A direct inversion method for surface structure determination from LEED intensities

Low energy electron diffraction (LEED) intensities have been measured for the (110) and (111) faces of GaP. The LEED intensities of the (110) face have been analyzed using a dynamical multiple-scattering model of the diffraction process. The intralayer multiple scattering is treated exactly, while for the interlayer multiple scattering, the renormalized-forward-scattering method is used. Comparison of the calculated and observed LEED intensities suggests that both the Ga and the P atoms on the (110) face may exhibit a contracted outermost layer spacing with a rippled geometry. The surface layer is compressed by about 5% such that the top layer spacing is reduced by 0.1 Å. The P atoms protrude from the surface, whereas the Ga atoms are displaced inward such that no nearest-neighbor bond lengths are altered. LEED intensity analysis of the first order beams indicates that the bond-rotational angle ω is approxiimately 27 °. The quality and stability of the LEED patterns of the Gap (110) and (111) faces have been compared with the LEED patterns of the GaAs (110) and (111) faces. It is concluded that the Gap (110) face is less stable than the GaAs (110) face, but the Gap (111) face is far more stable than the GaAs (111) face. Phosphorus atoms start vaporizing from the GaP (111) face at an annealing temperature of 650 °C. Continued heating at 650 °C for 10 min resulted in a complete vaporization of phosphorus atoms and left a pure gallium surface layer on the GaP (111) face. A clear 1×1 threefold symmetry LEED pattern was observed on this Ga and Gap (111) surface. This indicates that the gallium atoms crystallize on the Gap (111) face and it appears reasonable to conclude that a good Schottky contact would be relatively easy to obtain on the GaP (111) face.

We report on the temperature dependent low energy electron diffraction (LEED) studies of 12 nm epitaxial Sr3Ir2O7(001) thin films. The Debye temperature has been extracted from the temperature-dependence of LEED intensity at elevated temperatures and different electron kinetic energies. For the most surface sensitive LEED, obtained at the lowest electron kinetic energies, the extracted surface Debye temperature is 270 ± 22 K, which is much lower than the 488 ± 40 K Debye temperature obtained using higher electron kinetic energies. Surprisingly, the LEED diffraction intensity, at the lowest electron kinetic energies, increases rather than decreases, with increasing sample temperatures up to about 440 K. This anomalous behavior has been attributed to the reduction of the lattice vibrational amplitudes along the surface normal. This damping of the normal mode vibrations with increasing temperature results from the enhanced electronic screening via thermally activated carriers. This scenario is corroborated by the transport measurement, showing that Sr3Ir2O7is a narrow band Mott insulator with a band gap of about 32 meV. We have identified criteria for finding anomalous scattering behavior in other transition metal oxide systems.

The surface reconstructions of the (100) crystal faces of iridium, platinum and gold: I. Experimental observations and possible structural models

The structure of Rh(111)(2 × 2)-3CO from LEED intensities: Simultaneous bridge and near-top adsorption in a distorted compact hexagonal CO overlayer

Four aspects of low-energy electron diffraction (LEED) have been investigated: interpretation of spot patterns to determine the surface unit cell and possible ambiguities, development of a photographic method for measuring angles of incidence and determining alignment of the LEED instrument, study of reliability factors used for intensity analysis, and justification for equivalent beam averaging. The interpretation of LEED spot patterns to determine the geometry of the surface unit cell can be involved when there are several symmetrically equivalent structural domains contributing to the pattern. Complex patterns can be deciphered by the algorithm described in Chapter II. The algorithm determines a surface unit cell that is often unique but not always, as where a p(2 x 2) pattern from a fcc(111) surface can be produced by a true (2 x 2) overlayer or by three domains of a (2 x 1) structure. This ambiguity arises on surfaces with 6m symmetry, such as fcc(111) and hcp(0001), for spot patterns with threefold rotational symmetry. In Chapter III, a broadly applicable photographic method for measuring angles of incidence and determining the alignment of the LEED instruments is described. Two published methods for determining the angle of incidence are special cases of this general procedure. The procedure extends the photographic methods and facilitates the verification of the alignment of the components of the LEED instrument. Reliability factors are used to evaluate correspondence between computed and observed LEED intensity spectra. Zanazzi and Jona, Pendry, and Sobrero and Weinberg have proposed reliability factors that are examined in Chapter IV. Chapter V provides a theoretical analysis and shows that averaging over momentum space gives the best resolution of the surface structure while energy averaging smears out information in the intensity spectra. Chapter VI provides a theoretical basis for the procedure of equivalent beam averaging, which provides a first-order correction to LEED intensities for systematic error due to angular misalignment of the incident beam and corrects for misorientation (where the actual surface plane is at a slight angle to the desired crystal plane). The potential of higher-order corrections is discussed.

