Showing papers on "Mean free path published in 2002"
TL;DR: In this paper, the size effects of conductors in both lateral and mesoscopic dimensions were investigated and a coherent picture of the size dependent resistivity has been obtained by diffusive scattering of conduction electrons at the surface and the grain boundaries of the wire.
Abstract: As the lateral dimension of conductors approaches the mesoscopic regime, deviations of electric resistivity from that of bulk material are observed. Size effects come into play as the lateral dimension of the wire is in the range of the mean free path of the conduction electrons and below. In order to probe the size effects in systems confined in both lateral dimensions copper wires with widths ranging from 40 to 800 nm were prepared in a ${\mathrm{SiO}}_{2}$ matrix. The resistance of the wires was measured in the temperature range from 77 to 573 K. A size-dependent increase of the resistivity was found for decreasing wire widths. For the narrowest wires the resistivity is a factor of $2.6$ higher than the copper bulk value $(1.75 \ensuremath{\mu}\ensuremath{\Omega}\mathrm{cm}).$ The experimental data was compared to theoretical predictions over the whole investigated range of size and temperature using a semiclassical model. The model includes diffusive scattering of the conduction electrons at the surface and the grain boundaries of the wire. Very good agreement of theory with experimental data was found. In this way a coherent picture of the size dependent resistivity has been obtained.
513 citations
TL;DR: In this paper, it was proved that a conducting channel transmitting perfectly without backscattering is present independent of energy in metallic carbon nanotubes for scatterers with potential range larger than the lattice constant.
Abstract: It is proved that a conducting channel transmitting perfectly without backscattering is present independent of energy in metallic carbon nanotubes for scatterers with potential range larger than the lattice constant. In the case that several traveling channels are present, the conductance decreases from the ideal value determined by the number of traveling modes to the single-channel value when the length exceeds the mean free path determined by a Boltzmann transport equation. Further, inelastic scattering makes the conductance decrease in proportion to the inverse of the length in qualitative agreement with the Boltzmann result.
118 citations
TL;DR: An NMR technique is used to measure the short-time, three-dimensional displacement of grains in a system of mustard seeds vibrated vertically at 15 g, giving a direct measurement of the granular temperature profile.
Abstract: We have used an NMR technique to measure the short-time, three-dimensional displacement of grains in a system of mustard seeds vibrated vertically at 15 g. The technique averages over a time interval in which the grains move ballistically, giving a direct measurement of the granular temperature profile. The dense, lower portion of the sample is well described by a recent hydrodynamic theory for inelastic hard spheres. Near the free upper surface the mean free path is longer than the particle diameter and the hydrodynamic description fails.
100 citations
TL;DR: In this paper, the electrical resistivity of thin copper films sputtered onto silicon dioxide, in real time, is reported. And the authors show that the resistivity is strongly dependent on the film's thickness for thicknesses below the bulk mean free path of copper.
Abstract: Measurements of the electrical resistivity of thin copper films sputtered onto silicon dioxide, in real time, are reported. The electrical resistivity is shown to strongly depend on the film’s thickness for thicknesses below the bulk mean free path of copper (39 nm). Model fits to the electrical resistivity combined with ex situ atomic force microscopy and transmission electron microscopy suggest that the average grain size plays a dominant role in the resistivity during growth. Furthermore, observations are made on the relaxation of the electrical resistivity after the growth (by sputtering) is terminated, at room temperature. Both the magnitude and the time scale of change in the electrical resistivity are observed to be a function of the film’s thickness.
90 citations
TL;DR: In this article, a unified model that unifies the ballistic and diffusive transport mechanisms is applied to the carrier transport across potential barriers at grain boundaries in microcrystalline semiconducting materials.
Abstract: A recently developed model that unifies the ballistic and diffusive transport mechanisms is applied to the carrier transport across potential barriers at grain boundaries in microcrystalline semiconducting materials. In the unified model, the conductance depends on the detailed structure of the band edge profile and in a nonlinear way on the carrier mean free path. Equilibrium band edge profiles are calculated within the trapping model for samples made up of a linear chain of identical grains. Quantum corrections allowing for tunneling are included in the calculation of electron mobilities. The dependence of the mobilities on carrier mean free path, grain length, number of grains, and temperature is examined, and appreciable departures from the results of the thermionic-field-emission model are found. Specifically, the unified model is applied in an analysis of Hall mobility data for n-type μc-Si thin films in the range of thermally activated transport. Owing mainly to the effect of tunneling, potential b...
