Showing papers on "Mean free path published in 1977"

Energy propagation including scattering effects sengle isotropic scattering approximation

Abstract: The elastic energy propagation in a three dimensional infinite elastic medium, in which scatterers are distributed homogeneously and randomly, is investigated by a statistical method. A single isotropic scattering process is investigated. The elastic medium is characterized by the wave velocity V and the distribution of the scatterers is characterized by the mean free path l. It is assumed that the elastic energy is radiated spherically from the source at a time t=0 in a short time duration. A space-time distribution of the mean energy density of the scattered waves is obtained as Es(r, t)=(W0/4πlVtr)1n((Vt+r)/(Vt-r)) for Vt≥r, where r is the distance from the source and W0 is the total energy radiated. A uniform spatial distribution is constructed far behind the wave front and near the source. The mean energy density Es is proportional to t-2 for t_??_2r/V and independent of r and W0. Several important properties of coda waves observed near the hypocenter are explained qualitatively by this solution when heterogeneities in the earth are interpreted as the scatterers and Es corresponds to the power spectrum of coda waves.

Emission probability of hot electrons from silicon into silicon dioxide

Abstract: An experimental method is described for directly measuring the probability of electron emission from the silicon substrate into the SiO2 layer after the electron has fallen through a certain potential drop in traversing the depletion layer and reached the Si‐SiO2 interface. The method is based on optically induced hot‐electron injection in polysilicon‐SiO2‐silicon field‐effect‐transistor structures of reentrant geometry. The emission probability was studied as a function of substrate doping profile, substrate voltage, gate voltage, and lattice temperature. It was found that the hot electrons could be emitted by tunneling as well as by surmounting the Schottky‐lowered barrier. Over‐the‐barrier emission dominates at large substrate voltages, where the emission probability is high, and tunnel emission becomes appreciable and may even dominate at small substrate voltages where the emission probability is low. A simple model was developed based on the assumption that only those hot electrons lucky enough to escape collision with optical phonons were emitted. Using this model, we found that the expression P=A exp(−d/λ) described very well the dependence of the emission probability on doping profile, substrate voltage, and gate voltage. Here A=2.9 is a constant, λ is the optical‐phonon‐electron collision mean free path, d is the distance from the Si‐SiO2 interface where the potential energy is equal to the ’’corrected’’ barrier of (3.1 eV−βEOX1/2 −αEOX2/3ox), βEOX1/2 is the Schottky lowering of the barrier, and αEOX2/3 is a ’’barrier‐lowering’’ term introduced to account for the probability of tunneling. The temperature dependence of the collision mean free path was found to follow the theoretical relationship λ=λo tanh(ER/2kbT), with λo=108 A and ER=0.63 eV. This model is useful for evaluating potential hot‐electron‐related instability problems in IGFET and similar structures.

Solar particle propagation from 1 to 5 AU

Abstract: A statistical analysis of solar particle events, observed by the GSFC-UNH charged particle detector on board Pioneer 10 and Pioneer 11 from March 1972 to December 1974 (from 1 to 5 AU for each spacecraft), is carried out with the goal of experimentally determining the statistical average interplanetary propagation conditions from 3 to 30 MeV. A numerical propagation model is developed that includes diffusion with a diffusion coefficient of the form k r =k o r β , convection, adiabatic deceleration, and a variable coronal injection profile. The statistical analysis is carried out by individually analyzing each of five parameters (t max, ξ(tmax), Δt 5, τ) that are uniquely defined in a solar particle event. Each of the five parameter data sets were analyzed in terms of both a spacecraft-solar flare connection longitude ≤50°, and a numerical model that employed a variable exponential decaying coronal injection profile. The five individual parameter analyses are combined with the results that the statistical average radial interplanetary diffusion coefficient from 1 to 5 AU is given by 〈k r〉 = (1.2 ± 0.4) × 1021 cm2 s-1 with 〈β〉 = 0.0± 0.3 for 3.4 to 5.2 MeV protons and 〈k r〉 = (2.6 ± 0.6) × 1021 cm2 s-1 with (β) = 0.0± 0.3 for 24 to 30 MeV protons. Using the classical relationship for the radial scattering mean free path λr, i.e. k r = υλr/3, we obtain 〈λr〉 = 0.09 ± 0.03 AU and 0.075 ± 0.020 AU for the low and high energy data, respectively. These results show, from 1 to 5 AU and from 3 to 30 MeV, that 〈λr〉 is both independent of radial distance and approximately independent of rigidity (for 〈λr〉~P α, where P = rigidity, α = -0.15 ± 0.20). The above diffusion coefficients are inconsistent With both the predictions of the diffusion coefficient from present theoretical transport models and with the diffusion coefficient used in modulation studies at low energies.

