Continuity Equations For Electrons Research Articles

Probing Thermal Electrons in Gamma-Ray Burst Afterglows

Particle-in-cell simulations have unveiled that shock-accelerated electrons do not follow a pure power-law distribution, but have an additional low-energy “thermal” part, which owns a considerable portion of the total energy of the electrons. Investigating the effects of these thermal electrons on gamma-ray burst (GRB) afterglows may provide valuable insights into the particle acceleration mechanisms. We solve the continuity equation of electrons in energy space, from which multiwavelength afterglows are derived by incorporating processes including synchrotron radiation, synchrotron self-absorption, synchrotron self-Compton scattering, and γ–γ annihilation. First, there is an underlying positive correlation between the temporal and spectral indices due to the cooling of electrons. Moreover, thermal electrons result in simultaneous nonmonotonic variations of both the spectral and temporal indices at multiple wavelengths, which could be individually recorded by the 2.5 m Wide Field Survey Telescope and Vera Rubin Observatory Legacy Survey of Space and Time (LSST). The thermal electrons could also be diagnosed using afterglow spectra from synergistic observations in the optical (with LSST) and X-ray (with the Microchannel X-ray Telescope on board the Space Variable Objects Monitor) bands. Finally, we use Monte Carlo simulations to obtain the distribution of the peak flux ratio (R X) between the soft and hard X-rays, and of the time delay (Δt) between the peak times of the soft X-ray and optical light curves. The thermal electrons significantly raise the upper limits of both R X and Δt. Thus, the distribution of GRB afterglows with thermal electrons is more scattered in the R X−Δt plane.

Analytical Model for Current-Voltage Characteristics in Perovskite Solar Cells Incorporating Bulk and Surface Recombination.

The effects of surface recombination on the steady-state carrier profiles and photocurrent in perovskite solar cells are investigated in this paper. The continuity equations for both holes and electrons are solved considering carrier drift and diffusion under the exponential carrier generation profile in the perovskite layer and considering both bulk and interface carrier recombination. An analytical expression for the solar-induced photocurrent is derived. The rate of carrier recombination at the interfaces has a very significant effect on the carrier profile, photocurrent, and, hence, on the charge collection efficiency. The external current density is calculated considering the dark current and nominal solar spectrum-induced photocurrent. The proposed model is fitted and verified with published experimental results from various publications. The fittings of the model with experimental results provide information about the interface and bulk charge carrier transport parameters.

Boosting the efficiency up to 33 % for chalcogenide tin mono-sulfide-based heterojunction solar cell using SCAPS simulation technique

In the present article, an FTO/n-ZnO/SnS/Sb2S3/Au heterojunction photovoltaic cell structure was modeled and the cell performance in terms of output parameters viz. open circuit voltage (Voc), short-circuit current density (Jsc), efficiency (η) and fill factor (FF) by varying carrier concentration, and thickness of different layers involved, was studied at ambient conditions. The overall theoretical performance of the designed photovoltaic cell was examined using SCAPS 1-D simulation programme. The simulation programme operates by resolving semiconductor equations such as the Poisson equation, drift-diffusion equation, and continuity equation for both electrons and holes. The equations are generally solved in one-dimension (1D) in a steady state condition. The role of Sb2S3 HTL on the performance study of tin sulfide chalcogenide-based heterojunction photovoltaic cell (HPVC) was also analyzed. Moreover, the impact of functioning temperature between 273 K and 350 K on the performance of photovoltaic cell was observed, and an increase in temperature resulted in poor performance. The impact of different metal back contact work functions and some more electrical parameters viz. series-shunt resistances, defect concentration of layers and interfaces, and radiative recombination coefficients were also observed on HPVC. The simulation results revealed that the HTL Sb2S3 forms proper band alignment with the SnS chalcogenide absorber layer and enhanced the efficiency, η of HPVC by lessening the carrier recombination at the rear contact side. The dislocation and interface defect reduced significantly which leads to the smooth conduction of hole carriers, therefore, preventing of minority carriers to recombine within the absorber. A significant increase in the efficiency ∼33.24 % together with performance cell parameters Jsc ∼34.38 mA/cm2, Voc ∼1.09 V, and FF ∼88.49 % was observed.

