Structural parameters of multilayers from X-ray reflectivity: an easy-to-handle approach

An analytical approximation was derived for the calculation of the grazing-incidence X-ray reflectivity pattern in a defect-free multilayer. The approximation is valid in the low-reflectivity {\it {$\theta$}} ranges. For {\it k} = (4{\it {$\pi$}}sin {\it {$\theta$}})/{$\lambda$} > 0.28{\AA}${\sp {$-$}1}$ ({\it {$\theta$}} > 2{$^\circ$} with Cu {\it K{$\alpha$}} radiation), the formula deviates by at most 1% from the rigorous matricial approach in the case of most metallic multilayers. The main advantage of the approximation is that it allows the identification of features in the reflectance pattern, from which desired structural parameters (average layer thicknesses, external and internal roughness) can be estimated easily. This approach yields average structural parameters, best approximating those of a real multilayer but ignoring possible defects.