Wave-vector Dependent Dielectric Function Research Articles

Noncontact Friction in Electric Force Microscopy over a Conductor with Nonlocal Dielectric Response.

Electric force microscopy, in which a charged probe moves above a surface, can measure thermally generated electric field fluctuations from the sample. Noncontact friction measurements of energy loss from the probe have been performed over insulators, semiconductors, and conductors and have been interpreted in terms of the dielectric response of the sample. Noncontact friction over metal surfaces has recently been ascribed to dielectric relaxation of adsorbed molecules, motivating the examination of the baseline noncontact friction over a bare metal surface. The noncontact friction for a thin conducting film is calculated for a wavevector-dependent dielectric function, complementing previous calculations for insulators and semiconductors employing a dielectric continuum representation. Inclusion of the wavevector dependence in the dielectric response of a conductor enhances the friction and alters its dependence on tip-sample separation, relative to the continuum treatment.

First-Principles Method to Study Near-Field Radiative Heat Transfer

We present a general and convenient first principle method to study near-field radiative heat transfer. We show that the Landauer-like expression of heat flux can be expressed in terms of a frequency and wave-vector dependent macroscopic dielectric function which can be obtained from the linear response density functional theory. A random phase approximation is used to calculate the response function. We computed the heat transfer in three systems -- graphene, molybdenum disulfide (MoS$_2$), and hexagonal boron nitride (h-BN). Our results show that the near-field heat flux exceeds the blackbody limit up to four orders of magnitude. With the increase of the distances between two parallel sheets, a $1/d^2$ dependence of heat flux is shown, consistent with Coulomb's law. The heat transfer capacity is sensitive to the dielectric properties of materials. Influences from chemical potential and temperature are also discussed. Our method can be applied to a wide range of materials including systems with inhomogeneities.

Dielectric function for free electron gas: comparison between Drude and Lindhard models

The interaction between light and metals or heavily doped semiconductors is largely determined by their free conduction electrons. The frequency and wave vector dependent complex dielectric function is an essential ingredient of the description of its optical and transport properties. The aim of this paper is to give a didactic introduction how the conduction electrons in solids responds to an external time dependent electric field and to make a comparison between Drude and Lindhard dielectric function models for the electron gas. In within framework of Lindhard model we derived an expression for dielectric function that is similar to the familiar Drudes's formula. In particular, the differences and similarities between the complex conductivity obtained from the two models are analyzed.

Theory of dielectric loss in Graphene-on-substrate: A tight- binding model study

Graphene-on-substrate exhibits interesting dielectric behaviour due to screening of coulomb interaction induced by many body effects. In this communication we attempt to study the dielectric loss property of graphene within tight-binding model approach. The Hamiltonian consisting of electron hopping upto third-nearest-neighbour's with impurities in two in equivalent sub-lattices. The graphene-on-substrate raises the energy +Δ at one sub lattice and reduces energy -Δ at other sub lattice. Further we introduced coulomb interaction between π - electrons at the two sub lattices separately with the same effective coulomb interaction. We calculate polarization function Π(q, ω) which is a two particle Green's function arising due to charge-charge correlation by using Zubarev's Green's function technique. Finally we calculate dielectric function of graphene i.e. ε(q, ω) =1+Π(q,ω) at arbitrary wave vector q and frequency ra. The dielectric loss in graphene calculated from the imaginary part of dielectric function which is a measure of absorption spectrum. Only a few Fragmentary theoretical attempts have been made to utilize the full frequency and wave vector dependent dielectric function. We compute numerically the frequency dependent dielectric loss function for 100x100 momentum grid points. We observe a low energy Plasmon resonance peak and a high energy flat peak arising due to absorption of optical energy at substrate induced gap. With increase of small Plasmon wave vector, both low and high energy peaks approach each other. The dielectric loss at low energies exhibits a parabolic curve, but it exhibit a clear peak on introduction of higher order electron hopping's. The Coulomb interaction suppresses induced gap in graphene and decreases the optical energy absorption spectra. The increase of substrate induced gap shifts the high energy flat peak to higher energies and enhances the dielectric loss throughout the frequency range. Finally the effect of doping on dielectric loss is investigated and compared with the experimental results.

