Carrier Continuity Equations Research Articles

Optical and electrical characteristics of perovskite solar cells incorporating MoO3 as an active layer

Perovskite-based solar cell technologies have sparked much interest in recent decades. A solar cell’s efficiency is an essential factor in developing a highly efficient device. The power conversion efficiency (PCE) of Perovskite-based solar cells can be enhanced by adding new materials to the photon-absorbing layer and altering the electron and hole transport layers. Titanium dioxide (TiO2) is commonly used in electron transport layers (ETLs), but it has been shown that replacing TiO2 with molybdenum trioxide (MoO3) improves PCE. We use the OghmaNano software to simulate a perovskite-based solar cell and investigate the PCE for TiO2 and MoO3 ETL layers by altering their thickness. The influence of electron and hole drift diffusion, carrier continuity equations in the position space to describe charge flow within the device, Poisson’s equation, and charge carrier recombination have all been investigated in the context of solar cell simulation. It was observed that by substituting the ETL layer of TiO2 with MoO3 in the device, the PCE significantly increases.

Influence of nanoparticles’ polarization on the streamer branching and propagation in nanofluids

The mutual shielding effect between branches is thought to be one of the reasons for reduced propagation of streamer in nanofluids. However, the mechanism of how these nanoparticles induce streamer branching in oil is not clear. In this paper, a numerical model was established based on charge carrier continuity equations and field-dependent molecular ionization theory to study the propagation and branching of streamer. The effects of isolated particle with different size, permittivity, and location on streamer branching in oil are discussed in detail. It is found that isolated particle with larger size, or greater permittivity, or closer position from streamer would cause strong enough distortion of electric field around the particle. This changes the ionization distribution during the propagation of streamer to induce a side-branch. To simulate the state of “global uniformity and local clumping” of nanoparticles in nanofluids, a multi-nanoparticle system is established. The local clumped nanoparticles play a synergistic effect on electric field distortion. The reduced electric field, the increased propagating path, and the mutual shielding effect of streamer branches are responsible for the improved breakdown voltage of nanofluids.

A physics-based compact model of thermal resistance in RRAMs

In this paper, we present a physics-based compact model of thermal resistance in Resistive Random-Access Memory (RRAM) devices considering (a) thermal properties of electrode materials, (b) temperature-induced variations in material thermal conductivity, and (c) parasitic heat losses through the oxide surrounding the filament. Fully coupled numerical simulation data obtained from the self-consistent solution of the drift-diffusion equation (for vacancy migration), carrier continuity equation (for electronic conduction), and the Fourier heat diffusion equation (accounting for electro-thermal heating) has been used for developing and validating the proposed model. Excellent agreement is observed between the model and the numerical simulation results. The proposed model is validated with experimentally measured conductive filament temperature obtained from two different temperature sensing methods. Finally, we present a modeling framework to estimate the potential thermal-cross talk in RRAM crossbar arrays. Our results illustrate that a power-dependent thermal resistance model significantly improves the accuracy in estimating the electro-thermal effects in RRAMs.

THE EFFECT OF IRRADIATION ENERGY ON THE ELECTRICAL POWER OF A MONOFACIAL SILICON SOLAR CELL IN THE DYNAMIC FREQUENCY REGIME UNDER MONOCHROMATIC ILLUMINATION

In this work, we studied the influence of the irradiation energy on the electric power of a monofacial solar cell in frequency dynamic regime under monochromatic illumination. After solving the minority charge carrier continuity equation in the presence of irradiation energy, we establish new expressions for the minority charge carrier density and electrical parameters such as photocurrent density, photovoltage and electrical power. Starting from these equations, we have represented the profiles of some electrical parameters such as the electrical power finally to highlight the effect of the irradiation energy on the latter.

