Electron Reflection Coefficient Research Articles

Grain size distribution and heat conductivity of copper processed by equal channel angular pressing

We report the results of measurements of the grain size distribution function and the thermal conductivity of ultrafine-grained copper produced by equal channel angular pressing (ECAP), with special attention to the evolution of these quantities with the number of pressing cycles. To explain the experimental findings, the equilibrium grain size distribution function (GSDF) evolving during ECAP has been calculated on the basis of a simplified theoretical model. The model involves a single unknown physical parameter—the most probable grain size. With this parameter fitted to the experimental data the calculated GSDF fairly closely reproduces the experimental data. A model for thermal conductivity of ECAP processed copper has been proposed, which relates thermal conductivity to the GSDF parameters and the coefficient of electron reflection at grain boundaries.

Spin-dependent transport in Fe andFe∕Aumultilayers

In situ resistance measurements of epitaxial Fe layers and $\mathrm{Au}∕\mathrm{Fe}$ bilayers were used to quantify the scattering in giant magnetoresistance (GMR) spin valve structures. The semiclassical Boltzmann transport equation, incorporating first-principles local density functional calculations, fitted the thickness dependence of the conductivity. Fits to the data indicate that Fe has a large spin asymmetry with bulk relaxation times ${\ensuremath{\tau}}_{\ensuremath{\downarrow}}=3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ and ${\ensuremath{\tau}}_{\ensuremath{\uparrow}}=2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. These give a conductivity equal to that of bulk Fe. The interface scattering from the $\mathrm{Fe}∕\mathrm{GaAs}$, the $\mathrm{Fe}∕\text{vacuum}$, and the $\mathrm{Au}∕\text{vacuum}$ interfaces is purely diffuse. This is in contrast to the high electron reflection coefficients determined from kinematical calculations using scanning tunneling microscope images. Fits to conductivity measurements of $\mathrm{Au}∕\mathrm{Fe}∕\mathrm{GaAs}(001)$ indicate that the Au films have the conductivity of bulk material modified only by interface scattering. The GMR of $\mathrm{Au}∕\mathrm{Fe}∕\mathrm{Au}∕\mathrm{Fe}∕\mathrm{GaAs}(001)$ structures is 1.8% at room temperature and 2.9% at 10 K. The magnetoresistance is reduced by the presence of partial diffuse scattering at the inner interfaces, as indicated by the fits to both the GMR and the Au conductivity. The GMR in $\mathrm{Fe}∕\mathrm{Au}$ structures is intrinsically low due to a large electron band mismatch between Au and Fe band structures.

Surface excitation parameter for semiconducting III–V compounds

In the rapid development of mesoscopic science, the study of surface excitations in solids and overlayer systems plays a crucial role. The surface excitation parameter which describes the total probability of surface plasmon excitations by an electron traveling in vacuum before impinging on or after escaping from a semiconducting III–V compound has been calculated for 200–2000eV electrons crossing the compound surface. These calculations were performed using the dielectric response theory with sum-rule-constrained extended Drude dielectric functions established by the fits of these functions to optical data. Surface excitation parameters calculated for InSb, InAs, GaP, GaSb or GaAs III–V compounds were found to follow to a simple formula, i.e. Ps=aE−b, where Ps is the surface excitation parameter and E is the electron energy. These surface excitation parameters were then applied to determine the elastic reflection coefficient for electrons elastically backscattered from III–V compounds using the Monte Carlo simulations. Good agreement was found for the electron elastic reflection coefficient between calculated results and experimental data.

Calculation of the effective gas interaction probabilities of the secondary electrons in a dc magnetron discharge

In sputter magnetrons the electrons emitted from the target, the so-called secondary electrons (SE), can be recaptured by the target. As a result, not all emitted SE will interact with the discharge gas. The effective gas interaction probability (EGIP) is the probability that an emitted SE interacts with the discharge gas, and thus is not recaptured by the target. To calculate the EGIP an analytical model is developed. The model is verified by comparing its results with those of a Monte Carlo model.The EGIP of an individual SE is strongly, and in a complex manner, dependent on the electric and magnetic field to which the electron is subjected and on its initial starting conditions. Therefore, it is useful to introduce the average EGIP of the discharge which is a weighted average of the individual EGIP values. The influence on the EGIP of different parameters, such as the initial energy of the SE, the electron reflection coefficient and the electric and magnetic field is discussed. For typical discharge conditions at a pressure of 0.5 Pa values for the average EGIP in the range of 0.25–0.35 are found. This means that the recapture probability lies typically between 65% and 75%, showing that it is necessary to take into account this process to accurately model and simulate the magnetron discharge.

