Showing papers on "Mean free path published in 1983"
TL;DR: In this paper, the density of states for thermal vibrations on a fractal is calculated with careful attention paid to the normalization condition, and a set of missing modes is identified which may be the origin of the two-level systems hypothesized for amorphous structures.
Abstract: The density of states for thermal vibrations on a fractal is calculated with careful attention paid to the normalization condition. It is found that at the crossover between Debye-type excitations (long wavelength) and "fracton" excitations (short-length scale) the density of states is discontinuous. The size of the discontinuity is related to the ratio of the fracton dimensionality to the Euclidean dimensionality. Application is made to percolating structures. A set of missing modes is identified which may be the origin of the two-level systems hypothesized for amorphous structures. The specific heat of epoxy resin exhibits a crossover from a Debye-type region ($Tl8$ K) to a region (8-50 K) where the vibrational density of states depends linearly on the frequency. Over the same frequency regime, the thermal conductivity exhibits an effective phonon mean free path of the order of (or less than) a lattice constant. We interpret this behavior in terms of quantized fractons, with an energy range 8-50 K, and we suggest that these fracton states are localized. This is consistent with the usual interpretation of a precipitous drop in the phonon mean free path at the crossover energy of 8 K. Analogous behavior is argued for the thermal properties of glasses which exhibit a similar structure in the thermal conductivity. Recent neutron-irradiated quartz experiments tend to confirm this interpretation.
181 citations
TL;DR: In this article, a simple expression for the ionisation coefficient for impact ionisation is derived on the basis of a new approach which exploits the difference between momentum and energy-relaxation rates for hot electrons.
Abstract: A simple analytic expression for the ionisation coefficient for impact ionisation is derived on the basis of a new approach which exploits the difference between momentum- and energy-relaxation rates for hot electrons. The basic mechanism whereby an electron gains sufficient energy to ionise is lucky to drift in which the electrons relax momentum but not energy. The electrons gain energy by drift and not by ballistic motion, and a few lucky ones reach the threshold. Those which thermalise may also contribute through the lucky-drift mechanism, starting from the average hot-electron energy. Good agreement with Baraff's theory is obtained. It is shown that neither the Schockley lucky electron nor the Wolff thermalised electron contribute significantly, in agreement with Baraff. However, the concept of Schockley's lucky electron is an essential part of the lucky-drift mechanism. The theory is simply extended to accommodate electrons injected at energies above zero, and some calculations are presented on this topic. A discussion is given of the effect of real band structure and it is concluded that the theory based on parabolic bands remains good provided the mean free path is taken as an average quantity over the relevant energy range. It is argued that the theory has wide application to semiconductors with moderate-to-large energy gaps because of the predominance of nonpolar scattering at high energies. A specific model of a nonparabolic band structure is discussed in which the electron distribution function has a Gaussian form, rather than the Maxwellian form associated with parabolic bands, and a weak negative differential resistance is exhibited.
160 citations
TL;DR: In this article, the electron properties in a parallel plate capacitively coupled rf discharge were studied with results from a Monte-Carlo simulation, and the dc component of the sheath potential was found to be a function of the ratio λ/d, where is the electron mean free path and d is the electrode spacing.
Abstract: Electron properties in a parallel plate capacitively coupled rf discharge are studied with results from a Monte‐Carlo simulation. Time averaged, spatially dependent electron distributions are computed by integrating, in time, electron trajectories as a function of position while oscillating the applied electric field at rf frequencies. The dc component of the sheath potential is solved for in a self‐consistent manner during the simulation. For conditions where the secondary emission coefficient for electrons from the electrodes is large, the electron distribution is spatially differentiated, being dominated by an e‐beam component near the electrodes while being nearly in equilibrium with the applied electric field in the body of the plasma. The dc component of the sheath potential is found to be a function of the ratio λ/d, where λ is the electron mean free path and d is the electrode spacing.
159 citations
TL;DR: In this paper, an effective numerical method for solving boundary value problems for the Landau Fokker-Planck equation is developed and applied to calculate the electron velocity distribution function in model solar transition regions.