87 citations
TL;DR: In this article, the mean free path of cosmic ray particles in partially turbulent electromagnetic fields is calculated for two particular turbulence models: slab-like dynamical and random sweeping turbulence, and the rigidity dependence and absolute value of the mean-free path for these specific turbulence models are calculated.
Abstract: The parallel mean free path of cosmic ray particles in partially turbulent electromagnetic fields is a key input param- eter for cosmic ray transport. Here the parallel mean free paths of cosmic ray protons, electrons and positrons are calculated for two particular turbulence models: slab-like dynamical and random sweeping turbulence. After outlining the general quasilinear formalism for deriving the pitch-angle Fokker-Planck coecient in weak turbulence from the particle's equation of motion, the rigidity dependence and the absolute value of the mean free path for these specific turbulence models are calculated. Approximations for the mean free path for realistic Kolmogorov-type turbulence power spectra which include the steepening at high wavenumbers due to turbulence dispersion and/or dissipation are given.
82 citations
TL;DR: In this article, the sign reversal of the directed flow parameter in the central rapidity region in Au+Au collisions at s =200 A ǫGeV is studied within the Ultra-relativistic Quantum Molecular Dynamics Model.
78 citations
TL;DR: In this article, a mesoscopic superconducting lead nanowires with high aspect ratio and diameter ranging from 40 to 270 nm have been grown by electrodeposition inside nanoporous polycarbonate membranes.
Abstract: Mesoscopic superconducting lead nanowires with high aspect ratio and diameter ranging from 40 to 270 nm have been grown by electrodeposition inside nanoporous polycarbonate membranes. Nanowires with a diameter less than 50 nm were insulators due to a poor crystal structure. The others are shown to be type II superconductors because of their small electronic mean free path, instead of being type I which is usual for the bulk form of lead. An increase in the thermodynamic critical field H-c is observed and is attributed to the small transversal dimension leading to an incomplete Meissner effect. Finally, it is demonstrated that this enhancement agrees with numerical simulations based on the Ginzburg-Landau theory. (C) 2002 Elsevier Science B.V. All rights reserved.
55 citations
TL;DR: In this paper, the effective mean free paths (MFPs) were obtained for the Au 4f photoelectrons and CKLL Auger electrons in the PEY acquisition mode (with the respective inelastic contributions) with the same kinetic energies in the constant final state acquisition mode.
53 citations
TL;DR: In this article, the second-rank tensor of thermal transport properties as a function of temperature up to 800 °C was measured in different directions by a transient method, and the thermal diffusivity of phonons was described as D = 1/3 v l, where v is the phonon velocity and l the mean free path length of phonon.
Abstract: The thermal diffusivity of quartz, orthoclase, and sanidine was measured in different directions by a transient method, to determine the second-rank tensor of thermal transport properties as a function of temperature up to 800 °C. Thermal diffusivity of phonons is described as D=1/3 v l, where v is the phonon velocity and l the mean free path length of phonons. In quartz the thermal diffusivity at room temperature is 3.60 mm2 s−1 in [1 0 0] and 7.00 mm2 s−1 in [0 0 1] direction. A 1/T dependency of thermal diffusivity is observed for both directions up to 550 °C with a pronounced anisotropy (A=62%; A=(D
max
−
D
min)/D
average), which decreases with increasing temperature. Close to the α–β-phase transition, we observed a minimum in thermal diffusivity and a negligible anisotropy. Up to 573 °C the maximam of thermal diffusivity, average phonon velocity, and mean free path length are observed in [0 0 1] direction. However, above the temperature of phase transition the maximum values of the properties are observed in [1 0 0] direction. The observed behavior is explained by a model which interrelates velocity and mean free path length of phonons. A further contribution to the thermal diffusivity behavior is related to the higher symmetry of β-quartz, resulting in a reduced phonon–phonon-scattering probability. At ambient temperature, orthoclase and sanidine show similar values of thermal diffusivities (≈1 mm2 s−1) and a temperature-independent anisotropy behavior between 22 and 350 °C of ≈30%. For both feldspars a small 1/T temperature dependence of thermal diffusivity up to 350 °C is observed. The transparent sanidine in gemstone quality shows a strong increase in thermal diffusivity above 350 °C proportional to T 3. The contribution of the radiative heat-transfer mechanism leads to values more than two times higher in sanidine than in a milky-cloudy orthoclase at 800 °C. For the feldspars the mean free path length of phonons shows a small temperature dependence on reaching ≈0.4–0.5 nm at 800 °C and thus already in the range of the interatomic distances of ≈0.27–0.34 nm. The pronounced difference in thermal diffusivity behavior between quartz and orthoclase, which have a related tectosilicate structure, is connected to additional cations of K, Na, and Al within the feldspar structure.
