Optimization of layered synthetic microstructures for narrowband reflectivity at soft X-ray and EUV wavelengths

Mathematics

Scientific paper

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Extreme Ultraviolet Radiation, Metal Films, Microstructure, Reflectance, Ultraviolet Reflection, X Ray Scattering, Film Thickness, Iridium, Matrices (Mathematics), Optimization, Platinum, Silicon, Wavelengths

Scientific paper

The production of layered synthetic microstructures (LSM), optimized to produce maximum reflectivity over the 100-600 A waveband, is considered. Only two combinations of materials, iridium-silicon and platinum-silicon, are considered. The matrix method for determining the reflectivity of an LSM is reviewed, and a criterion is developed for obtaining the maximum reflectivity at a single wavelength for a periodic LSM. It is shown that LSMs are useful for obtaining high reflectivities in the soft X-ray and EUV portions of the spectrum, particularly at angles approaching normal incidence. Nonperiodic LSM structures, optimized over a narrow band centered at a given wvelength, can yield higher reflectivities than the periodic LSM optimized at that wavelength. The reflectivities of a periodic LSM and an optimized nonperiodic LSM approach the same value asymptotically as the number of layers is increased. This asymptotic reflectivity can thus be used as a criterion to test potential material combinations at wavelengths of interest.

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