Steady-state Charge Distribution Research Articles

Spatiotemporal imaging of charge transfer in photocatalyst particles.

The water-splitting reaction using photocatalyst particles is a promising route for solar fuel production1-4. Photo-induced charge transfer from a photocatalyst to catalytic surface sites is key in ensuring photocatalytic efficiency5; however, it is challenging to understand this process, which spans a wide spatiotemporal range from nanometres to micrometres and from femtoseconds to seconds6-8. Although the steady-state charge distribution on single photocatalyst particles has been mapped by microscopic techniques9-11, and the charge transfer dynamics in photocatalyst aggregations have been revealed by time-resolved spectroscopy12,13, spatiotemporally evolving charge transfer processes in single photocatalyst particles cannot be tracked, and their exact mechanism is unknown. Here we perform spatiotemporally resolved surface photovoltage measurements on cuprous oxide photocatalyst particles to map holistic charge transfer processes on the femtosecond to second timescale at the single-particle level. We find that photogenerated electrons are transferred to the catalytic surface quasi-ballistically through inter-facet hot electron transfer on a subpicosecond timescale, whereas photogenerated holes are transferred to a spatially separated surface and stabilized through selective trapping on a microsecond timescale. We demonstrate that these ultrafast-hot-electron-transfer and anisotropic-trapping regimes, which challenge the classical perception of a drift-diffusion model, contribute to the efficient charge separation in photocatalysis and improve photocatalytic performance. We anticipate that our findings will be used to illustrate the universality of other photoelectronic devices and facilitate the rational design of photocatalysts.

Silicon nanocluster anion-argon cation recombination via hybrid continuum-molecular dynamics calculations

Prediction of the charge distribution on particles in an aerosol is critical not only in electrical mobility based characterization methods, but also in understanding the role that charging plays in particle growth in gas phase synthesis reactors. The latter is particularly important in non-thermal plasma synthesis reactors, wherein nanoclusters form and grow from vapor phase precursors in a high electron and high ion density environment. In plasmas, because free electrons are much less massive and much more mobile than positive gas ions, nanocluster charge distributions are biased negative. However, neutral or even positively charged nanoclusters may exist, depending on the rate of nanocluster-gas ion recombination, and nanocluster-nanocluster collisions may greatly contribute to nanocluster growth if not Coulombically suppressed. To better understand the charge distribution on nanoclusters in non-thermal plasma synthesis systems, we applied a recently developed collision rate calculation method, i.e. the continuum-molecular dynamics (C-MD) method, to examine recombination of Sinz nanoclusters (n=47,91,266,&494, z=−1,&−2) and Ar+ cations at 300 K and pressures from 103.5−106 Pa, in argon neutral gas. With collision rate coefficients from the C-MD approach, nanocluster steady-state charge distributions were calculated. C-MD determined recombination rate coefficients are found to be higher than those from the traditionally-used limiting sphere theory approach of Fuchs outside of the continuum limit, leading to charge distributions which, although biased towards negative charge levels, are less biased than predicted by the traditional limiting sphere method, with differences particularly noticeable at lower pressures. Application of C-MD recombination coefficients in steady-state charge distribution calculations shows that the fraction of positively charged nanoclusters in a non-thermal plasma would be negligibly small; however, there is an appreciable fraction of neutral nanoclusters, and hence nanocluster-nanocluster collisions cannot be neglected in modeling particle growth in plasma reactors.

High-performance tunable resonant electro-optical modulator based on suspended graphene waveguides.

The exceptional tunable waveguiding characteristics of graphene surface plasmons have remained unrivaled since it has inspired many electro-optical (EO) devices in terahertz (THz) and mid-infrared (MIR) photonic circuits. We propose and numerically investigate a low-loss, highly extinctive resonant EO modulator based on a suspended graphene plasmonic waveguide. Unlike other resonance-based modulators, the input power has negligible interaction with lossy resonance cavity in on-state, remarkably reducing the losses. Achieving the insertion loss (IL) of 1.3 dB and the extinction ratio (ER) of 22 dB within a footprint less than 3 µm2 substantiates the superiority of the proposed structure. The charge transport simulations are first conducted to calculate the steady-state charge distribution. The three-dimensional finite-difference time-domain (3D-FDTD) method is utilized to monitor the guided wave propagation and modulation properties. We show that the transmission spectrum is highly dependent upon geometric parameters of the structure, and the modulator can be effectively tuned to operate at the desired wavelength by applying a suitable gate voltage. Simulation results show the modulation bandwidth of 71 GHz corresponding to the total capacitance of 4.8 fF within the active area. The novel EO modulator structure has shown great potentiality and flexibility to find other applications in MIR and THz integrated circuits like controllable notch filters and switches.