Solar Particle Propagation from 1 to 5 AU

Abstract: A statistical analysis of solar particle events, observed by the GSFC-UNH charged particle detector on board Pioneer 10 and Pioneer 11 from March 1972 to December 1974 (from 1 to 5 AU for each spacecraft), is carried out with the goal of experimentally determining the statistical average interplanetary propagation conditions from 3 to 30 MeV. A numerical propagation model is developed that includes diffusion with a diffusion coefficient of the form k r =k o r β , convection, adiabatic deceleration, and a variable coronal injection profile. The statistical analysis is carried out by individually analyzing each of five parameters (t max, ξ(tmax), Δt 5, τ) that are uniquely defined in a solar particle event. Each of the five parameter data sets were analyzed in terms of both a spacecraft-solar flare connection longitude ≤50°, and a numerical model that employed a variable exponential decaying coronal injection profile. The five individual parameter analyses are combined with the results that the statistical average radial interplanetary diffusion coefficient from 1 to 5 AU is given by 〈k r〉 = (1.2 ± 0.4) × 1021 cm2 s-1 with 〈β〉 = 0.0± 0.3 for 3.4 to 5.2 MeV protons and 〈k r〉 = (2.6 ± 0.6) × 1021 cm2 s-1 with (β) = 0.0± 0.3 for 24 to 30 MeV protons. Using the classical relationship for the radial scattering mean free path λr, i.e. k r = υλr/3, we obtain 〈λr〉 = 0.09 ± 0.03 AU and 0.075 ± 0.020 AU for the low and high energy data, respectively. These results show, from 1 to 5 AU and from 3 to 30 MeV, that 〈λr〉 is both independent of radial distance and approximately independent of rigidity (for 〈λr〉~P α, where P = rigidity, α = -0.15 ± 0.20). The above diffusion coefficients are inconsistent With both the predictions of the diffusion coefficient from present theoretical transport models and with the diffusion coefficient used in modulation studies at low energies.

Entrance Windows in Germanium Low-Energy X-Ray Detectors

Abstract: We have found experimentally that high-purity Ge low-energy X-ray detectors have a relatively thick entrance window which renders them practically useless below ~ 2.3 KeV. A simple X-ray fluorescence experiment establishes clearly that the window is physically in the Ge material itself. Experiments with detectors made from different Ge crystals, and with Schottky barrier contacts of different metals indicate that the effect is due to a basic property of the transport of electrons near a surface. Theoretical considerations and a Monte Carlo calculation show that the window is caused by the escape of warm electrons which are the end product of a photo event. The mean free path of the electrons becomes longer as they lose energy by optical phonon collisions and they can be trapped at the surface before they are picked up by the electric field.

In situ measurement of Hall effect, magnetoresistance, resistivity, and TCR of bismuth films

Abstract: In situ measurements of Hall effect, magnetoresistance, resistivity, and temperature coefficient of resistivity of bismuth films (700–2600 A) were carried out in a specially designed evacuation chamber. The films were deposited on a glass substrate at 150°C and at a pressure of ∼10−6 Torr. The values of the mean free path and specular scattering parameter obtained were 14100 A and 0.5, respectively. The effect of the grain boundary on the electrical resistivity was also accounted for in the light of the Mayadas‐Shatzkes theory.

