Objective As the critical dimensions of integrated circuits continue to decrease, conventional deep-ultraviolet (DUV) lithography machines can no longer satisfy the demand for superior resolution. Currently, extreme ultraviolet (EUV) lithography machines are the most promising for lithography. Generally, an EUV optical system comprises a source, an illumination system, and projection optics. The illumination system, which is located between the source and projection optics, is a key component of an EUV lithography machine. Its primary function is to modulate the spatial and angular spectral distributions of light beam emitted from the source. Simultaneously, it can achieve a uniform illumination of the mask and form multiple illumination modes in the pupil plane. In the early 1990s, scientists attempted to use micro-optics devices to shape illumination light (also referred to as pupil shaping), during which the main pupil shaping schemes included diffractive optical elements (DOEs), micro-lens arrays (MLAs), and micro-mirror arrays (MMAs). However, when the exposure wavelength is reduced to 13.5 nm, most of the pupil-shaping schemes that yield excellent performance in DUV lithography machines are no longer applicable. Currently, the mainstream scheme for pupil shaping in EUV lithography involves the use of double facet mirrors. We can achieve pupil shaping without light loss by changing the facetmapping relationship; additionally, the light emitted from the intermediate focus can offer uniform illumination on the mask. Obtaining a facetmapping relationship is a core issue in pupil shaping. In this study, we investigate the pupil-shaping technique of EUV lithography and present an algorithm that can rapidly determine the facetmapping relationship to provide a reference for studies pertaining to EUV pupil-shaping techniques. Methods We investigated an EUV pupil-shaping technique in this study. First, we analyzed the principle of pupil shaping based on double facet mirrors and achieved uniform illumination on a mask. In addition, we clarified the pupil characteristic parameters of different illumination modes. Subsequently, we introduced a facet-grouping algorithm based on backtracking and tabu search, which effectively reduced the complexity of facet mapping. Moreover, we used the improved artificial bee colony algorithm (IABC) for facet matching to optimize the illumination uniformity on the mask. We obtained the facet-mapping relationship of different illumination modes using facet-grouping and facet-matching algorithms. Finally, to verify the effectiveness of the proposed algorithms, we assessed various illumination modes obtained using the algorithms above by employing LightTools. Results and Discussions The facet-grouping algorithm effectively groups all pupil facets and ensures that at least one pupil facet in each pupil facet set functions in the required illumination mode. The MATLAB software is used to obtain all sets of pupil facets, and then we can obtain the numbers of all working pupil facets under 14 illumination modes. Based on the results, the illumination areas on the pupil facets plane under the 14 illumination modes are obtained (Fig. 8). Compared with the facet - matching optimization algorithms based on the genetic algorithm (GA) and ant colony (ACO) algorithm, the facet-matching optimization algorithm based on the IABC performs better, i.e., its objective function converges more rapidly and its matching results are better; furthermore, it can solve large-scale facet matching more effectively (Fig. 10 ). The simulation results of LightTools show that the facet-grouping and facet matching algorithms introduced in this study can form multiple illumination modes in the pupil plane (Fig. 12) while achieving highly uniform illumination on the mask (conjugate plane) (Fig. 13 ). Conclusions In an EUV lithography illumination system, the pupil-shaping technique based on double faceted mirrors can form different illumination modes and requires facet mapping. Herein, we present an algorithm that can rapidly determine facet-mapping relationships. By grouping and matching the field and pupil facets, we obtained the facet-mapping relationships of different illumination modes. The proposed algorithm can be defined as a two-step process. First, the pupil facets are categorized based on backtracking and tabu search. This enables the formation of multiple illumination modes in the pupil plane while reducing the complexity of facet mapping. Second, the facet-matching problem is abstracted as an assignment problem and solved using an IABC, which can yield facet-matching results more rapidly and effectively. The algorithm presented herein can be used to obtain the facet-mapping relationships of different illumination modes. The simulation results show that the facet-mapping relationship determined by the algorithm can achieve highly uniform illumination on the mask (conjugate plane) and form multiple illumination modes in the pupil plane.
