X-ray reflectivity of multilayers with non-continuous interfaces

X-ray specular reflectivity and diffuse scattering calculated using the traditional multilayer model, which assumes continuous, non-intersecting interfaces, are capable of fitting the experimental data obtained on multilayers with non-continuous interfaces. However, wrong refined electron densities and interface roughness are the consequence of an inappropriate structure model. A modification of the Parratt optical formalism combined with the application of the distorted-wave Born approximation was suggested for evaluation of the small-angle x-ray scattering in multilayers with non-continuous interfaces. The influence of the multilayer discontinuity on the small-angle x-ray scattering is characterized by modified Fresnel reflection and transmission coefficients of individual interfaces and by changes in the optical paths in individual layers. The suggested theoretical approach is illustrated on Fe/Au multilayers. Parameters of the structure model obtained from the small-angle x-ray scattering were verified by comparison with results of transmission electron microscopy.