Polarization Charge Density Research Articles

Electrostatic interactions of charges and dipoles near a polarizable membrane

A variational method is used to determine the polarization charge density induced on the surfaces of a dielectric slab (a coarse-grained model of a membrane) by electric point charges and extended dipoles. The results are used to obtain analytic expressions for the polarization energy and the resulting forces acting on and between pairs of charges positioned in various geometries relative to the membrane. The polarization effects are shown to be substantial and often non-trivial on the nanometre scale, compared to direct Coulomb interactions.

Polarization effects in AlGaN/GaN and GaN/AlGaN/GaN heterostructures

The influence of AlGaN and GaN cap layer thickness on Hall sheet carrier density and mobility was investigated for Al0.32Ga0.68N/GaN and GaN/Al0.32Ga0.68N/GaN heterostructures deposited on sapphire substrates. The sheet carrier density was found to increase and saturate with the AlGaN layer thickness, while for the GaN-capped structures it decreased and saturated with the GaN cap layer thickness. A relatively close fit was achieved between the measured data and two-dimensional electron gas densities predicted from simulations of the band diagrams. The simulations also indicated the presence of a two-dimensional hole gas at the upper interface of GaN/AlGaN/GaN structures with sufficiently thick GaN cap layers. A surface Fermi-level pinning position of 1.7 eV for AlGaN and 0.9–1.0 eV for GaN, and an interface polarization charge density of 1.6×1013–1.7×1013 cm−2, were extracted from the simulations.

Polarization Charge Densities at p‐GaN/n‐AlGaN Heterojunctions Evaluated by Capacitance–Voltage Characteristics

We propose a new method to evaluate the polarization charge density induced at hetero-interfaces using capacitance–voltage characteristics of p–n heterojunctions and have applied this method to p-GaN/n-AlGaN heterojunction diodes. This method uses p–n heterojunction structures instead of undoped ones, so the obtained result is less influenced by background impurities or deep levels. Furthermore, it is possible to evaluate the negative polarization charge densities for GaN on top of AlGaN heterostructures. The experimental results indicate that the negative polarization charges with their densities more than 5 × 1012 cm—2 are induced at the GaN/AlGaN hetero-interfaces for the Al mole fractions above 11%.

Density functional approach to the effective interaction between charges withindielectric cavities

A variational approach based on a functional of the polarization charge density atinterfaces between different dielectric bodies is used to calculate the energy ofelectrostatic interaction between two electric charges embedded in eithertwo spherical dielectric cavities or in one spheroidal cavity. An effective,distance-dependent dielectric function is extracted from these results, which isexact within the macroscopic theory of dielectrics. We show that differentdielectric functions must be associated with pairs of equally or oppositelycharged ions and with pairs of ions in cavities of the same or differing radii.

Direct measurement of the polarization charge in AlGaN/GaN heterostructures using capacitance–voltage carrier profiling

The polarization charge at AlxGa1−xN/GaN heterostructure interfaces arising from differences in spontaneous polarization between AlxGa1−xN and GaN and the presence of piezoelectric polarization in strained layers has been directly measured using capacitance–voltage carrier profiling in GaN/AlxGa1−xN/GaN heterostructures with varying Al composition grown by molecular-beam epitaxy. The measured polarization charge densities (2.36±0.30×1012 e/cm2, 6.79±0.48×1012 e/cm2, and 6.92±0.74×1012 e/cm2 for 5%, 12%, and 16% AlxGa1−xN/GaN interfaces, respectively) reveal substantial bowing in the polarization charge as a function of Al composition, and are in reasonable agreement with those calculated using a model that accounts for the nonlinearity of the spontaneous and piezoelectric polarizations as functions of Al composition. Our results yield an explicit expression for polarization charge as a function of Al composition at an AlxGa1−xN/GaN interface.

