Space Charge Potential Research Articles

Reassessment of the Effect of Space Charge Potential on the Electrical Conductivity of Polycrystalline Ceramics

Reassessment of the Effect of Space Charge Potential on the Electrical Conductivity of Polycrystalline Ceramics

Grain and grain boundary behaviors and electrical transport properties of TiO<sub>2</sub> nanowires under high pressure

In this work, anatase Titanium dioxide (TiO<sub>2</sub>) nanowires are synthesized by the hydrothermal method, and its grain and grain boundary behaviors and electrical properties are investigated by alternating current (AC) impedance method under high pressure (up to 34.0 GPa). The relationship between the frequency dependence of impedance <i>Z''</i> and pressure indicate that the conduction mechanism of anatase phase TiO<sub>2</sub> nanowires in the test pressure range is electronic conductivity. It should be noted that the characteristic peaks of <i>Z''</i> move toward high frequency region with pressure increasing, demonstrating that the effect of grain interior on impedance becomes apparent. Additionally, the overall variation trends of grain and grain boundary resistance go downward with pressure increasing, and the descent rate of grain boundary is larger than those of grain before and after phase transition. However, in a range of phase transition (8.2–11.2 GPa, from anatase to baddeleyite phase), grain boundary resistance shows a discontinuously change (increases to 11.2 GPa and then decreases). Based on the different variation trends of grain and grain boundary resistance, it becomes obvious that the phase transition from anatase to baddeleyite phase first occurs at the surface of grain, and then extends to the interior of grain gradually. Also, as an intrinsic characteristic, the relaxation frequency is independent of the geometrical parameters. The pressure dependence of activation energy is obtained by fitting the pressure dependence of relaxation frequency. The activation energy of grain and grain boundary decrease with pressure increasing, implying that the contribution of pressure on the conductivity of sample is positive. Furthermore, the space charge potential for the whole test pressure range is positive, which is determined by the relationship between pressure and relaxation frequency. This fact illustrates that the anion defects are easily formed in the space charge region, and the oxygen defects are the main inducement for TiO<sub>2</sub> phase transformation.

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

Oxygen transport in single-crystal LaAlO3 substrates

The rates of oxygen incorporation into, and oxygen diffusion in, cubic, nominally undoped ${\mathrm{LaAlO}}_{3}$ were investigated by means of isotope exchange experiments and subsequent time-of-flight secondary ion mass spectrometry analysis. $^{18}\mathrm{O}$ diffusion profiles were introduced into single-crystal samples by annealing in isotope-enriched molecular oxygen ($^{18}\mathrm{O}_{2}$) at various temperatures in the range $873\phantom{\rule{4.pt}{0ex}}\text{K}\ensuremath{\le}T\ensuremath{\le}1173\phantom{\rule{4.pt}{0ex}}\text{K}$ at an oxygen activity of $a{\mathrm{O}}_{2}=0.2$ or at various oxygen activities $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\le}a{\mathrm{O}}_{2}\ensuremath{\le}1$ at $T=983\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. All measured isotope profiles consisted of a sharp drop at the surface, attributed to hindered diffusion through a depletion space-charge zone, followed by a shallow decrease, attributed to faster diffusion in a uniform bulk phase. A numerical description of an entire isotope profile with a single solution of the diffusion equation yielded the tracer diffusion coefficient ${D}^{*}$, the surface exchange coefficient ${k}^{*}$, and the surface space-charge potential ${\mathrm{\ensuremath{\Phi}}}_{0}$. The relatively high activation enthalpy of oxygen diffusion of $\mathrm{\ensuremath{\Delta}}{H}_{{D}^{*}}=(0.90\ifmmode\pm\else\textpm\fi{}0.06)\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ was attributed to oxygen vacancies interacting with cation vacancies. The activation enthalpy for oxygen surface exchange was surprisingly low ($\mathrm{\ensuremath{\Delta}}{H}_{{k}^{*}}<3\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$) in view of the large band gap of ${\mathrm{LaAlO}}_{3}$ ($\ensuremath{\approx}\phantom{\rule{0.28em}{0ex}}5.6\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$).

