Asymmetric skew X-ray diffraction at fixed incidence angle: application to semiconductor nano-objects

A procedure for obtaining three-dimensionally resolved reciprocal-space maps in a skew X-ray diffraction geometry is described. The geometry allows tuning of the information depth in the range from tens of micrometres for symmetric skew diffraction down to tens of nanometres for strongly asymmetric skew geometries, where the angle of incidence is below the critical angle of total external reflection. The diffraction data are processed using a rotation matrix formalism. The whole three-dimensional reciprocal-space map can be measured by performing a single azimuthal rotation of the sample and using a two-dimensional detector, while keeping the angle of incidence and the X-ray information depth fixed (FIXD method). Having a high surface sensitivity under grazing-incidence conditions, the FIXD method can be applied to a large variety of Bragg reflections, particularly polar ones, which provide information on strain and chemical composition separately. In contrast with conventional grazing-incidence diffraction, the FIXD approach reveals, in addition to the lateral (in-plane) components, the vertical (out-of-plane) component of the strain field, and therefore allows the separation of the scattering contributions of strained epitaxial nanostructures by their vertical misfit. The potential of FIXD is demonstrated by resolving the diffraction signal from a single layer of InGaN quantum dots grown on a GaN buffer layer. The FIXD approach is suited to the study of free-standing and covered near-surface nano-objects, as well as vertically extended multilayer structures.