Characterization of multilayers by Fourier analysis of x-ray reflectivity

We discuss a new method to characterize multilayer structures with grazing-incidence reflectivity measurements using hard x-ray radiation, such as Cu-K-alpha or Mo-K-alpha radiation. The method is based on the analysis of the reverse Fourier transforms of the reflectivity at the Bragg peaks in q-space, the reflectivity data being obtained from an angular scan (theta-2 theta). This method is faster than curve fitting of the reflectivity data, results in an accurate value of the density and thickness of both materials, and needs no pre-assumptions about the material composition and the parameters of the multilayer. The method makes a distinction between interface roughness and layer thickness errors, and is independent of measurement of the critical angle. A minor disadvantage is that only an average value of the layer thickness is determined, rather than the Individual layer thicknesses. As an example our method is used to analyze small-angle reflectivity measurements of Mo/Si and Co/C multilayers. The parameters thus obtained are used to model a structure, which is subsequently used to predict the near-normal incidence reflectivity at soft x-ray wavelengths. The accuracy thus found corresponds to a relative error of 5%. The densities of a Mo/Si multilayer are determined independently with critical angle measurements to verify the values obtained from the grazing incidence reflectivity measurements. The results of the analysis of the Co/C multilayer are compared to values obtained using a conventional method based on the kinematical theory. However, the conventional method requires additional data of soft x-ray reflectivity measurements. The new method yields the same values for the multilayer parameters but does not require the extra soft x-ray measurements. (C) 1997 American Institute of Physics.