Conventional Low-energy Electron Diffraction Research Articles

Time-dependent density-functional theory simulation of electron wave-packet scattering with nanoflakes

Low-energy electron scattering with nanoflakes is investigated using a time-dependent density functional theory (TDDFT) simulation in real time and real space. By representing the incident electron as a finite-sized wave packet, we obtain diffraction patterns that show not only the regular features of conventional low-energy electron diffraction (LEED) for periodic structures but also special features resulting from the local atomic inhomogeneity. We have also found a signature of $\ensuremath{\pi}$ plasmon excitation upon electron impact on a graphene flake. The present study shows the remarkable potential of TDDFT for simulating the electron scattering process, which is important for clarifying the local and periodic atomic geometries as well as the electronic excitations in nanostructures.

Determination and correction of distortions and systematic errors in low-energy electron diffraction

We developed and implemented an algorithm to determine and correct systematic distortions in low-energy electron diffraction (LEED) images. The procedure is in principle independent of the design of the apparatus (spherical or planar phosphorescent screen vs. channeltron detector) and is therefore applicable to all device variants, known as conventional LEED, micro-channel plate LEED, and spot profile analysis LEED. The essential prerequisite is a calibration image of a sample with a well-known structure and a suitably high number of diffraction spots, e.g., a Si(111)-7×7 reconstructed surface. The algorithm provides a formalism which can be used to rectify all further measurements generated with the same device. In detail, one needs to distinguish between radial and asymmetric distortion. Additionally, it is necessary to know the primary energy of the electrons precisely to derive accurate lattice constants. Often, there will be a deviation between the true kinetic energy and the value set in the LEED control. Here, we introduce a method to determine this energy error more accurately than in previous studies. Following the correction of the systematic errors, a relative accuracy of better than 1% can be achieved for the determination of the lattice parameters of unknown samples.

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 Å.

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.

Local structural and compositional determination via electron scattering: Heterogeneous Cu(001)-Pd surface alloy

We have measured the structure and chemical composition of ultrathin Pd films on Cu(001) using low-energy electron microscopy. We determine their local stoichiometry and structure, with 8.5 nm lateral spatial resolution, by quantitatively analyzing the scattered electron intensity and comparing it to dynamical scattering calculations, as in a conventional low-energy electron diffraction (LEED)-IV analysis. The average t-matrix approximation is used to calculate the total atomic scattering matrices for this random substitutional alloy. As in the traditional LEED analysis, the structural and compositional parameters are determined by comparing the computed diffraction intensity of a trial structure to that measured in experiment. Monte Carlo simulations show how the spatial and compositional inhomogeneity can be used to understand the energetics of Cu-Pd bonding.

Low energy electron diffraction and low energy electron microscopy microspot I∕V analysis of the (4×4)O structure on Ag(111): Surface oxide or reconstruction?

A low energy electron diffraction (LEED) I/V analysis was performed of the (4 x 4) oxygen structure on Ag(111). Two data sets were used, one recorded with a conventional LEED system and a second with a low energy electron microscope (LEEM). The data sets agree well with each other, demonstrating that I/V structure analyses can be performed with the same quality with LEEM as with conventional LEED. The structure obtained confirms the recently proposed model that involves a reconstruction of the Ag(111) surface. Previous models based on a thin layer of Ag(2)O that had been accepted for more than 30 years are disproved. The reconstruction model contains two units of six triangularly arranged Ag atoms and a stacking fault in one half of the unit cell. The six O atoms per unit cell occupy sites in the trenches between the Ag(6) triangles. Small lateral displacements of the Ag atoms lift the mirror symmetry of the structure, leading to two nonequivalent groups of O atoms. The atoms of both groups are located approximately 0.5 Angstrom below the top Ag layer, on fourfold positions with respect to the top layer Ag atoms. Ag-O distances between 2.05 and 2.3 Angstrom are found. The oxygen atoms exhibit large static or dynamic displacements of up to 0.3 Angstrom at 300 K.