53 citations
TL;DR: The effects of accelerating voltage and collection angle on the mean free path for all inelastic electron scattering (lambdap), which is an important parameter for determining specimen thickness by using electron energy-loss spectroscopy, were investigated with crystalline Si and amorphous SiO2.
Abstract: The effects of accelerating voltage and collection angle on the mean free path for all inelastic electron scattering (lambdap), which is an important parameter for determining specimen thickness by using electron energy-loss spectroscopy, were investigated with crystalline Si and amorphous SiO2. First, thickness of Si film was measured with the convergent-beam electron diffraction method, while thickness of SiO2 particles was estimated from their spherical shape. Then from electron energy-loss spectra, lambdap was evaluated for Si film and SiO2 particles by changing the accelerating voltage (100 to approximately 300 kV) and the collection angle for the scattered electrons. Under the condition of no objective aperture, lambdap for Si film and SiO2 particles was found to increase with the increase of accelerating voltage and to take values of 180+/-6 nm (Si) and 247+/-8 nm (SiO2) at 300 kV. Also, it was found that lambdap in both cases decreases drastically with the increase of collection angle in the range smaller than 25 mrad, while it tends to take a constant value at the collection angle larger than 25 mrad at 200 kV.
TL;DR: In this article, the authors extended the modified formalism of Sheng, Xing, and Wang to allow the calculation of the conductivity of a thin metallic film bounded by a rough fractal surface.
Abstract: We have extended the modified formalism of Sheng, Xing, and Wang@J. Phys.: Condens. Matter11 L299 ~1999!# to allow the calculation of the conductivity of a thin metallic film bounded by a rough fractal surface. We utilized the so-called k-correlation model proposed by Palasantzas and Barnas @Phys. Rev. B 48, 14 472 ~1993!; 56, 7726 ~1997!#, to describe the height-height autocorrelation function corresponding to a self-affine roughness. This extension permits the calculation of the conductivity of the film as a function of the r.m.s. roughness amplitude d, of the lateral correlation length j, of the mean free path in the bulk l, and of the roughness exponent H. We found that the degree of surface irregularity, represented by the roughness exponent H characterizing the surface, does influence the conductivity of the film, as first discovered by Palasantzas and Barnas. However, this influence manifests itself for large bulk mean free paths l’1000 nm and for large correlation lengths j’5 nm, in which case the conductivity of the film for H51 exceeds by about 30% the conductivity for H50.2, an effect which is smaller than that reported by Palasantzas and Barnas. For correlation lengths j below 1 nm and mean free paths l’100 nm, the influence of the roughness exponent H on the conductivity is reduced to below 10%, and for smaller mean free paths and correlation lengths the conductivity becomes insensitive to H. We also found that Mathiessen’s rule is severily violated in the case of thin metallic films. The resistivity of the film coincides roughly with the surface-limited resistivity only in the case of ultrathin films t,5 nm. For thicker films 100 nm.t.5 nm, the resistivity of the film exceeds by some 20 to 30 % the value dictated by Mathiessen’s rule. And conversely, the apparent surface-induced resistivity estimated assuming the validity of Mathiessen’s rule, exceeds by nearly one order of magnitude the true surfaceinduced resistivity, except in the case of ultrathin films t, 5n m.
TL;DR: In this paper, the authors discuss zero-frequency transport properties of spin-1/2 chains and show that a careful analysis of quantum Monte Carlo data on the imaginary axis allows to distinguish between intrinsic ballistic and diffusive transport.
Abstract: We discuss zero-frequency transport properties of various spin-1/2 chains. We show that a careful analysis of quantum Monte Carlo data on the imaginary axis allows to distinguish between intrinsic ballistic and diffusive transport. We determine the Drude weight, current-relaxation lifetime, and the mean free path for integrable and nonintegrable quantum spin chains. We discuss, in addition, some phenomenological relations between various transport-coefficients and thermal response functions.
TL;DR: In this article, the effect of scattering with nonzero impact parameters between constituents in relativistic heavy-ion collisions is investigated, where the characteristic range of the collision kernel is varied from approximately 1.0 fm to zero while leaving the mean free path unchanged.
