Transmission High-energy Electron Diffraction Research Articles

A treatment of RHEED from a rough surface of a crystal by an optical potential method

The general formalism of the optical potential method has been applied to the problem of reflection high energy electron diffraction (RHEED) from the rough surface of a crystal. For the case where short-range disorder dominates an explicit analytical expression for the effective absorption potential has been obtained, and procedures for evaluating this potential have been developed which utilize the conventional approaches and computer routines developed earlier for transmission high energy electron diffraction (THEED). This potential has been combined with dynamical RHEED calculations for a molecular beam epitaxy (MBE) growing surface. It is found that under certain circumstances the optical potential due to the roughness of the MBE growing surface has an appreciable effect on the shape of the corresponding RHEED rocking curve.

Inclusion of the weak beam effects in the bloch-wave simulation of dynamical diffraction by using the bethe potential

The Bloch wave method of high energy transmission electron diffraction involves diagonalization of an nxn matrix, where n is the number of beams included in the simulation. This method is used widely in quantitative electron diffraction as the simulation method because of its flexibility in treating electron diffraction of arbitrary incident beam directions, while the multislice method of simulation is mostly used for low index zone axes of large unit cell crystals. The number of beams included in the simulation is limited by the computing time and the memory size of the computer. The computing time of the Bloch wave method is proportional to the n2. Thus only a limited number of beams can be included in the simulation. The truncation of beams may introduce a systematic error, if the number of beams included fails to converge. This is illustrated by fig. 1, in which the thickness pendelösung for MgO crystal along [001] zone axis is calculated with different number of beams in ZOLZ only, with no absorption, no Debye-Waller factor, atomic scattering factors for neutral spherical Mg and O atoms, and a = 4.2112 Å.

Perturbation theory in high-energy transmission electron diffraction

A perturbation theory for many-beam high-energy transmission electron diffraction in noncentrosymmetric crystals is described for both the nondegenerate and degenerate cases. This perturbation theory differs from the conventional quantum-mechanical perturbation theory by perturbing the electron wavevectors instead of the total electron energy, which is constant for elastically scattered electrons. The relations between the perturbation theory and some other approximations commonly used in electron diffraction are discussed. It is shown that the few-beam approximation and the Kambe approximation are both applications of degenerate perturbation theory. Finally, as an example, this degenerate perturbation theory is applied to obtain an analytical solution to a four-beam case with two systematic (0 and g) and two nonsystematic (h and l) beams. This four-beam solution shows that the intensity of a four-beam interaction depends on all the four three-phase invariants involved, and also shows that the effects of the g beam on the three-beam interaction of 0, h and l are localized to the region near the Bragg condition of g. This may serve as a guide for future experiments using three-beam interactions for the measurement of structure-factor phases of an unknown structure.

Brillouin zones and Kikuchi lines for crystals under electron channeling conditions

The geometry of the Kikuchi lines in high- and low-energy electron diffraction patterns is defined in terms of intersections of the Brillouin zone boundaries with a sphere of reflections. Full treatment of the cases of two-dimensional and one-dimensional real lattices reveals previously unknown boundaries in the form of parabolic surfaces (2D) and paraboloids of revolution (1D). These boundaries are applied to K lines which arise from electron channeling. Correlation is made with the previous explanations of parabolas and circles in the reflection high-energy electron diffraction (RHEED) and transmission high-energy electron diffraction (THEED) patterns and K2 and K1 lines in low-energy electron diffraction (LEED) patterns. Experimental convergent-beam RHEED patterns of a reconstructed MgO (111) surface are presented in which parabolas due to the surface periodicity are shown for the first time.

Structural characterization of unhydrogenated amorphous GaAs

Films of unhydrogenated amorphous gallium arsenide have been deposited by reactive rf sputtering. Substrate temperature or deposition power or argon pressure were allowed to change, in different deposition runs, to obtain groups of specimens deposited with only one variable parameter. Transmission electron microscopy (TEM) and transmission high energy electron diffraction (THEED) measurements have been made in order to determine the structure and the morphology of the films. The THEED patterns show that the structure has a short range order and a weak dependence on deposition conditions. The TEM micrographs show that the morphology of the films is strongly affected by the deposition conditions.

Evolution of microstructure of nitrogen ion implanted iron at high temperatures

Pure polycrystalline iron layers are implanted with nitrogen ions of 50 keV with 2, 4, 6, or 8 × 10 17 ions/cm 2 respectively at 100, 175 or 250°C and subsequently annealed. In all cases, the implantation temperature is always equal to the subsequent annealing temperature. The microstructure after implantation and versus duration of annealing is examined with in situ high-voltage electron microscopy and transmission high-energy electron diffraction. The refinement of structure analysis using electron diffraction data is described. The integrated intensities and interplanar spacings of the individual reflections are derived by a spectrum fitting procedure. Remaining overlapping peaks can be separated by spectrum fitting. The evolution of precipitate size and phase transformation is discussed in terms of growth and dissolution processes. Three different phase transition processes are observed during annealing. At 100 °C, the implantation-induced α′-martensite, at 175°C, the α′-Fe 16N 2 precipitates and at 250°C, the ϵ-iron nitride phase are observed to transform or dissolve with increasing annealing times. Hereafter, the microstructure is characterized by α″-Fe 16N 2, γ′-Fe 4N and ζ-Fe zN precipitates, respectively.

Charge ordering in magnetite at low temperatures.

The ordering of the ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions on the octahedral sites of magnetite (${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$) at temperatures below the Verwey metal-insulator transition has been studied by quantitative high-energy transmission electron diffraction. We find that there are ten independent charge-ordering models (including the Verwey model) for the low-temperature structure that satisfy the Anderson condition if the symmetry is Cc (monoclinic). Dynamical electron diffraction patterns are simulated and compared with experiment for these charge-ordering models, using atomic coordinates obtained from neutron diffraction work. We find that one of these ten charge-ordering models agrees best with experiment and that the electrons in this model form a characteristic wave. Our calculations of electron correlation energy show that this model has the second lowest energy, while the Verwey model has the lowest. This indicates the importance of electron-phonon interactions in stabilizing the structure.

On differentiation of the scattering matrix in dynamical transmission electron diffraction

High-energy transmission electron diffraction from thin crystals under conditions of multiple scattering is considered. An expression is derived for the Jacobian of the scattering-matrix mapping, containing all partial derivatives of the scattering-matrix elements with respect to structure-matrix elements. (This structure matrix describes the scattering crystal and incident-beam direction). These results may be used to determine the regions of convergent-beam electron-diffraction (CBED) patterns which are most sensitive to changes in particular structure-factor amplitudes and phases (due, for example, to the effects of crystal bonding) and to develop more-efficient CBED algorithms based, for example, on a perturbation series in the incident-beam direction. A two-beam example is given.

Electron diffraction and lattice image simulations with the inclusion of HOLZ reflections

The formulae that can be used to calculate wave functions for transmission high-energy electron diffraction including reflections from higher-order Laue zones (HOLZs) are summarized by using the Bloch wave formulation and the multislice formulation for the dynamical electron diffraction theory, respectively. In the multislice formulation, three different algorithms of calculating phase grating functions, fraction projection algorithm (FPA), section projection algorithm (SPA) and conditional projection algorithm (CPA) are examined. Electron diffraction patterns and lattice images for the YBa 2Cu 3O 7 crystals are simulated and compared with Bloch wave calculations. In summary, the FPA calculations do not include HOLZ reflections; the SPA and CPA give much stronger HOLZ reflection intensities than the Bloch wave algorithm. Experimental diffraction patterns support the Bloch wave results. However, there is no detectable difference found in the simulated lattice images by using the above-mentioned computing schemes, which suggests that the HOLZ reflections only play a minor role in forming lattice images.

The top-bottom iV-beam phase contrast effect from finite crystals II. Theory

Abstract The top-bottom contrast effect which has been observed in dark-field images of aperiodic surface detail and which was discussed in Part I is shown to arise as a result of N-beam refraction reversal in one or more of the important Bloch wave components, formed by high-energy transmission electron diffraction. The effect is shown to arise in two-beam as well as N-beam diffraction. In particular, the zero-contrast condition, whereby the contrast from one or other surface is suppressed, and found experimentally in Part I, is found to arise as a consequence of a finite-crystal Bloch wave degeneracy.

Electron Diffraction Analysis of the Structure of SiO2 Gel-Film

ABSTRACTThe structure of self-supported SiO2 gel-films prepared from acid and basic TEOS solutions is analysed by high energy transmission electron diffraction method. The reduced radial distribution function (RDF) curves show that all the films are already well dense despite the low drying temperature (≤50°C) and short drying time (≤30 s). The Si-O bond length of the gelfilms prepared from highly acid and basic solutions is about 1.58 Å; it is smaller than that of bulk vitreous silica (1.61 Å) but similar to that of BO Å thick evaporated a-SiO2 film.

High Energy Transmission Electron Diffraction From Surface Monolayers During Silicon Oxidation

ABSTRACTWe have examined the behaviour of the clean Si (111) 7x7 reconstructed surface during exposure to oxygen over a range of temperature and pressure in a UHV transmission electron microscope (TEM). We present preliminary results of our study, discussing both the etching of the silicon surface by oxygen at elevated temperatures and lower oxygen pressures, and its roughening and oxidation at higher oxygen pressures. We achieve great sensitivity to the structure of the surface monolayers by analysing the diffraction of high energy electrons by these surface layers and can resolve the movement of individual monatomic surface steps. Our most dramatic result to date is a demonstation that surface steps do not move during the growth of native oxide.

Structure of amorphous silicon layers deposited under ultrahigh vacuum at different substrate temperatures

The reflective high energy electron diffraction and transmission electron diffraction data have shown that the structure of amorphous silicon films deposited under ultrahigh vacuum conditions, namely, the pattern and degree of atom coordination, is weakly dependent on deposition temperature within the range 100–400 °C but may be considerably varied by subsequent heat treatment at the same temperatures.

Bloch-wave channeling and HOLZ effects in high-energy electron diffraction

The circular arcs and high-order Laue zone (HOLZ) fine lines observed in both Kikuchi-line and convergent-beam electron diffraction (CBED) patterns have been shown to be consistent with the concept of Bloch-wave channeling of fast electrons along rows of atoms. This interpretation has the advantages that it provides a direct correlation between HOLZ lines and the crystal periodicity along the incident-beam direction, and forms a basis which could be incorporated into a more rigorous electron diffraction theory in the future for understanding the extreme Laue and Bragg cases of electron diffraction, as well as the intermediate reflection and transmission high-energy electron diffraction (RTHEED). Examples are given of all three types of CBED, RHEED and RTHEED patterns from Pt and GaAs single crystals, which show the common dynamical diffraction effects, circular arcs and HOLZ fine lines, resulting from Bloch-wave channeling.

Lattice parameter and orientation of xenon on graphite at low pressures.

A study of xenon adsorbed on (0001) graphite has been performed using transmission high-energy electron diffraction (THEED). The single crystal diffraction patterns have been obtained at a range of pressures 1.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$1.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ Torr and temperatures 50T80 K, which covers the incommensurate monolayer, commensurate monolayer, and bilayer phases. The lattice-parameter misfit, m, has been measured to \ifmmode\pm\else\textpm\fi{}0.1%, and the misorientation \ensuremath{\theta} to \ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{} accuracy. The misfit in the incommensurate phase is parametrized as m=B(T-${T}_{0}$${)}^{\ensuremath{\beta}}$, with \ensuremath{\beta}=0.80\ifmmode\pm\else\textpm\fi{}0.03 and B and ${T}_{0}$ as functions of ${\mathrm{log}}_{10}$(p). A tricritical point (I-C monolayer, bilayer) is observed at p=2.0\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ Torr, T=62.5\ifmmode\pm\else\textpm\fi{}1 K. The small misorientation (0\ensuremath{\le}\ensuremath{\theta}0.4\ifmmode^\circ\else\textdegree\fi{}) is a well-defined function of m in the monolayer phase, with an aligned-rotated transition at m=1.5\ifmmode\pm\else\textpm\fi{}0.5%. These features are compared with other experiments and with theoretical predictions.

In-Situ Transmission Electron Microscopy Studies of the Oxidation of Si (111) 7X7

ABSTRACTThe kinematical approximation is valid for High-Energy Transmission Electron Diffraction from monolayers in planview. We use this fact to study quantitatively the attack of Si (111) 7×7 by 02. Oxygen is found to bind in the bridging position of the adatom backbonds and render the structure very stable during subsequent 02 exposure. Electron-beam exposure during dosing additionally creates rapid disordering which is presumed to represent SiOx formation.

Magneto-optical properties of highly Al-substituted (Y,Bi)/sub 3/(Fe,Al)/sub 5/O/sub 12/ sputtered films in short wavelength region

The films were prepared on 7059 glass substrates by RF sputtering. The effect of Al substitution on the magnetic and structural properties of Bi-substituted films is discussed. The limit of Bi substitution into the garnet phase was clarified for Al-substituted and nonsubstituted films. The microstructure of the films at the limiting composition and segregation compositions was examined by transmission electron microscopy and transmission high-energy electron diffraction observations. The electron and X-ray diffraction analyses for this composition range showed some diffraction peaks which could not be assigned to the garnet phase or the Bi/sub 2/Fe/sub 4/O/sub 9/ phase.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A top–bottom contrast effect in dark-field images arising fromN-beam dynamic refraction

The refraction effect associated with an off-Bragg diffracted beam in high-energy transmission electron diffraction is analysed. It is found that the wave vectors of Bloch-wave components of a beam associated with a finite excitation error are significantly shortened or lengthened as a consequence of dynamic scattering, with the direction of change being determined by the sign of the excitation error. By consideration of the dark-field image formed from the off-Bragg reflection and its associated refractive fine structure it is shown that a top-bottom effect exists, which can be demonstrated by comparing images of the same field for positive and negative excitation errors. This is discussed in two dimensions for a crystal of triangular cross section and one horizontal face, in the two orientations of apex up and apex down, with numerical and graphical evaluations from linear three-beam diffraction.

Experimental studies of surface resonance scattering processes in rheed

A high energy electron diffraction experimental has been carried out in which both the reflection high energy electron diffraction pattern (RHEED) and transmission high energy electron diffraction pattern (THEED) are recorded together from the edge of a GaAs bulk crystal specimen. The combined diffraction pattern shows clearly the existence of the surface resonance waves when the surface resonance diffraction conditions are satisfied, and the close correlation between the intensity enhancement and the surface resonance waves. Strong intensity dependence of the specular reflection and surface resonance spot on the positions of the specular reflection spot along the Kikuchi envelopes, and experimental identification of the surface resonace region, demonstrates the relationship of the resonance diffraction processes to the three-dimensional diffraction conditions. However, the fact that the wavefield for the surface-channelled electrons is confined to a few atomic layers on the surface is indicated by the elongatition of the transmitted diffraction spots. Generation of diffusely scattered electrons by the surface-channelled electrons produces diffuse bands in the diffraction pattern, parallel to the surface.

Morphology and structure of gold, silver and copper layers obtained by sputtering during ion bombardment of targets from these metals

The mechanism by which gold, silver and copper layers are formed by sputtering during the ion bombardment of targets of these metals has been investigated experimentally. Empirical evidence is given to show that, during the bombardment of metal foils with an appropriate thickness under certain conditions with argon ions, sputtering on both sides of the target occurs, namely forward and transmission sputtering. Transmission electron microscopy, scanning electron microscopy and transmission high energy electron diffraction were used to study the morphologies and structures of the layers obtained by both types of sputtering. Some possible applications of such layers are suggested.