Showing papers on "Mean free path published in 2000"

Minimum Thermal Conductivity of Superlattices

Abstract: The phonon thermal conductivity of a multilayer is calculated for transport perpendicular to the layers. There is a crossover between particle transport for thick layers to wave transport for thin layers. The calculations show that the conductivity has a minimum value for a layer thickness somewhat smaller then the mean free path of the phonons.

Transient thermal processes in heavy ion irradiation of crystalline inorganic insulators

Abstract: A review of matter transformation induced in crystalline inorganic insulators by swift heavy ions is presented. The emphasis is made on new results obtained for amorphizable materials such as Gd3Ga5O12, GeS, and LiNbO3 and for non-amorphizable crystals such as SnO2, LiF and CaF2. Assuming that latent tracks result from a transient thermal process, a quantitative development of a thermal spike is proposed. The only free parameter is the electron–lattice interaction mean free path λ. With this parameter it is possible to quantitatively describe track radii, whatever the bonding character of the crystal is, in a wide range of ion velocities assuming two specific criteria: tracks may result from a rapid quenching of a cylinder of matter in which the energy deposited on the lattice has overcome either the energy necessary to reach a quasi-molten phase in the case of amorphizable materials or the cohesion energy in the case of non-amorphizable materials. The evolution of the λ parameter versus the band gap energy of the considered insulator will be presented. On the basis of this discussion some predictions are developed.

Molecular-dynamics simulation of thermal conductivity of silicon crystals

Abstract: We investigate the thermal conductivity of bulk silicon crystals based on molecular-dynamics (MD) simulations. If it is taken that the system size must be larger than the phonon mean free path, several hundreds of millions of atoms must be computed for crystals with large thermal conductivity values such as Si. We demonstrate in this work that the thermal conductivity of Si crystals can be simulated by MD techniques using several thousands of atoms with periodic boundary conditions. We identify that the key issues generating size artifacts in small molecular-dynamics systems are the frequency cutoff imposed by the simulation domain length and the correlation artifacts caused by the periodic boundary conditions. Our method relies on the spectral Green-Kubo formulation combined with a model-based extrapolation. The obtained thermal conductivity results are in good agreement with the reference data. Both the Green-Kubo formulation and the Boltzmann transport equation lead to the prediction that the thermal conductivities of bulk crystals depend on the frequency of the thermal disturbance. This result has important implications for high-frequency electronic devices.

Size effects in the electrical resistivity of polycrystalline nanowires

Abstract: Grain-boundary and surface scattering are known to increase the electrical resistivity of thin metallic films and wires. The length scale at which these produce appreciable effects is of the order of the electronic mean free path. For the well-studied case of thin films, both mechanisms can, in principle, be used to explain the observed thickness dependence on resistivity. In order to evaluate which of these mechanisms is more relevant, we have carried out an experimental study of the width dependence of the resistivity of narrow thin-film polycrystalline gold wires (nanowires), and computed the expected behavior on the basis of both surface and grain-boundary scattering mechanisms independently. We find that the resistivity increases as wire width decreases in a manner which is dependent on the mean grain size and cannot be explained adequately by either model alone. We propose a modification to the well-known model of Mayadas and Shatzkes, incorporating the variation of mean grain size on wire dimensions.

Spin dependence of the inelastic electron mean free path in Fe and Ni: Explicit calculations and implications

Abstract: We present explicit calculations of the dependence of the inelastic electron mean free path on spin direction and energy, for propagation in the bulk of the ferromagnetic metals Fe and Ni. The substrate electrons are modeled within the framework of an empirical tight-binding description of the 3d, 4s, and 4p bands combined with intra-atomic Coulomb interactions between electrons in the 3d shell. The analysis of spin-flip contributions to the inelastic mean free path incorporates the role of spin-wave emission. We discuss the energy variation of the spin asymmetry in the mean free path, along with other issues. For electrons a few eV above the vacuum level, we find that the mean free path of minority-spin electrons is very short. (c) 2000 The American Physical Society.

2D-1D coupling in cleaved edge overgrowth

Abstract: We study the scattering properties of an interface between a one-dimensional (1D) wire and a two-dimensional (2D) electron gas. Experiments were conducted in the highly controlled geometry provided by molecular bean epitaxy overgrowth onto the cleaved edge of a high quality GaAs /AlGaAs quantum well. Such structures allow for the creation of variable length 1D-2D coupling sections. We find ballistic 1D electron transport through these interaction regions with a mean free path as long as 6 mm. Our results explain the origin of the puzzling nonuniversal conductance quantization observed previously in such 1D wires.