Abstract: The effect of scattering with nonzero impact parameters between constituents in relativistic heavy-ion collisions is investigated. In solving the relativistic Boltzmann equation, the characteristic range of the collision kernel is varied from approximately 1.0 fm to zero while leaving the mean free path unchanged. Modifying this range is shown to significantly affect spectra and flow observables. The finite range is shown to provide effective viscosities, shear, bulk viscosity, and heat conductivity, with the viscous coefficients being proportional to the square of the interaction range.
TL;DR: In this article, a statistical survey shows that the observation probability of the "torus" distribution amounts to nearly 20% and that the distribution pattern depends on the local magnetic field directions and turbulence levels.
Abstract: [1] A‘torus’-like velocity distribution of the helium pickup ions has been detected in interplanetary space by GEOTAIL. A statistical survey shows that the observation probability of the ‘torus’ distribution amounts to nearly 20% and that the distribution pattern depends on the local magnetic field directions and turbulence levels. These results support the recent finding of a low pitch angle scattering rate and a large mean free path.
TL;DR: In this article, the Bretonnet-Silbert model was used to calculate the electrical resistivity and the thermoelectric power of liquid less-simple metals, such as Zn, Cd, Hg, In, Tl, Sn, Pb, Sb, and Bi.
Abstract: Electronic transport properties, namely the electrical resistivity and the thermoelectric power, of liquid less-simple metals, Zn, Cd, Hg, In, Tl, Sn, Pb, Sb, and Bi, are calculated using Ziman's theory. The effective electron-ion and ion-ion interactions are described by the Bretonnet-Silbert model. The static structure factors are evaluated by the self-consistent Variational Modified Hyper-netted Chain (VMHNC) integral equation of liquids. The results for the electrical resistivity are fairly good when compared with experimental data, but the agreement improves significantly when the blurring of the Fermi surface due to the finite electron mean free path is accounted for. The values of the thermoelectric power, for most systems, have the same sign and order of magnitude as the experimental ones. The results for the thermopower also show that the contribution of the energy dependent term of the electron-ion potential is significant for the concerned systems.
TL;DR: In this paper, a theory of the transport of an anisotropic pulse of charged particles injected into the interplanetary magnetic field is applied to a ground level event on 24 May 1990.
Abstract: A theory of the transport of an anisotropic pulse of charged particles injected into the interplanetary magnetic field is applied to an anisotropic ground level event on 24 May 1990. For this event the kinetic regime is considered when the mean free path is comparable with the distance from particle source. Both the source angular particle distribution and the angular dependence of a detector response are included. The theoretically predicted temporal profiles are compared with the particle intensity records measured by several neutron monitors with different asymptotic directions.
TL;DR: In this article, the influence of nonstoichiometric disorder on in-plane resistivity and SC-transition has been investigated for Nd2−xCexCuO4+δ single crystal films (x=0.15 and 0.18).
Abstract: The influence of nonstoichiometric disorder on the in-plane resistivity and SC-transition has been investigated for Nd2−xCexCuO4+δ single crystal films (x=0.15 and 0.18). It is shown that with increasing of δ the in-plane normal state resistivity increases (the mean free path diminishes) and SC-transition temperature decreases with essential broadening of the transition region. The observed evolution from homogeneous metallic (and superconducting) Nd2−xCexCuO4+δ system to inhomogeneous dielectric one is described as Anderson-type disorder-induced transition in a two-dimensional electron system.
TL;DR: In this paper, the authors present annual 0.3-40 MeV nucleon-1 anomalous cosmic ray (ACR) oxygen and helium energy spectra from the 1991-1999 cosmic-ray recovery phase of solar cycle 22.
Abstract: We present annual 0.3-40 MeV nucleon-1 anomalous cosmic-ray (ACR) oxygen and helium energy spectra from the 1991-1999 cosmic-ray recovery phase of solar cycle 22. These observations were made with the Low Energy Charged Particle instruments aboard the Voyager 1 and Voyager 2 spacecraft while at helioradial positions ranging from 34 to 76 AU. The peak intensities of both species increased by 2 orders of magnitude during this period, while the energies of peak O and He intensity decreased from ~9 to 1.3 MeV nucleon-1 and from ~35 to 6 MeV nucleon-1, respectively. Using these observations along with published O measurements from the Solar Anomalous Magnetospheric Particle Explorer at 1 AU, we investigate ACR transport phenomena. We make estimates related to transport parameters such as the relative change in the scattering mean free path over time, the rigidity dependence of the mean free path, and the distance between the Sun and the solar wind termination shock.
