The potential profile in LEED theory

The effect of variations in the inner potential at a crystal surface on low-energy electron diffraction (LEED) is investigated. It is shown in particular that surface structural determination using LEED is sensitive to the local value of the inner potential if energies roughly below 100 eV are used. It is however not sensitive to scattering effects at potential steps, except if intensities near beam emergences are considered, in which case LEED is shown to be a suitable tool for examining these potential steps.     

As(0001) surfaces: Auger,loss, and photoelectron spectroscopic studies

The (0001) surfaces of arsenic single crystals have been characterized by Auger, loss, and X-ray photoelectron spectroscopy. A comparison of the results leads to an unusual suggestion for excitation, conduction, and emission modes in the low-energy region. It is proposed that the dominant 20 eV near-elastic loss is the excitation of N₁(4s) electrons to a conduction level 2 eV above the instrumental vacuum level. It is also proposed that two low-energy “Auger-like” peaks at 12 eV and 1.5 eV are electrons emitted at the surface from permitted bands in the bulk. A strong correlation among Auger and loss signals, integrated secondary-electron emission, elastic peak heights and the Kikuchi display is also reported. A study of the Kikuchi correlation of the 12 eV peak suggests that the surface Debye-Waller effect on As(0001) is a long-range, collective oscillation rather than short-range, individual atomic disorder.     

半导体应变超晶格结构与界面的X射线双晶衍射研究

本文应用X射线在畸变晶体中的动力学衍射理论,分析了超晶格衍射峰强度分布的规律,计算了应变超晶格中界面变化,层厚波动对双晶摇摆曲线的影响,并初步探讨了超晶格衍射峰之间的小峰消失以及衍射峰宽化的原因,研究表明,衍射峰强度分布依赖于超晶格周期中层厚、成份及应变的综合效果,界面和层厚波动将对摇摆曲线产生一定影响,而晶格弯曲是使衍射峰宽化的主要原因。     

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 %.     

A simple method to determine the step heights on ultrathin heteroepitaxial films

The step heights or first interlayer spacings on ultrathin heteroepitaxial films of Fe on Au(001) have been determined from the energy-dependent angular profiles of the specular diffraction beam obtained from low energy electron diffraction (LEED). This method requires little effort in calculation and can be used as a guide in the widely used dynamical LEED calculation of the energy-dependent peak intensity. It is also very general and can be applied to other ultrathin heteroepitaxial films as long as the scattering factors of constituent atoms have slow varying phases relative to the phase change due to step height in the low energy regime.     

Computations of relativistic LEED intensities and spin-polarisations for tungsten (001)

The effects of relativistic corrections in low-energy electron diffraction intensity calculations are assessed by reference to relativistic and non-relativistic computations for tungsten (001). Small changes are observed in the calculated intensities and band structures and a significant degree of spin-polarisation is predicted for the diffracted beams. The spin-polarisation profiles are more complicated than those observed in gas-phase experiments because of the influence of multiple scattering. The results suggest that LEED could provide a strong source of polarised electrons for use in scattering experiments. It is suggested that in future LEED experiments both spin-polarisation and intensity measurements should be performed on the diffracted electron beams.     

Atomic structures by direct transform of diffraction patterns

We propose all the diffraction patterns can be directly transformed to provide three-dimensional atomic structures for the system studied. Depending on the scattering process, either the holography or Patterson transform scheme is used. For diffraction patterns which are generated from a localized emitter source or dominated by an inelastic-scattering feature like core-level photoelectron or low-energy Kikuchi electron, holography transform is needed. On the other hand, for diffraction patterns which were dominated by elastic-scattering, like grazing-incidence X-ray diffraction, electron correlated thermal diffuse scattering or low-energy electron diffraction curves, Patterson transform is needed. To prove our point, high-fidelity and artifact-free three-dimensional atomic structures obtained by transform of low-energy Kikuchi electron patterns and low-energy electron diffraction curves are presented. The future of these direct methods by transforming diffraction patterns will be discussed.     

The atomic structure of alloy surfaces: Ni3Al{001}

The atomic structure of the {001} surface of Ni₃Al has been determined by LEED (low-energy electron diffraction) intensity analysis to correspond to simple truncation of the bulk structure with the Ni-Al mixed layer on top rather than the pure Ni layer. The first interlayer spacing is essentially equal to the bulk interlayer spacing between {001} planes. First-principles calculations of the cohesive energies of slabs terminating in the two types of layers also indicate that the mixed layer termination is more stable.     

Theory of secondary electron emission

The fine structure in angle-resolved secondary electron spectra is shown to be related to the total reflectivity in low-energy electron diffraction (LEED). Theoretical results for tungsten are compared with experimental data. For non-normal emission, spin-orbit coupling is predicted to produce spin polarization of the emitted electrons.     

