Source optimization (SO) is an extensively used resolution enhancement technology which can improve the imaging performance of optical lithography. To improve the computational efficiency of traditional SO, compressive sensing (CS) has been involved. In the CS-SO theory, the source pattern needs to be presentation as sparsely as possible by sparse basis, because the sparsity of source pattern can significantly improve the recovery performance of CS-SO. Therefore, the selection of the sparse basis can affect the performance of CS-SO. Discrete Fourier transform (DFT) basis, especially its variant discrete cosine transform (DCT) basis has been widely used in CS. Furthermore, some overcomplete bases have also been used in many fields. In this paper we present a comparison of sparse-based full chip SO with spatial basis, DCT basis, DFT basis, overcomplete DCT (ODCT) basis, overcomplete DFT (ODFT) basis and haar wavelet basis. The full chip SO problem is formulated as a cost function of multi-objective adaptive optimization, and then a soft threshold iterative (IST) algorithm is used to obtain the optimized source pattern. The simulation results show that the sparse-based method can effectively improve the imaging performance. Exactly, in terms of imaging fidelity, spatial, DCT, DFT, ODCT, and haar wavelet bases are similar, and better than the ODFT basis. However, in terms of optimizing speed, the spatial and DCT basis can converge to an acceptable SO solution at a faster speed than other bases.
Fast source pupil optimization (SO) has appeared as an important technique for improving lithographic imaging fidelity and process window (PW) in holistic lithography at 7-5nm node. Gradient-based methods are generally used in current SO. However, most of these methods are time-consuming. In our previous work, compressive sensing (CS) theory is applied to accelerate the SO procedure, where the SO is formulated as an underdetermined linear problem by randomly sampling monitoring pixels on mask features. CS-SO theory assumes that the source pattern is a sparse pattern on a certain basis, then the SO is transformed into a L1-norm or Lp-norm (0<p<1) image reconstruction problem. However, above methods are relaxation approaches of L0-norm method for convenient achievement. In this paper, to our best knowledge, transformed L1 penalty (TL1) and the difference of convex functions algorithm (DCA) for TL1 (DCATL1) are first developed to solve this inverse lithography SO problem in advantages. The source pattern is optimized by minimizing cost function pattern error with TL1 penalty. The DCATL1 method decomposes this cost function into the difference of two convex functions. By linearizing one convex function, the SO procedure can be transformed into a sequence of strongly convex minimization sub-problems, which can be accurately and efficiently solved by the Fast Alternating Direction Method of Multipliers (Fast ADMM) algorithm. Compared to previous methods, DCATL1 method can simultaneous realize fast and robust SO.
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