Showing papers on "Mean free path published in 1989"

Theory of giant magnetoresistance effects in magnetic layered structures with antiferromagnetic coupling.

Abstract: We present a simple theoretical description of recently measured giant magnetoresistance effects in Fe/Cr layered structures. The resistivity is calculated by solving the Boltzmann transport equation with spin-dependent scattering at the interfaces. The magnitude of the effect depends on the ratio of the layer thickness to the mean free path and on the asymmetry in scattering for spin-up and spin-down electrons. Good agreement with experiment is found for both sandwich structures and superlattices.

Magnetoresistance oscillations in a two-dimensional electron gas induced by a submicrometer periodic potential

Abstract: A new type of magnetoresistance oscillation periodic in 1/B is observed when the carrier density Ns of a two-dimensional electron gas is weakly modulated with a period smaller than the mean free path of the electrons. Experiments with high mobility AlGaAs-GaAs heterojunctions where Ns is modulated by holographic illumination at T ≤ 4.2 K show that the period of the additional quantum oscillation is determined by the separation a of the interference fringes. This period corresponds to Shubnikov-de Haas oscillations where only the electrons within the first reduced Brillouin zone with |k| < π/a contribute.

Lateral tunneling, ballistic transport, and spectroscopy in a two-dimensional electron gas.

Abstract: We report a direct observation, via electron energy spectroscopy, of lateral tunneling and lateral ballistic-electron transport in a two-dimensional electron gas (2D EG). This was accomplished through the use of a novel transistor structure employing two potential barriers, induced by 50-nm wide metal gates deposited on a GaAs/AlGaAs selectively doped heterostructure. Hot electrons with very narrow energy distributions (\ensuremath{\simeq}5 meV wide) have been observed to ballistically traverse 2D EG regions \ensuremath{\simeq}170 nm wide with a mean free path of about 480 nm.

Mean free path effects in superfluid 4 He

Abstract: The mean free path effects in superfluid He II was studied with a vibrating wire method in the temperature range from Tλ down to 20 mK under the saturated vapour pressure. The transition from the hydrodynamic regime to the ballistic regime was clearly observed at around 0.7 K with a 47 µm diameter wire. In the hydrodynamic regime the usual Stokes' approximation was found to be insufficient to interpret the results. In the ballistic regime the results can be explained quantitatively with the kinetic theory of phonons. However, below about 0.15 K there appear non-linear effects such as the distortion of the resonance line shape and a hysteresis behavior, which become stronger with decreasing temperature.

Thermoelectric power and electrical resistivity of crystalline antimony telluride (Sb2Te3) thin films: Temperature and size effects

Abstract: Crystalline Sb2Te3 thin films of different thicknesses have been prepared by subsequent annealing (at 500 K) of vacuum deposited, as‐grown, amorphous thin films of Sb2Te3 prepared on glass substrates at room temperature. Thermoelectric power and electrical resistivity of these annealed (crystalline) films have been determined as a function of temperature. The size dependence of thermoelectric power and electrical resistivity have been analyzed by the effective mean free path model of size effect. It is found that both the thermoelectric power and the electrical resistivity are linear functions of the reciprocal of thickness of the films. The data from the analyses of thermoelectric power and electrical resistivity have been combined to evaluate important material parameters such as carrier concentration, their mean free path, Fermi energy, and effective mass. The values of some of these are compared with the previous available values from literature.

Derivation of the electron inelastic mean free path from the elastic peak intensity

Abstract: Measurements of the elastic peak intensity make possible estimation of the true inelastic mean free path (IMFP). Corresponding experiments are relatively simple and can be performed for any sample. The theoretical models can be used to derive the relation between elastic peak intensity and IMFP for single and multiple elastic scattering. In the present work both models were based on the differential scattering cross-sections calculated within the partial wave expansion method. Examples of calculations of the IMFP using both theoretical models are presented.

