Effects of a near-surface transition layer on x-ray reflection and scattering

The influence of smooth (not step-like) variation of the dielectric function near a surface on the reflectivity and scattering of x rays is investigated theoretically with the model function ε(z) = 1 - 0.5(1 - ε+)(l + tanh(z/(2L))) taken as an example. It is shown that the presence of the transition layer can essentially change the shape of the differential scattering intensity diagram, especially when the incidence angle of the x-ray beam is greater than the critical angle of the total external reflection (TER). The results of measurements of the x-ray reflection coefficient and the differential scattered intensity are discussed. The model of the near-surface transition layer is shown to describe quantitatively the specific features of experimental curves for the incident beam beyond the TER region, whereas these experimental data cannot be explained in the framework of a step-like model of the dielectric function, taking into account the scattering from surface roughness.