Semiconductor Equations Research Articles

Local smooth solutions to the Euler-Poisson equations for semiconductor in vacuum

In this paper, we study the initial-boundary value problem to the Euler-Poisson equations for semiconductors, which involves the vacuum for the electronic density, a challenging case because of its degeneracy and singularity. The main issue is to investigate the local well-posedness of smooth solutions to the isentropic system with an adiabatic exponent γ>1, a degenerate hyperbolic-elliptic system on the free boundary. By setting the system to the Lagrangian coordinates, we reduce it to the quasi-linear wave equation coupling the Poisson equations, where the initial degeneracy can be explicitly expressed by the function ρ0γ−1 of the initial density ρ0, which equals to the distance function near boundaries. By applying the Hardy inequality and weighted Sobolev spaces depending on the distance function, we can overcome the degeneracy and singularity of the system caused by the vacuum, and we technically establish some crucial priori estimates and then prove the existence and uniqueness of the local smooth solution. This is the first result on the smooth solution to the Euler-Poisson equations for semiconductors in vacuum.

Two-dimensional analysis of electrical behavior in composite semiconductor shell structures with magnetic field tuning

To precisely investigate the electric properties and reveal the intrinsic interaction mechanisms between multiple fields in the composite magneto-electric-semiconductor shell structure, two-dimensional analyses were conducted within the framework of the third-order shear deformation theory and the coupled field theory. The governing equations for the composite piezoelectric semiconductor (PS) shell structures were derived using the principle of virtual work. Field distributions of the composite PS shell structures were obtained by expanding basic field quantities into Fourier series along the width direction and using the differential quadrature method. Prior to analysis, the convergence and correctness of the adopted method were evaluated. Several numerical examples were presented to demonstrate how magnetic manipulation can tune electrical behavior. It was found that inhomogeneous shear strain induced by applied magnetic fields is the key factor affecting potential variation in the composite PS shells. The appearance of potential barriers and wells in the composite PS shell structure with an opposite c axis is explained thoroughly. Additionally, the effect of magnetic field non-uniformity on the composite PS shell structure was investigated using an equivalent body force model, offering valuable insights for designing thin-film devices.

SCAPS-1D Analysis of Non-Toxic Lead-Free MASnI3 Perovskite-Based Solar Cell Using Inorganic Charge Transport Layers

Perovskite solar cells (PSCs) have gained a lot of attention due to their high efficiency and low cost. In this research paper, a methylammonium tin iodide (CH3NH3SnI3) based solar cell was simulated using a one-dimensional solar cell capacitance simulation (SCAPS-1D) tool. The SCAPS-1D tool is based on Poisson and the semiconductor equations. After thorough investigation, the initial device presents the following parameters; power conversion efficiency (PCE)=15.315%, fill factor (FF)=64.580%, current density (Jsc)=29.152 mA/cm2, and open circuit voltage (Voc)=0.813 V. The effect of absorber and ETL thicknesses were explored systematically. The performance of the simulated device was significantly influenced by the thickness of the absorber and ETL. The optimized absorber thickness was 0.5 µm and the ETL thickness was 0.02 µm, giving rise to an optimized PCE of 15.411%, FF of 63.525%, Jsc of 29.812 mA/cm2, and Voc of 0.814 V. Additionally, the effect of temperature on the optimized device was evaluated and found that it affects the performance of the device. This model shows the prospect of CH3NH3SnI3 as a perovskite material to produce toxic-free environment-friendly solar cells with high efficiency.

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.

Optimization of electrothermal response of GAAFET using Taguchi's approach and an artificial neural network

This work aims to propose a numerical optimization of the electrothermal behavior of a gate-all-around field effect transistor (GAAFET). The electrothermal model is composed of semiconductor equations coupled with heat conduction equations. The finite element method was adopted for the discretization of equations describing the electrothermal model. The effects of geometric and electrical parameters such as gate length (Lg), oxide thickness (tox), nanowire radius (R), trap density (Nt), ramp parameter (α),gate voltage (Vg), and drain voltage (Vd) were analyzed based on a Taguchi L27(37) orthogonal array. Optimization of the control factors was performed. Multiple linear and nonlinear regressions, as well as an artificial neural network, were used. Numerical analysis revealed that the overall optimal drain current and peak temperature device reach the maximum drain current with lower temperature. The analysis of variance shows that the maximum contribution (39 % for the drain current and 36 % for Tmax) is occupied by the ramp coefficient (α) while the other parameters have a small contribution (less than 3 %) to optimize the performance of the GAAFET transistor. The statistical analysis reveals that the developed artificial neural network model is efficient for the prediction of the electrical and thermal characteristics of the GAAFET transistor. The results of this study are promising for advancing our understanding of these innovative transistor technologies, enabling them to be efficiently integrated into the next generation of electronic products.