Numerical Analysis of Streamer Discharge Propagation Characteristics in Natural Ester

Natural ester is viewed as the most promising future alternative to mineral oil due to its high degradability, but its inferior breakdown characteristics prevent its application of large power equipment. The purpose of this research is to investigate the breakdown characteristics of natural ester. First, the natural ester's ionization potential and molecular number density are calculated. Then, an improved natural ester streamer discharge model is developed using the Poisson's equation and the carrier continuity equation, taking into account the effect of temperature on carrier mobility and incorporating the computed ionization potential and other factors. The results for different lightning impulse voltages were analyzed by COMSOL software. Comparing the mineral oil, the results indicate that the natural ester breakdown voltage is close to and slightly lower than that of the mineral oil but the acceleration voltage is very similar to the breakdown voltage. The lower ability of esters in prevention against the development of fast and energetic streamers is consistent with the description of the experimental results. In addition, the model takes into account the effect of temperature on the carrier mobility. As the applied voltage increases, the change of temperature in the streamer channel accelerates the carrier motion and promotes the propagation of the streamer. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Influence of layer thickness on the power conversion efficiency of tin halide-based planar heterojunction solar cells.

In recent years, perovskite-based solar cell technologies have sparked much interest. Organic-inorganic halide perovskites (OIHPs) are a type of perovskite that has shown promise in various optoelectronic applications. The power conversion efficiency (PCE) of organic-inorganic perovskite materials is improving with new materials development. However, inorganic materials studied in labs have limited PCE. Lead-free tin halide CH3NH3SnX3 shows good PCE. In this work, we study the electrical characteristics of tin halide as a perovskite absorbing layer in planar heterojunction solar cells with the help of GPVDM solar cell simulation software. A comparative study of power conversion efficiency has been done for tin halide of chloride, bromide, and iodide. The effect of electron and hole drift-diffusion, carrier continuity equations in position space to represent charge flow within the device, Poisson's equation, and charge carrier recombination has been studied in detail.

Driftfusion: an open source code for simulating ordered semiconductor devices with mixed ionic-electronic conducting materials in one dimension

The recent emergence of lead-halide perovskites as active layer materials for thin film semiconductor devices including solar cells, light emitting diodes, and memristors has motivated the development of several new drift-diffusion models that include the effects of both electronic and mobile ionic charge carriers. In this work we introduce Driftfusion, a versatile simulation tool built for modelling one-dimensional ordered semiconductor devices with mixed ionic-electronic conducting layers. Driftfusion enables users to model devices with multiple, distinct, material layers using up to four charge carrier species: electrons and holes plus up to two ionic species. The time-dependent carrier continuity equations are coupled to Poisson’s equation enabling transient optoelectronic device measurement protocols to be simulated. In addition to material and device-wide properties, users have direct access to adapt the physical models for carrier transport, generation and recombination. Furthermore, a discrete interlayer interface approach circumvents the requirement for boundary conditions at material interfaces and enables interface-specific properties to be introduced.

Benchmarking of Analog/RF Performance of Fin-FET, NW-FET, and NS-FET in the Ultimate Scaling Limit

In this work, we examine and benchmark the analog/RF performance metrics of silicon-based multigate devices, such as Fin-FET, gate-all-around nanowire (NW)-FET, and gate-all-around nanosheet (NS)-FET, in the ultimate scaling limit of sub-5-nm technology node. The performance analysis of multigate devices is done using a fully calibrated 3-D technology computer-aided design (TCAD) simulation based on self-consistent solutions of Poisson’s equation, drift-diffusion transport equation, and carrier continuity equation with quantum correction terms for accounting band-to-band tunneling and confinement effects. Our performance benchmarking suggests that NS-FET with (100) surface orientation is a more favorable candidate over NW-FET and Fin-FET for analog/RF applications with higher voltage gain (32 V/V), higher peak cutoff frequency (373 GHz), and higher maximum oscillation frequency (389 GHz) at the 5-nm technology node. The performance benefits of NS-FET are found to be retained by decreasing the channel length, increasing the effective device width, and stacking the multichannel. Furthermore, our studies identify the proper directions to optimizations for achieving high-frequency and high-gain RF operations with multigate devices.

