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Showing papers on "Electric potential published in 2021"


Journal ArticleDOI
Li Li1
TL;DR: In this article, the magnetic potential and electric potential were determined from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calderon problem.
Abstract: We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calderon problem by usin...

23 citations


Journal ArticleDOI
TL;DR: In this paper, a new high-latitude empirical model is introduced, named for Auroral energy Spectrum and High-Latitude Electric field variability (ASHLEY), which aims to improve specifications.
Abstract: In this study, a new high-latitude empirical model is introduced, named for Auroral energy Spectrum and High-Latitude Electric field variabilitY (ASHLEY). This model aims to improve specifications ...

23 citations


Posted ContentDOI
TL;DR: In this article, a novel magneto-electro-elastic model of 2D functionally graded materials (FGMs) beams is developed for investigating the nonlinear dynamics of FGMs.
Abstract: In the paper, a novel magneto-electro-elastic model of bi-directional (2D) functionally graded materials (FGMs) beams is developed for investigating the nonlinear dynamics. It is shown that the asymmetric modes induced by the 2D FGMs may significantly affect the nonlinear dynamic responses, which is tremendously different from previous studies. Taking into account the geometric nonlinearity, the nonlinear equation of motion and associated boundary conditions for the beams are derived according to the Hamilton’s principle. The natural frequencies and numerical modes of the beams are calculated by the generalized differential quadrature method. The frequency responses of the nonlinear forced vibration are constructed based on the Galerkin technique incorporating with the incremental harmonic balance approach. The influences of the material distributions, length–thickness ratio, electric voltage, magnetic potential as well as boundary condition on the nonlinear resonant frequency and response amplitude are discussed in details. It is notable that increasing in the axial and thickness FG indexes, negative electric potential and positive magnetic potential can lead to decline the nonlinear resonance frequency and amplitude peak, which is usually applied to accurately design the multi-ferroic composite structures. Furthermore, the nonlinear characteristics of motion can be regulated by tuning/tailoring the 2D FG materials.

19 citations


Journal ArticleDOI
TL;DR: In this article, a numerical analysis of electro-thermo-convection in a 2-D differentially heated square cavity filled with a dielectric liquid is presented, where fully coupled governing equations of electric potential, charge transport, Navier-Stokes equations, and the energy equation are implemented in the finite-volume framework of OpenFOAM.

19 citations


Journal ArticleDOI
TL;DR: In this article, a finite-volume method (FVM) based numerical model for the solid-liquid phase change heat transfer of dielectric PCM under the influence of electric field is presented.

17 citations


Journal ArticleDOI
Jun Huang1
TL;DR: In this article, a reference system is introduced to describe hard-sphere interactions between charged particles in the electrolyte solution, and a hybrid density-potential functional for the grand canonical potential of the electric double layer (EDL) is derived.

16 citations


Journal ArticleDOI
TL;DR: In this article, the completed investigation of a possible superconducting phase in monolayer indium selenide is determined using first-principles calculations for both the hole and electron doping systems.
Abstract: In this paper, the completed investigation of a possible superconducting phase in monolayer indium selenide is determined using first-principles calculations for both the hole and electron doping systems. The hole-doped dependence of the Fermi surface is exclusively fundamental for monolayer InSe. It leads to the extensive modification of the Fermi surface from six separated pockets to two pockets by increasing the hole densities. For low hole doping levels of the system, below the Lifshitz transition point, superconductive critical temperatures ${T}_{c}\ensuremath{\sim}55--75$ K are obtained within anisotropic Eliashberg theory depending on varying amounts of the Coulomb potential from 0.2 to 0.1. However, for some hole doping above the Lifshitz transition point, the combination of the temperature dependence of the bare susceptibility and the strong electron-phonon interaction gives rise to a charge density wave that emerged at a temperature far above the corresponding ${T}_{c}$. Having included nonadiabatic effects, we could carefully analyze conditions for which either a superconductive or charge density wave phase occurs in the system. In addition, monolayer InSe becomes dynamically stable by including nonadiabatic effects for different carrier concentrations at room temperature.