Performance of bipolar diffusion chargers: Experiments with particles in the size range of 100 to 900 nm

ABSTRACTAccurate measurement of particle size distribution using electrical-mobility techniques requires knowledge of the charging state of the sampled particles. A consistent particle charge distribution is possible with bipolar diffusion chargers operated under steady-state condition. Theoretical steady-state charge distributions for bipolar charging are well established but recent studies have shown that the performance of particle chargers is a strong function of particle size, particle concentration, ion source, and charger operating conditions. Most of these studies have focused on particles smaller than 100 nm and the applicability of these results for particles larger than 100 nm must be investigated. In this study, experimentally obtained singly-charged and doubly-charged fractions are compared against theoretical predictions for particles in the size range of 100 to 900 nm. The experimental results show that the commercial soft X-ray charger performs as theoretically-predicted over the range of ...

Charging and coagulation of radioactive and nonradioactive particles in the atmosphere

Abstract. Charging and coagulation influence one another and impact the particle charge and size distributions in the atmosphere. However, few investigations to date have focused on the coagulation kinetics of atmospheric particles accumulating charge. This study presents three approaches to include mutual effects of charging and coagulation on the microphysical evolution of atmospheric particles such as radioactive particles. The first approach employs ion balance, charge balance, and a bivariate population balance model (PBM) to comprehensively calculate both charge accumulation and coagulation rates of particles. The second approach involves a much simpler description of charging, and uses a monovariate PBM and subsequent effects of charge on particle coagulation. The third approach is further simplified assuming that particles instantaneously reach their steady-state charge distributions. It is found that compared to the other two approaches, the first approach can accurately predict time-dependent changes in the size and charge distributions of particles over a wide size range covering from the free molecule to continuum regimes. The other two approaches can reliably predict both charge accumulation and coagulation rates for particles larger than about 0.04 micrometers and atmospherically relevant conditions. These approaches are applied to investigate coagulation kinetics of particles accumulating charge in a radioactive neutralizer, the urban atmosphere, and an atmospheric system containing radioactive particles. Limitations of the approaches are discussed.

The effect of single-particle charge limits on charge distributions in dusty plasmas

An analytical expression for the stationary particle charge distribution in dusty plasmas is derived that accounts for the existence of single-particle charge limits. This expression is validated by comparison with the results of Monte Carlo charging simulations. The relative importance of the existence of charge limits for various values of the ratio of electron-to-ion density and ion mass is examined, and the effect of charge limits on the transient behavior of the charge distribution is considered. It is found that the time required to reach a steady-state charge distribution strongly decreases as the charge limit decreases, and that the existence of charge limits causes high-frequency charge fluctuations to become relatively more important than in the case without charge limits.

The Bipolar Diffusion Charging of Nanoparticles: A Review and Development of Approaches for Non-Spherical Particles

Theoretical and experimental analyses of the steady state, bipolar diffusion charge distribution on nanoparticles are reviewed. This charge distribution plays a critical role in electrical mobility measurements of nanoparticle size distribution functions, where it is approximated via empirical regression equations. While the regression approach has been broadly successful, there remain several unresolved issues related to charge distribution calculations. Specifically, research to date has not revealed a method to reliably calculate nanoparticle-ion collision rates in the presence of strong attractive potentials, charge distribution predictions do not routinely consider the mass and (electrical) mobility distributions of the charging ions, and calculation approaches applicable to both spherical and nonspherical particles have not been compared to experimental data. In light of these issues, we examine the steady-state bipolar charge distribution on gold nanospheres and gold nanorods via tandem differentia...

