Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects

Abstract

The generalized dynamical theory of X-ray scattering by single crystals containing randomly distributed microdefects has been applied to characterize structural imperfections in the Czochralskigrown dislocation-free silicon sample annealed at 1080 C during 6 h. Measurements of rocking curves for 111 and 333 reflections of CuK a1 radiation have been performed by the high-resolution double-crystal diffractometer. The sizes and concentrations of oxygen precipitates and dislocation loops, which have been determined by independent fitting of the two rocking curves, are in good agreement confirming the validity of the developed theory.Obob §enna¾ dinamiqeska¾ teori¾ rasse¾ni¾ rentgenovskih luqej monokristallami, soderwa §imi sluqajno raspredelennye mikrodefekty, primenena dl¾ diagnostiki strukturnyh nesoverxenstv v obrazce bezdislokacionnogo kremni¾, vyra §ennogo metodom Qohral#skogo i otowwennogo pri 1080 C v teqenie 6 q. Izmereni¾ krivyh kaqani¾ dl¾ otrawenij 111 i 333 izluqeni¾ CuK a1 byli vypolneny na vysokorazrexaˇ §em dvuhk-ristal#nom difraktometre. Razmery i koncentracii precipitatov kisloroda i dislokacionnyh petel#, kotorye byli opredeleny putem nezavisimoj podgonki dvuh krivyh kaqani¾, nahod¾ts¾ v horoxem vzaimnom soglasii, podtverwdaˇ §em pravil#nost# razrabotannoj teorii.

Double- and triple-crystal X-ray diffractometry of microdefects in silicon

“…Such joint treatment of measured diffraction profiles was carried out in the iterative way, when MD characteristics determined from TCD profiles were used as initial ones at the treatment of DCD profiles, and vice versa. At the treatment of the measured diffraction profiles, we used the model of a defect structure in the investigated silicon sample, which supposed the presence of randomly distributed disk-shaped oxygen precipitates and chaotically oriented circular dislocation loops with Burgers vectors b = 〈110〉/2 [1,15,18]. The proposed method has allowed to simultaneously determine characteristics of small and large MDs in the crystal bulk, namely, the characteristics of small oxygen precipitates of the radius R P = (7.7 ± 0.2) nm, thickness h P = (2.2 ± 0.05) nm, and numeric density…”

“…Of course, the key role in the adequate treatment of measurement results is played by applying the formulas of the generalized statistical dynamical theory for X-ray scattering by real single crystals, which allows to self-consistently describe the coherent and diffuse scattering intensities. The exclusive importance of account for the simultaneous presence of various-type MDs for the correct interpretation of diffraction patterns from silicon crystals (see, e.g., also [6,20,15]) should be emphasized as well.…”

“…In this work, the analytical expressions for the description of X-ray diffraction profiles measured by DCD [13][14][15][16] and TCD [17][18][19] from single crystals with homogeneously distributed defects of several types and disturbed surface layers, which take into account also the DS intensity from defects in monochromator and analyzer, have been used to develop the combined method for the characterization of defect structures in single crystals with joint treatment of DCD and TCD profiles. It should be emphasized that the used approach [13][14][15][16][17][18][19] allows to consider the X-ray scattering in crystals containing MDs of arbitrary sizes due to account for multiple DS effects in coherent and diffuse components of the diffracted intensity.…”

Unique Informativity of the Diffuse Dynamical Combined Diffractometry of Materials and Products of Nanotechnologies

“…Указанная динамическая теория рассеяния в кристаллах с де-фектами была построена впервые сорок лет назад для кристаллов со слабыми отклонениями от периодичности [15][16][17] и двадцать пять лет назад -обобщена на случаи произвольных отклонений, что по-зволило провести в рамках динамической теории классификацию дефектов [18][19][20][21][22][23], а пять-десять лет назад -обобщена на случаи дефектов, размеры которых соизмеримы с длиной экстинкции, и кристаллов с упругим изгибом и дефектами [38][39][40][41][42][43][44][45][46][47][48][49].…”

Implementation of statistical dynamic diffraction theory for defective semiconductor heterostructure modelling

“…An alternative method was used by Molodkin and several other authors (Molodkin, Olikhovskii, Kislovskii, Len & Pervak, 2008;Molodkin, Olikhovskii, Kislovskii, Vladimirova & Skakunova, 2008;Molodkin et al, 2007;Olikhovskii et al, 2002;Kislovskii et al, 2002), who developed a 'generalized dynamic theory' based on using perturbation theory to solve fluctuating polarizability in momentum space. This model bypasses the limitations of the kinematic model for small defect sizes by including the dynamic effects of defects and a redistribution of the dynamic scattering within the material.…”