Laws Of Electrostatics Research Articles

A new constituent of electrostatic energy in semiconductors

This work revisits the classical concept of electric energy and suggests that the common definition is likely to generate large errors when dealing with nanostructures. For instance, deriving the electrostatic energy in semiconductors using the traditional formula fails at giving the correct electrostatic force between capacitor plates and reveals the existence of an extra contribution to the standard electrostatic energy. This additional energy is found to proceed from the generation of space charge regions which are predicted when combining electrostatics laws with semiconductor statistics, such as for accumulation and inversion layers. On the contrary, no such energy exists when relying on electrostatics only, as for instance when adopting the so-called full depletion approximation. The same holds for charged or neutral insulators that are still consistent with the customary definition, but which are in fact singular cases. In semiconductors, this additional free energy can largely exceed the energy gained by the dipoles, thus becoming the dominant term. Consequently, erroneous electrostatic forces in nanostructure systems such as for MEMS and NEMS as well as incorrect energy calculations are expected using the standard definition. This unexpected result clearly asks for a generalization of electrostatic energy in matter in order to reconcile basic concepts and to prevent flawed force evaluation in nanostructures with electrical charges.

(Invited) Physics of Electronic Transport in Low-Dimensionality Materials for Future FETs

The scaling of electronic devices has continued unabated for the past 5 decades, despite repeated predictions of the "end of scaling". The "more than Moore" slogan has been, and still is, viewed by industry as a need to explore realistic low-to-medium-risk avenues, some already in production -- such as strained Si/Ge or high-κ dielectrics, some yet to be translated to products in the near future or never -- such III-V semiconductors or tunnel-FETs. On the contrary, Academia has looked far ahead, even beyond carbon-based electronics (carbon nanotubes, graphene, nanoribbons). Now that the ULSI technology is looking at a feature size of 5 nm by 2026, even more “improbable” alternatives are considered, including transition metal dichalcogenides (TMDs), silicene/ane, germanene/ane (together with other *enes and *anes), topological insulators, Weyl semimetals, and other strongly correlated fermion systems. Here I will first discuss the fact that, if we really wish to scale to 5 nm, simple electrostatic scaling laws demand that we take two-dimensional materials very seriously, despite their thermodynamic instability (Mermin-Wagner theorem) and the related technological difficulties. I will first consider how electronic transport in non mirror-symmetric 2D crystals (e.g., silicene, germanene, stanene, TMDs of the 1T/T’ crystal structure) may be severely affected by coupling of the electrons with the acoustic flexural modes (ZA-phonons). I will then consider whether graphene has any chance of replacing Si by looking at how the extremely promising electronic properties it exhibits in its ideal form become much less interesting when it becomes a component of some non-ideal structure (such when supported and gated and/or in nanoribbon form). Finally, I will discuss a couple of very interesting admittedly improbable but fun ideas: 1. The Bose-Einstein condensation in bilayer systems (motivating UT-Austin’s BiSFETs) as an example of how issues of practical implementation may regrettably transform an excellent idea into a pure academic exercise; and 2. Monolayer tin (“stannanane”) as a 2D topological insulator with potential applications in spintronics and low-power high-performance devices (… assuming we can make it, of course…). For the entire discussion I will keep density functional theory (DFT), empirical pseudopotentials, and transport equations in the background. This work qas done in collaboration with Shela Aboud, Bo Fu, Jiseok Kim, Sudarshan Narayanan, Ana Suarez Negreira, Zhun-Yong Ong, Cathy Sachs, and William Vandenberghe.

The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential.

The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension-of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of the bulk phases and the intrinsic polarization of the interface. The coefficient of the dielectro-Marangoni effect (surface flow due to gradient of the normal electric field) is found. A model of the Langevin type for the surface dipole moment and the intrinsic surface polarizability is presented.

