Showing papers on "Free electron model published in 1970"

Classical theory of the scattering of intense laser radiation by free electrons

Abstract: Thomson theory of arbitrarily intense elliptically polarized plane electromagnetic wave scattering by free electrons, solving electron equations of motion

Electrical properties of materials

Abstract: 1. The electron as a particle 2. The electron as a wave 3. The electron 4. The hydrogen atom and the periodic table 5. Bonds 6. The free electron theory of metals 7. The band theory of solids 8. Semiconductors 9. Principles of semiconductor devices 10. Dielectric materials 11. Magnetic materials 12. Lasers 13. Optoelectronics 14. Superconductivity 15. Metamaterials

On the theory of surface states in nearly free electron systems

Abstract: The existence of surface states in band gaps of a nearly free electron band structure is investigated. While in gaps at the Brillouin zone boundary one finds such a state only for positive potential matrix element, there a surface state always exists for band gaps inside the Brillouin zone.

Straggling of Heavy Charged Particles: Comparison of Born Hydrogenic-Wave-Function Approximation with Free-Electron Approximation

Abstract: Statistical fluctuations in the energy loss of heavy charged particles in this absorbers resulting from collisions with atomic electrons are determined for collision cross sections obtained from the first Born approximation calculated with hydrogenic wave functions. A comparison is given with the results calculated with a $\frac{1}{{\ensuremath{\epsilon}}^{2}}$ collision spectrum.

Electrically excited flowing gas laser and method of operation

Abstract: A method of and apparatus for producing spatially uniform discharges including producing laser action in a flowing gas by electrical means using first means to create electrons and second means to maintain the optimum electron environment to produce lasing action. Apparatus for and a method of producing spatially uniform discharges substantially throughout a large volume of gaseous medium by generating in an enclosure a substantially uniform density of free electrons in the medium and controlling the electron temperature of the free electrons to increase their average energy without substantially increasing their density that at a predetermined level and uniformity of both the density and temperature of the medium, a stable and uniform discharge is produced in the medium suitable for the intended use of the medium such as the generation and amplification of light waves by means of devices including gaseous media in which stimulated emission of radiation is provided by electrical means to create free electrons and maintain the optimum electron environment to produce lasing action, there being a particular relationship between the density of free electrons, gas pressure and gas velocity.

Generation of Light from Free Electrons

Abstract: Experimental study of the Purcell effect shows that the radiance and character of the light generated by free electrons interacting with a metallic diffraction grating are not compatible with a simple electrostatic-image theory. A variety of experiments indicates other possibilities for theoretical explanation and shows how new experiments are expected to determine a more compatible theory of operation. Although light has been produced throughout the wavelength range from 4 to 0.2 μm, quantum effects appear to be unnecessary in describing the results. Rather, an extension of high-frequency electron-tube theory into multiwavelength three-dimensional optics is indicated.

Electrons in Liquid Metals and other Disordered Systems

Abstract: In the past decade, a quantitative theory of the electrical properties of liquid metals has been built up, based upon a model of nearly free electrons scattered by the screened pseudopotentials of the assembly of ions. Within the uncertainties of our knowledge of the pseudopotentials, this simple theory agrees with the experimentally observed resistivity and thermoelectric power of non-transition metals and their alloys. It now seems that higher-order corrections to the n. f. e. formula in such systems are not large enough to be easily observed. Current interest is shifting to systems where the n. f. e. model should not be valid; liquid semiconductors, metallic vapours, metal-ammonia solutions, impurity band semiconductors, and semiconductivity glasses. The experimental situation is not reviewed, but attention is drawn to some basic theoretical questions, such as the nature of the atomic or molecular potentials, the role of electron-electron interaction, the character of the metal-insulator transition, and the quantum mechanical interpretation of such classical physical processes as the localization, percolation, and hopping of electrons in highly disordered materials.

The theory of radical recombination luminescence in semiconductors

Abstract: 1. According to the mechanism considered, an event of recombination of free atoms or radicals on the surface leads to the appearance of a free electron+free hole pair. If the subsequent recombination of an electron and a hole, accompanied by emission of a quantum, occurs through the level of the activator, the “basic” band arises. If, however, this recombination occurs through the local level of the chemisorbed atom (radical) itself, the “supplementary” band arises. 2. The experimental data (dependence of the “basic” band on the nature of the activator and its independence from the nature of the gas, and, conversely, the dependence of the “supplementary” band on the nature of the surrounding medium and its independence from the nature of the activator) fit well into this model.