16 citations


Journal ArticleDOI
TL;DR: In this article, photo-excited surface plasmons are coupled to the surface states to generate an electron gas, which is routed to a nano-antenna array through the giant electric field created by surface states.
Abstract: Surface states generally degrade semiconductor device performance by raising the charge injection barrier height, introducing localized trap states, inducing surface leakage current, and altering the electric potential. We show that the giant built-in electric field created by the surface states can be harnessed to enable passive wavelength conversion without utilizing any nonlinear optical phenomena. Photo-excited surface plasmons are coupled to the surface states to generate an electron gas, which is routed to a nanoantenna array through the giant electric field created by the surface states. The induced current on the nanoantennas, which contains mixing product of different optical frequency components, generates radiation at the beat frequencies of the incident photons. We utilize the functionalities of plasmon-coupled surface states to demonstrate passive wavelength conversion of nanojoule optical pulses at a 1550 nm center wavelength to terahertz regime with efficiencies that exceed nonlinear optical methods by 4-orders of magnitude. Semiconductor surface states often stand in the way of device performance, but here, the authors take advantage of them for wavelength conversion. They present a compact, passive conversion device insensitive to optical alignment by using plasmon-coupled surface states that enable the efficient conversion without nonlinear phenomena.

15 citations


Journal ArticleDOI
TL;DR: In this article, the authors showed that the movement of liquid metal is directly driven by viscous forces of solution rather than interfacial tension and analyzed flow characteristics on a liquid metal surface.
Abstract: The Marangoni effect, induced by the surface tension gradient resulting from the gradient of temperature, concentration, or electric potential gradient along a surface, is commonly utilized to manipulate a droplet. It is also the reason for unique behaviors of liquid metal such as moving, breathing, and large-scale deformation under an electric field, which have aroused tremendous interest in academics. However, liquid metal droplets are usually treated as solid marbles, which neglect their fluidic features and can hardly explain some unusual phenomena, such as a droplet under a stationary electric field that moves in the opposite direction in different solutions. To better clarify these discrepancies, this study reveals that the movement of liquid metal is directly driven by viscous forces of solution rather than interfacial tension. This mechanism was determined by analyzing flow characteristics on a liquid metal surface. Additionally, experiments with liquid metal free falling in solution, liquid metal droplet movement experiments on substrates with different roughness, and liquid metal droplet movement experiments under high current density were additionally conducted to verify the theoretical interpretation. This research is instrumental for a greater understanding of the movement of liquid metal under an electric field and lays the foundation for the applications of liquid metal droplets in pumping, fluid mixing, and many other microfluidic fields.

14 citations


Journal ArticleDOI
TL;DR: In this paper, the influence of the electric and magnetic quantities on the reversible adhesion between a half-space of the multi-ferroic composite material and a rigid conical indenter is investigated.

13 citations


Journal ArticleDOI
TL;DR: In this paper, the analytical solutions of the Klein-Gordon equation for any l states of the modified effective mass potential under the modified unequal scalar and vector Coulomb-Hulthen potential were presented.
Abstract: In this study, the analytical solutions of the Klein–Gordon equation for any l states of the modified effective mass potential under the modified unequal scalar and vector Coulomb–Hulthen potential...

Journal ArticleDOI
TL;DR: In this article, the authors provide an applicable method to predict the distribution of the electric potential inside the winding of an electrical machine with a reasonable set of parameters and provide an introduction to the fundamental process of voltage stress on electrical machine windings and discusses drivers for upcoming challenges in the field of winding insulation and partial discharges.
Abstract: This article provides an applicable method to predict the distribution of the electric potential inside the winding of an electrical machine with a reasonable set of parameters. It extends the understanding of the winding impedance in terms of the inter-winding behavior and gives us the opportunity to properly design the insulation system during the development phase of an electrical machine. Predictions are backed up by measurements and an in-depth look at the measurement setup. The results proof nonuniform potential distribution and show that the potential difference between individual turns exceeds the amplitude of the phase voltage. Our findings also establish an interrelation between the winding impedance and the potential oscillations inside the winding. The article provides an introduction to the fundamental process of voltage stress on electrical machine windings and discusses drivers for upcoming challenges in the field of winding insulation and partial discharges.

Journal ArticleDOI
TL;DR: In this paper, the dynamics of droplets and oscillation of electrified meniscus at low flow rates in an external electric field were investigated, where the evolution of droplet formation was recorded by a high-speed digital camera.

