Sheath Impedance Research Articles

Ionization by bulk heating of electrons in capacitive radio frequency atmospheric pressure microplasmas

Electron heating and ionization dynamics in capacitively coupled radio frequency (RF) atmospheric pressure microplasmas operated in helium are investigated by particle-in-cell simulations and semi-analytical modeling. A strong heating of electrons and ionization in the plasma bulk due to high bulk electric fields are observed at distinct times within the RF period. Based on the model the electric field is identified to be a drift field caused by a low electrical conductivity due to the high electron–neutral collision frequency at atmospheric pressure. Thus, the ionization is mainly caused by ohmic heating in this ‘Ω-mode’. The phase of strongest bulk electric field and ionization is affected by the driving voltage amplitude. At high amplitudes, the plasma density is high, so that the sheath impedance is comparable to the bulk resistance. Thus, voltage and current are about 45° out of phase and maximum ionization is observed during sheath expansion with local maxima at the sheath edges. At low driving voltages, the plasma density is low and the discharge becomes more resistive, resulting in a smaller phase shift of about 4°. Thus, maximum ionization occurs later within the RF period with a maximum at the discharge center. Significant analogies to electronegative low-pressure macroscopic discharges operated in the drift-ambipolar mode are found, where similar mechanisms induced by a high electronegativity instead of a high collision frequency have been identified.

Radio frequency-compensated Langmuir probe with auxiliary double probes

A radio frequency (rf) compensation design using auxiliary double probes connected in parallel with a main measurement probe was developed for Langmuir probe diagnostics. This probe structure can reduce the sheath impedance of the main probe. In our probe design, the sheath capacitance of the probe can be increased and its sheath resistance can be decreased with increasing dc bias differential voltage between the auxiliary double probes. The I-V characteristic curve and electron energy distribution functions measured by our probe system had sufficient rf compensation performance in inductively coupled plasmas.

A New Bioimpedance Research Device (BIRD) for Measuring the Electrical Impedance of Acupuncture Meridians

The aim of this article is to introduce an electrical bioimpedance device that uses an old and little-known impedance measuring technique to study the impedance of the meridian and nonmeridian tissue segments. Three (3) pilot experimental studies involving both a tissue phantom (a cucumber) and 3 human subjects were performed using this BIRD-I (Bioimpedance Research Device) device. This device consists of a Fluke RCL meter, a multiplexer box, a laptop computer, and a medical-grade isolation transformer. Segment and surface sheath (or local) impedances were estimated using formulae first published in the 1930s, in an approach that differs from that of the standard four-electrode technique used in most meridian studies to date. Our study found that, when using a quasilinear four-electrode arrangement, the reference electrodes should be positioned at least 10 cm from the test electrodes to ensure that the segment (or core) impedance estimation is not affected by the proximity of the reference electrodes. A tissue phantom was used to determine the repeatability of segment (core) impedance measurement by the device. An applied frequency of 100 kHz was found to produce the best repeatability among the various frequencies tested. In another preliminary study, with a segment of the triple energizer meridian on the lower arm selected as reference segment, core resistance-based profiles around the lower arm showed three of the other five meridians to exist as local resistance minima relative to neighboring nonmeridian segments. The profiles of the 2 subjects tested were very similar, suggesting that the results are unlikely to be spurious. In electrical bioimpedance studies, it is recommended that the measuring technique and device be clearly defined and standardized to provide optimal working conditions. In our study using the BIRD I device, we defined our standard experimental conditions as a test frequency of 100 kHz and the position of the reference electrodes of at least 10 cm from the test electrodes. Our device has demonstrated potential for use in quantifying the degree of electrical interconnection between any two surface-defined test meridian or nonmeridian segments. Issues arising from use of this device and the measurement Horton and van Ravenswaay technique were also presented.

“SensArray” voltage sensor analysis in an inductively coupled plasma

A commercially manufactured PlasmaVolt™ sensor wafer was studied in an inductively coupled plasma reactor in an effort to validate sensor measurements. A pure Ar plasma at various powers (25–420W), for a range of pressures (10–80mT), and bias voltages (0–250V) was utilized. A numerical sheath simulation was simultaneously developed in order to interpret experimental results. It was found that PlasmaVolt™ sensor measurements are proportional to the rf-current through the sheath. Under conditions such that the sheath impedance is dominantly capacitive, sensor measurements follow a scaling law derived from the inhomogeneous sheath model of Lieberman and Lichtenberg, [Principles of Plasma Discharges and Materials Processing (Wiley, New York, 2005)]. Under these conditions, sensor measurements are proportional to the square root of the plasma density at the plasma-sheath interface, the one-fourth root of the electron temperature, and the one-fourth root of the rf bias voltage. When the sheath impedance becomes increasingly resistive, the sensor measurements deviate from the scaling law and tend to be directly proportional to the plasma density. The measurements and numerical sheath simulation demonstrate the scaling behavior as a function of changing sheath impedance for various plasma conditions.