01 Jan 2002
TL;DR: In this article, the influence of nonstoichiometric disorder on the in-plane resistivity and SC-transition has been investigated for single crystal films (x=0.15 and 0.18).
Abstract: The influence of nonstoichiometric disorder on the in-plane resistivity and SC-transition has been investigated for
Nd{2-x}Ce{x}CuO{4+\delta} single crystal films (x=0.15 and 0.18). It is shown that with increasing of $\delta$ the in-plane normal state resistivity increases (the mean free path diminishes) and SC-transition temperature decreases with essential broadening of the transition region. The observed evolution from homogeneous metallic (and superconducting)
Nd{2-x}Ce{x}CuO{4+\delta} system to inhomogeneous dielectric one is described as Anderson-type disorder-induced transition in a two-dimensional electron system.
TL;DR: In this article, the kinetic energy dependence of ions trapped in a radiofrequency (RF) hexapole ion trap was investigated and the consequences for multipole-storage-assisted dissocn. (MSAD) in which ions are accumulated for prolonged periods of time in the multipole ion traps of an electrospray ion source were discussed.
Abstract: The kinetic energy dependence of ions trapped in a radiofrequency (RF) hexapole ion trap was calcd. as a function of space charge, mean free path, mass, RF potential and charge. The av. kinetic energy of the ions increases with increasing space charge, mean free path and the ion charge state. For a trapped ion in a given Coulombic field, the mass of the ion and the amplitude of the applied RF potential did not affect the av. kinetic energy. The consequences for multipole-storage-assisted dissocn. (MSAD), in which ions are accumulated for prolonged periods of time in the multipole ion trap of an electrospray ion source, are discussed. As a result of radial stratification inside the ion trap, MSAD can lead to the preferential excitation of ions with larger m/z values. Such discrimination would have neg. consequences for the detection of labile noncovalent adducts, which are normally detected at higher m/z values than their constituent species. [on SciFinder (R)]
TL;DR: A fully kinetic theory model of the sheath of a dc glow discharge includes a direct numerical solution of Boltzmann equations for the spatial and velocity dependence of the electron and Ar+ distribution functions with a self-consistent electric field calculated from the Poisson equation.
Abstract: A fully kinetic theory model of the sheath of a dc glow discharge is presented. This model includes a direct numerical solution of Boltzmann equations for the spatial and velocity dependence of the electron and Ar + distribution functions with a self-consistent electric field calculated from the Poisson equation. The solution is obtained using a collocation method that employs Legendre quadrature points for both angular and spatial variables, and nonclassical speed quadrature points for velocity. The results of the steady state direct numerical solution are compared with a particle-in-cell Monte Carlo simulation. As anticipated, it is found that the space and energy-dependent ion distribution function varies strongly with a decrease in the ratio of the Debye length to the ion mean free path.
TL;DR: In this article, the crossover behavior of a disordered quantum wire with specular boundary conditions was analyzed in weak and strong localization regimes by the magnetic diffusion length, and the applicability of the analytical formulas to resistance measurements in the strong localization regime was discussed.
Abstract: Magnetic-field-dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak- and strong-localization regimes by the magnetic diffusion length ${L}_{B}.$ This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length ${l}_{B}$ for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results is included.
TL;DR: In this paper, the results of the analytical kinetic theory of plasma are discussed, which highlight the determining role slow collisional particles play in such plasma phenomena as ion-acoustic wave damping and nonlinear electron-density perturbations due to the inhomogeneous intensity of the plasma-heating electromagnetic field.
Abstract: Under conditions which are usually associated with collisionless plasma, and in which the mean free path of charged particles considerably exceeds the characteristic size of the spatial inhomogeneities involved, plasmas always contain slow particles whose mean free path proportional to the fourth power of their velocity is less than the inhomogeneity scale. Although relatively few in number, these subthermal particles play a dominant role in such 'weakly collisional' plasmas. In this paper, the results of the analytical kinetic theory of plasma are discussed, which highlight the determining role slow collisional particles play in such plasma phenomena as ion-acoustic wave damping and nonlinear electron-density perturbations due to the inhomogeneous intensity of the plasma-heating electromagnetic field. It is shown that by affecting these plasma properties the subthermal electrons correspondingly make an impact on parametric instabilities such as plasma radiation filamentation and stimulated Mandelstam– Brillouin scattering. Theoretical predictions are compared with numerical solutions of the Boltzmann equation. The concept of nonlocal plasma transfer processes, attracted to the interpretation of such solutions, is also discussed.
