Thin film with surface disorder in the average t-matrix approximation

The Average t-Matrix Approximation (ATA) is generalized for an inhomogeneous impurity concentration. For a thin film with surface impurities the ATA leads to complex surface energies.     

Theory of spin-polarized low-energy electron diffraction from ferromagnetics

A theory of elastic scattering of low-energy electrons is outlined, in which the electron-solid interaction contains two spin-dependent contributions: an elastic exchange-correlation part in the real ion-core potential and an inelastic imaginary part describing electron-hole excitation. Numerical calculations for the Fe(110) surface predict, for an unpolarized primary beam, large spin polarization effects (up to 60%), which are highly sensitive to the magnetization of the topmost stomic layer.     

The determination of surface debye temperatures from low-energy electron diffraction data

The temperature dependence of low-energy electron diffraction (LEED) intensities has often been interpreted with kinematic theory in terms of an effective Debye temperature θ_D^eff of the surface atoms. The validity of this procedure, often questioned in the literature, is tested with a computer experiment in which LEED spectra are calculated from dynamical theory (layer-KKR method) for a model of Ag{111} with a given value of θ_D^eff and then the usual kinematic formulae are used to re-extract the value of θ_D^eff. The results of the experiment indicate that this procedure yields rough values of the surface Debye temperature for electron energies higher than about 40 eV, which fluctuate substantially and tend to be somewhat smaller than that originally introduced into the model. At energies lower than about 40 eV the kinematically deduced values of θ_D^eff are too large by 10 to 15 %.     

Calculations of low-energy electron diffraction intensities from the polar faces of ZnO

If it is assumed that surface compounds obtained by gas adsorption on metal single crystals faces, are formed by adsorption of atoms on the “sites” of an undisturbed substrate, or of a slightly disturbed substrate, one is lead also to assume that the structures of surface compounds have high symmetries. For well-defined coincidence mesh between the surface compound and the substrate, by applying the 2D space groups (with or without a colored character), information can be obtained concerning the distribution of the adsorbed atoms, or the reconstruction of the substrate. In order to be able to go as far as a complete model, it is necessary to know the concentration of the adsorbed atoms accurately. The hypothesis of a high symmetry has been applied to simple surface compounds: the models of the structures which have been obtained are compared with previously proposed models.     

Measurement of surface defects by low-energy electron diffraction

Low-energy electron diffraction is capable of detection of non-periodic arrangements by spot profile analysis (SPA-LEED). All kinds of defects may be identified by a qualitative and nevertheless systematic evaluation of the diffraction pattern with respect to spot shape, background and energy dependance. It is shown that the kinematical approximation provides far reaching results. The importance and achievements of the newly developed high-resolution instrumentation is demonstrated. The quantitative evaluation provides data on defect density and distribution, which are not available otherwise, as demonstrated with examples. A comparison of imaging and diffraction techniques shows the special advandages of diffraction with respect to quantitative analysis.     

A method to obtain kinematic intensities from low-energy electron diffraction data

In order to use low-energy electron diffraction as a tool for surface crystallography, it would be useful to extract the single scattering, or kinematic part, from the intensity data. Details of a method to do this by taking data with different diffraction geometry but at fixed momentum transfer are presented. The method is illustrated by data from Ni and Ag. The temperature dependence of the averaged intensity is presented. The multiple scattering contributions to the averaged intensity can be accounted for by an effective atomic scattering factor. Conditions for the applicability of the method are discussed. From the resulting kinematic intensities, the surface atomic arrangements can be determined by simple modifications of conventional crystallographic analysis.     

Correlation of electron self-energy with geometric structure in low-energy electron diffraction

In low-energy electron diffraction (LEED) studies of surface geometries where the energy dependence of the intensities is analyzed, the in-plane lattice parameter of the surface is usually set to a value determined by x-ray diffraction for the bulk crystal. In cases where it is not known, for instance in films that are incommensurate with the substrate, it is desirable to fit the in-plane lattice parameters in the same analysis as the perpendicular interlayer spacings. We show that this is not possible in a conventional LEED I(E) analysis because the inner potential, which is typically treated as an adjustable parameter, is correlated with the geometrical structure. Therefore, without having prior knowledge of the inner potential, it is not possible to determine the complete surface structure simply from LEED I(E) spectra, and the in-plane lattice parameter must be determined independently before the I(E) analysis is performed. This can be accomplished by establishing a more precise experimental geometry. Further, it is shown that the convention of omitting the energy dependency of the real part of the inner potential means geometrical LEED results cannot be trusted beyond a precision of approximately 0.01 ?.     

