Equation For Charge Density Research Articles

Heat transfer intensification of NEPCM-water suspension filled heat sink cavity with notches cooling tubes by applying the electric field

The effects of an electric field on heat transfer, free convection, and entropy generation of nano-encapsulated phase change material (NEPCM) dissolved in water in a complex inclined chamber are studied. The enclosure consists of a rectangular cavity heated from below and the remaining walls are considered adiabatic. The fluid is cooled by eight cooling tubes, each with four notches. The effects of the electric field, inclination angle (ζ = 45° and ζ = 90°), and Rayleigh number (Ra = 103, 104, and 105) in equal concentration of NEPCM (ϕ = 2 %) are studied using ANSYS Fluent CFD code. The dimensionless form of fluid governing equations, electric potential equation, electric charge density equation, and entropy generation equation are used to set the primitive parameters. Grid verification and validation tests are performed to ensure the reliability of the solution. Calculations show that with increasing Ra, the average Nusselt number (Nuave) decreases from ζ = 45° to 90°, but when an electric field is applied, the results are reversed. As the Rayleigh number increases in conjunction with the electric field, the buoyancy effect becomes more pronounced. Furthermore, owing to its high heat transfer potential and lowest irreversibility, the straight cavity (ζ = 90°) is desirable at Ra = 105.

Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation

An efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal $L$ sums in spherical-harmonic expansions, so that fast convergence in single-$L$ sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients ${A}_{L}$ that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.

Solution to the Modified Helmholtz Equation for Arbitrary Periodic Charge Densities

We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential. The method is an extension of Weinert’s pseudo-charge method [Weinert M, J Math Phys, 1981, 22:2433–2439] for solving the Poisson equation for the same class of charge density distributions. The inherent differences between the Poisson and the modified Helmholtz equation are in their respective radial solutions. These are polynomial functions, for the Poisson equation, and modified spherical Bessel functions, for the modified Helmholtz equation. This leads to a definition of a modified pseudo-charge density and modified multipole moments. We have shown that Weinert’s convergence analysis of an absolutely and uniformly convergent Fourier series of the pseudo-charge density is transferred to the modified pseudo-charge density. We conclude by illustrating the algorithmic changes necessary to turn an available implementation of the Poisson solver into a solver for the modified Helmholtz equation.

Kerker mixing scheme for self-consistent muffin-tin based all-electron electronic structure calculations

We propose a computationally efficient Kerker mixing scheme for robust and rapidly converging self-consistent-field calculations using all-electron first-principles electronic structure methods based on the muffin-tin partitioning of space. The mixing scheme is composed of the Kerker preconditioner in combination with quasi-Newton methods. We construct the Kerker preconditioner in the muffin-tin sphere by determining the screened Coulomb potential in real space, solving a modified Helmholtz equation by adopting Weinert's pseudocharge method for calculating the Poisson equation for periodic charge densities without shape approximation to the solution of the modified Helmholtz equation. Implemented in a full-potential linearized augmented plane-wave (FLAPW) method, we found that the Kerker preconditioning scheme (i) leads to a convergence to self-consistency that is independent of system size, (ii) is extremely robust in the choice of the mixing and preconditioning parameters, (iii) scales linearly with system size in computational cost, and (iv) conserves the total charge. We have related the preconditioning parameter to the density of states of the delocalized electrons at the Fermi energy and developed a model to choose the preconditioning parameter either prior to the calculation or on the fly. Our computationally validated model supports the hypothesis that, in the absence of Kerker preconditioning, the delocalized $s$ and $p$ electrons of simple and transition metals are the primary cause for the slowing of the convergence speed and that the stronger, localized $d$ and $f$ electrons account for only a small fraction of the charge sloshing problem. The presented formulation of the Kerker preconditioning scheme establishes an efficient methodology for the simulation of magnetic and nonmagnetic metallic large-scale material systems by means of muffin-tin-based all-electron methods.