Abstract: An effective numerical method for solving boundary value problems for the Landau Fokker-Planck equation is developed and applied to calculating the electron velocity distribution function in model solar transition regions. Numerical results illustrating the speed, pitch angle, and spatial dependence of the distribution function are presented. From these it is concluded that the widely invoked assumption that in weakly inhomogeneous collisional plasma the angle-averaged distribution function remains close to local Maxwellian distribution is incorrect. Instead, the distribution function forms an anisotropic, high-velocity tail in the lower temperature regions due to the diffusion of fast electrons antiparallel to the temperature gradient. Roughly speaking, this effect is of quantitative significance for spectroscopic work and heat conduction provided lambda(d ln T/dx)/sub max/ > or approx. =10/sup -3/, where lambda = (kT)/sup 2//..pi..e/sup 4/n ln ..lambda.. is an effective mean free path for thermal electrons.
153 citations
TL;DR: In this paper, the variable cross-section hard sphere (VHS) model was used to define a mean free path in a real gas, which properly accounts for the temperature exponent of the coefficient of viscosity of the gas.
Abstract: Attention is drawn to the inconsistency in the conventional procedure for the definition of a mean free path in a real gas through the classical hard sphere result. It is shown that the variable cross‐section hard sphere, or VHS, model can be used to define a mean free path that properly accounts for the temperature exponent of the coefficient of viscosity of the gas. In addition, the VHS model is shown to have advantages over the classical inverse power law models for numerical and analytical studies.
153 citations
TL;DR: In this paper, it was shown that the generalized Enskog kinetic theory is quantitatively accurate in describing the thermal fluctuations at finite wavelengths and frequencies, as is wavelength-dependent hydrodynamics, as long as the wavelength is greater than the mean free path.
Abstract: Density, longitudinal, and transverse-current correlation functions for hard spheres at various densities and wavelengths have been generated by computer simulation and compared with both the generalized Enskog kinetic theory and wavelength-dependent hydrodynamics. It is shown that even for dense gases the generalized Enskog kinetic theory is quantitatively accurate in describing the thermal fluctuations at finite wavelengths and frequencies, as is wavelength-dependent hydrodynamics, as long as the wavelength is greater than the mean free path. At liquid densities neither theory can account for the viscoelastic relaxation effects, directly observed in the transverse-current correlation function by shear-wave propagation, at a wavelength somewhat above the first diffraction maximum. However, wavelength-dependent hydrodynamics quantitatively describes the neutron scattering function at wavelengths from this point (above the first diffraction maximum) through the diffraction maximum (where the de Gennes narrowing occurs) to the mean-free-path limit. Furthermore, viscoelastic effects in the long-wavelength regime can be accounted for by introducing into hydrodynamics time-dependent transport coefficients. At still longer wavelengths, viscoelastic relaxation times become short compared with hydrodynamic relaxation times and ordinary hydrodynamics with constant transport coefficients describes the neutron scattering function.
109 citations
TL;DR: A vibrating wire viscometer has been constructed using superconducting wire of diameter 58 µm in the form of a semicircular loop of radius 1.4 cm fixed at both ends and oscillating in a direction perpendicular to the plane of the loop as discussed by the authors.
Abstract: A vibrating wire viscometer has been constructed using superconducting wire of diameter 58 µm in the form of a semicircular loop of radius 1.4 cm fixed at both ends and oscillating in a direction perpendicular to the plane of the loop. The use of the viscometer to measure the viscosity of normal phase3He is described and the corrections that have been applied to the data to allow for the finiteQ of the resonance, a quasiparticle mean free path comparable to the wire diameter, and a viscous penetration depth comparable to the size of the channel containing the wire are discussed. The measured viscosities show small departures from the ηT
2=const law of Fermi liquid theory similar to those observed in some but not all previous measurements. The values of the viscosity at the superfluid transition temperature agree with those obtained in other measurements.
64 citations
TL;DR: In this article, the authors examined the conductivity of ion waves in plasmas and found that the reduction in conductivity is independent of the wave amplitude, thus differing from the reduction due to saturation found recently by numerical solution of the Fokker-Planck equation.
Abstract: Electron energy transport in plasmas is examined in the context of ion waves which are intermediate between collisionless isothermal ion acoustic waves and collisional adiabatic sound waves. The conductivity is found to be much less than the Spitzer‐Harm result for wavelengths less than 1000 electron mean free paths. This is expected to be relevant to laser‐produced ablating plasmas in which the temperature can vary considerably over a distance of 10 to 100 mean free paths. The reduction in conductivity is independent of the wave amplitude thus differing from the reduction due to saturation found recently by numerical solution of the Fokker–Planck equation. At short wavelengths the heat flow approaches an upper limit which depends on the phase velocity of the wave. Diffusive ion wave damping is strong over a large range of wavelengths.