Comparative study of the effects of simulation models on the electronic and electrical parameters of a silicon pv cell


 For silicon solar cells simulation studies, one dimensional (1D), two dimensional 2D) and t
 
 hree dimensional (3D) models are used. Depending of model proposed and assumptions done for the study, the electronic and electrical parameters and then the performance of the solar cell can be influenced.
 This situation raises the problem of the relevance of the choice of the study model and the quality of the resulting results. This work, propose comparative study of the electronic and electric parameters of 1D model, 3D analytical model and 3D empirical model. In this study, continuity equations of excess minority electrons are solved for 1D and 3D models and analytical expressions of electronic parameters (density of electrons δ, intrinsic junction recombination velocity Sf0 and recombination velocity at back surface Sb) and electric parameters (Jsc, Voc, η) are derived. The influence of the model chosen on the electric and electronic parameters of the PV cell have been presented.
 It appears in this study that the choice of the simulation model has a large influence on the electronic and electrical parameters the PV cell. The one-dimensional formulation (1D) overestimates the solar cell efficiency comparatively to the three-dimensional (3D) formulations. The study put in evidence also that for the same grain size, the solar cell efficiency resulting of 3D classical formulation is overestimates than one resulting of 3D empirical formulation.
 

Data-driven discovery of electron continuity equations in electron swarm map for determining electron transport coefficients in argon

In this study, we develop a novel method for determining electron transport coefficients from electron swarm maps measured by a scanning drift-tube experiment. In our method, two types of electron continuity equations that describe either the spatial or the temporal evolution of an electron swarm are discovered in the electron swarm map. The electron transport coefficients can be determined from the coefficients in the discovered equations. Therefore, we can determine the Townsend ionization coefficient, ionization rate coefficient, center-of-mass drift velocity, mean arrival-time drift velocity, longitudinal diffusion coefficient, and longitudinal third-order transport coefficient. These transport coefficients in argon are determined over a wide range of reduced electric fields, E/N, from 29.7 to 1351.6 Td (1 Td = 10−21 Vm2) using our method. We establish that the consideration of high-order transport coefficients, which have been systematically ignored so far, is important for the proper determination of low-order transport coefficients, specifically the electron drift velocity and longitudinal diffusion coefficient, in the presence of ionization growth.

On the altitude profile of lower ionospheric D-region response time delay during solar flares

The D-region ionosphere is sluggish in nature while responding to the incoming solar radiation. We study the altitude (h) profile of mid-latitude D-region response time delay (Δt) during three chosen solar flares, namely, C5.2, M5.2, and X2.2 classes. We solve “electron continuity equation” numerically at each and every h to obtain Δt-h profile. We investigate the 1) latitudinal variation (over both Northern and Southern hemispheres) and 2) seasonal variation (throughout the year) of Δt-h profiles of each of these solar flares separately. We go over noteworthy variations of Δt-h profile for both 1) and 2) with reasonably different results over different hemispheres. Also, we study some contrasting behaviours of Δt-h profile of X2.2 class for both 1) and 2) in comparison to C5.2 or M5.2 classes. We conclude the outcome with possible explanations.

A spectral element method for modelling streamer discharges in low-temperature atmospheric-pressure plasmas

Streamers are ionization fronts that occur in gases at atmospheric and sub-atmospheric pressures. Numerical studies of streamers are important for practical applications but are challenging due to the multiscale nature of this discharge type. This paper introduces a spectral element method for modelling streamer discharges. The method is developed for Cartesian grids but can be extended to be used on unstructured meshes. The streamer model is based on the Poisson equation for the electric potential and the electron continuity equation. The Poisson equation is discretized via a spectral method based on the integral representation of the solution. The hierarchical Poincaré-Steklov (HPS) scheme is used to solve the resulting set of equations. The electron continuity equation is solved by means of the discontinuous Galerkin spectral element method (DGSEM). The DGSEM is extended by an alternative definition of the diffusion flux. A subcell finite volume method is used to stabilize the DGSEM scheme, if required. The entire simulation scheme is validated by solving a number of test problems and reproducing the results of previous studies. Adaptive mesh refinement is used to reduce the number of unknowns. The proposed method is found to be sufficiently fast for being used in practical applications. The flexibility of the method provides an interesting opportunity to broaden the range of problems that can be addressed in numerical studies of low-temperature plasma discharges.

