Design and fabrication of W/Si multilayer mirrors for the K-edge of Ti

The periodic mulitlayer with high reflectivity and small full width at half maximum (FWHM) in hard x-ray range, while the reflectivity of non-periodic multilayer decreases and FWHM increase. Therefore, the optimum coating design must be found out as a compromise between the requirements for the reflectivity and the FWHM. We have used purely numerical techniques to design broad angular multilayer mirror in angle intervals (2.9°-3.1°), which is starting from an appropriate periodic multilayer structure. In our method, the risk of local minimization of the merit function disappears, because we refined the desired depth-distribution of the period using a direct numerical algorithm and the analytical solution as a starting point for computer calculation. The plateau reflectivity can be obtained in a few minutes. The main feature of our approach is the use of an analytical solution as a starting point for direct computer search, and the desired results can be given in a reasonable time. This technique is able to design almost any given reflectivity spectrum both energy- and angle-dependent and in a reasonable amount of time. The periodic and non-periodic W/Si multilayer for grazing incidence multilayer mirrors at the K-edge of Ti (0.275 nm) were both designed and fabricated by high vacuum DC magnetron sputtering coater model JGP560C6, and the multilayer films were characterized by X-ray reflectivity measurements on a laboratory x-ray diffractometer(XRD) and the atomic force microscope (AFM). We find good agreement of the changing trend of surface roughness between the simulation of XRD and measurement of AFM.