Fast micromirror selection and angle setting algorithm for freeform pupil in the illumination system for immersion lithography machines

As lithography resolution improves, the performance requirements for illumination pupils in immersion lithography machines have become increasingly stringent, particularly regarding energy balance and polarization properties. These characteristics are primarily achieved by adjusting the angular distribution of the micromirror array (MMA). For technology nodes below 40 nm, the impact of light polarization on imaging must be considered. This paper proposes a micro-mirror selection and angle setting algorithm to maintain key characteristics of the freeform pupil, ensuring energy balance in both unpolarized and polarized states. Energy balance in the unpolarized state is influenced by the eccentricity of light, while energy balance in the polarized state depends on both the eccentricity and polarization properties of light. To validate the accuracy of the algorithm, simulations were conducted using freeform pupil illumination optical models for both unpolarized and polarized states. The results demonstrated a significant improvement in energy balance, with a reduction to 0.08% in both states. For engineering applications, the computational speed of the algorithm was enhanced, reducing the calculation time from 600 to 0.1 s.