Charging of nanoparticles in stationary plasma in a gas aggregation cluster source

Clusters that grow into nanoparticles near the magnetron target of the gas aggregation cluster source (GAS) may acquire electric charge by collecting electrons and ions or through other mechanisms like secondary- or photo-electron emissions. The region of the GAS close to magnetron may be considered as stationary plasma. The steady state charge distribution on nanoparticles can be determined by means of three possible models—fluid model, kinetic model and model employing Monte Carlo simulations—of cluster charging. In the paper the mathematical and numerical aspects of these models are analyzed in detail and close links between them are clarified. Among others it is shown that Monte Carlo simulation may be considered as a particular numerical technique of solving kinetic equations. Similarly the equations of the fluid model result, after some approximation, from averaged kinetic equations. A new algorithm solving an in principle unlimited set of kinetic equations is suggested. Its efficiency is verified on physical models based on experimental input data.

The mass–mobility distributions of ions produced by a Po-210 source in air

We utilized a differential mobility analyzer–mass spectrometer (DMA–MS) with a high resolving power (~45) parallel plate DMA to measure the masses and mobilities of positive and negative ions generated in dry, particle free air with a 10mCi Po-210 α-irradiation source. We are able to chemically identify 6 positive ions and 25 negative ions in spectra. The positive ions detected were generated by protonation, and included protonated acetone (59Da), protonated bis-(2-ethylhexyl)phthalate (391Da), and protonated cyclic polydimethylsiloxanes. The negative ions detected were all deprotonated, and included Teflon-derived perfluoralkanoate ions, long chain alcohol derived alkoxide ions, and the nitrate ion, which, despite its low mass and high mobility was the most abundant ion in negative spectra. Most detected ions can be traced back to system components or to compounds used in the manufacture of system components. Though clearly the detected ions are system specific, the conditions employed were similar to those used in many laboratory scale aerosol measurement systems. The mobility–mass relationship for measured ions was compared to prior mass-mobility measurements of ions produced via α-irradiation, as well as to the predictions of gas molecule scattering calculations, which took as inputs semi-emipirical AM1 based structural models. Through this comparison we show that (1) a universal mobility–mass relationship cannot be applied to all ions and (2) for most ions, gas molecule scattering with diffuse scattering rules can be used to accurately predict ion mobilities. Ion spectra collected with the same system but several months apart were also compared, demonstrating that although similar species are detected, the generated ion spectrum can vary over time. Finally, Brownian dynamics simulations with measured polydisperse ion properties were utilized to determine the expected steady-state charge distribution for particles exposed to the measured ions. Via simulations, we find that the presence or absence of the negative nitrate ion has a strong effect on the steady-state charge distribution and that in most systems it is high concentrations of this ion (relative to others) which can bias charge distributions to negative polarity. Conversely, absence of the nitrate ion shifts charge distributions towards the positive mode.

Characterization of Cross-Sectioned Gallium Nitride High-Electron-Mobility Transistors with In Situ Biasing

AlGaN/GaN high-electron-mobility transistors (HEMTs) were characterized in cross-section by Kelvin probe force microscopy (KPFM) during in situ biasing. The HEMTs used in this study were specially designed to maintain full and representative transistor functionality after cross-sectioning perpendicular to the gate width dimension to expose the active channel from source to drain. A cross-sectioning procedure was established that produces samples with high-quality surfaces and minimal degradation in initial transistor performance. A detailed description of the cross-sectioning procedure is provided. Samples were characterized by KPFM, effectively mapping the surface potential of the device in two-dimensional cross-section, including under metallization layers (i.e., gate, field plates, and ohmic contacts). Under the gate and field plate layers are where electric field, temperature, and temperature gradients are all most commonly predicted to have peak values, and where degradation and failure are most likely, and so this is where direct measurements are most critical. In this work, the surface potential of the operating device was mapped in cross-section by KPFM. Charge redistribution was observed during and after biasing, and the surface potential was seen to decay with time back to the prebias condition. This work is a first step toward directly mapping and localizing the steady-state and transient charge distribution due to point defects (traps) before, during, and after device operation, including normally inaccessible regions such as under metallization layers. Such measurements have not previously been demonstrated for GaN HEMT technology.

