Electron transmission measurements of electron mean free path in supported thin films from 1–5 keV

Measurements are made of the transmission of medium energy electrons through in vacuo deposited films in order to determine the inelastic electron mean free path as a function of energy. Films of Al, Ge and Au are deposited in small increments on 20–30 Å carbon substrates supported by “holey” carbon films. The no-loss electron current is measured for each thickness as a continuous function of incident energy in the range of 1–5 keV. Although this preliminary experiment does not result in a precise separation of elastic and inelastic scattering effects, the attenuation lengths estimated are in reasonable agreement with measured and calculated in-elastic mean free paths. Elastic scattering cross sections appear to be smaller than estimated by simple theory.     

Ultrasonic determination of the temperature dependence of the electron mean free path in cesium single crystal

The ultrasonic attenuation of high frequency longitudinal waves has been measured in transverse and oblique magnetic fields to determine the temperature dependence of the phonon-limited mean free path in cesium single crystals. Below 2.5°K, the mean free path varies as T^4.8. The results are compared with electrical resistivity measurements in cesium.     

Experimental determination of the energy dependence of electron inelastic mean free path in silicon oxide and silicon nitride

The energy dependence of the electron inelastic mean free path, λ(E), in silicon oxide and silicon nitride is experimentally determined via Auger electron spectroscopy according to Auger signal attenuation with varying film thickness. Silicon-oxide- and silicon-nitride films are formed on different metal substrates by means of plasma-enhanced chemical vapor deposition. Analysis of the results and their comparison with theoretical data indicate that, in the chosen material, variations in the electron mean free path versus their energy are estimated more reliably by means of experiments than through the use of universal theoretical curves. It appears that the results obtained in this work can help in the more accurate determination of the width and location of interfaces in multilayer structures.     

The limitation of electron mean free path in small silver particles

By evaluating, with help of Mie's theory, absorption measurements of spherical silver particles — (between 24 and 210 Å in diameter) — suspended as colloid in photosensitive glasses we found that the absorption coefficient at the wavelength of absorption peak (λ=0.405 μ) remains constant, whereas the refractive index increases by about a factor of 5 when the particle size decreases. Within accuracy of measurements and the differences of bulk optical constants of various authors this deviation from the bulk values can be described by the “free path effect”, the influence of conduction electron collisions with particle surfaces. The results are compared with the quantum mechanical theory ofKawabata andKubo.     

Evidence of anisotropic mean free path as furnished by galvanomagnetic measurements

If in the Boltzmann equation, written with an ansiotropic relaxation time,τ(k), a suitable substitution of variables is carried out, it is found that Kohler's rule is valid as long as the quotient of the mean free path,l(k), and an average relaxation time remains constant. Deviations from Kohler's rule in the case of comparing field and temperature dependence of the galvanomagnetic effects for different metals and varying crystal orientation lead to the conclusion that the anisotropy of the relaxation time changes with temperature.     

Measurement of the electron mean free path using a bending effect

It has been observed experimentally that elastically bending a metal whisker increases its resistance. Such an increase in resistance depends on the metal, the temperature and the orientation of the whisker axis. This effect is observable below 6°K for Zn, 8°K for In, 20°K for Sn, and 300°K for Bi. It is suggested that the effect may be due to an enhancement of surface scattering due to the bending of the whisker. A calculation for such an effect for an “ideal metal” is presented along with data for Zn and Bi. This work has been supported by the Air Force Office of Scientific Research under grant number 68-1548.     

Spatial variation of the electron mean free path near a surface

The electron plasmon-emission-mean-free-path in semi-infinite Jellium is evaluated as a function of position, and of electron emergence angle. The usual assumption that this free path is spatially non-varying inside the “metal” is found to be a reasonable approimation to reality by virtue of the fact that the surface plasmon emission probability increases where that of the bulk plasmon decreases (and vice-versa). The inverse mean free path, however, does not fall to zero for an appreciable distance (on the order of angstroms) outside the surface defined by the vanishing of the electron density.     

Scaling of resistance and electron mean free path of single-walled carbon nanotubes

We present an experimental investigation on the scaling of resistance in individual single-walled carbon nanotube devices with channel lengths that vary 4 orders of magnitude on the same sample. The electron mean free path is obtained from the linear scaling of resistance with length at various temperatures. The low temperature mean free path is determined by impurity scattering, while at high temperature, the mean free path decreases with increasing temperature, indicating that it is limited by electron-phonon scattering. An unusually long mean free path at room temperature has been experimentally confirmed. Exponentially increasing resistance with length at extremely long length scales suggests anomalous localization effects.     

Observations on the determination of electron mean free paths from RF size effect measurements

Numerical calculations of the line shape of the rf size effect for 0.1 mm thick potassium plates in the transmission geometry at 1.25 MHz, show that the amplitude of the fundamental resonance is proportional to exp (?1.22d/l), while that of the second resonance is proportional to exp (?0.92d/l), whered andl are the plate thickness and electron mean-free path, respectively. In the case of the fundamental, our result differs significantly from the exp (?1.57d/l) dependence usually assumed for the purpose of determiningl, and indicates that the conventional analysis leads to an overestimate ofl by approximately 30%. The amplitude dependence found here can be explained physically in terms of the finite skin depth, and in the case of the second resonance, in terms of the strength of the electric field splash at the center of the plate.     