An Indirect Method for Measuring Electron Density of Atmospheric Pressure Plasma Jets

An indirect method for measuring the electron density of radio frequency atmospheric pressure plasma jets (RF-APPJ) based on the discharge voltage and current waveforms is presented. An equivalent circuit of the plasma discharge is assumed by taking into account the electrode capacitance, serial resistance and inductance of the bulk plasma, as well as the sheath impedance. Based on the circuit model, the electron density can be obtained according to Ohm's law. By using this method, the effects of the electrode shape and discharge gap on the electron density are discussed.

Microwave-Frequency Effects on Microplasma

Capacitively coupled microplasma generation becomes more efficient at microwave frequencies. Helium and argon microplasmas are characterized using excitation frequencies of 450 MHz, 900 MHz, and 1.8 GHz. These microplasmas are tested at both atmospheric pressure and 0.4 torr. We have experimentally determined the microplasma's electrical impedance, which consists of bulk plasma resistance and capacitive sheath reactance. These two parameters were measured by fitting theoretical power reflection coefficients to experimental forward and reflected microwave power as a function of frequency. Microplasma resistance decreases with increasing frequency, showing that the generation of free electrons depends on the driving frequency. In addition, the reactive sheath impedance and the microwave electrode voltage also decrease with an increase of frequency. A 3-D microplasma simulation shows that a narrower sheath width exists for higher frequency microplasma, and this is responsible for reducing the reactive impedance and the peak-to-peak electrode voltage. At higher microwave frequency, the decreased electrode voltage reduces both the plasma potential and the ion kinetic energy losses, thus increasing the electron density.

Theory and fluid simulations of boundary-plasma fluctuations

Theoretical and computational investigations of boundary-plasma microturbulence which take into account important effects of the geometry of diverted tokamaks—in particular, the effect of X-point magnetic shear and the termination of field lines on divertor plates—are presented. We first generalize our previous ‘heuristic boundary condition’ which describes, in a lumped model, the closure of currents in the vicinity of the X-point region to encompass three current-closure mechanisms. We then use this boundary condition to derive the dispersion relation for low-beta flute-like modes in the divertor-leg region under the combined drives of curvature, sheath impedance and divertor tilt effects. The results indicate the possibility of strongly growing instabilities, driven by sheath boundary conditions, and localized in either the private or common flux region of the divertor leg depending on the radial tilt of divertor plates. We revisit the issue of X-point effects on blobs, examining the transition from blobs terminated by X-point shear to blobs that extend over both the main SOL and divertor legs. We find that, for a main-SOL blob, this transition occurs without a free-acceleration period as previously thought, with X-point termination conditions applying until the blob has expanded to reach the divertor plate. We also derive propagation speeds for divertor-leg blobs. Finally, we present fluid simulations of the C-Mod tokamak from the BOUT edge fluid turbulence code, which show main-SOL blob structures with similar spatial characteristics to those observed in the experiment, and also simulations which illustrate the possibility of fluctuations confined to divertor legs.

Fault location algorithm for cross-bonded cables using the singularity of the sheath impedance matrix

This paper proposes a fault location algorithm for cross-bonded cables. The algorithm uses nonlinear equations that describe the voltage drops between both ends of core conductors and sheaths in terms of the phase voltages and currents of both the local and remote ends. Arranging these equations about the sheath currents yields a sheath impedance matrix, which is singular independently of the fault distance. Due to this singularity, the equations have no solution or an infinite number of solutions. The proposed algorithm finds the condition for which a solution to the equations exists. Since the equation of the condition is linear and explicit, the fault location can be found easily. Test results indicate that the algorithm accurately estimates the fault distance regardless of fault impedance, fault type, and fault section.

Simple method for ion current measurement at RF biased electrode

Samples are usually placed on an RF bias electrode for an inductively coupled plasma device. The RF current and voltage waveforms at the bias electrode were measured. The current through the stray capacitance was cancelled by an LC cancel circuit. Only the sheath impedance at the bias electrode was considered as the equivalent circuit. The RF voltage greatly depended on the RF power, but the RF current slightly depended on the RF power. The conduction current could be related to the plasma density. The incident ion current to the bias electrode was given by the half value of the amplitude of the conduction current. The obtained incident ion current agreed with those obtained from different methods.