Excitation spectrum of mesoscopic proximity structures

Abstract: We investigate one aspect of the proximity effect, viz., the local density of states of a superconductor-normal metal sandwich. In contrast to earlier work, we allow for the presence of an arbitrary concetration of impurities in the structure. The superconductor induces a gap in the normal metal spectrum that is proportional to the inverse of the elastic mean free path l for rather clean systems. For a mean free path much shorter than the thickness of the normal metal, we find a gap size proportional to l that approaches the behavior predicted by the Usadel equation (diffusive limit). We also discuss the influence of interface and surface roughness, the conseqeunces of a non-ideal transmittivity of the interface, and the dependence of our results on the choice of the model of impurity scattering.

Molecular dynamics of flows in the Knudsen regime

Abstract: Novel technological applications often involve fluid flows in the Knudsen regime in which the mean free path is comparable to the system size. We use molecular dynamics simulations to study the transition between the dilute gas and the dense fluid regimes as the fluid density is increased.

The mean free path for electron conduction in metallic fullerenes

Abstract: The electrical resistivity, p, of a metal is usually interpreted in terms of the mean free path (the average distance, l, an electron travels before it is scattered). As the temperature is raised, the resistivity increases and the apparent mean free path is correspondingly reduced. In this semi-classical picture, the mean free path cannot be much shorter than the distance, d, between two atoms. This has been confirmed for many systems and was considered to be a universal behaviour. Recently, some apparent exceptions were found, including alkali-doped fullerenes and high-temperature superconductors. However, there remains the possibility that these systems are in exotic states, with only a small fraction of the conduction electrons contributing to the conductivity; the mean free path would then have to be correspondingly larger to explain the observed resistivity. Here we report a model calculation of electron conduction in alkali-doped fullerenes, in which the electrons are scattered by intramolecular vibrations. The resistivity at large temperatures implies l or = d. At high temperatures, the semi-classical picture breaks down, and the electrons cannot be described as quasiparticles.

Charged-Particle Resonance Conditions and Transport Coefficients in Slab-Mode Waves

Abstract: Transport of charged particles in cold plasma is considered The full dispersion relation for slab-mode waves is employed, and the quasi-linear particle scattering is discussed Previous results of the dispersive-wave model on the ion mean free path are recalled and further developed For small cross-helicities, the model predicts ion mean free paths that are not affected by the steepening of the turbulence spectrum at high wavenumbers, if the dissipation-range spectral index is q < 6 Large cross-helicities, |Hc| ~ 1, of the left-hand polarized waves, however, imply an approximately constant mean free path of the nonrelativistic protons, which may account for the long-standing flatness problem of the mean free path of solar flare particles The mean free path in a mixture of slab-mode and isotropic fast-mode waves is also shown to agree with observations only in the case of |Hc| ~ 1, contradicting a previously published result Finally, it is shown that, owing to an interplay of resonances with whistlers and proton-cyclotron waves, electron bulk speeds can be considerably larger than the Alfven speed This implies limitations on diffusive acceleration of electrons at low Mach number shocks below ultrarelativistic energies

Modeling of back diffusion of electrons in argon

Abstract: Back-diffusion of electrons to cathode is studied by Monte Carlo simulation for realistic argon cross sections. In particular we study the influence of different aspects of back-diffusion modeling with an aim to simplify the models used in modeling of plasma displays, low pressure gas breakdown and detectors of high energy particles. It was found that the initial electron energy distribution is one of the critical parameters and affects the calculated escape factors very much. The same is true for reflection while angular distribution of initial electrons has a very small influence on the escape factors. The model of cross sections combined with the selection of realistic initial conditions was shown to represent the back-diffusion in argon very well giving good agreement with the available experimental data. Most importantly it was found that the range of electrons returning to the cathode exceeds by far a mean free path and that the number of collisions that they make before returning is quite large. Thus it was found that for a relatively high pressure of around 10 torr the range exceeds d= 1 cm (at E/N =12 Td , 1 Td = and therefore application of the escape ratios below that value of p d (where p is the pressure) is questionable, i.e. under those conditions calculations should be performed for the actual geometry.

Amplification and diffusion of spontaneous emission in strongly scattering medium

Abstract: We experimentally examined the threshold of the spectral collapse in dye embedded in a strongly scattering medium as a function of the excitation beam diameter and the transport mean free path in order to find a condition to minimize the threshold. We found a critical transport mean free path, below which the threshold pulse energy is almost independent of the mean free path. Experimental observations are well explained by a theoretical model based on the rate and diffusion equations, which shows that the luminescence spectra are also dependent on the position in the medium.