Efficient computation of optical excitations in two-dimensional materials with the Xatu code

Here we describe an efficient numerical implementation of the Bethe-Salpeter equation to obtain the excitonic spectrum of semiconductors. This is done on the electronic structure calculated either at the simplest tight-binding level or through density functional theory calculations based on local orbitals. We use a simplified model for the electron-electron interactions which considers atomic orbitals as point-like orbitals and a phenomenological screening. The optical conductivity can then be optionally computed within the Kubo formalism. Our results for paradigmatic two-dimensional materials such as hBN and MoS2, when compared with those of more sophisticated first-principles methods, are excellent and envision a practical use of our implementation beyond the computational limitations of such methods. Program summaryProgram Title: XatuCPC Library link to program files:https://doi.org/10.17632/kj4rt95pvc.1Developer's repository link:https://github.com/alejandrojuria/xatuLicensing provisions: GPLv3Programming language: C++, Fortran, PythonNature of problem: The exciton spectrum is obtained as the solution of the Bethe-Salpeter equation for insulators and semi-conductors. Constructing the equation involves determining the screening of the electrostatic interaction and then determining the matrix elements of the interaction kernel, which are computationally-intensive tasks, specially if one takes a purely ab-initio approach.Solution method: The Bethe-Salpeter equation can be efficiently set up and solved assuming that the basis of the reference electronic structure calculation, obtained either from tight-binding models or density functional theory with actual localized orbitals, corresponds to point-like localized orbitals. This, in addition to using an effective screening instead of computing the dielectric constant, allows to obtain the interaction kernel at very low computational cost and, thereof, the exciton spectrum as well as the light absorption of materials.Additional comments including restrictions and unusual features: The code requires using at least C++11, given that it uses version-specific features. All linear algebra routines have been delegated to the Armadillo library.

Investigation of Trap Density Effect in Gate-All-Around Field Effect Transistors Using the Finite Element Method

Trap density refers to the density of electronic trap states within dielectric materials that can capture and release charge carriers (electrons or holes) in a semiconductor channel, affecting the transistor’s performance. This study aims to investigate the influence of trap density on the electrothermal behavior of nanowire gate-all-around GAAFET devices. The numerical solution of Poisson’s equations and continuity equations, coupled with the heat conduction model, has been used to predict the temperature inside the GAAFET device. The finite element method has been used to discretize the semiconductor equations. Investigations have been carried out on a number of physical and geometric parameters, such as oxide thickness, nanowire radius, and gate length. Their effects on output characteristics and device temperature have been discussed. A thinner oxide thickness, lower device radius, and longer channel length led to a higher current flow. Results also reveal that high trap densities can have significant impacts on the degradation of electronic devices, particularly in the context of semiconductor devices like transistors.

Equivalent circuit of a silicon–lithium p–i–n nuclear radiation detector

Nuclear radiation detectors are indispensable for research in the field of nuclear radiation, X-ray spectroscopy and other areas. Interest in silicon p–i–n detectors of nuclear radiation is increasing today due to the possibility of their operation under normal conditions. In this paper, an equivalent circuit of a silicon–lithium p–i–n nuclear radiation detector is proposed. The proposed circuit is obtained using the classical Shockley equation for silicon semiconductors and the telegraph equations. The parameters of the equivalent circuit were determined using the multiple regression method. As a result of simulation of the model in the MATLAB Simulink graphical development environment, the amplitude-frequency and phase-frequency characteristics of the proposed model were obtained. Using the Monte Carlo method, the alpha-decay of the uranium isotope {}_{92}{}^{233}mathrm{U}, thorium isotope {}_{90}{}^{227}mathrm{Th} and americium isotope {}_{95}{}^{241}mathrm{Am} the alpha-decay spectrum was obtained. Obtained alpha-decay spectra coincides with the experimental data, presented in previous works of other authors.

