X-ray reflection by rough multilayer gratings: Dynamical and kinematical scattering

X-ray reflectivity by rough multilayer gratings is treated in the framework of kinematical and dynamical theories. The kinematical scattering integral is calculated without the restrictions of the Fraunhofer approximation. Th e dynamical theory is presented by the matrix modal eigenvalue approach. In both theories we generalize the Fresnel reflection and transmission coeffi cients for the case of grating diffraction. We obtain one unique formalism which permits us to compare the results of both theories directly. Furtherm ore, interface and sidewall roughnesses are taken into account. The dynamic al approach allows us to explain the experimental results obtained from a p artially etched GaAs/lnP periodic multilayer grating. [S0163-1829(99)05308- 4].