Showing papers on "Mean free path published in 1996"
TL;DR: In this article, the energy dependence of electron inelastic mean free path and stopping power in alkali halides and metal oxides has been investigated in the 50 eV to 10 keV energy range.
Abstract: Calculations of electron inelastic mean free paths and stopping powers for several alkali halides (KF, KC1, KBr, and KI) and metal oxides (BeO, MgO, SiO 2 and Aj 2 O 3 ) have been performed in the 50 eV to 10 keV energy range The complex dielectric formalism, improved to include the energy gap, was used for estimating the valence part of the transport characteristics, whereas the part related to electron-core interactions was evaluated according to Gryzinski's theory An extended comparison of these calculations with the available experimental data as well as with other theoretical predictions is presented Trends of the energy dependence of the inelastic mean free path and stopping power in alkali halides are studied The role of the plasmon deexcitation process as a source for low-energy electrons in secondary electron emission spectra is discussed The presented data can be used in Monte-Carlo simulations of electron transport in the considered materials
102 citations
TL;DR: In this article, the authors studied the kinetics of a collection of inelastically colliding smooth disks in a plane, in a state of constant shear rate, by performing an analysis of the pertinent Boltzmann equation.
Abstract: The kinetics of a collection of inelastically colliding smooth disks in a plane, in a state of constant shear rate, is studied by performing an analysis of the pertinent Boltzmann equation. The fact that the granular temperature T satisfies T∝γ2l2/e, where l is the mean free path, γ is the shear rate and e≡1−e2, where e is the coefficient of normal restitution, leads to the observation that when γ∝√e the limit e→0 of the above problem corresponds to a system of elastically colliding particles in equilibrium (at temperature T). This observation enables the construction of a systematic perturbative expansion (for the single particle distribution function) in powers of √e , in which the equilibrium (Maxwellian) distribution function serves as zeroth order. The limitations of this expansion are discussed alongside possible generalizations. Explicit expressions for the single particle distribution function to O(e) and expressions for the corresponding stress tensor are obtained. The phenomenon of normal stress...
101 citations
TL;DR: In this article, an assessment of the various new predictions for electron parallel mean free paths at 1 AU, especially their rigidity dependencies, is made by looking at the effects of these predictions on heliospheric modulation of galactic electron at energies below ∼300 MeV.
Abstract: With several new incentives, revisiting electron modulation using a comprehensive numerical model is appropriate. First, one has better confidence in the galactic electron spectrum at energies ≤ 300 MeV, second, several good independent observations of modulated electron spectra at 1 AU at solar minimum and along the Ulysses trajectory have been made, and third, progress has been made about theoretical predictions for mean free paths in the heliosphere. In this work, as a first approach, an assessment of the various new predictions for electron parallel mean free paths at 1 AU, especially their rigidity dependencies, is made by looking at the effects of these predictions on heliospheric modulation of galactic electron at energies below ∼300 MeV. Electron modulation is most suitable at these energies because adiabatic energy changes are still negligible and drift effects become less important. Several spectra are shown together with the radial dependence in the equatorial plane of the electron fluxes associated with each approach that was used. It was found that a damping turbulence model with composite slab, two-dimen-sional geometry gave parallel mean free paths that resulted in reasonable electron modulation at these energies. However, several other important modulating parameters have to be considered of which diffusion perpendicular to the averaged magnetic field is arguably the most important.
88 citations
TL;DR: A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation and the distribution of reflection eigenvalues is shown to be the Laguerre ensemble of random-matrix theory.
Abstract: A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre ensemble of random-matrix theory. The statistical fluctuations of the albedo (the ratio of reflected and incident power) are computed for arbitrary ratio of sample thickness, mean free path, and absorption or amplification length. On approaching the laser threshold all moments of the distribution of the albedo diverge. Its modal value remains finite, however, and acquires an anomalous dependence on the illuminated surface area.
82 citations
TL;DR: In this paper, the authors analyzed the heat flow and temperature and density distributions in a rarefied gas between two parallel plates at rest with different uniform temperatures by a finite difference method where the collision term is computed direct numerically.
