Parametric source-mask-numerical aperture co-optimization for immersion lithography

Source mask optimization (SMO) is a leading resolution enhancement technique in immersion lithography at the 45-nm node and beyond. Current SMO approaches, however, fix the numerical aperture (NA), which has a strong impact on the depth of focus (DOF). A higher NA could realize a higher resolution but reduce the DOF; it is very important to balance the requirements of NA between resolution and the DOF. In addition, current SMO methods usually result in complicated source and mask patterns that are expensive or difficult to fabricate. This paper proposes a parametric source-mask-NA co-optimization (SMNO) method to improve the pattern fidelity, extend the DOF, and reduce the complexity of the source and mask. An analytic cost function is first composed based on an integrative vector imaging model, in which a differentiable function is applied to formulate the source and mask patterns. Then, the derivative of the cost function is deduced and a gradient-based algorithm is used to solve the SMNO problem. Simulation results show that the proposed SMNO can achieve the optimum combination of parametric source, mask, and NA to maintain high pattern fidelity within a large DOF. In addition, the complexities of the source and mask are effectively reduced after optimization.