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On the similarities between micro/nano lithography and topology optimization projection methods

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Abstract

The aim of this paper is to incorporate a model for micro/nano lithography production processes in topology optimization. The production process turns out to provide a physical analogy for projection filters in topology optimization. Blueprints supplied by the designers cannot be directly used as inputs to lithographic processes due to the proximity effect which causes rounding of sharp corners and geometric interaction of closely spaced design elements. Therefore, topology optimization is applied as a tool for proximity effect correction. Furthermore, it is demonstrated that the robust projection filter can be used to account for uncertainties due to lithographic production processes which results in manufacturable blueprint designs and eliminates the need for subsequent corrections.

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Notes

  1. These values are strongly dependent on the technology at hand. Values \(\alpha _{\mathrm {f}} = 0.013~\mathrm {\mu m}\), \(\alpha _{\mathrm {b}} = 34~\mathrm {\mu m}\) and \(\tau = 0.512\) were reported for a ZEP520 resist material and a more modern EBL system. It can be expected that the backscattering component will approximately lead to a uniform increase of the background exposure for such large differences between \(\alpha _{\mathrm {f}}\) and \(\alpha _{\mathrm {b}}\).

  2. It should be pointed out that the term regularization is often used in lithography to describe techniques for cleaning the dose pattern which differs from topology optimization where regularization is used for ensuring existence of the solution.

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Acknowledgments

The authors would like to thank Lars Hagedorn Frandsen of the DTU Fotonik department for fruitful discussions on the topic. This research was supported by the NextTop project sponsored by the Villum Foundation and the KU Leuven - BOF PFV/10/002 OPTEC - Optimization in Engineering Center.

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Authors and Affiliations

  1. Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, 3001, Leuven, Belgium

    Miche Jansen

  2. Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Nils Koppel’s Allé, Building 404, 2800, Lyngby, Denmark

    Boyan S. Lazarov & Ole Sigmund

  3. Department of Architecture, Urbanism and Planning, KU Leuven, Kasteelpark Arenberg 1, 3001, Leuven, Belgium

    Mattias Schevenels

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  1. Miche Jansen
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  2. Boyan S. Lazarov
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  4. Ole Sigmund
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Correspondence to Miche Jansen.

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Jansen, M., Lazarov, B.S., Schevenels, M. et al. On the similarities between micro/nano lithography and topology optimization projection methods. Struct Multidisc Optim 48, 717–730 (2013). https://doi.org/10.1007/s00158-013-0941-6

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  • DOI: https://doi.org/10.1007/s00158-013-0941-6

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