Electron Heating at SNR Collisionless Shocks

Abstract: The hot gas in supernova remnants is heated by collisionless shocks, generally propagating in low density (~ 1 atom cm-3 media), where the shock transition occurs on a length scale much shorter than the typical particle mean free path to Coulomb collisions. Conservation laws for energy, momentum, and particle numbers across the shock predict postshock particle temperatures proportional to their masses, that is, electron temperature ion temperature. Electrons and ions will, of course, equilibrate by Coulomb collisions, but collisionless processes might bring about faster equilibration. I review theoretical and observational work on this important point and speculate on reasons for discrepancies where they exist.

Solving the Boltzmann equation in the case of passing to the hydrodynamic flow regime

Abstract: As the hydrodynamic regime is approached, the gas flow is usually accompanied by the formation of narrow highly nonequilibrium zones (Knudsen layers) with the characteristic size on the order of the mean free path λ for molecules. The structure of these zones is determined by fast kinetic processes. In unsteady flows, an initial layer with the time scale on the order of the mean free time τ0 = λ/vT (here, vT is the molecular thermal velocity) occurs as well. In the macroscopic scale l0 @ λ, the flow parameters vary smoothly beyond these zones [1]. From a computational standpoint, solving the Boltzmann equation with steps hx < λ and τ < τ0 is inefficient everywhere over the calculation domain. Moreover, it can result in the early cessation of the iterative process as soon as the error of the numerical method becomes equal to the small difference of two successive approximations. When passing to the macroscopic steps λ ! hx < l0, τ0 ! τ < t0 , where t0 = l0/vT , the problem of a large factor standing ahead the collision integral arises [2]. In terms of the dimensionless variables t = t*/t0, x = x*/l0, ξ = ξ*/vT (here, the asterisk denotes dimensional variables), the Boltzmann equation takes the form

Wave transport along surfaces with random impedance

Abstract: We study transport and diffusion of classical waves in two-dimensional disordered systems and in particular surface waves on a flat surface with randomly fluctuating impedance. We derive from first principles a radiative transport equation for the angularly resolved energy density of the surface waves. This equation accounts for multiple scattering of surface waves as well as for their decay because of leakage into volume waves. We analyze the dependence of the scattering mean free path and of the decay rate on the power spectrum of fluctuations. We also consider the diffusion approximation of the surface radiative transport equation and calculate the angular distribution of the energy transmitted by a strip of random surface impedance.

Conductance quantization in nanoscale vertical structure silicon field-effect transistors with a wrap gate

Abstract: Experimental results of quantum ballistic transport in single quantum contact by using vertical structure silicon field effect transistors with a wrap gate are presented. Based on dc measurement, the conductance–voltage characteristics show quantized plateaus at multiples of 2e2/h. The devices were prepared by electron beam lithography and by combinations of various types of etching. The channel is fabricated by the chemical vapor deposition of amorphous silicon and solid-phase crystallization. The vertical structure allows a channel length as short as 30 nm, which is defined by the film thickness. The effective channel is reduced by the depletion potential, resulting in a much narrower channel width compared to the geometrical width of 60 nm. Thus, the effective size of the silicon transistor is smaller than the elastic mean free path of 40 nm, resulting in the conduction quantization at 3–5 K.

Inelastic scattering models in transport theory and their small mean free path analysis

Abstract: In this paper we perform an asymptotic analysis of a singularly perturbed linear Boltzmann equation with inelastic scattering operator in the Lorentz gas limit, when the parameter corresponding to the mean free path of particles is small. The physical model allows for two-level field particles (ground state and excited state), so that scattering test particles trigger either excitation or de-excitation processes, with corresponding loss or gain of kinetic energy. After examining the main properties of the collision mechanism, the compressed Chapman–Enskog expansion procedure is applied to find the asymptotic equation when the collisions are dominant. A peculiarity of this inelastic process is that the collision operator has an infinite dimensional null-space. On the hydrodynamic level this is reflected in the small mean free path approximation being rather a family of diffusion equations than a single equation, as is the case in classical transport theory. Also the appropriate hydrodynamic quantity turns out to be different from the standard macroscopic density. Copyright © 2000 John Wiley & Sons, Ltd.

