Low-energy Electron Diffraction Theory Research Articles

Light scattering and absorption by two-dimensional arrays of nano and micrometer monodisperse spherical silver particles

The problem of light scattering and absorption is considered for a free-standing two-dimensional array (monolayer) of nano- and micrometer spherical silver particles. To solve this problem for short- and imperfect long-range ordered arrays the statistical theory of multiple scattering of waves is used. The key points of the developed semi-analytical method are described. The method is based on the quasicrystalline approximation and the multipole expansion of electromagnetic fields and the dyadic Green's function in terms of vector spherical wave functions. Results for the angular distribution of scattered light, the coefficients of coherent transmission and reflection, incoherent scattering, and absorption of a monolayer are obtained for a spectral range corresponding to the nanoparticle plasmonic resonance. Some features of light propagation through two-dimensional arrays of particles with different spatial order are investigated and discussed. The results are in close agreement with the existing experimental data for a partially ordered array and the calculations for a regular array obtained under the extended low-energy electron diffraction theory.

Atomic structure of “multilayer silicene” grown on Ag(111): Dynamical low energy electron diffraction analysis

We have investigated the atomic structure of the “multilayer silicene” grown on the Ag(111) single crystal surface by using low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). We measured the intensity of the LEED spot as a function of the incident electron energy (I–V curve) and analyzed the I–V curve using a dynamical LEED theory. We have found that the Si(111)(3×3)-Ag model well reproduces the I–V curve whereas the models consisting of the honeycomb structure of Si do not. The bias dependence of the STM image of multilayer silicene agrees with that of the Si(111)(3×3)-Ag reconstructed surface. Consequently, we have concluded that the multilayer silicene grown on Ag(111) is identical to the Si(111)(3×3)-Ag reconstructed structure.

Theory of low-energy electron diffraction for nanomaterials—subclusters, automatedsearches

To enable the determination of detailed structures of nanomaterials, we have previously made thetheory of low-energy electron diffraction (LEED) much more efficient for complex and disorderedsystems, calling it NanoLEED: our cluster approach speeds up the computation to scale asnlogn, rather thanthe standard n3 or n2,with n the number of atoms, for example. Strong multiple scattering may occasionally cause poorconvergence: this is solved here by treating all scattering within subclusters of a few atoms (e.g. aSiH3 group) with accurate matrix inversion. For the structure determination of complexnanostructures, an efficient search method is also essential: for that purpose amodified version of tensor LEED is here adapted to nanostructures, and calledNanoTensorLEED.

Photonic band gap in thin wire metamaterials

We investigate the band structure of a class of photonic crystals made from only thin wires. Using a different method, we demonstrate that a complete photonic band gap is possible for such materials. Band gap materials normally consist of space filling dielectric or metal, whereas thin wires occupy a very small fraction of the volume. We show that this is related to the large increase in scattering at the Brillouin zone boundary. The method we developed brings together the calculation techniques in three different fields. The first is the calculation of scattering from periodic, tilted antennas, which we improve upon. The second is the standard technique for frequency selective surface design. The third is obtained directly from low energy electron diffraction theory. Good agreements with experiments for left handed materials, negative materials, and frequency selective surfaces are demonstrated.

Dissociative electron attachment on surfaces and in bulk media

A theory of dissociative electron attachment to molecules condensed at surfaces and embedded within bulk media is developed. The theory of low-energy electron diffraction is used to obtain the width for electron-molecule resonance scattering in the condensed phase from the width for the gas phase. It is then employed for the calculation of dissociative attachment in the framework of the nonlocal complex potential theory. Specific calculations using the effective mass approximation are carried out for electron attachment to $\mathrm{C}{\mathrm{H}}_{3}\mathrm{Cl}$ and $\mathrm{C}{\mathrm{F}}_{3}\mathrm{Cl}$ molecules physisorbed on the surface of a Kr film. The role of image states and image-potential resonances is analyzed. The results show an increase by several orders of magnitude in the cross section for physisorbed molecules as compared with gas-phase molecules. This is in general agreement with the measured cross sections. However, the position of the peak in the cross section for $\mathrm{C}{\mathrm{H}}_{3}\mathrm{Cl}$ is significantly shifted towards higher energies as compared to experiment [K. Nagesha et al., J. Chem. Phys. 114, 4934 (2001)], and the magnitude of the calculated cross section for $\mathrm{C}{\mathrm{F}}_{3}\mathrm{Cl}$ at the surface is significantly higher than the measured value. Possible reasons for disagreements are analyzed.