Nonlinear Carrier Dynamics in a Single Photon Avalanche Diode: Stability, Bifurcation, and Quenching Condition

Nonlinear carrier dynamics during quenching of a single photon avalanche diode (SPAD) are investigated. A Lienard type differential equation is derived from carrier continuity equations and it is solved analytically and numerically. Universal characteristics of the quenching carrier dynamics, i.e., stability, bifurcation, and quenching conditions, are analyzed on a trace-determinant plane of the Jacobian matrix and on a phase plane as functions of the quenching resistance (QR). With a finite QR or a resistive quenching (RQ), the breakdown voltage is found to be an attractor leading to a nonquenched final state. In order to produce a successful quenching, i.e., a status identified as an unstable fixed point (FP) with a zero-carrier state, two conditions are found to be necessary: 1) bias voltage dropping below breakdown voltage to ensure carrier decrease and 2) carrier extinction (CE) in this carrier decreasing period. The two conditions together lead to a threshold of QR. On the other hand, a capacitive quenching (CQ) appearing as a special case of RQ with an infinite resistance is found to show a completely different bifurcation character. CQ is derived to be equivalent to a logistic equation giving a transcritical bifurcation at the breakdown voltage and a final state identified as a stable FP with natural CE. Finally, two time constants both governed by an excess voltage are derived. In particular, one of them, a lifetime of impact ionizations, is found to be equivalent to the ``avalanche frequency'' of an impact ionization avalanche transit-time diode (IMPATT).

A Second-Order Stabilized Control Volume Finite Element Method for Self-Heating Effects Simulation of Semiconductor Devices based on Triangular Elements

A second-order control volume finite element method combined with the multiscale flux approximation (CVFEM-MS) based on triangular elements is proposed to numerically investigate the self-heating effects of semiconductor devices. The multiscale fluxes are combined with a selected set of second-order vector basis functions to stabilize the discretization of carrier continuity equations with respect to triangular elements. Numerical results reveal that the proposed method is robust and accurate, even on the mesh of low-quality, where the detrimental impacts caused by the severe self-heating on the terminal currents can be obviously observed for a bipolar transistor model.

Electrical and optical simulation of typical perovskite solar cell by GPVDM software

Nowadays solar cell is one of the best techniques for energy harvesting, we are using CH3NH3PbI3 perovskite material for solar cells applications. One of the most exciting developments in photovoltaics over recent years has been the emergence of perovskite (CH3NH3PbI3) as a promising new material for low-cost, high-efficiency photovoltaics. In this paper, we are assuming the layer of perovskite free from defects. A solar cell simulation software GPVDM, which works as a popular solar cell simulation tool (AMPS: Analysis of microelectronic and photonic structures) was used. The simulation model solves drift–diffusion of electron and hole, carrier continuity equations in position space to describe the movement of charge within the device, poison’s equation, and recombination of charge carriers.

Design of an indium arsenide cell for near-field thermophotovoltaic devices

An indium arsenide photovoltaic cell with gold front contacts is designed for use in a near-field thermophotovoltaic (NF-TPV) device consisting of millimeter-size surfaces separated by a nanosize vacuum gap. The device operates with a doped silicon radiator maintained at a temperature of 800 K. The architecture of the photovoltaic cell, including the emitter and base thicknesses, the doping level of the base, and the front contact grid parameters, are optimized for maximizing NF-TPV power output. This is accomplished by solving radiation and charge transport in the cell via fluctuational electrodynamics and the minority charge carrier continuity equations, in addition to accounting for the shading losses due to the front contacts and additional series resistance losses introduced by the front contacts and the substrate. The results reveal that these additional loss mechanisms negatively affect NF-TPV performance in a non-negligible manner, and that the maximum power output is a trade-off between shading losses and series resistance losses introduced by the front contacts. For instance, when the cell is optimized for a 1 x 1 mm2 device operating at a vacuum gap of 100 nm, the losses introduced by the front contacts reduce the maximum power output by a factor of ~ 2.5 compared to the idealized case when no front contact grid is present. If the optimized grid for the 1 x 1 mm2 device is scaled up for a 5 x 5 mm2 device, the maximum power output is only increased by a factor of ~ 1.08 with respect to the 1 x 1 mm2 case despite an increase of the surface area by a factor of 25. This work demonstrates that the photovoltaic cell in a NF-TPV device must be designed not only for a specific radiator temperature, but also for specific gap thickness and device surface area.