Interaction of SO3 with c-ZrO2(111) films on Pt(111)

Single-crystalline sulfated c-ZrO2(111) films of the cubic (c) type have been prepared by reactive deposition of Zr onto Pt(111) in an O2 atmosphere and subsequent exposition to a SO3 atmosphere. The morphology, atomic structure, and composition have been examined by scanning tunneling microscopy, low-energy electron diffraction (LEED), Auger electron spectroscopy, and density functional theory (DFT) calculations. The clean c-ZrO2(111) films display a (2x2) surface structure. During SO3 exposure at room temperature, a clear (radical3xradical3)R30 degrees structure develops. At about 700 K, the SO3-induced (radical3xradical3)R30 degrees structure disappears and the bright (2x2) LEED pattern of the clean ZrO2 films reappears. The energies of plausible c-ZrO2(111)/SO3 structures have been examined by DFT. The (radical3xradical3)R30 degrees structure found in the experiments turned out to be the most stable one for temperatures below 700 K. At temperatures around 700 K, a disordered low coverage structure may exist, which can not be observed by conventional LEED. A comparison of cubic zirconia surfaces with the alternative tetragonal system yields similar results for the SO3 adsorption in the DFT calculations and shows that c-ZrO2 surfaces are good models for the industrial used tetragonal ZrO2 supports.

A molecular T-matrix approach to calculating Low-Energy Electron Diffraction intensities for ordered molecular adsorbates

We present a novel approach to calculating Low-Energy Electron Diffraction (LEED) intensities for ordered molecular adsorbates. First, the intra-molecular multiple scattering is computed to obtain a non-diagonal molecular T-matrix. This is then used to represent the entire molecule as a single scattering object in a conventional LEED calculation, where the Layer Doubling technique is applied to assemble the different layers, including the molecular ones. A detailed comparison with conventional layer-type LEED calculations is provided to ascertain the accuracy of this scheme of calculation. Advantages of this scheme for problems involving ordered arrays of molecules adsorbed on surfaces are discussed.

低エネルギー電子顕微鏡／光電子顕微鏡の開発と応用 ＬＥＥＭによるＳｉ（１１１）およびＨ／Ｓｉ（ＩＩＩ）上のＣｕナノ構造形成過程の動的観察と構造解析

The growth processes of Cu nano-structure on hydrogen terminated Si(111) surfaces were investigated by low energy electron microscopy (LEEM). The structure analysis of the Cu nano-structure was also carried out by low energy electron diffraction (LEED) using a LEEM apparatus. Cu nano-structures grow preferentially at step edges and domain boundaries. LEED patterns observed in LEEM show a different dependence on electron energies observed by using the conventional grid-type LEED optics. Taking this difference into consideration, we carried out a structure analysis of Cu nano-structures. It is shown that the Cu nano-structure is a β-phase Cu-Si alloy structure, and has {554} and {15 16 13} facets.

Avoidance ofghost atoms in holographic low-energy electron diffraction (LEED)

It is pointed out that real-space images recovered from LEED I /Edata by the current holographic reconstruction algorithm can containstrong artifacts which can be misinterpreted as atomic images(`ghost atoms'), thereby misguiding a subsequent structuralrefinement through conventional LEED. We show that such ghost atomscan be avoided by using an alternative approximation to the kernelin the reconstruction integral. This is demonstrated for bothcalculated and experimental intensities of the structure considered,i.e. a (2×2) phase of 6H-SiC(0001̄). A theory is alsodeveloped for a practical implementation of a more general kernelwhich fully takes account of the scattering of an electron by thesubstrate atoms before its first encounter with the adatom(beam splitter).

