Background Dielectric Constant Research Articles

Magnetic-field effects on the Van der Waals interaction of a semiconductor surface plasma with a neutral atom

A theoretical determination of magnetic-field effects on the Van der Waals interaction of a neutral atom with a semiconductor surface plasma is reported here. The magnetic field is taken to be perpendicular to the surface, and the semiconductor plasma is taken to be semi-infinite in extent. A local description of the dynamics of the magnetoplasma is employed, and nonlocal structure of plasma response is neglected. The Van der Waals interaction energy is evaluated in second-order perturbation theory to dipole terms, and the effects of a background dielectric constant are included. Our calculational procedure reflects the central role played by the concept of a dynamic plasma image of the neutral adatom in the semiconductor surface. The incorporation of magnetic-field effects, which is carried out here, involves a careful accounting of the anisotropic polarizability of the magnetoplasma in modifying the dynamic plasma image. The explicit evaluation of Van der Waals interaction energy presented here shows that the plasma part of this interaction energy is significantly changed by the magnetic field in semiconductors at field strengths for which the cyclotron frequency is comparable with the plasma frequency. The detailed magnetic-field dependence of the interaction energy obtained here should be subject to experimental confirmation using the highly precise and accurate time-of-flight diffusion method for measuring atom-surface binding energy.

Critical concentration for metallization of doped germanium and silicon

An elementary model for the metal-non metal transition in n-type Ge and Si is considered. The model is based on recent theoretical work on electron-hole droplets in illuminated semiconductors. The energy of the metallic phase is computed from experimentally known values of the conduction band effective masses and the background dielectric constant. The critical concentration is determined approximately by comparing the energy of the metallic phase with the energy of an isolated donor atom (a bound electron-impurity ion pair). The theoretical estimates of the critical concentration agree in order of magnitude with experiments. The trend in chemical shifts is reproduced.

Electron energy loss studies in solids; The transition metal dichalcogenides

Abstract The theory of characteristic electron energy losses is discussed in terms of the electronic band structure of a solid. The relationship between the observed plasmon energies, the average interband energy gap and the background dielectric constant of the solid is developed. The transmission energy loss spectra of a number of the layer-type transition metal dichalcogenides, MX2, where M=Zr, Hf, Nb, Ta, Mo and W and X=S and Se, have been measured in the range of 0–50 eV. In the experiments, a beam of 50 keV electrons is incident along the c-axis of the crystals and electrons inelastically scattered through an angle of 1 m radian are selected for energy analysis. This ensures that the momentum transfer and hence the electric vector for the excitations lies in the basal plane of the crystal (E⊥c). Kramers-Kronig analysis has been applied to the energy loss data to deduce the complex dielectric function of each material. From this function, all other ‘optical’ constants, such as the reflectivity, and the oscillator integral function and joint density of states function have been calculated. The results give substantial support to the existing band model for the family of materials and, in addition, provide the basis for a quantitative understanding of the band structure of individual compounds.

Plasmon dispersion relation in zero‐gap semiconductors

AbstractFrequency‐dependent, long‐wavelength random‐phase approximation (RPA) polarizabilities of a n‐type zero‐gap semiconductor are calculated for parabolic and spherical bands. The long wavelength plasmon dispersion relation is established. The dispersion of plasmons is mainly determined by the wave vector dependence of the intraband (free‐electron‐gas type) polarizability. For high electron concentrations, due to Γ8–Γ8 interband polarizability, in the standard plasmon dispersion relation, the concentration‐dependent background dielectric constant has to be used. For low electron concentrations the frequency and wave vector dependence of the Γ8–Γ8 interband polarizability makes the above procedure inaccurate. A more accurate procedure is derived.

’’Impurity’’ induced localized hole states of a one dimensional linear chain: Magnus green salt

The effect of an interstitial (off chain) negative halide ion on the one dimensional molecular orbital or ’’tight binding’’ states of a 20 site metal ion linear chain is examined. It is assumed that the halide ion shifts the chain site potentials an amount given by the Coulomb potential resulting from a negative point charge placed at the halide ion site. The eigenvalues and eigenvectors of the 20 site problem have been obtained numerically. For an initially unperturbed metal 5dz2 bandwidth of 1 eV and a background dielectric constant ε=1, the binding energy of a 5dz2 hole is found to be 0.46 eV. This value is in good agreement with twice the observed conductivity activation energy, ? 0.6 eV, in extrinsic samples of the linear chain platinum compound Magnus’s green salt. The general dependence of the eigenvalues and eigenvectors will also be presented as a function of bandwidth and background dielectric constant.

Reflectance of an array of charged conducting layers

The theoretical reflectance of a charged conducting layer and an array of layers is studied using a hydrodynamic model. In both cases, the reflectance depends strongly on the polarization of the incident radiation and the angle of incidence. When the wavelength is long compared to the spacing between layers, the layered array behaves like an anisotropic continuum. Refraction suppresses the anisotropy of the medium when the background dielectric constant is large, because the direction of wave propagation is nearly perpendicular to the layers even for large angles of incidence.

Polariton Theory of Resonance Raman Scattering in Insulating Crystals

A multibranch polariton theory of Raman scattering in insulators is presented; actual calculations of the resonance cross section are carried out for an undamped two-branch model, for various values of photon-exciton coupling and background dielectric constant, including values appropriate to CdS. One obtains a double peaking with incoming photon frequency, corresponding to the experimentally observed in- and out-going photon resonances. Comparison with bare- and generalized-exciton computations shows that the results of the three theories are nearly the same for "smaller" couplings, as in CdS, except in the immediate region of the higher-energy peak; as the coupling increases from values near those in CdS, the predictions of the three theories begin to differ more substantially. When the exciton continuum is included by perturbation theory, the nearly similar predictions of the polariton and exciton theories, for frequencies below the bare-exciton frequency, are in agreement with experimental data on LO-phonon Raman scattering in CdS.

Polariton Theory of Resonance Raman Scattering in Insulating Crystals

A multibranch polariton theory of Raman scattering in insulators is presented; actual calculations of the resonance cross section are carried out for an undamped two-branch model, for various values of photon-exciton coupling and background dielectric constant, including values appropriate to CdS. One obtains a double peaking with incoming photon frequency, corresponding to the experimentally observed in- and out-going photon resonances. Comparison with bare- and generalized-exciton computations shows that the results of the three theories are nearly the same for smaller couplings, as in CdS, except in the immediate region of the higher-energy peak; as the coupling increases from values near those in CdS, the predictions of the three theories begin to differ more substantially. When the exciton continuum is included by perturbation theory, the nearly similar predictions of the polariton and exciton theories, for frequencies below the bare-exciton frequency, are in agreement with experimental data on LO-phonon Raman scattering in CdS.