Abstract: Heat flow and temperature and density distributions in a rarefied gas between two parallel plates at rest with different uniform temperatures are analyzed numerically on the basis of the full nonlinear Boltzmann equation for hard‐sphere molecules and the Maxwell‐type boundary condition by a finite difference method where the collision term is computed direct numerically. The accurate results are presented for the case in the density measurement by Teagan and Springer [Phys. Fluids 11, 497 (1968)], where the temperature ratio is 1.326, the value of the accommodation coefficient is 0.826, and the ratio of mean free path to plate spacing (Knudsen number Kn) is 0.0658≤Kn≤0.7582. It is found that there is a considerable difference between the present density distribution and the experimental data. The reason for this discrepancy is also discussed. The accurate numerical results of the linearized problem are also presented for comparison.
68 citations
TL;DR: In this article, the authors measured the spin dependent bulk and interface resistivities of multilayered Co/Cu wires with a diameter of 80 nm and a length of 6 μm in a geometry where the current was perpendicular to the layer plane.
Abstract: Multilayered Co/Cu wires with a diameter of 80 nm and a length of 6 μm were produced by electrodeposition in nanoporous polycarbonate membranes. Their magnetoresistance has been measured in a geometry where the current was perpendicular to the layer plane. The anisotropic part of the magnetoresistance was limited to 1.5%. The study, for layer thicknesses ranging from 3 to 100 nm interpreted in terms of the Valet and Fert model, gave estimates of the spin dependent bulk and interface resistivities and their change with temperature. The large Co bulk resistivity value, caused by a large amount of Cu impurities, limited the magnetoresistance in our samples to 20% at room temperature and 30% at 20 K. The Cu spin flip mean free path was found to be temperature independent and determined by scattering at Co impurities in the Cu layer. It was measured for two sets of samples with different amounts of Co impurities.
63 citations
TL;DR: In this paper, a general expression for the position-dependent differential inverse mean free path (DIMFP) of an electron penetrating into vacuum from a solid is derived, which can be divided up into a bulk and a surface term.
63 citations
TL;DR: In this article, the mean escape depth of photoelectrons leaving a target without being scattered inelastically was submitted to extensive theoretical analysis, and the authors derived a simple explicit expression for this function by solving a kinetic equation and by the Monte Carlo technique.
Abstract: • Escape depth of photoelectrons leaving a target without being scattered inelastically was submitted to extensive theoretical analysis. Dependence of the mean escape depth on the X-ray angle of incidence and the electron initial angular distribution inside the sample was considered. The Monte Carlo algorithm was developed basing on a differential elastic scattering cross-section calculated within the partial-wave expansion method and a realistic electron-atom mteraction potential. The mean escape depth was evaluated by means of the depth distribution function found analytically by solving a kinetic equation and by the Monte Carlo technique. The agreement between the results obtained from two methods is excellent. Elastic scattering was found to reduce considerably the escape depth. This reduction may reach up to 25% in the case of heavy elements in the practical X-ray photoelectron spectroscopy analysis. It was shown that the mean escape depth expressed in units of the electron transport mean free path is a universal function of the ratio of the inelastic to the transport mean free paths, the asymmetry parameter and the X-ray angle of incidence. A simple explicit expression for this function is proposed.
59 citations
TL;DR: In this paper, the concept of phonon scattering involving what is known as Umklapp processes is generalized to quasicrystals and it is shown that such processes in quasICrystals lead to a power law temperature dependence of the mean free path of delocalized quasilattice excitations, contrary to the exponential temperature dependence for periodically structured crystals at intermediate temperatures.
Abstract: The concept of phonon scattering involving what is known as Umklapp processes is generalized to quasicrystals. It is shown that such processes in quasicrystals lead to a power law temperature dependence of the mean free path of delocalized quasilattice excitations, contrary to the exponential temperature dependence of the phonon mean free path characteristic for periodically structured crystals at intermediate temperatures. This result provides a plausible explanation for the plateau-type feature in the quasilattice thermal conductivity λph(itT) of highly ordered icosahedral quasicrystals in the Al−Mn−Pd and Al−Re−Pd systems.
