Frank Stern

Bio: Frank Stern is an academic researcher from Silver Spring Networks. The author has contributed to research in topics: Wave function & Lattice constant. The author has an hindex of 5, co-authored 5 publications receiving 426 citations.

Elementary Theory of the Optical Properties of Solids

Abstract: Publisher Summary This chapter describes elementary theory of the optical properties of solids. One of the most powerful tools for studying the properties of solids is the measurement and analysis of their optical properties. Some of the results required for such an analysis are described in the chapter with emphasis on the detailed development of simple models. It expresses many of the results in numerical form and has dictated the use of meter–kilogram–second (mks) units throughout. The treatment is elementary in the sense that no physics beyond Maxwell's equations and simple quantum mechanics is used in the chapter. Dispersion relations as applied to the analysis of optical properties are discussed in the chapter. It summarizes some of the classical results for two very important physical systems, the free-electron gas and the optical lattice vibrations in ionic crystals. These systems are sufficiently simple that detailed results can be obtained very easily, yet realistic enough that the results give quite a good representation of at least some of the properties of real solids.

Calculation of the Cohesive Energy of Metallic Iron

Abstract: The cohesive energy of metallic iron is calculated for the bodycentered cubic structure in a singlet spin state at 0\ifmmode^\circ\else\textdegree\fi{}K. The potential field acting on each electron is taken to be that of the ion core and of the remaining valence electrons in the same lattice cell; thus the calculation becomes equivalent to one for the free atom as the lattice constant is increased. Tight-binding wave functions are used, but they are modified by expanding the contributions from neighboring atoms in a power series within a cell, and orthogonalizing to core states. Evaluating the complete wave function in each cell eliminates the need for multicenter integrals otherwise required in the tight-binding method. The wave functions for wave vectors in directions of high symmetry have a rather simple form, and can be described by a few parameters. States near the bottom of the $3d$ band tend to have a more diffuse charge distribution than do the states near the top of the band. Thus the x-ray scattering factor per electron for a partially filled $3d$ band will be less than that for a full band. Calculations of the energy of the solid are made for three values of the atomic sphere radius, ${r}_{s}$, using atomic wave functions from the $3{d}^{7}4s$ configuration. The indicated configuration in the solid is close to $3{d}^{7}4s$, making the calculation approximately self-consistent. The calculated width of the occupied portion of the $3d$ band is 0.33 ry. We find the cohesive energy of metallic iron to be 0.43\ifmmode\pm\else\textpm\fi{}0.2 ry per atom, which is consistent with the experimental value, 0.32 ry. The equilibrium lattice constant and the compressibility are both found to be in good agreement with experiment. An attempt to replace the Coulomb hole used in the main calculation by an exchange hole, using a single Slater determinant wave function, gave far too little binding.

Temperature Dependence of Optical Absorption in p -Type Indium Arsenide

Abstract: The absorption maximum near 0.17 ev found in $p$-type InAs at 300\ifmmode^\circ\else\textdegree\fi{}K shifts to lower energies at lower temperatures, and to a stationary value of 0.19 ev above 420\ifmmode^\circ\else\textdegree\fi{}K. The peak absorption coefficient has a minimum value near 370\ifmmode^\circ\else\textdegree\fi{}K and increases with increasing and decreasing temperatures. The observed absorption agrees with theoretical expectation provided a term linear in wave vector is included in the energy near the center of the Brillouin zone. Analysis of the data suggests that the energy maximum of the valence band lies 0.003\ifmmode\pm\else\textpm\fi{}0.003 ev above the energy at the center of the zone, that the spin-orbit splitting is 0.43 ev, and that the density-of-states effective mass of the heavy-hole band is approximately $0.41m$ at energies well below the top of the band. The temperature coefficient of the intrinsic energy gap above room temperature is about -0.00033 ev/\ifmmode^\circ\else\textdegree\fi{}K for an absorption coefficient of 40 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Band parameters for III–V compound semiconductors and their alloys

Abstract: We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures

Abstract: We present detailed experimental studies and modeling of the nonlinear absorption and refraction of GaAs/AlGaAs multiple quantum well structures (MQWS) in the small signal regime. Nonlinear absorption and degenerate four-wave mixing in the vicinity of the room temperature exciton resonances are observed and analyzed. Spectra of the real and imaginary parts of the nonlinear cross section as a function of wavelength are obtained, and these are in excellent agreement with experimental data. A simple model for excitonic absorption saturation is proposed; it accounts qualitatively for the very low saturation intensities of room temperature excitons in MQWS.

Some properties of semiconducting IrSb3

Abstract: Polycrystalline p‐type samples of IrSb3 and Ir0.5Rh0.5Sb3 have been made by hot isostatic pressing of powders. A number of properties such as thermal expansion coefficient, sound velocity, thermal conductivity, electrical conductivity, Seebeck coefficient, and carrier concentration have been measured. These compounds show promise as thermoelectric materials.

Origin of effective fields in magnetic materials

Abstract: The origin of the effective magnetic fields at the nuclei of magnetic materials which have been determined by M\"ossbauer, nuclear magnetic resonance, electron paramagnetic resonance, specific heat, and nuclear polarization methods is investigated theoretically by means of the exchange polarization mechanism. Exchange-polarized iron series Hartree-Fock calculations were carried out for (a) free ions and neutral atoms, (b) ions in a (crude) crystalline field (as in a salt), and (c) spin densities and configurations which conform with energy band and neutron magnetic scattering observations for the ferromagnetic metals. The effective field data for metals, ferrites, rare-earth garnets, and salts are then discussed and it is shown that the dominant contribution to the effective field (in almost every case) arises from the (exchange) polarization of the core electrons by the spin density of the unpaired outer electrons. For the transition metals, the role of the conduction electrons is analyzed including some new contributions not previously considered. The data for ions like ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Mn}}^{++}$ may be understood mainly on the basis of the core polarization term but such factors as covalent bonding, charge transfer, crystal field effects (such as distortions from cubic symmetry) must also be included. For ions like ${\mathrm{Fe}}^{++}$ and ${\mathrm{Co}}^{++}$ the (large) field due to unquenched orbital angular momentum must also be considered and several cases in which the orbital field dominates are discussed. The exchange polarization method and the accuracy of the analytic spin-polarized Hartree-Fock functions are discussed with regard to the sensitivity of the internal field to orbital descriptions, the effect of crystalline environments, and to expansion and contraction of the spin density. Each factor is investigated in detail by means of accurate exchange-polarized calculations. In conjunction with these studies a restricted Hartree-Fock calculation for ${\mathrm{Mn}}^{++}$ was carried out (and is reported as an Appendix) which is more accurate than existing calculations and indicates the accuracy of earlier analytic Hartree-Fock calculations.