Showing papers on "Mean free path published in 1992"
TL;DR: It is found that a model that takes into account the k dependence of the dielectric function and the effect of the field set up by the incoming electron on the outgoing electron gives the best description.
Abstract: Two models to reproduce experimental inelastic-electron-scattering cross sections determined from reflection-electron-energy-loss spectroscopy (REELS) are considered. The models take into account the momentum transfer in the inelastic processes. Inputs for the models are the dielectric function and the inelastic electron mean free path, which are both taken from previous works. It is found that a model that takes into account the k dependence of the dielectric function and the effect of the field set up by the incoming electron on the outgoing electron gives the best description
228 citations
TL;DR: In this article, the size of the sheath around the particle is determined by a Debye length that results from linearizing the Poisson-Vlasov equation, and the results are valid as long as the ratio of particle radius to debye length is small.
Abstract: Collisionless orbit theory is used to model isolated particles in low‐pressure discharges with and without the presence of negative ions. The key results are as follows: (1) Debye–Huckel theory works well for approximating the potential profile around the particle, and (2) the size of the sheath around the particle is determined by a Debye length that results from linearizing the Poisson–Vlasov equation. These results are valid as long as the ratio of particle radius to Debye length is small and the ratio of Debye length to mean free path is small.
215 citations
TL;DR: In this paper, the shot noise in metal contacts with small elastic electron mean free path was calculated, and the value was three times smaller than that of a tunnel junction with equal resistance.
189 citations
TL;DR: Analytical results on the magnetoresistance in limiting cases where either the mean free path is much greater or less than the layer thickness, as well as numerical results for the realistic situation found in Fe/Cr superlattices when they are comparable.
Abstract: We consider multilayered structures consisting of magnetic and nonmagnetic metals. We derive analytic expressions for the conductivities by treating the scattering at the interfaces between layers in the same way as that throughout the layers (bulk). The application of an external magnetic field reorients the magnetization in the magnetic layers, which in turn alter the mean free path of the conduction electrons. This is the origin of the giant magnetoresistance seen in iron-chromium (Fe/Cr) superlattices. We present analytic results on the magnetoresistance in limiting cases where either the mean free path is much greater or less than the layer thickness, as well as numerical results for the realistic situation found in Fe/Cr superlattices when they are comparable.
130 citations
TL;DR: In this article, the authors developed a model based upon a set of quantum moment equations obtained from the Wigner function equation-of-motion (EoM) and demonstrated that these effects modify the electron density distribution and current density distribution both in the channel and near the source.
Abstract: Ultra-small MESFETs have characteristic lengths comparable to quantum lengths: wavelength, mean free path, etc. In a first attempt to incorporate these quantum lengths, the authors develop a model based upon a set of quantum moment equations obtained from the Wigner function equation-of-motion. Interesting time-dependent current oscillation behavior has been observed when a step voltage is applied to the initial steady state. The oscillation frequency is peaked around 500 GHz, which is related to the plasma response of the carriers in the channel. Quantum effects, such as barrier repulsion and penetration, have been demonstrated in the simulation. These effects modify the electron density distribution and current density distribution both in the channel and near the source. Modifications of the frequency spectrum of the oscillation current due to the quantum effects are obvious. >
91 citations
TL;DR: The ``mean free path'' of electrons injected selectively into the outer spin-polarized edge channel of the lowest Landau level is investigated, interpreted in terms of the spin-orbit interaction, which also leads to a local g-factor enhancement at the edge.
Abstract: We investigate experimentally the ``mean free path'' of electrons injected selectively into the outer spin-polarized edge channel of the lowest Landau level. A simple model allows us to determine the characteristic length between two spin-flip scattering events directly from the measured resistance plateaus. Typical spin-flip equilibration lengths between 100 \ensuremath{\mu}m and 1 mm are found. The size of the observed equilibration lengths is interpreted in terms of the spin-orbit interaction, which also leads to a local g-factor enhancement at the edge.
89 citations
TL;DR: It is shown that with appropriate boundary conditions diffusion theory gives an excellent description of transport from the interior to the output surface of a sample and the transport velocity is smaller than the velocity in the high-index material.
Abstract: We measure microwave intensity inside and transmission through random samples of polystyrene spheres with different output reflectors. We show that with appropriate boundary conditions diffusion theory gives an excellent description of transport from the interior to the output surface of a sample. From these measurements we determine the transport mean free path and the surface reflectivities without additional assumptions regarding the interface or the scattering form factor. From a comparison with a measurement of the diffusion coefficient we determine the transport velocity and find that it is smaller than the velocity in the high-index material.