Journal ArticleDOI
TL;DR: In this article, an investigation of the underlying mechanism behind the interface charge barrier between oil and oil immersed paper is presented, and the results show that the amount of interface charge changes with the type of oils and papers, and is much larger than the Maxwell-Wagner-Sillars (MWS) polarization charge.
Abstract: This paper presents an investigation of the underlying mechanism behind the interface charge barrier between oil and oil immersed paper. Two types of oils and two types of cellulose papers are selected in the study. The interface charges of the samples are measured by the pulsed electro-acoustic (PEA) method and the zeta potentials of different oil-paper combinations are also measured. The results show that the amount of interface charge changes with the type of oils and papers, and is much larger than the Maxwell-Wagner-Sillars (MWS) polarization charge. The difference in the amount of interface charges cannot be attributed to the difference in the conductivity and permittivity of the materials. It is suggested that the barrier for charge transport across the interface, which is formed due to the electric double layer, should be taken into consideration to explain the interface charge behavior in oil-paper insulation.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the heat transfer and pressure drop of Alumina/oil nanofluid flow in a miniaturized square channel in the presence of strong DC electric fields.
Abstract: The present work aims to investigate the heat transfer and pressure drop of Alumina/oil nanofluid flow in a miniaturized square channel in the presence of strong DC electric fields. The high voltage was applied using a thin wire on top of the channel. The bottom of the channel was used as both a ground electrode and a heated surface. Results showed that increasing particle concentration caused heat transfer augmentation for all Reynolds numbers. Applying a strong electric potential of 15.51 kV resulted in considerable heat transfer enhancement of 52% for the nanofluid with 0.3% volume fraction, at the Reynolds number of 7. This considerable enhancement can be attributed to the formation of the ion injection-based secondary flows and motion of the particles. The generated secondary flow disrupts the boundary layer and increases the heat absorption from the heated surface. The experiments were confined to the volume fraction of 0.3% since the rapid agglomeration of particles occurred on electrode and walls at the volume fraction of 0.5%.

Journal ArticleDOI
TL;DR: In this article, the impact of Joule heating due to electric double layer (EDL) and viscous dissipation on electroosmotic mixed convection flow in a vertical microchannel with asymmetric heat fluxes is established.

Journal ArticleDOI
TL;DR: In this article, a quasi-one-dimensional Poisson-Nernst-Planck system for ionic flow through a membrane channel is studied, where the cross-section area of the channel is included in the system to provide certain information of the geometry of the three-dimensional channel.
Abstract: A quasi-one-dimensional Poisson–Nernst–Planck system for ionic flow through a membrane channel is studied. Nonzero but small permanent charge, the major structural quantity of an ion channel, is included in the model. The system includes three ion species, two cations with the same valences and one anion, which provides more correlations/interactions between ions compared to the case included only two oppositely charged particles. The cross-section area of the channel is included in the system, which provides certain information of the geometry of the three-dimensional channel. This is crucial for our analysis. Under the framework of geometric singular perturbation theory, more importantly, the specific structure of the model, the existence and local uniqueness of solutions to the system for small permanent charges is established. Furthermore, treating the permanent charge as a small parameter, through regular perturbation analysis, we are able to derive approximations of the individual fluxes explicitly, and this allows us to examine the small permanent charge effects on ionic flows in detail. Of particular interest is the competition between two cations, which is related to the selectivity phenomena of ion channels. Critical potentials are identified and their roles in characterizing ionic flow properties are studied. Some critical potentials can be estimated experimentally, and this provides an efficient way to adjust/control boundary conditions (electric potential and concentrations) to observe distinct qualitative properties of ionic flows. Mathematical analysis further indicates that to optimize the effect of permanent charges, a short and narrow filter, within which the permanent charge is confined, is expected, which is consistent with the typical structure of an ion channel.

Journal ArticleDOI
TL;DR: A Darwin field model is presented, which results in a two-step algorithm, where the discrete representations of the electric scalar potential and the magnetic vector potential are computed consecutively.
Abstract: In the absence of wave propagation, transient electromagnetic fields are governed by a composite scalar/vector potential formulation for the quasi-static Darwin field model Darwin-type field models are capable of capturing inductive, resistive, and capacitive effects To avoid possibly non-symmetric and ill-conditioned fully discrete monolithic formulations, here, a Darwin field model is presented, which results in a two-step algorithm, where the discrete representations of the electric scalar potential and the magnetic vector potential are computed consecutively Numerical simulations show the validity of the presented approach

