Polarization Charge Density Research Articles

Vacuum polarization of planar charged fermions with Coulomb and Aharonov–Bohm potentials

Vacuum polarization of charged massless fermions is investigated in the superposition of Coulomb and Aharonov–Bohm (AB) potentials in 2 + 1 dimensions. For this purpose, we construct the Green function of the two-dimensional Dirac equation with Coulomb and AB potentials (via the regular and irregular solutions of the radial Dirac equation) and then calculate the vacuum polarization charge density in the so-called subcritical and supercritical regimes. In the supercritical regime, the Green function has a discontinuity in the complex plane of “energy” due to the singularities on the negative energy axis; these singularities are situated on the unphysical sheet and related to the creation of infinitely many quasistationary fermionic states with negative energies. We expect that our results will be helpful in gaining deeper understanding of the fundamental problem of quantum electrodynamics which can be applied to the problems of charged impurity screening in graphene taking into consideration the electron spin.

Electromagnetic properties of zigzag graphene nanoribbons with single-row line defect

In this paper, electromagnetic properties of the zigzag graphene nanoribbon (ZGNR) with a single-row line defect are studied by using the first-principles method based on the density functional theory. The energy band structures, transmission spectra, spin polarization charge densities, total energies, and Bloch states of the ZGNR are calculated when the line defect is located at different positions inside a ZGNR. It is shown that ZGNRs with and without a line defect at nonmagnetic and ferromagnetic states are metals, but the reasons for it to become different metals are different. At the antiferromagnetic state, the closer to the edge of ZGNR the line defect, the more obvious the influence on electromagnetic properties of ZGNR is. In the process of the defect moving from the symmetrical axis of ZGNR to the edge, the ZGNR has a phase transition from a semiconductor to a half metal, and then to a metal gradually. Although the ZGNR with a line defect close to the central line is a semiconductor, its band gap is smaller than the band gap of perfect ZGNR, owing to the new band introduced by the defects. When the line defect is located nearest to the boundary, the ZGNR is stablest. When the line defect is located next nearest to the boundary, the ZGNR is unstablest. When the line defect is located nearest or next nearest to boundary, the ground state of the ZGNR is a ferromagnetic state. However, if the line defect is located at the symmetric axis of ZGNR (M5) or nearest to the symmetric axis, the ground state would be an antiferromagnetic state. At the antiferromagnetic state, the phase transition of M5 from a semiconductor to a half metal can be achieved by applying an appropriate transverse electric field. Without a transverse electric field, M5 is a semiconductor, and the band structures of up-and down-spin states are both degenerate. With a transverse electric field, band structures of up-and down-spin states near the Fermi level are both split. When the electric field intensity is 2 V/nm, M5 is a half metal. These obtained results are of significance for developing electronic nanodevices based on graphene.

Validity of one-dimensional QED for a system with spatial symmetry

We examine the accuracy of an intrinsically one-dimensional quantum electrodynamics to predict accurately the forces and charges of a three-dimensional system that has a high degree of symmetry and therefore depends effectively only on a single coordinate. As a test case we analyze two charged capacitor plates that are infinitely extended along two coordinate directions. Using the lowest-order fine structure correction to the photon propagator we compute the vacuum's induced charge polarization density and show that the force between the charged plates is increased. Although a one-dimensional theory cannot take the transverse character of the virtual (force-mediating) photons into account, nevertheless it predicts, in lowest order of the fine-structure constant, the Coulomb force law between the plates correctly. However, the quantum correction to the classical result is slightly different between the 1d and 3d theories with the polarization charge density induced from the vacuum underestimated by the 1d approach.

Optimized spatial matrix representations of quantum Hamiltonians

We examine the accuracy of several approaches to represent the quantum mechanical Schrödinger, Klein–Gordon and Dirac Hamilton operators by optimized spatial matrices. Two of the approaches are based on periodic and reflecting boundaries and have an error scaling with the number of spatial grid points that is significantly better than the ones based on the usual approaches where the momentum operator is approximated by finite-difference schemes. These N×N matrices are optimum in the sense that their eigenvalues and eigenvectors are exact representations on the spatial grid for the continuous solutions of the corresponding force-free Hamiltonian. As an example, we apply these techniques to compute the vacuum’s polarization charge density from the Dirac and Foldy–Wouthuysen theory.