Calculation of Auger Lifetimes in HgCdTe

Band-to-band Auger recombination mechanisms in HgCdTe are investigated as functions of temperature in the small modulation limit by using realistic electronic structures obtained by empirical pseudopotential calculations and their corresponding wavevector-dependent dielectric functions. The calculated Auger lifetimes are compared with the semiempirical Beattie-Landsberg-Blakemore (BLB) model, which has been extensively employed to reproduce experimental data. The Auger-1 lifetime can be fitted well to the BLB model with a constant overlap integral |F 1 F 2| = 0.16, near the lower limit of the range reported in the literature. The role of the Auger-7 process in p-type HgCdTe is also investigated and the ratio γ between the intrinsic Auger-7 and Auger-1 lifetimes is found to be about 10.

A numerical study of Auger recombination in bulk InGaN

Direct interband and intraband Auger recombination due to electron-electron-hole and hole-hole-electron transitions in bulk InGaN is investigated by first-order perturbation theory including Fermi statistics, realistic electronic structures obtained by nonlocal empirical pseudopotential calculations, and their corresponding wavevector-dependent dielectric functions. Our results confirm that the intraband Auger coefficient is negligible in alloy compositions relevant for solid-state lighting and indicate that the resonant enhancement associated with interband transitions for wavelengths ranging from blue to green cannot account for the efficiency droop experimentally observed in GaN-based light emitting diodes.

Full-Band Monte Carlo Simulation of HgCdTe APDs

A full-band Monte Carlo model has been developed for understanding the carrier multiplication process in HgCdTe infrared avalanche photodiodes. The proposed model is based on a realistic electronic structure obtained by pseudopotential calculations and a phonon dispersion relation determined by ab initio techniques. The calculated carrier–phonon scattering rates are consistent with the electronic structure and the phonon dispersion relation, thus removing adjustable parameters such as deformation potential coefficients. The computation of the impact ionization transition rate is based on the calculated electronic structure and the corresponding wavevector-dependent dielectric function. The Monte Carlo model is applied to investigate key performance figures of long-wavelength infrared (LWIR) and mid-wavelength infrared (MWIR) HgCdTe avalanche photodetectors such as carrier multiplication and noise properties. Good agreement is achieved between simulations and experimental results. The multiplication process in LWIR (λc = 9.0 μm at 80 K) and MWIR (λc = 5.1 μm at 80 K) devices is found to be initiated only by electrons, as expected from excess noise measurements. This single-carrier multiplication behavior can be traced back to the details of the computed valence-band structure and phonon scattering rates.

Theory of high field carrier transport and impact ionization in wurtzite GaN. Part I: A full band Monte Carlo model

High field electron and hole transport in wurtzite phase GaN is studied using an ensemble Monte Carlo method. The model includes the details of the full band structure derived from nonlocal empirical pseudopotential calculations. The nonpolar carrier-phonon interaction is treated within the framework of the rigid pseudoion approximation using ab initio techniques to determine the phonon dispersion relation. The calculated carrier-phonon scattering rates are consistent with the electronic structure and the phonon dispersion relation thus removing adjustable parameters such as deformation potential coefficients. The impact ionization transition rate is computed based on the calculated electronic structure and the corresponding wave-vector dependent dielectric function. The complex band structure of wurtzite GaN requires the inclusion of band-to-band tunneling effects that are critical at high electric fields. The electric-field-induced interband transitions are investigated by the direct solution of the time dependent multiband Schrödinger equation. The multiband description of the transport predicts a considerable increase in the impact ionization coefficients compared to the case in which tunneling is not considered. In the second part of this work it will be shown that the proposed numerical model correctly predicts the carrier multiplication gain and breakdown voltage of a variety of GaN avalanche photodetectors that have been recently fabricated by several research groups.

