Optimal phase conflict removal for layout of dark field alternating phase shifting masks

Piotr Berman, Andrew B. Kahng, Devendra Vidhani, Huijuan Wang, Alex Zelikovskry

    Research output: Contribution to conferencePaper

    14 Citations (Scopus)

    Abstract

    We describe new, efficient algorithms for layout modification and phase assignment for dark field alternating-type phase-shifting masks in the single-exposure regime. We make the following contributions. First, the problem of minimizing the number of phase conflicts that must be removed to ensure 2-colorability of the conflict graph is transformed to the T-join problem. Second, we give new exact and approximate algorithms for the resulting T-join problem. The exact algorithm is linear in space and substantially faster for sparse graphs than previously known algorithms. The output of the approximate algorithm is much closer to the optimum than the algorithm suggested in [9]. These algorithms are applied within a `one-shot' phase assignment method suggested in [9] for co-optimization of layout and phase assignment for alternating phase-shifting masks. Preliminary computational experience is promising.

    Original languageEnglish (US)
    Pages121-126
    Number of pages6
    StatePublished - Jan 1 1999
    EventProceedings of the 1999 International Symposium on Physical Design, ISPD-99 - Monterey, CA, USA
    Duration: Apr 12 1999Apr 14 1999

    Conference

    ConferenceProceedings of the 1999 International Symposium on Physical Design, ISPD-99
    CityMonterey, CA, USA
    Period4/12/994/14/99

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    All Science Journal Classification (ASJC) codes

    • Electrical and Electronic Engineering

    Cite this

    Berman, P., Kahng, A. B., Vidhani, D., Wang, H., & Zelikovskry, A. (1999). Optimal phase conflict removal for layout of dark field alternating phase shifting masks. 121-126. Paper presented at Proceedings of the 1999 International Symposium on Physical Design, ISPD-99, Monterey, CA, USA, .
    Berman, Piotr ; Kahng, Andrew B. ; Vidhani, Devendra ; Wang, Huijuan ; Zelikovskry, Alex. / Optimal phase conflict removal for layout of dark field alternating phase shifting masks. Paper presented at Proceedings of the 1999 International Symposium on Physical Design, ISPD-99, Monterey, CA, USA, .6 p.
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    abstract = "We describe new, efficient algorithms for layout modification and phase assignment for dark field alternating-type phase-shifting masks in the single-exposure regime. We make the following contributions. First, the problem of minimizing the number of phase conflicts that must be removed to ensure 2-colorability of the conflict graph is transformed to the T-join problem. Second, we give new exact and approximate algorithms for the resulting T-join problem. The exact algorithm is linear in space and substantially faster for sparse graphs than previously known algorithms. The output of the approximate algorithm is much closer to the optimum than the algorithm suggested in [9]. These algorithms are applied within a `one-shot' phase assignment method suggested in [9] for co-optimization of layout and phase assignment for alternating phase-shifting masks. Preliminary computational experience is promising.",
    author = "Piotr Berman and Kahng, {Andrew B.} and Devendra Vidhani and Huijuan Wang and Alex Zelikovskry",
    year = "1999",
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    Berman, P, Kahng, AB, Vidhani, D, Wang, H & Zelikovskry, A 1999, 'Optimal phase conflict removal for layout of dark field alternating phase shifting masks', Paper presented at Proceedings of the 1999 International Symposium on Physical Design, ISPD-99, Monterey, CA, USA, 4/12/99 - 4/14/99 pp. 121-126.

    Optimal phase conflict removal for layout of dark field alternating phase shifting masks. / Berman, Piotr; Kahng, Andrew B.; Vidhani, Devendra; Wang, Huijuan; Zelikovskry, Alex.

    1999. 121-126 Paper presented at Proceedings of the 1999 International Symposium on Physical Design, ISPD-99, Monterey, CA, USA, .

    Research output: Contribution to conferencePaper

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    T1 - Optimal phase conflict removal for layout of dark field alternating phase shifting masks

    AU - Berman, Piotr

    AU - Kahng, Andrew B.

    AU - Vidhani, Devendra

    AU - Wang, Huijuan

    AU - Zelikovskry, Alex

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    N2 - We describe new, efficient algorithms for layout modification and phase assignment for dark field alternating-type phase-shifting masks in the single-exposure regime. We make the following contributions. First, the problem of minimizing the number of phase conflicts that must be removed to ensure 2-colorability of the conflict graph is transformed to the T-join problem. Second, we give new exact and approximate algorithms for the resulting T-join problem. The exact algorithm is linear in space and substantially faster for sparse graphs than previously known algorithms. The output of the approximate algorithm is much closer to the optimum than the algorithm suggested in [9]. These algorithms are applied within a `one-shot' phase assignment method suggested in [9] for co-optimization of layout and phase assignment for alternating phase-shifting masks. Preliminary computational experience is promising.

    AB - We describe new, efficient algorithms for layout modification and phase assignment for dark field alternating-type phase-shifting masks in the single-exposure regime. We make the following contributions. First, the problem of minimizing the number of phase conflicts that must be removed to ensure 2-colorability of the conflict graph is transformed to the T-join problem. Second, we give new exact and approximate algorithms for the resulting T-join problem. The exact algorithm is linear in space and substantially faster for sparse graphs than previously known algorithms. The output of the approximate algorithm is much closer to the optimum than the algorithm suggested in [9]. These algorithms are applied within a `one-shot' phase assignment method suggested in [9] for co-optimization of layout and phase assignment for alternating phase-shifting masks. Preliminary computational experience is promising.

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    Berman P, Kahng AB, Vidhani D, Wang H, Zelikovskry A. Optimal phase conflict removal for layout of dark field alternating phase shifting masks. 1999. Paper presented at Proceedings of the 1999 International Symposium on Physical Design, ISPD-99, Monterey, CA, USA, .