Background: Defect compensation is one of the enabling techniques for high-volume manufacturing using extreme ultraviolet lithography. Aim: The advanced evolution strategy algorithm based on covariance matrix adaption is applied to compensation optimization to improve the convergence efficiency and algorithm operability. Approach: The advanced algorithm optimizes the solution population by sampling from the self-adapted covariance matrix of mutation distribution. Results: Optimization simulations for three different masks validated the algorithm’s advantage in convergence efficiency and searching ability compared with original differential evolution, evolution strategy, genetic algorithm (GA), and Nelder–Mead simplex method. The advanced algorithm employs fewer user-defined parameters and is proved to be robust to variations of these parameters. Conclusions: The advanced algorithm obtains better results compared with GA for best-focus, through-focus, and complex-pattern optimizations. With the inherent invariance property, appropriate operability, and robustness, we recommend applying this algorithm to other lithography optimization problems.
An efficient pixel-based mask optimization method via particle swarm optimization (PSO) algorithm for inverse lithography is proposed. Because of the simplicity of principles, the ease of implementation and the efficiency of convergence, PSO has been widely used in many fields. In this study, PSO is used to solve the inverse problem of mask optimization. The pixel-based mask patterns are transformed into frequency space using discrete cosine transformation and the frequency components are encoded into particles. The pattern fidelity is adopted as the fitness function to evaluate these particles. The mask optimization method is implemented by updating the velocities and positions of these particles. Simulation results show that the image fidelity has been efficiently improved after using the proposed method.
Source optimization is one of the key techniques for achieving higher resolution without increasing the complexity of mask design. An efficient source optimization approach is proposed on the basis of particle swarm optimization. The pixelated sources are encoded into particles, which are evaluated by using the pattern error as the fitness function. Afterward, the optimization is implemented by updating the velocities and positions of these particles. This approach is demonstrated using three mask patterns, including a periodic array of contact holes, a vertical line/space design, and a complicated pattern. The pattern errors are reduced by 69.6%, 51.5%, and 40.3%, respectively. Compared with the source optimization approach via genetic algorithm, the proposed approach leads to faster convergence while improving the image quality at the same time. Compared with the source optimization approach via gradient descent method, the proposed approach does not need the calculation of gradients, and it has a strong adaptation to various lithographic models, fitness functions, and resist models. The robustness of the proposed approach to initial sources is also verified.
In recent years, with the availability of freeform sources, source optimization has emerged as one of the key techniques for achieving higher resolution without increasing the complexity of mask design. In this paper, an efficient source optimization approach using particle swarm optimization algorithm is proposed. The sources are represented by pixels and encoded into particles. The pattern fidelity is adopted as the fitness function to evaluate these particles. The source optimization approach is implemented by updating the velocities and positions of these particles. The approach is demonstrated by using two typical mask patterns, including a periodic array of contact holes and a vertical line/space design. The pattern errors are reduced by 66.1% and 39.3% respectively. Compared with the source optimization approach using genetic algorithm, the proposed approach leads to faster convergence while improving the image quality at the same time. The robustness of the proposed approach to initial sources is also verified.
Source mask optimization (SMO) is one of the required techniques for lithography below 32 nm. Source representation is one important factor that affects both the imaging simulation and optimization processes of SMO, especially the global SMOs such as the SMO using genetic algorithm (GA-SMO). We propose a source representation which accelerates the GA-SMO. The proposed representation uses a group of circular poles to describe the freeform illumination source whose pupil filling ratio (PFR) is small. Compared with conventional Cartesian-grid and polar-grid pixelated representations, the proposed multipole source representation can represent the low-PFR freeform illumination source with fewer variables, which speeds up both the GA convergence and lithography imaging simulation. Numerical experiments show that the GA-SMO using the proposed multipole source representation method is about seven times faster than that using polar-grid pixelated source representation on the premise that other simulation conditions are the same and optimization qualities are comparable.
Source mask optimization (SMO) is considered to be one of the technologies to push conventional 193nm lithography to its ultimate limits. In comparison with other SMO methods that use an inverse problem formulation, SMO based on genetic algorithm (GA) requires very little knowledge of the process, and has the advantage of flexible problem formulation. Recent publications on SMO using a GA employ a binary-coded GA. In general, the performance of a GA depends not only on the merit or fitness function, but also on the parameters, operators and their algorithmic implementation. In this paper, we propose a SMO method using real-coded GA where the source and mask solutions are represented by floating point strings instead of bit strings. Besides from that, the selection, crossover, and mutation operators are replaced by corresponding floating-point versions. Both binary-coded and real-coded genetic algorithms were implemented in two versions of SMO and compared in numerical experiments, where the target patterns are staggered contact holes and a logic pattern with critical dimensions of 100 nm, respectively. The results demonstrate the performance improvement of the real-coded GA in comparison to the binary-coded version. Specifically, these improvements can be seen in a better convergence behavior. For example, the numerical experiments for the logic pattern showed that the average number of generations to converge to a proper fitness of 6.0 using the real-coded method is 61.8% (100 generations) less than that using binary-coded method.
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