62 citations
TL;DR: For spin-polarized low-energy electrons diffracted from ferromagnetic Ni(001), the exchange-and the spin-orbit-induced scattering asymmetries Aex and Aso of two diffracted beams have been simultaneously measured at T = 300 K and T = 520 K for several constant energies as functions of the polar angle of incidence as discussed by the authors.
56 citations
TL;DR: In this paper, the Onsager cross-coefficients b1 and b2, coupling growth and heat flow, are calculated for atomically rough surfaces of hcp 4He crystals, based on the premise that growth is limited by the collision of phonons and rotons with the interface.
Abstract: The growth coefficient K (the velocity of growth per unit chemical potential difference) and the Onsager cross-coefficients b1 and b2, coupling growth and heat flow, are calculated for atomically rough surfaces of hcp 4He crystals. The calculation is based on the premise, suggested by Andreev and Parshin, that growth is limited by the collision of phonons and rotons with the interface. The calculated K is compared with that obtained by Keshiskev et al. from the damping of melting-freezing waves. The theory assumes that the excitations are in the ballistic regime where their mean free path is large compared to the wavelength of the melting-freezing waves. In the experiment only the phonons satisfy this condition, yet the theory agrees with the data even when roton scattering is important Irreversible thermodynamics requires that the cross coefficients b1 and b 2 be equal. This is shown by direct calculation. The value of b1 and b2 depends on the ratio of two integrals over the phonon transmission coefficient and it is evaluated for two models of the transmission. The theory agrees fairly well with a recent measurement of b1. A calculation of the dissipation in the hydrodynamic regime, where the free path is short, shows that the damping of melting-freezing waves should have a different dependence on frequency compared to the ballistic regime.
49 citations
TL;DR: In this paper, the authors derived the mean free path for an electron or hole in any semiconductor obeys a simple universal law which implies a common phonon energy for electron and hole scattering and a dependence of mean free paths on threshold energy ( lambda varies as Ei-12/).
Abstract: Mean free paths associated with the scattering of electrons and holes are derived from experiments on impact ionisation in wide-gap semiconductors using the lucky-drift model. It is found that the mean free path for an electron or hole in any semiconductor obeys a simple universal law which implies a common phonon energy for electron and hole scattering and a dependence of mean free path on threshold energy ( lambda varies as Ei-12/). The latter dependence is plausible in terms of a simple view of scattering of high-energy carriers in a nonparabolic band. This universal model is derived on the basis of experimental data reported by various authors in Si, Ge, GaAs, and InP. Results for GaSb and its alloys appear to be anomalous, whereas data from GaInAs in InGaAsP tend to support the model. The model predicts the ratio of ionisation coefficients k= beta / alpha and its dependence on field and temperature. It is shown that k in any semiconductor is determined by only the ratio of threshold energies of electrons and holes. A comparison with reported values is made and brief discussions of the spin-orbit resonance effect in AlGaSb and of the enhancement in GaAs/AlGaAs multilayers are given.
TL;DR: In this article, the transmission coefficient of very low energy electrons ( ⩽ 10 eV) normally incident on epitaxial films of Cu and Ag on W(110) is modulated by interference between scattering from the vacuum/metal and metal/metal interfaces.
TL;DR: In this article, the conductivity of a zero-temperature electron gas in an environment allowing for random scattering and random tunnelling is extended by treating the conductor phase with an electron-phonon coupling taken into account.
Abstract: A recently proposed theory for the behaviour of a zero-temperature electron gas in an environment allowing for random scattering and random tunnelling is extended by treating the conductor phase with an electron-phonon coupling taken into account. The conductivity is expressed in terms of two frequency- and temperature-dependent kernels for which self-consistency equations are derived. Solution of these equations in the DC limit shows that phonon-controlled tunnelling processes dominate the conductivity if the electronic mean free path approaches the De Broglie wavelength. The resulting competition between scattering and tunnelling gives rises to anomalies of the temperature-dependent resistivity which are frequently observed in high-resistivity conductors as, e.g. liquid and amorphous alloys or A15 compounds.
TL;DR: In this article, the mean free path of a nucleon for two colliding nuclei has been calculated in terms of the imaginary part of the optical potential and the k effective mass.
Abstract: The mean free path of a nucleon for two colliding nuclei has been calculated in terms of the imaginary part of the optical potential and the k effective mass. The energy range 10--30 MeV/nucleon appears to be optimum for mean free paths in the range 3--4 fm.
TL;DR: In this paper, the relative contribution of multiple scattering events in the backward direction was found to increase with the sample thickness and to saturate around t that satisfies the relation t = KZ − n.