Real-time monitoring of phase transitions of vacuum deposited organic films by molecular beam deposition LEED

We describe a special low energy electron diffraction (LEED) system that allows us to record diffraction patterns during the adsorption process of vacuum-deposited organic thin films. With this instrument that combines Knudsen cells within a reverse view LEED instrument we can evaporate three different organic materials independently and simultaneously from each other. In contrast to conventional LEED, this molecular beam deposition LEED (MBD–LEED) allows us to study the kinetics of structural phase transitions from the sub-monolayer regime up to several layers without changing the position of the sample which is located on a temperature-controlled sample holder. The performance of the device is demonstrated by a growth study of perylene-3,4,9,10-tetracarboxylic-dianhydride on Ag(110). A phase transition was in situ observed after the preparation of a single domain oriented homogeneous monolayer (“brick stone”) structure to a condensed (“herring bone”) structure which is commensurate in one direction.

A new approach to obtaining Kikuchi electron diffraction patterns for holographic imaging

A newly developed method is reported here for taking Kikuchi electron diffraction patterns using conventional low-energy electron diffraction facilities. Kikuchi electron forward-scattering diffraction patterns from a single crystal Cu(111) surface have been obtained using a hemispherical rear-view LEED screen and camera interfaced to a computer. The new technique allows us to take a set of Kikuchi electron diffraction images over a wide primary energy range (50–950 eV in steps of 5 eV) within a couple of hours. With this technique we show that the Kikuchi electron, like the photoelectron and Auger electron, can be considered as being emitted from inside the crystal.

Homoepitaxial growth on Pd(100)

We have studied the temperature- and coverage-dependent variation of diffraction-spot profiles during growth of Pd on Pd(100), using conventional low-energy electron diffraction (LEED). The crystal temperature is varied from 100 to 500 K during deposition, and the coverage is varied from 0 to 5 monolayers. The diffraction spot profiles are separable into two components: the Bragg peak, reflecting layer occupations; and a broad “foot”, reflecting the distribution of particles within layers. Between 200 and 400 K, the broad component adopts a ring-like appearance, with intensity maxima bracketing the Bragg peak. Development of the ring structure is associated with the onset of diffusion at 170–200 K (activation barrier of 12–14 kcal/mol). The diameter of the ring indicates an average separation between island centers of 28 ± 5 Å, at 300 K and at coverages below the onset of coalescence. Oscillations in the ring intensity as a function of coverage occur out-of-phase with oscillations in the Bragg intensity, and are associated with the successive filling of individual layers. By 500 K, both oscillations disappear, apparently due to the advent of step propagation as a major mechanism for film growth when diffusional processes accelerate.

A direct inversion method for surface structure determination from LEED intensities

LOW-ENERGY electron diffraction (LEED) has become the most successful technique in surface crystallography1, but because of the complexity of the surface-electron scattering interactions, analyses of LEED data are still conducted on a trial-and-error basis: a direct-inversion method for treating LEED intensity data remains an attractive goal2. Building on recent theoretical and experimental developments in electron holography from surface structures3–16, we show here that three-dimensional images with atomic resolution can be obtained by a direct transform of conventional LEED intensity spectra.

A real-space multiple scattering theory of low energy electron diffraction: a new approach for the structure determination of stepped surfaces

A new theory of Low Energy Electron Diffraction (LEED) is presented in which the relevant multiple scattering equations are solved in the angular momentum representation within the framework of real-space multiple scattering theory (RS-MST). This approach avoids the plane wave basis used in many conventional LEED techniques and its associated limitations when applied to the calculation of LEED intensities from open surfaces containing small bulk interplanar spacings. In particular, high Miller index, stepped surfaces which lie beyond the present capabilities of conventional LEED, can now be treated in a relatively efficient and convergent manner. The new theory is tested by evaluating I–V spectra from the (100), (311), (331) surfaces of Cu which are compared with the results of a layer doubling (LD) LEED calculation. Excellent agreement is obtained in the (100) and (311) cases, for which the LD approach is expected to be applicable. The (311) surface is about the highest index fcc surface which can reasonably be attempted with the existing approaches. The results obtained for the case of the (331) surface using the LD and the RS-MST approaches agree up to about E = 100 eV, beyond which the LD process fails to converge. We discuss and contrast the convergence properties of both methods.

