The method for determination of the single-crystal defects' parameters is proposed and experimentally certified. This method is based on the joint analysis of deformation dependences (DD) of the total integrated reflective power (TIRP), which are obtained within the approximations of 'thin' and 'thick' crystals in the Laue geometry. The semi-phenomenological models of the TIRP DD, which have been developed by authors within the scope of the dynamical x-ray scattering theory [1, 2], are used and improved. The physical nature of proposed-method high information capability is revealed.

The dynamical recurrence relation for amplitudes of coherent waves in the multilayered structure with Coulomb‐type defects (2D and 3D defects or microdefects) has been derived and the expression for the diffuse component of reflection coefficient of this structure has been obtained with account for the dynamical redistribution of intensities of transmitted and diffracted coherent waves in each layer. The derived formulas, which self‐consistently take into account both the diffuse scattering contribution to the diffracted intensity and its extinction due to diffuse scattering, have been applied to analyze the rocking curve of InGaAs/GaAs multilayered structure with quantum well. Layer thicknesses and chemical compositions as well as strains and concentration profiles of chemical elements in layers have been found. Additionally, characteristics of dislocation loops in the substrate of the multilayered structure have been determined. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamical wave fields formed in imperfect single crystals by diffusely scattered waves have been considered in the two-beam case of diffraction for the homogeneous distribution of microdefects with large sizes. Wave vectors of the constituent plane waves include the complex dispersion corrections accounting for multiple diffuse scattering processes. The corresponding dynamical diffuse scattering amplitudes and cross-sections in vacuum have been derived for both reflection and transmission directions. The diffuse component of crystal reflectivity has been calculated in the approximation of semiinfinite crystal and has been integrated over exit angles for two microdefect types: spherical clusters and prismatic dislocation loops. The obtained formula for the diffuse reflectivity has been analyzed and compared with the known kinematical one.

The methods of high-resolution double- and triple-crystal X-ray diffractometry are used to investigate the defect structure of highly perfect silicon single crystals grown by the float-zone method. Predominant microdefect type is established, and quantitative values of microdefect characteristics are determined from the measured diffraction profiles, which are analysed by using formulas of the generalized dynamical theory of X-ray scattering by imperfect single crystals.

Basic equations of the dynamical scattering theory in momentum space have been considered in the two-beam approximation for single crystals containing randomly distributed microdefects commensurable with extinction length. The amplitudes of coherent and diffusely scattered waves inside the crystal have been found by using the perturbation theory with average and fluctuating parts of crystal polarizability as small parameters. In the complex dispersion corrections to the wave vectors of coherent and diffuse waves. the imaginary parts of which describe the attenuation of these waves due to diffuse scattering, the dynamical effects in diffuse scattering and their dependences on the incidence angle have been taken into account. These corrections also take account of the influence of any multiple diffuse scattering processes. The coherent component of crystal reflectivity has been calculated in the approximation of semiinfinite crystal for an arbitrary diffraction geometry.

The known method of the 'integral' diffuse scattering has been generalized in the Bragg case of x-ray diffraction for crystals, which contain large microdefects commensurable with the extinction length. In the framework of the developed statistical dynamical theory, relatively simple analytical expressions have been derived for coherent and diffuse components of reflectivity of single crystals with randomly distributed microdefects.To test the characterization possibilities of the proposed method, the rocking curves (RCs) of Czochralski-grown silicon single crystal annealed at 1080 degreesC for 6 h have been measured for 111 and 333 reflections of Cu K-alpha1 radiation using a high-resolution double-crystal x-ray diffractometer. The fitting results for the two RCs are in good mutual agreement and demonstrate the high information ability of the method.

On the base of the dynamical theory of X-ray scattering by real crystals, the theoretical model describing both coherent and diffuse components of the reflection coefficient (RC) in the whole angular range including the total reflection range is developed. The analytical expressions for the RC components are obtained for the Bragg diffraction in single crystals containing randomly distributed microdefects. The coefficient of extinction (due to the diffuse scattering), which is involved in both coherent and diffuse RC components, is connected explicitly with parameters of various-type microdefects. The proposed model enables to consider both small and large microdefects having the radii that are comparable with the extinction length. To test this model, the measurements of RC's from thermally treated Si single crystal have been carried out by using the high-resolution double-crystal X-ray diffractometer.