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Control of polarization and apodization with film materials on photomasks and pellicles for high NA imaging performance

Deviations from paraxial image models are significant at numerical apertures (NA) planned to support immersion lithography. Apodization and rotation of polarization by high numerical optics are well-characterized phenomena. Similar behaviors follow from intrinsic properties of photomask patterns at high spatial frequencies. Diffraction efficiencies differ from values predicted using Kirchhoff boundary conditions, and depend on polarization. Pellicles also apodize diffraction patterns because reflection losses depend on angle of incidence and polarization. These effects are large enough to influence contrast, critical dimension and depth of focus of images thru pitch. These vectorial effects may degrade image quality, or invalidate models for optical proximity correction (OPC) that do not properly comprehend them. What matters for the image is the cumulative contribution of mask pattern, pellicle and optics. The objective in this study is to provide a systematic and unified mapping the optical landscape of mask patterned film and pellicle membrane materials as well as their impacts to vectorial imaging performance. We conclude that to optimize image performance, it is essential to balance the diffraction beam's angle, phase and amplitude. And there are non-unique reticle (mask scatter and pellicle membrane) material solutions to enable high (NA) immersion lithography.