Theory of low-energy electron diffraction for detailed structural determination of nanomaterials: Finite-size and disordered structures

We describe how a recent efficient theory of low-energy electron diffraction (LEED) enables the determination of finite-size and disordered nanostructures. Our cluster approach, called NANOLEED, speeds up the computation to scale as $n\phantom{\rule{0.2em}{0ex}}\mathrm{log}\phantom{\rule{0.2em}{0ex}}n$, rather than the usual ${n}^{3}$ or ${n}^{2}$, with $n$ the number of atoms, for example, thereby making nanostructures accessible. To illustrate this method's capability to determine nanoscale structure, we apply it to calculate LEED intensities for Si nanowires of various lengths and thicknesses as well as for various deviations of these nanowires from the ideal Si bulk structure.

Theory of low-energy electron diffraction for detailed structural determination of nanomaterials: Ordered structures

To enable the determination of detailed structures of nanomaterials, we extend the theory of low-energy electron diffraction (LEED) to become more efficient for complex and disordered systems. Our new cluster approach speeds up the computation to scale as $n\phantom{\rule{0.2em}{0ex}}\mathrm{log}\phantom{\rule{0.2em}{0ex}}n$, rather than the current ${n}^{3}$ or ${n}^{2}$, with $n$ the number of atoms, for example, making nanostructures accessible. Experimental methods to measure LEED data already exist or have been proposed. Potential application to ordered nanoparticles are illustrated here for ${\mathrm{C}}_{60}$ molecules adsorbed on a $\mathrm{Cu}(111)$ surface, with and without coadsorbed metal atoms, as well as for adsorbed carbon nanotubes. These demonstrate sensitivity to important structural features such as size and deformation of the nanostructures.

Structure of the hydrogen-stabilizedMgO(111)−(1×1)polar surface: Integrated experimental and theoretical studies

The surface structure of $\mathrm{MgO}(111)\text{\ensuremath{-}}(1\ifmmode\times\else\texttimes\fi{}1)$ bulk and thinned single crystals have been investigated by transmission and reflection high-energy electron diffraction, low-energy electron diffraction (LEED), and x-ray photoelectron and Auger electron diffraction. The $(1\ifmmode\times\else\texttimes\fi{}1)$ polar surface periodicity is observed both after 800 \ifmmode^\circ\else\textdegree\fi{}C annealing in air and also after oxygen plasma cleaning and annealing in ultrahigh vacuum. The x-ray photoelectron spectroscopy and diffraction results were analyzed by simulations based on path-reversed LEED theory and by first-principles calculations to help distinguish between different mechanisms for the stabilization of this extremely polar oxide surface: (1) stabilization by adsorption of a hydrogen monolayer; maintaining the insulating nature of the surface and (2) stabilization of the clean O or Mg terminated $1\ifmmode\times\else\texttimes\fi{}1$ surface by interlayer relaxations and two-dimensional surface metallization. The analysis favors stabilization by a single OH layer, where hydrogen sits on top of the O ions with O-H bond distance of 0.98\AA{}. The in-plane O and Mg positions fit regular rocksalt sites, the distance between the topmost O and Mg plane is 1.04 \AA{}, contracted by $\ensuremath{\sim}14%$ with respect to bulk MgO distance of 1.21 \AA{}, while the interlayer separation of the deeper layers is close to that of bulk, contracted by less than 1%. The presence of a monolayer of H associated with the terminal layer of oxygen reduces significantly the surface dipole and stabilizes the surface.

