Inelastic Low-energy Electron Diffraction Research Articles

Inelastic low energy electron diffraction at metal surfaces

The role of incident electrons penetration under a metal surface in electron energy loss spectroscopy is considered within the fully quantum-mechanical approach. The stabilized jellium model of the surface in the semi-infinite geometry and the time-dependent local density approximation for the dynamical response are used. The travel of the projectile electron inside the target metal is treated within the kinematic low energy electron diffraction theory. Confirming our simplified hard-wall reflection model results [Phys. Rev. B 59 (1999) 9866], the dramatic enhancement of the multipole plasmon peak as compared with the dipole-mode calculations is obtained for Na and Cs, which is in a qualitative agreement with the experiment. However, for K the calculation fails to explain the experiment, which discrepancy is discussed and the future improvements of the method are outlined.

Investigation of the oxidized (001) tungsten surface by means of ILEED

Inelastic low energy electron diffraction (ILEED) effects have been applied to investigate the initial stages of oxidation on a (001) oriented single tungsten crystal. The electron energy loss spectra (EELS) have been measured as a function of the primary electron energy, E p. The energy was kept within the range: 45 eV < E p < 100 eV. To show the diffraction effect after loss we have used the kinetic model. The electron intensity, I = I( E), integrated over a ring input slit of a CMA, has been calculated as a function of the kinetic energy. The calculation has been performed in the k vector representation. The experimental and the theoretical results have been compared and shown to be in quantitative agreement with each other. A set of EEL spectra measured as a function of E p for the tungsten surface covered with a monolayer of oxide has shown the diffraction effect which was adequate to a (2 × 1) structure of an overlayer. As a result of the band transition investigation an agreement with some features of electronic structure of WO 3 has been found. The peaks at 4.0 eV and 7.2 eV observed in experimental EEL spectrum at E p = 55 eV are also present in a simulated EEL spectrum based on the density-of-states (DOS) function calculated for WO 3.

Investigations of the band transitions in ruthenium (0001)

Inelastic low energy electron diffraction (ILEED) effects have been found in electron energy loss spectroscopy (EELS) of the ruthenium (0001) surface. In the experiment a cylindrical mirror analyzer (CMA) has been used. The EEL spectra were measured as a function of the primary electron energy E for E < 100 eV. The energy losses within 10 eV from the elastic peak were studied. Disregarding the electron-phonon interaction the looses are due to the electron-electron interaction in this region. Thus, observed loss peaks have been discussed taking into account band transitions in a ruthenium crystal.

An ILEED study of the density-of-states function of tungsten

Electron energy loss spectroscopy (EELS) and inelastic low-energy electron diffraction (ILEED) have been combined to study the density-of-states (DOS) function in tungsten. The EELS spectra measured as a function of the primary electron energy E p ( E p < 100 eV) by means of a CMA spectrometer are interpreted in terms of the angular-resolved EELS taking into account the electron diffraction phenomena. As a result, we could correlate the EELS spectrum measured at a particular value of E p with the one-dimensional DOS function. In addition, the LEED intensity theory, which we used in this work, has permitted us to estimate whether the correlation should be made with the surface-localized DOS (i.e. SDOS) or the bulk DOS (i.e. BDOS). Our experimental ILEED results are in good agreement with the theoretical DOS function published by Christensen and Feuerbacher [Phys. Rev. B 10 (1974) 2349]. In particular the energy gap in the theoretical electron structure along the [110] direction has been confirmed experimentally.

High-resolution temperature-dependent inelastic low-energy electron diffraction applied to the surface-plasmon dispersion of aluminum (100)

Elastic and inelastic low-energy-electron-diffraction measurements on a clean A1(100) surface have been obtained with a new high-resolution electron diffractometer. These data, together with data obtained independently at another laboratory, provide the experimental basis for the determination of the surface-plasmon dispersion relation. A survey of specular elastic scattering is used to select elastic resonances which may be described by single scattering theory. Inelastic data are presented which are associated by two-step inelastic scattering with the selected elastic diffraction resonances. The temperature dependence of the inelastic coherent and diffuse scattering is also examined and its effect on the measurement of the surface-plasmon dispersion relation is discussed.

