Comparison of sparse-based full chip source optimization with different bases

Abstract

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.