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 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.

Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios

“…For calculation of deformation in the buffer layer GaN experimental DC were normalized to 0006 reflection of the sapphire substrate at 2θ = 41.680°. Theoretical DC were calculated using the plane wave methods [15,16]. Ideal structural parameters for all the layers were taken from the papers [17,18].…”

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

“…6) were performed in the non-dispersive scheme of the home-made TCD with a higher resolution at symmetrical Si(111) reflections in Bragg diffraction geometry of characteristic CuK 1 -radiation on all three flat crystals [39]. To describe defect structure in the investigated Cz-Si sample, the model was used supposing the presence of two microdefect types (see, e.g., Ref.…”

“…Radii and number densities of spherical oxygen precipitates and circular dislocation loops in Cz-Si sample annealed at 1150C during 50 h [39]. consideration of both diffuse and coherent components of diffraction patterns.…”

“…consideration of both diffuse and coherent components of diffraction patterns. The availability of the explicit analytical expressions for diffuse scattering intensity, which take the anisotropy of displacement fields around dislocation loops with discrete orientations into account [39], was also important. C) Anneal at 1160C during 50 h. The investigated Si single crystal was cut from Cz-Si ingot with p-type conductivity (  10 cm) and initial oxygen concentration about 1.110 18 cm 3 .…”

“…On the other hand, the appropriate shape of the equal intensity lines on all the maps can only be ensured by the predominant contribution of diffuse scattering from dislocation loops. The analysis of these maps demonstrated that the shape of equal intensity lines is typical for the case of circular dislocation loops with 〈111〉 orientations of Burgers vectors [39]. The radii of these (large) dislocation loops R L were estimated using the measured reciprocal space maps and their cross sections (Figs.…”