Two-dimensional electron gas at thePbTiO3/SrTiO3interface: Anab initiostudy

In the polar catastrophe scenario, polar discontinuity accounts for the driving force of the formation of a two-dimensional electron gas (2DEG) at the interface between polar and non-polar insulators. In this paper, we substitute the usual, non-ferroelectric, polar material with a ferroelectric thin film and use the ferroelectric polarization as the source for polar discontinuity. We use ab initio simulations to systematically investigate the stability, formation and properties of the two-dimensional free-carrier gases formed in PbTiO$_3$/SrTiO$_3$ heterostructures under realistic mechanical and electrical boundary conditions. Above a critical thickness, the ferroelectric layers can be stabilized in the out-of-plane monodomain configuration due to the electrostatic screening provided by the free-carriers. Our simulations also predict that the system can be switched between three stable configurations (polarization up, down or zero), allowing the non-volatile manipulation of the free charge density and sign at the interface. Furthermore, the link between ferroelectric polarization and free charge density demonstrated by our analysis constitutes compelling support for the polar catastrophe model that is used to rationalize the formation of 2DEG at oxide interfaces.

Coulomb screening in graphene with topological defects

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green’s function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green’s function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.

Tuning the polarization-induced free hole density in nanowires graded from GaN to AlN

We report a systematic study of p-type polarization-induced doping in graded AlGaN nanowire light emitting diodes grown on silicon wafers by plasma-assisted molecular beam epitaxy. The composition gradient in the p-type base is varied in a set of samples from 0.7%Al/nm to 4.95%Al/nm corresponding to negative bound polarization charge densities of 2.2 × 1018 cm−3 to 1.6 × 1019 cm−3. Capacitance measurements and energy band modeling reveal that for gradients greater than or equal to 1.30%Al/nm, the deep donor concentration is negligible and free hole concentrations roughly equal to the bound polarization charge density are achieved up to 1.6 × 1019 cm−3 at a gradient of 4.95%Al/nm. Accurate grading lengths in the p- and n-side of the pn-junction are extracted from scanning transmission electron microscopy images and are used to support energy band calculation and capacitance modeling. These results demonstrate the robust nature of p-type polarization doping in nanowires and put an upper bound on the magnitude of deep donor compensation.

带电沙尘暴对电磁波传播过程的影响

Based on the polarization charge density and Rayleigh scattering theory, the impact of wind and sand electrostatic field on the optical properties of sand is discussed through numerical calculation and simulation. The results show that in considering the effects of sand electrostatic field, the sand scattering efficiency to electromagnetic waves firstly increases and then decreases with the charge distribution angle increasing, and the absorption efficiency to electromagnetic waves keeps a constant, but its magnitude is much larger than that of not considering the environmental electric field. In addition, the sandstorm attenuation to electromagnetic waves increases with the increase of particle concentration and humidity. Those results illustrate that it is necessary to consider the function of sandstorm electrostatic field in the remote sensing of sandstorm. ©, 2015, Chinese Optical Society. All right reserved.

Effect of dielectric constant on estimation of properties of ionic liquids: an analysis of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Influence of dielectric constant values in estimation of thermodynamical properties (vapor pressure, vaporization enthalpy, density and viscosity) of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids with COSMO-RS.

Effect of inserted AlN layer on the two-dimensional electron gas in AlxGa1-xN/AlN/GaN

This paper investigates the changes of electron transport properties in AlxGa1-xN/GaN with an inserted AlN layer. The polarization charge density and two-dimensional electron gas (2DEG) sheet density in AlxGa1-xN/AlN/GaN double heterojunction high electron mobility transistors (HEMT) affected by the spontaneous polarization and piezoelectric polarization in AlxGa1-xN and AlN barrier are studied. Relations of interface roughness scattering and alloy disorder scattering with the AlN thickness are systematically analyzed. It is found that the alloy disorder scattering is the main scattering mechanism in AlxGa1-xN/GaN heterojunction high-electron-mobility transistors, while the interface roughness scattering is the main scattering mechanism in AlxGa1-xN/AlN/GaN double-heterojunction structure. It is also known that the 2DEG sheet density, interface roughness scattering and alloy disorder scattering are depended on the thickness of the inserted AlN layer. The 2DEG sheet density increases slightly and the mobility increases obviously by inserting an AlN layer about 13 nm. Taking Al mole fraction of 0.3 as an example, if without AlN layer, the 2DEG sheet density is 1.47 1013 cm-2 with the mobility limited by the interface roughness scattering of 1.15 104 cm2V-1-1, and the mobility limited by alloy disorder scattering of 6.07 102cm2V-1-1. After inserting an AlN layer of 1 nm, the 2DEG sheet density increases to 1.66 1013cm-2, and the mobility limited by the interface roughness scattering reduces to 7.88 103cm2V-1-1 while the mobility limited by alloy disorder scattering increases greatly up to 1.42 108 cm2V-1-1.