Journal ArticleDOI
TL;DR: In this paper, transient optical spectroscopy is used to quantify the temperature-dependence of charge separation and recombination dynamics in P3TEA:SF-PDI2 and PM6:Y6, two non-fullerene organic photovoltaic (OPV) systems with a negligible driving force and high photocurrent quantum yields.
Abstract: Transient optical spectroscopy is used to quantify the temperature-dependence of charge separation and recombination dynamics in P3TEA:SF-PDI2 and PM6:Y6, two non-fullerene organic photovoltaic (OPV) systems with a negligible driving force and high photocurrent quantum yields. By tracking the intensity of the transient electroabsorption response that arises upon interfacial charge separation in P3TEA:SF-PDI2, a free charge generation rate constant of ≈2.4 × 1010 s−1 is observed at room temperature, with an average energy of ≈230 meV stored between the interfacial charge pairs. Thermally activated charge separation is also observed in PM6:Y6, and a faster charge separation rate of ≈5.5 × 1010 s−1 is estimated at room temperature, which is consistent with the higher device efficiency. When both blends are cooled down to cryogenic temperature, the reduced charge separation rate leads to increasing charge recombination either directly at the donor-acceptor interface or via the emissive singlet exciton state. A kinetic model is used to rationalize the results, showing that although photogenerated charges have to overcome a significant Coulomb potential to generate free carriers, OPV blends can achieve high photocurrent generation yields given that the thermal dissociation rate of charges outcompetes the recombination rate.

Journal ArticleDOI
01 Sep 2021-Energy
TL;DR: In this paper, the authors presented a continuous model for improving energy harvesting from the aeroelastic flutter induced vibrations based on the use of magneto-electro-elastic (MEE) materials.

Journal ArticleDOI
01 Jan 2021
TL;DR: In this paper, the electric field induced second harmonic generation (E-FISH) was applied to a laminar non-premixed counterflow flame by applying modulated direct current (DC) electric field with a microsecond duration zero volt pulse.
Abstract: The application of an electric field to a flame modifies the flame characteristics due to the collective motion of charged particles generated within the flame. The applied field mobilises electrons and ions depending on their polarity, leading to localised regions of space charge with sufficient density to either locally amplify or shield the applied electric field. A fundamental understanding of the local electric field is essential for both electrically and plasma-assisted combustion, because it determines electric body force as well as electron temperature. In this work, we propose a method, which is independent of gas composition and temperature, to measure the local electric field using electric field induced second harmonic generation (E-FISH). We successfully apply this method to a laminar nonpremixed counterflow flame by applying modulated direct current (DC) electric field with a microsecond duration zero volt pulse. Electric potential and space charge distribution are also deduced from the measured electric field. Furthermore, we show the importance of electron attachment to O2 forming O2− by changing the polarity of the applied DC electric field. When the anode is in the oxygen stream, a region of negative charge is obtained near the anode, whereas, when the anode is in the fuel stream, no region of negative charge is found. We also find the qualitative trends of the measured electric fields reasonably agree with previously reported one-dimensional modelling results. The limitations of the methodology are addressed, and we show that the ability to modulate the DC voltage on sub-microsecond timescales is required for accurate quantitative measurements.

Journal ArticleDOI
TL;DR: In this paper, a light beam can induce a persistent in-plane photoelectric voltage along, instead of across, silicon-water interfaces, which is attributed to the following movement of a charge packet in the vicinity of the silicon surface, whose formation is driven by the lightinduced potential change across the capacitive interface and a high permittivity of water with large polarity.
Abstract: External photo-stimuli on heterojunctions commonly induce an electric potential gradient across the interface therein, such as photovoltaic effect, giving rise to various present-day technical devices. In contrast, in-plane potential gradient along the interface has been rarely observed. Here we show that scanning a light beam can induce a persistent in-plane photoelectric voltage along, instead of across, silicon-water interfaces. It is attributed to the following movement of a charge packet in the vicinity of the silicon surface, whose formation is driven by the light-induced potential change across the capacitive interface and a high permittivity of water with large polarity. Other polar liquids and hydrogel on silicon also allow the generation of the in-plane photovoltage, which is, however, negligible for nonpolar liquids. Based on the finding, a portable silicon-hydrogel array has been constructed for detecting the shadow path of a moving Cubaris. Our study opens a window for silicon-based photoelectronics through introducing semiconductor-water interfaces.