Theoretical investigation of the temperature characteristics and output parameters of an industrial crystalline silicon solar cell with a microfluidic cooling system

Operating temperature is a key factor affecting the output power of a crystalline silicon solar cell (c-Si SC). Based on solving basic semiconductor equations, Maxwell equations and heat flow equations by finite difference method, this work has theoretically investigated the influences of microfluidic cooling system on the temperature distributions and output parameters of an industrial c-Si SC packaged as a module form, where the cooling system is installed the interface between the aluminum electrode and back ethylene vinyl acetate layer and the cooling medium flowing through microchannel is selected as water. Under the influences of the cooling system, the back surface temperature of the c-Si SC is fixed at about water temperature and the front surface temperature will decrease with the water temperature decreasing. The temperature distributions of c-Si active layer and aluminum layer decrease approximately linearly along the two layer’s thickness directions. The cooling effects of the cooling system are mainly determined by water temperature and when the filling factor of microchannel is larger than 0.1, its influences on the temperature distribution of the c-Si SC are small. In the environmental temperature range from −15 °C to 60 °C, the increase rates of Voc, FF and η per degree Celsius with the water temperature decreasing are about 0.0014 V, 0.036% and 0.05%, respectively.

An Opto-Electro-Thermal Model for Black-Silicon Assisted Photovoltaic Cells in Thermophotovoltaic Applications

Black silicon (b-Si)-assisted photovoltaic cells have textured b-Si surfaces, which have excellent light-trapping properties. There has been a limited amount of work performed on the theoretical modelling of b-Si photovoltaic cells, and hence, in this work, a coupled optical-electrical-thermal model has been proposed for the simulation of b-Si photovoltaic cells. In particular, the thermal aspects in b-Si photovoltaic cells have not been discussed in the literature. In the proposed model, the finite-difference time-domain (FDTD) method was used to study the optical response of the b-Si photovoltaic cell. Semiconductor equations were used for the electrical modelling of the cell. For the thermal model, the Energy Balance Transport Model was used. The developed model was used to simulate b-Si photovoltaic cells under thermophotovoltaic sources. The impacts of heat generation on the electrical performance of thermophotovoltaic cells are discussed. Simulation results from this study showed that black silicon layer improved efficiency and power output in thermophotovoltaic cells compared to thermophotovoltaic cells with no surface texture. In addition, heat generation due to Joule heating and electron thermalization in b-Si-assisted thermophotovoltaic cells reduced the open-circuit voltage and electrical performance.

Analytical and Numerical Investigation of Nanowire Transistor X-ray Detector

Recently, nanowire detectors have been attracting increasing interest thanks to their advantages of high resolution and gain. The potential of using nanowire detectors is investigated in this work by developing a physically based model for Indium Phosphide (InP) phototransistor as well as by performing TCAD simulations. The model is based on solving the basic semiconductor equations for bipolar transistors and considering the effects of charge distribution on the bulk and on the surface. The developed model also takes into consideration the impact of surface traps, which are induced by photogenerated carriers situated at the surface of the nanowire. Further, photogating phenomena and photodoping are also included. Moreover, displacement damage (DD) is also investigated; an issue arises when the detector is exposed to repeated doses. The presented analytical model can predict the current produced from the incident X-ray beam at various energies. The calculation of the gain of the presented nanowire carefully considers the different governing effects at several values of energies as well as biasing voltage and doping. The proposed model is built in MATLAB, and the validity check of the model results is achieved using SILVACO TCAD device simulation. Comparisons between the proposed model results and SILVACO TCAD device simulation are provided and show good agreement.