83 citations
TL;DR: In this article, the positive ion current collected by cylindrical Langmuir probes has been measured in an RF argon plasma using an RF compensation technique whereby the probe was forced to follow the RF fluctuation in the local plasma potential.
Abstract: The positive ion current collected by cylindrical Langmuir probes has been measured in an RF argon plasma. The current-voltage characteristics were measured using an RF compensation technique whereby the probe was forced to follow the RF fluctuation in the local plasma potential. The I-V curves from probes of different radii and material show an ion current which is always greater than that predicted by the orbital motion theory and that agrees well with the radial motion theory. This is because the ions travel to the probe from a distance which is limited by the vessel geometry or by the collisional mean free path. The role of the possible collisions, ion-ion and ion-neutral, in the ion trajectories is analysed. It is suggested that the criterion for the application of the orbital motion theory should be tested whenever this theory is used for the determination of the charged particle density.
83 citations
TL;DR: The resistivity of ultrathin single-crystalline Pb and Pb-In layers with thicknesses d smaller than the bulk mean free path l, is measured during deposition onto Si(111)-(6-6)Au surfaces at about 110 K.
Abstract: The resistivity of ultrathin single-crystalline Pb and Pb-In layers with thicknesses d smaller than the bulk mean free path l, is measured during deposition onto Si(111)-(6\ifmmode\times\else\texttimes\fi{}6)Au surfaces at about 110 K. The structure of the layers is monitored by reflection high-energy electron diffraction (RHEED). Oscillations of the RHEED specular beam intensity are highly correlated with fine structures of the resistivity. The quantum-size-effect theory is used for a quantitative analysis of the data. The fine structure, volume impurities, small-scale roughness, and large-scale thickness fluctuations are taken into account. The impact of the layer-by-layer growth mode of ultrathin metal films on the thickness dependence of the resistivity is discussed.
78 citations
TL;DR: By a simple redefinition of the mean free path, good agreement is obtained between simulation results and Maxwell theory for slip length for Knudsen number.
Abstract: We study the phenomenon of slip length using molecular dynamics and direct simulation Monte Carlo simulations of a dilute gas. Our work extends the range of Knudsen numbers that have been previously studied. Bhattacharya and Lie suggest a logarithmic dependence of slip length on Knudsen number. By a simple redefinition of the mean free path, we obtain good agreement between simulation results and Maxwell theory for slip length. The anomalies seen by Bhattacharya and Lie appear to be due to their definition of the mean free path
78 citations
TL;DR: In this paper, the authors used far-infrared reflectivity measurements to probe the low-energy response of Rb3C60 and derived a value for the characteristic energy scale associated with reflectivity, which allows them to estimate a value of the gap energy 2δ of 3−5 kTC, in reasonable agreement with tunnelling measurements.
Abstract: AN understanding of the superconductivity and other electronic properties of the alkali-metal-doped fullerenes1 will require measurements of their solid-state physical properties. In the normal state one would like to know the electron effective mass, the Fermi energy and conduction bandwidth, and the mean free path for electron transport; the superconducting state, meanwhile, can be characterized at the most basic level by length and energy scales such as the coherence length, penetration depth and superconducting energy gap. Here we describe the use of far-infrared reflectivity measurements to probe the low-energy response of Rb3C60. We derive a value for the characteristic energy scale associated with reflectivity, which allows us to estimate a value for the gap energy 2δ of 3–5 kTC, in reasonable agreement with tunnelling measurements2. Combining this result with data obtained in previous studies, we estimate other length and energy scales, such as the bandwidth and penetration depth.
TL;DR: In this paper, the attenuation parameter (AP) was calculated for 45 elements (Be, C, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Pb) and
Abstract: The attenuation parameter (AP), which quantitatively describes the influence of elastic electron scattering on the electron spectroscopies, has been calculated for 45 elements (Be, C, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Pb) and for energies of 250, 500, 1000 and 1500 eV. The calculations were performed with a Monte Carlo algorithm in which elastic scattering is modelled by use of the partial wave expansion method. The results show a linear relationship between the AP and the inelastic mean free path (IMFP), and a linear least-squares fit of the data provides a simple formula to calculate the AP for a given material and energy. The depth distribution function (DDF), which in the most general sense discribes the attenuation properties of signal electrons, can be calculated analytically using this AP. The possibility of using the calculated AP values in combination with this DDF to extract IMFP data from an overlayer experiment has also been explored. Evidence is found, and discussed, that the presentedalgorithm can be used to convert IMFPs to attenuation lengths (AL).
