layer-KKR Method Research Articles

Band structure of surface states and resonances for clean Cu(1 1 0) surface

We have used the layer KKR method to calculate the Shockley and Rydberg surface states and resonances for Cu(1 1 0) for a given model of the surface potentials. This method has not been used before to predict all of the surface band structure for the energy range from the bottom of the conduction band to ∼7 eV above the vacuum level. The previous methods that used only local electron interactions in ab initio calculations could not produce the Rydberg surface barrier bands while those relying on nearly-free-electron parameterisation of bands could not deal with d-bands.

EELS investigation of FeCo/SiO2 nanocomposites

The factors that determine the local magnetic properties of FeCo/SiO2 nanocomposite powders and films have been analysed by electron energy-loss spectroscopy (EELS) and transmission electron microscopy (TEM). Attention has been given to the chemical composition, the local electronic structure and the atomic arrangement. The results show that the nanoparticles from sol-gel prepared powders are generally Fe-rich, whereas they are Co-rich in sol-gel prepared films. In addition, a subnanometre oxide layer at the surface of the FeCo nanoparticles has been clearly observed in the powder sample. It is found that the magnetic moment should be partly governed by alloying effects. Numerical values of the near-surface magnetic moment have been obtained using the ab-initio layer-KKR method. These values should be helpful in understanding the layer-by-layer changes of the white line ratio close to the surface of the nanoparticles.

Theory of surface electromigration on heterogeneous metal surfaces

We report a calculation of the magnitude of the wind force for the self-electromigration of adatoms on heterogeneous metal surfaces. Using a layer-KKR method we computed the wind valence of adatoms within small monolayer islands and voids on Cu(100). We show that the electromigration driving force felt by an adatom is significantly altered by the scattering of carriers among neighboring atoms within the island. Using the results of these calculations as input to kinetic Monte-Carlo simulations, we explore how this inhomogeneity of the wind force is manifest in the driven surface diffusion of Cu islands on a current-carrying Cu(100) substrate.

Applications of the layer-KKR method to photonic crystals

A brief introduction of the layer-Korringa-Kohn-Rostoker method for calculations of the frequency band structure of photonic crystals and of the transmission and reflection coefficients of light incident on slabs of such crystals is followed by two applications of the method. The first relates to the frequency band structure of metallodielectric composites and demonstrates the essential difference between cermet and network topology of such composites at low frequencies. The second application is an analysis of recent measurements of the reflection of light from a slab of a colloidal system consisting of latex spheres in air.

On the possibility of observation of electronic states of metallic atomic wire on Ni(001) surface with angle-resolved photoemission

The possibility of the observation of the one-dimensional electronic state on a metallic atomic wire on a metallic surface by using the angle-resolved photoelectron spectrum is investigated. The ARUPS program of the one-step model with the layer KKR method has been used where the so-called ‘6 eV satellite’ is excluded because it is out of the scope of this calculation. The muffin-tin potentials we used were produced using the self-consistent full-potential LMTO method. Nickel atomic wires on a nickel(001) surface have been considered as an example of the atomic wire. A peak about 6 eV below the Fermi level was observed in our calculated spectra. This peak has dispersion only along the direction of the atomic wire and has had no interaction with other atomic wires. Thus, the peak is identified as an isolated one-dimensional electronic state on the atomic wire. The result can be applied to any metallic surfaces.

Computation of Complex Band Structures and Transmission Spectra of 2-D Photonic Crystals Using a Layer-KKR Method

The photonic band structures of 2-D photonic crystals consisting of cylindrical dielectric rods on a square and on a triangular lattice are computed by a layer-KKR method. The matrices involved in the present method are substantially smaller than those required for the plane-wave method. Unlike the KKR method, a root searching procedure is not needed. In addition, with this method, the attenuation lengths for frequencies within the forbidden bands are computed together with the band structure. Reflection and transmission characteristics of crystals of finite thicknesses, as well as defective and composite crystals, are also computed.

Surface sensitivity in self-consistent calculation of angle-resolved photoemission for Cu(100)

Because the well-known slab model is of no avail to calculate the electronic band structure in the surface-normal direction, it is very difficult to perform a direct experimental check of the calculated surface electronic structure by first-principles self-consistent calculations. In our calculation for Cu(100), we substitute self-consistent potentials of the Cu atom made by LAPW into the well-established photoemission calculation program code with the layer-KKR method. The result shows us that the angle-resolved ultraviolet photoemission spectroscopy (ARUPS) spectrum is very sensitive to the surface and the self-consistency of the calculation. Thus, we can use such a calculation to check electronic potentials made by self-consistent first-principles calculation.

