Sensitivity of triple-crystal X-ray Diffractometers to microdefects in silicon

Abstract

The dynamical theory, which describes both diffraction profiles and reciprocal space maps measured from imperfect crystals with account for instrumental factors of triplecrystal 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 reciproc al space maps. The sensitivities of reciprocal space maps and diffraction profiles to defect characteristics have been compared. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.