Capabilities of using white x-rays for the reconstruction of surface morphology from coherent reflectivity

We present a new method to reconstruct the surface profile of a sample from coherent reflectivity data of a white x-ray beam experiment. As an example the surface profile of a laterally confined silicon wafer has been reconstructed quantitatively from static speckle measurements using white coherent x-rays from a bending magnet in the energy range between 5 < E < 20 keV. As a consequence of using white radiation, speckles appear in addition to the Airy pattern caused by scattering at the entrance pinhole. Nevertheless, the surface profile of a triangularly shaped specimen was reconstructed considering sufficient oversampling between the beam-footprint and the effective sample width. For the profile reconstruction the Error-Reduction phase retrieval algorithm was modified by including the spectral illumination function and a Fresnel propagator term. The simultaneous use of different x-ray energies having different penetration depth provides information on the evolution of the surface profile from the near-surface towards the bulk. The limitations of present experiment can be overcome using white or pink radiation from a source with higher photon flux.