Coronal and interplanetary transport of solar energetic protons and electrons

Abstract: We present a new method to separate interplanetary and coronal propagation, starting from intensity variations observed by spaceprobes at different heliolongitudes. In general, a decrease in absolute intensities is observed simultaneously with an increase in temporal delays. The coupling of these two effects can be described by Reid's model of coronal diffusion and can in principle be used to determine the two coronal time constants, diffusion time tc and escape time A. In addition, a least-squares fit method is used to determine the parameters of interplanetary transport, assuming a radial dependence as λ(r) = λ0(r/1 AU)b. The method is applied to the two solar events of 27 December, 1977 and 1 January, 1978 which were observed by the spaceprobes Helios 1, Helios 2, and Prognoz 6. Energetic particle data are analysed for 13–27 MeV protons and ∼-0.5 MeV electrons. For the regions in space encountered during these events the mean free path of electrons is smaller than that of protons. Straight interpolation between the two rigidities leads to a rather flat rigidity dependence λ(P) ∼ Pn with n = 0.17–0.25. This contradicts the prediction of a constant mean free path or of the transition to scatter-free propagation below about 100 MV rigidity. In three of the four cases the mean free path of 13–27 MeV protons is of the order 0.17 AU, the mean free path of electrons of the order 0.06 AU. For protons we find b ∼- 0.7 for the exponent of the radial variation.

Persistent Currents in Two-Dimensional Metallic Cylinders: a Linear Response Analysis

Abstract: Diamagnetic persistent currents are shown to exist in a two-dimensional metallic cylinder threaded by magnetic flux, and the average over impurity configurations is calculated in the weak-scattering, small flux limit. Electron-electron and hole-hole propagators give rise to a reduction in the current which is exponential in Lx/2l, where Lx is the perimeter and l is the elastic mean free path. The current is proportional to the length of the cylinder, when this length is large.

Impact ionization coefficient and energy distribution function at high fields in semiconductors

Abstract: Impact ionization coefficients in semiconductors are numerically calculated following Keldysh’s method [Sov. Phys. JETP 21, 1135 (1965)]. This requires deriving expressions for an energy‐dependent mean free path l(e) and an energy‐dependent impact ionization scattering rate rii(e). In the derivation of rii(e), a nonparabolic e‐k relation as well as a smooth transition from the phonon‐assisted impact ionization to the phononless impact ionization are considered. Numerically calculated impact ionization coefficients for electrons and holes in Ge, Si, and GaAs agree very well with experimental data. The calculated Keldysh energy distribution function is also compared with the standard Maxwellian distribution. The average mean free path l, which is a function of the electric field, has values within the range often quoted in the literature.

Coherent enhancement of the hot-electron mean free path by superlattice transmission resonances.

Abstract: We report a strong enhancement of the optical responsivity in GaAs/AlGaAs multi-quantum-well infrared detectors. This is explained by a resonant increase in the hot-electron mean free path as a result of the coherent transmission resonances in the continuum states above the energy barriers of the super-lattice

Calculation of optical transport and localization quantities.

Abstract: By combining a coherent-potential approximation with our previous work on localization, we calculate the mean free path l, the diffusion coefficient D, the localization parameter kl, where k is the renormalized wave vector, the localization length ${L}_{c}$, and other related quantities. Our results for D near the critical regime are in surprisingly impressive agreement with recent experimental data by Drake and Genack in a sample of titania spheres in air. Our calculations indicate that optical localization can be experimentally realized by either lowering the concentration of the titania spheres or lowering the standard deviation of the radii distribution.

Escape probability of geminate electron–ion recombination in the limit of large electron mean free path

Abstract: We investigated theoretically the geminate electron–ion recombination in the limit of large electron mean free path by using the concept of diffusion in energy space. The energy diffusion equation is derived and the energy diffusion coefficient is evaluated. An analytical expression for the escape probability of the electron–ion pair is derived. It reproduces the numerical results very well which were obtained previously by using a Monte Carlo method. Experimental implications of the present theoretical findings are discussed.

