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Applied Physics B

, 122:222 | Cite as

Large-scale segmentation errors in optical gratings and their unique effect onto optical scattering spectra

  • Martin HeusingerEmail author
  • Thomas Flügel-Paul
  • Uwe-Detlef Zeitner
Article

Abstract

In this paper, we analyze the influence of large-scale segmentation errors in the morphology of high-performance optical gratings. It is thus assumed that the optical grating under consideration (typical lateral extends S are 10–1000 mm) can be spatially decomposed into a great many but unique sub-segments (\(\ll S\); typical extends are 10–100 \(\upmu \mathrm{m}\)). Any violation of the perfect periodicity will result in the generation of stray light, especially Rowland ghosts, which radiate into a small angular region around the grating’s diffraction orders. In this paper, we focus on three different kinds of segmentation errors. On the one hand, there are statistic as well as deterministic alignment errors between otherwise perfect sub-segments. On the other hand, we analyze the effect of chirping of geometrical parameters, i.e., the groove width, within every sub-segment. Most importantly, we find that the particular type of imperfection results in a unique characteristic of the according stray light spectrum which thus acts as a fingerprint. We come to this conclusion on three different ways. First, we rely on a simple theoretical model that is based on scalar diffraction theory. Second, we have performed rigorous numerical simulations for a high aspect ratio purely dielectric spectrometer grating (\(\hbox {period} = {667}\,\mathrm{nm}\)). Third, the very same grating was then fabricated by e-beam lithography and its stray light spectrum was measured with a purposely designed optical setup. Eventually, all different routes to analyze the problem turn out to be in very good agreement, and we are confident that stray light measurements can be used as an important tool in the detection of fabrication imperfections.

Keywords

Diffraction Efficiency Diffraction Order Alignment Error Segmentation Error Direct Laser Writing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    T. Eversberg, K. Vollmann, Spectroscopic Instrumentation (Springer, Berlin, 2015)CrossRefGoogle Scholar
  2. 2.
    H.T. Nguyen, B.W. Shore, S.J. Bryan, J.A. Britten, R.D. Boyd, M.D. Perry, Opt. Lett. 22(3), 142–144 (1997)ADSCrossRefGoogle Scholar
  3. 3.
    U.D. Zeitner, M. Oliva, F. Fuchs, D. Michaelis, T. Benkenstein, T. Harzendorf, E.B. Kley, Appl. Phys. A 109(4), 789–796 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, A. Duparré, Appl. Opt. 53(4), A35–A41 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    M.D. Perry, C. Shannon, E. Shults, R.D. Boyd, J.A. Britten, D. Decker, B.W. Shore, Opt. Lett. 20(8), 940–942 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    J.E. Harvey, S. Schröder, N. Choi, A. Duparré, Opt. Eng. 51(1), 013402–1 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    T.M. Elfouhaily, C.A. Guérin, Waves Random Media 14(4), R1–R40 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D.H. Penalver, J.E. Harvey, Opt. Expr. 19(10), 9820–9835 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    Y. Zhao, G.C. Wang, T.M. Lu, Characterization of Amorphous and Crystalline Rough Surface-Principles and Applications (Academic Press, London, 2000)Google Scholar
  10. 10.
    A.R. Pawloski, A. Acheta, S. Bell, B. La Fontaine, T. Wallow, H.J. Levinson, in Proceedings of the SPIE Advanced Lithography, pp. 615318–615318 (2006)Google Scholar
  11. 11.
    E. Gogolides, V. Constantoudis, G. Kokkoris, in Proceedings of the SPIE Advanced Lithography, pp. 868505–868505 (2013)Google Scholar
  12. 12.
    S. Chauhan, M. Somervell, M. Carcasi, S. Scheer, R.T. Bonnecaze, C.A. Mack, C.G. Willson, J. Micro/Nanolithogr. MEMS MOEMS 13(1), 013012–013012 (2014)CrossRefGoogle Scholar
  13. 13.
    T.A. Germer, in Proceedings of the SPIE Advanced Lithography, pp. 65180Z–65180Z (2007)Google Scholar
  14. 14.
    T. Schuster, S. Raer, K. Frenner, W. Osten, in Proceedings of the SPIE 7155, Ninth International Symposium on Laser Metrology, pp. 71550W–71550W (2008)Google Scholar
  15. 15.
    A. Kato, F. Scholze, Appl. Opt. 49(31), 6102–6110 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    H. Gross, M.A. Henn, S. Heidenreich, A. Rathsfeld, M. Bär, Appl. Opt. 51(30), 7384–7394 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    E. Gogolides, V. Constantoudis, G.P. Patsis, A. Tserepi, Microelectr. Eng. 83(4), 1067–1072 (2006)CrossRefGoogle Scholar
  18. 18.
    C.A. Palmer, E.G. Loewen, R.G.L. Thermo, Diffraction Grating Handbook (Newport Corporation Springfield, Ohio, 2005)Google Scholar
  19. 19.
    D.R. Lobb, I.S. Bhatti, in Proceedings of the ICSO—International Conference on Space Optics (2010)Google Scholar
  20. 20.
    S. Kraft, J.L. Bézy, U. Del Bello, R. Berlich, M. Drusch, R. Franco, A. Gabriele, B. Harnisch, R. Meynart, P. Silvestrin, in Proceedings of the SPIE Remote Sensing, pp. 88890T–88890T (2013)Google Scholar
  21. 21.
    G. Kopp, P. Pilewskie, C. Belting, Z. Castleman, G. Drake, J. Espejo, K. Heuerman, B. Lamprecht, P. Smith, B. Vermeer, in Proceedings of the IGARSS—Geoscience and Remote Sensing Symposium, pp. 3518–3521 (2013)Google Scholar
  22. 22.
    J. Leckey, International archives of the photogrammetry. Remote Sens. Spat. Inf. Sci. XL-7/W3, 213–217 (2015)Google Scholar
  23. 23.
    W. Freese, T. Kämpfe, W. Rockstroh, E.B. Kley, A. Tünnermann, Opt. Expr. 19(9), 8684–8692 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    G. de Zwart, M.A. van den Brink, R.A. George, D. Satriasaputra, J. Baselmans, H. Butler, J.B. van Schoot, J. de Klerk, in Proceedings of the Microlithography’97, pp. 817–835 (1997)Google Scholar
  25. 25.
    C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, New York, 2008)Google Scholar
  26. 26.
    B.W. Smith, Optical Projection Lithography (Woodhead, Cambridge, 2014)CrossRefGoogle Scholar
  27. 27.
    M. Eibelhuber, T. Glinsner, T. Uhrmann, P. Lindner, Photon. Spectr. 49(2), 34–37 (2015)Google Scholar
  28. 28.
    A.I.M. Greer, B. Della-Rossa, A.Z. Khokhar, N. Gadegaard, Nanoscale Res. Lett. 11(1), 1–9 (2016)CrossRefGoogle Scholar
  29. 29.
    S. Bagheri, K. Weber, T. Gissibl, T. Weiss, F. Neubrech, H. Giessen, ACS Photon. 2(6), 779–786 (2015)CrossRefGoogle Scholar
  30. 30.
    U.D. Zeitner, F. Fuchs, E.B. Kley, in Proceedings of the SPIE Astronomical Telescopes and Instrumentation, pp. 84502Z–84502Z (2012)Google Scholar
  31. 31.
    M.G. Moharam, T.K. Gaylord, E.B. Grann, D.A. Pommet, JOSA A 12(5), 1068–1076 (1995)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of applied Physics IAPJenaGermany
  2. 2.Fraunhofer Institute for applied optics and precision engineering IOFJenaGermany

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