RPA dielectric function for real solids

A study was made of the wave vector dependent (zero-frequency) RPA dielectric function for diamond. The diagonal part of the RPA was computed with Hartree–Fock wave functions and energies (HF RPA), and with Hartree-Fock wave functions and screened exchange plus Coulomb hole correlated energies (SECH RPA). The HF RPA was found to be smaller than the experimental value as represented by the Penn model, while the SECH RPA showed that correlated energies account for about half of the difference between the HF RPA and the Penn model. Local field effects were then included by calculating the full RPA dielectric matrix out to 7 sets of reciprocal lattice vectors, inverting this matrix, and taking the reciprocal of the first diagonal term of the inverse. The dielectric function obtained by this procedure was found to be smaller, and thus farther from experiment, than the SECH RPA. The diagonal RPA was also calculated with Hartree energy bands, and the result was a significant improvement over the RPA computed with Hartree–Fock or correlated Hartree- Fock bands. It was found that the dielectric function is not very sensitive to the wave functions used in the calculation, that is, the Hartree and Hartree Fock wave functions gave similar results.

Electron and Hole Transport in Bulk ZnO: A Full Band Monte Carlo Study

Electron and hole transport in wurtzite phase ZnO is studied using an ensemble full band Monte Carlo method. The model includes an accurate description of the electronic structure obtained with the nonlocal pseudopotential method and numerically calculated impact ionization transition rates based on a wavevector-dependent dielectric function. Results of transport simulations at both low and high electric fields are presented. It is found that the low field electron mobility is close to 300 cm 2 V -1 s -1 at room temperature, and the peak electron drift velocity is 2.2 × 10 7 cm/s at a field of 275 kV/cm. The determination of the ionization coefficients is affected by some uncertainties due to the incomplete knowledge of the high energy phonon scattering rates. Nevertheless, the present calculations of the ionization coefficients provide a reasonably accurate estimate of the impact ionization process.

Dielectric and optical properties of dense plasmas

The interaction of matter with radiation concerns almost every area in physics. The exposure of matter to radiation may change its behavior. The focus of the present review are strongly correlated Coulomb systems under the influence of electromagnetic fields. Within linear response, the dynamical and non local (frequency and wave vector dependent) dielectric function and related quantities such as the polarization function and the response function, are expressed via equilibrium correlation functions. In particular, relations for the dynamical conductivity, the dynamical local field factor, the dynamical collision frequency and the dynamical structure factor are given with respect to current-current correlation functions and force-force correlation functions. Instead of a simple Drude formula which introduces a relaxation time in a semi-empiric way, a systematic quantum statistical approach is given which is able to describe the dynamical behavior of the collision frequency. The evaluation of correlation functions is performed within a systematic quantum statistical approach and compared to molecular dynamics simulations. The results obtained are of interest with respect to the production of radiation, the excitation of matter in electromagnetic fields, the diagnostics of matter etc. Applications to the dynamical conductivity, Bremsstrahlung, Thomson scattering and optical reflectivity are discussed.

Dielectric critical behaviour at a metal–insulator transition under lattice compression

We study dielectric critical behaviour around a continuous metal–insulator transition in crystalline Cesium Iodide induced by changing the lattice parameter. The ab initio calculations of band structure and various quantities related to the dielectric response are performed in the transition region, within the local density approximation of the density functional theory. These calculations allow us to establish the power-law singularities of various quantities on two sides of the transition. The exponents obtained here are mean-field like due to the approximation in which interactions and disorder are treated. The critical behaviour is discussed by applying the scaling principle to the wavevector and frequency dependent dielectric function. We further investigate the effect of dielectric anomalies on optical properties by calculating the reflectance around transition region taking the ionic contribution to the dielectric function also into account. We find that the reflectance as a function of frequency shows very different kind of behaviour on both sides of the metal–insulator transition.