Roles of V-shaped pits on the improvement of quantum efficiency in InGaN/GaN multiple quantum well light-emitting diodes

The roles of V-shaped pits on the improvement of quantum efficiency in InGaN/GaN multiple quantum well (MQW) light-emitting diodes are investigated by numerical simulation. The simulation results show that V-shaped pits cannot only screen dislocations, but also play an important role on promoting hole injection into the MQWs. It is revealed that the injection of holes into the MQW via the sidewalls of the V-shaped pits is easier than via the flat region, due to the lower polarization charge densities in the sidewall structure with lower In concentration and {10–11}-oriented semi-polar facets.

Influence of strain induced by AlN nucleation layer on the electrical properties of AlGaN/GaN heterostructures on Si(111) substrate

The crack-free metal-organic chemical vapor deposition (MOCVD) grown AlGaN/GaN heterostructures on Si substrate with modified growth conditions of AlN nucleation layer (NL) and its influence on the electrical and structural properties of conductive GaN layer are presented. From the Hall electrical measurements, a gradual decrease of two-dimensional electron gas (2DEG) concentration near heterointerface as the function of NL thickness is observed possibly due to the reduction in difference of piezoelectric polarization charge densities between AlGaN and GaN layers. It also indicates that the minimum tensile stress and a relatively less total dislocation density for high pressure grown NL can ensure a 20 % increment in mobility at room temperature irrespective of the interface roughness. The thickness and pressure variations in NL and the subsequent changes in growth mode of AlN contributing to the post growth residual tensile stress are investigated using X-ray diffraction and Raman scattering experiments, respectively. The post growth intrinsic residual stress in top layers of heterostructures arises from lattice mismatches, NL parameters and defect densities in GaN. Hence, efforts to reduce the intrinsic residual stress in current conducting GaN layer give an opportunity to further improve the electrical characteristics of AlGaN/GaN device structures on Si.

Theoretical model of the polarization Coulomb field scattering in strained AlGaN/AlN/GaN heterostructure field-effect transistors

The theoretical model of the polarization Coulomb field scattering (PCF) caused by the polarization charge density variation at the AlGaN/AlN interface in strained AlGaN/AlN/GaN heterostructure field-effect transistors has been developed. And the theoretical values for the electron drift mobility, which were calculated using the Matthiessen's rule that includes PCF, piezoelectric scattering, polar optical-phonon scattering, and interface roughness scattering, are in good agreement with our experimental values. Therefore, the theoretical model for PCF has been confirmed.

Space-time dynamics of the vacuum's polarization charge density

Using numerical solutions to the quantum-field theoretical Dirac equation, we study the space-time evolution of the vacuum's polarization charge and current densities induced by an external electric force in one spatial dimension. We discuss a simple analytical model that can predict the dynamics of the polarization dynamics for arbitrary external force configurations. We then study the corrections to these predictions when the external force becomes supercritical and real electron-positron pairs can be created. By coupling the Dirac equation to the Maxwell equations, we examine how the dynamics of the polarization density is affected, if we allow the corresponding induced charges to interact with each other.

A two-dimensional fully analytical model with polarization effect for off-state channel potential and electric field distributions of GaN-based field-plated high electron mobility transistor

In this paper, we present a two-dimensional (2D) fully analytical model with consideration of polarization effect for the channel potential and electric field distributions of the gate field-plated high electron mobility transistor (FP-HEMT) on the basis of 2D Poisson's solution. The dependences of the channel potential and electric field distributions on drain bias, polarization charge density, FP structure parameters, AlGaN/GaN material parameters, etc. are investigated. A simple and convenient approach to designing high breakdown voltage FP-HEMTs is also proposed. The validity of this model is demonstrated by comparison with the numerical simulations with Silvaco—Atlas. The method in this paper can be extended to the development of other analytical models for different device structures, such as MIS-HEMTs, multiple-FP HETMs, slant-FP HEMTs, etc.