Inelastic low-energy electron diffraction from a silicon (111) 7 × 7 surface

Inelastic low-energy electron diffraction from a silicon (111) 7 × 7 surface

Apparatus for the measurement of angle-resolved spectra of electrons emerging from single crystals

An apparatus to measure inelastic low-energy electron diffraction (ILEED) and energy- and angular-dependent secondary electron emission, (EADSEE), is described. The apparatus can measure EADSEE for incident beam energies of up to 200 eV and ILEED for beam energies up to 50 eV, with energy and angular resolutions of about 0.15 eV and 1.5°, respectively. General design criteria are discussed, and detail is provided where a little-known technique has been employed.

Precision determination of surface plasmon dispersion on Al(111) films via inelastic low-energy electron diffraction: C B Duke et al, (Proc 19th Nat Symp Am Vac Soc) J Vac Sci Technol, 10 (1), Jan/Feb 1973, 183–187

Precision determination of surface plasmon dispersion on Al(111) films via inelastic low-energy electron diffraction: C B Duke et al, (Proc 19th Nat Symp Am Vac Soc) J Vac Sci Technol, 10 (1), Jan/Feb 1973, 183–187

Quantum Field Theory of Inelastic Diffraction. IV. Applications to Al(100) and Al(111)

Results are presented of numerical calculations of the inelastic-low-energy-electron-diffraction (ILEED) intensities of electrons inelastically scattered into the (00) beam from Al(100) and Al(111) via the emission of bulk and surface plasmons. The calculations are based on the isotropic-scatterer version of the theory described in Paper III of this series. The results exexhibit three important systematic features. First, dynamical effects (i.e., those not evident in a kinematical two-step model) are prominent in plots of diffracted intensity versus incident-beam energy (energy profiles), smaller in plots of these intensities versus the electron's exit angle (angular profiles), and unimportant in plots of scattered intensities versus energy loss (loss profiles). Second, dynamical effects in the energy profiles are readily discernible even for weak electron-ion-core scattering. Finally, the contributions to the diffracted intensities due to the "three-step" diffraction-before-and-after-loss processes are found to be exceedingly small relative to those associated with the "two-step" processes of diffraction before or after loss. These features permit us to draw two important conclusions from our analysis. First, the extraction from experimental ILEED intensities of surface-plasmon dispersion relations may be based on a kinematical two-step model provided the analysis is confined to a consideration of loss and angular profiles. Second, the consequences of the vestiges of momentum conservation normal to the surface in a kinematical-model calculation of the excitation of bulk plasmons cannot be distinguished clearly from those of multiple elastic scattering. Thus kinematical momentum-conservation conditions for motion normal to the surface seem to be entirely irrelevant in the interpretation of ILEED intensities.

Inelastic Low-Energy Electron Diffraction Measurements on Al (111)

An experimental study has been made of electrons in the energy range 40–80 eV, inelastically scattered and diffracted from a clean Al(111) surface. The surface is prepared by epitaxial vapor deposition on a Si(111) single-crystal surface in ultrahigh vacuum immediately preceding the measurements. The inelastic electron intensity at a given energy loss and angle is obtained as the energy derivative of the amplified electron current from a Faraday collector having a retarding field analyzer and limited angular acceptance. The energy derivative comes from the digitally computed average of a repeatedly measured difference in dc signal accompanying a fixed increment in retarding field. Using this method inelastic angular and loss profiles at 15° incidence have been obtained in the vicinity of a Bragg maximum of the 00 elastic beam. The profiles show structure related to the surface and volume plasmon momenta by a two-step model of inelastic diffraction. Dispersion data inferred by applying this model to the “loss-before-diffraction” structure are compared with results from other sources. The surface plasmon dispersion obtained from inelastic low energy electron diffraction measurements shows promise as a new means of characterizing solid crystalline surfaces.

Elastic and Inelastic Low-Energy Electron Diffraction (LEED) from Solids

A brief survey of some of the recent literature on elastic and inelastic low-energy electron diffraction (LEED) from solids is given, Our present knowledge of the electron-solid force law is discussed. The state of the art of theoretical model calculations of LEED intensity profiles is described and compared with the current status of experimental measurements. Prescriptions for obtaining surface crystallographic information directly from the experimental LEED profiles are described. The use of inelastic LEED as a spectroscopic probe of the electronic excitations of the surface region of solids is also mentioned.

