A model for multilayer analysis in a coated extreme ultra-violet lithography projection system

Reflection-enhancing multilayer coating is one of the key technologies in Extreme Ultra-Violet Lithography (EUVL). The typical thickness of the Mo/Si multilayer coatings generally adopted in EUVL is about 300 nm, which is much greater than the operating wavelength of 13.5 nm. The EUV is reflected completely back to the vacuum before punching the substrate. This changes the actual reflective surface by dozens of waves and creates extra aberrations. In this study, an equivalent working surface model for multilayer analysis based on the energy conservation principle was developed. Under the premise of the same energy modulation function for real and model film systems, each multilayer film coated optical element with complex energy propagation is transformed into a single surface. Optical design software can be used to assess these virtual surface in terms of estimation and optimization. Finally, the model was applied to a same Schwarzschild system but with different coating solutions. And the best solution was confirmed in which the coating-induced aberrations could be compensated for by image defocus.