Role of excimer formation and induced photoemission on the Ar metastable kinetics in atmospheric pressure Ar–NH3 dielectric barrier discharges

Tunable diode laser absorption spectroscopy was used to record the space-and time-resolved number density of argon metastable atoms, Ar(1s3) (Paschen notation), in plane-to-plane dielectric barrier discharges (DBDs) operated in a Penning Ar–NH3 mixture at atmospheric pressure. In both low-frequency (LF 650 V, 50 kHz) discharges and dual LF–radiofrequency (RF 190 V, 5 MHz) discharges operated in α–γ mode, the density of Ar(1s3) revealed a single peak per half-period of the LF voltage, with rise and decay times in the sub-microsecond time scale. These results were compared to the predictions of a 1D fluid model based on continuity and momentum equations for electrons, argon ions (Ar+ and Ar2 +) and excited argon 1s atoms as well electron energy balance equation. Using the scheme commonly reported for Ar-based DBDs in the homogeneous regime, the Ar metastable kinetics exhibited much slower rise and decay times than the ones seen in the experiments. The model was improved by considering the fast creation of Ar2 * excimers through three-body reactions involving Ar(1s) atoms and the rapid loss of Ar2 * by vacuum ultraviolet light emission. In optically thin media for such photons, they can readily reach the dielectric barriers of the DBD electrodes and induce secondary electron emission. It is shown that Ar2 * and photoemission play a significant role not only on the Ar metastable kinetics, but also on the dominant ionization pathways and possible α–γ transition in dual frequency RF–LF discharges.

Two stream instabilities in unmagnetized nonrelativistic quantum plasma

The objective of this study is to analyse instabilities and growth rate in unmagnetized dense non-relativistic collisionless quantum plasma under the impact of dynamics of ions. Model of quantum hydrodynamics is used to observe the streaming instabilities in highly dense inhomogeneous unmagnetized quantum plasma at low temperature. The model includes continuity and momentum equations for degenerate electrons and nondegenerate ions which interact with each other due to electrostatic field. Using normal mode analysis and linearization, perturbed potential is obtained in terms of unperturbed parameters with the help of first order perturbation in densities and velocities of electrons and ions while neglecting higher order perturbations. Variation in growth rates for detected instabilities is observed by using appropriate quantum plasma parameters.

Nonlinear evolution of Buneman instability in inhomogeneous plasmas using Adomian decomposition method

Nonlinear development of the Buneman instability in current-driven plasmas is investigated using Adomian decomposition method (ADM). Considering the continuity and momentum transfer equations for electrons and ions and using Poisson’s equation, a nonlinear diffusion equation with positive and negative nonlinear diffusion coefficients is obtained. Assuming the inhomogeneity of the collision frequency, the nonlinear equation is solved using ADM. Results show that by increasing the time and electron velocity, the amplitude of the electron density increases. Furthermore, it is shown that the collision frequency can decrease the amplitude of the electron density which leads to stabilizing the plasma system. Finally, it is found that ADM is a convergent method in the Buneman instability with real parameters.

High-order Scharfetter-Gummel-based schemes and applications to gas discharge modeling

A generalized Scharfetter-Gummel method is proposed to construct the numerical flux for one-dimensional drift-diffusion equations. Instead of taking a constant approximation of the flux as Scharfetter and Gummel did in [1], we consider a p-degree polynomial with p≥1. The high order moments of the approximating flux function serve as intermediaries to bring numerical correction to the Scharfetter-Gummel flux, that the other end turns out to be the solution derivatives. Therefore, local solution reconstructions are required. The resulting schemes are high order and discretize at the same time the convective and diffusive fluxes without having to employ separately different methods to do so. The new schemes with p=1 and p=2 are employed to simulate atmospheric pressure discharge where they are applied to the continuity equations for electrons and ions, and solved simultaneously with Poisson's equation. Numerical results indicate that our method are robust and highly accurate.