44 citations
TL;DR: This method captures the effects of the resonant scattering of the individual scatterer exactly, and by using a coated sphere as the basic scattering unit, multiple scattering contributions may be incorporated in a mean-field sense.
Abstract: We present an approach for efficient, accurate calculations of the transport properties of random media. It is based on the principle that the wave energy density should be uniform when averaged over length scales larger than the size of the scatterers. This method captures the effects of the resonant scattering of the individual scatterer exactly, and by using a coated sphere as the basic scattering unit, multiple scattering contributions may be incorporated in a mean-field sense. Its application to both ``scalar'' and ``vector'' classical waves gives exact results in the long-wavelength limit as well as excellent agreement with experiment for the mean free path, transport velocity, and the diffusion coefficient for finite frequencies. Furthermore, it qualitatively and quantitatively agrees with experiment for all densities of scatterers and contains no adjustable parameter. This approach is of general use and can be easily extended to treat different types of wave propagation in random media. \textcopyright{} 1996 The American Physical Society.
44 citations
TL;DR: In this article, a model for calculating the electron inelastic mean free path and stopping power in insulators in the 50 eV-10 keV energy range is presented, where both valence and core electron contributions have been considered.
Abstract: A model for calculating the electron inelastic mean free path and stopping power in insulators in the 50 eV–10 keV energy range is presented. Both valence and core electron contributions have been considered. The valence part has been estimated following the dielectric theory modified to include the energy gap; the core contribution has been evaluated on the basis of the classical binary encounter theory. Inelastic mean free path and stopping power calculations based on this model have been performed for several alkali halides: LiF, NaCl, KCl and CsI. They are compared to existing experimental data and Penn model’s predictions for the mean free path and to Bethe’s values for the stopping power; a fair agreement is found for incident electron energies higher than 100‐200 eV.
TL;DR: In this paper, the multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation, which does not rely on the diffusion approximation and becomes asymptotically exact in the regime of most interest.
Abstract: The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach, which does not rely on the diffusion approximation, becomes asymptotically exact in the regime of most interest, where the scattering mean free path is much larger than the wavelength . Quantitative predictions are derived in that regime, concerning various observables pertaining to optically thick slabs, such as the mean angle-resolved reflected and transmitted intensities, and the width of the enhanced backscattering cone. Special emphasis is put on the dependence of these quantities on the anisotropy of the cross section of the individual scatterers, and on the internal reflections due to the optical index mismatch at the boundaries of the sample. The large index mismatch regime is studied analytically, for arbitrary anisotropic scattering. The regime of very anisotropic scattering, where the transport mean free path is much larger than the scattering mean free path , is then investigated in detail. The relevant Schwarzschild - Milne equation is solved exactly in the absence of internal reflections.
TL;DR: In this article, it was shown that the mean free path is the limiting factor of thermal conductivity for isotropic polymers and that the integration of such a material must take care of minimizing the boundary resistance to the adjacent solid.
Abstract: Using the simple kinetic formula of thermal conductivity, it is shown that the mean free path is the limiting factor of thermal conductivity. Standard arguments on phonon-phonon interaction lead to realize that isotropic polymers cannot exceed thermal conductivities k ∼ 1 W/mK. Orientation of polymers gives a strong enhancement of k in orientation direction, due to the effect of phonon focussing. For the simplest chain, the polyethylene molecule, up to 37 W/mK have been measured. Possible values of 70 W/mK can be extrapolated for material with the modulus of the chain. Even higher values can be envisaged for perfect crystalline material. The integration of such a material must take care of minimizing the boundary resistance to the adjacent solid.
TL;DR: In this paper, the lifetime broadening Γ of the density of states in the superconductor is considered and the relationship between temperature and magnetic field dependencies of the pair potential Δ is evaluated.
