Higher-order Laue Zone Patterns Research Articles

HANSIS software tool for the automated analysis of HOLZ lines

A software tool, named as HANSIS (HOLZ analysis), has been developed for the automated analysis of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns. With this tool, the angles and distances between the HOLZ intersections can be measured and the data can be presented graphically with a user-friendly interface. It is capable of simultaneous analysis of several HOLZ patterns and thus provides a tool for systematic studies of CBED patterns.

Analysis of Local Lattice Strain Around Oxygen Precipitates in Czochralski-Grown Silicon Wafers Using Convergent Beam Electron Diffraction

The local lattice strain field around oxygen precipitates in Czochralski-grown silicon (CZ-Si) wafers has been measured quantitatively using convergent beam electron diffraction (CBED). As a result of the strain analysis from higher-order Laue zone patterns in the CBED disk, strain of the silicon lattices was found in the vicinity of oxygen precipitates, i.e., platelet type and polyhedral type. The strain along the normal direction to the precipitate is compressive, and the strain along the parallel direction to the precipitate is tensile. The lattice strain field around the precipitate decreases monotonically as a function of distance from the precipitate/matrix interface. Further, the morphological change in the growth process of the precipitate is important for the formation of the local lattice strain.

Determination of the range of lattice distortion in AIN sintered body by higher order laue zone pattern

To analyse the magnitude and range of lattice distortion which is responsible for the low thermal conductivity in aluminium nitride (AIN) crystal grains, the higher order laue zone (HOLZ) pattern of transmission electron microscopy was used. The HOLZ patterns obtained from various positions in the AIN crystal grain show that the AIN crystal lattice is distorted in the vicinity of the grain-boundary phase, and the magnitude of lattice distortion becomes large as it approaches the grain-boundary phase. Also, the range of distortion extends to approximately 300 nm from the grain-boundary phase.

Contrast of HOLZ lines in energy-filtered convergent-beam electron diffraction patterns from silicon

Higher-order Laue-zone (HOLZ) lines were investigated in convergent-beam electron diffraction patterns from silicon near the low-indexed zone axes [100], [110] and [111]. The visibility of these lines depends on the effective structure potentials of the reflections from the first Laue zone depending on their Debye–Waller factor. The contrast of the HOLZ lines is strongly reduced by inelastically scattered electrons. They can be excluded by an imaging Ω filter for energy losses above 2 eV. The diffraction patterns were compared with many-beam calculations. Without absorption, an excellent agreement could be achieved for the [111] and [100] zone axes, while the simulation of the [110] zone-axis pattern needed a calculation with absorption. The reason for this observation is explained in the Bloch-wave picture. Calculations with absorption, however, lead to artefacts in the intensity distribution of the [100] HOLZ pattern. In order to obtain agreement with the experiment, the Debye–Waller factor had to be modified in different ways for the different zone axes. This corresponds to a strong anisotropy of the Debye–Waller factor. To confirm this observation, the temperature dependence of the intensity distributions of the HOLZ patterns was investigated between 50 and 680 K. At room temperature, the parameter D in the Debye–Waller factor exp(−Ds2) was determined as 0.13, 0.26 and 0.55 Å2 for the zone axes [100], [111] and [110], respectively. The reliability of the conclusions is discussed.

Applications of Convergent Beam Electron Diffraction to Extract Quantitative Information in Materials Science

Convergent beam electron diffraction (CBED) provides more quantitative, precise and local information on crystals than the traditional selected-area diffraction (SAD). Some of the results of our applications of CBED will be shown, with an emphasis on quantitative analyses of crystal structure in materials science: (i) The critical voltage and the intersecting Kikuchi line methods are combined with the CBED technique to accurately determine the structure factors and temperature factors; (ii) a large angle CBED is applied to determine the atomic coordinates in a unit cell; (iii) higher order Laue zone patterns are used to determine absolute lattice parameters and local lattice distortion

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.

Higher order Laue zone patterns in convergent beam electron diffraction and determinations of local lattice parameters in .ALPHA.- and .ALPHA.2-phases of a Cu-20at%Al alloy.

In order to clarify the applicability of higher order Laue zone (HOLZ) patterns in convergent beam electron diffraction to the determinations of local lattice distortions in two-phase alloys, we discussed experimental conditions affecting the accuracy, and observed HOLZ patterns of a Cu-20at%Al alloy, in which small particles of α2-phase with one dimensional long period superstructure are precipitated in the matrix of fcc α-phase. It was shown that the accuracy is affected by specimen thickness as well as beam direction, and that lattice parameters along the [100] and [010] axes can be determined from a [114] HOLZ patterm with an error less than one part in a thousand. The [114] HOLZ patterns were obtained both from small regions in α-matrix and α2-particles. Slight changes in lattice parameters were detected as a function of position with a high spatial resolution.

Higher Order Laue Zone Patterns and Determination of Local Lattice Parameter

Higher Order Laue Zone Patterns and Determination of Local Lattice Parameter

Application of Higher Order Laue Zone Patterns to Lattice Parameter Determination in Cu-based Alloys

Examen des diagrammes de Laue pour etudier la validite d'un traitement cinematique pour determiner la valeur exacte des parametres cristallins. Le calcul base sur la theorie de la diffraction electronique dynamique montre que la localisation des lignes du diagramme depend de la grandeur du potentiel cristallin, et la valeur des parametres cristallins donnes par le traitement cinematique est derivee de la valeur exacte, a condition d'utiliser un etalon pour la correction de la deviation. Application aux alliages Cu-Al, Cu-Mn, Cu-Ni, Cu-Zn et Cu-Ga. Comparaison avec les resultats predits a partir de la composition chimique des alliages