Continuity Equations For Electrons Research Articles

Conductivity enhancement of silicon nanowires

Current-voltage (I-V) characteristics for various silicon wires of different length-to-width ratios were numerically calculated by solving the Poisson equation and the current continuity equations for electrons and holes self-consistently. We found that, as the silicon wire became thinner or the length-to-width aspect ratio becomes higher, the I-V data deviated more from the Ohmic relation: the current density at a certain bias voltage was larger. In the case of a 500-nm-long silicon wire with n-type doping of 1 × 1016 cm3, for example, the current density of a silicon wire at a bias voltage of 2 volts increased by nearly threefold as the length-to-width ratio of wires was increased from 1 to 25. This behavior is attributed to an enhanced field at the source due to the strong stray field configuration near the contacts at both ends of a wire and to the large carrier build-up in the middle. Our result suggests that a classical treatment of nanowire transport with a proper account of the nonuniform field distribution along the wire may partly explain the conductivity enhancement phenomenon often observed in various nanowires and nanotubes.

Simulation of the spin polarization and the charge transport in Zener tunnel junctions based on ferromagnetic GaAs and ZnO

Simulations of the tunneling current as a function of voltage for a Zener diode where both sides are ferromagnetic have been performed. The current is evaluated as a function of the voltage and of the magnetization on each side of the diode. Calculations are made using an in-house developed simulator which solves the Poisson, electron and hole continuity equations self-consistently. The drift-diffusion model is used to calculate the charge carrier distribution. The current expressions were modified to consider degenerate semiconductors. Our simulator includes a non-local tunneling transport model which was modified to account for the spin polarization of the carriers. The tunneling magnetoresistance is obtained from the I–V characteristics for parallel and antiparallel configurations of the magnetization vectors in each side of the device. Two different devices were analyzed, one that corresponds to Mn-doped GaAs in which the ferromagnetism is stronger on the p side of the diode, and the other that corresponds to ZnO where there are likely to be many more carriers on the n side of the diode. We found good agreement between the results of our simulations and the theoretical predictions of the tunneling magnetoresistance, especially at room temperature. We also found that larger bandgap materials show larger tunneling current but lower tunnel magnetoresistance.

Fluid modelling of capacitively coupled radio-frequency discharges: a review

This paper reviews the basis and the successes with the fluid modelling of capacitively coupled radio-frequency discharges, produced within a parallel-plate cylindrical setup at (single) 13.56–80 MHz frequencies, 6 × 10−2–6 Torr pressures and 50–1000 V rf-applied voltages, in SiH4-H2, H2 and N2. The two-dimensional, time-dependent model used in the simulations accounts for the production, transport and destruction of the charged particles (via the electron and ion continuity and momentum-transfer equations, and the electron mean energy transport equations), and of the excited species and/or radicals (via their rate balance equations, including very complete kinetic descriptions with several collisional–radiative production/destruction mechanisms, coupled to the two-term electron Boltzmann equation), accounting also for the self-consistent development of the rf field (via the solution to Poisson's equation). The charged particle transport equations are solved with and without corrective flux terms (due to inertia and friction effects), whose influence on results is discussed. In the case of silane–hydrogen mixtures, the model further includes a phenomenological description of the plasma–substrate interaction to calculate the deposition rate of a-Si : H thin films. In general, the model gives good predictions for the self-bias voltage, the coupled power and the intensities of radiative emission transitions (both average and spatially resolved), underestimating the electron density by a factor of 3–4.

Influence of nitrogen addition on fundamental discharge properties in alternating current plasma display panels

AbstractIn order to clarify the influence of the addition of nitrogen on the fundamental properties of plasma display panel (PDP) discharges in a Ne/Xe (10%) gas mixture, the PDP discharges in Ne/Xe/N2 gas mixtures have been simulated using a one‐dimensional fluid model that is based on the continuity equations for electrons, ions, excited atoms and molecules, with the Poisson equation and the electron energy balance equation. Based on the simulation results, we found that a pulsed discharge with a short time ( 100 ns) occurs once during every half cycle. At a nitrogen concentration of more than 100 ppm, a phase delay of the gap voltage and discharge current in Ne/Xe gas mixture PDP discharges began to appear. © 2012 Wiley Periodicals, Inc. Electron Comm Jpn, 95(10): 37–43, 2012; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.10399

Numerical Modelling of Mutual Effect among Nearby Needles in a Multi-Needle Configuration of an Atmospheric Air Dielectric Barrier Discharge