Mean free path of low‐energy protons upstream of selected interplanetary shocks

Abstract: There are two fundamentally different approaches in calculating the mean free path of energetic charged particles. The first approach is concerned with the particle data. Here measured time intensity profiles are fitted to theoretical models and a best fit value for the mean free path is obtained. For undisturbed propagation of solar particles this theoretical model usually is a numerical solution of a Fokker-Planck equation. In the case of quasi-parallel interplanetary shocks the mean free path can be determined from the exponential increase of the particles intensity in the upstream region of the shock. The second approach starts with the magnetic field properties. One often-applied model assumes that the scattering of the particles is due to Alfven waves that propagate along the guiding field. Here the particles are scattered resonantly by the components of the field fluctuations perpendicular to the guiding field. A second model assumes that a different type of magnetohydrodynamic wave, the magnetosonic wave, in addition to Alfven waves plays an important role in particle scattering. The scattering by magnetosonic waves is a nonresonant interaction. We discuss the time intensity profiles of low-energy protons (35–1600 keV) associated with interplanetary shocks observed by ISEE 3 during the period August 1978 to December 1981. For five shock-associated particle intensity increases, we calculate the amount of scattering upstream of the shock by fitting the intensity increase as an exponential in time. The anisotropy in the solar wind frame is analyzed. We hereby test the validity of our diffusion model. We compare the mean free paths obtained from the particle data with mean free paths derived from magnetic field data. Here we first calculate the amount of resonance scattering from the power density spectrum of the magnetic field fluctuations and then include the effect of magnetosonic waves. The main difference between these two models lies in the predicted rigidity dependence of the mean free path. For all five events, pure resonance scattering predicts mean free paths that increase with particle rigidity; this disagrees with the observed particle behavior. Quite good agreement is obtained by the model of a mixture of Alfven waves and magnetosonic waves; here a more complicated rigidity dependence is possible. Therefore we conclude that magnetosonic waves together with Alfven waves are responsible for scattering of particles, at least in the upstream region of interplanetary shocks.

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Abstract: Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.

Recombination of electron–ion pairs for arbitrary mean free path

Abstract: A theory is developed of the dependence of the steady‐state electron–ion pair recombination rate constant on the electron mean free path. The problem, in classical mechanics, is reduced to the stochastic dynamics of the electron in the one‐dimensional effective potential V(R)=−kTRc/R −2kT ln R. Rc is the Onsager length Ze2/4πekT. For a large mean free path λ, the recombination rate is determined by energy relaxation of electrons which cross the transition state of V(R) at RT=Rc/2, whereas for small λ the Debye result for spatial diffusion‐controlled recombination is obtained. The theory gives the dependence of the rate in the crossover regime where λ is comparable to Rc. The results are in good agreement with experiment and Monte Carlo simulations.

Substrate current model for submicrometer MOSFETs based on mean free path analysis

Abstract: The nonequilibrium effects of hot carriers are investigated to analyze avalanche generation for submicrometer MOSFET devices. A simple analytical expression for the impact ionization utilizing the mean free path concept is developed. It is incorporated into a conventional drift-diffusion equation solver (PISCES) to obtain the substrate current in submicrometer MOSFET devices. The transconductance for high drain bias and breakdown conditions are analyzed based on the proposed impact ionization model. >

The kinetic boundary layer around an absorbing sphere and the growth of small droplets

Abstract: Deviations from the classical Smoluchowski expression for the growth rate of a droplet in a supersaturated vapor can be expected when the droplet radius is not large compared to the mean free path of a vapor molecule. The growth rate then depends significantly on the structure of the kinetic boundary layer around a sphere. We consider this kinetic boundary layer for a dilute system of Brownian particles. For this system a large class of boundary layer problems for a planar wall have been solved. We show how the spherical boundary layer can be treated by a perturbation expansion in the reciprocal droplet radius. In each order one has to solve a finite number ofplanar boundary layer problems. The first two corrections to the planar problem are calculated explicitly. For radii down to about two velocity persistence lengths (the analog of the mean free path for a Brownian particle) the successive approximations for the growth rate agree to within a few percent. A reasonable estimate of the growth rate for all radii can be obtained by extrapolating toward the exactly known value at zero radius. Kinetic boundary layer effects increase the time needed for growth from 0 to 10 (or 2 1/2) velocity persistence lengths by roughly 35% (or 175%).

Fabrication of Ballistic Quantum Wires and Their Transport Properties

Abstract: Quantum wires with width less than the elastic mean free path and comparable to the Fermi wavelength are fabricated using high resolution electron beam lithography and ion beam etching. The low temperature magnetotransport properties of the quasi-ballistic channels reveal novel phenomena resulting from the ballistic motion of electrons. We propose new side-gate transistors. The two dimensional electron gas remaining at both sides of the channel is utilized to narrow the conduction width. This technique may open the way to control electrostatically an Aharonov-Bohm phase shift in the GaAs-AlGaAs loop.