Variation Mechanisms of Ground-State and Optical-Excitation Properties in Quasi-One-Dimensional Two-Band Electron Systems

We study i) the ground-state and optical-excitation properties of halogen-bridged binuclear metal complexes, which are known as MMX chain compounds, by the strong-coupling expansion for a one-dimensional two-orbital extended Peierls-Hubbard model, and ii) the dynamics of domain walls between the neutral and ionic phases in mixed-stack charge-transfer complexes, by solving the time-dependent Schrödinger equation for a one-dimensional extended Peierls-Hubbard model with alternating energy levels. We find in i) that competition between electron-electron and electron-lattice interactions and competition between short- and long-range interactions are both important for the electronic phase variation, and in ii) that charge and lattice dynamics immediately after photoexcitations is complex and not explained simply within the domino picture. MMX chain charge polarization charge density wave mixed-stack charge-transfer complex neutral-ionic phase transition photoinduced phase transition

Polarization charges and polarization-induced barriers in AlxGa1−xN/GaN and InyGa1−yN/GaN heterostructures

Polarization charges are measured and the formation of large electrostatic barriers arising primarily as a consequence of the presence of polarization-induced charge densities is deduced from capacitance–voltage analysis of n-type AlxGa1−xN/GaN and InyGa1−yN/GaN heterostructures. In structures consisting of 5–10 nm AlxGa1−xN or InyGa1−yN surrounded by n-GaN, capacitance–voltage profiling studies combined with elementary electrostatic analysis yield experimental estimates of polarization charge densities, which are compared with values expected based on the combined effects of spontaneous and piezoelectric polarization. These results imply the existence of electrostatic barriers that are due primarily to the large polarization charge densities at each heterojunction interface and the resulting potential difference maintained across the thin AlxGa1−xN or InyGa1−yN layers. The electrostatic barriers formed in these structures are large in comparison to the heterojunction conduction-band offsets, demonstrating the utility of polarization-based engineering of electrostatic barriers in nitride semiconductor heterostructures.

Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach

This paper provides a pedagogical introduction to a variational formulation of electrostatic interactions between free charges close to a dielectric interface. A functional is constructed which, upon minimization, yields a polarization charge density h(r) which satisfies the usual laws of electrostatics. The initial functional of a volume charge density is shown to reduce to a functional of a surface polarization charge density when the interface between dielectrics is sharp. The variational procedure is first shown to provide an elegant systematic solution in cases with very simple geometries, for which analytic solutions are well known. Numerical implementations of the variational procedure using adequate grids are tested against exact results, in the perspective of applying the method to geometrically more complex situations, like ion channels through membranes, which are well beyond analytic treatment. Contact is made with related work on the solvation of biomolecules, based on a functional of the polarization itself. The relative advantages and shortcomings of the two formulations are briefly discussed.

A quantum mechanical-Poisson–Boltzmann equation approach for studying charge flow between ions and a dielectric continuum

This paper presents a theoretical model for the investigation of charge transfer between ions and a solvent treated as a dielectric continuum media. The method is a combination of a semiempirical effective Hamiltonian with a modified Poisson–Boltzmann equation which includes charge transfer in the form of a surface charge density positioned at the dielectric interface. The new Poisson–Boltzmann equation together with new boundary conditions results in a new set of equations for the electrostatic potential (or polarization charge densities). Charge transfer adds a new free energy component to the solvation free energy term, which accounts for all interactions between the transferred charge at the dielectric interface, the solute wave function and the solvent polarization charges. Practical calculations on a set of 19 anions and 17 cations demonstrate that charge exchange with a dielectric is present and it is in the range of 0.06–0.4 eu. Furthermore, the pattern of the magnitudes of charge transfer can be related to the acid–base properties of the ions in many cases, but exceptions are also found. Finally, we show that the method leads to an energy decomposition scheme of the total electrostatic energy, which can be used in mechanistic studies on protein and DNA interaction with water.

Investigations into local piezoelectric properties by atomic force microscopy

We describe nanoscale characterization of sol-gel produced ferroelectric thin films of lead–zirconate–titanate. We have performed quantitative localized measurements of surface polarization charge density using atomic force microscopy techniques in conjunction with electric field calculations. We show that domains with radii of 40 nm may by written and subsequently characterized, and we analyze the dependence of domain size on write voltage and write time, and show that surface contaminants influence the formation of domains.