Excitation and suppression of synchrobetatron resonances in high-intensity hadron linacs

The space-charge potential can be a source of various resonances in high-intensity hadron bunches traveling in linear accelerators at relatively low energy. Those natural resonances, which may occur even without external driving fields, have to be avoided carefully to minimize undesired beam loss. We perform self-consistent multiparticle simulations systematically to locate major resonance stop bands in the tune diagram, starting from equipartitioned and nonequipartitioned beams. Serious excitation of synchrobetatron resonances is confirmed, depending on the emittance condition at injection. It is demonstrated that a synchrobetatron difference resonance of any order can be suppressed strongly by controlling the ratio of the transverse and longitudinal projected emittances. The equipartitioned linac design is shown to broaden the usable operating area in the tune space, though that has almost nothing to do with thermodynamic effects.

Injection of positrons into a dense electron cloud in a magnetic dipole trap

The creation of an electron space charge in a dipole magnetic trap and the subsequent injection of positrons have been experimentally demonstrated. Positrons (5 eV) were magnetically guided from their source and injected into the trapping field generated by a permanent magnet (0.6 T at the poles) using a cross field E × B drift, requiring tailored electrostatic and magnetic fields. The electron cloud is created by thermionic emission from a tungsten filament. The maximum space charge potential of the electron cloud reaches −42 V, which is consistent with an average electron density of (4±2)×1012 m−3 and a Debye length of (2±1) cm. We demonstrate that the presence of this space potential does not hamper efficient positron injection. Understanding the effects of the negative space charge on the injection and confinement of positrons represents an important intermediate step toward the production of a confined electron–positron pair plasma.

Statistics of variations in atmospheric electrical parameters based on a three-dimensional model and field observations

In this work, we study the space-time statistical features of variations in the atmospheric electric field (Ez) and space charge in the atmospheric boundary layer using a three-dimensional model and analysis of observational data. The model is a combination of large-eddy simulation supplemented with a subgrid kinematic model for scalar and the three-dimensional Poisson equation for the electric potential. Based on the calculated evolution of three-dimensional distributions of the space charge and electric potential, the variability of the spectral slopes of variations in the space charge, vertical potential difference, and the vertical component of the electric field Ez is investigated. The vertical profiles of Ez and the frequency power spectra of Ez variations at different heights computed are in reasonable agreement with the observed ones. It is shown that the cross-correlation of Ez at spatially separated points located on one straight line near the earth's surface decreases with increasing distance with a characteristic scale of a few tens meters and has a dependence on the angle between this line and the direction of the wind. Mean large-scale horizontal electric field defined through the position and amplitude of the potential extrema at the same height depends on height non-monotonically having a maximum value of about 5 V/m. Scaling exponents of structure functions for Ez variations are found to be significantly larger than those for space charge variations.

A Critical Examination of the Mott–Schottky Model of Grain-Boundary Space-Charge Layers in Oxide-Ion Conductors

The electrical properties of grain boundaries in ionic conductors are studied most frequently and most easily by Electrochemical Impedance Spectroscopy (EIS). The resistance data obtained in this manner are typically analyzed with the Mott–Schottky space-charge model to extract a space-charge potential. In this study, taking CeO2 containing acceptor-dopant cations and oxygen vacancies as our model system, we calculate impedance spectra by solving the drift–diffusion equation for oxygen vacancies for a bicrystal geometry with space-charge layers at the grain boundary. Three different cases are considered for the behavior of the acceptor-dopant cations: a uniform distribution (Mott–Schottky), an equilibrium distribution (Gouy–Chapman), and a distribution frozen-in from a much higher temperature (restricted equilibrium). Analyzing our impedance data for the restricted-equilibrium case with the Mott–Schottky model, we find that the obtained space-charge potentials are substantially underestimated. In view of such a discrepancy not normally being apparent (the true values being unknown), we propose a specific set of EIS experiments that allow the Mott–Schottky model to be discounted.