A numerical study has been conducted to understand the mutual effect among nearby needles in a multi-needle electrode dielectric barrier discharge. In the present paper, a fluid-hydrodynamic model is adopted. In this model, the mutual effect among nearby needles in a multi-needle configuration of an atmospheric air dielectric barrier discharge are investigated using a fluid-hydrodynamic model including the continuity equations for electrons and positive and negative ions coupled with Poisson’s equation. The electric fields at the streamer head of the middle needle (MN) and the side needles (SNs) in a three-needle model decreased under the influence of the mutual effects of nearby needles compared with that in the single-needle model. In addition, from the same comparison, the average propagation velocities of the streamers from MN and SNs, the electron average energy profile of MN and SNs (including those in the streamer channel, at the streamer head, and in the unbridged gap), and the electron densities at the streamer head of the MN and SNs also decreased. The results obtained in the current paper agreed well with the experimental and simulation results in the literature.

EMPIRICAL DETERMINATION OF THE ENERGY LOSS RATE OF ACCELERATED ELECTRONS IN A WELL-OBSERVED SOLAR FLARE

We present electron images of an extended solar flare source, deduced from RHESSI hard X-ray imaging spectroscopy data. We apply the electron continuity equation to these maps in order to determine empirically the form of the energy loss rate for the bremsstrahlung-emitting electrons. We show that this form is consistent with an energy transport model involving Coulomb collisions in a target with a temperature of about 2 × 107 K, with a continuous injection of fresh deka-keV electrons at a rate of approximately 10–2 electrons s–1 per ambient electron.

COSMIC-RAY ELECTRON EVOLUTION IN THE SUPERNOVA REMNANT RX J1713.7–3946

A simple formalism to describe nonthermal electron acceleration, evolution, and radiation in supernova remnants (SNRs) is presented. The electron continuity equation is analytically solved assuming that the nonthermal electron injection power is proportional to the rate at which the kinetic energy of matter swept up in an adiabatically expanding SNR shell. We apply this model to \fermi\ and HESS data from the SNR \rxj, and find that a one-zone leptonic model with Compton-scattered cosmic microwave background (CMB) and interstellar infrared photons has difficulty providing a good fit to its spectral energy distribution, provided the source is at a distance $\sim 1\ \kpc$ from the Earth. However, the inclusion of multiple zones, as hinted at by recent {\em Chandra} observations, does provide a good fit, but requires a second zone of compact knots with magnetic fields $B\sim 16\ \mu$G, comparable to shock-compressed fields found in the bulk of the remnant.

Scrape-off layer tokamak plasma turbulence

Two-dimensional (2D) interchange turbulence in the scrape-off layer of tokamak plasmas and their subsequent contribution to anomalous plasma transport has been studied in recent years using electron continuity, current balance, and electron energy equations. In this paper, numerically it is demonstrated that the inclusion of ion energy equation in the simulation changes the nature of plasma turbulence. Finite ion temperature reduces floating potential by about 15% compared with the cold ion temperature approximation and also reduces the radial electric field. Rotation of plasma blobs at an angular velocity about 1.5×105 rad/s has been observed. It is found that blob rotation keeps plasma blob charge separation at an angular position with respect to the vertical direction that gives a generation of radial electric field. Plasma blobs with high electron temperature gradients can align the charge separation almost in the radial direction. Influence of high ion temperature and its gradient has been presented.

Study of the characteristics of a streamer discharge in air based on a plasma chemical model

A detailed research on the streamer discharge local mechanism is necessary to enhance and develop the streamer theory. In the present paper, the characteristics of a streamer discharge in air at an atmospheric pressure are investigated using a hydrodynamic model based on plasma chemistry. Aside from continuity equations for electrons and ions, as well as Poisson's equation for the electric field, the model includes the electron mean energy density equation and the neutral particle density continuity equation. The electric field strength and the velocities of streamer propagations obtained from proposed model are in good agreement with experimental and simulation results in literature. The mean electron energy is nearly constant in the streamer channel, except for a peak value at the streamer tip. Although the mole fraction of oxygen is only about 0.2 in air, oxygen ions are the dominant charged particles in the streamer discharge. At the electrode surface, the charged particle densities significantly decrease in the direction of the electrode because of surface reactions.

