Showing papers on "Mean free path published in 1985"

Injected-hot-electron transport in GaAs

Abstract: Using the new experimental technique of hot-electron spectroscopy we have, for the first time, observed electrons in extreme nonequilibrium. When the transit-region width is comparable to the calculated hot-electron mean free path, two peaks are observed in the measured spectrum. The high-energy peak corresponds to quasiballistic electrons suffering few, if any, collisions in the transit region. The low-energy peak is due to excitation of the Fermi sea by the injected hot electrons.

Photoemission from activated gallium arsenide. II. Spin polarization versus kinetic energy analysis.

Abstract: The spin polarization of the electrons emitted by a GaAs photocathode under circularly polarized light excitation is investigated as a function of the electron kinetic energy. The photocathode is activated by cesium and oxygen coadsorption under ultrahigh-vacuum conditions to achieve a negative electron affinity. The spin polarization is measured by Mott scattering. The study is performed with a very-high-energy resolution (20 meV), at 300 and 120 K, under well-focused ${\mathrm{Kr}}^{+}$-laser light excitation (photon energy ranging from 1.55 to 2.60 eV). The polarization-versus-energy distribution curves show typical features related to those observed in the energy distribution curves, which are analyzed in detail in the preceding paper [H.-J. Drouhin, C. Hermann, and G. Lampel, Phys. Rev. B 31, 3859 (1985)]. A model is developed to account for the largest measured polarization, which arises from electrons excited from the heavy-hole band and emitted without suffering any collision: A (2/3) maximum value is expected, which is reduced by spin precession in the internal D'yakonov and Perel' (DP) field, due to the absence of space-inversion symmetry in GaAs. An estimation of the hot-electron mean free path (\ensuremath{\sim}0.1 \ensuremath{\mu}m for photon energy above 1.96 eV) is deduced. The photoemission polarizations of the electrons excited from each of the two other valence bands are also calculated using a nonparabolic Kane band model. The L and X subsidiary minima give rise to polarization plateaus originating from energy relaxation in the band-bending region. The main contribution to the photocurrent is due to electrons which were thermalized in the central minimum of the bulk crystal and have relaxed their energy in the band-bending region prior to emission into vacuum. Their polarization is studied in relation with the luminescence polarization, measured on the same samples, in the framework of a one-dimensional diffusion model. An additional depolarization, occurring during the escape process, is evidenced and attributed to the DP relaxation mechanism in the band-bending region. Finally, the performances of GaAs photocathodes as monochromatic and polarized electron sources are analyzed with use of the physical concepts developed in the present paper and in the preceding one.

Energy and material dependence of the inelastic mean free path of low‐energy electrons in solids

Abstract: Calculations have been made of the inelastic mean free paths (IMFP’s) of 100–2000‐eV electrons in C, Mg, Al, Al2O3, Cu, Ag, Au, and Bi. These calculations have been based on experimental optical data and on theory. The optical data gives the dependence of the differential inelastic scattering cross section at zero momentum transfer on electron energy loss; the data used here satisfy optical sum rules closely. Theory is needed to specify the dependence of the differential inelastic scattering cross section on momentum transfer; results for free‐electron‐like solids were assumed to be applicable to the present materials. The calculated IMFP’s show significant deviations from the dependencies on electron energy and material expected from the formulas of Seah and Dench, Szajman et al., and Ashley.

Resistive ballooning modes in an axisymmetric toroidal plasma with long mean free path

Abstract: Tokamak devices normally operate at such high temperatures that the resistive fluid description is inappropriate. In particular, the collision frequency may be low enough for trapped particles to exist. However, on account of the high conductivity of such plasmas, one can identify two separate scale lengths when discussing resistive ballooning modes. By describing plasma motion on one of these, the connection length, in terms of kinetic theory the dynamics of trapped particles can be incorporated. On the resistive scale length, this leads to a description in terms of modified fluid equations in which trapped particle effects appear. The resulting equations are analyzed and the presence of trapped particles is found to modify the stability properties qualitatively.

Measurement of the Neutral Copper Vapor Density around Current Zero of a 500-A Vacuum Arc Using Laser-Induced Fluorescence

Abstract: The technique of laser-induced fluorescence was applied to measure the time dependence of the copper vapor density from 280 ?s before to 400 ?s after current zero of a vacuum arc driven by a sinusoidal current of 500-A rms. Atomic densities between 5 × 1017 m-3 and 5 × 1014 m-3 were observed at the center of the gap with a local resolution of better than 1 mm3. The observed densities were more than an order of magnitude smaller than those predicted by model calculations according to Rich and Farrall [16], and the density decay after current zero occurred much more slowly than expected. Both findings indicate that the correlation of recovery of dielectric strength to metal vapor density after current zero is different from the recovery criterion based on the ratio of the mean free path for atomic collisions to the gap length.