Noninvasive monitoring of ion energy drift in an inductively coupled plasma reactor

A noninvasive method for monitoring ion current and ion kinetic energy has been used to monitor drift in an inductively coupled, rf-biased plasma reactor. The technique detects a slow decrease in ion current over time caused by the deposition of a conductive layer on the dielectric window of the inductive source. Accompanying this drift in ion current are changes in ion energy which, depending on conditions, may be large or small, increasing or decreasing. The changes in ion energy are explained by three different kinds of mechanisms: bias voltage effects, sheath impedance effects, and ion transit-time effects. For each mechanism, a simple analysis is given that allows one to estimate the resulting drift in ion energy for a given drift in ion current. The mechanisms of ion energy drift, and the monitoring technique itself, are not limited to the particular experimental conditions of this study; rather, they apply to a wide range of plasmas and reactors. Drifts in ion energy caused by the mechanisms reported here have undoubtedly occurred in many plasma reactors but have gone largely or entirely unnoticed for lack of any reliable method to detect them.

Dynamic model and electrical characteristics for rf-biased electronegative plasma sheath

The dynamic model for the sheath of an RF-biased electronegative plasma is developed. The low-pressure high-density plasma conditions are assumed and considered as an electric-field-free boundary. The Bohm criterion for collisionless sheath is assumed to be valid and the presheath region is separately considered in calculating the sheath properties. The electron density n/sub e/ and the electronegativity /spl alpha/ /spl equiv/ n/sub -//n/sub e/ are taken to be determined independently of the sheath dynamics. The time-resolved wave forms of the sheath potential and thickness are obtained. The characteristics for the RF power dissipation mechanisms are also investigated. The RF bias power is assumed to be dissipated through two power loss channels - the first is due to ion acceleration in the sheath and the second is due to the electron heating at the plasma-sheath boundary. From the power loss point of view, the equivalent circuit model is developed and the sheath impedance is calculated. The electronegativity, as well as the current and RF bias frequency, is found to be an important factor in determining the electrical characteristics for the RF-biased electronegative plasma sheath.

Modeling of harmonic contributions to non-symmetrical RF plasmas

An analytical solution for the harmonic contributions to the dynamics of an asymmetrically driven capacitively coupled plasma is obtained under the assumptions of time-independent, collisionless ion motion, inertialess electrons and uniform current density. Modeling is performed considering the effect of an arbitrary Nth harmonic sinusoidal current. The overall effect is determined by summing up the effects due to all the current harmonics. The expressions for the instantaneous and time averaged electric field within the sheath, the non-linear oscillation motion of the electron sheath boundary, the effective sheath impedance, the bulk plasma impedance and finally the overall plasma impedance are obtained. Experimental results are shown to be in good qualitative agreement with the theoretical model.

Ion current analysis in pulsed RF plasma as a fundamental research of plasma-based ion implantation

Analysis of the target current in plasma-based ion implantation (PBII) has been performed using a simple equivalent circuit model. It was found that a current for charging the stray capacitance dominates the initial phase of the voltage pulse. The target voltage decay after turning off the power supply depends on the sheath impedance and the stray capacitance as well. It is therefore very important to reduce the stray capacitance in order to suppress unfavorable effects, such as sputtering with low energy ions.

Ion energy distributions and sheath voltages in a radio-frequency-biased, inductively coupled, high-density plasma reactor

Ion energy distributions were measured at a grounded surface in an inductively coupled, high-density plasma reactor for pure argon, argon–helium, and argon–xenon discharges at 1.33 Pa (10 mTorr), as a function of radio-frequency (rf) bias amplitude, rf bias frequency, radial position, inductive source power, and ion mass. The ground sheath voltage which accelerates the ions was also determined using capacitive probe measurements and Langmuir probe data. Together, the measurements provide a complete characterization of ion dynamics in the sheath, allowing ion transit time effects to be distinguished from sheath impedance effects. Models are presented which describe both effects and explain why they are observed in the same range of rf bias frequency.

Experimental test of models of high-plasma-density, radio-frequency sheaths

Measurements of the rf-bias current and voltage applied to the substrate electrode of a high-density plasma reactor, combined with dc measurements of the ion current at the electrode and capacitive probe measurements of the plasma potential, enabled a rigorous, quantitative test of models of the electrical properties of the sheath adjacent to the electrode. The measurements were performed for argon discharges at 1.33 Pa (10 mTorr), ion current densities of 1.3--13 ${\mathrm{m}\mathrm{A}/\mathrm{c}\mathrm{m}}^{2}$, rf-bias frequencies of 0.1--10 MHz, and rf-bias voltages from less than 1 to more than 100 V. From the measurements, the current, voltage, impedance, and power of the sheath adjacent to the electrode were determined and were compared to model predictions. The properties of the opposing sheath, adjacent to grounded surfaces, were also determined. The behavior of the two sheaths ranged from nearly symmetric to very asymmetric. Changes in the symmetry are explained by models of the sheath impedance.