Electrical properties of Ca-doped ceria electrolytes prepared by proteic sol-gel route and by solid-state reaction using mollusk shells

Ca-doped ceria (CCO) electrolytes were prepared using two processing approaches, proteic sol-gel synthesis using gelatin (SG) and solid-state reaction (SSR). Mollusk shell powder was used in the SSR method as the main source of Ca. Materials sintered at 1350–1450 °C exhibited relative density above 95% and different microstructural features regarding grain size and morphology. Impedance spectroscopy in air revealed a comparatively better total electrical response of materials prepared by the proteic sol-gel route. CCO ceramics prepared by the SG route have bulk conductivity four times higher than the highest conductivity of samples processed by the SSR route. Electrical properties of the grain boundaries of both series of materials reveal distinct oxygen vacancy concentration profiles and space charge potentials. The role of processing route and sintering schedules was discussed taking into consideration the distinct impact of Ca interaction in the grain boundaries.

Probing Metastable Space-Charge Potentials in a Wide Band Gap Semiconductor.

While the study of space-charge potentials has a long history, present models are largely based on the notion of steady state equilibrium, ill-suited to describe wide band gap semiconductors with moderate to low concentrations of defects. Here we build on color centers in diamond both to locally inject carriers into the crystal and probe their evolution as they propagate in the presence of external and internal potentials. We witness the formation of metastable charge patterns whose shape-and concomitant field-can be engineered through the timing of carrier injection and applied voltages. With the help of previously crafted charge patterns, we unveil a rich interplay between local and extended sources of space-charge field, which we then exploit to show space-charge-induced carrier guiding.

Spectral weight reduction of two-dimensional electron gases at oxide surfaces across the ferroelectric transition

The discovery of a two-dimensional electron gas (2DEG) at the hbox {LaAlO}_3/hbox {SrTiO}_3 interface has set a new platform for all-oxide electronics which could potentially exhibit the interplay among charge, spin, orbital, superconductivity, ferromagnetism and ferroelectricity. In this work, by using angle-resolved photoemission spectroscopy and conductivity measurement, we found the reduction of 2DEGs and the changes of the conductivity nature of some ferroelectric oxides including insulating Nb-lightly-substituted hbox {KTaO}_3, hbox {BaTiO}_3 (BTO) and (Ca,Zr)-doped BTO across paraelectric-ferroelectric transition. We propose that these behaviours could be due to the increase of space-charge screening potential at the 2DEG/ferroelectric regions which is a result of the realignment of ferroelectric polarisation upon light irradiation. This finding suggests an opportunity for controlling the 2DEG at a bare oxide surface (instead of interfacial system) by using both light and ferroelectricity.

Mitigation of grain boundary resistance in La2/3-xLi3xTiO3 perovskite as an electrolyte for solid-state Li-ion batteries

In this work, we report that modification of the chemical composition of grain boundaries of La2/3-xLi3xTiO3 double perovskite, one of the most promising Li-ion conducting solid electrolytes, can be a convenient and versatile way of controlling the space charge potential, leading to a mitigated electrical resistance of the grain boundaries. Two groups of additives are investigated: lithium-enriching agents (Li3BO3, LiF) and 3d metal ions (Co2+, Cu2+), both expected to reduce the Schottky barrier. It is observed that Li-containing additives work effectively at a higher sintering temperature of 1250 °C. Regarding copper, it shows a much stronger positive impact at lower temperature, 1150 °C, while the addition of cobalt is always detrimental. Despite overall complex behavior, it is documented that the decreased space charge potential plays a more important role in the improvement of lithium conduction than the thickness of the grain boundaries. Among the proposed additives, modification of La2/3-xLi3xTiO3 by 2 mol.% Cu2+ results in the space charge potential reduction by 32 mV in relation to the reference sample, and the grain boundary specific conductivity increase by 80%, as measured at 30 °C. Introduced additive allows to obtain a similar effect on the conductivity as elevating the sintering temperature, which can facilitate manufacturing procedure.Graphic abstract

