X-Ray Diffraction from Multilayer Structures with Statistically Distributed Microdefects

Abstract

The statistical dynamical theory of X‐ray diffraction is applied to the analysis of simulated rocking curves (RCs) from multilayer systems with randomly distributed microdefects. Recursion formulae for calculating RCs in the general case of multiple diffraction on multilayer crystals are obtained for the Bragg‐Bragg and Laue‐Laue cases. The behaviour of coherently and incoherently scattered intensities for epitaxial films, heterostructures, and superlattices is discussed. It is shown that the alternation of the perfect and imperfect layers of the superlattice leads to the increase of the coherently scattered intensity of satellite peaks.

Darwin's approach to X-ray diffraction on lateral crystalline structures

“…Most crystalline structures are non-ideal, e.g., they contain defects. Statistical dynamical diffraction theory (in the case of a plane-wave illumination) (Bushuev, 1989;Punegov, 1990Punegov, , 1991Punegov, , 1993Pavlov & Punegov, 1998, 2000 using Takagi's equations (Takagi, 1962) is one possible way to describe X-ray dynamical diffraction in such structures. However, Darwin's theory (Darwin, 1914a,b), which was originally developed for an ideal crystal, can also be modified for use with non-ideal crystals.…”

X-ray scattering by porous silicon modulated structures

“…Based on the method of recurrence relations [15], we will consider X ray scattering from an N layer porous crystal. The layers are enumerated from below.…”

High-resolution X-ray diffraction in crystalline structures with quantum dots

“…We recall that a solution of type (33) for the model of scattering elements with a one-dimensional quasi-periodic lattice was obtained in the framework of a different theoretical approach [118]. We recall that a solution of type (33) for the model of scattering elements with a one-dimensional quasi-periodic lattice was obtained in the framework of a different theoretical approach [118].…”

“…If a heterostructure consists of N layers, including the substrate, and the coefficient of reflection R c NÀ1 q x ; q z from N À 1 lower layers is known, the amplitude coefficient of reflection from a heterostructure R c N q x ; q z is computed using the recursive formula [33] If a heterostructure consists of N layers, including the substrate, and the coefficient of reflection R c NÀ1 q x ; q z from N À 1 lower layers is known, the amplitude coefficient of reflection from a heterostructure R c N q x ; q z is computed using the recursive formula [33] …”