The surface structure of Bi(111) was investigated by low-energy electron diffraction (LEED) intensity analysis for temperatures between 140 and $313\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and by first-principles calculations. The diffraction pattern reveals a $(1\ifmmode\times\else\texttimes\fi{}1)$ surface structure and LEED intensity versus energy simulations confirm that the crystal is terminated with a Bi bilayer. Excellent agreement is obtained between the calculated and measured diffraction intensities in the whole temperature range. The first interlayer spacing shows no significant relaxation at any temperature while the second interlayer spacing expands slightly. The Debye temperatures deduced from the optimized atomic vibrational amplitudes for the two topmost layers are found to be significantly lower than in the bulk. The experimental results for the relaxations agree well with those of our first-principles calculation.

Band structure treatment of low energy electron diffraction intensities

Irrationally related lattices and LEED intensities

Analysis of dynamical low-energy electron diffraction mechanisms

The evolution and structure of graphene layers on 4H-SiC(0001) and the corresponding interface are investigated by scanning tunneling microscopy (STM) and low energy electron diffraction (LEED). The surface is characterized by the so-called (6p3£6p3)R30± reconstruction, whose structural properties are still unclear but at the same time are crucial for the controlled growth of homogeneous high-quality large-terrace graphene surfaces. We analyse the properties of three phases in this reconstruction with periodicities (6p3£6p3)R30±, (6£6) and (5£5). Their LEED intensities strongly depend on the surface preparation procedure applied. The graphitization process imprints distinct features in the STM images as well as in the LEED spectra. An easy and practicable determination of the number of graphene layers is outlined by means of LEED intensities.

Multiple scattering effects in the fourier transform deconvolution procedure for leed analysis

An error-analysis procedure that gives statistically significant error estimates for surface-structure parameters extracted from analyses of measured low-energy electron and positron diffraction (LEED and LEPD) intensities is proposed. This procedure is applied to a surface-structure analysis of Cu(100) in which experimental data are simulated by adding Gaussian-distributed random errors to the calculated intensities for relaxed surface structures. Quantitative expressions for the variances in the surface-structural parameters are given and shown to obey the expected scaling laws for Gaussian errors in the experimental data. The procedure is shown to describe rigorously parameter errors in the limit that the errors in the measured intensities are described by uncorrelated Gaussian statistics. The analysis is valid for structure determinations that are of sufficient quality to admit errors that have magnitudes within the region of convergence of a linear theory that relates perturbations of diffracted intensities to perturbations in structural parameters. It is compared with previously proposed error-estimation techniques used in LEED, LEPD, and x-ray intensity analyses.

The atomic structure of alloy surfaces: Ni 3Al{001}

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.

The direct growth of hexagonal boron nitride (h-BN) by industrially scalable methods is of broad interest for spintronic and nanoelectronic device applications. Such applications often require atomically precise control of film thickness and azimuthal registry between layers and substrate. We report the formation, by atomic layer epitaxy (ALE), of multilayer h-BN(0001) films (up to 7 monolayers) on Co(0001). The ALE process employs BCl3/NH3 cycles at 600 K substrate temperature. X-ray photoelectron spectroscopy (XPS) and low energy electron diffraction (LEED) data show that this process yields an increase in h-BN average film thickness linearly proportional to the number of BCl3/NH3 cycles, with BN layers in azimuthal registry with each other and with the Co(0001) substrate. LEED diffraction spot profile data indicate an average BN domain size of at least 1900 Å. Optical microscopy data indicate the presence of some domains as large as ∼20 μm. Transmission electron microscopy (TEM) and ambient exposure studies demonstrate macroscopic and microscopic continuity of the h-BN film, with the h-BN film highly conformal to the Co substrate. Photoemission data show that the h-BN(0001) film is p-type, with band bending near the Co/h-BN interface. Growth of graphene by molecular beam epitaxy (MBE) is observed on the surface of multilayer h-BN(0001) at temperatures of 800 K. LEED data indicate azimuthal graphene alignment with the h-BN and Co(0001) lattices, with domain size similar to BN. The evidence of multilayer BN and graphene azimuthal alignment with the lattice of the Co(0001) substrate demonstrates that this procedure is suitable for scalable production of heterojunctions for spintronic applications.