Journal ArticleDOI
TL;DR: In this paper, the authors describe how recombination at interfaces is related to the distribution of electric potential within the device based on drift-diffusion simulations and show that interface recombination in PSCs can only be fully understood when the whole device is considered.
Abstract: The main losses in perovskite solar cells (PSCs) are often related to their charge-transport layers (CTLs). While it has been shown how losses related to charge extraction and recombination at the CTL interfaces can be minimized individually, a comprehensive picture is still lacking. In this work, we describe how recombination at interfaces is related to the distribution of electric potential within the device based on drift-diffusion simulations. Our results show that interface recombination in PSCs can only be fully understood when the whole device is considered. We find that devices with poor conductivity in the CTLs or small built-in potential will suffer from fast recombination at interfaces and that the interface recombination can be avoided by improving these. To illustrate our results, we present a framework that provides an intuitive way to understand electrical potential and compare losses in PSCs. We show that the simulation data can be well understood within the framework for the whole range of parameters studied.

Journal ArticleDOI
TL;DR: In this paper, a tethered balloon equipped with an instrumented platform was used to examine the altitude distribution of principal quantities of the lowest atmospheric region of the global electric circuit, radon volumetric activity, and aerosol particles concentration.

Journal ArticleDOI
TL;DR: In this paper, a coupled finite element procedure for the situation where the domains of the mechanical and electrostatic problems coincide is developed. But the procedure is not suitable for the case of large volume increase in the tube due to the triggering of instabilities.
Abstract: Soft dielectric elastomers with high relative permittivity, very low modulus and high electric breakdown strength have emerged as promising materials for various applications as sensors, actuators and in energy harvesting and soft robotics. We study the intricate deformation behaviour of a soft dielectric elastomer tube of finite length and closed ends, that carries a dead load, is internally pressurised by an injected fluid and has a high electric potential applied across its walls. As for soft tubes in the absence of a potential, this electro-hyperelastic problem involving very large deformations, exhibits a multitude of possibilities, including homogeneous deformation, inhomogeneous bifurcation, snap-through instabilities and post bifurcation behaviour in the form of propagation of axisymmetric bulges. We develop a coupled Finite Element procedure for the situation where the domains of the mechanical and electrostatic problems coincide. The procedure can handle volume flow rate controlled electro-elastic problems. We use it to study the many aspects of the deformation behaviour and limitations placed by competing failure mechanisms on practical utilisation of the large areal strains and axial actuations that can be produced. If electrical breakdown can be avoided by ingenious design of loading sequences, the large volume increase in the tube due to the triggering of instabilities can be harnessed and has far-reaching technological implications.

Journal ArticleDOI
TL;DR: In this article, the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel have been studied and the Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation).
Abstract: The objective of this research is to study the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel. A two-phase model of a nanofluid, Maxwell’s model of thermal conductivity [1], and no-slip velocity and thermal boundary conditions have been used in this study. Hall effects, Joule heating (due to magnetic and electric fields), and viscous heating aspects are under consideration. Governing equations for the present flow configuration have been modeled and simplified by enforcing the lubrication scheme. Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation). Resulting expressions are solved numerically through the NDSolve command in Mathematica and plotted in order to understand the effects of different dimensionless parameters on the temperature, stress, heat transmission rate, and fluid’s velocity. Graphical results demonstrated that the thermal transmission rate is augmented by increasing the Hartmann number, Brinkman number, and Debye-Huckel parameter while decreases for zeta potential ratio, Joule dissipation parameter, and electro-osmotic velocity. A decrease in axial velocity is noted near the lower wall for higher values of $${m}^{\ast}$$ .

Journal ArticleDOI
TL;DR: In this article, the effect of the position and amount of surface charges on cylindrical polytetrafluoroethylene (PTFE) insulators with different surface conductivities is studied.
Abstract: The effect of the position and amount of surface charges on cylindrical polytetrafluoroethylene (PTFE) insulators with different surface conductivities is studied. The surface potential decay property with time is investigated subjected to different electric fields. A simulation model for charge transport is established. The results show that the surface potential decays exponentially after surface treatment. The decay rate of surface charges increases with the surface conductivity. At $t = 180$ seconds, the decay rates of surface potentials for different surface conductivity are 2%, 42%, 60% and 84%, respectively. For samples with the same surface conductivity, the decay rates of surface potentials under different initial values are about 57%, and the decay rates at different accumulated locations are about 62%. It is demonstrated that the surface charge decay rate has little difference when initial charges with different amount and positions are introduced. However, the dissipation of surface charges can be promoted by applying a voltage of the same polarity. When the surface conductivity is increased to 5.1 × 10−16 S, the potential decay rate under the applied voltage increases to 76%. Furthermore, the flashover voltage decreases with the increase of surface conductivity. As a result, the effect of homopolar surface charges on the flashover voltage is reduced.

