Analytic determination of the three-dimensional distribution of dislocations using synchrotron X-ray topography

Abstract

A technique, using a symmetric reflection via azimuthal rotation of a sample, is presented for characterization of the three-dimensional distribution of dislocations in single crystals. An analytic formula is derived to transform the three-dimensional geometry of a straight dislocation into its two-dimensional projection onto the detector plane. By fitting topographs to the formula, the orientations and locations of dislocations are quantitatively determined. The dislocations in a thermally stressed Si wafer are examined as an example.