01 Jun 2002-Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms
TL;DR: In this article, simple analytical expressions for the transport of low energy electrons in insulating specimens are derived by assuming isotropic random walk, which explains why the measured fraction of the emitted secondary electrons (with respect to the generated ones) is often found to be larger than 50% for materials having a negative affinity, such as cesiated diamond surfaces or rare gas solids.
Abstract: Simple analytical expressions for the transport of low energy electrons in insulating specimens are derived by assuming isotropic random walk. The proposed approach explains why the measured fraction of the emitted secondary electrons (with respect to the generated ones) is often found to be larger than 50% for materials having a negative affinity, such as cesiated diamond surfaces or rare gas solids. The correspondence between parameters involved in the present approach and those used in an exponential attenuation function of the form B exp(−z/〈s〉) are given. One direct consequence is the possibility to extract from the experimental secondary yield curves, physical information on the dynamics of low energy electrons (range and transport mean free path) in insulators.
TL;DR: In this article, the velocity of dislocations was measured as a function of dislocation character and length at various temperatures and stresses, and the local effective stress was estimated from the curvature of the dislocation.
Abstract: In situ deformation experiments were performed on pure Ge. In addition to qualitative observations being made, the velocity of dislocations was measured as a function of dislocation character and length at various temperatures and stresses. The local effective stress was estimated from the curvature of the dislocations. Combining the in situ results with double-etch-pit experiments allows estimation of the mean free path of kinks. Then a set of material parameters are calculated within the framework of the Hirth–Lothe theory.
TL;DR: In this article, the time-resolved emission spectra and the excitation spectra of the main emissions have been measured for the rst time in stressed and unstressed RbI crystals using synchrotron radiation of 10{30 eV at 8 K.
Abstract: The time-resolved emission spectra and the excitation spectra of the main emissions have been measured for the rst time in stressed and unstressed RbI crystals using synchrotron radiation of 10{30 eV at 8 K. It has been shown that the applied elastic uniaxial stress (EUS) oers promise for the separation of the elementary multiplication mechanisms of electronic excitations. A dierent influence of EUS on the self-trapping of excitons or holes at 8 K has been discussed. The mean free path of free excitons decreases, while that of valence holes increases in a stressed RbI crystal.
TL;DR: The constant collision frequency model for a transitional plasma, i.e. one that is between collisionless and fully collisional, is developed for the situation where there is a flux of positive ions and electrons into the plasma as mentioned in this paper, which is then used to describe the outer region of an electronegative plasma and thus obtain a plasma balance equation for the whole plasma.
Abstract: The constant collision frequency model for a transitional plasma, i.e. one that is between collisionless and fully collisional, is developed for the situation where there is a flux of positive ions and electrons into the plasma. This is then used to describe the outer region of an electronegative plasma and thus obtain a plasma balance equation for the whole plasma. Chlorine is chosen as an exemplar gas for which the differences are explored between this model and another that has been suggested based on the ambipolar diffusion coefficient derived by Thompson (Thomson J B 1959 Proc. Phys. Soc. 73 818). The differences appear to be experimentally measurable. Corresponding values for estimating the effect using a constant ion mean free path model are also given.
TL;DR: In this paper, the zero-bias anomaly in the dependence of the tunneling density of states on the energy ∈ of the particle for two-and one-dimensional multilayered structures is studied.
Abstract: The zero-bias anomaly in the dependence of the tunneling density of states ν(∈) on the energy ∈ of the tunneling particle for two- and one-dimensional multilayered structures is studied. We show that for a ballistic two-dimensional (2D) system the first-order interaction correction to density of states due to the plasmon excitations studied by Khveshchenko and Reizer is partly compensated by the contribution of electron-hole pairs, which is twice as small and has the opposite sign. For multilayered systems the total correction to the density of states near the Fermi energy has the form δν/ν 0 =max(‖∈‖,∈*)/4∈ F , where ∈* is the plasmon energy gap of the multilayered 2D system. For a 2D system with finite-range interaction the particle-hole contribution precisely cancels with the contribution of the zero-sound mode, in agreement with the Fermi liquid theory. In the case of one-dimensional conductors we study multiwall nanotubes with the elastic mean free path exceeding the radius of the nanotube. The dependence of the tunneling density-of-states energy, temperature and on the number of shells is found.