Multilayer-coating-induced aberrations in extreme-ultraviolet lithography optics.

Current research on optical coatings has focused on amplitude effects, which are well understood and predictable. However, phase effects introduced by multilayer coatings remain less explored. Prior studies have established the multiplicative nature of amplitude changes but have not fully addressed how coatings alter wavefront phase. This gap motivated the development of a mathematical framework to describe phase effects in general cases. The need for precise aberration estimation in lithography optics has driven interest in this area. Existing models have not yet captured field-dependent aberrations caused by coatings. Researchers have yet to quantify how graded or uniform coatings influence optical performance. This uncertainty has limited the ability to optimize coating designs for lithography applications. The lack of field-dependent aberration data has hindered progress in reducing optical distortions.

This study aimed to develop a mathematical formalism for describing phase effects caused by multilayer coatings in extreme-ultraviolet lithography. The goal was to create an analytical method for estimating wavefront aberrations introduced by these coatings. Researchers focused on both field-independent and field-dependent aberrations. The study sought to differentiate between uniform and graded multilayer coatings in their optical effects. A specific case involved a plane mirror tilted at 8.2 degrees to a converging beam. The analysis aimed to identify and quantify various types of aberrations up to second order. The study also aimed to determine whether coatings could introduce anamorphic magnification. The ultimate purpose was to provide a framework for improving optical design in lithography systems.

The researchers used a mathematical formalism to model phase effects in multilayer coatings. They developed an analytical method to estimate wavefront aberrations in general cases. The study considered both uniform and graded coatings for field-independent aberrations. For field-dependent aberrations, only uniform coatings were analyzed. The analysis was based on a coated plane mirror tilted at 8.2 degrees to a converging beam. The numerical aperture of the beam was set at 0.1 for calculations. The method identified aberrations such as piston, defocus, tilt, astigmatism, and anamorphic magnification. The study applied the formalism to a specific optical setup to derive numerical results.

The study identified several aberrations introduced by multilayer coatings up to second order. These included field-dependent piston and field-squared-dependent piston effects. Defocus, field-independent tilt, and astigmatism were also observed. Anamorphic magnification was found to be caused by the coating itself. Graded coatings showed significantly smaller aberration coefficients than uniform ones. The field-independent aberration coefficients for graded coatings were ten times smaller. The analysis confirmed that coatings can introduce optical distortions. The numerical aperture of 0.1 and 8.2-degree tilt were used to calculate specific values.

The authors concluded that multilayer coatings can introduce various wavefront aberrations in lithography optics. Both field-independent and field-dependent effects were identified using the mathematical formalism. Graded coatings reduced aberration magnitudes compared to uniform coatings. The study showed that coatings can cause anamorphic magnification. The formalism provides a general method for estimating phase effects. The analysis was applied to a specific optical setup with a tilted mirror and converging beam. The findings suggest that coating design can influence optical performance. The results support the need for further study on optimizing coating structures.