Analytical Modeling of Threshold Voltage for Dual-Metal Double-Gate Gate-All-Around (DM-DG-GAA) MOSFET

This paper presents, analytical modeling of surface potential,threshold voltage and DIBL for a Dual-Metal Double-Gate Gate-All-Around (DM-DG-GAA) MOSFET considering the parabolic approximation of surface potential. Poisson’s three-dimensional (3D) charge density equation has been solved by using proper boundary conditions to formulate the surface potential throughout the channel length. In this work, two gate metals of distinct work functions are used for gate electrode to create a step profile in channel potential. The potential step profile in surface potential reduces the SCEs in DM-DG-GAA MOSFET. The developed surface potential model is further considered to formulate the threshold voltage (Vth)model by using an effective conductive path and Fermi potential difference. The modeled threshold voltage is further used to find the Drain Induced Barrier Lowering (DIBL) effect. The threshold voltage and the DIBL are discussed with different values of device physical parameters like gate oxide (sio2) thickness, gate length ratio, channel thickness, and screening gate work function. This paper compares the SCEs of DM-DG-GAA MOSFET with Dual-Gate Gate-All-Around (DG-GAA) MOSFET and the results showing that DM-DG-GAA MOSFET offering better short channel characteristics than DG-GAA MOSFET. The model results are verified with simulation results generated from 3D device simulator ATLAS from SILVACO.

Effect of site energy fluctuation on charge transport in disordered organic molecules.

Effect of dynamics of site energy disorder on charge transport in organic molecular semiconductors is not yet well-established. In order to study the relationship between the dynamics of site energy disorder and charge transport, we have performed a multiscale study on dialkyl substituted thienothiophene capped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecular solids. In this study, we explore the structural dynamics and correlated charge transport by electronic structure calculations, molecular dynamics, and kinetic Monte-Carlo simulations. We have also proposed the differential entropy dependent diffusion and charge density equations to study the electric field drifted diffusion property and carrier density. In this investigation, we have addressed the transformation mechanism from dynamic to static disorder in the extended stacked molecular units. Here, the decrease in the charge transfer rate due to site energy fluctuations reveals the dispersion transport along the extended π-stacked molecules. Furthermore, the calculated current density for a different set of site energy difference values shows the validity and the limitations of the Einstein relation. Based on the calculated ideality factor, we have classified the charge transport in these molecules as either the Langevin or the Shockley-Read-Hall type mechanism. Through the calculated mobility, current density, and ideality factor analysis, we categorize the applicability of molecules of interest for photovoltaic or light emitting diode applications.

Effects of surface density of states Ns(E) on the number of effective triboelectric phonons in triboelectric nanogenerators (TENGs): An analytical and numerical study

In this work, the concept of triboelectric phonon energy (Eph) is coupled with the triboelectric charge density equation instead of the work function of the metal (WM) to understand electron transfer between a metal and a dielectric. The driving force to initiate electron transfer during a contact-separation process is assumed to be Eph (lattice vibration, heat) because such Eph can kick off electrons from a metallic surface toward a vacuum. These electrons can then be accommodated into the surface density of states Ns(E) on the dielectric surface under the condition that Eph ≥ WM to initiate an electron transfer process. When equilibrium is reached, the number of effective triboelectric phonons (Nphonon) is calculated as a function of Ns(E) along the tunneling distance. As a numerical result, it is found that Nphonon is dependent on Ns(E).

Modeling the effect of damage on electrical resistivity of melt-infiltrated SiC/SiC composites

Electrical resistivity (ER) measurements are a possible health monitoring technique for ceramic matrix composite components in future aerospace applications. In order to use ER measurements to detect and identify damage, it is necessary to understand how each specific damage state will affect the ER response. In this study, finite element models are developed and applied to quantify the effect of specific damage states on the ER response in a melt-infiltrated silicon carbide (SiC) fiber-reinforced SiC composite. The ER of several damage states are calculated by simulating the electric current flow through the damaged microstructure. This is achieved by performing the numerical solution of the steady-state conservation of charge density equation. Numerical results reveal the effect of various cracking features on the ER response such as type of cracking, extent of cracking, crack density and fiber/matrix debonding.

