Space Charge Saturation Research Articles

Injection-limited and space-charge-limited conduction in wide bandgap semiconductors with velocity saturation effect

Carrier conduction in wide bandgap semiconductors (WBS) often exhibits velocity saturation at the high-electric field regime. How such effects influence the transition between contact-limited and space-charge-limited current (SCLC) in a two-terminal device remains largely unexplored thus far. Here, we develop a generalized carrier transport model that includes contact-limited field-induced carrier injection, space charge, carrier scattering, and velocity saturation effect. The model reveals various transitional behaviors in the current–voltage characteristics, encompassing Fowler–Nordheim emission, trap-free Mott–Gurney (MG) SCLC, and velocity-saturated SCLC. Using GaN, 6H–SiC and 4H–SiC WBS as examples, we show that the velocity-saturated SCLC completely dominates the high-voltage (102–104 V) transport for typical sub-μm GaN and SiC diodes, thus unraveling velocity-saturated SCLC as a central transport mechanism in WBG electronics.

Time-domain signal analysis of dielectric response of nonlinear SDBD thruster in near space

The nonlinear time domain response signals of surface dielectric barrier discharge (SDBD) are the basis for studying the energy loss of SDBD thruster. This paper is based on the construction of a double layer lumped parameter circuit model in solid dielectric and discharge plasma regions; based on virtual instrument technology, a test device for AC dielectric characteristics of a nonlinear SDBD thruster was built to obtain the time domain signals of AC voltage and response current. According to the characteristic spectral curve of the voltage and the response current signal in the time domain, the response current is decomposed into resistive current (conduction current) and capacitive current (relaxation current) by an appropriate algorithm. The experimental results show that the response current in the discharge plasma region is mainly the capacitive current, and the peak capacitive current is about 2.9 times of the peak resistance current; Relaxation planned loss is the main form of energy loss in the discharge plasma region. Due to space charge limiting current effect and space charge saturation effect, the static and dynamic resistance of discharge plasma region have platform area and negative resistance characteristics respectively; Both static and dynamic capacitance have negative capacitor characteristics.

Mobility of charge carriers in mineral oil and ester fluids

New, more stringent environmental requirements for electrical insulation liquids have led to the development of novel, more environment-friendly liquid dielectrics. Ester fluids, introduced several decades ago, provide a viable alternative to traditional mineral insulating liquids. In order to expand the practical applications of these novel dielectric fluids, their dielectric and electrical parameters should be established. One of the critical parameters that affects and governs the development of pre-breakdown processes in insulating liquids is the mobility of charge carriers. In the present paper, the mobility of charge carriers in commercially available synthetic and natural insulating ester fluids and in a mineral insulating oil were obtained using two methods, the time of flight and the space charge saturation current methods. The mobility was obtained for a wide range of electrical field magnitudes. It was found that the mobility of charge carriers is greater in the mineral oil than in both, the natural and synthetic, ester fluids. It was also established that the mobility is higher for higher applied electric field. The results of this work will help in characterizing liquid dielectrics and in optimizing high-voltage systems in which liquid dielectrics, including natural and synthetic ester fluids, are used.

Space Charge Effects on Ion Mobility Spectrometry.

We study the space charge limited maximal current density j″ of mobility-selected ions that can be transmitted in ion mobility spectrometry (IMS). Theory and experiments focus on differential mobility analyzers (DMAs), but are readily generalizable to other IMS devices. Repulsion between the ions in the cloud leads to beam spreading, with significant broadening once the ion number density n becomes comparable to the space charge saturation limit nsat = εoEo/(eΔ). Δ is the distance traversed by the ions in the direction of an externally imposed electric field Eo, and e is the charge on each ion. For ions of electrical mobility Z, j″ is then limited below j″sat = ZEoensat = ZεoEo2/Δ. A theory including diffusion and space charge effects is developed that reduces to Burgers' exactly solvable equation. The theory is tested in experiments with room temperature electrosprays (ES) of 100mM [ethyl3N+-formate-] in methanol. This spray produces primarily a single ionic species at very high initial concentration n, which may be tuned above or below nsat by varying the distance from the ES emitter to the inlet slit of the DMA. Mobility-selected ion densities n > 3.108 ions/cm3 are achieved, with n~nsat, and with drastically broadened mobility peak shapes having the approximate top hat-predicted shapes. However, the largest n values approaching nsat are not quantitatively measurable because the densest sprays do not fill the outlet slit length. Graphical Abstract .