Experimental characterization of flowrate-dependent bipolar diffusion charging efficiencies of sub-50 nm particles

Accurate knowledge of charging efficiency of particles passed through a bipolar diffusion charger is critical for accurate electrical mobility-based size distribution measurements. It is generally assumed that particles attain a steady-state charge distribution in bipolar diffusion chargers, but this assumption must be tested for its robustness. In this study, the role of flowrate on charging efficiency of particles was established as a function of particle size, charger type, charge polarity, and layout of chargers. The study only focused on singly-charged and uncharged particles entering the neutralizer. The different chargers or neutralizers studied here include 85Kr neutralizers (TSI 3077 and TSI 3077a), a 210Po neutralizer, and a soft X-ray charger (TSI 3087). The 210Po and soft X-ray chargers were seen to largely charge particles to their predicted steady-state charge distribution for all flowrates and particle sizes studied. The 85Kr neutralizers, however, show complex flow-rate dependence of charging efficiency for particles smaller than 50nm. The flowrate dependence was non-monotonic, with a minimum charging efficiency observed at ~1.0lmin−1 flow rate. For flowrates lower than 1.0lmin−1, the decrease in charging efficiencies with increasing flowrate was shown to be because of decreasing particle residence time in the neutralizing region. At high flows (>1.0lmin−1), the increase in charging efficiencies was experimentally established to be because of particle–ion interaction just downstream of the neutralizer. Thus, when 85Kr neutralizers are used for mobility measurements, their flowrate-dependent charging efficiencies must be considered for particles smaller than 50nm.

Application of the Soft X-Ray TSI Advanced Aerosol Neutralizer to Aerosol Measurements Made by a Grimm SMPS

Scanning Mobility Particle Sizer (SMPS) spectrometers are subject to several restrictions when a radioactive source is employed to bring the aerosol to a steady-state charge distribution. An alternative solution, commercially available, is represented by the soft X-ray neutralizer. The present study investigates the outcome of a combination of a Grimm SMPS, which employs a 241Am radioactive source, with the soft X-ray advanced aerosol neutralizer (TSI model 3087). To date, the latter device has been interfaced only with TSI’s Electrostatic Classifiers. Particle size distribution of sodium chloride aerosol was measured with both neutralizers and it was found that the particle number concentration agreed to be within 9% for the 10 - 700 nm range. This difference mainly corresponds to the bias reported by TSI, when the X-ray device is mounted on a TSI spectrometer. It was concluded that the X-ray neutralizer could be usefully employed, as a standalone device, in combination with Grimm Electrostatic Classifiers.

Brownian dynamics determination of the bipolar steady state charge distribution on spheres and non-spheres in the transition regime

A Brownian Dynamics (BD) method to calculate the steady state charge distribution on spherical and non-spherical aerosol particles is presented which circumvents ion-particle collision rate calculation. BD calculations are performed using both monodisperse and measured polydisperse ion properties under atmospheric pressure, room temperature conditions. Calculations reveal that for spherical particles in both the nano- and submicrometer size ranges, the fractions of charged particles are noticeably underpredicted by flux matching theory-based regression expressions. In the examination of non-spherical particles (aggregates, linear chains and cylinders), two models for accumulated particle charge are employed: (1) accumulated charge distributes itself along a particle surface, and (2) accumulated charge is immobile. Independent of model, it is found that particles having a Projected Area (PA) to diffusion based surface area (πRs2) ratio close to unity behaves similar to a sphere of the same mobility diameter. However, model specific behavior is observed for highly non-spherical particles (PA/πRs2<0.5). With distributed charge, highly non-spherical particles acquire more charges than an equivalent mobility sphere in the sub 100nm range, yet acquire less charge than spheres in the submicrometer range. Conversely, with immobile charges, non-spherical particles are found to be more charged than equivalent mobility diameter spheres in both the nano- and submicrometer size ranges. The results of BD calculations are used to develop accurate regression expressions for the charge distribution on spherical and non-spherical particles considering three situations: conducting particles (where both Coulomb and image potentials are accounted for), non-conducting particles where charge is distributed, and non-conducting particles where charge is immobilized.