Thermodynamic variational method for liquid alloys with chemical short-range order.

Abstract: We present a first-principles study of chemical short-range ordering in liquid (s,p)-bonded alloys. Our approach is based on an optimized pseudopotential technique for the construction of the interatomic potentials and a thermodynamic variational technique based on the Gibbs-Bogoliubov inequality and hard-sphere Yukawa reference potentials (we use the analytical solution of the mean spherical solution for the equal-diameter case). The analysis of the redistribution of the valence electrons upon alloying allows us to elucidate the electronic origin of the ordering potential. In the case of a moderately strong ordering interaction, the application of the Gibbs-Bogoliubov variational technique yields a reasonably accurate prediction of the structure factors and of the thermodynamic excess functions. For very strong ordering potentials, a free minimization of the variational upper bound to the exact free energy gives unrealistic results. This is a consequence of the complete decoupling of number-density and concentration fluctuations in the mean-spherical approximation to the equal-diameter hard-sphere Yukawa mixture. We find that realistic solutions may be found by imposing the condition that the exact and the reference-system ordering potentials be the same at the mean effective atomic diameter. This constrained minimization of the variational free energy yields good results for the structure factors, but rather bad ones for the thermodynamic excess functions. We are able to show that this is due to a neglect of the finite electronic mean free path of the electrons in those concentration regions where it is comparable to the mean interatomic distance.

Electronic transport properties of metallic multi-layer films

Abstract: General expressions for the electrical resistivity and the temperature coefficient of resistivity of metallic multi-layer films are derived. It is assumed that the films consist of thin alternating layers of two different metals. The calculations are made within the framework of the Boltzmann kinetic theory. The background mechanisms of scattering of conduction electrons in the layers are described by two different relaxation times. The scattering at the interfaces between the layers is taken into consideration using boundary conditions. The modifications of bulk relaxation times evoked by the presence of the grain boundaries are obtained by means of the Mayadas-Shatzkes method. The analysis shows that the geometrical size effect can be expected when thicknesses of the particular layers become of the same order of magnitude as the mean free paths of conduction electrons in the bulk metals.

Model calculation of the thermal conductivity of polymer crystals

Abstract: A linear lattice model without adjustable parameters provides an accurate description of the magnitude and temperature dependence of the thermal conductivity of Kc of polyethylene crystals parallel (∥) and perpendicular (⟂) to the chain direction. The model shows that heat is transported principally by phonons polarized transverse (T) to the chain direction. Phonons polarized longitudinal (L) to the chain direction contribute about 20% to the heat transport along the chain direction, and negligibly to heat transport perpendicular to the chain direction. Thermal resistance is caused by LTT three-phonon umklapp scattering in the parallel direction, and by TTT scattering in the perpendicular direction. The calculated values for large crystals are K = 465 W m−1 K−1, K = 0.16 W m−1 K−1 at 300 K, in agreement with experimental estimates and implying an anisotropy ratio of K/K ≈ 3000. The axial thermal conductivity of polyethylene crystals is extremely high and comparable to that of copper. Comparison with experimental data on semicrystalline samples at lower temperature yields a crude value of mean free path for boundary scattering of about 50 nm, agreeing in order of magnitude with the size of crystalline blocks.

Arc-evaporated carbon films: Optical properties and electron mean free paths

Abstract: The real and imaginary parts of the complex refractive index, n(..omega..) = n(..omega..)+ik(..omega..), of arc-evaporated carbon films have been obtained over the range of photon energies h..omega.. from 0.5 to 62.0 eV. Values of k(..omega..) obtained from transmission measurements in this energy range were combined with values of k(..omega..) from the literature in the infrared and soft-x-ray regions. A Kramers-Kronig analysis then yielded the values of n(..omega..). The density of the arc-evaporated carbon films was found to be 1.90 +- 0.05 g cm/sup -3/ by the ''sink-float'' method, and their thicknesses were determined optically. A sum-rule calculation yielded the effective numbers of valence and core electrons to be 4.2 and 1.8, respectively. The experimental values determined for n(..omega..) have been used to estimate values of the inelastic mean free path ..lambda..(E) for electrons of energy E from 200 to 3000 eV in amorphous carbon. Good agreement is found between ..lambda..(E) and experimentally determined values of electron attenuation length L(E) from the literature.

Transport and magnetic measurements on UPt3

Abstract: Experiments on the normal phase of UPt3 show a large positive magnetoresistivity, almost temperature‐independent, linear in field, and a positive thermoelectric power which is not linear in temperature as T→0. The superconducting phase is characterized by a high thermal conductivity with a strong T2 term, by a coherence length smaller than the mean free path, and by lower and upper critical fields H(0)c1∼60 Oe and Hc2(0)∼26 kOe.

