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.
Highlights
Optimization techniques play an important role in the improvement of the pattern fidelity and depth of focus (DOF) of current optical lithography systems
Most methods are based on a scalar imaging model that is no longer accurate for a numerical aperture ðNAÞ > 0.6.10 In high-NA immersion lithography systems, the vector nature of the electromagnetic field must be taken into account
This paper proposes a parametric source-mask-NA co-optimization (SMNO) method using a vector imaging model to improve the pattern fidelity and DOF
Summary
Optimization techniques play an important role in the improvement of the pattern fidelity and depth of focus (DOF) of current optical lithography systems. We proposed a pixelated SMO based on a vector imaging model that significantly improved the simulation precision for lithography at the 45-nm node and beyond.[11,12]. Current pixelated SMO methods dramatically increase the complexity and fabrication cost of the optimized To overcome these limitations, this paper proposes a parametric source-mask-NA co-optimization (SMNO) method to improve the pattern fidelity within a large DOF and the complexity of the source and mask patterns. This paper is the first to solve for the parametric SMNO problem based on a vector imaging model. The simulations show that, in comparison with the SMO method, the proposed SMNO method can achieve the optimal combination of source, mask, and NA to achieve superior imaging performance over a wider DOF.
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