Structure and formation of the Al( [formula omitted])- [formula omitted]R27°-Na phase: a LEED, DFT and HRCLS study

Adsorption of 0.2 ML Na on Al(1 0 0) at room temperature yields a disordered Al(1 0 0)-(1×1)-Na phase, which transforms reversibly to a well-ordered Al(1 0 0)- ( 5 × 5 )R27° -Na phase on cooling below 250 K. Based on low energy electron diffraction (LEED) and high resolution core-level spectroscopy (HRCLS) measurements, and on ab initio calculations, it is concluded that the structure of the Al(1 0 0)- ( 5 × 5 )R27° -Na phase consists of Na atoms occupying substitutional sites. The structural parameters obtained from LEED and density functional theory analyses are in quantitative agreement. Adsorption of 0.2 ML Na at 100 K yields an Al(1 0 0)- c(2×2)-Na island structure, which transforms irreversibly into the ( 5 × 5 )R27° -Na structure by annealing above 190 K. The nature of the reversible and irreversible phase transformations to the ( 5 × 5 )R27° structure is investigated by HRCLS and LEED.

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.

Photoelectron diffraction intensity calculation by using tensor low-energy electron diffraction theory

We applied the tensor low-energy electron diffraction (LEED) approximation to photoelectron diffraction (PED) for efficient structural searches of complex surfaces including multiple parameters to be optimized. It turned out that the tensor LEED scheme can be included into the multiple-scattering cluster model usually utilized for PED intensity calculation with slight modification concerning the treatment of the atomic displacements of photoelectron emitters. The results of numerical calculation for a simple system show that the approximation is applicable to PED over almost the same range of displacements as in tensor LEED.

Electron inelastic mean free path, electron attenuation length, and low-energy electron-diffraction theory

Low-energy electron diffraction (LEED) theory is used for describing the electron transport in crystalline solids with the purpose of determining the electron attenuation length. The inelastic scattering of the primary electron in the electron gas of the material is introduced into the LEED theory in terms of the electron inelastic mean free path derived by Tanuma, Powell, and Penn from the Lindhard dielectric function and optical data [Surf. Interface Anal. 17, 911 (1991)]. The theorem of flux reversal for electrons in situations of inward and outward propagation is deduced from local inversion symmetry and specific boundary conditions at the sources. The theory is applied to 50\char21{}400 eV electrons incident on the three low-index surfaces of copper, and a fair agreement is found with a previous Monte Carlo simulation of the electron transport in amorphous copper. In addition to the inelastic electron-electron gas scattering, the inelastic electron-phonon scattering has a significant effect on the attenuation length in a crystalline material. The temperature parameter, necessary in a LEED calculation, does not occur in current Monte Carlo simulations. Common scattering potential models, at low energy, for LEED and for Auger electron spectroscopy and x-ray photoemission spectroscopy are discussed.

Fivefold surface of quasicrystalline AlPdMn: Structure determination using low-energy-electron diffraction

The atomic structure of the fivefold symmetric quasicrystal surface of icosahedral AlPdMn has been investigated by means of a dynamical low-energy-electron diffraction (LEED) analysis. Approximations were developed to make the structure of an aperiodic, quasicrystalline surface region accessible to LEED theory. A mix of several closely similar, relaxed, bulklike lattice terminations is favored, all of which have a dense Al-rich layer on top followed by a layer with a composition of about 50% Al and 50% Pd. The interlayer spacing between these two topmost layers is contracted from the bulk value by 0.1 \AA{}, to a final value of 0.38 \AA{}, and the lateral density of the two topmost layers taken together is similar to that of an Al(111) surface. The LEED structural result is qualitatively consistent with data from ion scattering spectroscopy, which supports an Al-rich termination.

Structure of Ni(100)-c(2 x 2)-Na: A LEED analysis.

The structure of Ni(100)-c(2\ifmmode\times\else\texttimes\fi{}2)-Na has been investigated by analysis of extensive new low-energy electron-diffraction (LEED) data. The structure is found to contain Na atoms adsorbed in fourfold hollow sites on an unreconstructed and essentially unrelaxed substrate. The Na-Ni layer spacing is 2.38\ifmmode\pm\else\textpm\fi{}0.04 \AA{} and the first Ni-Ni layer spacing is 1.75\ifmmode\pm\else\textpm\fi{}0.01 \AA{}. These results are in good agreement with the conclusions of an early study by Demuth et al. [J. Phys. C 8, L25 (1975)]. Good agreement between experimental and calculated LEED intensities is obtained using the dynamic theory of LEED, with a conventional, muffin-tin potential for the adsorbed Na atoms and a step potential at the surface. The good agreement pertains not only to the energy positions and relative intensities of peaks in intensity-energy spectra for the diffracted beams, but also to the relative beam intensities, which span a range of nearly two orders of magnitude.