Kinematic simulation of convergent beam low-energy electron diffraction patterns

Kinematic simulations are used to investigate the geometrical properties of convergent beam low-energy electron diffraction patterns from an Si(0 0 1) surface. Compression of a low-energy electron microscope immersion lens is included explicitly and the sensitivity of patterns to surface reconstruction and dimer buckling is investigated. Key pattern features and whole pattern symmetries are identified from the simulations and interpreted geometrically. Advantages over conventional low-energy electron diffraction techniques are identified.     

The Coulomb sum for electron scattering in the relativistic random phase approximation

The Coulomb sum value for electron scattering is estimated using the relativistic random phase approximation (RPA) in the field theory for nuclear matter. RPA correlations due to σ-, ω- and ϱ-meson exchanges reduce the sum value of the relativistic Hartree approximation by about 15–20%.     

Computations of profiles of low-energy electron diffraction beams for arrays of ordered islands

In an attempt to determine the influence of the presence of adjacent islands on LEED beam profiles, an excluded area model has been proposed to describe the relative positions of ordered islands on a crystal surface. On the basis of this model, overlayers of different island density have been created on a finite lattice using a simple computer algorithm. The LEED from these overlayers has been calculated kinematically. Although the placement of the islands is not random, this does not perturb the LEED beam profile observably. Therefore, the kinematically diffracted intensity depends solely on the distribution of island sizes. Using this result, the intensity and half-width as functions of coverage have been calculated for one model of island growth.     

A study of ion-core potentials used in low-energy electron diffraction calculations

Various models for the construction of ion-core potentials presently used in LEED intensity spectra calculations are tested for nickel. We find that self-consistent iterations of these ion-core potentials do not produce significant improvement over the simple linear superposition scheme in building LEED potentials. For the exchange part of the potential, the non-local Hartree-Fock scheme works poorly compared to the Slater approximation. The better results of the Slater exchange are attributed to its compensating for the omission of correlation effects from the Hartree-Fock formula.     

A study of the nitridation of silicon surfaces by low-energy electron diffraction and auger electron spectroscopy

Low-energy electron diffraction (LEED) and Auger electron spectroscopy (AES) have been used to study the initial stages of the nitridation of silicon. Most of the experiments involved pressures of 10^?5?10^?7 torr of ammonia and silicon temperatures in the range 800–1100°C. An earlier study of the nitridation of the Si (111) surface, has been extended to allow comparison between the (111), (311) and (100) faces of silicon. These surfaces provide a series of unit meshes with different shapes and symmetries while retaining some common geometrical features. Of particular interest for epitaxial theory is the growth of an impurity induced nitride structure, which is common to both Si(111) and Si (311). This may be explained if the nucleation and orientation of the niti ide are determined by the geometry of localised sites, common to both substrates. Subsequent growth of the nitride layer is then dominated by intra-layer bonding, so that the difference in substrate symmetries has little effect.     

Spin polarization in low-energy electron diffraction from Au(110): Theory and experiment

A special LEED system has been constructed, in which the gun is movable in front of the grids and diffracted beams can be extracted through a probe hole in the screen. The polarization is subsequently measured by means of Mott scattering. The Au(110) surface is of particular interest, because it shows a reversible structure transition, which manifests itself in LEED intensities as a change from a (1 × 2) pattern at low temperatures to a (1 × 1) pattern at higher temperatures. For the (1 × 1) structure, spin polarization was measured, with values up to 70%, and calculated for a number of beams as a function of energy and scattering angle. Theoretical and experimental results are in reasonable agreement. In particular, the polarization is found to depend sensitively on geometrical, electronic and vibronic properties of the surface.The experimental work was sponsored by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 128     

On the validity of the random phase approximation for pairing vibrations of closed shell nuclei

Energy loss measurements on solid xenon applying 51 keV-electrons are reported. The spectrum shows excitonic structure and a plasma loss. From the energy loss function —Im1/g3 optical constants are calculated by means of a Kramers-Kronig transform. They are compared with optical absorption spectra and found to be in good agreement. An appendix gives detailed information about the calculation of —Im 1/g3 from energy loss measurements.     

Spin polarization in low-energy electron diffraction from Pt(111): Experiment and theory

Spin polarization in low-energy electron diffraction from the (111) surface of platinum, which is geometrically unreconstructed, was measured by means of a Mott detector. Corresponding relativistic calculations yield mostly excellent agreement with the data and clearly favour an ion-core scattering potential model containing an energy-dependent exchange approximation.