Ion–Aerosol Flux Coefficients and the Steady-State Charge Distribution of Aerosols in a Bipolar Ion Environment

Fuchs’ theory, as corrected by Hoppel and Frick, is widely used to compute flux coefficients of ions to aerosol particles and the resultant charge distribution. We have identified approximations made in previous works that limit the theory's accuracy. Hoppel and Frick used two characteristic speeds or kinetic energies to calculate the flux coefficients of ions to aerosol particles in lieu of an average of the flux coefficients over the Maxwell–Boltzmann distribution of ion speeds. In the present work, we show that this approximation artificially reduces the number of multiply charged particles. Ion capture may be enhanced by three-body trapping, a process wherein an ion has a collision with a neutral gas molecule and loses sufficient kinetic energy to be captured by the particle. The gas kinetic theory approach to three-body trapping has been refined to better account for the collision between the ion and a neutral gas molecule within the potential presented by the particle. Approximations to the calculation of energy losses and the probability of ion capture have been relaxed. The possibility that an image charge may be induced on the ion as well as on the particle is allowed. While the previous work was limited to electrically conductive particles, both the ion and the particle are allowed to have any dielectric constant in the present work, and the finite size of the ions is taken into account when calculating minimum capture radii for the ion–particle interactions. The resulting ion flux coefficients differ from previous results both in the low nanometer regime and in the continuum regime. We explore the influence of key parameters on the charge distribution, including dielectric constant, temperature, and pressure, to understand how operating conditions may affect the interpretation of differential mobility analyzer measurements of particle size distributions. Finally, an empirical expression for the new charge distribution is given to facilitate rapid calculations. © 2013 American Association for Aerosol Research

Population Balances of Micron-Sized Aerosols in a Bipolar Ion Environment

The present work re-examines the assumptions that are required for a steady-state charge distribution analysis to be valid. First, the common approximation that there are only 11 charge states available to the distribution is relaxed to allow for 201 charge states to be available to the particle distribution. This is found to have large repercussions on the behavior of the distribution for radii greater than 0.5 μm. The steady-state assumption itself is then re-examined by calculating the time required to reach steady state for many different ion-pair production rates and initial particle charge states as a function of radius. In the steady-state model, the ion populations are often assumed to decouple completely from the aerosol; this is shown to be false throughout the troposphere. Finally, the number of positive and negative charge states needed to accurately model a particle population of a given size is determined. © 2013 American Association for Aerosol Research

Lithium interactions with Na+-coupled inorganic phosphate cotransporters: insights into the mechanism of sequential cation binding

Type IIa/b Na(+)-coupled inorganic phosphate cotransporters (NaPi-IIa/b) are considered to be exclusively Na(+) dependent. Here we show that Li(+) can substitute for Na(+) as a driving cation. We expressed NaPi-IIa/b in Xenopus laevis oocytes and performed two-electrode voltage-clamp electrophysiology and uptake assays to investigate the effect of external Li(+) on their kinetics. Replacement of 50% external Na(+) with Li(+) reduced the maximum transport rate and the rate-limiting plateau of the P(i)-induced current began at less hyperpolarizing potentials. Simultaneous electrophysiology and (22)Na uptake on single oocytes revealed that Li(+) ions can substitute for at least one of the three Na(+) ions necessary for cotransport. Presteady-state assays indicated that Li(+) ions alone interact with the empty carrier; however, the total charge displaced was 70% of that with Na(+) alone, or when 50% of the Na(+) was replaced by Li(+). If Na(+) and Li(+) were both present, the midpoint potential of the steady-state charge distribution was shifted towards depolarizing potentials. The charge movement in the presence of Li(+) alone reflected the interaction of one Li(+) ion, in contrast to 2 Na(+) ions when only Na was present. We propose an ordered binding scheme for cotransport in which Li(+) competes with Na(+) to occupy the putative first cation interaction site, followed by the cooperative binding of one Na(+) ion, one divalent P(i) anion, and a third Na(+) ion to complete the carrier loading. With Li(+) bound, the kinetics of subsequent partial reactions were significantly altered. Kinetic simulations of this scheme support our experimental data.

