results of a theoretical model considering the contribution of the rf sheath oscillation to rf plasma production. Conditions under which the rf electrode does not affect the microwave plasma, or acts only as “rf biasing,” are low voltage applied to the electrode, high microwave plasma density, and low rf driving frequency. These non interacting conditions are also related quantitatively. The theoretical model is found to account fully for the experimental results.

Sheath dynamics of electrodes stepped to large negative potentials

Results are presented of particle simulations of the time-dependent behavior of the plasma sheath surrounding an electrode whose potential is abruptly changed from 0 to some negative value. The surrounding plasma is assumed isotropic and collisionless, and the electrode is a sphere or infinite cylinder. Potential steps up to −1000kTe/e are considered. The time histories and frequency spectra of sheath and plasma oscillations initiated by the potential step are studied. The energy in sheath oscillations (frequency <ωp) escapes by nonlinear coupling to plasma oscillations (frequency ωp). The time scale for sheath–plasma coupling depends strongly on the ion-to-electron mass ratio. Both linear and nonlinear ion acoustic waves are excited by the response to the potential step. Near a small (radius 1λD) cylindrical electrode, trapped ions are shown to make an important contribution to the sheath ion density. The height of the transient peak in collected current for a cylindrical electrode displays strong dependence on the ion-to-electron temperature ratio, for sufficiently large potential steps.

Space and time resolved electric field vector distribution in radiofrequency discharges between unequal area electrodes

Two dimensional space and time-resolved electric field vector distributions have been determined in asymmetric, capacitively coupled, low frequency (35 kHz) and radio-frequency (4 MHz) discharges in Ar/2.9%K mixtures. The electric field was measured using a non perturbative spectroscopic technique based on the Stark mixing observed in the laser induced fluorescence of NaK molecules. Sheath oscillations are clearly visible, and show the different discharge conditions which prevail close to the different electrodes. The field direction is almost stationary in time. The electric field distribution is nearly radially uniform in front of the large electrode, while geometrical effects seem to affect the discharge close to the small electrode. Edge effects are visible at a distance of 2 mm from the electrode edges. In low frequency discharges the ionic current is about the same at both electrodes, whereas the current density is very different, due to the different charge densities. In RF discharges conditions were found for which different discharge sustaining regimes occur at each electrode: «alpha» regime near the large electrode, «gamma» regime near the small electrode

Pecvd RF Discharge Models Review

AbstractThis paper presents a concise and subjective summary of the rapid progress that has been made in the understanding of the essential features of RF discharges. The paper concentrates on introducing the important concepts used in modeling the rf discharge. The discharges have been modeled from several distinctly different approaches. These include circuit, beamdiffusion, plasma fluid or continuum, and particle kinetic models. The treatments have their usefulness depending on the application. The circuit models give easily parameterized results, power deposition, and phase angles between voltage and current, however, they do not describe the important plasma chemistry and the source terms for deposition and etching. The newer continuum models efficiently give self-consistent plasma parameters for higher pressure discharges but synergistic ion and neutral interactions with surfaces are difficult to include. The particle kinetic models can include many effects without approximations, however they need extensive data sets and long computer run times. The coupling of improved diagnostics and the different theories has resulted in a convergence of their conclusions. There are four distinct energy-gain mechanisms in the RF discharge : a bulk plasma excitation; electron beam excitation resulting from secondary emission from ion collisions with the electrodes; wave-riding acceleration on the sheath oscillation (collisional: Kushner); and a noncollisional plasma electron-sheath boundary interaction (Godyak). The relative contributions are sensitive functions of the gas mixture, pressure, frequency and RF voltage.

Glow-discharge sheath electric fields: Negative-ion, power, and frequency effects.

Using Stark-mixed laser-induced fluorescence, space-time--resolved maps of sheath electric fields in discharges through ${\mathrm{BCl}}_{3}$ and Ar are measured as a function of concentration, power density (0.14--0.41 W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$), and frequency (dc to 10 MHz). Sheath oscillations are observed throughout this frequency range and are discussed qualitatively in terms of characteristic times for ion and electron transport. Double layers are observed in low-frequency discharges containing more than 5% ${\mathrm{BCl}}_{3}$ and are attributed to a buildup in negative-ion concentration; it is argued that different ratios of negative-ion to electron density in the plasma and sheath are responsible for double-layer formation at the plasma-sheath boundary. These maps should prove useful as input for particle transport simulations in plasma-processing and light-source applications. They also provide stringent tests for self-consistent sheath theories.

Constant frequency oscillations in a bounded thermally produced plasma

Measurements are reported of a constant frequency oscillation in a current-carrying thermal plasma. A collision-free theory is presented which includes a standing wave in the plasma together with a sheath oscillation. It is postulated that the ion velocity distribution function becomes flattened at v =±ω/k and this gives good agreement between theory and experiment.

Low-Frequency Oscillations in a Thermal Cesium Plasma

The oscillation modes present in the ``TOPSY'' thermally generated cesium plasma device have been investigated experimentally; oscillation frequency spectra and three-axis (r,θ,z) maps of relative phase have been studied as functions of axial magnetic field strength, electron density, axial drift current, plasma column length, and ionizer sheath polarity. Both conducting and nonconducting cold end plates were used. Two distinct modes were observed: a low-frequency oscillation (∼1 kHz) which was identified as an ion acoustic wave excited by axial circulating currents in the periphery of the plasma column, and a higher-frequency oscillation (7 to 50 kHz) whose frequency behavior showed close agreement with the theory of the ``universal'' resistive drift-wave instability, but which failed to show the azimuthal propagation predicted by this theory. The lack of observed azimuthal phase shift could not be explained in terms of the transit-time-controlled potential-relaxation oscillations predicted for thermally generated plasmas, by sheath oscillations, or by the reflection of the drift waves at the plasma/end plate sheaths. Both modes were spontaneously present in the ``quiescent'' plasma (i.e., with no net drift current) and were neither further excited nor significantly altered in the presence of strong drift currents.