TL;DR: In this article, an approximate analytical expression for the non-equilibrium carrier density throughout the depletion region of a Schottky diode was obtained for the case of the mean free path less than a fraction of the Debye length.
Abstract: An approximate analytical expression is obtained for the non-equilibrium carrier density throughout the depletion region of a Schottky diode. This expression is used to obtain a generalized expression for the J-V characteristics of the diode. It is shown that for the case of the mean free path less than a fraction of the Debye length the current approaches the Schottky diffusion-limited result. On the other hand for the mean free path greater than this amount the current approaches Bethe's thermionic result. Furthermore, knowing the non-equilibrium carrier density permits the calculation of the transit time of the carriers through the depletion region.
TL;DR: In this paper, a biased resistor at low temperature T is modelled by a degenerate Fermi gas whose electrons scatter from phonons in thermal equilibrium and impurities while moving in the presence of a finite electric field E.
Abstract: A biased resistor at low temperature T is modelled by a degenerate Fermi gas whose electrons scatter from phonons in thermal equilibrium and impurities while moving in the presence of a finite electric field E. A nonperturbative solution of the Boltzmann equation valid for thin films yields a Fermi‐like steady state distribution characterized by an effective temperature T* (>T). For large fields the energy scale (T*) is set by the energy (eEl*) absorbed in an inelastic mean free path (l*∝T*−3/2). This yields T* proportional to E2/5. At low temperatures and frequencies the Johnson noise temperature is T*, independent of the bath temperature for large fields.
Patent•
26 Jul 1983TL;DR: In this paper, a high concentration of positive molecular ions of hydrogen or deuterium gas is extracted from a positive ion source having a short path length of extracted ions, relative to the mean free path of the gas molecules, to minimize the production of other ion species by collision between the positive ions and gas molecules.
Abstract: A high concentration of positive molecular ions of hydrogen or deuterium gas is extracted from a positive ion source having a short path length of extracted ions, relative to the mean free path of the gas molecules, to minimize the production of other ion species by collision between the positive ions and gas molecules. The ion source has arrays of permanent magnets to produce a multi-cusp magnetic field in regions remote from the plasma grid and the electron emitters, for largely confining the plasma to the space therebetween. The ion source has a chamber which is short in length, relative to its transverse dimensions, and the electron emitters are at an even shorter distance from the plasma grid, which contains one or more extraction apertures.
TL;DR: In this article, a one dimensional discrete layer model and a continuum model are solved exactly in order to gain insight into the effect of elastic backscaterring on the attenuation depth Λ.
TL;DR: A theory of substitutional as well as amorphous RKKY-type spin glasses has been developed following a qualitative idea first suggested by Smith and more recently by Mydosh as discussed by the authors.
Abstract: A theory of substitutional as well as amorphous RKKY-type spin glasses has been developed following a qualitative idea first suggested by Smith and more recently by Mydosh. The theory has been developed to a stage where quantitative calculations become possible on realistic systems. The paramagnetic to spin-glass transition has been described as a percolation of temperature dependent clusters of spins in a continuum. The glass transition temperature has been obtained as a function of the magnetic impurity concentration, after taking the effects of frustration and finite mean free path into account. Different 'critical' temperatures for different experimental probes with characteristic time and length scales have also been studied.
TL;DR: In this paper, the authors calculated the inductive susceptance and admittance of a thin semiconductor film in the direction perpendicular to the film, as a function of the sample length, doping, and temperature for voltages smaller than the thermal voltage.
Abstract: Impedance and admittance of a thin semiconductor film in the direction perpendicular to the film is calculated as a function of the sample length, doping, and temperature for voltages smaller than the thermal voltage. The calculation is based on the approximate solution of the Boltzmann equation in the relaxation time approximation. When the sample length is smaller than the mean free path, the conductance becomes independent of the sample length. In this limit the inductive susceptance is proportional to the sample length. When the sample length becomes comparable to the mean free path, the inductive susceptance reaches the maximum value, and then decreases. Our calculation shows that for high mobility GaAs samples at 77 K, the size effect may be important for films thinner than 5 μm. The results of the calculation are interpreted in the frame of a simple equivalent circuit which includes the bulk resistance, in series with the resistance due to the finiteness of the sample length, in series with the ind...
TL;DR: In this article, a diffraction model incorporating the dynamical partial structure factors is applied to calculate the resistivity and thermopower of amorphous Mg-Zn alloys.