Diffuse LEED intensities of disordered crystal surfaces: I. Correlations between statistics and multiple diffraction

It is shown that the diffraction of slow electrons from disordered crystal surfaces is correlated with the problem of thermodynamical statistics. The correlation functions are completely determined by the self-energies and interaction energies of neighboring complexes. These quantities solve the problem of a-priori probabilities and the cooperative phenomenon of correlation functions of these complexes. If the calculation of a certain set of multiple scattering amplitudes is possible, the remaining problem of determining the diffuse LEED pattern becomes solvable. The calculation of angular beam profiles follows the same lines as already described for the kinematic theory of X-ray diffraction.     

Linear photoelectron diffraction: application of a rapid approximation for surface structural studies

The linear superposition approximation proposed by Wander, Pendry and Van Hove for efficient low-energy electron diffraction calculations (“linear LEED”) is applied to photoelectron diffraction (“linear PD”). As with linear LEED, linear PD works very well for calculating the effect of displaced atoms. However, due to strong forward scattering at higher energies, linear PD requires that atoms do not move into or out of alignment. This limitation can be removed by suitable simple adjustments to the basic approximation, promising to make the method effective for structural searches of complex surfaces.     

Surface parameters of clean nickel (001) determined by LEED averaging

The low-energy electron diffraction from clean Ni(001) has been studied in detail over a large range of temperature and diffraction geometries with particular emphasis on the reproducibility of the data and internal consistency of the analysis. Averaging the data at constant momentum transfer extracts the kinematic intensity for both the specular and non-specular beam. The results are analyzed to obtain both structural and electron diffraction parameters. The electron total attenuation coefficient and its energy dependence are determined from both the widths of peaks in the averaged data and from the integrated elastic intensity and are consistent with one another and with previous determinations for Ni(111) and Ni(001). While both the inner potential and the relaxation of the interplanar spacing cause shifts in peak positions, their effects can be separated in the analysis because the latter also causes changes in the relative peak intensities and in the peak shapes. The resulting inner potential, as well as its energy dependence, agree with earlier determinations for Ni(111) and with theoretical calculations to within an uncertainty of about 2 V. From analysis of peak shapes in the averaged data, it is concluded that the surface interplanar spacing is within ±4% of the bulk interplanar spacing at 380 K. This result agrees with estimates obtained from dynamical theories. It is shown that the excess atomic thermal vibrations near the surface, and not experimental uncertainties, limit the accuracy to which this spacing can be determined.     

Theoretical spin polarization and intensity profiles in LEED from low-index surfaces of tungsten

Subsequent to the recent measurement of spin polarization effects in LEED, a relativistic LEED theory has been modified such as to facilitate computations for energies up to about 200 eV. Application to several low-index surfaces of tungsten yields intensity-energy profiles in good agreement with experiment. The calculated spin polarization profiles exhibit large maxima and show encouraging agreement with the as yet limited experimental data. Contraction of the top layer spacing with respect to the bulk spacing is found to produce drastic changes in parts of the polarization profiles. LEED spin polarization analysis could therefore provide a sensitive means of surface structure determination. Further, some polarization maxima coincide in energy with sizeable intensity values. This offers promising prospects for the construction of a low-energy spin polarization detector on a double diffraction basis and of an intense source of polarized electrons.     

Inversion of low-energy electron diffraction data with no pre-knowledge factor beyond optical holography

In this review, I describe how low-energy (typically below 500eV) electron diffraction spectra can be inverted to produce three-dimensional coordinates of atoms neighbouring a reference atom with no prior knowledge of what type or types of atom are present. The reference atom may be one of many equivalent near-surface atoms from which a core-level photoelectron is excited or, in the case of diffuse low-energy electron diffraction, one of many equivalent adsorbate atoms (lacking in long-range order) on the surface of a crystalline substrate. Other variants apply to low-energy electron diffraction, Kikuchi electron diffraction and time-reversed versions in which the wavenumber (energy) and direction of the incident beam are varied. I show that, for such low-energy electron diffraction spectra, the relative phases between the reference wave and scattered waves have a known geometric form if the spectra are taken from within a small angular cone in the near-back-scattering directions. By using the back-scattering small cone at each direction of interest, a simple algorithm is developed to invert the spectra and extract object atomic positions with no input of calculated dynamical factors. The article also reviews key ideas and works which led to the current understanding of this field.     

Photon emission from sputtered atoms — The observation of apparent local thermodynamic equilibrium in the excitation

We develop, here, our previous LEED Kikuchi pattern theory in order to include the plamion excitation. Therefore, we assume that the intensity of electrons which have suffered plasmon excitations is given by a Poisson distribution. The theory is applied to calculate the contrast change of the aluminium (111) Kikuchi band due to the plasmon excitation, and the calculated values show a good agreement with our experiment. They confirm especially that the contrast due to the one plasmon excitation is larger than the contrast due to phonon excitation only.     

