CHARACTERIZATION OF MULTILAYERS BY FOURIER-ANALYSIS OF X-RAY REFLECTIVITY

We discuss a new method to characterize multilayer structures with gra zing-incidence reflectivity measurements using hard x-ray radiation, s uch 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 a ngular 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 th e material composition and tile parameters of the multilayer. The meth od makes a distinction between interface roughness and layer thickness errors, and is independent of measurement of the critical angle. A mi nor disadvantage is that only an average value of the layer thickness is determined, rather than the Individual layer thicknesses. As an exa mple our method is used to analyze small-angle reflectivity measuremen ts of Mo/Si and Co/C multilayers. The parameters thus obtained are use d 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 meas urements to verify the values obtained from the grazing incidence refl ectivity measurements. The results of the analysis of the Co/C multila yer are compared to values obtained using a conventional method based on the kinematical theory. However, the conventional method requires a dditional data of soft x-ray reflectivity measurements. The new method yields the same values for the multilayer parameters but does not req uire the extra soft x-ray measurements. (C) 1997 American Institute of Physics.