Hybrid gyrokinetic ion/fluid electron simulation of toroidal tearing modes

The effects of toroidicity and kinetic ions on the resistive tearing mode are systematically studied with the gyrokinetic particle-in-cell simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] and compared with analytic theory. A new field solver in toroidal geometry has been developed for the simulation of low-n (n = 1, 2) modes in tokamaks. It is found that the toroidal effect significantly reduces the growth rate of the tearing mode. The toroidal effect can also increase the radial width of the tearing mode and change the scaling between the radial mode width and resistivity due to the toroidal pressure term in the electron continuity equation. The kinetic effects of ions can decrease the growth rate of the tearing mode. The plasma flux-surface shaping is found to have significant effect on the tearing mode.

Investigation of the performance parameters of P3HT: PCBM solar cell: The role of temperature

The temperature dependence of solar cells is a fundamental problem determines the device performance at unstable operating and environmental conditions. In this paper considering the temperature dependence of practical parameters, we have used an analytical drift-diffusion model to calculate the characteristic parameters of solar cell. We applied the Modified Tauc-lorentz temperature dependent model to describe the dielectric function of active layer, in order to study the performance of an organic P3HT: PCBM solar cell at different temperatures. Solving the steady-state continuity equation for electrons and holes regarding the dissociation probability of Onsager Braun along with bimolecular recombination rate, we have calculated the carrier’s concentration in P3HT: PCBM organic active layer. The absorption coefficient and its temperature dependence is compared with the results of similar experimental data.

Study of the effect of the thickness of the photosensitive layer of perovskite on its efficiency using SCAPS-1D software

Photovoltaic cells are the best way to convert solar energy into electrical energy by absorbing photons emitted by the sun. This paper presents the results of studies of the effect of the thickness of the absorbing layer of perovskite on the quantum efficiency of the solar cell, as well as on its efficiency. These results were obtained by modelling in the software product SCAPS-1D. Perovskite photovoltaic is getting to be a distinctly predominant option for the conventional solar cells achieving maximum efficiency of 22.1% and more. This work is concerned about the design and analyses of lead-based perovskite solar cell model with the architecture of TiO2/CH3NH3PbI3/spiro-OMeTAD. The analysis of solar cell architecture is done using the Solar Cell Capacitance Simulator (SCAPS). It is a computer-based software tool and is well adapted for the analyses of homo and heterojunctions, multi-junctions and Schottky barrier photovoltaic devices. This software tool runs and simulates based on the Poisson’s and continuity equation of electrons and holes. For this model, it is used to optimize the various parameters such as thickness, the defect density of absorber layer, doping concentrations (ND and NA) of Electron Transport Material (ETM) and Hole Transport Material (HTM)

Numerical analysis of electron density and response time delay during solar flares in mid-latitudinal lower ionosphere

Impacts of solar flare vary at different parts of the lower ionosphere depending on it’s proximity to the direct exposure of incoming solar radiation. The quantitative analysis of this phenomena can be attributed to ‘solar zenith angle ( $\chi (t)$ )’ profile over ionosphere. We numerically solve the ‘electron continuity equation’ to obtain the lower ionospheric electron density profile ( $N_{e}(t)$ ). The electron production rate ( $q(t)$ ) is governed by the (i) X-ray profile ( $\phi (t)$ ) of the flare, (ii) $\chi (t)$ -values during the flare occurrence etc. For analyzing the X-ray profile during flares, we use the GOES-15 satellite observations. Since we’re working on electron continuity equation based simplified ionospheric model, we confined our analysis for comparatively stable mid-latitude ionosphere only. We choose three flares each from C, M and X-classes for $N_{e}(t)$ -profile computation. We observe that temporal $N_{e}(t)$ -profiles differ when computed for lower ionosphere over different discrete latitudes. Further, we compute the spatial $N_{e}(t)$ -profile across mid-latitude at the time when $\phi (t)=\phi _{max}$ . Now we assume that, these flares repeat themselves every day of a year ( $DoY$ ) at the same time of a day and we compute $N_{e}(t)$ -profiles for each day. We found a seasonal effect on $N_{e}(t)$ -profile due to solar flare. Further, we investigate the response time delay ( $\Delta t$ ) of the lower ionosphere, which is the time difference between incidence of X-ray and the respective change in $N_{e}(t)$ -profiles during solar flares. Strong seasonal effects on $N_{e}(t)$ -profile and $\Delta t$ are the unique results of this work.

