Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods

Pang, Liang; Hu, Peter; Peng, Danping; Chen, Dongxue; Cecil, Tom; He, Lin; Xiao, Gao; Tolani, Vikram; Dam, Thuc; Baik, Ki‐Ho; Gleason, Bob

doi:10.1117/12.843578

“…ILT masks can have non-orthogonal target shapes, especially if methods such as level set are used for ILT[21].…”

mentioning

confidence: 99%

Benchmarking of mask fracturing heuristics

Chan¹,

Gupta²,

Han³

et al. 2014

2014 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Aggressive resolution enhancement techniques such as inverse lithography (ILT) often lead to complex, non-rectilinear mask shapes which make mask writing extremely slow and expensive. To reduce shot count of complex mask shapes, mask writers allow overlapping shots, due to which the problem of fracturing mask shapes with minimum shot count is NP-hard. The need to correct for e-beam proximity effect makes mask fracturing even more challenging. Although a number of fracturing heuristics have been proposed, there has been no systematic study to analyze the quality of their solutions. In this work, we propose a new method to generate benchmarks with known optimal solutions that can be used to evaluate the suboptimality of mask fracturing heuristics. We also propose a method to generate tight upper and lower bounds for actual ILT mask shapes by formulating mask fracturing as an integer linear program and solving it using branch and price. Our results show that a state-of-the-art prototype [version of] capability within a commercial EDA tool for e-beam mask shot decomposition can be suboptimal by as much as 3.7× for generated benchmarks, and by as much as 3.6× for actual ILT shapes.

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“…Beyond the broad categories of optical domain and spatial domain representations, the chosen approach can involve 0-1 bounded pixels, 125,127 discrete coding strings for genetic algorithms, 128 level set methods, [129][130][131][132] and variational formulations for fast solution using adjoint variables. In practice, the optimization formulation is inevitably an idealization of a very complex set of engineering requirements, and considerable ingenuity is often involved in devising a formulation that meshes well with the variable representation and optimization algorithm employed.…”

Section: Optimization Of Masks and Sources (Smo)mentioning

confidence: 99%

Computational lithography: Exhausting the resolution limits of 193-nm projection lithography systems

Melville¹,

Rosenbluth²,

Waechter³

et al. 2011

Journal of Vacuum Science & Technology B, Nanotechnology an

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Articles you may be interested inAnalysis and optimization approaches for wide-viewing-angle λ/4 plate in polarimetry for immersion lithographyIn the recent past, scaling of semiconductor fabrication systems has been dominated by wavelength and numerical aperture modifications. This is now no longer the case for 193-nm immersion projection lithography (193i) systems as there are no technical paths for continued benefit from the in these areas. Instead, a range of techniques including patterning processes and system optimization are being used to push the limits of the system. This paper will review the elements that are now driving scaling for a system of fixed wavelength and numerical aperture.

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“…Due to aggressive RET techniques such as ILT, mask shapes are now often curved and non-rectilinear [21] [6]. Fracturing these polygons using traditional methods with acceptable fidelity can dramatically increase the shot count [24].…”

Section: Introductionmentioning

confidence: 99%

Benchmarking of Mask Fracturing Heuristics

Chan

¹

,

Gupta

²

,

Han

³

et al. 2017

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Aggressive resolution enhancement techniques such as inverse lithography (ILT) often lead to complex, non-rectilinear mask shapes which make mask writing extremely slow and expensive. To reduce shot count of complex mask shapes, mask writers allow overlapping shots, due to which the problem of fracturing mask shapes with minimum shot count is NP-hard. The need to correct for e-beam proximity effect makes mask fracturing even more challenging. Although a number of fracturing heuristics have been proposed, there has been no systematic study to analyze the quality of their solutions. In this work, we propose a new method to generate benchmarks with known optimal solutions that can be used to evaluate the suboptimality of mask fracturing heuristics. We also propose a method to generate tight upper and lower bounds for actual ILT mask shapes by formulating mask fracturing as an integer linear program and solving it using branch and price. Our results show that a state-of-the-art prototype [version of] capability within a commercial EDA tool for e-beam mask shot decomposition can be suboptimal by as much as 3.7× for generated benchmarks, and by as much as 3.6× for actual ILT shapes.

show abstract

Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods

Cited by 19 publications

References 14 publications

Benchmarking of mask fracturing heuristics

Benchmarking of mask fracturing heuristics

Computational lithography: Exhausting the resolution limits of 193-nm projection lithography systems

Benchmarking of Mask Fracturing Heuristics

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