Search for anomalous fragments in 1.8A-GeV 40Ar reactions in nuclear emulsions.

Abstract: Results are presented from an investigation of the mean free path in nuclear emulsion of multiply charged fragments, produced by 1.8A-GeV argon nuclei. Charge identification of 6965 fragments with charges Z> or =2, producing 2192 secondary interactions, has been made. No dependence of the mean free path on the distance from the preceding collision is observed and thus our result is consistent with the nonexistence of anomalons.

Electrical resistivity in amorphous metals: Consequences of phonon ineffectiveness in the diffraction model

Abstract: : Electrical transport in amorphous metals is analyzed in the context of the Baym-Faber-Ziman theory. The theory is generalized to incorporate electron mean free path effects through the Pippard-Ziman condition on the electron-phonon interaction. A variety of model t-matrices are considered. The geometrical structure factors are modeled by Percus-Yevick hard sphere forms and a single branch Debye phonon spectrum is assumed. Detailed results for electrical resistivity rho vs. temperature T and the TCR are presented for extensive ranges of 2kF/kp and electron mean free path. The results, incorporating the Pippard-Ziman condition, are consistent with the observed rho vs. T in low resistivity glassy metals. However, although inclusion of the Pippard-Ziman condition dramatically improves agreement with the data, quantitative agreement is not obtained in high resistivity amorphous metals.

Porous media gas diffusivity from a free path distribution model

Abstract: A model for the effective diffusivity in porous media is developed from simple considerations. This derivation is analogous to those used in force path models for electron and phonon diffusion in solids. (AIP).

Dependence of the Phase-Coherence Time in Weak Localization on Electronic Mean Free Path and Film Thickness

Abstract: Magneto-resistance measurements on thin disordered films yield the phase-coherence time τ i of the conduction electrons (weak localization). The dependence of τ i on film thickness and residual resistivity are reported for disordered Au, Ag and Mg films in the temperature range between 4.5 and 20 K. The resistivity of the films was varied between .13 and 1.1×10 -6 Ωm. The temperature dependence of 1/τ i follows a T p -law. The exponent is essentially two, but varies slightly with the resistivity. 1/τ j depends much less on the resistivity than the linear prediction of the theory. No direct influence of the film thickness on τ i was observed. This excludes the impurity induced Coulomb interaction as the relevant mechanism and suggests that τ i is essentially determined by electron-phonon interaction. However, at the present time there is no theory available that reproduces the experimental results. Measurements of the (temperature independent) Hall-constant suggest that the thin films are rather homogeneou...

Evidence of anomalous behavior of relativistic alpha particles emitted in 12C-emulsion interaction at 4.5 GeV/nucleon.

Abstract: This paper presents evidence of the anomalous interaction mean free path of the relativistic alpha particles emitted from the interaction of /sup 12/C with emulsion nuclei at 4.5 GeVc per nucleon. The tracks were followed systematically through the stack. The detailed measurements show clearly that the interaction mean free path is anomalously shorter for a fewer centimeters after their emission. The results have been compared with other results obtained from both accelerator and cosmic-ray data.

A theory of diffuse light scattering by lungs.

Abstract: We present a theoretical treatment of backscattered light from the interior of a lung illuminated by a thin beam of light normally incident on the pleural surface. An approximate formula is developed describing how the backscattered intensity varies with distance from the point of light entry. This is shown to depend markedly on the optical mean free path and on the effective extinction coefficient. We attempt to relate the optical mean free path to the mean alveolar size. This relationship is found to depend primarily on septal reflection and refraction. Reflection is treated quantitatively. Refraction is much more difficult and may have to be approached empirically. We present here the rudiments of a technique with implications for the possibility of dynamic stereology.

Breakdown of hybridisation at elevated temperatures in some intermetallic compounds

Abstract: The 'classical' s-d scattering theory is applied to account for the anomalous temperature dependence of the resistivity in some intermetallic compounds, which possess very narrow peaks in the electronic density of states, due to d or f states. At temperatures where h(cross)/ tau e-ph approximately=J, where tau e-ph is the electron-phonon scattering time and J a hybridisation integral, the hybridisation is broken, and at higher temperatures the resistivity follows a linear rho =a+bT law. The temperature-independent part a is due to phonons scattering the d or f states, into which the s electrons (which carry most of the electric current) are scattered by the hybridisation integral J. The bT term is due to phonon scattering of the more itinerant s (or p) states into s states. This term does not saturate because the mean free path of the s electrons is still about 10 interatomic spacings, even at high temperatures. The thermoelectric power has a maximum when h(cross)/ tau e-ph approximately=J.