Modeling of glow discharge controlled by a dielectric barrier

Numerical calculations of spatio-temporal characteristics of the homogeneous barrier discharge in helium are performed by means of a one-dimensional fluid model. This model consists of the continuity equations for electrons, ions and excited atoms, with the current conservation equation and the electric field profile; the time evolution of the discharge current, gas voltage and the surface density of charged particles on the dielectric barrier were calculated. The simulation results showed that the peak values of the discharge current, gas voltage and electric field in the first half period are asymmetric to the second half. When the current reaches its positive or negative maximum, the electric field profile and the electron and ion densities represent similar properties to the typical glow discharge at low pressures. Key words: Atmospheric pressure glow discharge, numerical simulation, helium gas.

Effect of light path folding on the properties of electron transport in dyesensitized solar cell

In this paper, an electron continuity equation with light path folding is developed based on the reflection structure of photoanode in a dye sensitized solar cell (DSC). The characteristics of modulated photocurrent frequency response are calculated, and the effects of light path folding on electron transport property are studied under different absorption and reflection conditions. Intensity modulated photocurrent spectroscopy measurements show that the established model reflectes the actual characteristic of the response to modulated photocurrent frequency when the light path is folded inside the DSC. The kinetic of electron transfer process depends on the light absorption coefficient, film thickness and large particle reflection ability and other factors in DSC with reflector structure. The deep trap is filled and residence time of electron in trap is shortened. It is attributed to the fact that the light path folding reduces the effect of trap/detrap and accelerates the electron transportation.

An Electronic Model for Solar Cells Including Active Interfaces and Energy Resolved Defect Densities

We introduce an electronic model for solar cells taking into account heterostructures with active interfaces and energy resolved volume and interface trap densities. The model consists of continuity equations for electrons and holes with thermionic emission transfer conditions at the interface and of ODEs for the trap densities with energy level and spatial position as parameters, where the right-hand sides contain generation-recombination as well as ionization reactions. This system is coupled with a Poisson equation for the electrostatic potential. We show the thermodynamic correctness of the model and prove a priori estimates for the solutions to the evolution system. Moreover, existence and uniqueness of weak solutions of the problem are proven. For this purpose we solve a regularized problem and verify bounds of the corresponding solution not depending on the regularization level.

2D-Numerical Simulation of Illuminated I–V Characteristic in PIN (NIP) pc-Si Solar Cells Deposited by LPCVD Technique

In order to investigate the performance of polycrystalline silicon (pc-Si) p(+)in(+) or n(+)ip(+) solar cells deposited by LPCVD technique, two-dimensional numerical resolution of transport equations in semiconductors devices (Poisson's and continuity equations of electrons and holes) is used. The geometrical model assumes that the pc-Si layer is composed by single crystalline grains separated by amorphous silicon transition zones commonly called grain boundaries which are perpendicular to the growth surface and which include the usual density of states (DOS) with exponential band-tails and Gaussian distributed deep levels. From the simulated results of the illuminated I-V characteristics under AM 1.5 solar spectrum, it is found that the photovoltaic parameters (short circuit current J(SC), conversion efficiency eta, open circuit voltage V-OC and fill factor FF) are strongly sensitive to pc-Si quality layer in terms of grain size, intrinsic layer.

Simulation of current filamentation in a dc-driven planar gas discharge–semiconductor system

We have performed a theoretical study of self-organized current filamentation in a dc-driven planar gas discharge–semiconductor system at very low currents and under cryogenic conditions. The discharge instability and the observed formation of current filaments are explained by a thermal mechanism, as proposed in our previous paper. We have found, for the first time, a stationary periodic current structure in a two-dimensional Cartesian geometry from first principles, by numerically solving the general system of continuity equations for ions and electrons, the Poisson equation for the electric field in the gas, together with the equation for gas temperature and the equation for electric field in the semiconductor. The space charge induced electric field redistribution, which usually leads to a discharge instability and is automatically included in the first three equations of the system, is practically absent at the very low currents considered, and thus it cannot be responsible for the discharge instability. This is why another mechanism of filamentation (thermal) should be considered. The calculated periodic current structure agrees with the hexagonal current pattern observed in the experiment, as well as with the periodic current structure found in the frame of the previously developed simple model. This serves as a corroboration of the fact that the thermal effect is essential for pattern formation under the conditions considered.

Estimated threshold base current and light power output of a transistor laser with InGaAs quantum well in GaAs base

We have solved the continuity equation for electrons in the base of an InGaP–GaAs–GaAs heterojunction bipolar transistor laser (TL) in which the position of an InGaAs quantum well (QW) in GaAs base is variable. The injected minority carrier is related to the two-dimensional carrier in QW via virtual states (VSs). The values for optical gain in the QW are obtained by considering subband energies and envelope functions in presence of strain, polarization dependent momentum matrix element and Lorentzian lineshape. Relating the gain with threshold current and the latter with base current via VS current, the threshold base current and power output from the TL are estimated. Good agreement between the calculated and the experimental threshold base currents is obtained and the match for light output power is satisfactory within experimental uncertainty. Our calculated charge distribution in the base shows similar behaviour as in the charge control analysis of the experimental data.

