Equivalent multilayer bandwidth and comparison between 13.4 nm and 14.4 nm for EUV throughput calculation

In the calculation of wafer throughput for EUV production tools, the multilayer mirrors are often approximated as a passband with a flat response equal to the highest reflectivity of the mirrors and a bandwidth equal to the FWHM of the reflectivity curve. However, the actual reflectivity response of the mirrors is an extended curve which peaks at wavelengths typically between 11-15 nm. With a broadband source, photons with wavelengths outside the FWHM of the mirror are also reflected, contributing to the throughput of the multimirror optical system. We present calculations to compare this simple model with the actual reflectivity curve for Mo/Si mirrors. The result shows that the model is a good approximation for throughput calculations. In this paper, the optimal parameter values and center wavelengths for maximum throughput were also calculated for Mo/Si mirrors at different incidence angles and a values. The simulation results confirm that for near-normal incidence, the optimal center wavelength for maximum integrated reflectivity is near 14.4 nm, in agreement with the previous work by R. Stuik et al.(1) As the off-normal incidence angle (phi) increases, the integrated reflectivity is reduced faster at longer wavelengths. The maximum integrated reflectivity centered at 13.4 nm is closer to that at the optimal center wavelengths for larger value of phi. The effect is more distinct for smaller sigma. For phi equal to 15 degrees (NA similar to 0.25) and peak reflectivity of 70%, the maximum integrated reflectivity of a 9-mirror optical system at 13.4 run is only 2% less than that at 14.4 nm. If a 2-nm thick SiO2 capping layer with roughness of 0.2 nm is included in the simulation, the optimal wavelength is unaffected and only the integrated reflectivity is reduced.