Influence of Discharge Geometry on Power Dissipation and Sheath Impedances in Silane Discharges

The influence of the interelectrode distance on the power consumed in rf silane glow discharges, for two different electrode sizes and at two different silane pressures is reported. The effect of the increasing grounded surface area in contact with the discharge is analysed by using a simplified calculation of the rf and grounded sheath impedances. At all cases the power consumed in the discharge increases with interelectrode distance and is higher for higher pressures, for a constant excitation voltage. The sheath impedances are always higher for lower pressures except for the case of the ground sheath when using the large electrode set.

Dynamic model of the radio-frequency plasma sheath in a highly asymmetric discharge cell

A self-consistent fluid model for the radio-frequency sheath at the powered electrode of a highly asymmetric discharge cell is developed and solved. The model assumes time-independent ion motion and inertialess electrons. The voltage on the powered electrode, assumed to be sinusoidal, is shared between the powered sheath and a series resistance that represents the remainder of the discharge. The model includes ion collisions, sheath conduction currents, and secondary electron emission from the electrode surface. Model results are compared with previous sheath models and with experiment. Current wave forms predicted by the model closely resemble the nonsinusoidal current wave forms measured in highly asymmetric cells. The model accurately predicts the shape of sheath voltage wave forms, but not their dc components. The magnitudes and phases of sheath impedances predicted by the model agree with experimental measurements performed in argon discharges at pressures of 4.0--133 Pa.

Measurements and analysis of antenna impedance aboard the Geotail spacecraft

A practical method of estimating the effective impedance of electric dipole antennas aboard the scientific spacecraft Geotail has been developed. The principle of the newly proposed method is to derive the complex impedance of the dipole antennas immersed in the space plasma by means of the analysis of signal waveforms captured when a calibration signal was imposed directly onto the antennas. The derived complex antenna impedance is expressed as frequency responses of its real and imaginary parts. During the flight of Geotail in the Earth's magnetosphere, the impedance measurements were conducted in various regions of the magnetosphere. It has been confirmed, from the analysis of the measured data, that the impedance of the Geotail antenna forms an equivalent electric circuit consisting of a resistance and a capacitance connected in parallel. It has been found that the resistance value is easily changed by the extremely rare ambient plasma density in the magnetosphere. The validity of the measured values have been examined along a theory of probes in a sheath region, taking into account antenna potentials which are lifted up due to the photoelectron emissions from the antenna surface. The analyzed result shows that the measured values of the antenna resistance are consistent with those within the sheath calculated from the theory. Correlation plots of the capacitance values obtained from both the measurements and the calculations have shown that the major parts of the measured capacitance represent the “sheath capacitance,” but other parts might result from a combination of the sheath impedance and the plasma impedance, in addition to the free‐space capacitance.

Experimental test of models of radio-frequency plasma sheaths

The ion current and sheath impedance were measured at the radio-frequency-powered electrode of an asymmetric, capacitively coupled plasma reactor, for discharges in argon at 1.33–133 Pa. The measurements were used to test the models of the radio frequency sheath derived by Lieberman [IEEE Trans. Plasma Sci. 17, 338 (1989)] and Godyak and Sternberg [Phys. Rev. A 42, 2299 (1990)], and establish the range of pressure and sheath voltage in which they are valid.

Sheath impedance effects in very high frequency plasma experiments

The frequency dependence (13.56–70 MHz) of the ion energy distribution at the ground electrode was measured by mass spectrometry in a symmetrical capacitive argon discharge. Reduced sheath impedance at very high frequency allows high levels of plasma power and substrate ion flux while maintaining low levels of ion energy and electrode voltage. The lower limit of ion bombardment energy is fixed by the sheath floating potential at high frequency, in contrast to low frequencies where only the radio frequency voltage amplitude is a determinant. The capacitive sheaths are thinner at high frequencies which accentuates the high frequency reduction in sheath impedance. It is argued that the frequency dependence of sheath impedance is responsible for the principal characteristics of very high frequency plasmas. The measurements are summarized by simple physical descriptions and compared with a particle-in-cell simulation.