Theoretical study of the effect of piezoelectric bone matrix on transient fluid flow in the osteonal lacunocanaliculae.

A new theoretical generation mechanism of the transient streaming potential considering variations in the surface potential on the wall in a lacunocanalicular system, is proposed based on the assumption of the piezoelectric bone matrix. To obtain the streaming potential analytically, a modified transient charge density equation is proposed. An osteon is modeled as a piezoelectric solid phase having fluid-filled cavities (lacunae) connected by channels (canaliculae) to obtain the pressure gradients in the canaliculae and the electric boundary conditions on the canalicular walls. In addition, this study focused on modeling of the negatively charged glycocalyx that fills the annular fluid space between the osteocytic process and the canalicular wall. It is assumed that the annular fluid space of the canaliculi can be represented as a two-layer configuration for flow through a gap (between the tips of the glycocalyx and the canalicular wall) overlaying the porous glycocalyx. The transient streaming potential and bone fluid flow affected by the generated total potential are analyzed using the one-dimensional lacunocanalicular fluid path, which is surrounded by the piezoelectric bone matrix. A significant increase in the streaming potential is predicted for the case with piezoelectricity. The peak streaming potential value with the piezoelectricity is found to be up to 58.8% greater compared with that without piezoelectricity. The electroviscous effect due to the total electric potential gradients on the fluid velocities in the canaliculi is negligible. These findings imply that the piezoelectric effect caused by deformation of the bone matrix should be considered for prediction of the streaming potential in the lacunocanaliculae. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res.

Improving the performance of a numerical model to simulate the EHD interaction effect induced by dielectric barrier discharge

Over the past decade, there has been a growing interest in dielectric-barrier-discharge (DBD) plasma actuators. The lack of a general model to accurately simulate the related phenomena is one of the primary limitations in studying such type of actuators. One of the most frequently used models of this type was proposed by Suzen and Huang (S-H). Despite the numerous efforts made to improve this model, including a recent work of the authors, some deficiencies still exist.In this study, new modifications have been introduced to improve the performance and accuracy of the S-H phenomenological model. Here, a relation between the electrical-potential and charge-density equations has been made in the form of a boundary condition for charge distribution on the dielectric surface. Some semi-empirical relations are extracted for computing the plasma extension as well as the Debye length which is very important in simulation of the near-wall flow field. Furthermore, the one-equation for estimation of actuator-generated-thrust is corrected by these modifications. The main advantage of the modified model is that the model does not need to further calibration to predict accurately the Debye length, plasma extension and maximum charge density parameter in a range of voltages and frequencies. Promising results have been achieved in the simulation of the induced jet structures in the flat-plate boundary-layer for air as the working fluid.

Study of influencing characteristics on boundary-layer separation controlled by using DBD plasma actuator with modified model

For more effectively utilizing state of the plasma flow characteristics, to control separation of boundary layer from the subsonic to supersonic, the vortex flow, viscous coupling including shock induced separation, to improve combustion stability and efficiency, thereby minimizing the parasitic resistance and controlling separation bubble issue effectively. Therefore, the main research focus of this paper will be divided into two parts. The first part, the experimental design and measurement will be implemented under atmosphere temperature and pressure conditions, including the actuator for driving the high-voltage AC dielectric plasma between the geometric parameters and the actuating voltage and the relationship between the discharge characteristics of actuator. The second part, we apply the finite volume method to solve the Navier-Stokes equations, and combines the modified physical model of electrostatic field. Through the applied AC voltage and charge density equation for solving Maxwell's equations and the way of obtaining an electric field, investigate the dielectric discharge flow affecting the acceleration effects of normal atmospheric pressure plasma and its impact on the boundary layer flows of thin plate. According to the mentioned above, considering the number of different geometric parameters and different actuator free flow conditions, the impact of physical parameters, for instance, electric potential, electric density and body forces which generated by plasma actuator in computational model, and their further interactions with thin plate boundary layer flow, and then the induced velocity field are discussed in detail.

