Determination of penetration depths and analysis of strains in single crystals by white beam synchrotron X-ray topography in grazing Bragg-Laue geometries

White beam synchrotron radiation topography has been performed on a silicon wafer of well-defined and precharacterized dislocation structure in grazing Bragg-Laue geometries. The complicated projective geometries on the topographs are exploited to give a direct determination of the penetration depth of the X-rays. This is achieved via quantitative analysis of the projected lengths of direct dislocation images on the topographs. Experimental results obtained are then compared with theoretical predictions based on kinematical, and dynamical diffraction theories, respectively. Dynamical theory predicts particularly shallow penetration depths in these geometries, whereas kinematical theory predicts much deeper penetration depths. However, one would expect that the mode of diffraction which operates is controlled by the local lattice perfection. Direct evidence is obtained here that in the vicinity of dislocation intersections with the crystal surface, the penetration depth is determined by kinematical, rather than dynamical theory. Thus, care is required when utilizing grazing Bragg-Laue geometries to enable strain analysis in thin subsurface layers, since beyond a threshold strain value, penetration depths will no longer be determined by dynamical diffraction theory. The viability of imaging techniques in grazing Bragg-Laue geometries is discussed in detail on the basis of these results, and those obtained previously by other workers.