Space charge saturation in multipactor discharges with parallel magnetic field

Numerical and theoretical models were developed to investigate space-charge effects in a multipactor discharge with an applied magnetic field. The magnetic field was assumed to be parallel to the RF electric field, and only the space-charge effects in the direction perpendicular to the fields were studied. Inclusion of space-charge effects allowed investigation of a saturation mechanism driven by electron diffusion. Numerical simulations showed that saturation of the multipactor discharge could be reached as diffusion balanced the electron production due to secondary emission. It was found that the steady state density reaches a limit as RF voltage was increased. Fluid equations for the electron motion were used to describe electron diffusion and derive an expression for the steady-state electron density in a typical multipactor discharge. It was found that in the presence of a magnetic field, electrons may be trapped by executing a slow rigid-rotor rotation, as described by the Brillouin condition. The electron behavior was found to be dynamic, satisfying the electron trapping condition while the electrons were moving between electrodes and violating the Brillouin condition near the electrodes leading to larger diffusion losses. Numerical simulations show that Brillouin trapping due to an applied parallel magnetic field can significantly increase saturation density by up to two orders of magnitude.

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir–Blodgett law

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r)=φ(r(τ))) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle–beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

Dielectric properties of natural ester, synthetic ester midel 7131 and mineral oil diala D

The insulating liquids used in industrial applications are typically mineral oils. In recent years however, significant attention has been paid to alternative insulating fluids, including synthetic and natural ester liquids. In order to expand their practical applications, it is important to have detailed information on their dielectric properties. In this present paper, the dielectric properties of synthetic ester, Midel 7131; mineral oil, Shell Diala D; and vegetable (rapeseed) oil have been investigated. It has been shown that Midel 7131 has a higher ac breakdown voltage (27.6 kV) as compared with Diala D oil (26.4 kV) and rapeseed oil (24.6 kV). However, the breakdown voltage of the Diala D oil has the smallest standard deviation (7%) amongst the tested liquids (13% for Midel 7131 and 11% for rapeseed oil). Statistical analysis of the breakdown voltages has been conducted and it has been shown that the ac breakdown voltages can be described by a normal distribution. dc I-V characteristics have been measured and the space charge saturation regime has been observed for all three liquids starting from ~9 kV for positive energisation and ~10 kV for negative energisation in the point-plane topology. Apparent mobilities of the charge carriers in the tested liquids have been obtained using I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> -V curves; these mobilities can be used for calculation of the space charge influenced distribution of the electric field in liquid insulators stressed with dc voltage. Such analysis can be important for design and exploitation of HVDC power systems.

Simulations of multipactor breakdown in low-pressure background gas for angled dielectrics in DC

We report on 2D particle-in-cell (PIC) simulations of electrical breakdown incorporating single-surface multipactor with background-gas ionization. The system for study is a semi-infinite, two-electrode Bergeron geometry with an angled dielectric in steady-state fields, with a background gas at variable low pressure. For pressures below a few tens of Pa (a few hundred mTorr), discharges are dominated by multipactor breakdown initiated by a triple-point source; the breakdown condition is well-characterized by an average secondary-emission coefficient greater than unity at the onset of anodic current, otherwise a dark-current develops due to space-charge saturation. The magnitude of the anode current is driven by the development of a multipactor front comprising an enhanced current front followed by a steady-state tail in which dielectric-surface fields no longer support net secondary-emission, resulting in a non-multiplicative arc. Additional avalanche phenomena occur with increased pressure >133.3 Pa (>1 Torr), where space-charge coupling leads to oscillations in an otherwise DC discharge, largely driven by the development and quenching of the multipactor front.

Exciton transport and electron mobility of organized aggregates of cationic dye thiocyanates

Films of cationic dye thiocyanates adsorbed on copper based substrates form organized structures by a process of templated self-assembly. The growth process is initiated by strong S-bonding of thiocyanate ions to Cu sites, followed by repetitive and alternate bonding of dye cations and thiocyanate anions by electrostatic and dipolar forces. Rhodamine B thiocyanate and several other cationic dye thiocyanates solid films deposited this way exhibit J-aggregation behavior with large red-shifts in the absorption spectrum. Photoelectrochemical experiments with Rhodamine B thiocyanate deposited CuSCN cathodes indicated exciton diffusion lengths of order of 100 nm and space charge saturation current measurements suggested nearly three orders of magnitude enhancement of the electron mobility in the J-aggregated film. The photovoltaic properties of heterojunctions sandwiching J-aggregated dye films between n- and p-type semiconductor surfaces are investigated for potential application as solar cells and photon detectors.