Mathematical Modeling Application in Energy Conversion and Energy Storage

The use of mathematical modeling to predict and investigate the effect of process variables in the research and engineering field of energy conversion and energy storage has also received special attention from scientists and industrial designers in this field due to their importance in the global economy. This review article investigates the applications of mathematical modeling and simulation in energy conversion and energy storage processes, and finally, with a case study, the application of mathematical modeling in the desired processes to be tested and compared with the reported results in the papers. In the first part, the main emphasis is on energy conversion, especially on the structure of solar cells and fuel cells and mathematical modeling methods, and predicting the effect of operating variables on their performance. The basic principles of modeling solar cells and fuel cells to understand the relationships governing the current, voltage, performance, and power of PV modules are to be discussed. And with a case study, modeling of the process to estimate the performance of PV modules and SOFC in various conditions has been investigated. In the second part, the main focus is on the mathematical modeling of energy storage devices including batteries and supercapacitors. Supercapacitors and batteries are electrochemical energy storage devices that can be charged within a few seconds to a few minutes. This efficient energy storage is based on the electrocatalytic effect of the electrode with a high surface area. The mathematical equations governing the battery and supercapacitor are discussed in the article, and battery and supercapacitor performance are to be simulated as a case study. Due to the Multiphysics nature of energy conversion and storage systems, the simulation is performed in two stages. In the first step, the semiconductor equations are applied and the electrical response of the electrochemical device is modeled. In the second step, if needed, the thermal equations can be entered into the main calculations and the net amount of heat and the temperature profile in the desired device is evaluated. The main goals and ideas of compiling this review article are expressing the importance and role of electrochemical and electrocatalysts in energy production and storage processes and paying attention to the governing mechanism and mathematical equations and highlighting important and common models used in different parts of energy conversion and storage in a coherent article.

Slow Shallow Energy States as the Origin of Hysteresis in Perovskite Solar Cells

Organic-inorganic metal halide perovskites have attracted a considerable interest in the photovoltaic scientific community demonstrating a rapid and unprecedented increase in conversion efficiency in the last decade. Besides the stunning progress in performance, the understanding of the physical mechanisms and limitations that govern perovskite solar cells are far to be completely unravelled. In this work, we study the origin of their hysteretic behaviour from the standpoint of fundamental semiconductor physics by means of technology computer aided design electrical simulations. Our findings identify that the density of shallow interface defects at the interfaces between perovskite and transport layers plays a key role in hysteresis phenomena. Then, by comparing the defect distributions in both spatial and energetic domains for different bias conditions and using fundamental semiconductor equations, we can identify the driving force of hysteresis in terms of slow recombination processes and charge distributions.

Transistor Laser Antenna: Electromagnetic Model in Transmit and Receive Modes

Transistor laser can drive recent innovative technologies like optical antennas and rectennas. To this end, this semiconductor device requires an accurate electromagnetic model capable of determining the antenna characteristics like radiation pattern, directivity, gain, bandwidth, and polarization. Nonetheless, the current semiconductor models of transistor laser describe the absorption and emission of light mainly by simplified expressions and circuit models. These models usually overlook the actual physical geometry and full-wave light-emitting analysis of the device. In this article, a comprehensive computational electromagnetic modeling and characterization is presented for transistor laser. The existing semiconductor and electromagnetic equations are reorganized in a systematic fashion, coupled, and solved numerically to get the electromagnetic field components emitted or absorbed by the device. These fields determine the radiation pattern, directivity, gain, bandwidth, and polarization of transistor laser in transmit and receive modes. The equations involved in the above electromagnetic model are the Poisson and continuity equations incorporating radiative and non-radiative recombination rates, the vector magnetic potential equation interacting with the Hamiltonian operator of electrons in valance and conduction bands, the equation of the dielectric properties fluctuations of semiconductor layers, and the Poynting vector determining the power flow. The constructed model demonstrates agreement with the general performance of the device in experimental reports.

A new hybrid method for shape optimization with application to semiconductor equations

<p style='text-indent:20px;'>The aim of this work is to reconstruct the depletion region in pn junction. Starting with famous drift diffusion model, we establish the simplified equation for the considered semiconductor. There we call the shape optimization technique to formulate a minimization problem from the inverse problem at hand. The existence of an optimal solution of the optimization problem is proved. The proposed numerical algorithm is a combined Domain Decomposition method with an efficient hybrid conjugate gradient guided by differential evolution heuristic algorithm, the finite element method is used to discretize the state equation. At the end we establish several numerical examples, to prove the validity of theoretical results using the proposed algorithm, in addition we show some simulation of the depletion region approximation under two different functioning modes.</p>

Improved spatial soliton theory on the example of photorefractive gallium arsenide