Time resolved screening of the piezoelectric field in InGaAs/GaAs V-shaped quantum wires of variable profile

InGaAs/GaAs V-shaped quantum wires grown in grooves with either (111) or (411) sidewalls have been studied by ps-transient photoluminescence as a function of the excitation intensity. The optical nonlinearity associated with the screening of the internal piezoelectric field is temporally monitored by the blue-shift of the spectrally resolved photoluminescence, occurring in the first 150 ps after the laser pulse, followed by the recovery of the unperturbed energy resonance at longer delays. Such an energy shift strongly depends on the photoexcited carrier density and reaches a maximum value of about 14 meV in the (411) wires. Despite their larger piezoelectric field, we observe a smaller energy shift in wires with (111) sidewalls, due to the enhanced confinement which localizes the wire wave-function at the bottom of the groove. The observed energy shifts are consistent with the theoretical calculation of the polarization charge density induced by the strain via the piezoelectric effect.

Electron Transfer through a Monolayer of Hexadecylquinolinium Tricyanoquinodimethanide

Electron transfer through a Langmuir−Blodgett monolayer of hexadecylquinolinium tricyanoquinodimethanide (C16H33Q−3CNQ) sandwiched between metal electrodes is studied carefully. Either current rectification (rectification ratio as high as ∼20) for positive bias applied on the metal overlayer or symmetric current voltage curves were observed for samples with the highest resistivity. More leaky devices (resistivity of about a decade lower) show rectification (with a smaller ratio ≤5) for a negative bias on the top electrode. These results are analyzed regarding various mechanisms: (1) Aviram and Ratner proposal for a molecular diode, (2) geometrical asymmetry of the metal/Langmuir−Blodgett monolayer/metal structure, and (3) a polarization charge density effect. This study leads us to confirm that the observed electron-transfer properties through the C16H33Q−3CNQ LB monolayers are not only due to possible geometrical asymmetry in the metal/LB monolayer/metal structure but are also related to the strong asymmetry of the donor−π- bridge−acceptor C16H33Q−3CNQ molecules.

Simulation of volume polarization in reaction field theory

In the reaction field theory of solvation, penetration of charge density outside the cavity nominally enclosing the solute leads to a volume polarization that contributes in addition to the commonly recognized surface polarization. In principle the exact volume polarization charge density is spread everywhere outside the cavity, but its effect can be closely and concisely simulated by a certain additional surface polarization charge density. Formal comparison is made to conductorlike screening models, and it is found that these improve on common approaches that neglect volume polarization by automatically including the simulation of volume polarization. A revised method to numerically determine this simulation is also described.

Time-resolved screening of the piezoelectric field in InGaAs/GaAs V-shaped quantum wires of variable profile

InGaAs/GaAs V-shaped quantum wires grown in grooves with either (111) or (411) sidewalls have been studied by ps-transient photoluminescence as a function of the excitation intensity. The optical nonlinearity associated with the screening of the internal piezoelectric field is temporally monitored by the blue shift of the spectrally resolved photoluminescence, occurring in the first 150 ps after the laser pulse, followed by a red shift at longer delays. Such an energy shift strongly depends on the photoexcited carrier density and reaches a maximum value of about 14 meV in the (411) wires. Despite their larger piezoelectric field, we observe a smaller energy shift in wires with (111) sidewalls, due to the enhanced confinement which localizes the wire wavefunction at the bottom of the groove. The observed energy shifts are consistent with the theoretical calculation of the polarization charge density induced by the strain via the piezoelectric effect.

Detection and control of ferroelectric domains by an electrostatic force microscope

An electrostatic force microscopy (EFM) method has been used for the detection and control of the microdomain in ferroelectric single crystal [triglycine sulfate (TGS)] and thin film piezoelectric transducer (PZT). In this method, EFM is operated in a dynamic contact mode that allows a simultaneous measurement of the topographic and domain contrast images. Through the analysis of the force between the tip and ferroelectric surface, the surface charge density of TGS single crystal is obtained. Polarization charge density of TGS obtained in this method is 2.7 μC/cm2 at room temperature. A complex pattern was written on a PZT film by the polarization reversal. The line shape or the intensity of the reoriented domain does not show any noticeable dependence on the writing speed. The threshold bias for writing on a PZT film studied in this work was 4 V.

Ab initiostudy of the dielectric properties of silicon and gallium arsenide using polarized Wannier functions

We present a first-principles calculation of the electronic properties of crystalline silicon and gallium arsenide in a uniform electric field. Polarized Wannier-like functions which are confined in a finite region are obtained by minimizing a total-energy functional which depends explicitly on the macroscopic polarization of the solid. The polarization charge density and the electronic dielectric constant are computed via finite differences. The results coincide with those of the linear response approach in the limit of vanishing electric field and infinite localization region.

