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

Abstract

The dynamical diffraction model has been developed for the quantitative description of rocking curves (RCs) measured in the Bragg diffraction geometry from single crystals containing homogeneously distributed microdefects of several types and with arbitrary sizes. The analytical expressions for coherent and diffuse RC components, which take self-consistently multiple-scattering effects into account and depend explicitly on microdefect characteristics (radius, concentration, strength, etc.), have been derived with taking into account the instrumental factors. The developed model has been applied to determine the characteristics of oxygen precipitates and dislocation loops in silicon crystals grown by Czochralsky and float-zone methods using RCs measured by the high-resolution double-crystal x-ray diffractometer. It has been shown, particularly, that completely dynamical consideration of Huang as well as Stockes-Wilson diffuse scattering (DS) in both diffuse RC component and coefficient of extinction of coherent RC component due to DS, together with taking asymmetry and thermal DS effects into account, provides the possibility to distinguish contributions into RC from defects of different types, which have equal or commensurable effective radii.