Elastic and Inelastic Low-Energy Electron Diffraction (ELEED, ILEED) from an Al(100) Surface

Elastic and inelastic low-energy electron diffraction (ELEED, ILEED) observations have been made on a clean surface of Al (100). Measurements on the (10) and (11) elastic diffraction beams were made using normally incident electrons in the energy range 30≤E≤170 eV. Peaks in the energy loss distribution are seen near 5.5, 10, 15, 26, and 31 eV, the dominant peaks near 10 and 15 eV corresponding to surface and bulk plasmon excitations, respectively. Two types of structure are observed in the inelastic angular profiles: one closely correlated with the structure in the elastic angular profile and the second being substructure corresponding to different ILEED conditions. Intensity profiles (as a function of incident energy) for the (10) and (11) elastic and inelastic diffraction beams have been measured. These profiles also show primary and secondary structure. The experimental results agree with the theoretical predictions of Duke et al.

Surface Magnons and Analytic Continuation in the Cubic Systems

Magnetic excitations localized on the (001) surface of a cubic Heisenberg ferromagnet are considered theoretically by extending previous calculations by several authors, where only a simple cubic spin lattice was considered, to b. c. c. and f. c. c. spin lattices. The method can be easily generalized to any crystal symmetry, or any orientation of the axis of magnetization, assumed normal to the surface. This extension of the theory makes it possible to undertake in the future a comparison of theoretical calculations of the surface magnon despersionrelation, with, for instance, results of experiments with inelastic low energy electron diffraction on surfaces of, e. g. , some ferromagnetic rare-earth salts. The relationship has been shown between the surface spectrum and the analytic continuation to the complex k 3 plane of the bulk magnon dispersion relation, where a very close analogy can be found with the theory of surface electronic states in semiconductors.

Measurement of Surface-Plasmon Dispersion in Aluminum by Inelastic Low-Energy Electron Diffraction

Analysis of the inelastic differential cross section for low-energy ($10\ensuremath{\lesssim}E\ensuremath{\lesssim}{10}^{3}$ eV) electron scattering from single-crystal solid surfaces permits the determination of the dispersion relation of the excitations created by the electron. With energies measured in eV and momenta parallel to the surface, ${p}_{\ensuremath{\parallel}}$, in ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, the surface-plasmon dispersion for Al(111) is $\ensuremath{\hbar}{\ensuremath{\omega}}_{s}({p}_{\ensuremath{\parallel}})=10.1\ensuremath{-}0.7{p}_{\ensuremath{\parallel}}+10{{p}_{\ensuremath{\parallel}}}^{2}$ and its damping is ${\ensuremath{\Gamma}}_{s}({p}_{\ensuremath{\parallel}})=0.9+0.7{p}_{\ensuremath{\parallel}}$.

Excitation Dispersion from Inelastic Low-Energy Electron Diffraction

Combined inelastic scattering and diffraction (inelastic diffraction) provide a means of observing low-energy electrons which have produced electronic excitation in bulk single crystals. In principle, the energy-versus-momentum dispersion of the excitations can be inferred, provided the momentum supplied by the lattice can be determined. The present work shows the feasibility of extracting dispersion data from inelastic diffraction measurements. A close analogy is found between inelastic and elastic diffraction (LEED) intensities at normal and at varying incidence, respectively. This identifies the diffracting reciprocal-lattice element and its momentum contribution in the inelastic case. Dispersion data in the 11 azimuth of a tungsten (110) surface are compared with the free-electron volume and surface-plasmon dispersion relations. Discrepancies are found indicating departure from free-electron-like behavior. Also, the excitation which has been previously assigned to a surface plasmon fails to show the appropriate dispersion characteristics. Inner potential corrections are discussed, and the equivalence of the inner potential for elastic and inelastic diffraction is pointed out.

Sideband diffraction: A prediction of the quantum field theory of inelastic low-energy electron diffraction from solids

A quantum field theory of inelastic electron diffraction is proposed and utilized to calculate the differential inelastic scattering cross section in fourth-order perturbation theory. The vestiges of momentum conservation normal to the surface cause the occurence of a new phenomenon: sideband diffraction.