Identification and characterization of high order incoherent space charge driven structure resonances in the CERN Proton Synchrotron

Space charge is typically one of the performance limitations for the operation of high intensity and high brightness beams in circular accelerators. In the Proton Synchrotron (PS) at CERN, losses are observed for vertical tunes above $Q_y=6.25$, especially for beams with large space charge tune shift. The work presented here shows that this behaviour is associated to structure resonances excited by space charge due to the highly symmetric accelerator lattice of the PS, typical for first generation alternating gradient synchrotrons. Experimental studies demonstrate the dependency of the losses on the beam brightness and the harmonic of the resonance, and simulation studies reveal the incoherent nature of the resonance. Furthermore, the calculation of the Resonance Driving Terms (RDT) generated by the space charge potential shows that the operational working point of the PS is surrounded by multiple space charge driven incoherent resonances. Finally, measurements and simulations on both lattice driven and space charge driven resonances illustrate the different behaviour of the beam loss depending on the source of the resonance excitation and on the beam brightness.

Ionically Generated Built‐In Equilibrium Space Charge Zones—a Paradigm Change for Lead Halide Perovskite Interfaces

AbstractMethylammonium lead iodide (MAPI) is the archetype of the intensively researched class of perovskites for photovoltaics. Nonetheless, even equilibrium aspects are far from being fully understood. Equilibrium space charge effects at the MAPI/TiO2 and MAPI/Al2O3 interfaces are discussed, which are of paramount significance for solar cells. Different from the photovoltaic literature in which such built‐in potentials are considered as being generated solely by electronic charge carriers, a generalized picture that considers the equilibrium distribution of both ionic and electronic carriers is applied. Experimental evidence is given that shows it is the ions that are responsible for the equilibrium space charge potential, the reason being a pronounced ion adsorption at the contacts. The electronic redistribution is a sheer consequence of the so‐established electric field. Experiments with mesoporous oxide as well as experiments with MAPbBr3 (MAPBr) indicate photovoltaic relevance and material generality in terms of the choice of the lead‐based perovskite. The occurrence of space charge effects at heterojunctions generated by ionic redistribution is not only a novel concept in photovoltaics, it also provides a new path to modifying charge‐selective interfaces, as well as a better understanding of the behavior in mesoporous systems.

Variability and origins of grain boundary electric potential detected by electron holography and atom-probe tomography.

A number of grain boundary phenomena in ionic materials, in particular, anomalous (either depressed or enhanced) charge transport, have been attributed to space charge effects. Developing effective strategies to manipulate transport behaviour requires deep knowledge of the origins of the interfacial charge, as well as its variability within a polycrystalline sample with millions of unique grain boundaries. Electron holography is a powerful technique uniquely suited for studying the electric potential profile at individual grain boundaries, whereas atom-probe tomography provides access to the chemical identify of essentially every atom at individual grain boundaries. Using these two techniques, we show here that the space charge potential at grain boundaries in lightly doped, high-purity ceria can vary by almost an order of magnitude. We further find that trace impurities (<25 ppm), rather than inherent thermodynamic factors, may be the ultimate source of grain boundary charge. These insights suggest chemical tunability of grain boundary transport properties.

Plasma anisotropy around non-spherical conductive dust particle

This paper presents a computational model that allows self-consistent simulation of plasma distributions around isolated strongly charged dust grains with different geometries: spherical, ellipsoidal, and diskshaped dust particles. All particles in this work were considered conductive and were oriented so that cylindrical symmetry was preserved in the computational area. Dust particles of various shapes were placed in an external field, and the process of ion focusing and the formation of a wake behind them were studied. As a result of the calculation by this model, self-consistent distributions of the space charge and plasma potential around non-spherical dust particles, as well as the dependence of the main characteristics of the wake - the magnitude of the first potential maximum and its position - on the magnitude of the external field was obtained. The analysis of spatial distributions showed that near the dust grains of the same electric capacity almost identical spatial distributions of the space charge and potential are formed. When normalizing the dependence of the wake maximum value on the root of the electric capacitance, all data are described by a single parametric curve with good accuracy, which allows one to predict the plasma parameters around the dust particle without resorting to direct calculations.&nbsp;