Abstract: Current—voltage ( I—V ) characteristics of point contacts between the superconductors Sn, In, or Nb and a normal metal were measured in a magnetic field. The d V /d I curves of the point contacts show features caused by Andreev reflection at the S-N interface which persist well above B c bulk of the bulk sample. Shortening of the elastic mean free path in the contact area of the superconductor caused by structural defects results in type-II superconductivity in the point contact and an enhancement of B c PC . A satisfactory description of the d V /d I curves within the BTK theory was only possible by taking into account a lifetime broadening Γ of the density of states in the superconductor. Γ is found to be independent of temperature and increases in a magnetic field. Furthermore, Γ is sufficiently higher for Nb than for Sn. The temperature and magnetic field dependencies of the pair potential Δ are also evaluated and discussed.
TL;DR: For moderately clean superconductors with the mean free path approaching the coherence length from the clean side, the transverse force on a moving vortex starts to be dominated by variations in the pairing interaction produced by vortex motion as discussed by the authors.
Abstract: For moderately clean superconductors with the mean free path approaching the coherence length from the clean side, the transverse force on a moving vortex starts to be dominated by variations in the pairing interaction produced by vortex motion. We calculate the force and the Hall conductivity using the microscopic theory of nonstationary superconductivity and find that they are modified, as compared to the effective-action result, by an electric potential induced due to charge neutrality. \textcopyright{} 1996 The American Physical Society.
TL;DR: A Monte Carlo calculation including a mean free path, a phase function for particle scattering, and an absorption rate is developed for well-stirred, dense suspensions of silica particles with different sizes.
Abstract: An optical device for measuring high particle concentrations is presented. The sensor consists of two optical fibers used for the emission and reception of the light scattered by particles in suspension. To describe the light path in this medium, we developed a Monte Carlo calculation including a mean free path, a phase function for particle scattering, and an absorption rate. A similarity law links concentration variations to a homothetic space transformation. A comparison between our calculation and experimental data is given for well-stirred, dense suspensions of silica particles with different sizes. A good fit is found when the model parameters (mean free path and phase function) are chosen according to the data given by a particle sizer.
TL;DR: In this article, a massively parallel direct simulation Monte Carlo method is used to calculate low-pressure internal gas flow fields which show temperature jump and velocity slip at the reactor boundaries. But this method is not suitable for particle response times in these low pressure systems (for which continuum diffusion theory is needed).
Abstract: An understanding of particle transport is necessary to reduce contamination of semiconductor wafers during low‐pressure processing. The trajectories of particles in these reactors are determined by external forces (the most important being neutral fluid drag, thermophoresis, electrostatic, viscous ion drag, and gravitational), by Brownian motion (due to neutral and charged gas molecule collisions), and by particle inertia. Gas velocity and temperature fields are also needed for particle transport calculations, but conventional continuum fluid approximations break down at low pressures when the gas mean free path becomes comparable to chamber dimensions. Thus, in this work we use a massively parallel direct simulation Monte Carlo method to calculate low‐pressure internal gas flow fields which show temperature jump and velocity slip at the reactor boundaries. Because particle residence times can be short compared to particle response times in these low‐pressure systems (for which continuum diffusion theory ...
TL;DR: In this paper, an investigation was made of electrical properties of tungsten films of thickness in the range of 30-140 nm, grown by laser ablation deposition in ultrahigh vacuum on [1012] sapphire substrate.
Abstract: An investigation was made of electrical properties of tungsten films of thickness in the range of 30–140 nm, grown by laser ablation deposition in ultrahigh vacuum on [1012] sapphire substrate. From the data on the size effect and the temperature dependence of the resistivity r, supported with reflection high energy electron diffraction measurements, we find that the films, deposited onto clean substrates kept at temperatures higher than 500 °C, grow epitaxially with high quality crystalline structure. The effective electron mean free path changes from 300 to 1400 nm while the residual resistance ratio RRR=r (295 K)/r (4.2 K) changes from 7 to 35. At low temperatures we find the temperature dependent part ρ(T)≊ATn, with A=1.56 mΩ cm K−n, n=3–3.4 for the temperatures T<20 K. From the fit of the data to the equations of the classical size effect theory it was found that the main source of electron scattering at helium temperatures is interface scattering with a specular coefficient q≊0.3 and the bulk electron mean free path l∞ (4.2 K)∼200 μm, which is up to 103 times larger than the film thickness.
