Information on in-and out-of-plane correlated roughness in multilayers from x-ray specular reflectivity

Specular reflectivity measurements of artificial multilayers often exhibit a broadening of high order Bragg peaks and an intensity drop off that is slower than expected from the q(-4) Fresnel dependence modified with a static Debye-Waller factor accounting for the interfacial roughness. This behaviour is described on the basis of a model that takes into account the finite size of the detector slit, which determines the instrumental resolution. The amplitude of the interface roughness as well as the in- and out-of-plane correlation lengths strongly affect the shape of the specular x-ray spectra. Information about in-plane and out-of-plane correlated roughness can be obtained, therefore, not only from diffuse scattering data but also from the quasi-specular reflectivity by relaxing the instrumental resolution. Moreover, for systems with short correlation lengths, quasi-specular reflectivity scans are more informative than rocking curves across Bragg reflections. The model is applied to the interpretation of x-ray scattering results on two multilayer systems: MgO(0 0 1)/[Fe(2ML)/V(16ML)](30) and Si/SiO2/[CoFeB(3 nm)/MgO(1.5 nm)](15). The simulation of the experimental reflectivity scans properly describes the broadening of the higher order Bragg peaks, the damping of Kiessig fringes, and the increased intensity at higher scattering vectors as compared with the purely specular reflectivity.