Inverse pupil wavefront optimization for immersion lithography

As the critical dimension of integrated circuits is continuously shrunk, thick mask induced aberration (TMIA) cannot be ignored in the lithography image process. Recently, a set of pupil wavefront optimization (PWO) approaches has been proposed to compensate for TMIA, based on a wavefront manipulator in modern scanners. However, these prior PWO methods have two intrinsic drawbacks. First, the traditional methods fell short in building up the analytical relationship between the pupil wavefront and the cost function, and used time-consuming algorithms to solve for the PWO problem. Second, in traditional methods, only the spherical aberrations were optimized to compensate for the focus exposure matrix tilt and best focus shift induced by TMIA. Thus, the degrees of freedom were limited during the optimization procedure. To overcome these restrictions, we build the analytical relationship between the pupil wavefront and the cost function based on Abbe vector imaging theory. With this analytical model and the Fletcher-Reeves conjugate-gradient algorithm, an inverse PWO method is innovated to balance the TMIA including 37 Zernike terms. Simulation results illustrate that our approach significantly improves image fidelity within a larger process window. This demonstrates that TMIA is effectively compensated by our inverse PWO approach.