Electron mean free path and conduction-band density-of-states in solid methane as determined from low-energy electron transmission experiments

Recently, Plenkiewicz et al. developed a theoretical model for analyzing the current I_t transmitted by a thin dielectric film as a function of incident electron energy E. The purpose of this paper is to apply this model to the analysis of recent I_t(E) results for solid methane. The analysis permits the determination of both the electron mean free path as a function of energy and the electronic conduction-band density-of-states in the quasi-elastic scattering region. The differences between our results and Kunz's solid methane band structure calculations are also discussed.     

The influence of the electron mean free path on phase-slip centers in indium whiskers

The relaxation of nonequilibrium quasiparticles at phase-slip centers in superconducting current carrying indium whiskers has been investigated. Very close to the critical temperature the “quasiparticle diffusion length” Λ depends on temperature. For lower temperatures Λ is temperature independent and shows the mean free path dependence $\text{Λ～ l}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ as predicated by theory.     

Pion mean free path in nuclear matter

The mean free paths for true absorption and inelastic scattering-as well as true absorption alone-of pions in symmetric nuclear matter are deduced from two sets of optical model parameters.     

Nucleon mean free path in nuclear matter

In calculations of nuclear reaction yields at incident energies of some tens of MeV consistently better agreement with experiments is obtained by assuming a nucleon mean free path in nuclear matter longer than that deduced from the Fermi gas model and free nucleon-nucleon cross sections.     

用概率知识推导Tait平均自由程

通过一些简单的概率假设，给出了Tait平均自由程的新的推导，并讨论了对强度分布的影响。     

Systematic trends in the transport mean free path with electron energy and atomic number

The inelastic mean free path, λ_i, and the transport mean free path, λ_tr, hold the key to understanding the effects of elastic scattering of electrons in electron spectroscopy techniques such as Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). Systematic trends in the variation of λ_tr and χ=λ_i/λ_tr with atomic number, Z, and electron energy, E, are explored using the differential elastic scattering cross-section data of Czyzewski et al. (J. Appl. Phys., 68 (1990) 3066). At low Z, λ_tr increases with energy in accord with the predictions of the Born approximation, but at higher Z, a more complex behaviour is revealed. In the first and second transition metal series, χ varies little with energy over much of the kinetic energy range probed in XPS in accord with the energy scaling ideas from the semi-classical scattering theory of Tilinin (Soviet Physics JETP, 67 (1992) 1570). In the third transition series, a pronounced minimum is found at around 200 eV, with χ for Au lower than for the corresponding transition metals. The results identify regions of the periodic table where elastic scattering effects are particularly pronounced.     

Anisotropy of the electron mean free path in the thermal conductivity of very pure gallium

In order to determine the anisotropy of the bulk mean free pathl _b, we have measured the thermal conductivity of 6–9's pure gallium single crystals as a function of size and crystal orientation between 1.4 and 4.2°K. The results were analyzed by adapting the existing theory for the electrical conductivity of thin wires to the thermal case. The results show that the reciprocal of the bulk mean free path can be expressed as a linear function ofT ³ for all three orientations. The residual contributions to this quantity are highly anisotropic, as expected. The electron-phonon contributions are, on the other hand, nearly equal in magnitude and exhibit a ratio of 3:4:4 for the A:B:C axis, respectively. In addition, an unusual dependence upond ⁻², whered is the specimen diameter, was observed for the C-axis. It is possibly related to the fact that for this direction only 6% of the entire free electron Fermi surface takes part in conduction which, as a consequence, may be largely dominated by Umklapp scattering. Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force under Grant No. AF-AFOSR 1051-66.     

Attenuation mean free path of hadrons in super-families

Summary Results are presented from the collaboration work of groups of Moscow State University and Waseda University with Pamir X-ray film chamber of thick Pb type. Hadrons in 58 families with energy >100 TeV are studied. The attenuation m.f.p. is 233±40 g/cm² in Pb. Paper presented at the Special Session on very high-energy cosmic-ray interactions (super-families) of the XXIV International Cosmic-Ray Conference, Rome, August 28–September 8, 1995.     

Experimental determination of the mean free path of screened edge magnetoplasmons in a two-dimensional electron gas

Magnetic oscillations of the photovoltage in a two-dimensional electron system with the back gate, exposed to microwave radiation, are studied. The oscillations result from the interference of screened edge magnetoplasmons (EMPs). The mean free path of the EMPs is quantitatively determined by analyzing the dependence of the oscillation amplitude on the electron density. The dependences of the mean free path of the EMPs on the two-dimensional electron density, microwave frequency, electron relaxation time, and the magnetic field are studied. It is found that the dependences agree qualitatively with the known theoretical calculations.