TL;DR: Two kinds of quantum interference effects in transport are studied-the Aharonov-Bohm effect and the weak-localization effect-in quasi-one-dimensional wires and rings to address issues concerning the phase-coherence length, spin-orbit scattering, and the flux cancellation mechanism which is predicted to be present when the elastic mean free path exceeds the sample width.
Abstract: We study two kinds of quantum interference effects in transport-the Aharonov-Bohm effect and the weak-localization effect-in quasi-one-dimensional wires and rings to address issues concerning the phase-coherence length, spin-orbit scattering, and the flux cancellation mechanism which is predicted to be present when the elastic mean free path exceeds the sample width. Our devices are fabricated on GaAs/Al x Ga 1-x As and pseudomorphic Ga x In 1-x As/Al x In 1-x As heterostructure materials and the experiments carried out at 0.420 K temperatures
TL;DR: In this article, an exact solution of the Boltzmann transport equation (BTE) was proposed to solve the diffusion problem in a short-base bipolar junction transistor (BJT), where the electron scattering mean free path and recombination length are both assumed independent of energy.
Abstract: Al~tract--The usual diffusion-equation description of transport in the base of a junction transistor breaks down if the base length is comparable to the minority carrier mean free path. We present a rigorous analytic treatment of this problem, based on an exact solution of the Boltzmann transport equation (BTE). A key ingredient of our approach is formulation of the boundary conditions for the distribution function f(r, k, t) at the base-emitter interface. Numerical solution of the BTE shows that there are significant corrections (of order 100%) to the diffusion-equation estimates of both the static current gain and the frequency cut-off in a short-base bipolar junction transistor (BJT). In a model where the electron scattering mean free path and the recombination length are both assumed independent of energy, the steady-state BTE reduces to an integral equation for the electron concentration. We present an approximate analytical solution of this equation that gives an excellent agreement with the exact numerical solution. The analytic solution is asymptotically exact in the limit of ultra-short base lengths, where the minority-carrier transport can be regarded as thermionic, as well as in the long-base limit (where the diffusion equation is rigorously valid). On the basis of our analytic solution, we propose and test a new expression for the effective (concentration-dependent) diffusivity, that interpolates between the diffusive and thermionic limits.
TL;DR: The potential gradient length in the sheath in front of the target is small as compared to the mean free path length; the velocity distributions of ions and electrons as determined by the electric field are far from being Maxwellians there.
Abstract: The scrape off layer (SOL) of a confined plasma (Fig. 1a) is in many respects in a state far from, thermodynamic equilibrium:
The energy diffusing outward from the plasma core across the separatrix is condensed in the thin SOL to a strong energy flux along the magnetic field.
The recycling of cold neutrals from the limiter or divertor target gives rise to a strong temperature gradient from the hot midplane region to the relatively cold recycling zone.
For long mean free path length in the plasma relative to the extension of the recycling zone the thermalization in the recycling zone may be incomplete.
The potential gradient length in the sheath in front of the target is small as compared to the mean free path length; the velocity distributions of ions and electrons as determined by the electric field are far from being Maxwellians there.
Thus the follwing topics will be discussed in this paper:
Parallel transport (electron heat flow, ion viscosity)
Recycling
Sheath structure (grazing incidence of magnetic field, secondary electrons).
Boundary conditions for fluid models
Numerical illustrations for these kinetic effects are given from a 1d particle-in-cell code including Coulomb collisions [1]. Not treated are kinetic effects connected with instabilities, perpendicular transport, neutrals and impurities.
TL;DR: In this article, the first direct measurement of a collisional Bohm presheath from plasma potential measurements is given, where the presheaths were measured in N2 and CF4 plasmas using an emissive probe.
Abstract: The first direct measurement of a collisional Bohm presheath from plasma potential measurements is given. By measuring the presheath thickness in front of a grounded wafer stage, a determination of the collision mean free path for ions in an electron cyclotron resonance etching tool has been made. Presheaths were measured in N2 and CF4 plasma using an emissive probe. The presheath thickness in N2 was found to be linearly dependent on the mean free path. Measurements of CF4 plasmas, for which the collision cross sections are unknown, have shown results similar to those found for nitrogen. This result has enabled an extrapolation to be made of the effective cross section for collisions in plasmas created from CF4.
TL;DR: In this paper, the effect of collisions on the ion distribution function and sheath potential variation is investigated theoretically and experimentally, and the theory starts from the charge exchange model of ion kinetics, presents a convenient self-consistent description of the unipolar ion sheath and extends a former asymptotic analysis to 0 to the Debye sheath.