Back Surface Recombination Velocity Dependent of Absorption Coefficient as Applied to Determine Base Optimum Thickness of an n+/p/p+ Silicon Solar Cell

The monochromatic absorption coefficient of silicon, inducing the light penetration depth into the base of the solar cell, is used to determine the optimum thickness necessary for the production of a large photocurrent. The absorption-generation-diffusion and recombination (bulk and surface) phenomena are taken into account in the excess minority carrier continuity equation. The solution of this equation gives the photocurrent according to absorption and electronic parameters. Then from the obtained short circuit photocurrent expression, excess minority carrier back surface recombination velocity is determined, function of the monochromatic absorption coefficient at a given wavelength. This latter plotted versus base thickness yields the optimum thickness of an n+-p-p+ solar cell, for each wavelength, which is in the range close to the energy band gap of the silicon material. This study provides a tool for improvement solar cell manufacture processes, through the mathematical relationship obtained from the thickness limit according to the absorption coefficient that allows base width optimization.

Effect of high-K dielectric on differential conductance and transconductance of ID-DG MOSFET following Ortiz-Conde model

Differential conductance and transconductance of double-gate MOSFET are analytically computed in presence of high-K dielectric following Ortiz-Conde model. Poisson’s equation and carrier continuity equation are simultaneously solved incorporating the effect of back-gate, and independent-gate model is considered for electrical characterization. Percentage change of conductance and transconductance are calculated, and results are compared with published literature. Effect of high-K dielectric is analyzed with that obtained for conventional SiO2 materials where comparison is taking place with identical bias and structural parameters. Saturation of transconductance is obtained for high-K dielectrics for higher VGS and lower VDS, indicating the subthreshold condition. Pinch-off condition is also evaluated from the plot of differential conductance. Results are extremely useful for utilizing the device for analog and digital circuits with nano-device.

Dynamics of photo-induced charge carriers in anodized titania nanotube array

Theoretical development of anodized TiO2 nanotube array was made by using high field conduction theory. The theory reveals that the high electric field (>106 V cm−1) due to low resistance offered by titanium electrode in the beginning of anodization results the rapid formation of compact TiO2 layer defined by pilling-bedworth ratio (PBR). The increasing thickness in the oxidized layer proportionally develops the stress in the oxide layer which results micro-cracks in the TiO2 layer to minimize the energy strain by increasing the surface area. These cracks steer the formation of TiO2 nanotube array throughout the anodization process. The presence of fluoride ions in the as prepared electrolyte etches at these preferred sites (micro-cracks) and leads the formation of bowl like ordered foot prints. The etching in the oxide layer undergoes continuously until an equilibrium is reached between electrochemically assisted oxidation and chemically assisted dissolution process. Furthermore, on account of frequent use of TiO2 nanotube array in light harnessing applications, the theoretical dynamics of photo-induced charge carriers were also studied using carrier continuity equation under quasi state condition.

Effect of structure parameters on performance of N-polar GaN/InAlN high electron mobility transistor

Based on the drift-diffusion transport model, Fermi-Dirac statistics and Shockley-Read-Hall recombination model, the effect of the structure parameters on the performance of N-polar GaN/InAlN high electron mobility transistor is investigated by self-consistently solving the Schrodinger equation, Poisson equation and carrier continuity equation. The results indicate that the saturation current density of the device increases and the threshold voltage shifts negatively with GaN channel thickness increasing from 5 nm to 15 nm and InAlN back barrier thickness increasing from 10 nm to 40 nm. The maximum transconductance decreases with GaN channel thickness increasing or InAlN back barrier thickness decreasing. The change trends of the various performance parameters become slow gradually with the increase of the thickness of the GaN channel layer and InAlN back barrier layer. When the GaN channel thickness is beyond 15 nm or the InAlN back barrier thickness is more than 40 nm, the saturation current, the threshold voltage and the maximum transconductance tend to be stable. The influence of the structure parameter on the device performance can be mainly attributed to the dependence of the built-in electric field, energy band structure and the two-dimensional electron gas (2DEG) on the thickness of the GaN channel layer and InAlN back barrier layer. The main physical mechanism is explained as follows. As the GaN channel thickness increases from 5 nm to 15 nm, the bending of the energy band in the GaN channel layer is mitigated, which means that the total built-in electric field in this layer decreases. However, the potential energy drop across this GaN channel layer increases, resulting in the fact that the quantum well at the GaN/InAlN interface becomes deeper. So the 2DEG density increases with GaN channel thickness increasing. Furthermore, the saturation current density of the device increases and the threshold voltage shifts negatively. Moreover, due to the larger distance between the gate and the 2DEG channel, the capability of the gate control of the high electron mobility transistor decreases. Similarly, the depth of the GaN/InAlN quantum well increases with InAlN back barrier thickness increasing from 10 nm to 40 nm, which results in the increase of the 2DEG concentration. Meanwhile, the electron confinement in the quantum well is enhanced. Therefore the device saturation current and the maximum transconductance increase with InAlN back barrier thickness increasing.

