Freeform surface off-axis illumination design with the Monge-Ampère equation method in optical lithography

Off-axis illumination (OAI) is a promising resolution-enhancement technology in optical lithography. This paper aims to provide some practical OAI solutions for optical lithography by using freeform surfaces. An integrated Monge-Ampère (MA) equation method is presented here to find these solutions. By this method, the OAI design is converted into a nonlinear boundary problem for the elliptic MA equation. Then, the L² Monge-Kantorovich theory is used to find an initial design for the iterative scheme of the MA method. The prescribed OAI patterns are successfully achieved with energy efficiency of more than 99.9% and relative standard deviation of irradiance of less than 0.009. Smooth freeform surfaces that are much easier to fabricate are obtained, and the achieved OAI designs have large tolerance to the spread angle of the collimated beam. This may be a significant step toward a practical technique for OAI design in optical lithography.