X-ray reflection by multilayer surface gratings

X-ray reflection by multilayer gratings has been investigated theoretically and experimentally. A theoretical treatment based on the DWBA method has been developed and compared with the full dynamical and the kinematical approaches. All three theories are treated in one uniform formalism, removing the usual restrictions of the Fraunhofer approximation in order to simplify the direct numerical comparison. Contrary to the wide spread opinion the DWBA shows good agreement especially for the intense grating truncation rods. The regions of validity of the DWBA are proved by exact dynamical calculations. The dynamical diffraction by the multilayered grating has been formulated by a matrix formalism generalizing the Fresnel transmission and reflection coefficients for diffraction, which describe the interaction of the scattering by different grating truncation rods. The concept of Ewald's sphere allows a transparent interpretation of the different scattering phenomena and the influence of Umweganregung on the scattering pattern. The theories are applied on first experimental results of epitaxial multilayer gratings. (C) 1998 Elsevier Science B.V. All rights reserved.