Numerical simulation and validity of the surface photovoltage method in amorphous silicon with a Schottky contact

The steady-state surface photovoltage technique (SPV) is widely used to evaluate minority photocarriers diffusion length for the characterization of photovoltaic device performance. This contact technique shows the difficulty to evaluate the true minority photocarriers diffusion length (Lp) of hydrogenated amorphous silicon (a-Si:H) even though the space charge region is reduced. In this work, we propose a formula to predict more accurately minority diffusion length Lp depending on apparent diffusion length (Lapp) and space charge width (W). This formula is deduced by Moore’s analytical solution in relation to other forms. All transport phenomena taken into account, a complete one-dimensional numerical simulation of the SPV on an Au/a-Si:H Schottky structure is developed. The apparent diffusion length Lapp and the space charge width W are determined using SPV simulation. The standard density of states (DOS) of the a-Si:H is used. Poisson’s equation and the two continuity equations for charge carriers are numerically solved. The SPV assumptions involving W are explored for a set of parameters of the a-Si:H DOS. This numerical simulation shows a linear dependence of Lapp up on the valence band tail energy, which agrees well with the experimental results. The Lp values obtained by the new formula are compared to Lapp and discussed for a typical DOS parameters of a-Si:H.

Time-dependent internal Quantum Efficiency and diffusion Modulation Transfer Function of N/P photodiodes

The minority carrier continuity equation has been solved with the Green’s function approach in a N/P photodiode under the low-level injection assumption. The analytical solution obtained with this approach depends on the three spatial coordinates and on time. The diffusion and the collection of the excess minority carriers have been studied during the transitional period corresponding to very short integration times. The internal Quantum Efficiency and the diffusion Modulation Transfer Function have been calculated according to time. The simulations showed that they evolve with time until their steady-state values. When the integration time is very short, this evolution has to be taken into account for the estimation of the sensitivity of a photodiode and the contrast on an image of a sensor based on several adjacent N/P-type photodiodes.

Methodology for 3-D Substrate Network Extraction for SPICE Simulation of Parasitic Currents in Smart Power ICs

A 3-D simulation of substrate currents is crucial to analyze parasitic coupling effects due to minority carrier injection in smart power ICs. In this paper, a substrate parasitic extraction methodology is introduced by dividing the IC layout into elementary elements to solve the continuity equation for minority carriers in the volume based on the finite-difference method. A substrate parasitic network is derived from the mesh generated through the existing mixed-signal design flow. The induced substrate model is included in circuit simulators such as SPICE to predict the effects of substrate couplings during the design phase. Furthermore, this analysis enables optimization of layout with minimal parasitic effects. By linking the substrate model to the active components, the couplings between the integrated circuit with the substrate parasitic currents can be analyzed during circuit simulations. Simulations and measurements on an high voltage driver reveal consistent results and therefore confirm the validity of the method. Therefore, the approach developed herein is effective to predict parasitic couplings due the injection of minority carriers.

Numerical simulation of the magnetoresistance effect controlled by electric field in p–n junction

The magnetoresistance effect of a p–n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier generation-recombination model are introduced into a drift-diffusion transport model and carrier continuity equations. All the equations are discretized by the finite-difference method and the box integration method and then solved by Newton iteration. Taking advantage of those models and methods, an abrupt junction with uniform doping is studied systematically, and the magnetoresistance as a function of doping concentration, SiO2 thickness and geometrical size is also investigated. The simulation results show that the magnetoresistance (MR) can be controlled substantially by the gate and is dependent on the polarity of the magnetic field.