Abstract

Understanding the morphology of multilayer structures (MLS's) is an important step toward the preparation of high-quality multilayer mirrors for use in the extreme ultraviolet. To gain information about the structure, the x-ray reflectivity is measured at grazing angles. These data are then analyzed using any of a number of models to gain information about such characteristics as d spacing, spacing uniformity, heavy element fill factor (Γ), and diffusion boundary widths. Several models have been used with varying degrees of success to describe the x-ray diffraction of multilayers. The matrix method, in which the reflectivity is explicitly calculated at each interface, is exact for abrupt interfaces, but to include diffusion it is necessary to divide each boundary into many layers, which slows the calculations considerably. Traditional x-ray diffraction models allow for rapid calculations, but make approximations that are not generally applicable to multilayers. The kinematical model, in which only one reflection is allowed within the sample, is only accurate for low reflectivities, and thus is not valid near the Bragg peaks of the MLS. The dynamical model allows for multiple reflections, but is not accurate away from Bragg peaks at grazing incidence.

© 1994 Optical Society of America