Electrodynamics of a Semiclassical Free-Electron Gas

With a view toward explaining measurements of ultrasonic attenuation in metals, the coefficient of shear viscosity of a free electron gas interacting with thermal phonons and local crystal inhomogeneities is computed. The methods employed are essentially those developed for the problem of electrical conductivity. By means of a variational principle, a general formal solution is obtained. The effective mean free path is found to be somewhat smaller and of a somewhat more complicated (though not qualitatively different) temperature dependence than that associated with electrical conduction. The effect of a transverse magnetic field is determined for the case when a time of relaxation exists.

A study is carried out of quantum effects in the dependence of ultrasonic attenuation in metals on the intensity of an applied magnetic field. It is found that the coefficient of absorption of acoustic waves exhibits an oscillatory behavior as a function of the strength of the applied magnetic field. This paper limits its scope to the case in which $\ensuremath{\omega}\ensuremath{\tau}$, the product of the frequency of the sound wave and the relaxation time for the electrons, is much smaller than unity. The oscillations predicted in this work have an amplitude proportional to ${(\frac{\ensuremath{\hbar}{\ensuremath{\omega}}_{0}}{{\ensuremath{\zeta}}_{0}})}^{\frac{3}{2}}$ for propagation at right angles to the magnetic field, and they are negligibly small for propagation in the direction of the magnetic field. The latter result is in contrast with the one described in the preceding paper (for $\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\gg}1$), where giant oscillations of the attenuation can occur.

Ultrasonic Attenuation in Metals by Electron Relaxation

Strong surface and impurity scattering in III-V semiconductor-based nanowires (NW) degrade the performance of electronic devices, requiring refined concepts for controlling charge carrier conductivity. Here, we demonstrate remote Si delta (δ)-doping of radial GaAs-AlGaAs core-shell NWs that unambiguously exhibit a strongly confined electron gas with enhanced low-temperature field-effect mobilities up to 5 × 10(3) cm(2) V(-1) s(-1). The spatial separation between the high-mobility free electron gas at the NW core-shell interface and the Si dopants in the shell is directly verified by atom probe tomographic (APT) analysis, band-profile calculations, and transport characterization in advanced field-effect transistor (FET) geometries, demonstrating powerful control over the free electron gas density and conductivity. Multigated NW-FETs allow us to spatially resolve channel width- and crystal phase-dependent variations in electron gas density and mobility along single NW-FETs. Notably, dc output and transfer characteristics of these n-type depletion mode NW-FETs reveal excellent drain current saturation and record low subthreshold slopes of 70 mV/dec at on/off ratios >10(4)-10(5) at room temperature.

It is shown that the feasibility of obtaining high-power short-wavelength radiation by reflection of electromagnetic waves from a bunch of relativistic electrons is limited by the high transparency of these bunches and the finite dimensions of the leading edge of the electron buildup in such bunches. A comparison is made of coherent (across an electron beam) and noncoherent scattering processes and it is shown that the latter predominate. Simple expressions are obtained for estimating the experimental feasibility of such frequency conversion.

We consider the transmission and reflection of electromagnetic waves by an obstacle inside a waveguide. The method employed is an adaptation of the null-field approach (T-matrix method). The geometry is more or less arbitrary, but only for a waveguide with constant cross section can we obtain the scattered field in a not too formal way. For a circular cross section we derive comparatively explicit expressions for the transmission and reflection coefficients of the obstacle, and we give numerical results for spherical and spheroidal obstacles in rotationally symmetric geometries. As an important part of the theory, we have derived some apparently new transformations between the cylindrical and spherical vector waves and also expansions of the free-space Green’s dyadic in cylindrical vector waves.

The density-density correlation function has been calculated for a modulation-doped GaAs/AlAs superlattice. The superlattice is modelled to be an infinite periodic sequence of layers which consists of two dissimilar layers, one of GaAs and the other of AlAs, per unit cell. The conduction electrons are assumed to be confined to GaAs layers. Our calculation shows that although the electron gas is confined in the GaAs layers, the plasma oscillations can interact with the lattice vibrations of both GaAs and AlAs. The interaction between AlAs lattice vibrations and the plasmons significantly contributes to the light-scattering spectrum. It is therefore argued that the experimentally measured frequencies of the coupled plasmon-phonon modes and their lineshapes for a modulation-doped GaAs/AlAs superlattice cannot correctly be described by the previous theoretical calculations which have been performed for a layered electron gas embedded in a homogeneous dielectric background. For the special case of a homogeneous dielectric background, our results, however, agree with the previously reported calculations.

The body-centered and face-centered cubic monatomic metals are represented by a model consisting of an ion point lattice embedded in an electron gas. The Born-von Kármán lattice dynamics are modified to include the role which the conduction electrons play in acoustical wave motion. This leads to relations connecting the dynamic parameters with the elastic constants, and yields the Fuchs relations in an elementary manner. The discrepancy in the Cauchy relation is shown to be just the bulk modulus of the electron gas. In studying the contribution of the conduction electrons to the thermal motion, two extreme cases are treated: 1.—the electron gas does not partake of the thermal motion appreciably; 2.—the electron gas follows the ion motion almost exactly. The secular equations are given for both cases. The Debye characteristic temperature in the T3 region of atomic heat is computed analytically for both cases when the departure of the elastic constants from the isotropy condition is not too large.