Theory of negative ion formation in CO chemisorbed on Ni(110): the 2∑ shape resonance

The lifetime, energy and angular distributions for resonance electron scattering by the 2∑ shape resonance of CO chemisorbed on Ni(110) are calculated using a layer-KKR method. This calculation is based upon a multiple scattering approach to negative ion formation at surfaces in which the substrate scattering is fully incorporated. The results are compared to the experimental study of Jones et al. [Chem. Phys. Lett. 161 (1989) 467] and a prior coupled-angular-modes (CAM) study by Teillet-Billy and coworkers that considered only the screening of the negative ion by the metallic substrate [Nucl. Instrum. Methods 58 (1991) 393].

Theory of surface electromigration on metals: application to self-electromigration on Cu(111)

We present a calculation of the force, due to electron scattering, acting upon an adatom at the surface of a current-carrying metal, i.e., the so-called “wind” force in surface electromigration. The force is calculated from the Feynman-Hellmann theorem in which the electron scattering states are computed with full multiple scattering corrections by a layer-KKR method. In contrast to previous jellium models, this approach allows the proper treatment of electron scattering by both the surface barrier and the substrate and its effect upon the current-carrying states at the surface. The electron scattering force is computed for the self-electromigration of Cu adatoms on Cu(111). At room temperature, the effective valence of the adatom is found to be ≈ −21. We conclude that surface electromigration of Cu on Cu(111) is dominated by the electron scattering force and that any direct force originating from charge transfer to the adatom is likely to be unimportant in this case. The implications of the computed value of the wind force for the mass transport at a current-carrying metal surface are discussed.

A Simple Derivation of the Layer-Kkr Theory of Leed

ABSTRACTThe equations of the layer-KKR method for finding the intensities of electrons diffracted by a semi-infinite layered structure are derived in a simple way by use of three identities relating spherical and plane waves and by use of a compact notation. The third identity, which transforms a sum of outgoing spherical waves on a twodimensional array intoa sum of plane waves or beams, is a very useful simplification of the derivation, which does not appear in texts on LEED. Explicit linear equations are derived for amplitudes of outgoing spherical waves produced by diffraction of an incident beam first by a singleBravais net and then generalized to a composite layer made up of several Bravais nets; matrix elements of the beam reflection and transmission matrices for a single Bravais netand for a composite layer are given, and also the exact interlayer matrix equation for the reflection matrix of the semi-infinite structure.

Electron reflectivity calculation for hydrogen on Pd(111)

The nonselfconsistent layer KKR method was used to calculate both electron reflectivities up to 12 eV above the vacuum level and angle resolved photoemission for hydrogen on Pd(111) modeled by an ordered adlayer. Spectral features sensitive to the hydrogen adsorption are related to the band structure in the particular direction in the reciprocal space in both the occupied and empty state regions. Special attention was dedicated to the relation between the input potentials and the structural parameters. In particular we have confirmed the existence of the surface resonance near the M̄ point in the surface Brillouin zone with the specific dispersion related to H coverage.

Relativistic theory of photoemission and bremsstrahlung from ferromagnets

On the basis of an effective Dirac-Hamiltonian, which describes the interaction of a quasiparticle or quasihole with a semi-infinite crystalline ferromagnet well below the Curie temperature, a one-step-model Green function theory of energy-, angle- and spin-resolved ultraviolet photoemission and bremsstrahlung is formulated. The elastic photocurrent spin density matrix is evaluated in a manner analogous to a Schrodinger-equation-based layer-KKR method (due to Pendry). Since the authors spin-dependent formalism includes both spin-orbit coupling and magnetic exchange, its applicability extends from ferromagnets a fortiori to non-magnetic materials, in particular those with strong spin-orbital coupling.

The chain method of LEED/MEED intensity analysis for the study of NaCl structure

The chain method of LEED/MEED intensity analysis for metal surfaces is generalised to cover the case of insulators and semiconductors which have two non-equivalent atoms A and B per two-dimensional unit mesh. Some test calculations are performed for MgO(100) surface and the results are compared with those obtained from the layer-KKR method. It is found that the generalised chain formula is computationally fast for normal-incidence LEED and is particularly useful for off-normal LEED and MEED.

