Dynamical scattering of X-rays by real binary crystals and problem of point defects

Abstract

One of the important subjects in the material science of semiconductor compounds is a problem of stoichiometry. The methods based on the measurement of kinematical integral reflectivity (IR) , R. , for the quasi-forbidden reflection (QFR) of X-rays were formerly used for investigation of the GaAs composition. To determine the value of deviation from stoichiomerry, A =C A-C B where C t is a concentration of the component A or B, one should make some corrections for extinction phenomena which is difficult to take into account for a real (with defects) crystal. The reflectivity of a real crystal for a QFR, R t , may be also described within the dynamical theory taking into account the Debye-Waller static factor , L H , the extinction coefficient (ii ds , and parameter A. To determine these characteristics the experimental thickness pendulum oscillation of Rf (t) (200 reflection, A,=0.1198nm) was measured and analysed for the first time. By this the Honl corrections of atomic formfactors for anomalous dispersion were made. Another independent approach consisted in analysis of the experimental energetic dependence of the R.(A) for the wavelengths situated between the two absorption K-edges was used too. Relatively close values of the L H and (ii ds for GaAs crystals with dislocations as well as parameter A were obtained by fitting of the R. (/) and R t (A) nonlinear functions, calculated by the theory , to the experimental data.

Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects I. Generalized Dynamical Theory

“…It is important to note here that, as distinct from other approaches, in the present theory similarly to Refs. [46][47][48] neither any averaging of the equations nor averaging of any coefficients in the equations is introduced artificially. Instead, only for those quantities which are reduced to the sum over lattice points (i.e., which are self-averaged) such averaging over lattice points is replaced by averaging over the defect ensemble.…”

“…The infinite set (4) can be represented then, analogously to Refs. [46][47][48], as two sets, namely, one for two amplitudes of coherent transmitted (D 0 ) and diffracted (D H ) plane waves with the wave vectors k ¼ K 0 and k ¼…”

“…Here, as distinct from Refs. [46][47][48], we have retained on the right-hand side not only the terms with amplitudes of coherent waves, which describe the diffuse scattering with momentum transfer q, but also the terms which are responsible for the diffuse scattering of diffusely scattered waves with momentum transfers q 0 6 ¼ q into those with given q.…”

“…It should be remarked that the dispersion corrections (28) are similar to those derived first in one-beam approximation [46] (see also Refs. [47,48]) and describe the phys. stat.…”

“…Here it should be remarked that the application of the optical potential method from nuclear physics to the scattering of particles and X-rays by single crystals with defects, which has been made by Dederichs [31,32], has given the correct description of the coherent component of the scattering intensity and its attenuation due to diffuse scattering, but does not allow to describe explicitly the diffuse component of scattering intensity. The more general approach [19,23,25,[46][47][48], which has been proposed in Ref. [46] earlier than that one of Dederichs [31], is free of such disadvantage and permits to describe in explicit terms the dynamical effects in both coherent and diffuse scattering.…”