Semi-implicit level set formulation for lithographic source and mask optimization

Multi-objective and multi-solution source mask optimization using NSGA-II for more direct process window enhancement

Source and mask optimization (SMO) technology is increasingly relied upon for resolution enhancement of photolithography as critical dimension (CD) shrinks. In advanced CD technology nodes, little process variation can impose a huge impact on the fidelity of lithography. However, traditional source and mask optimization (SMO) methods only evaluate the imaging quality in the focal plane, neglecting the process window (PW) that reflects the robustness of the lithography process. PW includes depth of focus (DOF) and exposure latitude (EL), which are computationally intensive and unfriendly to gradient-based SMO algorithms. In this study, we propose what we believe to be a novel process window enhancement SMO method based on the Nondominated Sorting Genetic Algorithm II (NSGA-II), which is a multi-objective optimization algorithm that can provide multiple solutions. By employing the variational lithography model (VLIM), a fast focus-variation aerial image model, our method, NSGA-SMO, can directly optimize the PW performance and improve the robustness of SMO results while maintaining the in-focus image quality. Referring to the simulations of two typical patterns, NSGA-SMO showcases an improvement of more than 20% in terms of DOF and EL compared to conventional multi-objective SMO, and even four times superior to single-objective SMO for complicated patterns.

An Improved 3D OPC Method for the Fabrication of High-Fidelity Micro Fresnel Lenses

Based on three-dimensional optical proximity correction (3D OPC), recent advancements in 3D lithography have enabled the high-fidelity customization of 3D micro-optical elements. However, the micron-to-millimeter-scale structures represented by the Fresnel lens design bring more stringent requirements for 3D OPC, which poses significant challenges to the accuracy of models and the efficiency of algorithms. Thus, a lithographic model based on optical imaging and photochemical reaction curves is developed in this paper, and a subdomain division method with a statistics principle is proposed to improve the efficiency and accuracy of 3D OPC. Both the simulation and the experimental results show the superiority of the proposed 3D OPC method in the fabrication of Fresnel lenses. The computation memory requirements of the 3D OPC are reduced to below 1%, and the profile error of the fabricated Fresnel lens is reduced 79.98%. Applying the Fresnel lenses to an imaging system, the average peak signal to noise ratio (PSNR) of the image is increased by 18.92%, and the average contrast of the image is enhanced by 36%. We believe that the proposed 3D OPC method can be extended to the fabrication of vision-correcting ophthalmological lenses.

Source and mask optimizing with a defocus antagonism for process window enhancement

With the continuous reduction of critical dimension (CD) of integrated circuits, inverse lithography technology (ILT) is widely adopted for the resolution enhancement to ensure the fidelity of photolithography, and for the process window (PW) improvement to enlarge the depth of focus (DOF) and exposure latitude (EL). In the photolithography, DOF is a critical specification which plays a vital role for the robustness of a lithographical process. DOF has been investigated to evaluate the optimization quality of ILT, but there is not a clear scenario to optimize the DOF directly. In this paper, the source and mask optimization (SMO) based on defocus generative and adversarial method (DGASMO) is proposed, which takes the source, mask and defocus as variables, and the inverse imaging framework employs the Adam algorithm to accelerate the optimization. In the optimization process, the penalty term constantly pushes the defocus outward, while the pattern fidelity pushes the defocus term inward, and the optimal source and mask are constantly searched in the confrontation process to realize the control of DOF. Compared to SMO with the Adam method (SMO-Adam), the PW and DOF (EL = 15%) in DGASMO maximally increased 29.12% and 44.09% at 85 nm technology node, and the PW and DOF (EL = 2%) at 55 nm technology node maximally increased 190.2% and 118.42%. Simulation results confirm the superiority of the proposed DGASMO approach in DOF improvement, process robustness, and process window.

Global optimisation of source and mask in inverse lithography via tabu search combined with genetic algorithm

Source mask optimisation (SMO) is a resolution enhancement technology that is utilised in the advanced process node of optical lithography to achieve acceptable imaging quality and fidelity. It is crucial in enhancing the convergence performance and optimisation capability of pixel-based SMO. In this study, an SMO approach that employs a genetic algorithm (GA), combined with the tabu search method (TS), is proposed. GA-TS, a hybrid-type global optimisation algorithm, has an outperforming capacity to avoid local optima owing to the excellent local searching function of TS. Furthermore, an edge-optimisation strategy was implemented to optimise the mask for a low-complexity mask layout. The simulation results confirm that the proposed approach exhibits exceptional optimisation capability and convergence performance.

Memory efficient constrained optimization of scanning-beam lithography

This article describes a memory efficient method for solving large-scale optimization problems that arise when planning scanning-beam lithography processes. These processes require the identification of an exposure pattern that minimizes the difference between a desired and predicted output image, subject to constraints. The number of free variables is equal to the number of pixels, which can be on the order of millions or billions in practical applications. The proposed method splits the problem domain into a number of smaller overlapping subdomains with constrained boundary conditions, which are then solved sequentially using a constrained gradient search method (L-BFGS-B). Computational time is reduced by exploiting natural sparsity in the problem and employing the fast Fourier transform for efficient gradient calculation. When it comes to the trade-off between memory usage and computational time we can make a different trade-off compared to previous methods, where the required memory is reduced by approximately the number of subdomains at the cost of more computations. In an example problem with 30 million variables, the proposed method reduces memory requirements by 67% but increases computation time by 27%. Variations of the proposed method are expected to find applications in the planning of processes such as scanning laser lithography, scanning electron beam lithography, and focused ion beam deposition, for example.