Cluster multiple-scattering theory for medium-energy electron diffraction.

A theory of medium-energy (100--5000-eV) electron diffraction (MEED) is developed from a multiple-scattering, curved-wave theory of photoelectron diffraction. It may be called ``near-field expansion in clusters.'' Only selected important scattering events are included and these are computed in times proportional to electron wave number by using a generalized scattering-factor method (conventional low-energy electron-diffraction methods require computations proportional to at least the fourth power of the wave number, while the ``chain'' method for MEED scales as at least the square of the wave number). This removes the most serious barrier to a multiple-scattering analysis for surface-structure determination. A direct summation over atoms and scattering paths is used, avoiding any assumptions of periodicity in the surface structure. The theory allows a clearer understanding of the relationship between diffraction intensities and surface structure than heretofore possible.

Roughening of Si (111) surface under high-temperature thermal cycling

High-resolution low-energy electron diffraction has been used to study the generation of defects on the surface of commercial Si (111) wafers under high-temperature thermal cycling in ultrahigh vacuum. We observed a gradual increase of single-atomic step density from 0.15 to 0.30% after several thermal annealings at ∼1200 °C. However, a reduction of step density, accompanied by a change of step height from single-atomic to double-atomic step height, was observed after the sample was annealed to near melting temperature (∼1400 °C). At the same time, the surface was broken into micrograins having a small mosaic orientation. Due to the limited instrumental resolution, these low-density step structures and the small-angle mosaic structures cannot be resolved by using the conventional low-energy electron diffraction technique.

Further observations with low-energy electron diffraction for the Cu(100)-(2 × 2)-S surface structure: spot-profile and multiple-scattering analyses

This study involves analyses by low-energy electron diffraction (LEED) for surface structures formed by S adsorbed on the (100) surface of copper. A LEED spot-profile investigation for a surface that shows a (2 × 2) diffraction pattern, supplemented by the effects of antiphase scattering, indicates that the domain boundaries do not correspond to microregions with local c(2 × 2) structure but rather that the beam elongations observed are consistent with local regions of the c(4 × 2) type in the approach to ¼ monolayer coverage. Diffracted-beam intensity-versus-energy curves calculated for the (2 × 2), c(2 × 2), and (2 × 1) translational symmetries, for fixed adsorption sites and S–Cu interlayer spacings, show that the intensity curves of corresponding beams can remain closely independent of actual symmetry and coverage even as the polar angle of incidence θ departs from the normal (although differences between the curves do tend to increase with θ). This observation can help simplify calculations of LEED intensities from adsorption systems with large unit meshes when the adsorbed species are in a constant environment; also, it provides an economical route for checking values of θ estimated from positions of diffraction spots on conventional LEED screens. When the latter is tested on the off-normal intensity data used in our previous analysis of the Cu(100)-(2 × 2)-S surface structure (Surf. Sci. 177, 329 (1986)), θ is indicated to be modified by 1° from the previously estimated value, but this does not significantly affect the determined S–Cu nearest neighbour bond length.

A Leed Investigation of (111) Oriented Si, Ge and GaAs Surfaces Following Pulsed Laser Irradiation

ABSTRACTThe low energy electron diffraction (LEED) patterns obtained from clean (111) oriented Si, Ge and GaAs single crystals subsequent to their irradiation with the output of a pulsed ruby laser in an ultra-high vacuum (UHV) environment suggest that metastable (1×1) surface structures are produced in the regrowth process. Conventional LEED analyses of the Si and Ge surfaces suggest that they terminate in registry with the bulk but that the two outermost interlayer spacings differ from those of the bulk. For the case of Si these changes are a contraction of 25.5 ± 2.5% and an expansion of 3.2 ± 1.5% between the first and second and second and third layers respectively.