This article presents a critical look at the standard theory of bright and dark photorefractive screening solitons. We pay attention to the commonly overlooked fact of the inconsistency of the theory in the context of the accordance of soliton solution with the microscopic band transport models. Taking into account the material equations for the semi-insulating semiconductor (SI-GaAs) and including the nonlinear transport of hot electrons, a simple differential equation has been developed to determine the distribution of refractive index changes in the material for a localized optical beam. An amendment to the standard solution of (1 + 1)D solitons has been proposed, which particularly should be used for dark solitons to obtain the plausible self-consistent solutions

Effect of flexoelectricity on piezotronic responses of a piezoelectric semiconductor bilayer

Based on three-dimensional equations of piezoelectric semiconductors, we take flexoelectricity into consideration to develop a deformation–polarization–carrier coupling analysis model for the bending of a piezoelectric semiconductor (PS) composite bilayer, which is composed of a piezoelectric semiconductor layer and an elastic layer. Using the derived equations, we investigate the macroscopic responses, such as the distribution of electromechanical field and carrier concentration, of the PS composite bilayer with bending deformation. The induced polarization in the PS composite bilayer exhibits an apparent size-dependent property due to the flexoelectric coupling effect, and thus has a remarkable influence on the piezotronic effect in the PS composite bilayer with nano-thickness. The obtained results are useful for designing novel piezoelectric semiconductor devices.

Simulation of Hydrogenated Amorphous Silicon-based Solar Cell: Investigation of J-V Characteristic in Optimum Thickness

One of the factors that influence the current density-voltage (J-V) characteristics of solar cells is the thickness of the constituent material’s layers. Thus, when the solar cell is constructed using p/i/n junctions type, each layer thickness will contribute to the resulting electrical characteristics. In this research, a simulation of solar cell’s electric current density calculation based on amorphous hydrogenated silicon has been carried out. The simulation is conducted to determine the numerical solution of the two-dimensional semiconductor equation, which is the distribution of the number of electron charge carriers and holes in the simulated solar cell device. It was started by determining the optimum thickness producing the best performance from each layer. Material performance indicators are seen based on the Jsc and Voc values. The p layer thickness in the p/i/n junction was simulated with the variation (70-220)Å/5500Å/300Å. The active layer was manufactured with variations of 150Å/(4500-7500)Å/300Å. Finally, we have also simulated the J-V characteristic of a solar cell by thickness variation for the n layer in the p/i/n junction is 150Å/5500Å/(100-350)Å. The results obtained from each simulation process are then re-simulated in each layer’s optimum thickness combination. Through a series of simulated processes of each layer, the best results were obtained when solar cells based on hydrogenated amorphous silicon were made at a thickness of 190Å/7500Å/150Å, with Jsc and Voc of 5.33 A/m and 0.65 V, respectively.

Numerical Simulation of Copper Indium Gallium Diselenide Solar Cells Using One Dimensional SCAPS Software

The effect of multivalent defect density, thickness of absorber and buffer layer thickness on the performance of CIGS solar cells were investigated systematically. The study was carried out using Solar Cells Capacitance Simulator (SCAPS) code, which is capable of solving the basic semiconductor equations. Employing numerical modelling, a solar cell with the structure Al|ZnO : Al|In2S3|CIGS|Pt was simulated and in it, a double acceptor defect (-2/-1/0) with a density of 1014 cm-3 was set in the absorber in the first instance. This initial device gave a power conversion efficiency (PCE) of 25.85 %, short circuit current density (Jsc) of 37.9576 mAcm-2, Photovoltage (Voc) of 0.7992 V and fill factor (FF) of 85.22 %. When the density of multivalent defect (-2/-1/0) was varied between 1010 cm-3 and 1017 cm-3 the solar cells performance dropped from 26.81 % to 16.87 %. The champion device was with multivalent defect of 1010 cm-3 which shows an enhancement of 3.71 % from the pristine device. On varying the CIGS layer thickness from 0.4 um to 3.6 um, an increase in PCE was observed from 0.4 um to 1.2 um then the PCE began to decrease beyond a thickness of 1.2 um. The best PCE was recorded with thickness of 1.2 um which gave Jsc of 37.7506 mAcm-2, Voc of 0.8059 V, FF of 85.2655 %. On varying the In2S3 (buffer) layer thickness from 0.01 um to 0.08 um, we observed that there was no significant change in photovoltaic parameters of the solar cells as buffer layer thickness increased.

The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors

The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors