Higher-order Laue Zone Research Articles

Convergent-beam electron diffraction study of modulations in semiconductor superlattices

Abstract The dependence of zone axis superlattice higher-order Laue zone (HOLZ) lines of reflections of AlAs/GaAs superlattices on the accelerating voltage of the electron microscope and the specimen thickness has been studied by conventional zone axis convergent-beam electron diffraction (CBED) and large-angle CBED Tanaka dark-field patterns. This is compared with satellite sidebands in a GeSi/Si strained-layer superlattice with a larger period of modulation. It is shown that zone axis superlattice HOLZ lines and satellite sidebands in Tanaka dark-field patterns are equivalent.

Energy-filtered convergent-beam electron diffraction in STEM

Abstract Energy-filtered convergent-beam electron diffraction (CBED) patterns were obtained from a 10A˚region of the specimen in a scanning transmission electron microscope (STEM) equipped with a digital image-acquisition system. For crystalline silicon, plasmon scattering causes a blurring of the low-order Bragg beams. Significant plasmon intensity was also observed at high angles with an angular distribution duplicating the zero-loss scattering. The plasmon-loss pattern contained a high-order Laue-zone (HOLZ) ring and Kikuchi bands from elastic, phonon, and plasmon multiple scattering. The HOLZ ring intensity relative to the diffuse background was not significantly different from the zero-loss pattern. Quantitative agreement between experimental silicon (100) CBED patterns and patterns calculated by the frozen-phonon technique was achieved. The silicon room-temperature vibration amplitude was determined to be 0.078±0.002A˚as compared with the value of 0.0764±0.0002A˚reported for X-ray measurement [P.J.E. Aldred and M. Hart, Proc. Roy. Soc. (London) A 332 (1973) 223, 239].

Convergent beam electron diffraction studies of strain in Si/SiGe superlattices

Abstract Convergent beam electron diffraction (CBED) and large angle CBED have been used to analyse strains in Si1-xGex/Si (001) superlattices with 0.17≤x≤0.33 and wavelengths in the range 200-650 Å. Studies were carried out using plan-view samples, thus largely avoiding thin foil strain relaxations. Rocking curves were obtained for low order and higher order Laue zone (HOLZ) reflections which showed superlattice peaks whose intensity envelope function was symmetric for diffracting planes in the [001] zone and asymmetric for planes inclined to [001]. A kinematical approach is used to give a simple explanation of these features and to investigate the relative contribution of layer strains and differences in layer structure factors and thicknesses. It is shown that strain can be measured either from the rocking curve asymmetry or by modelling the complete intensity envelope function. A quantitative analysis of the experimental results using both kinematical and dynamical simulations showed good agreement for the expected strains to within an accuracy of ±20%.

Dynamical treatment of the splitting of HOLZ lines from dislocations in silicon

The splitting of higher-order Laue-zone (HOLZ) lines of convergent-beam electron diffraction (CBED) due to the presence of dislocations in Si was investigated experimentally and theoretically. The parameters affecting the separation and relative positions of the fringes of split HOLZ lines were examined with experiments and/or computations. According to the results obtained, a method for identification of Burgers vector is discussed.

Primitive unit cell volumes obtained from unindexed convergent‐beam electron diffraction patterns

Provided that multiple reflection is present, a common occurrence with electron diffraction on microcrystallites, a single unindexed convergent-beam electron diffraction (CBED) pattern taken with the beam axis parallel to any direct lattice row allows the volume of the primitive cell to be calculated. The film measurements required are the diameters of the successive high-order Laue zones (HOLZ), the lengths of any two coprime vectors in the zero-order Laue zone (ZOLZ), and the angle between them. The primitive cell volume is an objective criterion allowing in a simplification in the identification of a phase under study by rapidly eliminating other possible phases. The computer program CELVOL for the calculation of the primitive cell volume from film measurements, or from literature cells, is available from the authors.

Fine details in satellite HOLZ reflection discs of CBED from a GaAs/AlAs multilayer

Fine details of satellite higher-order Laue zone (sHOLZ) reflection discs from a GaAs/AlAs multilayer in plan view are observed and investigated. Computer simulation based on the dynamical theory of electron diffraction shows good agreement with the experimental observations. Apart from the two lines reported previously, some weak lines and a few other features in sHOLZ reflection discs are found and investigated. The investigation confirms the previous two-line explanation and also reveals the origin of the additional weak lines and the other features. The weak lines are due to the interference between Bloch waves, and their location depends on specimen thickness. Some other features are determined to be caused by multiple diffraction from neighbouring sHOLZ reflections. The phenomenon of the interruption of lines in sHOLZ reflection discs, in comparison to the lines in fundamental higher-order Laue zone (fHOLZ) discs, originates mainly from sHOLZ reflection coupling. Furthermore, intensities of sHOLZ reflections are shown to depend on their structure factors rather than on the excitation of their corresponding fundamental reflections. Details of the computer simulation are given. Finally a simple method, not relying on computer simulation, to identify the lines in sHOLZ reflections is presented.

Convergent beam electron diffraction study of Pb2CoWO6 at 100 K

Abstract A study by convergent beam electron diffraction has been performed in order to clarify the symmetry of the phase III of Pb2CoWO6. Microdiffractions with higher-order Laue zone on monodomain areas have confirmed the cell proposed in our preceding study. In addition, an ‘axial’ glide plane (c) has been found normal to the b axis. In the conditions of observation, the convergent beam electron diffraction patterns lead to an apparent point group mmm. No breakdown of a mirror symmetry could be found. The discrepancy between this result and the existence of a spontaneous polarisation is discussed.

Effects of tetragonal distortion in thin expitaxic films on electron channeling patterns in scanning electron microscopy

The elastic strain state in a 25 nm (In,Ga)As epitaxic film deposited on a (001) GaAs substrate includes a Poisson expansion perpendicular to the interface. This creates a tetragonally distorted lattice in the film which shifts high-order Laue-zone (HOLZ) lines in electron channeling patterns (ECP) from the film compared to ECP's from pure GaAs. The line shifts are predictable, thereby allowing measurement of elastic strains parallel and perpendicular to the film/ substrate interface independently. The technique appears to have an accuracy close to 0.2%.

Structure of metastable Al–Ge phases determined from HOLZ Patterson transforms

Abstract The utility of Patterson transforms applied to higher-order Laue zone (HOLZ) reflections in convergent-beam electron diffraction (CBED) patterns from unknown crystal structures is discussed. For HOLZ diffraction from molecular Bloch states located on subsets of atom strings, the transforms contain sharp peaks defining accurate interatomic vectors. As an example, the HOLZ Patterson transforms for two metastable Al–Ge phases are described, where the rhombohedral phase (space group R&3bar;c) is probably isostructural with Zn4Sb3 and a monoclinic phase (space group P21/c) has a new polyanionic structure with tetrahedral coordination of Al by Ge.

Electron Microdiffraction Investigation of a GexSi1−x Buffer for Strain-Symmetrised Superlattice Structures

ABSTRACTA candidate GeSi buffer layer structure suitable for strain-symmetrised GeSi/Si superlattice overgrowth is grown by molecular-beam epitaxy and its strain state characterised using microdiffraction in a dedicated scanning transmission electron microscope. The structure consists of five alloy layers of increasing Ge concentration grown on a Si (100) substrate, with all but the last annealed at high temperature. Analysis of higher order Laue zone deficit lines in the microdiffraction patterns acquired from each layer indicate that relaxation is complete in all the layers. Images of the structure in the transmission electron microscope show good crystallinity of the final layer with low concentrations of threading dislocations.

Convergent beam electron diffraction study of lattice distortion in InGaAs/GaAs strained-layer superlattices grown by metalorganic chemical vapor deposition

The intensities of sidebands in convergent beam electron diffraction reflections from plan-view specimens of strain modulated InGaAs/GaAs superlattices are dependent on the natural lattice mismatch, the ratio of the thicknesses of the superlattice layers, the period (sum of layer thicknesses) of the superlattice, and the g vectors of the reflections. The intensities of kinematic higher-order Laue zone (HOLZ) reflections have been calculated from a simple model based on alternate contraction and expansion of lattice spacings of the superlattice layers. An accurate estimate of the In content of InGaAs can be deduced from the elastic strains in the superlattice layers so obtained.

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.

Dynamical Diffraction Effect on HOLZ-Pattern Geometry for Semiconductor Alloys of Sil-xGex and Gal-xInxAs

A network of dark lines for higher order Laue zone (HOLZ) reflections often appears in the bright-field disc of convergent beam electron diffraction under zone axis incidence. As geometry of the network (HOLZ pattern) depends sensitively on the crystal lattice parameters, the observation of HOLZ pattern has been applied to measure local change in the lattice parameters in various materials. The kinematical diffraction approximation has been usually employed in the analysis of observed HOLZ patterns, where the lattice parameters and the accelerating voltage exist as independent variables. However the positions of HOLZ lines depend also on the crystal potential for electrons, because the lines arise from intersections of dispersion spheres for the HOLZ reflections with the zeroth-order dispersion surface. In the kinematical analysis, an effective accelerating voltage Ee should be used in place of the actual one Ea, in order to compensate for line shift due to the dispersion effect.

