Dynamical theoretical model of the high-resolution double-crystal x-ray diffractometry of imperfect single crystals with microdefects

Molodkin, V. B.; Olikhovskii, S. I.; Kislovskii, E. N.; Vladimirova, T. P.; Skakunova, E. S.; Seredenko, R. F.; Sheludchenko, B. V.

doi:10.1103/physrevb.78.224109

Cited by 31 publications

(64 citation statements)

References 44 publications

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“…After accounting for the summation over X-ray polarizations, this ratio takes the form:   . The diffuse component of the reflection coefficient of the crystal with homogeneously distributed defects after the integration over output angles can be represented as follows [22,28]:…”

Section: Differential-integral Methodsmentioning

confidence: 99%

“…Also, these expressions can be used with some precautions to describe contributions from thermal diffuse scattering and diffuse scattering from point defects (see, e.g., Refs. [27,28]). …”

Section: Diffuse Component Of Imperfect Crystal Reflectivitymentioning

confidence: 99%

“…The fit of the measured diffraction profiles and reciprocal space maps was carried out at neglecting the contributions from the thermal diffuse scattering and diffuse scattering from point defects as being relatively small in the considered reciprocal space region [28].…”

Section: Defect Structure Of the Cz-si Crystal After High-energy Elecmentioning

confidence: 99%

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Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

Molodkin¹,

Olikhovskii²,

Len³

et al. 2016

Metallofiz. Noveishie Tekhnol.

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A short review of basic principles and limitations in obtaining the analytical expressions for the coherent and diffuse scattering intensities measured by the triple-crystal diffractometer (TCD) are presented. Explicit analytical expressions are given for both the diffuse components of TCD profiles and the reciprocal-lattice maps measured within the Bragg diffraction geometry from crystals containing microdefects of several types. These formulas are derived by using the generalized dynamical theory of X-ray scattering by imperfect crystals with randomly distributed microdefects. Some examples demonstrating possibilities of the developed theory for quantitative characterization of structural imperfections in real single crystals are represented. In particular, characteristics of the complicated microdefect structures fabricated in various silicon crystals grown by Czochralski technique and floating-zone melting method are determined by analytical treatment of the measured TCD profiles, rocking curves, and reciprocal space maps.Key words: dynamical scattering, triple-crystal diffractometer, double-crystal diffractometer, microdefects.В роботі представлено короткий огляд основних принципів, що використо-вуються при одержанні аналітичних виразів для когерентної та дифузної інтенсивностей розсіяння, виміряних трикристальним дифрактометром (ТКД). Одержано точні аналітичні вирази для дифузних компонент як ТКД-профілів, так і мап оберненого простору, виміряних у геометрії дифракції за Бреґґом для кристалів, які містять мікродефекти декількох типів. Ці фор-мули одержано при використанні узагальненої динамічної теорії розсіяння Рентґенових променів неідеальними кристалами з випадково розподілени-ми мікродефектами. Представлено деякі приклади, які демонструють мож-ливості розробленої теорії для кількісної характеризації недосконалостей структури в реальних монокристалах. Зокрема, шляхом аналітичного обро-бляння виміряних ТКД-профілів, кривих відбивання і мап оберненого прос-тору визначено характеристики складних структур мікродефектів, створе-них у кристалах силіцію методами Чохральського і зонного топлення.Ключові слова: динамічне розсіяння, трикристальний дифрактометр, двок-ристальний дифрактометр, мікродефекти.В работе представлен краткий обзор основных принципов, используемых при получении аналитических выражений для когерентной и диффузной интенсивностей рассеяния, измеряемых трёхкристальным дифрактомет-ром (ТКД). Получены точные аналитические выражения для диффузных компонент как ТКД-профилей, так и карт обратного пространства, изме-ренных в геометрии дифракции по Брэггу для кристаллов, содержащих микродефекты нескольких типов. Эти формулы получены при использова-нии обобщённой динамической теории рассеяния рентгеновских лучей не-идеальными кристаллами со случайно распределёнными микродефектами. Представлены некоторые примеры, демонстрирующие возможности разра-ботанной теории для количественной характеризации несовершенств структуры в реальных монокристаллах. В частности, путём аналитической обработки измеренных ТКД-...

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Section: Differential-integral Methodsmentioning

confidence: 99%

“…Also, these expressions can be used with some precautions to describe contributions from thermal diffuse scattering and diffuse scattering from point defects (see, e.g., Refs. [27,28]). …”

Section: Diffuse Component Of Imperfect Crystal Reflectivitymentioning

confidence: 99%

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Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

Molodkin¹,

Olikhovskii²,

Len³

et al. 2016

Metallofiz. Noveishie Tekhnol.

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“…According to the statistical dynamical theory, the diffraction profile measured by the double-crystal diffractometer (DCD) with widely open detector window from the crystal with defects is the sum of coherent (R coh ) and diffuse (R diff ) components of the crystal reflectivity [23]:…”

Section: Basic Theoretical Relationsmentioning

confidence: 99%

“…In recent years, these methods have been enhanced due to the developed theoretical basis of dynamical X-ray diffraction characterization, which allows to reliably determine the quantitative characteristics simultaneously for several types of microdefects with arbitrary radii (from nano-to micrometers) [23]. Thus, the possibility is opened for the adequate interpretation of dynamical diffraction profiles and diffuse scattering intensity distributions measured by high-resolution diffractometers from crystals with a complex defect structure.…”

Section: Introductionmentioning

confidence: 99%

Transformations of microdefect structure in silicon crystals under the influence of weak magnetic field

Vladimirova¹

2011

Semicond. Phys. Quantum Electron. Optoelectron.

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Abstract. Quantitative characterization of complex microdefect structures in annealed silicon crystals (1150 °С, 40 h) and their transformations after exposing for one day in a weak magnetic field (1 T) has been performed by analyzing the rocking curves, which have been measured by a high-resolution double-crystal X-ray diffractometer. Based on the characterization results, which have been obtained by using the formulas of the dynamical theory of X-ray diffraction by imperfect crystals with randomly distributed microdefects of several types, the concentrations and average sizes of oxygen precipitates and dislocation loops after imposing the magnetic field and their dependences on time after its removing have been determined.

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Quantum‐mechanical model for phase‐contrast imaging of non‐crystalline objects

Molodkin

Velikhovskii

Lizunova

et al. 2016

Materialwissenschaft Werkst

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The quantum-mechanical theoretical model for the quantitative description of phase contrast images from non-crystalline objects with arbitrary shapes has been developed. It takes into account multiple scattering effects both in the object (particularly, refraction and phase change) and in the crystals of monochromator and analyzer. Presence of homogeneously and inhomogeneously distributed microdefects and macrodeformations in monochromator-and analyzer-crystals, which influence significantly on the scattering pattern, has been taken into account.

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Dynamical theoretical model of the high-resolution double-crystal x-ray diffractometry of imperfect single crystals with microdefects

Cited by 31 publications

References 44 publications

Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

Transformations of microdefect structure in silicon crystals under the influence of weak magnetic field

Quantum‐mechanical model for phase‐contrast imaging of non‐crystalline objects

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