Graphene-Based Plasmonic Tunable Low-Pass Filters in the Terahertz Band

We propose the concept, synthesis, analysis, and design of graphene-based plasmonic tunable low-pass filters operating in the THz band. The proposed structure is composed of a graphene strip transferred onto a dielectric and a set of polysilicon DC gating pads located beneath it. This structure implements a stepped impedance low-pass filter for the propagating surface plasmons by adequately controlling the guiding properties of each strip section through graphene's field effect. A synthesis procedure is presented to design filters with desired specifications in terms of cut-off frequency, in-band performance, and rejection characteristics. The electromagnetic modeling of the structure is efficiently performed by combining an electrostatic scaling law to compute the guiding features of each strip section with a transmission line and transfer-matrix framework, approach further validated via full wave simulations. The performance of the proposed filters is evaluated in practical scenarios, taking into account the presence of the gating bias and the influence of graphene's losses. These results, together with the high miniaturization associated with plasmonic propagation, are very promising for the future use and integration of the proposed filters with other graphene and silicon-based elements in innovative THz communication systems.

A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere.

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three-dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions: when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.

Simulations of plasma obeying Coulomb's law and the formation of suprathermal ion tails in the solar wind

AbstractWe present a model for the velocity distribution function (VDF) of the suprathermal ion tail in the solar wind and its commonly observed spectrum, a power law in velocity of index −5. The mechanism for our model is acceleration from extremely small scale electric fields caused by the finite number of particles in the solar wind (or any plasma). The simulations produce a VDF with a broken power law at short times and a type of κ distribution VDF at later times. The simulation uses very few assumptions as it is based solely on Coulomb's law, and the results are robust to a range of parameters that, although outside the range of the solar wind at 1 AU, are close to those in the lower solar atmosphere. Furthermore, we provide predictions based on the following mechanism: the probability distribution function for the electric field (the electric field distribution function or EDF) dictates the final state of the plasma, which means that the VDF at any time is a convolution of the initial VDF and the EDF. We have also shown that by varying the power law index of the electrostatic force law, the relationship between the two is such that the EDF power law index is exactly 5 for Coulomb's law, harder for shorter‐range forces, and softer for longer‐range forces, converging to a power law of index 3 in the former limit and to a Maxwellian in the latter.

Optimum design of gravity and reinforced retaining walls using enhanced charged system search algorithm

This paper develops a methodology to obtain the optimum design of the gravity and reinforced cantilever retaining walls in terms of least-cost, having different cases of backfill satisfying the stability criteria, according to the height and properties of earth that the wall are required to support. An Enhanced Charged System Search Algorithm (ECSS) is utilized to find the economical sections as the output after minimizing the cost. The ECSS is one of the recently developed meta-heuristic algorithms that is inspired by the Coulomb and Gauss’s laws of electrostatics in physics. In order to evaluate the efficiency of this algorithm, some numerical examples are utilized. Comparing the results of the retaining wall designs obtained by the other methods illustrates a good performance of the ECSS.

Quadrupole terms in the Maxwell equations: Debye-Hückel theory in quadrupolarizable solvent and self-salting-out of electrolytes.

If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient γ± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally γ±. Comparison with experimental data for γ± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ≈ 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy.

MODELLING OF NEUTRAL VACANCIES IN FORSTERITE MINERAL

Density functional theory and generalized gradient approximation have been employed to study Mg , Si and O vacancies in the Mg2SiO4forsterite mineral. Microstructure of defect equilibrium geometries, electronic properties as well as chemical bonding in the region surrounding each one of the vacancies have been computed and discussed in detail. It is found that vacancies tend to increase covalent character of the chemical bonding for atoms situated in their vicinity independently of the type of vacancy. Nevertheless, obtained atomic distortion in the region surrounding vacancies generally obeys Coulomb electrostatic interaction law. Local energy states are found in the band-gap region due to the occurrence of vacancy-type defects. These findings are discussed in light of the available experimental data.

The principle of minimal episteric distortion of the water matrix and its steering role in protein folding

A significant episteric ("around a solid") distortion of the hydrogen-bond structure of water is promoted by solutes with nanoscale surface detail and physico-chemical complexity, such as soluble natural proteins. These structural distortions defy analysis because the discrete nature of the solvent at the interface is not upheld by the continuous laws of electrostatics. This work derives and validates an electrostatic equation that governs the episteric distortions of the hydrogen-bond matrix. The equation correlates distortions from bulk-like structural patterns with anomalous polarization components that do not align with the electrostatic field of the solute. The result implies that the interfacial energy stored in the orthogonal polarization correlates with the distortion of the water hydrogen-bond network. The result is validated vis-à-vis experimental data on protein interfacial thermodynamics and is interpreted in terms of the interaction energy between the electrostatic field of the solute and the dipole moment induced by the anomalous polarization of interfacial water. Finally, we consider solutes capable of changing their interface through conformational transitions and introduce a principle of minimal episteric distortion (MED) of the water matrix. We assess the importance of the MED principle in the context of protein folding, concluding that the native fold may be identified topologically with the conformation that minimizes the interfacial tension or disruption of the water matrix.