Electron transport and charge induction in cadmium zinc telluride detectors with space charge build up under intense x-ray irradiation

Under intense x-ray irradiation, wide band gap semiconductor radiation detectors fabricated from crystals with low hole transport properties develop a steady-state space charge distribution that results from a dynamic equilibrium between charge carrier dynamics and the incident photon field. At a high enough x-ray flux, this space charge can collapse the electric field within the detector, resulting in the paralyzation of photon counting (i.e., high-flux polarization). However, well before polarization causes a catastrophic device failure, there can be enough space charge present to significantly modify the electric field. A modified field affects the electron transport and, therefore, signal generation within the sensor, which can ultimately degrade the performance of high-rate photon counting electronics. In this study, we analytically solve the fundamental equation of charge conservation to derive the modified electron transport in the presence of an exponential space charge distribution that results from the incident x-rays. We use these space-time solutions to calculate and study the time dependence of the resulting charge-induced signals. The predicted induced signals are compared throughout with numerical solutions of the full charge transport equation. In addition, we present analogous closed-form signals for a uniform distribution relevant to a broader class of γ-ray applications. Finally, we use these solutions to derive a two-parameter family of modified Hecht curves that naturally predict a voltage offset that appears due to the space charge.

Space charge formation and its modified electric field under applied voltage reversal and temperature gradient in XLPE cable

The results of space charge evolution in cross-linked polyethylene power cables under dc electrical field at a uniform temperature and during external voltage polarity reversal are presented in the paper. A mirror image charge distribution was observed in the steady state, but the pre-existing field altered the way in which the steady state charge distribution was formed from that obtaining when the cable was first polarized. Polarity reversing charge was generated in the middle of the insulation and moved towards the appropriate electrodes under the influence of a field in excess of the maximum applied field. Our results show that the mirror effect is a steady state effect that is due to cross-interface currents that depend only on the interface field and not its polarity. Measurements on cable sections with an elevated mean temperature and temperature gradient show that the interface currents are temperature dependent, and that differences between the activation energies of the interface and bulk currents can eliminate, and possibly even invert the polarity of the space charge distribution.

Comment on the Calculation of the Steady-State Charge Distribution on Aerosols &lt; 100 nm by Three Body Trapping Method in a Bipolar Ion Environment

The theory of Fuchs (1963) is widely used for calculation of the steady-state charge distribution on (submicron) aerosol particles in a bipolar ion environment. Hoppel and Frick (1986) and others showed that the Fuchs theory is no longer valid for particle diameters in the order of magnitude of the ionic mean free path. In their 1986 and 1990 papers, Hoppel and Frick published a new calculation method based on the concept of thee-body trapping, which is applicable for small particles down to the size of ions. Some print and procedure mistakes were made in the named publications. Additionally some important calculation information was not given. In this article, the relevant equations are shown, corrected and appended. A recalculation of the charge distributions for small particles based on three-body trapping shows a pronounced difference in comparison to data calculated according to the theory of Fuchs.

Carrier relaxation dynamics and steady-state charge distributions in coupled InGaN∕GaN multiple and single quantum wells

We have examined the carrier capture dynamics and excitation dependent charge distributions of coupled InGaN∕GaN multiple quantum well samples. We measured the temporal evolution of time-delayed cathodoluminescence (CL) spectra to study the temperature- and excitation-dependent transfer of carriers from a surrounding confinement region into a coupled single quantum well. Samples possessing two different structures for the confinement region [i.e., number of quantum wells (QWs) and varying widths] were examined with CL. In order to study state filling of the SQW and QWs in the confinement region, we calculated the quasi-Fermi levels and carrier densities by utilizing a model that involves self-consistent solutions of the nonlinear Poisson-Schrödinger equation for wurtzite QWs including strain, deformation potentials, and polarization fields. Band-edge and effective mass parameters were first obtained from a strain- and In composition-dependent k⋅p calculation for wurtzite InxGa1−xN, using a 6×6 k⋅p Hamiltonian in the {0001} representation. The model shows that the difference in the quasi-Fermi levels between the confinement and SQW regions decreases with increasing excitation and temperature. Likewise, a reversal in the relative magnitude of the carrier densities between these two regions occurs at a certain temperature and excitation. Furthermore, the results for the model describing the steady-state excitation are consistent with those for the transient excitation in time-resolved CL, which also exhibit a marked increase in the rate of carrier transfer to the SQW region as the temperature increases.