A LEED and AES study of the structure,debye temperature,and oxidation of the (111) crystal face of thorium

The structure, and reactivity towards O₂ and CO, of the (111) crystal face of a single crystal of high purity thorium metal was studied using low-energy electron diffraction (LEED) and Auger electron spectroscopy (AES). After the sample was cleaned in vacuum by a combination of ion bombardment and annealing, a (1 × 1) LEED pattern characteristic of a (111) surface was obtained. Extended annealing of the cleaned sample at 1000 K produced a new LEED pattern characteristic of a (9 × 9) surface structure. A model of a reconstructed thorium surface is presented that generates the observed LEED pattern. When monolayer amounts of either O₂ or CO were adsorbed onto the crystal surface at 300 K, no ordered surface structures formed. Upon heating the sample following these exposures the (111) surface structure was restored accompanied by a reduction in the amount of surface carbon and oxygen. With continued exposure to either O₂ or CO and annealing, a new LEED pattern developed which was interpreted as resulting from the formation of thorium dioxide. Debye-Walter factor measurements were made by monitoring the intensity of a specularly reflected electron beam and indicated that the Debye temperature of the surface region is less than it is in bulk thorium. Consequently, the mean displacement of thorium atoms from their equilibrium positions was found to increase at the surface of the crystal. The presence of chemisorbed oxygen on the crystal surface affected the Debye temperature, raising it significantly.     

Spatial correlation of an electron and hole in quasi-two-dimensional electronic system in a strong magnetic field and its relationship to the light-scattering tensor

The spatial correlation of light-generated electrons and holes in a quasi-two-dimensional electron gas in a strong magnetic field is investigated in an approximation linear in the intensity of the exciting light. The correlation is due to the interaction of the electrons and holes with longitudinal optical (LO) phonons. The theory permits calculating, on the basis of a special diagrammatic technique, two distribution functions of an electron-hole pair with respect to the distance between the electron and the hole after the emission of N phonons: first, the function determining the total number of pairs which have emitted N phonons and, second, the function related to the rank-4 light-scattering tensor in interband resonance Raman scattering of light. A special feature of the system is that the electron and hole energy levels are discrete. The calculation is performed for a square quantum well with infinitely high barriers. The distribution function and the total number of electron-hole pairs before the emission of phonons as well as the distribution function corresponding to two-phonon resonance Raman scattering are calculated. The theory predicts the appearance of several close-lying peaks in the excitation spectrum under resonance conditions. The number of peaks is related to the number of the Landau level participating in the optical transition. The distance between peaks is determined by the electron-phonon coupling constant. Far from resonance there is one peak, which is much weaker than the peaks obtained under resonance conditions. Zh. éksp. Teor. Fiz. 111, 2194–2214 (June 1997)     

Reply to comment on the use of “Kramers-kronig analysis for the determination of the optical constants of thin surface films”

A LEED data reduction method is described and applied to Al (001) surface. The method consists of averaging rotation diagrams (azimuthal intensity profiles) obtained at constant electron energy between 500 and 1000 eV in the whole range of the colatitude angle of incidence. The method avoids certain difficulties, stemming e.g. from the energy dependence of the mean optical potential, that are present in other methods in which data obtained at different energies are averaged. The averaged data are analyzed using the two-beam Darwin theory. Values for the surface normal relaxation and mean optical potential are obtained from the study of the position, width and profiles of the averaged peaks. The (100) surface of aluminum is found not relaxed while the (110) surface is contracted. The values found for the mean optical potential are similar to those obtained from other sources. The precision of the averaging method for surface structure is not better than that of direct calculation. Experimental factors limiting the precision of the method (surface roughness, background interference due to Kikuchi lines) are specified.     

Low energy electron diffraction with position-sensitive detection: Intensity measurements and comparison with positron diffraction for NaF(001)

A novel low energy electron diffraction (LEED) system incorporating a position-sensitive detector has been used to measure beam intensities as a function of incident electron energy. The detector characteristics, and the control of the incident beam focus and current are described. The (0,0)-beam intensity for NaF(001) surface was measured over the incident energy range of 2–150 eV, and the results were compared with the corresponding results for low energy positron diffraction (LEPD) [A.P. Mills and W.S. Crane, Phys. Rev. B31 (1985) 3988] as well as earlier LEED results. The LEED plots were found to contain two types of peak not present in corresponding LEPD ones: (a) narrow peaks attributable to beam-threshold interferences, and (b) odd-order Bragg peaks. The absences of these types of peak in LEPD are attributed tentatively to (a) the large incident angular divergence in the LEPD measurement cited, and (b) the relatively weak scattering of low energy positrons by Na⁺ ions, respectively.     

Surface structure determination by quasidynamical LEED intensity evaluation

The quasidynamical method for LEED intensity calculations is applied to Ir(100)1 × 1 over a broad energy range, 100–500 eV. The comparison with experiment and full dynamical calculations shows that peak positions and peak widths are well reproduced, but relative peak heights and therefore also shapes of peak groups can be considerably modified. This behaviour is discussed and explained in terms of the forward and backward diffraction properties of single layers. Finally, a structure determination is tried using the Pendry r-factor for the quantitative comparison of the experimental and quasidynamical data. The resulting value for the surface relaxation agrees with that determined from the full dynamical evaluation within the usual error of structure determination by LEED.