Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. II

This paper reports computer simulations of X-ray six-beam (000, 220, 242, 044, −224, −202) diffraction in a perfect silicon crystal of large thickness where the super-transmission effect prevails,i.e.about 2 cm or more for an X-ray photon energy of 8 keV. Both the plane-wave angular dependence and the six-beam section topographs, which are obtained in experiments with a two-dimensional slit, are calculated. The angular dependence is computed by means of an eigenvalue problem in accordance with Ewald's theory. The section topographs are calculated by means of a fast Fourier transformation procedure from the angular to real space. It is shown that under the effect of X-ray super-transmission the quadrupole part of the photoelectric absorption as well as the Compton scattering give apparent contributions to the minimum absorption coefficient. Comparison of experimental and theoretical results by means of measuring the effective absorption coefficient is proposed. The section topographs for a thick crystal are asymmetric and polarization sensitive. These properties are explained through the angular dependence and the stationary phase method.

Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. I

This paper reports computer simulations of the transmitted-beam intensity distribution for the case of six-beam (000, 220, 242, 044, −224, −202) diffraction of X-rays in a perfect silicon crystal of thickness 1 mm. Both the plane-wave angular dependence and the six-beam section topographs, which are usually obtained in experiments with a restricted beam (two-dimensional slit), are calculated. The angular dependence is calculated in accordance with Ewald's theory. The section topographs are calculated from the angular dependence by means of the fast Fourier transformation procedure. This approach allows one to consider, for the first time, the transformation of the topograph's structure due to the two-dimensional slit sizes and the distance between the slit and the detector. The results are in good agreement with the results of other works and with the experimental data. This method of calculation does not require a supercomputer and it was performed on a standard laptop. A detailed explanation of the main features of the diffraction patterns at different distances between the slit and the detector is presented.

The contrast of inclusions compared with that of micropipes in back-reflection synchrotron white-beam topographs of SiC

Images of inclusions in synchrotron white-beam back-reflection X-ray topographs appear as spots of light contrast surrounded by darker rings, resembling images of micropipes, which appear as distinct white circles surrounded by dark rings. Section topographs taken across the centers of micropipes gave vertically displaced two-tailed images, arising from the helical tilt of the reflecting planes about the micropipes' screw dislocation axes. Section topographs taken across the inclusions showed no vertical displacement, only dark bars bracketing a region of depleted contrast, arising from the convex bulge of the reflecting planes lying above the inclusion. The features of the inclusion images could be reproduced in computer simulations based on the elastic displacement function of a spherical inclusion in a semi-infinite solid, and compared with others based on the displacement function of a screw dislocation in an infinite solid.

New contrasts of piezoelectric devices using synchrotron stroboscopic section topography at ESRF

The propagation modes of ultra-acoustic waves in quartz planar resonators have been studied by means of stroboscopic section topographs at ESRF. The images present a number of internal lines inside the section that allow a quantitative analysis of the vibration modes. When the excitation level increases, the shape of the lines enables the study of the dumping of the vibration along the surface of the device. Such analysis was made possible because of the small divergence of the white beam delivered by a third-generation synchrotron source.

Contrast in X-ray section topographs of perfect silicon crystals using the Laue–Laue three-beam case of diffraction

Section topographs taken in three-beam diffraction geometry and in the neighbourhood of this geometric position are presented. The experiments were performed using polychromatic and monochromatic X-ray radiation. The interference of the two diffracted waves produces new contrast phenomena compared to the two-beam case. The contrast changes are discussed on the basis of the Bethe approximation by means of the effective structure factor and with regard to the dispersion surface of the three-beam case.

Epitaxial Lateral Overgrowth of Gallium Arsenide Studied by Synchrotron Topography

ABSTRACTSynchrotron x-ray topographs of GaAs epitaxial lateral overgrowth (ELO) samples are made both in transmission and reflection geometries. The topographs show that the bending of the ELO layers is visible in most geometries. A simulation of the topographic images is implemented taking into account only the orientational contrast. Simulated back reflection section topographs are in good agreement with the experimental ones. The shape of the lattice planes in an ELO layer is calculated using the simulation data and compared to the measured surface profile of the same ELO stripe.