The Radon transform as a tool for 3D reciprocal-space mapping of epitaxial microcrystals

Abstract

This work presents a new approach suitable for mapping reciprocal space in three dimensions with standard laboratory equipment and a typical X-ray diffraction setup. The method is based on symmetric and coplanar high-resolution X-ray diffraction, ideally realized using 2D X-ray pixel detectors. The processing of experimental data exploits the Radon transform commonly used in medical and materials science. It is shown that this technique can also be used for diffraction mapping in reciprocal space even if a highly collimated beam is not available. The application of the method is demonstrated for various types of epitaxial microcrystals on Si substrates. These comprise partially fused SiGe microcrystals that are tens of micrometres high, multiple-quantum-well structures grown on SiGe microcrystals and pyramid-shaped GaAs/Ge microcrystals on top of Si micropillars.