Modeling of slender laminated piezoelastic beams with resistive electrodes—comparison of analytical results with three-dimensional finite element calculations

In this work a theory for a slender piezoelectric laminated beam taking into account lossy electrodes is developed. For the modeling of the bending behavior of the beam with conductivity, the kinematical assumptions of Bernoulli–Euler and a simplified form of the Telegraph equations are used. Applying d’Alembert’s principle, Gauss’ law of electrostatics and Kirchhoff’s voltage and current rules, the partial differential equations of motion are derived, describing the bending vibrations of the beam and the voltage distribution and current flow along the resistive electrodes. The theory is valid for applications that are used for actuation and for sensing. In the first case the voltage at a certain location on the electrodes is prescribed and the beam is deformed, whereas in the second case the structure is excited by a distributed external load and the voltage distribution is a result of the structural deformation. For a bimorph with constant width and constant material properties the beam is governed by two coupled partial differential equations for the elastic deformation and for the voltage distribution: the first one is an extension of the Bernoulli–Euler equation of an elastic beam, the second one is a diffusion equation for the voltage. The analytical results of the developed theory are validated by means of three-dimensional electromechanically coupled finite element simulations with ANSYS 11.0. Different mechanical and electrical boundary conditions and resistances of the electrodes are considered in the numerical case study. Eigenfrequencies are compared and the frequency responses of the mechanical and electrical quantities show a good agreement between the proposed beam theory and FE results.

A hybrid CSS and PSO algorithm for optimal design of structures

A new hybrid meta-heuristic optimization algorithm is presented for design of structures. The algorithm is based on the concepts of the charged system search (CSS) and the particle swarm optimization (PSO) algorithms. The CSS is inspired by the Coulomb and Gauss's laws of electrostatics in physics, the governing laws of motion from the Newtonian mechanics, and the PSO is based on the swarm intelligence and utilizes the information of the best fitness historically achieved by the particles (local best) and by the best among all the particles (global best). In the new hybrid algorithm, each agent is affected by local and global best positions stored in the charged memory considering the governing laws of electrical physics. Three different types of structures are optimized as the numerical examples with the new algorithm. Comparison of the results of the hybrid algorithm with those of other meta-heuristic algorithms proves the robustness of the new algorithm.

Optimum Design of Gravity Retaining Walls Using Charged System Search Algorithm

This study focuses on the optimum design retaining walls, as one of the familiar types of the retaining walls which may be constructed of stone masonry, unreinforced concrete, or reinforced concrete. The material cost is one of the major factors in the construction of gravity retaining walls therefore, minimizing the weight or volume of these systems can reduce the cost. To obtain an optimal seismic design of such structures, this paper proposes a method based on a novel meta‐heuristic algorithm. The algorithm is inspired by the Coulomb′s and Gauss’s laws of electrostatics in physics, and it is called charged system search (CSS). In order to evaluate the efficiency of this algorithm, an example is utilized. Comparing the results of the retaining wall designs obtained by the other methods illustrates a good performance of the CSS. In this paper, we used the Mononobe‐Okabe method which is one of the pseudostatic approaches to determine the dynamic earth pressure.

Near-field multiple scattering effects of plasmonic nanospheres embedded into thin-film organic solar cells

We investigate near-field multiple scattering effects of plasmonic nanospheres (NSPs) embedded into organic solar cells (OSCs). When NSPs are embedded into a spacer layer, the near-field scattering from the NSPs shows strong direction-dependent features, which significantly affects the optical absorption. When NSPs are embedded into an active layer, the absorption enhancement is attributed to the interplay between longitudinal and transverse modes supported by the NSP chain. The breakdown of electrostatic scaling law is confirmed by our theoretical model and should be accounted for optical designs of OSCs. The work provides the fundamental physical understanding and design guidelines for plasmonic photovoltaics.