A New Method for the Determination of the Bulk Electrical Resistivity and the Bulk Mean Free Path in Metals

Abstract: A new method to obtain the surface resistivity ρ s in one platelike sample is developed. The resistivity ρ s is given as the difference between the high-field magnetoresistivity in the Sondheimer geometry and that in the MacDonald-Sarginson geometry. The bulk resistivity ρ b is obtained from the apparent zero-field resistivity ρ 0 subtracted by ρ s . Using these values of ρ 0 and ρ b , the bulk mean free path l b is calculated according to the Fuchs-Sondheimer theory of the size effect for a thin film. This method has been applied to samples of zone-refined aluminium. For these samples a value of 0.18±0.01 fΩm 2 has been obtained at 4.2 K for the specific surface resistivity. The product of ρ b and l b is estimated to be 0.80±0.04 and 0.84±0.03 fΩm 2 for the single-crystal and the polycrystalline samples, respectively.

Two distinct classes of alpha particles and a possible correlation of anomalously short mean free paths with the cold component

Abstract: Investigation of 371 primary collisions of 56Fe on nuclear research emulsion at BEVALAC energies gives evidence for the existence of two distinct classes of reaction among the secondary alpha particles as projectile fragments. Moreover an examination of the mean free path gives a clear hint towards a correlation between an anomalously short mean free path and those alpha particles which belong to the cool class.

Thermal Layer Solutions of the Boltzmann Equation

Abstract: The steady Boltzmann equation in one space dimension with a small mean free path is solved for a gas contained between two plates at different temperatures The Solution consists of the Chapman-Enskog expansion together with boundary layer expansions near each plate These expansions are truncated at a finite order, and an additional error term is added, so that the sum is an exact Solution of the Boltzmann equation The analysis of the boundary layer equations requires a Solution of the Milne problem

Quasiparticle scattering time in P-wave superconductors

Abstract: The authors show that the quasiparticle scattering time, due to nonmagnetic impurities diverges at zero energy in anisotropic superconductors with zeroes in the order parameter at points and on lines on the Fermi surface. They assume S-wave scattering from the impurities and carry out the calculations in the weak coupling limit. As a result of the energy dependence of the scattering time, the quasiparticle mean free path diverges at zero energy. This is in contrast to the BCS result where the mean free path is equal to its constant normal state value. The consequences of this for the ultrasonic attenuation are discussed.

Determination of the mean free path of electrons in solids from the elastic peak - II. Experimental results

Abstract: The simple theoretical model described in Part I [1] is applied to evaluate experimental results determined by elastic peak electron spectroscopy and published previously. The inelastic mean free path λ determined from the elastic backscattering probabilityPe of 2.2 and 3.1 keV electrons on C, Si, Ge and Mo are in reasonable agreement with results of Seah and Penn. In the evaluation σeff elastic backscattering cross sections calculated with the Thomas—Fermi—Dirac potential model have been applied. This model, however, is not suitable for W and Au high atomic number elements. A detailed discussion is given on the problems associated with the measurement ofPe taking into consideration the CMA response, deconvolution and angular distribution of electron spectra. Another method for determining λ is given by comparing the elastic peaks of two elements and their σeff backscattering cross sections. Experimental results are presented for Al, Si, Ge, GaAs, GaP, InSb, GaSb, Sb, InP, SiO2 and Si3N4, atomic clean surfaces measured with a CMA atEP=1, 1.5, 2 and 3 keV at normal incidence. Good agreement was found with literature data collected by Ashley for Al−Si, Ge−GaAs. The IMPF λ of GaP and GaSb proved to be 10% larger than those of GaAs, results not available in the literature. New results as well are published for λ of Sb, InSb and InP. The good agreement with literature data justifies the application of the simplified model described in Part I.

Single‐crystal experiments on EuMo6S8 and EuMo5WS8

Abstract: Resistivity measurements have been made on EuMo6S8 and EuMo5WS8 single crystals in the temperature range 1.5–300 K under pressures between ambient and 20 kbar. In contrast to the recently reported results on sintered or melted material, the resistivity has a metallic behavior. No semiconductor behavior is observed in either type single crystal. The strong scattering effects lead to an electronic mean free path equal to the interatomic Mo‐Mo distance. The possibility of spin fluctuations associated with the molybdenum atoms is discussed. The superconductivity appears in either type crystal at about the same pressure (10 kbar).

Theory of electric conductivity measurements by an electrostatic probe in an atmospheric low-density continuum ionized gas

Abstract: A method has been developed and used to obtain theoretical predictions of the electric conductivity measured by an electrostatic probe in an atmospheric ionized gas, i.e., with mean free path very much less than probe radius. Three different methods for conductivity measurements have been analyzed: (1) attracting potential method; (2) transient response method; (3) space potential method.