Reflection and transmission of obliquely incident graphene plasmons by discontinuities in surface conductivity: observation of the Brewster-like effect

Scattering of graphene surface plasmons that are obliquely incident on a line discontinuity in graphene surface conductivity is investigated. The analysis is based on a solution of the quasi-static integral equation for surface charge density. It is shown that the reflection coefficient of the graphene plasmons reaches a minimum at a specific angle of incidence that depends on the ratio of conductivities of the two regions surrounding the discontinuity. This effect, which is similar to the well-known Brewster effect, is pronounced for abrupt discontinuities, but becomes weaker as the width of the transition region increases. The results obtained can be used for the design and analysis of devices based on graphene layers with non-uniform conductivity patterns. As an example, an approximate method is presented for obtaining the dispersion relation of waveguide modes in a graphene ribbon.

Near-field correction in the first-principles calculations by the exact two-center expansion for the inverse of the distance

We propose a method to deal with the so-called near-field corrections to the solution of the Poisson equation for full-potential first-principles calculations using the exact two-center expansion for the inverse of the distance between two points. It is demonstrated that the method gives a very satisfying solution to the Poisson equation for plane-wave charge densities which can be solved analytically. The present method gives reasonable total energy for lattice distortions where the conventional multipole expansion gives large errors.

A Finite-Volume Method for Electro-Thermoconvective Phenomena in a Plane Layer of Dielectric Liquid

This article presents a numerical algorithm for electro-thermoconvective phenomena in a dielectric liquid confined between two parallel plates. The liquid is under the simultaneous actions of a direct current electric field and a thermal gradient. Free charge carriers are considered to be introduced by unipolar injection. The fully coupled equations including a reduced set of Maxwell's equations, the Navier–Stokes equations, and the energy equation, together with the equations of state, are solved with a finite-volume method. A total variation-diminishing scheme is especially used to solve the convection-dominated charge density equation. The method is validated with four test cases that possess some analytical solutions. As an application example, we evaluate the heat transfer enhancement resulting from injection-induced electroconvection in a bounded cavity filled with silicone oil.

Effect of the Mobility Parameter on the Oscillatory Electroconvection of Dielectric Liquids Subject to Strong Unipolar Charge Injection

Two-dimensional numerical calculations were carried out for the isothermal electroconvection in a dielectric liquid induced by the unipolar charge injection. In the dimensionless form, the system is mainly governed by the injection strength number C, the electric Rayleigh number T, and a mobility number M. A strong injection case with C = 10 was considered. Along with the increase in driving parameter T, oscillatory electroconvection occurs. Critical values of T corresponding to the onset of such oscillatory convection were shown to be highly dependent on M and were accurately determined. Some precautions, including the algorithm for the charge density equation, were taken to reduce the numerical diffusion and to ensure the reliability of our findings.

Suppress of Substrate-Assisted Depletion Effects in Super Junction LDMOS on Thin Film SOI

Conventional super-junction lateral double diffused MOSFET (SJ-LDMOS) fabricated on Silicon on Insulator (SOI) substrate suffers from low breakdown voltage under the same on-resistance due to substrate-assisted depletion effect. To suppress this effect, it is important to find the charge density in the inversion layer under buried oxide. In this paper, we propose a charge density equation and its formulation. The results were used in a 3D device simulator to optimize the device structure. The experimental results confirm that the equation is useful to optimize device performance. The breakdown voltage of structure increased 54% and on-state-resistance decreased 58% compared to conventional SJ device. The device fabrication procedure is fully compatible with mainstream SOI CMOS process.

