X-RAY REFLECTION BY MULTILAYER SURFACE GRATINGS

X-ray reflection by multilayer gratings has been investigated theoreti cally and experimentally. A theoretical treatment based on the DWBA me thod has been developed and compared with the full dynamical and the k inematical approaches. All three theories are treated in one uniform f ormalism, removing the usual restrictions of the Fraunhofer approximat ion in order to simplify the direct numerical comparison. Contrary to the wide spread opinion the DWBA shows good agreement especially for t he intense grating truncation rods. The regions of validity of the DWB A are proved by exact dynamical calculations. The dynamical diffractio n by the multilayered grating has been formulated by a matrix formalis m generalizing the Fresnel transmission and reflection coefficients fo r diffraction, which describe the interaction of the scattering by dif ferent 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 gra tings. (C) 1998 Elsevier Science B.V. All rights reserved.