Source and mask optimization (SMO) should be applied in extreme ultraviolet lithography (EUVL) for 7-3 nm technology node. Ineluctable wavefront error (WFE) coming from projection optics or 3D mask effect is considered as a single field point effect instead of full field aware in traditional SMO flow. For getting more qualified SMO, a model of full-field wavefront error aware source and mask optimization (FFSMO) is invented. This method focuses on the tradeoff of lithographic imaging at different typical field point as a multi-objective problem. A new multi-objective cost function is established to improve the uniformity of pattern fidelity at different field point. Simulation results show that the proposed FFSMO method has better imaging uniformity at different field points than non-wavefront error aware SMO (SMO-Ideal) or single field point aware SMO (SMO-F2). For line and space pattern at 7nm node, the standard deviation of pattern error (PAE) reduced from 185.0 to 79.2 comparing with the single field point aware SMO. It is demonstrated that the effectiveness of this FFSMO model in terms of balancing and improving imaging uniformity and PW across full exposure field. For contact hole pattern, the standard deviation of pattern error (PAE) reduced from 233.7 to 75.6 comparing with the single field point aware SMO.
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.
With the increasing requirement of lithographic resolution, the degradation of 3D mask effect on imaging cannot be ignored. The researches of its polarization properties and effect on imaging are of great significance to the development of imaging-based aberration measurement techniques and computational lithography. In this paper, a novel method for comprehensive and quantitative characterization of 3D mask effect is proposed. By comparing the far-field spectrum of Kirchhoff model and 3D mask model, the 3D mask effect is comprehensively and quantitatively characterized as the form of polarization aberration. Pupil-spectrum comprehensive analysis method and background glitch noise culling method are proposed to improve the systematicness and accuracy of 3D mask characterization. The simulation comprehensively analyzes the effect of mask line width and absorber thickness on all polarization properties of the 3D mask effect, showing that this method can provide a more comprehensive analysis of the 3D mask effect compared with the previous methods.
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.
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
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