Fixed interface charges between AlGaN barrier and gate stack composed of in situ grown SiN and Al2O3 in AlGaN/GaN high electron mobility transistors with normally off capability

Using a generalized extraction method, the fixed charge density Nint at the interface between in situ deposited SiN and 5 nm thick AlGaN barrier is evaluated by measurements of threshold voltage Vth of an AlGaN/GaN metal insulator semiconductor high electron mobility transistor as a function of SiN thickness. The thickness of the originally deposited 50 nm thick SiN layer is reduced by dry etching. The extracted Nint is in the order of the AlGaN polarization charge density. The total removal of the in situ SiN cap leads to a complete depletion of the channel region resulting in Vth = +1 V. Fabrication of a gate stack with Al2O3 as a second cap layer, deposited on top of the in situ SiN, is not introducing additional fixed charges at the SiN/Al2O3 interface.

Extraction of Phthalic Acid from Aqueous Solution by Using Ionic Liquids: A Quantum Chemical Approach

Phthalic acid is an industrial chemical and it comes under the domain of endocrine disrupting chemicals (EDCs). Green solvents such as ionic liquids (ILs) posses good extractable capabilities for EDCs. COSMO–RS methodology is a widely accepted method for the design or selection of ionic liquids. COSMO–RS is a quantum chemical based method based on COSMO polarization charge densities. In this work the model has been used to screen the potential ionic liquids for the removal of phthalic acid from water. Five group of ILs with cations such as phosphonium, imidazolium, pyridinium, pyrolidinium and ammonium based were screened at infinite dilution. A total of 34 cations and 29 anions i.e. 986 possible ILs were screened and their selectivities and capacities predicted. The selectivities of the screened ILs are : phosphonium > pyrolidinium > imidazolium > ammonim > pyridinium. Some of the ionic liquids with selectivities were [TBP][CF3SO3] (16057), [OMPYR][BF4] (13265), [C4DMIM][CF3SO3] (11678), [MNH][DEC] (9650) and [C8MPY][CF3SO3] (4735). Experimental validation was done by comparing experimental logarithmic octanol–water partition coefficient values (Log Kow) with COSMO–RS predicted data on phthalic acid. The results of this study suggested that the ILs can be a possible substitute for the treatment of organic effluent rich water and wastewater

Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: acrolein in water.

We investigate here the vertical n → π(*) and π → π(*) transitions of s-trans-acrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a non-equilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute ground-state wave function by assuming a linear-response scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π(*) case and also improve considerably the shift for the π → π(*) transition.

Effects of surface states on two-dimensional electron gas in ZnMgO/ZnO heterostructures

The band profile and electronic properties of Zn-polar ZnMgO/ZnO heterostructures are investigated using self-consistent calculations of the Schrödinger, Poisson, and charge balance equations for 300 K, all based on the assumption that the two-dimensional electron gas (2DEG) originates from donor-like surface states on the ZnMgO (0001) surface. Two models with different surface state distributions are applied to explain the ZnMgO thickness dependence of the 2DEG density. Multi-subband occupation of the 2DEG is taken into account, and surface states are included using Fermi–Dirac statistics. The polarization charge density at the ZnMgO/ZnO interface and the surface donor energy are added as adjustable fitting parameters to optimize the fits of the two models to experimental data. The fitting results indicate that surface states are more likely to be localized at a single energy level. Lastly, the microscopic origin of the surface states is discussed.

Resolution-enhanced polarization imaging with focused thermal pulses

The non-destructive measurement of electrical polarization and space charge densities is a key technique in electret research. The principal idea behind these methods is a non-uniform deformation or heating, which gives rise to a short-circuit current that can be recorded in the time or frequency domain, and which carries information about the polarization depth profile. In recent years, thermal pulses and thermal waves have been used successfully to obtain three-dimensional polarization maps in polymeric electrets by scanning the beam of a pulsed or intensity-modulated cw laser across the sample surface. However, the polarization maps in these experiments were reconstructed using a relatively simplistic one-dimensional heat diffusion model that does not take into account lateral heat diffusion in the metal electrode. A two-dimensional “coupled neighbors” model was developed, where the current signal from several adjacent beam pointings along a scan line is coupled together, and a Monte Carlo method is used for the deconvolution. Simulations show that the new approach enhances the lateral resolution by a factor of 2−3×, since it avoids the information loss occurring when three-dimensional polarization measurements are processed with a one-dimensional thermal model. We also present an augmented, low-noise thermal-pulse instrument where thermal pulses are initiated by a pulse-modulated diode laser.