Simultaneous source-mask optimization: a numerical combining method

Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn; Taravade, Kunal N.; Stanton, William

doi:10.1117/12.865965

Cited by 13 publications

(4 citation statements)

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“…As a significant ILT approach, pixelated source optimization (SO) has been proven to be necessary for improving the imaging performance of lithography in advanced technology nodes [8], [9]. Furthermore, it has been successfully applied by several institutions, such as ASML [10]- [12] and IBM [13], [14], to modulate the intensity distribution and incident angles of lithography-illumination sources in industrial applications [15], [16]. However, the highly complex representation of the source impacts the performance of the pixelated SO method.…”

Section: Introductionmentioning

confidence: 99%

Inverse Lithography Source Optimization via Particle Swarm Optimization and Genetic Combined Algorithm

et al. 2023

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Inverse lithography technologies (ILTs) are critical for improving the imaging performance of lithography in advanced technology nodes. Pixel-based source optimization (SO), as an efficient part of ILTs, can be implemented via heuristic approaches to achieve high-performance lithographic imaging. In this paper, a SO approach based on a combination of the particle-swarm optimization and genetic algorithms (PSO-GA) is proposed to determine the optimal intensity distribution of the source via iterations. The pixelated source can be decoded into the optimized variables of the merit functions in the SO model. The proposed PSO-GA algorithm, as a highefficiency hybrid algorithm, can transform the discrete SO problem into the optimal search solution for the merit function, thereby inversely enhancing the lithographic-imaging performance. In the forward-imaging model in the lithography, the extraction of the mask's effective diffraction spectrum is implemented to calculate the layout of resist patterns. The simulation results highlight the superior performance of the proposed approach in achieving pixelated SO over the traditional GA and PSO algorithm in terms of convergence capacity.

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Section: Introductionmentioning

confidence: 99%

Inverse Lithography Source Optimization via Particle Swarm Optimization and Genetic Combined Algorithm

et al. 2023

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“…In contrast, most of the recent SMO algorithms compute a source pattern represented by grayscale pixels [18][19][20]. In these algorithms, the source patterns are discretized into matrices according to a specified pixel size, and each entry of the matrices is a variable [21]. The grayscale pixel can represent a continuum of real numbers from 0 to 1, and the freedom of the solution space is then greatly enlarged.…”

Section: Introductionmentioning

confidence: 99%

Efficient source mask optimization with Zernike polynomial functions for source representation

Wu¹,

Liu²,

Li³

et al. 2014

Opt. Express

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In 22nm optical lithography and beyond, source mask optimization (SMO) becomes vital for the continuation of advanced ArF technology node development. The pixel-based method permits a large solution space, but involves a time-consuming optimization procedure because of the large number of pixel variables. In this paper, we introduce the Zernike polynomials as basis functions to represent the source patterns, and propose an improved SMO algorithm with this representation. The source patterns are decomposed into the weighted superposition of some well-chosen Zernike polynomial functions, and the number of variables decreases significantly. We compare the computation efficiency and optimization performance between the proposed method and the conventional pixel-based algorithm. Simulation results demonstrate that the former can obtain substantial speedup of source optimization while improving the pattern fidelity at the same time.

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“…With the availability of free-form sources using diffractive optical elements (DOE), SO serves as a new option for achieving higher resolution without increasing the complexity of mask design. The proposal of source mask co-optimization (SMO) further permits the exploration of design spaces for both illuminations and masks [14][15][16][17][18]. Since both SO and MO rely on the complexity of computational lithography algorithms to explore all possible solutions, the design of objective functions has a significant impact on the quality of developed patterns [19], the manufacturability of sources and masks, and the convergence.…”

Section: Introductionmentioning

confidence: 99%

Fast source optimization involving quadratic line-contour objectives for the resist image

Yu¹,

Yu²,

Chao³

2012

Opt. Express

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In Abbe's formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.

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Simultaneous source-mask optimization: a numerical combining method

Cited by 13 publications

References 0 publications

Inverse Lithography Source Optimization via Particle Swarm Optimization and Genetic Combined Algorithm

Inverse Lithography Source Optimization via Particle Swarm Optimization and Genetic Combined Algorithm

Efficient source mask optimization with Zernike polynomial functions for source representation

Fast source optimization involving quadratic line-contour objectives for the resist image

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