Illumination System Pupil-Shaping Technique Based on Integer Programming and Energy Equalization

The illumination system in extreme ultraviolet lithography (EUVL) achieves pupil shaping by adjusting the facet-matching relationship of fly’s eyes. We propose an algorithm based on integer programming and energy equalization for solving the facet-matching relationship, which constrains the energy consistency across different pupil regions, enhancing pupil performance and achieving high uniformity at the mask plane. We model an illumination system to validate the proposed algorithm. Simulation results demonstrate that the proposed algorithm successfully realizes various illumination modes, achieving a maximum pupil ellipticity of 1.94%, maximum X/Y pupil pole balance of 1.45%, and maximum quadrant pole balance of 1.82%. Furthermore, it achieved an illumination field at the mask plane with a pre-correction nonuniformity of 0.45–0.59%.