Effect of Overscreening on the Localization of Hydrated Electrons

The problem of the ground state of hydrated electron is revisited with a focus on the effects due to nonlocal dielectric response of water. The standard variational analysis is performed. It takes into account – in addition to nonlocal polarization of nuclear modes – the electron repulsion from the closed shells of water molecules, a possibility to form a cavity around the electron and the interaction of the hydrated electron with the high frequency electronic degrees of freedom of water. The classical dielectric continuum limit, shown for a reference, gives the ground state hydration energy that is 2.5 times smaller than the experimental value. The situation alters dramatically if one accounts for the nonlocal dielectric response of water. If one takes literally the existing MD simulation data for the static wave-vector dependent dielectric response function (with an "over-screening" resonance at

Ensemble Monte Carlo calculation of hole transport in bulk 3C–SiC

In this article the first calculation of hole transport in the 3C phase of SiC is presented. The salient features of the model are the full band-structure computed by the empirical pseudopotential method, a numerically calculated hole-phonon scattering rate and the impact ionization transition rates. The coupling constants necessary to determine the scattering rates have been determined either from available data in the literature or by fitting the calculated mobility values to low field experimental results. The impact ionization transition rates have been determined directly from the band-structure based on a wave-vector dependent dielectric function. The steady state drift velocity as a function of the applied electric field strength is computed for different field directions and doping concentrations. The calculated results show the presence of an anisotropy in the drift velocity for the field applied along different directions, similar to what is found in silicon. The maximum values of the velocity are 1.63×107 cm s−1 and 1.43×107 cm s−1 for the (100) and (111) field directions, respectively. High field transport has also been studied. The calculated ionization coefficients show no appreciable anisotropy for the field applied along different directions. The second valence band contributes the most to the impact ionization rate. It is further found that the ionization threshold is relatively soft.

Transverse wavevector dependent and frequency dependent dielectric function, magnetic permittivity and generalized conductivity of interaction site fluids: MD calculations for the TIP4P water

The dielectric properties of interaction site models of polar fluids may be investigated in a computer experiment using not only the charge fluctuations but also correlations corresponding to a current of moving charges. This current may be associated with a generalized dynamical polarization or separated into electric and magnetic components. The first approach deals with the dielectric permittivity related to a generalized conductivity, whereas the second leads to the functions describing polarization and magnetization fluctuations separately. The latter functions are only the source for calculating the magnetic susceptibility for a system of interaction sites. The transverse wavevector dependent and frequency dependent dielectric functions and magnetic susceptibility are evaluated for the TIP4P water model over a very wide scale of wavelengths and frequencies using molecular dynamics simulations. The transverse part of the dielectric functions may differ drastically from their longitudinal component. A relationship between the two approaches is discussed and the limiting transition to the static dielectric constant in the infinite-wavelength regime is analysed. The propagation of transverse electromagnetic waves in TIP4P water is considered.

Wavevector and frequency dependent dielectric function dynamic structure factor and the instability of plasma waves in two component hot rare quantum and classical plasmas

The full wavevector and frequency dependent complex dielectric function for two component classical and quantum rare hot plasmas have been derived. The real part of dielectric function is obtained in the form of a series. Difference between quantum and classical real and imaginary parts of dielectric function have been brought out by making explicit calculations. The quantum nature of the plasma brings about significant changes in both parts depending upon the magnitude of quantum parameter,R (= 8.93(λth)/λ). Expressions for the dynamic structure factors for both two component classical and quantum plasma have been evaluated for different values of the mass of the positive componentm +, temperature T+ and wavevector k. It is found that the plasma exhibits well defined collective modes for certain values of ¦k¦ accompanied by varying disorder which depends upon the values of m+ as well as on ¦k¦ and T+. For the quantum case the collective modes are less well defined as compared to the corresponding classical case, thus proving that quantum nature introduces inherent disorder in the system. But for both the cases, increase in temperature destroys collective modes. Another feature is the appearance of a hump near Ω = 0 which becomes smaller and vanishes as the quantum parameter is decreased. Instability of plasma modes in the presence of constant electric field has also been worked out for the quantum case.

