Statistical error analysis of surface-structure parameters determined by low-energy electron and positron diffraction: Data errors.

It was not until five years after the discovery of low-energy electron diffraction (LEED) [9.1] that the positron was first observed [9.2]. By the time it became possible to form controllable, albeit very weak, low-energy positron beams in the 1970s, LEED had become an ubiquitous and powerful tool in surface structure determination. Thus, when the first observation of low energy positron diffraction (LEPD) was made in 1979 [9.3] one could well question whether it was too late for LEPD to be of any practical value in surface physics. As this review will chronicle, during the past ten years, LEPD has evolved from being a novelty to becoming a valuable technique for surface structure determination. The differences between LEPD and LEED are nontrivial; they not only raise questions of fundamental interest but also suggest that in some cases LEPD ultimately may prove superior to LEED for quantitative surface structure determination.

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.

Development of positron diffraction and holography at LLNL

Theory versus experiment in low-energy positron diffraction by Cu{111}

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 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.

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

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

Irrationally related lattices and 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 relatively simple apparatus has been developed for the direct measurement of the intensities of low energy electron diffraction (LEED) beams from the surface of a single crystal target. The energy and angular distributions of all the electrons inelastically scattered or emitted from a single crystal or polycrystalline target surface, monitored by LEED, can also be measured in this apparatus. LEED and electron or ultraviolet light induced electron emission measurements may be observed over a solid angle of emission of 3 π st. The apparatus includes a service area, for preparing crystal surfaces under u.h.v. conditions, and manipulation devices, for transferring the specimen from the service area to the measuring area, and orienting its surface for a wide range of angles of incidence of the primary electron beam.

Recently, we developed new total reflection high-energy positron diffraction (TRHEPD) apparatus [1] on a beam line of the linac-based intense positron beam of the Slow Positron Facility at KEK, Japan. The high intensity allows us to install a brightness-enhancement section, which to observation of clear positron diffraction patterns for crystal surfaces under total reflection condition. In this work, we investigated the atomic configuration of Pt-induced nanowires formed on a Ge(001) surface [2] using the apparatus. By means of the diffraction intensity analysis based on the dynamical diffraction theory, or TRHEPD rocking curve analysis, a previously proposed theoretical model [D. E. P. Vanpoucke et al., Phys. Rev. B 77, 241308(R) (2008)], composed of Ge dimers on the top layer and buried Pt arrays in the second and fourth layers, was confirmed to be the fundamental structure of the nanowire. We also investigated the atomic configuration of a rutile-TiO2(110) surface. It is well known that the structure of this surface transforms its periodicity from (1×1) to (1×2) by elevating the sample temperature above ~1100 K, whereas the detailed structure is yet to be revealed. There is a longstanding controversy between the structure models proposed by scanning tunneling microscopy, low energy electron diffraction, surface X-ray diffraction, first-principles calculation with density functional theory results, etc. To solve the problem, we have measured TRHEPD rocking curves and determined the atomic arrangements of the topmost crystal surface [3].

Band structure treatment of low energy electron diffraction intensities

Two-dimensional (2D) materials have attracted interest because of their excellent properties and potential applications. A key step in realizing industrial applications is to synthesize wafer-scale single-crystal samples. Until now, single-crystal samples, such as graphene domains up to the centimeter scale, have been synthesized. However, a new challenge is to efficiently characterize large-area samples. Currently, the crystalline characterization of these samples still relies on selected-area electron diffraction (SAED) or low-energy electron diffraction (LEED), which is more suitable for characterizing very small local regions. This paper presents a highly efficient characterization technique that adopts a low-energy electrostatically focused electron gun and a super-aligned carbon nanotube (SACNT) film sample support. It allows rapid crystalline characterization of large-area graphene through a single photograph of a transmission-diffracted image at a large beam size. Additionally, the low-energy electron beam enables the observation of a unique diffraction pattern of adsorbates on the suspended graphene at room temperature. This work presents a simple and convenient method for characterizing the macroscopic structures of 2D materials, and the instrument we constructed allows the study of the weak interaction with 2D materials.

Structure determination of ultra-flat stanene on Cu(111) using low energy electron diffraction