Experimental determination of the inelastic mean free path of electrons in GaP and InAs

Abstract: The inelastic mean free path (IMFP) of electrons is a fundamental material parameter needed for surface analysis. The IMFP data of semiconducting III–V compounds have been calculated by Tanuma et al., Kwei et al. and Gries. The present paper completes previous research and reports experimental studies on the IMFPs of GaP and InAs. Elastic peak electron spectroscopy (EPES) was used with Ni, Au and Ag reference samples. Both InAs(100) and GaP(100) have been studied in three laboratories, using different types of electron spectrometer analysers and energy ranges: HSA (0.2–5 keV), DCMA (0.2–2 keV), DESA 100 (0.5–2 keV). The surface of the samples was cleaned and amorphized by Ar+ ion bombardment with controlled parameters (energy, dose, etc.) to eliminate crystallinity effects. The surface composition of the ion-bombarded samples was determined in situ by XPS and Auger electron spectroscopy. Their crystallinity and incoherent elastic scattering were tested with Renninger plots of the elastic peak intensity, rotating the sample around its axis perpendicular to the surface. The IMFPs were calculated by a Monte Carlo algorithm using the NIST database of elastic scattering cross-sections. A reasonable agreement was found with theoretical IMFP values calculated by other authors. Copyright © 2000 John Wiley & Sons, Ltd.

Elastic scattering as a cause of quantum dephasing: the conductance of two-dimensional imperfect conductors

Abstract: A method is proposed for studying wave and particle transport in disordered waveguide systems of dimension higher than unity by means of exact one-dimensionalization of the dynamic equations in the mode representation. As a particular case, the T=0 conductance of a two-dimensional quantum wire is calculated, which exhibits ohmic behaviour, with length-dependent conductivity, at any conductor length exceeding the electron quasi-classical mean free path. The unconventional diffusive regime of charge transport is found in the range of conductor lengths where the electrons are commonly considered as localized. In quantum wires with more than one conducting channel, each being identified with the extended waveguide mode, the inter-mode scattering is proven to serve as a phase-breaking mechanism that prevents interference localization without real inelasticity of interaction.

The pathlength distribution of simulated aerogels

Abstract: The diffusion limited cluster aggregation (DLCA) model is a simple algorithm that simulates the growth of silica aerogels and can be used to compare with scattering experiments. In order to study the properties of helium liquids within aerogel we have extended application of the DLCA model to lengthscales larger than the mean free path. Of particular importance are the effects of the model's periodic boundary conditions. When these are accounted for the distribution function beyond a few hundred Angstroms develops into a simple exponential decay which can be extrapolated, allowing a precise determination of the mean free path, l. We find l is inversely proportional to the density, ρ , over the range investigated, 0.001 ρ

Ballistic transport at room temperature in deeply etched cross-junctions

Abstract: We measured the transmission through nanoscopic cross-junctions at variable temperature and bias. The devices were prepared by deep etching through a two-dimensional electron gas in InGaAs/InP samples. Our experiments show that the transmission characteristic is partly ballistic even at room temperature. The measurements are analysed in terms of an equivalent network, and the involved resistances are related to the electrons' mean free path. Different scattering mechanisms are considered to account for the transition from ballistic to diffusive transport.

Giant magnetoresistance of Fe/Cu/Fe(001) trilayers grown directly on GaAs(001)

Abstract: The giant magnetoresistance of crystalline Fe/Cu/Fe(001) epitaxial structures characterized by scanning tunneling microscopy are presented. Fe/Cu/Fe(001) trilayers capped with Au are grown directly on GaAs(001) using a new procedure for producing pure Fe layers with As-free Fe surfaces on GaAs(001). The temperature dependence of the magnetoconductance and sheet resistance measured from 4 to 300 K is modeled by the Boltzmann equation assuming that the mean free paths in the crystalline epitaxial layers are equal to those in bulk materials. The results of the simple model suggest that the coefficient of the specular scattering at the Fe/GaAs interface is R=0.45, while the scattering at the outer Au interface is diffuse. Spin asymmetry scattering at the metallic interfaces is ΔT=|T↑−T↓|=0.34, Tavg=(T↑+T↓)/2=0.79. The sheet resistance was best modeled using a low temperature mean free path of 25 nm in the Fe layer.

Nanometer-size InAs/AlSb quantum wires: Fabrication and characterization of Aharonov-Bohm quantum rings

Abstract: We report a fabrication method for laterally confining the two-dimensional electrons in InAs/AlSb single quantum wells into artificially patterned conducting wires. The minimum wire width is demonstrated to be ∼30 nm, among the smallest reported to date. The confining potential is approximately square and abrupt, and that makes the electron’s spatial distribution in the transverse direction the same as the physical width of the wire. The conducting electrons have close proximity to the surface charges, thus there is always a reduction in the elastic mean free path when the wire width decreases. Despite the reduction in mean free path, we find that the phase coherence length is approximately 1 μm at 2.2 K, a factor of 30 larger than the minimum feature size.