A fast method of LEED/MEED intensity calculation for the study of diatomic surfaces

The interchain scattering formula of LEED/MEED intensity calculations for the study of metal surfaces is generalized to study diatomic surfaces. The efficiency of the method is investigated by comparing the results of intensity calculations for the NaCl (100) surface structure with those obtained from the layer-KKR method. We find that the interchain scattering formula for diatomic surfaces has several computational advantages over the layer-KKR method and can be used to extend the calculation to higher incident energies.

Layer-by-layer low-energy electron diffraction and two-dimensional space group symmetry

The wave field of LEED in a 2D structure is symmetrised with respect to the structure's 2D space group (2D structure meaning diperiodic structure composed of one or several 2D periodic overlayers lying in register on the 2D periodic face of a crystal). Attention is focused on the layer-KKR (Korringa-Kohn-Rostoker) method, the wave representations of which are beams outside layers and partial waves inside layers. It is shown how the field of beams and the field of partial waves are made globally symmetric representations of the 2D space group, how the 2D translations of an individual layer (giving rise to local 2D von Laue diffraction conditions) divide the beams into independent bundles and, further, how local point-group symmetry arranges the bundles in 'irreducible sequences' and combines the partial waves into 'irreducible showers'. The theory is applied to three examples of overlayer structures on surfaces of face-centered cubic crystals, and the coding of the scheme of symmetrisation is discussed.

Surface crystallography of the c(2×2) sodium overlayer on Al(100)

Experimental LEED intensity-energy spectra are reported for clean Al(100) and for c(2×2) Na on Al(100). The experimental results are compared with spectra calculated with the layer-KKR method and found to be in good agreement for both the clean surface and the overiayer. For the overlayer, the best agreement is obtained for Na atoms in the four-fold hollow site at a perpendicular distance of 2.05 ± 0.1 Å.

LEED‐Intensitätsspektren verschiedener Oberflächen des kubisch‐raumzentrierten α‐Eisens

AbstractLEED intensity spectra of clean Fe(100)‐, Fe(110)‐ and Fe(111)‐surfaces are calculated and compared with experimental curves of various authors. The Layer KKR method succesfully used for fcc‐lattices was applied to bcc‐lattices up to electron energies of 500 eV. Good conformity of theoretical and experimental spectra was established by taking into consideration a sufficient number of beams (up to 61) and a sufficient number of phase shifts (up to 8).

The structure of overlayers: III. Nitrogen on Mo {001}

The Mo {001} c (2 × 2) — N structure formed upon adsorption of a monolayer of nitrogen on a clean Mo {001} surface is studied by means of low-energy electron diffraction (LEED). Diffracted intensities for a large number of integral-order and half-order beams are calculated with the layer KKR method for different structural models and compared with extensive experimental data. Best overall agreement between calculated and observed LEED spectra is found for a model in which N atoms are adsorbed in the four-fold pyramidal hollows formed by four adjacent Mo atoms on a net consistent with c (2 × 2) symmetry. However, the fit between theory and experiment is good only for certain beams, much less good for others. Attempts at improving the fit by varying the values of structural and non-structural parameters used in the calculations have not been succesful. We raise the question of the significance of a structure model for which the fit with experiment is wholly satisfactory only for certain beams.

Symmetrization of low-energy electron diffraction patterns

Using the layer-by-layer approach to low-energy electron diffraction (LEED) the authors explain how to symmetrize the beam scattering matrix for layers. The coincidence structure formed by the layers may be dense or open and may possess any of the 17 two-dimensional space group symmetries. The beams of the electron field become diffracted by the layers in a manner determined by von Laue's diffraction conditions. These conditions turn out to arrange the beams in mutually independent bundles. After establishing the transformation properties of bundles of beams under the point group part of the two-dimensional space group the authors derive a scheme for finding symmetrized combinations of interacting beams. The formalism is applied to the layer-KKR method for LEED calculation. In particular the symmetrization of the beam patterns created by three overlayer structures on surfaces of face-centred cubic crystals are described: the primitive 2*2 structure and the ( square root 2* square root 2)45 degrees structure on the (100) surface together with the ( square root 3* square root 3)30 degrees structure on the (111) surface.

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 %.