A sensitive method to detect strain in silicon crystals using X-ray dynamical diffraction

A very sensitive method to detect long-range strain in otherwise perfect crystalline materials is presented. In this method, a specimen is set vertically in a diffraction apparatus under the symmetrical Laue condition, in which the scattering vector is horizontal. The specimen is then rotated along the scattering vector, with the Bragg condition being kept satisfied. Experiments were carried out using Si crystals of 714 µm thickness with X-rays of 0.4 Å wavelength. The Si crystals were strained by scratching the surface with a glass-cutter. A characteristic behaviour of the integrated intensities was observed. When the specimens were rotated in the opposite direction, the integrated intensities were different and sharply enhanced integrated intensities of the higher order reflections were observed when the specimens were rotated from their initial vertical positions. The observed results can be explained using the dynamical theory of X-ray diffraction for distorted crystals, with the assumption that the specimens were bent along an axis lying on the specimen surface. This method of rotating the crystal along the scattering vector is a very sensitive method to detect minute strains induced by device fabrication processes. The detection limit for the presented specimen is estimated to be equivalent to a uniform bending with a radius of curvature of 7000 m.