A Self-Consistent Compact Model of Ballistic Nanowire MOSFET With Rectangular Cross Section

We propose a compact model of ballistic gate-all-around metal-oxide-semiconductor field-effect transistors. In this model, the potential distribution in the wire cross section is approximated by a quadratic function. This model potential has one unknown parameter, which determines the shape of the potential. The Schrödinger equation in the wire cross section can be approximately solved using the model potential, and the electron energy levels are derived analytically. The unknown parameter is determined by numerically solving a coupled equation for charge densities derived from electrostatics and quantum statistics. We calculate the device properties using the obtained unknown parameter. A Schrödinger-Poisson solver that simulates electron states in the wire cross section is used. The results obtained using it reveal that our model exhibits good agreement for both the lowest and excited energy levels. We estimate the ballistic current using the calculated energy levels and the Landauer formula, which shows good agreement with results simulated using the nonequilibrium Green's function formalism.

A unified charge-based model for SOI MOSFETs applicable from intrinsic to heavily doped channel

A unified charge-based model for fully depleted silicon-on-insulator (SOI) metal-oxide semiconductor field-effect transistors (MOSFETs) is presented. The proposed model is accurate and applicable from intrinsic to heavily doped channels with various structure parameters. The framework starts from the one-dimensional Poisson—Boltzmann equation, and based on the full depletion approximation, an accurate inversion charge density equation is obtained. With the inversion charge density solution, the unified drain current expression is derived, and a unified terminal charge and intrinsic capacitance model is also derived in the quasi-static case. The validity and accuracy of the presented analytic model is proved by numerical simulations.

ANALYSIS OF THE KINETICS OF SHRINKING OF THE IONIC-STRENGTH-SENSITIVE HYDROGEL WITH A MULTI-PHYSICAL MODEL

In this paper, a multiple-field model, which is termed the multi-effect-coupling ionic-strength-stimulus (MECis), is presented for analysis of the kinetics shrinking of the ionic-strength-sensitive hydrogel. The MECis model is composed of three sets of governing nonlinear partial differential equations (PDEs), which account for the three fields, namely the chemical, electrical and mechanical fields. In addition, three sets of the constitutive relations are also included in the present model, namely, the constitutive flux, the fixed charge density equation and the material law of the polymeric network. The total six sets of equations characterize the behavior of the mobile ion, the fixed charge and the solid network in both the hydrogel and solution domains. The MECis model is applied to analyze a practical kinetics shrinking problem that was published [Goel et al., 2006a]. The chemical, electric and mechanical behaviors of the hydrogel during the kinetics shrinking are also simulated in details by the present MECis model.

Multiphysics modeling of responsive characteristics of ionic-strength-sensitive hydrogel

A multiphysics model is developed in this paper for simulation of the volume transition mechanism of the smart hydrogel in response to the changes in the ionic strength of bathing solution as an important measure of the ionic concentration of that solution, which is termed the multi-effect-coupling ionic-strength-stimulus (MECis) model. In the present works, the ionic strength is treated as a main stimulus and incorporated into both the ionic convection-diffusion system in the Nernst-Planck flux and the fixed charge density equation characterized by Langmuir isotherm theory. Due to the diffusion and convection, the osmotic pressure is produced by the difference in the ionic concentration between the interior hydrogel and exterior solution, which drives the swelling of the smart hydrogel. The deformation of the ionic-strength-sensitive hydrogel is described by the momentum conservation law, in which the osmotic pressure is a main driving source. Apart from osmotic pressure, however, the repulsive force between the fixed charges is also considered in the mechanical equilibrium equation as another driving source for the swelling of the hydrogel. The simulation is conducted for one-dimensional steady-state problem, and then compared with the experimental data and other theories from open literature. The comparisons demonstrate that the MECis model can simulate well the swelling behavior of the ionic-strength-sensitive hydrogel qualitatively and quantitatively. Probably it is able to predict the responsive characteristics of the bathing solution including the distribution of diffusive ionic concentrations and electrical potential.