Abstract: The ion energy distribution of ions bombarding a negative wall depends on the sheath potential and on the ion kinetics in the boundary layer. In most discharges the electron Debye length lambda D is small compared to the ion mean free path lambda C. For weakly negative walls the sheath is, therefore, nearly collision free. In the case of highly negative walls, however, the sheath thickness increases and collisions in the sheath may become important. The effect of collisions on the ion distribution function and sheath potential variation is investigated theoretically and experimentally. The theory starts from the charge exchange model of ion kinetics, presents a convenient self-consistent description of the unipolar ion sheath and extends a former asymptotic analysis lambda D/ lambda C to 0 to the Debye sheath. In the experimental part a retarding field analyser is used to determine the ion energy distribution. Measurements were made in the negative glow of a DC glow discharge at pressures of several Pa in argon, nitrogen and oxygen.
TL;DR: In this article, the intensity and anisotropy time profiles of six relatively small relativistic electron events observed within 0.65 AU by one of the Helios spacecraft were fitted with the model of focused transport under the assumption of a particle mean free path λ independent of the radial distance.
Abstract: The intensity and anisotropy time profiles of six relatively small relativistic electron events observed within 0.65 AU by one of the Helios spacecraft were fitted with the model of focused transport under the assumption of a particle mean free path λ independent of the radial distance. For ∼0.5 MeV electrons it is found that the amount of interplanetary scattering varies from one solar event to the other, with local mean free paths λ between 0.02 and 0.15 AU. Comparison with previous results obtained close to 1 AU shows that there is no marked variation in the average scattering conditions with radial distance
TL;DR: In this article, the authors investigated low-frequency electromagnetic waves become unstable due to anisotropy of the electron distribution function and the chaotic magnetic field thus generated scatters the electrons with a specific effective mean free path Saturation of the instability due to wave-wave interaction, nonlinear scattering, wave propagation, and collisional damping is considered.
Abstract: Heat flux inhibition by electromagnetic instabilities in a hot magnetized plasma is investigated Low-frequency electromagnetic waves become unstable due to anisotropy of the electron distribution function The chaotic magnetic field thus generated scatters the electrons with a specific effective mean free path Saturation of the instability due to wave-wave interaction, nonlinear scattering, wave propagation, and collisional damping is considered The effective mean free path is found self-consistently, using a simple model to estimate saturation level and scattering, and is shown to decrease with the temperature gradient length The results, limited to the assumptions of the model, are applied to astrophysical systems For some interstellar clouds the instability is found to be important Collisional damping stabilizes the plasma, and the heat conduction can be dominated by superthermal electrons
TL;DR: In this paper, the experimental results for the combination coefficient between neutral particles and electrons suggested a free-molecule diffusion charging mechanism which was dependent on the electron mobility, transverse diffusion coefficient, mean free path, and mean kinetic energy (i.e. electron temperature).
TL;DR: In this paper, the electron mean free path (escape depth) in typical experiments is comparable to or less than the diameter of the molecular unit, which accounts for the weakness of the Fermi cut-off found in all photoemission studies.
TL;DR: Photoemission data in which the signal from the first atomic layer is well resolved from that of the bulk are used to determine accurately the kinetic-energy dependence of the inelastic-electron mean free path in the alkali metals.
Abstract: Photoemission data in which the signal from the first atomic layer is well resolved from that of the bulk are used to determine accurately the kinetic-energy dependence of the inelastic-electron mean free path in the alkali metals. At the higher kinetic energies, the data are in very good agreement with the theory of Penn. Below about 10 eV, the mean free path in the heavier alkali metals drops markedly below the theoretical values. This is attributed to electron decay processes involving the unoccupied d bands
TL;DR: In this article, a comparison of the attenuation of electrons in non-crystalline solids as described by the transport theory (TT), using the transport length as obtained in a quasiclassical approach, and by Monte Carlo (MC) calculations based on relativistic Mott cross sections for elastic scattering is presented.
TL;DR: The results show that a detectable amount of received photons follows trajectories near the source receiver line even for large values of optical depth, indicating the potential of a time-gated scanning imaging system to detect absorbing structures inside thick turbid media.
Abstract: Experimental results of light pulse transmission through thick turbid media are presented. Measurements have been carried out on polystyrene latex spheres by using a picosecond thin laser beam and a streak camera system. The results show that the shape of the received pulse depends mostly on the transport mean free path and on the absorption coefficient of the medium, indicating that both the absorption coefficient and the asymmetry factor of the scattering function can be obtained from the pulse shape. The results also show that a detectable amount of received photons follows trajectories near the source receiver line even for large values of optical depth, indicating the potential of a time-gated scanning imaging system to detect absorbing structures inside thick turbid media.
