Source and mask optimization (SMO) technology is an increasingly important resolution enhancement technology (RET) that can optimize the source and mask. Various SMO methods have made great progress in terms of computational efficiency and pattern fidelity. Besides, process window (PW) is also an important indicator to evaluate the performance of lithography imaging. PW consists of exposure latitude (EL) and depth of focus (DOF). However, currently, there are few SMO methods that can directly improve EL. In this paper, we propose an EL aware SMO (ELASMO) method by innovating a new penalty function for improving the exposure latitude. Compared to the conventional SMO, the proposed ELASMO can significantly enhance aerial image contrast and enlarge the exposure latitude from 5% to 11% under the premise of ensuring imaging fidelity. ELASMO achieves high-fidelity lithography in a larger process window.
As lithographic technology continues to advance, the size of nodes has continually been decreased while the control of defocus has become stringent in the actual lithography process. Defocus is always uncertain in the practical exposure process due to multi-factor impact, which is supposed to be considered as an important element of the aerial imaging model. It’s necessary to analyze the influence of defocus on the aerial image. In this paper, aerial image approximates to a second-order polynomial for different defocus through Taylor series expansion. Then the respective and the joint impacts of the first-order defocus term and the second-order defocus term on aerial image for various conditions have been studied by simulation. Simulation shows that annulus illumination source can reduce the impact of the first-order defocus term and the second-order defocus term is more valuable to be studied and controlled to improve lithographic resolution and process robust
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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