Enhancement of insulating properties of polyethylene blends by delocalization type voltage stabilizers

This paper reports on the effects of four voltage stabilizers, m-aminophenylboric acid, 2-methoxy-5-pyridineboric acid, m-aminobenzoic acid and 4-dimethylaminobenzoic acid, on the insulation properties of polyethylene blends. 1 wt% voltage stabilizers were added into low density polyethylene (LDPE) blend containing 10 wt% high density polyethylene (HDPE) by a solution method. Physicochemical and electrical properties of the blends were analyzed by infrared spectroscopy, thermo-gravimetric analysis, differential scanning calorimetry, electric tree initiation tests, space charge and surface potential decay measurements. The results showed that the addition of the voltage stabilizers had a little effect on the thermal stability and melting properties of the LDPE/HDPE blend. When the voltage stabilizers were included into the blends, the tree initiation voltage (TIV) increased, in particular the blend with m-aminobenzoic acid showed the highest increase of 41% compared to the reference LDPE/HDPE. It was found that space charge accumulations of the blends were apparently suppressed by adding voltage stabilizers. Moreover, the blend with the m-aminobenzoic acid had the least space charge accumulation. The surface potential decay rate of the blends was significantly increased after adding voltage stabilizers. Quantum chemical calculations illustrated that the HOMO-LUMO energy gap was closely related to the TIV of the blends, whereas the m-aminobenzoic acid has the lowest energy gap level and the best effect of restraining the electrical tree initiation. The trap level calculation showed that the trap depth in the blends decreased with the addition of the voltage stabilizers, which was beneficial to suppress the accumulation of space charge in the materials.

Insight into impurity scavenging effect of gadolinium-doped ceria electrolytes

In this study, Ce0.89+xGd0.1−2xSrxEu0.01O2−δ (x = 0–0.04) ceramic electrolytes sintered at different temperatures were prepared and the impurity scavenging effect of Sr2+ dopants on their grain boundary (GB) electrical properties were investigated. The phase compositions, microstructures, and ionic conductivities of the samples were investigated using X-ray diffraction, scanning electron microscopy, and AC impedance spectroscopy, respectively. The incorporation of Sr2+ improved the overall GB conduction of the electrolytes by decreasing their GB area and space-charge potential. It hindered conduction to some extent by weakening the impurity dilution effect. The scavenging effect could be observed only when the sintering temperature was higher than the eutectic temperature of Si GB impurities. At low sintering temperatures, the Sr2+ dopants could not scavenge the GB impurities and increased the GB impurity coverage proportion. The findings of this study provide insights into the optimisation of the GB electrical properties of oxygen-ion conductors by selecting appropriate dopants and sintering temperatures to induce the GB impurity scavenging effect.

Spectral Galerkin solver for intense beam Vlasov equilibria in nonlinear constant focusing channels.

A numerical method is described for producing stationary solutions of the Vlasov-Poisson system describing a relativistic charged-particle beam in a constant focusing accelerator channel, confined transversely by a general (linear or nonlinear) focusing potential. The method utilizes a variant of the spectral Galerkin algorithm to solve a nonlinear partial differential equation (PDE) in two degrees of freedom for the beam space charge potential in equilibrium. Numerical convergence with an increasing number of computed spectral modes is investigated for several benchmark problems. Preservation of the stationary phase space density is verified using a strongly nonlinear focusing channel based on the Integrable Optics Test Accelerator at Fermi National Accelerator Laboratory.

Space Charge Driven Resonances in the CERN PS

In the CERN Proton Synchrotron space charge driven resonances are excited around the operational working point due to the periodicity of the optics functions. In this paper, the resonances are studied using analytical methods, i.e. the evaluation of the resonance driving terms connected to the space charge potential of Gaussian distributions. Furthermore, the resonances are characterized in measurements and simulations for various beams. The beams considered are different in terms of brightness, in order to study the dependence of the resonance strength on the space charge force.