TL;DR: In this paper, the boundary layer problem of weakly ionized collision-dominated plasma in front of a negative absorbing wall is considered, where the electrons are assumed to be Boltzmann distributed; the ions are governed by symmetric charge exchange.
Abstract: The boundary layer problem of a weakly ionized collision-dominated plasma in front of a negative absorbing wall is considered. The electrons are assumed to be Boltzmann distributed; the ions are governed by symmetric charge exchange. The Debye length is small compared with the mean free path. A former kinetic analysis of the Knudsen layer is matched with an adapted macroscopic theory of the plasma body accounting for ionization, nonplanar geometry and filed-dependent ion mobility. The consistent analysis of plasma and boundary layer is illustrated with the examples of a cylindrical plasma column, a spherical probe in an infinitely extended plasma without ion generation, and a semi-infinite plasma with Saha ionization equilibrium distorted by wall losses.
TL;DR: In this article, the authors studied the scattering of high-frequency phonons injected into superfluid 4He with low-frequency (h(cross) omega /kB <1 K) thermal phonons in the liquid and showed that the measured scattering is much weaker than the hydrodynamic theory has previously predicted.
Abstract: The scattering of high-frequency (h(cross) omega /kB>10 K) phonons injected into superfluid 4He with low-frequency (h(cross) omega /kB<1 K) thermal phonons in the liquid is studied both experimentally and theoretically. Quantum evaporation enables the selective study of only the high-frequency phonons. The attenuation of evaporation signals as the temperature is increased from 70 mK to 250 mK for various liquid path lengths is interpreted in terms of four-phonon scattering involving the high-frequency injected phonons and the low-frequency thermal phonons. Monte Carlo simulations of the signal variation with temperature show that the measured scattering is much weaker than the hydrodynamic theory has previously predicted. However, when this theory is extended to include diagrams representing further possible routes of the four-phonon scattering process, there are significant cancellations between these extra diagrams and those considered earlier. This leads to a weaker interaction and to a much improved agreement with the experimental results.
TL;DR: In this article, the phonon mean free path (mfp) in YBa2Cu3O7−δ was estimated by performing a theoretical fitting procedure on bulk singlecrystal data.
Abstract: We estimate the phonon mean‐free path (mfp) in YBa2Cu3O7−δ by performing a theoretical fitting procedure on bulk single‐crystal data. This analysis indicates that the mfps of the phonons that are most responsible for the transport of heat are much longer than would be predicted from kinetic theory. These values are incorporated into a recently proposed treatment of the size effect to provide an estimate of the thermal conductivity of YBa2Cu3O7−δ films.
TL;DR: In this article, the authors show that the transport equation can be reduced to an advection-diffusion equation for the scalar flux, which describes lateral diffusive spreading with depth of an initially collimated beam of arbitrary spatial cross section and is of particular significance when scattering is highly forward peaked.
Abstract: In this paper, the authors show, using asymptotics, that under conditions when the angular distribution is forward peaked, the transport equation can be reduced to an advection-diffusion equation for the scalar flux. This equation describes lateral diffusive spreading with depth of an initially collimated beam of arbitrary spatial cross section and is of particular significance when scattering is highly forward peaked. Numerical results for the scalar flux for a planar source (when lateral diffusion vanishes) and in the presence of strongly anisotropic scattering are contrasted with benchmark Monte Carlo results as well as with the scalar flux obtained from a novel modifed multiple scattering method. The authors observe that the asymptotic model is only accurate over distances small compared with the transport mean free path. It is conjectured that carrying the asymptotic expansions to higher orders or using a different asymptotic scaling might extend the accuracy of the asymptotic model to higher orders in the transport mean free path.
TL;DR: In this article, a comparison between electron inelastic mean free path and attenuation length was made using the partial wave expansion method with a solid potential to evaluate the path length distribution of an electron transmitted through a solid film.
Abstract: The electron inelastic mean free path is of basic importance in theoretical and applied radiation physics and surface physics. It can be calculated using the dielectric function for the valence band and atomic generalized oscillator strengths for inner shells of a solid. Although the experimentally determined attenuation length is conceptually different from the theoretically calculated mean free path, they are frequently used interchangeably in a loosely defined manner. For electrons with energies below a few keV, elastic scattering plays an important role in connecting these two quantities. This work employed elastic scattering cross sections derived using the partial wave expansion method with a solid potential to evaluate the path length distribution of an electron transmitted through a solid film. Both the analytical multiple-scattering formulation and the numerical Monte Carlo simulation have been applied in this investigation. A comparison between electron inelastic mean free paths and attenuation lengths was made.