Interpretation of Positron Annihilation Curves for Lithium by Mijnarends' Method. Has the Fermi Surface of Lithium a Neck?

Abstract: The positron annihilation curves of Donaghy and Stewart for lithium have been reinterpreted using Mijnarends' method. In this way it has been possible to split the total number of counts into two parts, one corresponding to electron momenta inside the main Fermi surface, the other arising from higher momentum components of the conduction electron wave functions and core annihilation. Evidence is found for the possible existence of a neck in the Fermi surface in the (110) direction with a radius of the order of 13% of the free electron sphere radius. The need for more detailed experimental investigations of positron annihilation in lithium is emphasized. [Russian Text Ignored].

Optical Properties of β′ Phase CoAl, CoGa, and NiGa

Abstract: The optical properties of β′ phase CoAl, CoGa, and NiGa were studied as functions of composition and photon energy in the spectral region from 0.7 to 6.3 eV. Similar investigations were conducted on NiAl between 0.7 and 2.0 eV. The specimens were prepared by a mechanical polishing technique that was shown, by the use of annealing studies, to produce surfaces from which reliable optical data could be taken. Measurements were made by the use of two polarimetric techniques on a reflectometer that was designed by the authors. The results of the optical measurements indicate that some of the investigated alloys show free electron behavior in the infrared, although the limited spectral region of investigation did not permit the authors to apply the Drude free electron theory to the data with confidence. The possible presence of hybridized plasma oscillations is indicated by structure in the loss function. The prominent optical absorption structure which is displayed by these materials in the visible and ultraviolet regions of the spectrum, and which indicates the presence of interband transitions, has been interpreted by the use of a simple rigid band model.

Quantum and temperature effects on capacitance in degenerate P-N junctions

Abstract: The junction capacitance of a P-N diode is calculated in a general way accounting for quantum and classical penetration of the free carriers into the transition region. The most important result of this analysis, confirmed by the experimental measurements of the tunnel diode junction capacitance, is a significant reduction, that increases with the temperature, of the capacitance built-in voltage. The theory is based on the calculation of the density of mobile charges penetrating the transition region from the solution of the effective mass Schroedinger equation for the free carriers using the W.B.K. approximation. Knowing the carrier density allows one to solve in a general way Poisson's equation up to the electric field and then to determine the total charge Qe(ν) due to all the free electrons. From this one obtains the junction capacitance C j (ν) = −( d Q e d ν ) , where ν is the voltage applied to the diode.

Self-consistent screening of a pseudo-atom in a nearly-free electron metal

Abstract: For nearly free electron metals, we present a new self-consistent method of calculating, within the Screened Uniform Charge Model, the screening of a pseudo-atom. Each iterative cycle is as follows : from an approximate screening potential, wave-functions are calculated as if one pseudo-atom were perturbing an electron gas; from these wave-functions the change δρ in charge density can be calculated and from δρ a new screening potential is derived. A parameter in this cycle is adjusted so that the Friedel sum rule is satisfied. Calculations, which neglected exchange corrections, are presented in detail for sodium at two temperatures, 373°K and 480°K. The change with temperature in the s-wave ‘reduced phase shift’ is about 9%. The resistivity, thermopower, and temperature dependence of the resistivity of liquid sodium are calculated, and the results are in remarkable agreement with the experimental results. The advantages of our method over other screening methods are discussed. One of us (Md. M. I...

Characteristic Energy Loss Studies of V2O5 and Vanadium

Abstract: The characteristic energy losses of V2O5 are interpreted using collective oscillations of groups of electrons, forming the O2p valence band. These observations provide valuable information concerning the energy band model of this material. The losses observed on vanadium are interpreted as due to free electron bulk and surface plasmons and combinations of both. Characteristic ionization losses confirm the ODS peaks observed in the vanadium valence band and indicate high transition probabilities for the top and bottom of this band.