Unruh-Verlinde temperature and energy of (2+1)-dimensional matter coupled black hole via entropic force

Verlinde's recent work, which shows that gravity may be explained as an entropic force caused by the changes in information associated with the positions of material bodies, is extended to study the Unruh-Verlinde temperature and energy of a static spherically symmetric charged black hole. The results indicate that the Unruh-Verlinde temperature is equal to the Hawking temperature at the event horizon. The energy is dependent on the radius of the screen, which is also a consequence of the Gauss' laws of gravity and electrostatics.

A comparative study of smart passive piezoelectric structures interacting withelectric networks: Timoshenko beam theory versus finite element plane stresscalculations

The present paper is devoted to the coupling between mechanical, piezoelectric and electricfields in piezoelastic beams whose electrodes are connected by electric circuits witharbitrary impedances. Taking advantage of the linear piezoelectric constitutiverelations, the kinematic assumptions according to Timoshenko, the Gauss law ofelectrostatics as well as Kirchhoff’s voltage rule, the equations of motion for lateralvibrations are derived in the Laplace domain considering the direct and conversepiezoelectric effects. For beams with layerwise constant width, the governingequations are similar to the well-known Timoshenko beam equations, but the bendingmoment is extended by a so-called induced electric moment, which is influenced bythe electric circuits. In order to demonstrate the interaction of mechanical andelectrical fields, the theory that we develop is compared against plane stress finiteelement computations using ANSYS. For flexural vibrations with various mechanicalboundary conditions and electric impedances, an eigenfrequency analysis is performedand mechanical and electrical field variables are compared for different harmonicexcitations.

Unruh–Verlinde Temperature and Energy of Charged Black Hole via Entropic Force

Verlinde’s recent work, which showed that gravity may be explained as entropic force caused by the changes of information associated with the positions of material bodies, is extended to study the Unruh–Verlinde temperature and energy of a static spherically symmetric charged black hole. The results indicate that the Unruh–Verlinde temperature is equal to the Hawking temperature at the outer and inner horizons. The energy is dependent on the radius of the screen, which is also a consequence of the Gauss’ laws of gravity and electrostatics.

Orbital dynamics of two electrically charged conducting spheres

The similar forms of Coulomb’s law of electrostatics and Newton’s law of gravitation suggest that two oppositely charged spheres can orbit each other by means of the electrostatic force. We demonstrate electrostatic binary orbits using two oppositely charged graphite coated Styrofoam® spheres. The experiment was conducted on the NASA aircraft Weightless Wonder which simulates weightless conditions. Videos of 23 orbital attempts were analyzed to investigate the dynamics and orbital stability of the two sphere system. The results support predictions of a recently developed theory that establishes criteria for stable orbits between two conducting, electrically charged spheres.

Charged system search for optimum grillage system design using the LRFD-AISC code

Grillage systems are widely used in structures to cover large areas in bridge decks, ship hulls and floors. In this paper, the charged system search (CSS) algorithm is utilized to obtain the optimum design of grillage systems. This algorithm is inspired by the Coulomb and Gauss laws of electrostatics in physics and the governing laws of motion from Newtonian mechanics. The cross-sectional properties of beams are considered as the design variables. Comparison of the results with those of some previous studies shows the robustness of the new algorithm.

A novel heuristic optimization method: charged system search

This paper presents a new optimization algorithm based on some principles from physics and mechanics, which will be called Charged System Search (CSS). We utilize the governing Coulomb law from electrostatics and the Newtonian laws of mechanics. CSS is a multi-agent approach in which each agent is a Charged Particle (CP). CPs can affect each other based on their fitness values and their separation distances. The quantity of the resultant force is determined by using the electrostatics laws and the quality of the movement is determined using Newtonian mechanics laws. CSS can be utilized in all optimization fields; especially it is suitable for non-smooth or non-convex domains. CSS needs neither the gradient information nor the continuity of the search space. The efficiency of the new approach is demonstrated using standard benchmark functions and some well-studied engineering design problems. A comparison of the results with those of other evolutionary algorithms shows that the proposed algorithm outperforms its rivals.