The theory of the instantaneous triple-probe method for direct-display of plasma parameters in low-density collisionless plasmas

Abstract: An exact theory taking the ion temperature T1 into account is developed for a triple-probe in an orbital-motion-limited collisionless plasma, i.e. when charged particle mean free path>>Debye length>>probe radius. Formulae for determining electron temperature and electron density are given for both spherical and cylindrical probes. Analytical results show that the effect of T1 on measurements of plasma parameters is small when using a cylindrical probe and is negligible when compared to the errors obtained when using a spherical probe. The magnitude of the errors obtained in practical measurements are discussed. The possibility of ion temperature determination using this theory is also suggested. Experiments have been also done for confirmation.

Application of X-ray photoelectron spectroscopy to quantitative analysis without standards

Abstract: The application of X-ray photoelectron spectroscopy to quantitative analysis without standards is discussed considering the mean free path of ejected electrons calculated by Lotz's equation or Powell's equation and the photoionization cross section calculated according to Scofield. The relative value of mean free path experimentally obtained and the difficulties of the preparation of standards are described with regard to various solid solution samples and oxide compounds.

Theoretical Study of a Chemical Turbulence

Abstract: Recently Kuramoto and one of the present authors have carried out a computer simula­ tion for a chemically oscillating system and found a turbulence-like behavior similar to the hydrodynamic turbulence. The steady turbulent state of this system is theoretically studied. It is shown that there exist two characteristic regions of wavenumber k. One is a cascade region with ks~1, and the other is a dissipative region with kS> 1, where s is a characteristic length which is much larger than the reaction mean free path lr. Over these two regions = = =

A simple analysis of the transmission and backscattering of 10-30 keV electrons in solid layers

Abstract: A simple analytic treatment of elastic scattering transport of particles in a plane parallel plate is combined with Monte Carlo simulations. The effect of energy loss is studied for 10-30 keV electrons. The main features of transmission and backscattering are predicted in terms of a dimensionless parameter r/ lambda tr(0) where r is the Bethe range and lambda tr(0) is the initial transport mean free path.

Transport of Long-Mean-Free-Path Electrons in Laser-Fusion Plasmas

Abstract: The Fokker-Planck kinetic equation for suprathermal electrons which are confined in a spherical plasma by the sheath potential and collide with colder denser electrons and ions is investigated. In the region where the collisional mean free path, $\ensuremath{\lambda}$, is longer than the spatial scale length, $L$, the kinetic equation is reduced by averaging it along an orbit between reflections by the sheath. The electrons are seen to diffuse in impact parameter relative to the plasma core while slowing down in velocity. The resulting heat flow scales as $(\frac{L}{\ensuremath{\lambda}}){n}_{\mathrm{sth}}m{{v}_{\mathrm{sth}}}^{3}$.

Slowing‐down distances and times of 0.1‐ to 14‐MeV neutrons in hydrogenous materials

Abstract: The slowing‐down distances and times of fast neutrons are calculated by extending the early work of Fermi to the case in which the neutron mean free path is energy dependent. This calculation is essentially a one‐particle Monte Carlo treatment in which each path length is a mean free path and the neutron is always scattered through a scattering angle ϑ, such that cosϑ=〈cosϑ〉, the average of cosϑ in the laboratory system. The average results derived by this analytic method are shown to be in reasonable agreement with a detailed Monte Carlo computer calculation of the moderation of a 1‐MeV neutron down to 40 eV in pure hydrogen. These calculations illustrate the Monte Carlo method and the broad spread in time and energy of the neutron flux resulting from an instantaneous point source in hydrogen. The results also graphically illustrate the greater penetrating distances of 14‐MeV neutrons compared to 1‐MeV neutrons in hydrogenous materials. Pedagogic, computer‐oriented uses of this material are suggested.