Size and temperature dependence of thermoelectric power and electrical resistivity of vacuum-deposited antimony thin films

Abstract: Thin antimony films of thicknesses in the range 30 to 200 nm have been vacuum deposited on glass substrates at room temperature. After annealing for about an hour at 500 K, the thermoelectric power and electrical resistivity were measured in vacuum as a function of temperature. The thermoelectric power and electrical conductivity data were combined and simultaneously analysed using the effective mean free path theory of size effect in thin films developed by Tellier and Pichard et al. In addition, their temperature dependence was also analysed. It was found that the thermoelectric power is positive and increases with increasing temperature and is inversely proportional to the thickness of the film. The electrical resistivity was found to be temperature dependent with the temperature coefficient of resistivity being positive, and inversely proportional to the thickness of the film. Analysis combining the data from the thermoelectric power and electrical conductivity measurements has led to the determination of mean free path, carrier concentration, effective mass, Fermi energy and the parameter \(U_g = (d ln l_g /d ln E)_{E = E_F } \) The data were analysed for least squares fitting by local functions, such as the spline functions, which eliminates possible errors in conventional least squares fitting of data using non-local functions valid throughout the range.

Distribution of plasma density and potential around a mesothermal ionospheric object

Abstract: For an object moving at mesothermal speeds in a collisionless plasma it is shown that the ion thermal motion as well as the coupling of the disturbances in front of the object to the wake region play significant roles in modifying the plasma environment around the object. The case considered here is a dielectric cylinder moving transverse to its axis in ionospheric plasma. The radius of the cylinder is taken as much larger than the Debye shielding length of the ambient plasma but smaller than the mean free path of the charged particles. For this model, the Vlasov-Poisson system of equations is numerically solved to determine the distribution of charged particle densities and potential around the cylinder. An important feature of the present work is that a self-consistent solution is obtained without assuming any decoupling of the plasma in the wake and front regions and without neglecting thermal motion of the ions. The significance of this unified treatment of the environmental plasma in the prediction of possible ion shock wave disturbances is discussed. A range of ion Mach numbers which are typical of conditions found in the ionosphere is used to parameterize the dependence of the distribution of charged particle density on the object velocity. Finally, comparison of our results in the wake region with corresponding in situ measurements shows that the present model underestimates the measured ion depletion by less than an order of magnitude, in contrast to previous theoretical models which overestimate the measured ion depletion by several orders of magnitude.

Grain size-dependent Hall coefficient in polycrystalline copper films

Abstract: The Hall coefficients reported for polycrystalline copper films show a rather puzzling behaviour. This paper discusses systematic investigations of the temperature-dependent Hall coefficient for Cu films with known grain size. Grain boundary scattering will be shown to be dominant as soon as the grain size becomes smaller than the electronic mean free path due to scattering by phonons.

Computer analysis of Cs3Sb photocathodes

Abstract: The transport of photoelectrons through Cs 3 Sb photocathodes is studied by the Monte Carlo simulation technique. The mean free path, for energy loss to phonons, of energetic electrons in Cs 3 Sb has been found to be about 25 A. The modulation transfer function (MTF) of the Cs 3 Sb photocathodes, energy distribution and transit time spread (TTS) of emitted electrons have been obtained. In particular, the energy distribution of the emitted electrons has a very good agreement with the measured results. Computed results indicate that both the energy spread, defined as the full width of half-maximum of the energy distribution and the TTS of emitted electrons are significantly influenced by the incident photon energy. It is also proposed that reducing the thickness of the Cs 3 Sb photocathode is an effective method of decreasing the energy spread and TTS of emitted electrons.

Thickness measurement of thin dielectrics with electron spectroscopy

Abstract: Future generations of electronic components need new methods for thickness measurement. This paper demonstrates that electron spectroscopy is exact enough to measure thicknesses up to 15 nm with an accuracy better than 5%. The model of a constant mean free path of the electrons only varying with the material has to be modified. One has to observe the complete set of all parameters for such thickness measurements.

Dimensional Cross-Over in Thin Film Spin-Glasses

Abstract: Measurements of the electrical transport in the presence of a magnetic field for very thin spin-glass films of AuMn, AgMn and AuFe alloys, are reported. The influence of the effective dimensionality on the spin-glass order is studied by varying the film thickness between 4nm and 40nm. Weak electron localization and spin-glass resistivity measurements only provide a qualitative picture of the transition from spin-glass to Kondo behaviour in the thinnest films. Measuring the temperature dependence of the Hall resistivity on the other hand directly reflects the thickness dependence of the freezing temperature Tf. Our results clearly indicate that dimensionality effects as well as the reduced elastic mean free path influence the spin-glass transition. The experimental correlation length exponent v = 0.8 is smaller than the theoretically predicted value.