Theoretical Calculation of the Electronic Thermal Expansion of Simple Metals

Abstract: At low temperatures the excitation of conduction electrons in metals gives rise to an electronic contribution C=ΓT to the heat capacity, and also a contribution β∝T to the thermal expansion coefficient, where T is the absolute temperature. The electronic Gruneisen parameter is γ=VβB/C=(d lnΓ/d lnV), where V and B are the crystal volume and bulk modulus, respectively, at T=0. We have used a local pseudopotential model to calculate all the contributions to Γ and its volume derivative, including the electron‐phonon interactions in first‐order perturbation. The calculated γ is 1.18 for Na, 1.01 for K, and 1.63 for Al, while the measured γ is 1.8 for Al. The free electron model predicts γ=⅔. From our calculations it appears that the Umklapp interactions of electrons with transverse phonons give important contributions to Γ.

Electron radiation damage and the green edge emission of CdS

Abstract: The behaviour of the green edge cathodoluminescence (100 KeV) and photoluminescence emission of cadmium sulphide at liquid helium temperatures has been investigated before and after (i) monoenergetic electron irradiation (in the 100 400 keV range), (ii) heat treatments in sulphur vapour and cadmium vapour. The shorter wavelength emission band (5136.5 AA), attributed to the recombination of free electrons with bound holes does not change significantly under electron irradiation at liquid helium temperatures. The longer wavelength emission band (at approximately (5170 AA), attributed to the recombination of bound electrons with bound holes, is enhanced by irradiation with electrons of sufficient energy to displace sulphur atoms and shifts to higher energies.

Energy Distribution of Electrons Emitted from Silicon Surface‐Barrier Diodes

Abstract: The energy distribution of electrons emitted from surface‐barrier diodes made of p‐type silicon with aluminum contacts has been investigated in an attempt to clarify the behavior of electrons in a high electric field in silicon. Free electrons have been produced in the p‐type silicon by irradiated light and accelerated in the depletion layer of a reverse‐biased diode to escape into vacuum from the cesium‐treated surface of the thin aluminum contact. Energy distributions of the emitted electrons have been measured under various conditions using the retarding field method. The energy distributions of the electrons in the silicon have been obtained from those of the emitted electrons. They cover the energy region from 1.5 to 4 eV above the conduction‐band bottom of silicon. Different energy distributions have been found for [111] and [100] directions of the accelerating electric field. By using Keldysh's theory with known parameters, the mean‐free paths of hot electrons between phonon scattering have been de...

Free Carrier Faraday Effect in n-Type InSb with a Submillimeter-Wave Laser

Abstract: Free carrier Faraday rotation and ellipticity in n-type InSb have been measured at 105°K by the use of an HCN laser of 337 µm in the range of magnetic field including cyclotron resonance. The experimental results were in good agreement with the classical theory based on the Drude free electron model except in the vicinity of the cyclotron resonance field. The effective mass, the density and the relaxation time of conduction electrons were determined simultaneously only from the Faraday rotation by means of the best fit method. Near the cyclotron resonance field, the Faraday ellipticity showed a considerable discrepancy between measured and calculated values, which has not been explained even by considering the nonparabolicity of energy bands.

Electron collision frequency, ionospheric g factor, and the electron energy loss rate parameter in the ionosphere.

Abstract: Considering the rotational excitations of O2 and N2 an expression for the ionospheric G factor for air has been derived. In view of recent laboratory measurements an expression for has boon obtained and electron collision frequency profile has been constructed with the help of pressure data. With these parameters the electron energy loss parameter (Gν/N) air has been calculated which compares well with previous results. It is concluded that the contribution of the rotational excitation of O2 to the electron energy loss rate parameter is significant for the free electrons with small energies specially when the electron gas temperature Te is below 290°K.

Photon transmission through a hot electron atmosphere

Abstract: The problem of steady-state photon transmission through a planar atmosphere of free electrons is considered. The electrons are assumed to be in a local Maxweillian distribution with a density which is independent of position. The photons are allowed to undergo Compton and inverse Compton scattering. The quantities of interest are taken to be the spectral distribution of the transmitted flux and the temperature distribution through the atmosphere. That is, the interaction between photons and electrons is allowed to drive the local electron temperature to just that value such that no energy exchange takes place between electrons and photons. The analysis shows that the temperature can either increase or decrease as one traverses the atmosphere, depending upon the spectral distribution of the incoming flux.

Dimensionality Effects on the Fermi Gas

Abstract: It is shown how the elementary properties of one-, two-, and three-dimensional free electron gases may be obtained as special cases of a general formulation. The exercise is suitable for a student and furthermore suggests that the concept of nonintegral dimensionality may serve to describe finite geometries as intermediate between the usual integral types.