ANOTHER UNUSUAL ADSORPTION SITE FOR ALKALI ADSORPTION ON A METAL, FOUND BY AUTOMATED TENSOR LEED ON A NOTEBOOK COMPUTER: ${\rm{Rh}}\left( {111} \right) - \left( {\sqrt 3 \times \sqrt 3 } \right)R30^ \circ -{\rm{Na}}$

The surface structure of [Formula: see text] has been analyzed with dynamical low-energy electron diffraction (LEED) at 30 K: a simple Na overlayer is found adsorbed in the unusual hcp-hollow site. LEED theory and computer power have progressed to the point where such a detailed surface structure determination, which includes fitting many structural parameters, is routinely possible even with a portable computer, in this instance a 486/25 MHz notebook computer, using automated tensor LEED.

Adsorption and adsorbate-induced restructuring: a LEED perspective

The history of the surface crystallography of adsorbates on single crystals is reviewed, with emphasis on the development and contributions of low-energy electron diffraction (LEED). Highlighted aspects include: progress in LEED instrumentation and theory; atomic and molecular adsorption on metals and semiconductors; coadsorption; disordered overlayers; adsorbate-induced relaxations and reconstructions; and cluster-like bonding.

Low-energy electron diffraction calculations using a parallel supercomputer

A first implementation of a dynamical low-energy electron diffraction theory on a parallel supercomputer is described. The computational performance of the Duke-Laramore-Beeby LEED formulation is demonstrated using an Intel iPSC TM/860 parallel computer. The algorithm developed is highly parallelizable and scales nearly ideally with the number of nodes used. A performance equivalent to that experienced using a Cray YMP was attained with as few as 16 nodes. However, it was not possible to exceed significantly the YMP performance due to the increasing inter-node communication overhead. A simple mathematical model is described to explain this limitation, which is encountered in all parallel computing applications and hardware designs. The model indicates that an alternate parallelization scheme is required to attain greater performance.

Chemical substitution of surface atoms in structure determination by tensor low-energy electron diffraction.

We present a chemical perturbation method for surface-structure determination by low-energy electron diffraction (LEED). It is based on tensor LEED theory and is able to substitute selected surface atoms by other chemical species making full dynamical calculations for the structure unnecessary. The potential of the approach is demonstrated for the determination of the surface stoichiometry of substitutionally disordered alloys, for the switching from one adsorbate species to another, and for the generation of superstructures by substitution of surface atoms by vacancies.

Prediction of image-state excitation by secondary beams in inverse-photoemission spectroscopy.

Excitation of image states is predicted to occur frequently in inverse-photoemission spectroscopy due to diffracted electron beams traveling almost parallel to the surface. A simple kinematic model, as well as full calculations using inverse low-energy electron-diffraction theory, show the effect in the case of Cd(0001).

Scattering of electromagnetic waves by periodic structures

The authors consider periodic structures made of spheres embedded in a host material with a different dielectric function. They show how to calculate the reflection and transmission of electromagnetic waves by a slab of the material parallel to a given crystallographic plane. The method of calculation is based on a doubling-layer scheme which obtains the reflection and transmission matrix elements for the multilayer from those of a single layer. The reflection and transmission characteristics of the slab are related to the complex band structure of the photon field associated with the given crystallographic plane of the corresponding infinite crystal, which is introduced in the manner of the low-energy electron diffraction theory. They present numerical results which demonstrate the applicability of the method to real systems of current interest and point out some interesting physics which arose from their calculations. They show in particular that the nondegenerate bands of the photon field at the centre of the surface Brillouin zone do not couple to the incident radiation, leading to total reflection at normal incidence.