TL;DR: In this article, the authors examined the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field, and showed that the hybrid viscosities greatly exceed the standard cross-field viscosy when (l/It.) (it/lu), where t--(2_.t + l_ht)-t is the effective mean free path for the ions.
Abstract: We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length _coh, which is the average distance between the magnetic "kinks" that scatter the particles. For simplicity, we assume that the field is selfsimilar, and take 2cob to be a fixed fraction _ of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius 2L, which is much less than the ion-ion Coulomb mean free path 2u in hot accretion disks. However, we arrive at a formulation for a "hybrid" viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (l/It.)_ (it./lu), where t--(2_ .t + l_ht)-t is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by _ -= 2coffH), and also by the relative accretion rate M/-_/E, where A_/E= LE/c 2 and Le is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales. Subject headings: accretion, accretion disks -- black hole physics -- magnetic fields -- MHD -- plasmas
02 Oct 1996-Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms
TL;DR: In this article, the authors investigated the photon multiplicities for 150 GeV electrons/positrons traversing thin diamond and Si crystals and found that along axial directions up to 10 photons are emitted in 1.5 mm diamond for a radiative energy loss larger than 4 GeV.
Abstract: Detailed experimental investigations of photon multiplicities for 150 GeV electrons/positrons traversing thin diamond and Si crystals have been performed. Along axial directions up to 10 photons are emitted in 1.5 mm diamond for a radiative energy loss larger than 4 GeV. This corresponds to a mean free path for photon emission of about two orders of magnitude shorter than in an amorphous target. This is in agreement with an enhanced radiative energy loss of ∼ 30 times that in amorphous targets. The strongly enhanced photon emission leads to radiation cooling which can result in particles exiting the crystal with a reduced angle to the axis. For incidences along planar directions the average multiplicity is still above one, even for the thinnest crystals used in the present experiment, so a single-photon spectrum can only be obtained for thicknesses ≤50 μm, which, on the other hand, is comparable to the coherence lengths for GeV photons, leading to destruction of the coherent effects.
TL;DR: In this paper, the energy distribution of photoelectrons injected from a thin silver film coated with thin organic layers was investigated by measuring the mean free path for electrons with an energy above approximately 0.8 eV.
TL;DR: In this article, an analytic expression for the magnetoresistance of a symmetric granular array is derived from a semiclassical transport equation, and the solution is applied to a simple cubic structured system.
Abstract: An analytic expression for the magnetoresistance of a symmetric granular array is derived from a semiclassical transport equation, and the solution is applied to a simple cubic structured system. The influence of granular size, packing density, conductivity, electron mean free path, and interfacial resistance on magnetoresistance in granular systems is discussed in detail.
TL;DR: The mean free path ~mfp! of hot ballistic electrons, injected into high-purity GaAs, was measured and found to be several micrometers long and it is suggested that the dominant scattering is due to impact ionization of neutral impurities.
Abstract: The mean free path ~mfp! of hot ballistic electrons, injected into high-purity GaAs, was measured and found to be several micrometers long. The hot electrons were injected at energies just below the LO-phonon emission threshold and their mfp was measured by two techniques: first, by comparing different devices with different layer thickness; and second, in a single device, utilizing the cyclotron motion of ballistic electrons in tilted magnetic fields. We find the mfp scales roughly inversely with impurity concentration. We suggest that the dominant scattering is due to impact ionization of neutral impurities. @S0163-1829~96!52348-9#
TL;DR: The angular dependence of the resistivity and hence of the GMR for current in the plane of layers and perpendicular to the planes of the layers depends on the spin-dependent superlattice potential, and the details of the scattering potential.