Fast heuristic-based source mask optimization for EUV lithography using dual edge evolution and partial sampling

Extreme ultraviolet (EUV) lithography is essential in the advanced technology nodes. Source mask optimization (SMO) for EUV lithography, especially the heuristic-based SMO, is one of the vital resolution enhancement techniques (RET). In this paper, a fast SMO method for EUV based on dual edge evolution and partial sampling strategies is proposed to improve the optimization efficiency and speed of the heuristic algorithm. In the source optimization (SO) stage, the position and intensity of the source points are optimized in turn. Using the sparsity of the optimized source, a partial sampling encoding method is applied to decrease the variables' dimension in optimization. In the mask optimization (MO) stage, the main features (MF) and the sub-resolution assistant features (SRAF) are optimized in turn. A dual edge evolution strategy is used in the MF optimization and the partial sampling encoding method is used in SRAF optimization. Besides, the imaging qualities at different focal planes are improved by SRAF optimization. The optimization efficiency is greatly improved by the dimensionality reduction strategies. Simulations are carried out with various target patterns. Results show the superiority of the proposed method over the previous method, especially for large complex patterns.

Fast implicit active contour model for inverse lithography

We combine the ideas from level-set methods in computer vision and inverse imaging to derive a generalized active contour model for inverse lithography problems endowed with a locally implemented semi-implicit difference scheme. We introduce a cognitive analogy to move an initial guess of the interesting pattern contour by image-driven forces to the boundaries of the desired layout pattern. We develop an efficient semi-implicit numerical scheme implemented in the vicinity of the zero level-set and apply additive operator splitting (AOS) with respect to coordinate axes to solve consecutive one-dimensional linear systems of equations with the Thomas method. We demonstrate with simulation results that computation and convergence efficiency are jointly improved with reduced optimization dimensionality and a sufficient large step-size.

Source mask optimization for extreme-ultraviolet lithography based on thick mask model and social learning particle swarm optimization algorithm

Extreme ultraviolet (EUV) lithography plays a vital role in the advanced technology nodes of integrated circuits manufacturing. Source mask optimization (SMO) is a critical resolution enhancement technique (RET) or EUV lithography. In this paper, an SMO method for EUV lithography based on the thick mask model and social learning particle swarm optimization (SL-PSO) algorithm is proposed to improve the imaging quality. The thick mask model's parameters are pre-calculated and stored, then SL-PSO is utilized to optimize the source and mask. Rigorous electromagnetic simulation is then carried out to validate the optimization results. Besides, an initialization parameter of the mask optimization (MO) stage is tuned to increase the optimization efficiency and the optimized mask's manufacturability. Optimization is carried out with three target patterns. Results show that the pattern errors (PE) between the print image and target pattern are reduced by 94.7%, 76.9%, 80.6%, respectively.

Source mask optimization using the covariance matrix adaptation evolution strategy

Source mask optimization (SMO) is one of the indispensable resolution enhancement techniques to guarantee the image fidelity and process robustness for the 2Xnm technology node and beyond. The optimization capacity and convergence efficiency of SMO are important, especially for full-chip SMO. An SMO method using the covariance matrix adaptation evolution strategy (CMA-ES), together with a new source representation method, is proposed in this paper. Based on the forward vector imaging formulation, the encoding and decoding methods of the source and the mask, and the constructed merit function, the source and the mask are optimized using the CMA-ES algorithm. The solution search space and the search step size are adaptively updated during the optimization procedure. Considering the sparsity of the optimal source, the source is represented by a set of ideal point sources with unit intensity and adjustable positions. The advantageous spatial frequency components of the source for imaging performance improvement are identified through the aggregation of the point sources. Simulations and comparisons verify the superior optimization capacity and convergence efficiency of the proposed method.

Critical pattern selection method for full-chip source and mask optimization

Source and mask optimization (SMO) is one of the most important resolution enhancement techniques for integrated circuit manufacturing in 2X nm technology node and beyond. Nowadays full-chip SMO is alternatively realized by applying SMO to limited number of selected critical patterns instead of to full-chip area, since it is too computational expensive to be apply SMO in full-chip area directly. The critical patterns are selected by a pattern selection method which enables SMO in full-chip application by balancing the performance and computation consumption. A novel diffraction-based pattern selection method has been proposed in this paper. In this method, diffraction-signatures are sufficiently described with widths in eight selected directions. Coverage rules between the diffraction-signatures are specifically designed. Diffraction-signature grouping method and pattern selection strategy are proposed based on the diffraction-signatures and coverage rules. A series of simulations and comparisons performed using ASML's Tachyon software, which is one of the state of the art commercial SMO platforms, verify the validity of the proposed method.