Abstract: The resistivity and thermopower of amorphous Mg-Zn alloys have been computed as a function of temperature and composition. The diffraction model incorporating the dynamical partial structure factors is applied. The effect of the electron mean free path is investigated. The authors find that the resistivity is well described by the model, and that the inclusion of the mean free path does not change the results considerably. In the case of thermopower the diffraction model turns out to be inadequate: it gives a composition dependence which is against the experimental evidence. This suggests that there exists another scattering mechanism, which is not accounted for by the diffraction model. The choice of the various parameters of the model is discussed.
TL;DR: In this article, the authors studied the transition from Boltzmann to Stokes-Einstein behavior as the particle radius varies from small to large with respect to the mean free path.
Abstract: Tagged-particle motion in fluids is studied as a function of size and mass via variational solutions of the repeated-ring and self-consistent repeated-ring equations. For a massive particle, the transition from Boltzmann to Stokes-Einstein behavior is found as the particle radius varies from small to large with respect to the mean free path. New and more complicated effects are found for light particles. The theory appears to provide an explanation of the results of the computer simulation of Alder and Alley on size and mass dependence.
TL;DR: In this paper, the mean free path of protons in nuclei in the energy range 40-1000 MeV was determined using the nuclear radius R which reproduces the reaction and total cross sections consistently.
TL;DR: In this paper, a reanalysis of the correction to the Boltzmann conductivity due to maximally crossed graphs for degenerate bands explains why the conductivity scale in many-valley semiconductors is an order of magnitude higher than Mott's "minimum metallic conductivity."
Abstract: A reanalysis of the correction to the Boltzmann conductivity due to maximally crossed graphs for degenerate bands explains why the conductivity scale in many-valley semiconductors is an order of magnitude higher than Mott's "minimum metallic conductivity." With the use of a reasonable assumption for the Boltzmann mean free path, the lowest-order perturbation theory is seen to give a remarkably good, semiquantitative, description of the conductivity variation in both uncompensated doped semiconductors and amorphous alloys.
TL;DR: In this article, the integrodifferential equation governing the diffusion of minority carriers under the influence of both recombination by flaws and multiple photon absorption and emission via band-band transitions was solved by means of a variational principle.
Abstract: The integrodifferential equation governing the diffusion of minority carriers under the influence of both recombination by flaws and multiple photon absorption and emission via band‐band transitions recently developed by the author is solved by means of a variational principle. It is shown that for bulk material the effect of the reabsorbed recombination radiation (RRR) on carrier diffusion is negligible when the average mean free path of photons is larger than the diffusion length of the carriers. In the opposite case, this is not true and the results previously obtained by a different method are recovered. Applied to GaAs, these findings signify that if the diffusion length L due to flaws or recombination centers possesses a magnitude less than 1 μm, the effect of the RRR may safely be ignored. But, on the other hand, if L is greater than 1 μm, there exists an effective diffusion length Leff always larger than L, which is engendered by the RRR and which enhances carrier transport. This enhancement becom...
TL;DR: In this article, a general theory given previously for the calculation of the galvanomagnetic properties using an expansion of the vector mean free path in sets of Fermi surface harmonics is applied to copper single crystals containing 3D transition metal impurities.
Abstract: For pt.I see ibid., vol.12, p.3039 (1982). A general theory given previously for the calculation of the galvanomagnetic properties using an expansion of the vector mean free path in sets of Fermi surface harmonics is applied to copper single crystals containing 3d transition metal impurities. Both the anisotropic Fermi surface of Cu according to an H NFE TB band structure and the anisotropy of the impurity scattering in terms of scattering phase shifts are taken into account. The Kohler diagrams of magnetoresistivity are calculated for the (001) direction of the magnetic field. Furthermore the authors discuss the influence of 3d transition metal impurities on the galvanomagnetic properties in low, intermediate and high magnetic fields.
TL;DR: In this paper, the thermoelectric power of aluminum film was measured in the thickness range of 300-1600 A. From the size effect of electron diffusion term, the energy dependence of the mean free path of conduction electrons (U) and the Fermi surface area (V) were calculated to be U=0.957 and V=1.322.
Abstract: The thermoelectric power (TEP) of aluminum film was measured in the thickness range of 300–1600 A. From the size effect of electron diffusion term, the energy dependence of the mean free path of conduction electrons (U) and the Fermi surface area (V) were calculated to be U=0.957 and V=1.322. The phonon‐drag part of TEP also exhibited a size effect from which the mean free path of the dominant phonon mode was estimated to be 400 A. The effect of grain boundary scattering on thermoelectric power was also studied.