A two-dimensional hybrid model of the Hall thruster discharge

Particle-in-cell methods are used for ions and neutrals. Probabilistic methods are implemented for ionization, charge-exchange collisions, gas injection, and particle-wall interaction. A diffusive macroscopic model is proposed for the strongly magnetized electron population. Cross-field electron transport includes wall collisionality and Bohm-type diffusion, the last one dominating in most of the discharge. Plasma quasineutrality applies except for space-charge sheaths, which are modeled taking into consideration secondary-electron-emission and space-charge saturation. Specific weighting algorithms are developed in order to fulfil the Bohm condition on the ion flow at the boundaries of the quasineutral domain. The consequence is the full development of the radial plasma structure and correct values for ion losses at lateral walls. The model gains in insight and physical consistency over a previous version, but thrust efficiency is lower than in experiments, indicating that further model refinement of some phenomena is necessary.

Conduction and breakdown mechanismsin transformer oil

With a fast coaxial test setup using high speed electrical and optical diagnostics, prebreakdown current pulses and shadowgraphy images are measured for direct current (dc) breakdown in Univolt 61 transformer oil. Also, dc currents across the gap are measured using a high sensitivity electrometer. The conduction and breakdown mechanisms in transformer oil as function of applied hydrostatic pressures are quantified. Together, this information provides data on the development of current flow in the system. We have identified three stages in the conduction process prior to breakdown for highly nonuniform fields. Stage 1 is characterized by a resistive current at low fields. Increasing the applied electric field lowers the effective barrier at the metal/dielectric interface allowing a "tunneling" mechanism to begin, leading to the rapid rise in the injection current observed in stage 2. In stage 3, at high fields, the current reaches space charge saturation with an apparent mobility of 3/spl middot/10/sup -3/ cm/sup 2//V/spl middot/s prior to breakdown. The processes of final breakdown show a distinct polarity dependence. A strong pressure dependence of the breakdown voltage is recorded for negative needle/plane breakdown; a 50% reduction in breakdown voltage is observed when the hydrostatic pressure is lowered from atmospheric pressure to hundreds of mtorr. Positive needle discharges show a reduction of only about 10% in breakdown voltage for the reduced pressure case. Weak pressure dependence indicates the breakdown mechanism does not have a strong gaseous component. We will discuss possible links between conduction current and dc breakdown.

Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior

Experimental and theoretical results indicate that miniaturized micron-sized nonlinear beam phenomenology in photorefractives leads to a regime qualitatively distinct from solitonlike propagation on consequence of the specific role of space-charge saturation. In the highly modulated conditions typical of beams, this contribution amounts to an effective electron self-action.

Measurements of secondary electron emission effects in the Hall thruster discharge

The dependence of the maximum electron temperature on the discharge voltage is studied for two Hall thruster configurations, in which a collisionless plasma is bounded by channel walls made of materials with different secondary electron emission (SEE) properties. The linear growth of the temperature with the discharge voltage, observed in the channel with a low SEE yield, suggests that SEE is responsible for the electron temperature saturation in the thruster configuration with the channel walls having a higher SEE yield. The fact that the values of the electron temperature at saturation are rather high may indirectly support the recently predicted kinetic regime of the space charge saturation of the near-wall sheath in the thruster discharge. A correlation between the effects of the channel wall material on the electron temperature and the electron cross-field current was also observed.

Partial trapping of secondary-electron emission in a Hall thruster plasma

Secondary-electron emission at the ceramic walls of a Hall thruster modifies the potential jump of the wall Debye sheaths and thus the electron energy losses to the wall. Because of the low plasma collisionality the two counterstreaming beams of secondary electrons are not expected to be totally trapped within the bulk of the discharge. In order to analyze the effects of partial trapping of secondary electrons on the presheath∕sheath radial structure, a macroscopic model is formulated. The plasma response depends on the secondary electron emission yield and the trapped fraction of secondary electrons. The sheath potential and wall energy losses are determined mainly by the net current of secondary electrons in the sheaths. For any practical value of the secondary emission yield, the zero-trapping solution is very similar to the zero secondary emission case. Space charge saturation of the sheaths is unattainable for weak trapping. In all cases, secondary electrons have a weak effect on the presheath solution and the ion flux recombined at the walls.

