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.Osnovnye uravneni¾ dinamiqeskoj teorii rasse¾ni¾ v impul#snom prostranstve rassmotreny v dvuhvolnovom pribliwenii dl¾ monokristallov, soderwa §ih sluqajno raspredelennye mikrodefekty s radiusami por¾dka +kstinkcionnoj dliny. Amplitudy kogerentnyh i diffuzno rasse¾nnyh voln vnutri kristalla najdeny s ispol#zovaniem teorii vozmu §enij so srednej i fluktuacionnoj qast¾mi pol¾rizuemosti krustalla v kaqestve malyh parametrov. V kompleksnyh dispersionnyh popravkah k volnovym vektoram kogerentnyh i diffuznyh voln, mnimye qasti kotoryh opisyvaˇt zatuhanie +tih voln iz-za diffiznogo rasse¾ni¾, uqteny dinamiqeskie +ffekty v diffuznom rasse¾nii i ih zavisimost# ot ugla padeni¾. *ti popravki uqityvaˇt takwe vli¾nie lˇbyh mnogokratnyh processov diffuznogo rasse¾ni¾. Kogerentna¾ komponenta otrawatel#noj sposobnosti kristalla vyqislena v pribliwenii polubeskoneqnogo kristalla dl¾ proizvol#noj geometrii difrakcii.

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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.Dinamiqeskie volnovye pol¾, obrazuemye v nesoverxennyh monokristallah diffuzno rasse¾nnymi volnami, rassmotreny v dvuhvolnovom sluqae difrakcii dl¾ odnorodnogo raspredeleni¾ mikrodefektov bol#xih razmerov. Volnovye vektory sostavl¾ˇ §ih ih ploskih voln soderwat kompleksnye dispersionnye popravki, uqityvaˇ §ie processy mnogokratnogo diffuznogo rasse¾ni¾. Sootvetstvuˇ §ie amplitudy i seqeni¾ dinamiqeskogo diffuznogo rasse¾ni¾ v vakuume vyvedeny dl¾ napravlenij otraweni¾ i prohowdeni¾. Diffuzna¾ komponenta otrawatel#noj sposobnosti kristalla vyqislena v pribliwenii polubeskoneqnogo kristalla i prointegrirovana po uglam vyhoda dl¾ mikrodefektov dvuh tipov: sferiqeskih klasterov i prizmatiqeskih dislokacionnyh petel#. Vypolnen analiz poluqennoj formuly dl¾ diffuznoj otrawatel#noj sposobnosti i provedeno ee sravnenie s izvestnym kinematiqeskim vyraweniem.

The dynamical theory, which describes both diffraction profiles and reciprocal space maps measured from imperfect crystals with account for instrumental factors of triple‐crystal diffractometer (TCD), has been developed for adequate quantitative characterization of microdefects. Analytical expressions for coherent and diffuse scattering (DS) intensities measured by TCD in the Bragg diffraction geometry have been derived by using the generalized statistical dynamical theory of X‐ray scattering in real single crystals with randomly distributed defects. The DS intensity distributions from single crystals containing clusters and dislocation loops have been described by explicit analytical expressions. Particularly, these expressions take into account anisotropy of displacement fields around defects with discrete orientations. Characteristics of microdefect structures in silicon single crystals grown by Czochralsky‐ and float‐zone methods have been determined by analyzing the measured TCD profiles and reciprocal space maps. The sensitivities of reciprocal space maps and diffraction profiles to defect characteristics have been compared.

A strict dynamical theory of radiation scattering in defect crystals is developed involving no arbitrary assumptions. Final theoretical expressions are obtained for the case of Laue‐diffraction in monocrystals containing homogeneously distributed defects, in particular Coulomb‐like defects (clusters, dislocation loops). The theory gives an unified description of the thickness dependences of intensity scattering both, for thin and thick crystals, and predicts an effect of anomalous transmission of diffuse background in thick crystals. Experimental investigations on O‐ or Cu‐doped Si‐monocrystals are carried out which confirms the theory.

The theory of the dynamical X-ray diffuse scattering (DS) in single crystals with homogeneously distributed microdefects (point defect clusters, inclusions, new phase nuclei, dislocation loops, etc.) is developed. The thickness dependence of the DS intensity distribution in reciprocal lattice space is investigated by constructing both, iso-intensity contours and plane projections of threedimensional images. Possibilities to obtain a detailed information concerning various-kind microdefects characteristics by using distribution patterns of the DS intensity are discussed.

Two-dimensional maps of x-ray diffuse scattering (DS) in a reciprocal space for a real crystal containing Coulomb deformation centres (clusters or dislocation loops) were calculated using a new dynamical theory developed for a crystalline media with homogeneously distributed defects. Such maps were calculated for both the fundamental, 400, as well as the quasi-forbidden, 200, reflections of x-rays (CuKα 1 radiation) for a binary crystal (GaAs). They were also discovered experimentally in the GaAs films heavily doped with Si (up to 10 20 cm −3) by means of a Philips three-crystal diffractometer. The procedure for fitting calculated values of differential DS to the experimental data enabled not only the integral characteristics of the structure's perfection (Debye-Waller static factor, L H , and coefficient of extinction of radiation due to additional energy losses on defects, µ d) but also the average radius,r, and concentration,n, of microdefects (precipitates to be obtained).

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)