Acoustoelectric effect in a finite-length ballistic quantum channel

The dc current induced by a coherent surface acoustic wave (SAW) of wave vector q in a ballistic channel of length L is calculated. The current contains two contributions, even and odd in q. The even current exists only in a asymmetric channel, when the electron reflection coefficients r_1 and r_2 at both channel ends are different. The direction of the even current does not depend on the direction of the SAW propagation, but is reversed upon interchanging r_1 and r_2. The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of r_1 and r_2. It is shown that both contributions to the current are non zero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as function of qL. These oscillations are the hallmark of the coherence of the SAW and are completely washed out when the current is induced by a flux of non-coherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.

Angular distribution of electrons elastically reflected from polycrystalline metals (Pd, In)

Elastic peak electron spectroscopy (EPES) is based on measurements of elastic electron reflection coefficients. The angular distribution in EPES depends on different parameters such as atomic number of the substrate, the energy of the electron beam and the geometry of the analysis system. In this study, we compare the measured angular distribution of electrons elastically reflected from Pd and In surfaces with Monte-Carlo simulations. We have used a theoretical approach based on knowledge of electron trajectories and interaction effects inside the samples. For the experiments, we have constructed a special rotary energy analyser with a small aperture. The angular distributions of elastically backscattered electrons at 500 eV resulting from Monte-Carlo simulations of electron transport for Pd and In (atomic numbers 46 and 49) compare very well with the corresponding experimental measurements.

A method of determining the electron reflection coefficient from the emitter surface in a thermionic-emission converter

A method is proposed for determining the transparency of the potential barrier at the surface of the emitter in a thermionic-emission converter by means of measured arc voltage-current characteristics. That method can also be used to determine the barrier transparency for the collector by measuring the voltage-current characteristics when the current flows from the collector to the emitter. The method can be used to track the variation in the reflection coefficient from the plasma for the emission electrons.

Elastic reflection of low-energy electrons from polycrystalline gold targets

Monte Carlo calculations to study the influence of solid-state, polarization, exchange and relativistic effects on the angular distribution and the reflection coefficient for electrons elastically reflected from gold surfaces have been performed. Elastic differential cross sections were determined using relativistic Dirac equations with a solid-atom potential including the polarization and exchange effects. Inelastic differential inverse mean free paths were computed using the extended Drude dielectric function for volume and surface excitations. These showed that the polarization effect made a contribution to elastic differential cross sections at small scattering angles, whereas, the exchange and relativistic effects contributed to these cross sections at large scattering angles. These effects are important to the angular distribution and the elastic reflection coefficient for electron energies below 400 eV. Monte Carlo results calculated in this work are in very good agreement with experimental data.

Anomalous surface core-level shifts in the hydrogen-induced reconstruction of W {100}

Shifts are reported in the W 4 f 7 2 core-level binding energy of surface atoms involved in the hydrogen-induced restructuring of W {100}. A detailed analysis of the data reveals anomalously large shifts peaking at hydrogen fractional surface coverages θ H ≈ 0.33 and θ H ≈ 0.53, amounting to a shift to higher binding energy in the clean-surface core level of as much as 430 ± 50 meV. By comparison with data from W {100} at saturation ( θ H = 2), where the shift is only ∼ 100 meV to higher energy compared to the clean surface core level, and data for H adsorption on other crystal planes, the large shift is mostly attributed to the pinching of pairs of surface W atoms induced by H adsorption at low coverages. The shift of ∼ 370 ± 50 meV associated with this reconstruction alone, to the exclusion of the influence of the adsorbate, is considerably larger than expected by comparison with extensive data for both the clean surface reconstruction on W {100} itself and on a range of other single-crystal planes of W. It is concluded that the anomalous shift is consistent with a hydrogen-induced inward displacement of the surface potential barrier, as deduced by Herlt and Bauer from electron reflection coefficient measurements. The coverage dependence of the core-level shifts (in particular their two maxima at θ H ≈ 0.33 and 0.53) provides evidences for the nature of both commensurate and incommensurate phases formed at the surface.