Transverse wavevector dependent and frequency dependent dielectric function, magnetic permittivity and generalized conductivity of interaction site fluids: MD calculations for the TIP4P water

The dielectric properties of interaction site models of polar fluids may be investigated in a computer experiment using not only the charge fluctuations but also correlations corresponding to a current of moving charges. This current may be associated with a generalized dynamical polarization or separated into electric and magnetic components. The first approach deals with the dielectric permittivity related to a generalized conductivity, whereas the second leads to the functions describing polarization and magnetization fluctuations separately. The latter functions are only the source for calculating the magnetic susceptibility for a system of interaction sites. The transverse wavevector dependent and frequency dependent dielectric functions and magnetic susceptibility are evaluated for the TIP4P water model over a very wide scale of wavelengths and frequencies using molecular dynamics simulations. The transverse part of the dielectric functions may differ drastically from their longitudinal component. A relationship between the two approaches is discussed and the limiting transition to the static dielectric constant in the infinite-wavelength regime is analysed. The propagation of transverse electromagnetic waves in TIP4P water is considered.

Frequency and wave-vector dependent dielectric function of water: Collective modes and relaxation spectra

The longitudinal frequency and wave-vector dependent complex dielectric response function χ(k,ω)=1−1/ε(k,ω) is calculated in a broad range of k values by means of molecular dynamics computer simulation for a central force model of water. Its imaginary part, i.e., Im{ε(k,ω)}/|ε(k,ω)|2, shows two main contributions in the region of small k values: Debye-like orientational relaxation in the lower frequency part of the spectrum and a damped librational resonance at the high frequency wing. The Debye relaxation time does not follow a de Gennes-like pattern: τ(k) goes through a maximum at k≈k*≈1.7 Å−1, while the static polar structure factor S(k) peaks at k≈3 Å−1. The resonance frequency ω(k) and the decay decrement γ(k) show a dispersion law, indicative of a decaying optical-like mode, the libron. With an approximate normal mode approach, we analyze the origin of this mode on a molecular level which shows that it is due to a damped propagation of molecular orientational vibrations through the network of hydrogen bonds. At high k the decay, due to dissipation of collective into single particle motions, dominates. The static dielectric function is calculated on the basis of the response function spectra via the Kramers–Kronig relation. In the small k region ε(k) decreases from the macroscopic value ε≈80 to a value ≈15, i.e. it exhibits a Lorentzian-type behavior. This behavior is shown to be determined by higher order multipole correlation functions. In the intermediate and high k range, our results on ε(k) and χ(k) are in excellent agreement with data extracted from experimental partial pair correlation functions: ε(k) exhibits two divergence points on the k axis with a range of negative values in between where a maximum in χ(k) is found with χmax(k)≫1, indicative of overscreening. Consequences of quantum corrections to χ(k) with respect to a purely classical calculation are discussed and consequences are shown for the interaction energy between hydrated ions.

Positron annihilation in one component quantum and classical rare hot plasmas

Temperature dependent positron annihilation rates λ, which are intimately related to the static pair correlation function of the electrons at the site of the positron g ±(0), have been worked out for electron densities that can be obtained in a laboratory plasma, making use of the recently suggested frequency and wavevector dependent dielectric function for one component quantum and classical rare hot plasmas. For a given density of electrons, the temperature dependence of g ±(0) in the two cases is quite different for low temperatures, T less than ∼100 K and can be detected experimentally.

Calculation of the electron initiated impact ionization transition rate in cubic and hexagonal phase ZnS

The wave-vector dependent, electron initiated, impact ionization transition rates for the cubic and hexagonal phases of ZnS have been numerically determined using a pseudopotential calculated band-structure and wave-vector dependent dielectric function. The rates for both phases show a strong dependence on the relative band structures. A detailed band-by-band analysis of the transition rate in the first Brillouin zone has been performed to determine the wave-vector dependence of the rate. The energy dependent rates have also been computed by averaging the transition rate over energy. It is found that the hexagonal phase of ZnS exhibits a higher ionization transition rate than the cubic phase. A preliminary estimation of the nature of the threshold has been made using a previously published phonon scattering rate.