Surface Electric Field for Negative Corona Discharge in Atmospheric Pressure Air

The surface electric field (SEF) for the quasi-static negative corona discharge in atmospheric pressure air is investigated by the general fluid model which contains the continuity equations of electrons, positive ions, and negative ions coupled with Gauss' equation, considering the secondary electron emission. The SEF for the monopolar ion flow, which assumes that the whole interelectrode gap is filled with monopolar ions, is also investigated by the simplified model under the same boundary conditions at the anode. The results predict that the SEF remains constant at the onset value for both the negative corona plasma and the monopolar ion flow under a low corona current. With the increase of the corona current, the SEF is slightly strengthened for the negative corona plasma and significantly weakened for the monopolar ion flow in a wide range of conductor radii. The results for the monopolar ion flow are consistent with those deduced from the experimental data in the literature.

Analysis of electron recombination in dye-sensitized solar cell

A steady-state numerical model of dye-sensitized solar cell is based on continuity and transport equations for electrons, iodide and triiodide ions. The cell model consists of an active layer, where photovoltaic effect including diffusion of electrons in mesoporous TiO 2 and ions in electrolyte takes place, and a bulk electrolyte layer, where only ions diffuse. Exponential distribution of trap states in TiO 2 and Gaussian distributions of energy levels in the electrolyte within active layer are included in modeling of the recombination dynamics, according to Shockley-Read-Hall statistics and Marcus-Gerischer electron transfer theory. Recombinations at the front contact and a voltage drop at the platinum covered back contact are included in the model. Simulation results are compared with the measured current–voltage characteristics at different light intensities. In particular, light intensity dependence of open circuit voltage is studied over 4 decades. Optimization of cell efficiency regarding active layer and electrolyte layer thickness is carried out. Simulation results show that best efficiency is achieved when electrolyte layer thickness is minimized as much as possible and that active layer thickness is traded off with respect to recombination rates and/or diffusion limited current determined with the selection of the electrolyte.

Modeling of current–voltage characteristics of CdS/CdTe solar cells

AbstractAn analytical model is developed to study the current–voltage characteristics of CdS/CdTe thin film solar cells by incorporating exponential photon absorption, carrier trapping, and carrier drift in the CdTe layer. An analytical expression for the external voltage dependent photocurrent is derived by solving the continuity equation for both electrons and holes. The overall load current is calculated considering the actual solar spectrum. It is found that the solar cell efficiency critically depends on the hole transport in the CdTe layer and the recombination current dominates over the ideal diode current. The theoretical model is fitted with the published experimental data and shows a very good agreement.

Modeling of current–voltage characteristics of thin film solar cells

An analytical model is developed to study the current–voltage characteristics of thin film solar cells by incorporating exponential photon absorption, carrier trapping and carrier drift in the absorber layer. An analytical expression for the external voltage dependent photocurrent is derived by solving the continuity equation for both electrons and holes assuming the electric field remains uniform in the absorber layer. The analytical results are verified with the numerical self-consistent solution of the steady-state continuity equations and the Poisson’s equation. The overall load current is calculated considering the actual solar spectrum. It is found that the solar cell efficiency critically depends on the transport properties of the carriers that drift towards the bottom contact. The recombination current dominates over the ideal diode current in CdTe based solar cells. The theoretical model is fitted with the published experimental data on various thin film solar cells and shows a very good agreement.

Simulation of partial discharge sequences using fluid equations

Simulation methods employing continuity equations to describe particle transportation are used to examine the process of single discharge. However, it is difficult to simulate partial discharge (PD) behaviour accurately by these methods, because it will take too much computation time to simulate consecutive PD sequences. In this report, in order to save computation time, a simple three-dimensional network is used to simulate PD sequences in a small void under ac voltage. The model considers charge generation, charge transport and charge disappearance, and electrical field redistribution in three dimensions. The continuity equations for electrons, positive ions and negative ions, including the effects of ionization, attachment, recombination, electron diffusion and the transport of charge under electrical field are solved simultaneously with Poisson's equation. With this model, the phase-resolved PD pattern and the current forms of each PD are obtained. Moreover, considering the propagation process of each PD and its influence on surface charge distribution, the fall part of PD current form and the effect of previous discharge on the subsequent one are also studied.