Unusual behavior of the electron reflection coefficient of asymmetric double-barrier quantum structures in a finite-amplitude rf field

The time-dependent Schrodinger equation describing the resonance interaction of electrons with a radio-frequency (rf) field is solved for asymmetric resonance-tunneling structures with thin, high barriers. It is found that in a number of cases the resonance reflection coefficient of such structures decreases almost to zero as the amplitude of the rf field increases. The conditions under which the largest number of electrons incident on the structure (in a number of cases 100%) interacts efficiently with an rf field with frequency ω and pass into a neighboring resonance level, emitting or absorbing a quantum of energy ħω, are determined.

Andreev reflection in point contacts between the heavy-fermion superconductor UPt 3 and ordinary superconductors

The differential resistance d V/d l versus applied voltage V of UPt 3—Zn point contacts at very low temperatures shows the double-minimum structure around V = 0 characteristic for Andreev reflection due to superconducting Zn. In magnetic fields above B c of Zn the d V/d I curves exhibit only a shallow minimum at V = 0 which is attributed to superconducting UPt 3. A fit of the d V/d I curves on the basis of the Blonder—Tinkham—Klapwijk theory taking into account a lifetime broadening Γ of the quasiparticle density of states yields for Zn an energy gap Δ( T) perfectly following the BCS theory, a barrier strength Z ∼ 0.45 and Γ ⩾ ¼ Δ 0. The usual Z value contradicts the notion of extremely high reflection coefficient of electrons at the interface with heavy-fermiom compounds due to their heavy masses. All this suggest that UPt 3 behaves in the contacts as normal metal, possibly with strong pair breaking taking into account the high Γ value. This might be the reason for the failure to observe a Josephson coupling in contacts UPt 3 with Zn, Pb, and NbTi.

Quantum interferences and interlayer exchange coupling in Co/Cu/Co(001)

The reflection coefficients for electrons at the Cu/Co(001) interface have been calculated at the Fermi energy, as a function of spin and in-plane wave vector. The results are in agreement with recent observations of quantum interferences in Cu overlayers on Co(001), reported from spin-polarized photoemission experiments. Then they are used to calculate the interlayer exchange coupling in Co/Cu/Co(001); good agreement with experimental results is obtained.

Influence of surface excitations on electrons elastically backscattered from copper and silver surfaces.

The influence of surface excitations on electrons elastically backscattered from solid surfaces is investigated. Elastic-scattering differential cross sections are calculated using the partial-wave expansion method and the finite difference techique for solid atoms with the Hartree-Fock-Wigner-Seitz potential. An extended Drude dielectric function which allows the characteristic oscillator strength, damping constant, and critical-point energy for each subband of valence electrons is employed to estimate electron inelastic mean free paths for volume excitations. The same dielectric function is applied to evaluate the probability of surface excitations for incident and escape electrons by including the recoil effect without the small-angle approximation. Results of Monte Carlo simulations on the elastic reflection coefficient and the angular distribution of electrons elastically backscattered from Cu and Ag surfaces are presented. It is revealed that surface excitations significantly reduce the elastic reflection coefficient for low-energy electrons, but less significantly influence the angular distribution for large escape angles. Our results agree very well with experimental data.

Simple effective mass model to include the effects of GAMMA - X mixing in multiquantum barriers

An extended effective mass model is developed to account for the possibility of mixing of the electron wave function from the Γ conduction-band state to the X conduction-band state. The strength of the mixing is determined by a mixing parameter Δ in association with the assumption of a finite interface thickness. For a simple quantum well, the model Δ compares favorably with more complicated empirical pseudopotential models, featuring complete descriptions of the band structure. A multiquantum barrier (MQB) has been designed. Using the single-band effective mass approximation model, for use in visible laser diode structures for enhanced electron confinement, it is clear that within the limitations of the model when mixing effects are accounted for, the degradation in performance is negligible. The MOB design compared with a single barrier of equivalent thickness shows a doubling of the electron reflection coefficient.