Wall material effects in stationary plasma thrusters. II. Near-wall and in-wall conductivity

Simulations and experimental characterizations of a stationary plasma thruster are compared for four different wall materials to investigate near-wall conductivity (dielectric materials) and in-wall conductivity (conducting materials) in such a discharge. Using a one-dimensional transient fluid model that takes into account a possible electron temperature anisotropy, it is shown that electron-wall backscattering plays a crucial role by maintaining a relatively high electron temperature along the magnetic field lines which in turn drives large electron currents toward the walls. The large differences in discharge current observed experimentally for the dielectric materials are qualitatively recovered, confirming that near-wall conductivity results from the combined effects of secondary electron emission and electron backscattering. A clear correlation is found between the appearance of space charge saturation at the walls and a jump of the discharge current observed in experiments when varying the discharge voltage or the magnetic field. The anomalously high values of discharge current observed experimentally with graphite are also correctly recovered in simulations, which highlight a plasma short-circuiting effect resulting from in-wall currents.

Non-linear photoemission from polycrystalline molybdenum irradiated by 790 nm–150 fs laser pulses

The total yield photoemission of a polycrystalline molybdenum sample irradiated by 790 nm–150 fs laser pulses is measured in the absence of space charge saturation. The extracted charge versus the laser intensity, measured over three decades of the extracted charge, which represents a significant extension of the previous experiments, gives us the opportunity to test the so-called thermally assisted non-linear photoemission model. The present results show non-linear photoemission behavior that can be explained, as expected, by a thermally assisted 3-photon emission. However a pure 4-photon emission could not be discarded. To take aim at clarifying this question the related non-linear coefficients are calculated and a scaling law for the probability of different multiphoton orders is proposed.

Sheath and presheath potentials for anode, cathode and floating plasma-facing surfaces

Simple expressions for sheath and presheath potentials are provided for anode, cathode and electrically floating plasma-facing surfaces. The expressions are developed using a fully kinetic theory that includes the effects of secondary or thermionic electron emission from the plasma-facing surface. The emission can be space-charge limited and a criterion is provided for the onset of space-charge saturation.

Nonlinear photoemission from W and Cu investigated by total-yield correlation measurements

Nonlinear photoelectric emission from Cu and W is investigated by subpicosecond laser pulses. Using a pump and probe technique, total-yield correlation measurements are obtained without space-charge saturation. The effects of the heating of the conduction electrons induced by the laser pulses are shown, considering the peak to background contrast ratio of the experimental correlation trace. The present analysis clarifies the consequences of a transient nonequilibrium temperature difference between electrons and the lattice on the correlation trace, confirming for W the presence of a thermally assisted photoemission mechanism.

Boundary conditions including sheath effects at a plasma-facing surface

It has recently been reported that space-charge saturation occurs adjacent to almost every commonly used plasma-facing material for plasma temperatures above {approximately}50 eV. An electron emission coefficient, defined as the average number of surface-emitted electrons per incident plasma electron, which is near or above unity is responsible for the occurrence of space-charge saturation. With this motivation, a fully kinetic self-consistent theory capable of describing the plasma sheath under conditions of space-charge saturation is developed. The theory is then used to obtain boundary conditions which are suitable for incorporation into computer programs which simulate plasmas. {copyright} {ital 1997} {ital The American Physical Society}

An extended parametrization of gas amplification in proportional wire chambers

It is normally assumed that the gas amplification in proportional chambers is a function of Townsend's first ionization coefficient, α, and that α is a function of the anode surface electric field only. Experimental measurements are presented demonstrating the breakdown of the latter assumption for electric fields, X, greater than about 150 V/cm/Torr on the anode wire surface for a gas mixture of 80/20 argon/methane. For larger values of X, the parametrization of the proportional gas gain data requires an additional term related to the gradient of the electric field near the wire. This extended gain parametrization remains valid until the onset of nonproportional contributions such as positive ion space charge saturation effects. Furthermore, deviations of the data from this parametrization are used to measure the onset of these space charge effects. A simple scaling dependence of the gain data on the product of pressure and wire radius over the whole proportional range is also demonstrated.