The dynamical theory of diffraction in a crystal modulated by a surface acoustic wave in the case of spatially restricted X-ray beams

Abstract

The dynamical theory of X‐ray diffraction in a crystal modulated by a surface acoustic wave (SAW) is developed for spatially restricted beams. It is shown that this approach is applicable to X‐ray reciprocal space mapping. Rayleigh's surface‐wave model is used to describe ultrasonic excitation. Based on the recurrent relations, a numerical simulation of the dynamical diffraction in a crystal modulated by a SAW is performed. Within the framework of the triple‐axis diffraction scheme, the effect of the instrumental function on X‐ray diffraction data is studied.

Laue X-ray diffraction studies of the structural perfection of Al-doped thermomigration channels in silicon

“…The theory of dynamical Laue diffraction of X-rays in crystals was developed for a plane spatially infinite X-ray wave (Authier, 2001). However, for numerical simulation of Laue diffraction in a single crystal with sharp vertical channels the formalism of spatially restricted X-ray beams should be implemented, which was previously developed only for the Bragg geometry (Punegov et al, 2017;Punegov, 2019) For calculation of the angular distribution of diffraction intensity for symmetrical Laue geometry we will apply the numerical solution of the Takagi-Taupin equations (Takagi, 1962;Taupin, 1964) in the oblique-angled coordinate system: 2 sin(2# B )!/ is the angular parameter, ! is the deviation of the X-ray beam from the Bragg angle # B , is the wavelength of the X-ray radiation in vacuum, C is a polarization factor, and g = Àr 0 2 F g /(V c ) are the Fourier components of the X-ray polarizability with index g = 0, h, Àh.…”