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

Abstract

Abstract. 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. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Multi-Objective Defocus Robust Source and Mask Optimization Using Sensitive Penalty

“…Therefore, to tackle the focus variation, an analytical defocus expansion function was derived to predict the defocus aerial image in an inverse lithography technology (ILT) framework [10], so that a variational lithography model (VLIM) is derived to take into account exposure dose and focus variations [11]. Meanwhile, we previously proposed the source-mask-numerical aperture (NA) co-optimization (SMNO) method to extend the depth of defocus (DOF) by fine-tuning the NA [12,13], but it inevitably sacrificed resolution due to the reduction of NA. In addition, Peng et al [14] also studied SMO methods to improve the pattern fidelity in the case of an assigned defocus plane which operated at 100 nm defocusing, and our subsequent works have drawn on this approach [15,16], but it is hard to ensure global fidelity in different defocus variations.…”