Electron scattering in an arbitrarily bent planar quantum channel

The bend region of a two-dimensional quantum channel of constant width is shown to generate a well-type effective potential in the problem of electron wave scattering. For narrow channels the longitudinal modes of electron propagation should be considered as approximately independent. In the one-mode approximation the coefficient of electron reflection is calculated and its non-monotonic dependence on the incident electron momentum and the channel bend angle is determined. The local maxima in the reflection coefficient decrease exponentially with increasing electron momentum and increase with increasing channel bend.

Adsorption of MgO on Mo(110)

Adsorption of MgO on Mo(110) is studied by means of AES, LEED, EELS, and work function measurements. It is found that there is a reduction of the value of intramolecular bonding charge of adsorbed MgO molecules in the submonolayer region. This value for a single adsorbed molecule is 1.0 (in e-units), i.e. by about 40% less than in the bulk MgO crystal (1.6). During adsorption a substantial change of the shape of the current–voltage curve in Anderson's method, due to the dielectric properties of the adsorbate, occurs. Concentration dependences of work function and reflection coefficient of low energy electrons are obtained. Data about the growth mode and superstructures are presented. [Russian Text Ignored]

Direct measurements of the transport of nonequilibrium electrons in gold films with different crystal structures.

The transport of femtosecond-laser-excited nonequilibrium electrons across polycrystalline and single-crystalline gold films has been investigated through time-of-flight measurements. The thicknesses of the films range from 25 to 400 nm. Ballistic electrons as well as electrons interacting with other electrons and/or with the lattice have been observed. The ballistic component dominates the transport in the thinner films, whereas the interactive transport mechanism is dominant at the upper end of the thickness range. A slower effective velocity of the interactive component is observed in the polycrystalline samples, and is assumed to arise from the presence of grain boundaries. The reflection coefficient of excited electrons at the grain boundaries is extracted from the experiment and is estimated to be r\ensuremath{\simeq}0.12. The experiment also suggests that thermal equilibrium among the excited electrons is not fully established in the first \ensuremath{\sim}500 fs after excitation.

Electrical resistivity of nanocrystalline copper

Nanocrystalline copper samples have been prepared in an opposed-targets sputtering (OTS) system, and the dc resistivity of such samples has been measured and analyzed. The results show that nanocrystalline copper samples have a much higher resistivity and a larger temperature dependence of the resistivity than bulk copper. These features can be understood by grain-boundary-enhanced scattering of electrons. The coefficient of electron reflection by grain boundaries in a nanocrystalline copper sample and its temperature dependence have been deduced and are discussed.

E(k) above the Vacuum Level from Low Energy Electron Reflection. ΓK Line of Cu and Ni

Incidence angle dependent electron reflection coefficient curves R(E) measured in the 0 to 30 eV range on Cu(111) and Ni(111) surfaces are analysed. With incidence scanning in ΓK azimuth, some extrema of the dR/dE curves are shown to manifest bands along the ΓK line of the Brillouin zone. Comparing the experimental angular dispersion of these extrema with its calculated counterpart, bands along ΓK are mapped. Experimental technique and details of calculation are briefly discussed. [Russian Text Ignored].

Variations of temperature coefficient and noise in thin Al and Al/Si resistors subjected to high current density

Electromigration (EM) in thin Al and Al/Si resistors was investigated by measuring the effect of the stress on the resistance, the temperature coefficientα, the low-frequency noise spectrum (20 mHz-1 Hz) and, for some Al samples, on the residual resistance atT = 11 K. It was found that the temperature coefficient variations versus the stress time have a different behavior for Al and Al/Si, that is an oscillation in the first part of the life of the sample and decreases in the last one, in the first case, whereas, in the second, only the oscillation was detected. This behavior, observed for the first time, has been modeled by means of the Mayadas theory, by supposing a Gaussian distribution of the reflection coefficient for electrons at the grain boundaries. The measurement of the residual resistance also supports the hypothesis that the behavior ofa andR o (the resistance value at 273 K) is mainly due to the modification of the grain-boundary structure and cannot be explained by taking in account only the variation of the residual resistivity. Besides, the noise measurements give a further proof that the origin of the 1/fg spectra in thin films subjected to high current density must be ascribed to phenomena occurring at the grain-boundaries which are correlated to the phenomena causing temperature coefficient variations.