Device physics and simulation of Metal/Ferroelectric-Film/ p-type silicon capacitors

This paper introduces an electrostatic model for Metal/Ferroelectric/Silicon (MFS) capacitors. These structures consist of a metal gate, a dielectric stack which includes a ferroelectric film, and a p-type silicon substrate. The dielectric stack consists of a switching ferroelectric layer and two nonswitching dielectric or buffer layers. This model predicts the dependence of the polarization charge density P d, the electric field in the ferrolelectric film ε fe , the voltage across the dielectric stack V OX , the semiconductor surface potential ψ SC , and the semiconductor charge density Q SC on the gate-to-bulk voltage V GB under static conditions. The low- and high-frequency capacitance-voltage characteristics of MFS capacitors are calculated.

Surrogate Hamiltonian description of solvation dynamics. Site number density and polarization charge density formulations

We explore a recently developed theory of solvation dynamics that analyzes the molecular response of the solvent to a sudden change of the charge distribution of a solute particle immersed in it. We derive an approximate nonequilibrium distribution functionf∑h(Γ, t) for a “surrogate” Hamiltonian description of the solvation dynamics process. The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that allows us to introduce a simple reduction scheme in the many-body dynamics problem without losing essential solute-solvent static correlations that rule the equilibrium solvation. Withf∑h(Γ, t) in hand we calculate the solvation time correlation function in two ways. The first one, previously reported, is basically a “dielectric formulation” in which the local polarization charge density of the solvent is the primary dynamical variable that couples to the field of the solute. In the new development reported here, the “site number density formulation,” the primary dynamical variables comprise the set of local solvent site number densities. We find that the dielectric formulation is embedded in the solvent site number density formulation as shown, for example, by comparing the respective time correlation functions of the solvation dynamics. An important feature of our approach is that at every stage the coupling between the solute and solvent is formulated in terms of the solute-solvent intermolecular interactions, rather than some sort of cavity construction. Furthermore, both the solute and the solvent molecules are represented by interaction site models. Applications of the dielectric theory are illustrated with calculations of the solvation dynamics of a cation in water and an exploration of the effect of the details of the charge distribution on the solvation dynamics of a benzenelike solute in acetonitrile.

Applications of a molecular theory of solvation dynamics

We describe a recent dielectric theory of solvation dynamics in which the solute and solvent molecules are represented as interaction site models (ISMs), while measurable properties are expressed as averages over the fluctuating local solvent polarization charge density. No mention is made of cavities in a dielectric. The theory is based on linear response to surrogate or renormalized interactions rather than on the factual (bare or exact) interactions that would give the exact response if the calculation were continued to infinite order. Another novel feature is the use of the reference memory function approximation (RMFA), to combine static structure functions with frequency-dependent global properties such as the dielectric function epsilon omega to obtain functions of wavenumber and frequency such as the longitudinal dielectric function epsilon L(k, omega ).

Surrogate Hamiltonian description of solvation dynamics. Resolution of global responses into spatial profiles

We present a more formal development of our recent theory of solvation dynamics, allowing a more detailed examination of the mechanism of solvent response to the sudden change of the charge distribution of an immersed solute. A distinctive feature of the theory is that both the solute and the solvent molecules are described in terms of relatively realistic interaction site models. Furthermore, in the theory the solute-solvent coupling is formulated in terms of the solute-solvent site-site interactions, rather than by appealing to some sort of cavity construction. Appling the general formulation of nonequilibrium statistical mechanics we derive an approximate nonequilibrium distribution function f Σ h(Γ, t) for a “surrogate” Hamiltonian description of solvation dynamics. The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that allows us to introduce a simple reduction scheme in the many body dynamic problem, without losing the important solute-solvent static correlations that are important for the equilibrium solvation. With f Σ h(Γ, t) we can calculate not only the solvation time correlation function but also other observables of interest such as the evolution of the solvent polarization charge density around the solute. We also consider the spatial resolution of some of the measures of the solvent response to the sudden transition, namely the reaction potential and the electrostatic energy gap. Applications of the theory are illustrated with calculations of the solvation dynamics of a cation in acetonitrile and the solvation dynamics of formaldehyde in water.