Diffusion of fast electrons in the presence of a magnetic field

Abstract: The Boltzman equation, for energy deposited by fast electrons in the presence of an applied magnetic field, is solved in the diffuse beam approximation. The solution is obtained by a simple coordinate transformation which is valid both when λ/rL⩽0.25 (λ = mean free path, rL = Larmor radius) and when λ/rL ⩾4.5. The half‐space solution is used to determine the dose in a gas. The theoretical results are compared with experiments. It is found that agreement is better than *10% for cases of interest.

Determination of the Be-Auger-electron attenuation length in Be using 160-keV protons

Abstract: We report the first results of a method for determining the inelastic attenuation length of low‐energy electrons in the surface region of a solid from the yield of characteristic Auger electrons excited by proton bombardment. Samples of evaporated beryllium were bombarded by 160‐keV protons, and the attenuation length of 100‐eV electrons in Be was determined to be 6.1 A.

Avalanche injection and near avalanche injection of charge carriers into SiO 2

Abstract: A description is given of the avalanche injection of electrons from a p-n-junction into an adjacent SiO 2 layer. The resulting oxide current is found to decay due to the trapping of electrons in the SiO 2 . This decay can be characterized by the product of the concentration N of the trapping centers in the oxide and their capture cross section σ. We found N \sigma = 1.7 \times 10^{-1} cm-1. In addition, near avalanche injection is described. Here the oxide current is found to depend exponentially on the shortest acceleration distance of the hot carriers and is characterized by the mean free path of these carriers. A new result for the mean free path of the hot holes (λ h = 42 A) is given. Both types of injection find application in semiconductor memory cells.

Separation of solar and interplanetary diffusion in solar cosmic ray events

Abstract: A study has been made of the propagation of solar cosmic rays after their release from a flare under the assumption of diffusive motion around the sun and in interplanetary space (where κ1 is taken to be 0). For two-dimensional diffusion around the sun and for a diffusion coefficient κ11(r) = κ0rβ in interplanetary space, approximate analytic solutions have been found for the density N(t) and the anisotropy ξ(t). Both density and anisotropy are found to be prolonged at 1 AU relative to those for impulsive injection. By combining these, the diffusion coefficients at the sun and at 1 AU can be extracted separately. To check the approximate analytic solution, numerical computation over a wide range of propagation conditions indicates that mean free paths derived near 1 AU are accurate to within 13% (when they are fitted up to time of maximum, tm) or to within 25% (up to 2tm). The effect of one- or three-dimensional diffusion around the sun instead of two-dimensional diffusion is to change the derived mean free path by less than 25% (up to tm). The effect of a non-negligible loss (or escape) of particles at the sun has been evaluated; for all except the largest value of loss rate suggested, the error is small up to tm. Application of the solution to the ground level event of September 1, 1971, when the flare was ≈ 40° behind the west limb, gives a solar diffusion coefficient κs/rs² =1.5 h−1 and a mean free path at 1 AU of 0.15 AU for the case β = 0.

Ultrasonic-attenuation investigation of the mixed state in three vanadium samples of varying purity

Abstract: Ultrasonic-attenuation measurements were performed in three single-crystal vanadium samples, with resistivity ratios of 7.8, 245, and 450 as a function of magnetic field and temperature. Measurements obtained as a function of applied magnetic field were compared to the theoretical predictions of Houghton and Maki (HM) for the region near H/sub c//sub 2/. Because of the varying purity of the samples, the HM predictions for the dependence of the normalized attenuation on mean free path were also tested. In all cases, the experimental results were in good qualitative agreement with the HM predictions. Ultrasonic-attenuation measurements as a function of temperature compared well to the BCS theory and yielded critical temperatures of 4.69, 5.26, and 5.27 degreeK with corresponding zero temperature energy gaps of 2..delta.. (0)/kT/sub c/ = 3.6, 3.6, and 3.5 in order of increasing sample purity.

Thermoelectric power of gold‐silver alloy films

Abstract: Thermoelectric power, resistivity, and temperature coefficient of resistance of annealed Au−Ag alloy films, covering the entire composition range, have been measured. Using size effects in the electron transport theory, the energy dependence of the mean free path U and the Fermi surface area V have been determined.