The Characterization Of Multilayers Analyzers - Models And Measurements

A procedure is described for the detailed characterization of multilayer analyzers which can be effectively applied to their design, optimization and application for absolute x-ray spectrometry. An accurate analytical model has been developed that is based upon a simple modification of the dynamical Darwin-Prins theory to extend its application to finite multilayer systems. Its equivalence to the optical E&M solution of the Fresnel equations at each interface is demonstrated by detailed calculation comparisons for the reflectivity of a multilayer throughout the angular range of incidence of 0 to 90° . A special spectrograph and experimental method is described for the measurement of the absolute reflectivity characteristics of the multilayer. The experimental measurements at three photon energies in the 100-2000 eV region are fit by the analytical modified Darwin-Prins equation (MDP) for I( 0), generating a detailed characterization of two "state of the art" multilayers, a sputtered tungsten-carbon of 2d 21 70 A and a molecular lead stearate of 2d 100 A. The fitting parameters that are determined in this procedure are applied to help establish the structural characteristics of the particular multilayer.