Convergent Beam Electron Diffraction Zone Axis Pattern Map of Zirconium

The purpose in obtaining zone axis pattern map (zap map) from a given material is to provide a quick and reliable tool to identify cristaline phases, and crystallographic directions, even in small particles. Bend contours patterns and Kossel lines patterns maps from Zr single crystal in the [0001] direction have been presented previously. In the present communication convergent beam electron diffraction (CBED) zap map of Zr will be shown. CBED patterns were obtained using a Philips microscope model EM300, which was set up to carry out this technique. Convergent objective upper pole piece for STEM and some electronic modifications in the lens circuits were required, furthermore the microscope was carefully cleaned and it was operated at a vacuum eminently good.CBED patterns in the Zr zap map consist of zero layer disks, showing fine details within them which correspond to intersecting set of higher order Laue zone (HOLZ) deficiency lines.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

Determination of Positional Parameters by CBED

Convergent-beam electron diffraction (CBED) has been successfully applied to the determination of symmetries of perfect crystals and of characteristics of crystal imperfections. CBED is now entering a stage of quantitative studies. Vincent et al. first demonstrated for AuGeAs a method to determine atomic positions with use of CBED patterns, in which the positional parameters were determined by fitting the intensities of higher-order Laue-zone (HOLZ) reflections calculated under the (quasi) kinematical approximation with the experimental intensities.We report a simple case of the positional parameter determination for the low temperature phase of SrTiO3. This material undergoes a second order phase transformation at 110 K from the high temperature form of Pm3m to the low temperature form of I4/mcm upon the slight rotation of the oxygen octahedra or the condensation of the R25 mode (Fig. 1). The structure analysis of the phase I4/mcm means to determine the rotation angle ϕ and the isotropic Debye-Waller factor B of the oxygen ions.

Comparative investigation of microarea quasilattice parameters of Al–Si–Mn and Al–Cu–Fe icosahedral phases using HOLZ line patterns

Some differences between the higher-order Laue zone (HOLZ) line patterns of A176Si4Mn20 and A165Cu20Fe15 icosahedral phases (I phases) have been observed. These differences originate from the fact that A176Si4Mn2o belongs to a simple icosahedral quasilattice whereas A165Cu20Fe~5 belongs to an ordered face-centred icosahedral quasilattice, and from the minor difference in their quasilattice parameters. By computer simulation of these HOLZ line patterns using a 'standard' quasilattice parameter of 0.460 nm for the I phase of Aly6Si4Mn2o, the quasilattice parameter of the I phase of A165Cu2oFe~5 has been determined to be 0.8966 nm.

CONVERGENT BEAM ELECTRON DIFFRACTION STUDY OF Bi-BASED HIGH TEMPERATURE SUPERCONDUCTING LAYERED COMPOUNDS

Cleaved specimens of layered compounds Bi 2 Sr 2( CaCuO 2)n CuO 6, n = 0, 1 and 2 phases have been studied by convergent beam electron diffraction. The identity and the symmetry of the phases have been determined from the higher order Laue zone (HOLZ) rings and the symmetry of their [001] patterns. In the case of Bi 2 Sr 2 CuO 6, the [001] axial periodicity corresponds to the component of the wave vector of the monoclinic modulation along the c axis. Widely different axial periodicities have been obtained. This is interpreted as the manifestation of the variation of the monoclinic modulation. The presence of basal stacking fault lowers the symmetry of the [001] pattern.

Higher-order Laue zone diffraction from crystals containing transverse stacking faults

Abstract An accessible theory of higher-order Laue zone (HOLZ) diffraction from crystals containing transverse stacking faults is presented. This is used to investigate the sensitivity of intensity profiles to displacement vector, fault depth and absorption effects. In particular, the phenomenon of HOLZ line splitting is seen to arise as a natural consequence of the theory. A comparison with experimental results from 2Hb-MoS2 is made in which the evaluation of absorption parameters is shown to be an important consideration. Finally, some general implications of the results with regard to defect characterization are discussed.

An investigation of three-dimensional diffraction from 2Hb-MoS2

Abstract Three-dimensional diffraction from the [0001] axis of 2Hb-MoS2 is examined as a special case of diffraction from zone axes which consist of projected atomic strings containing more than one atom species. In particular, a complicating effect due to modified atomic form factors, which inevitably obscures the relationship between higher-order Laue zone (HOLZ) intensities and kinematic structure factors, is considered. After some discussion, these difficulties are shown to be unimportant for the specific case of 2Hb-MoS2. Finally, it is verified by computation and experiment that, to a good approximation, the innermost line of the doublet HOLZ ring intensities is weakly dependent on orientation and is proportional to the kinematic structure factor squared for a given reflection.