ABSTRACTFirst-principles calculations of the inelastic lifetime of low-energy electrons in Al. Cu and Au are reported. Quasiparticle damping rates are evaluated from the knowledge of the electron self-energy, which we compute within the GW approximation. Inelastic lifetimes are then obtained along various directions of the electron wave vector, with full inclusion of the band structure of the solid. Average lifetimes are also reported, as a function of the electron energy. In Al splitting of the band structure over the Fermi level yields electron lifetimes that are smaller than those of electrons in a free-electron gas. In Cu and Au, a major contribution from d electrons participating in the screening of electron-electron interactions yields electron lifetimes which are well above those of electrons in a free-electron gas with the electron density equal to that of valence (4s1 and 6s1 respectively) electrons.

The interaction of hot electrons with a free electron gas

The textured multilayer (ML) thin films of bismuth layered ferroelectric (FE) compounds, Bi2VO5.5 (BVO) and Bi4Ti3O12 (BTO) with different individual layer thicknesses were fabricated via pulsed laser deposition technique on Pt(111)/TiO2/SiO2/Si substrates. X-ray diffraction studies confirmed that BVO and BTO retained their respective crystal structures in these multilayer (ML) thin films. The atomic force microscopy and scanning electron microscopy studies showed smooth and dense microstructures. The polarization hysteresis (P–E) studies on a representative (BVBT30) ML thin film at 300 K confirmed the remnant polarization (2Pr) and coercive field (Ec) to be ~20 μC/cm2 and 250 kV/cm, respectively. The value of Pr obtained was greater than that of the single layer thin film of BVO (Pr ~ 5.6 μC/cm2). The room temperature dielectric constant (er′) and the loss (D) for BVBT30 ML measured at 100 kHz were 170 and 0.01, respectively. The frequency and temperature dependent dielectric constant, impedance, modulus and ac conductivity of these ML thin films were studied as a function of frequency (100 Hz–1 MHz) in the 25–300 °C temperature range. Two distinct electrical responses were observed in these films, which were attributed to the grain effects at low temperatures and grain boundary effects at higher temperatures. The frequency dependent electrical conductivity was fitted well with the double power law which evidenced two different types of contributions to the conductivity; the low frequency conductivity being due to the short range translational hopping and the high frequency conductivity was due to the localized or reorientational hopping.

A 96% polycrystalline alumina (Al2O3) based prototype packaging system with Au thick-film metallization successfully facilitated long term testing of high temperature SiC electronic devices for over 10,000 hours at 500°C previously. However, the 96% Al2O3 chip-level packages of this prototype system were not fabricated via a commercial co-fire process which is more suitable for large scale commercial production. The co-fired alumina materials adopted by the packaging industry today usually contain several percent of glass constituents to provide better adhesion and sealing at interfaces formed during a co-firing process at temperatures usually lower than the regular sintering temperature for alumina. In order to answer the question if co-fired alumina substrates can provide reasonable high temperature electrical performance comparable to those of regular 96% alumina sintered at 1700°C, this paper reports on the dielectric performance of a selected high temperature co-fired ceramic (HTCC) alumina substrate and a low temperature co-fired ceramic (LTCC) alumina (polycrystalline aluminum oxides with glass constituents) substrate from room temperature to 550°C at frequencies of 120 Hz, 1 KHz, 10 KHz, 100 KHz, and 1 MHz. Parallel-plate capacitive devices with dielectrics of these co-fired alumina and precious metal electrodes were used for measurement of the dielectric properties of the co-fired alumina materials in the temperature and frequency ranges. The capacitance and AC parallel conductance of these capacitive devices were directly measured by an AC impedance meter, and the dielectric constant and parallel AC conductivity of the dielectric were calculated from the capacitance and conductance measurement results. The temperature and frequency dependent dielectric constant, AC conductivity, and dissipation factor of selected LTCC and HTCC co-fired alumina substrates are presented and compared to those of 96% alumina. Metallization schemes for co-fired alumina for high temperature applications are discussed to address packaging needs for low power 500°C SiC electronics.

The reflection and transmission characteristics of electromagnetic waves by the uniaxially anisotropic chiral slab with the optical axis parallel to the interface are investigated. Formulas of the reflection and transmission coefficients (power) are derived. The curves of powers of the reflected and transmitted electromagnetic waves are presented for four cases of dielectric constants according to their signs. The effects of chirality parameter on the reflection and transmission are discussed. Especially, the dependences of pseudo-Brewster angles on the chirality parameter are plotted.

Reflectance data are presented for Si, Ge, GaP, GaAs, InAs, and InSb in the range of photon energies between 1.5 and 25 eV. The real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations. The results can be described in terms of interband transitions and plasma oscillations. A theory based on the frequency-dependent dielectric constant in the random phase approximation is presented and used to analyze these data above 12 eV, where the oscillator strengths coupling the valence and conduction bands are practically exhausted. The theory predicts and the experiments confirm essentially free electron-like behavior before the onset of $d$-band excitations and a plasma frequency modified from that of free electrons due to oscillator strength coupling between valence and $d$ bands and $d$-band screening effects. These complications are absent in Si. The energy loss functions obtained from optical and characteristic energy loss experiments are also found to be in good agreement. Arguments for interpreting structure in the reflectance curves above 16 eV in terms of $d$-band excitations are given.

: The calculation of the reflection coefficients for a plane transverse electromagnetic wave incident non-normally on a non-uniform plasma layer with a metal-backing wall is discussed. It is assumed that the plasma properties (plasma frequency and electron collision frequency) vary spatially only in the direction normal to the metal wall. The plasma layer is treated as a spatially non-uniform lossy dielectric material. For non-normal incidence, it is most convenient to consider an arbitrarily polarized incident electromagnetic wave to be composed of TE(transverse electric) and TM modes. The reflection coefficient for each of these different modes is then found separately.