Abstract: Most discussions of giant magnetoresistance (GMR) have focused on collinear cases where the magnetizations in adjacent layers are either parallel or antiparallel. To explore the relative importance of the superlattice potential and of the impurity scattering on the angular dependence of GMR, we calculate the electrical resistivity for noncollinear magnetizations. The electronic structure of the superlattice is modeled by a Kronig-Penney potential. When the magnetizations of the adjacent layers are neither parallel nor antiparallel, spinor forms of Bloch states and dispersion relations are derived. Then the conductivity as a function of the angle between magnetization directions of adjacent layers is calculated in the homogeneous limit where the mean free path is much larger than the layer thickness. We find the angular dependence of the resistivity and hence of the GMR for current in the plane of layers and perpendicular to the plane of the layers depends on the spin-dependent superlattice potential, and the details of the scattering potential. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, it was shown that asymmetrical changes in the electrical properties of semiconductor diodes occur after prolonged dc stressing at high field strengths of approximately 106 V/cm.
Abstract: Photon‐emission experiments on silicon‐rich hydrogenated amorphous silicon‐nitride metal–semiconductor–metal diodes, have shown the existence of hot electrons under applied field strengths of approximately 106 V/cm. The effective temperatures and mean free path between collision for the electrons were estimated from the spectra. It is shown that, in general, asymmetrical changes in the electrical characteristics of the devices occur after prolonged dc stressing at high fields. Two drift mechanisms can be distinguished. The first is called ‘‘cathodic’’ drift and is driven by recombination between band‐tail carriers in the semiconductor. The other is called ‘‘anodic’’ drift, and results from the effects of hot electrons at the anode. The spatial and time dependence of these drift mechanism is explained using a simple model.
TL;DR: In this article, the authors used the photon correlation method to investigate the autocorrelation function of light through a dense intralipid suspension in the presence of an absorber and demonstrated that the parameter of the scattering can be obtained through the absorption effect with diffusing-wave spectroscopy.
TL;DR: In this paper, the effects of Nd substitutions on the recently discovered anomalous superconducting behavior near the HC2(T) line of the C15-Laves phase compound CeRu2 were reported.
Abstract: Results are reported of the effects of Nd substitutions, on the recently discovered anomalous superconducting behaviour near the HC2(T) line of the C15-Laves phase compound CeRu2. Small amount of Nd-doping enhances both the TC and HC2 substantially, while retaining the anomalous superconducting behaviour (observed in good single crystals of pure CeRu2) with all its characteristic features. These results provide clear indication that: (1) the enhanced magnetic susceptibility is playing a very crucial role in the anomalous superconducting behaviour of CeRu2; (2) the large electronic mean free path is not a stringent for the observation of such an anomalous behaviour.
TL;DR: In this paper, it is shown that if the mean-free path divided by the macroscopic scale length is constant, it is possible to introduce self-similar variables in the Boltzmann equation for the neutral particles.
Abstract: The kinetics of neutral atoms in a plasma undergoing charge‐exchange, ionization, and recombination is considered. It is shown that if the mean‐free path divided by the macroscopic scale length is constant, it is possible to introduce self‐similar variables in the Boltzmann equation for the neutral particles. This equation is then solved analytically, and the nonlocal transport of heat and particles is calculated. Since the mean‐free path increases with increasing energy, a one‐sided, high‐energy tail is formed in the neutral distribution function. This tail may contribute significantly to the heat and particle fluxes. When this is the case, the fluid approximation of these quantities breaks down at arbitrarily short mean‐free paths.
TL;DR: In this paper, the effective inelastic mean free path (EIMFP) for electrons in some elemental solids was calculated using Monte Carlo simulation in the range 50-2000 eV.
TL;DR: In this paper, the authors studied the thermoelectric voltage of germanium point contacts as a function of temperature for various contact sizes and doping concentrations and showed that reduction of the contact area causes a decrease of thermopower that originates from quenching of the phonon-drag contribution by boundary scattering when the mean free path of phonons becomes larger than the contact size.
Abstract: We studied the thermoelectric voltage of germanium point contacts as a function of temperature for various contact sizes and doping concentrations. Reduction of the contact area causes a decrease of thermopower that originates from quenching of the phonon-drag contribution by boundary scattering when the mean free path of phonons becomes larger than the contact size.