Conventional and modified Schwarzschild objective for EUV lithography: design relations

The design criteria of a Schwarzschild-type optical system are reviewed in relation to its use as an imaging system in an extreme ultraviolet lithography setup. Both the conventional and the modified reductor imaging configurations are considered, and the respective performances, as far as the geometrical resolution in the image plane is concerned, are compared. In this connection, a formal relation defining the modified configuration is elaborated, refining a rather naive definition presented in an earlier work. The dependence of the geometrical resolution on the image-space numerical aperture for a given magnification is investigated in detail for both configurations. So, the advantages of the modified configuration with respect to the conventional one are clearly evidenced. The results of a semi-analytical procedure are compared with those obtained from a numerical simulation performed by an optical design program. The Schwarzschild objective based system under implementation at the ENEA Frascati Center within the context of the Italian FIRB project for EUV lithography has been used as a model. Best-fit functions accounting for the behaviour of the system parameters vs. the numerical aperture are reported; they can be a useful guide for the design of Schwarzschild objective type optical systems.