Journal ArticleDOI
TL;DR: In this paper, the effects of equal and opposite normal stresses applied at the top and bottom surfaces of a piezoelectric semiconductor plate of crystals of class 6mm were investigated.
Abstract: We study the effects of equal and opposite normal stresses applied at the top and bottom surfaces of a piezoelectric semiconductor plate of crystals of class (6 mm). A first-order plate theory is established to model the stress-induced thickness-extensional deformation which is coupled to the in-plane extensional deformation of the plate. Analytical solutions are obtained for a rectangular plate under uniform or local normal stresses on the surfaces of the plate. In the case of a uniform load, a combination of parameters is identified which characterizes the strength of the coupling effect of interest, i.e., the thickness stress-induced redistribution of mobile charges. In the case of a local load applied to the central part of the plate, it is found that a local potential barrier is created. The potential barrier is accompanied by local distributions of mobile charges. The dependence of the potential barrier on various physical and geometric parameters is examined.

Journal ArticleDOI
TL;DR: In this article, a dye-sensitized cation-exchange membrane was used for light-to-ionic power conversion and measured photovoltages were consistent with charge separation of a proton from its photoacid conjugate base that is driven by intrinsic liquid-junction-forming crossover of acid.
Abstract: Junctions that form at interfaces of electronic semiconductors can lead to space–charge regions, which when properly designed result in diode behavior through current rectification. Space–charge regions are not unique to semiconductor interfaces and also form at ion-exchange-membrane interfaces, with properties that can be tuned by varying the concentration of ions in the contacting phases. Using this as a guide, and motivated by traditional dye-sensitized solar cells, we bathed photoacid-dye-sensitized cation-exchange membranes in aqueous solutions of varied electrolyte concentration and analyzed them for their ability to exhibit photovoltaic action. As predicted by Donnan membrane theory and semiconductor diode theory, the thermodynamic properties of each contacting phase determined the magnitude and sign of the net built-in electric potential difference. Measured open-circuit photovoltages were directly related to these electric potential differences, albeit the sign of the photovoltages was opposite (“reverse”) of that expected based on the sign of net electric potential differences across the membrane. Mechanistic details gleaned using transient absorption spectroscopy indicate that our photoacid dyes only photogenerate protons as the mobile charged species. Because our dye-sensitized cation-exchange membranes were infiltrated with protons, this means that minority-carrier hydroxides were not able to elicit photovoltaic action by standard minority-carrier-dominated effects. Instead, measured photovoltages are consistent with charge separation of a proton from its photoacid conjugate base that is driven by intrinsic liquid-junction-forming crossover of acid, which results in bulk membrane polarization and “reverse” photovoltaic action. These observations inform design guidelines for the use of water as a protonic semiconductor in devices for light-to-ionic power conversion.

Proceedings ArticleDOI
01 Feb 2021
TL;DR: PCEsolve as mentioned in this paper proposes a new data-driven meshless 2D analysis method, called PCEsolve, of electric potential and electric fields based on the physics-constrained deep learning scheme.
Abstract: Computing the electric potential and electric field is important for modeling and analysis of VLSI chip and high speed circuits. For instance, it is an important step for DC analysis for high speed circuits as well as dielectric reliability and capacitance extraction for VLSI interconnects. In this paper, we propose a new data-driven meshless 2D analysis method, called PCEsolve, of electric potential and electric fields based on the physics-constrained deep learning scheme. We show how to formulate the differential loss functions to consider the Laplace differential equations with voltage boundary conditions for typical electrostatic analysis problem so that the supervised learning process can be carried out. We apply the resulting PCEsolve solver to calculate electric potential and electric field for VLSI interconnects with complicated boundaries. We show the potential and limitations of physics-constrained deep learning for practical electrostatics analysis. Our study for purely label-free training (in which no information from FEM solver is provided) shows that PCEsolve can get accurate results around the boundaries, but the accuracy degenerates in regions far away from the boundaries. To mitigate this problem, we explore to add some simulation data or labels at collocation points derived from FEM analysis and resulting PCEsolve can be much more accurate across all the solution domain. Numerical results demonstrate that the PCEsolve achieves an average error rate of 3.6% on 64 cases with random boundary conditions and it is 27.5× faster than COMSOL on test cases. The speedup can be further boosted to ~ 38000× in single-point estimations. We also study the impacts of weights on different components of loss functions to improve the model accuracy for both voltage and electric field.