A Hybrid Eigenmode Restoration Algorithm for Computational Lithography Problems Based on Mode Matching Principle

The mode matching method is an efficient solution to conventional microwave waveguide problems for its dimensionality advantages. It is theoretically extendable to computational lithography problems in nano scales with periodic boundary condition. The high computational complexity of conventional mode matching limits its application significance in highly complicated nano scale problems. This paper introduces an optimized efficient mode matching method for computational lithography problems whose complexity is O(
$\text{N}^{1.5}$
). This bottleneck is breached by transforming governing equations with Lanczos algorithm. A novel hybrid eigenmode restoration algorithm is proposed to solve the eigenmode accuracy loss by involving the Arnoldi method. Benchmark cases verify the accuracy of the restored eigenmode and mode matching method with from microwave to nano scale problems. The efficiency is further optimized by exploring the relevance between iteration step and structure complexity. The non-uniform iteration step is introduced for efficiency optimization. A real mask component is modelled as a multi-junctional waveguide structure with periodic boundary condition. Simulation results validate the effectiveness of the proposed method and efficiency benefits are discussed through comparison with other solvers including HFSS and RCWA. Results indicate that the proposed method possesses good flexibility and application significance for computational lithography problems with high complexity.