Electron density profile inside a cylindrical plasma with elliptical cross section in a microwave discharge

In a microwave discharge, the profile of electron number density inside a cylindrical plasma with elliptic cross section is analytically calculated. Using separation of variables way for the electron continuity equation (as function of position and time) and so solving it, the electron number density profile is calculated. It is shown that the profile of electron number density in a cylindrical plasma with elliptical cross section is in the form of Mathieu functions. The characteristic diffusion length for the elliptical cylinder plasma is obtained, and it is seen that it is different with the characteristic diffusion length for the circular cylinder plasma. In the steady state, the normalized density profiles of lowest even and odd modes are plotted. Furthermore, the components of normalized electron number density gradient are plotted. In the limit that plasma cylinder with elliptical cross section being converted to plasma cylinder with circular cross section, the obtained results are confirmed.

An existence result for a class of electrothermal drift-diffusion models with Gauss–Fermi statistics for organic semiconductors

This work is concerned with the analysis of a drift-diffusion model for the electrothermal behavior of organic semiconductor devices. A “generalized Van Roosbroeck” system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like Gauss–Fermi statistics and mobility functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder’s fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that self-heating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal drift-diffusion model for organic semiconductors on a sound analytical basis.

Utilizing Band Diagrams To Interpret the Photovoltage and Photocurrent in Photoanodes: A Semiclassical Device Modeling Study

The photovoltage and photocurrent both serve as important design metrics when assessing the performance of photoanodes within photoelectrochemical cells. However, to date, wide disagreement persists (even in the recent literature) regarding how the photovoltage should be physically interpreted; this lack of consensus is further coupled to physical interpretations of the photocurrent. In this work, we utilize state-of-the-art device modeling to help clarify the physical origins of both the photovoltage and photocurrent in photoanodes. Our methodology is based on directly solving the governing electron and hole continuity equations, coupled self-consistently with Poisson’s equation, with appropriate boundary conditions. Through a systematic examination of a model photoanode, hematite, we correlate directly measurable current–voltage characteristics with operational band diagrams. It is shown that, by directly mapping specific operating points of either equal current or equal voltage (both illuminated and in the dark) to band diagram plots, one is able to obtain substantial insights into the physical nature of both the photocurrent and photovoltage. Throughout this analysis, the fundamental distinction between electrostatic and electrochemical perturbations under arising illumination is underscored. By aiding the community-wide effort to arrive at a consensus on these concepts, we aim to further enable the design of higher-efficiency photoanodes.

Predictions of circuit interruption including non-equilibrium electron densities

Calculations and predictions of arc properties, for example, for arc welding and circuit interruption, are generally made by solving the energy balance equation to obtain temperature profiles, assuming local thermodynamic equilibrium. Results for high power circuit breakers have needed to attribute turbulence as the principal energy loss, with larger turbulence parameters for SF6 than for air to fit the superior experimental performance of SF6. In the present paper, predictions of circuit interruption are obtained by solving the electron continuity equation together with the energy balance equation for a simple low current arc, with no imposed convective flow and thus no need for turbulence. It is found that circuit interruption depends critically on electron–ion recombination coefficients and also electron-neutral attachment coefficients, large values of which reduce electron densities and thus electrical conduction. SF6 is found to be superior to air because of its very large attachment coefficient. The results suggest that in the search for a replacement gas for SF6, because of its global warming potential of 24 000 times that of carbon dioxide, material properties of high electron recombination and attachment are desirable, as well as the high enthalpy density which follows from the results where convective flow is the principal energy loss.

Two-dimensional simulation of transition from primary to secondary streamer discharge in air

A Two-dimensional simulation of the atmospheric pressure needle-plane streamer discharge is presented in this paper. The model consists of three continuity equations for electrons and ions coupled with Poisson’s equation. Photon flux was estimated by the impact of the ionization reactions. The distributions of the electric field and photon flux from the primary streamer to the secondary streamer are discussed, where velocity of the primary streamer was 2.16×105 m/s and the radius of the filament of the secondary streamer varied from 0.012 cm to 0.02 cm. The variation in photon flux was similar to that of the electric field. When the streamer was close to the cathode, the photon flux exponentially increased from 4.5×1026 m-3s-1 to 2.42×1028 m-3s-1. The secondary streamer was similar to a uniform filament because of a uniform electric field.