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Roughness and Scatter in Optical Coatings

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Optical Characterization of Thin Solid Films

Part of the book series: Springer Series in Surface Sciences ((SSSUR,volume 64))

Abstract

The measurement of light scattering from optical components has received increased attention in the last decade. In addition to being a serious source of noise, light scattering can lead to a reduced optical throughput, degrade the imaging quality, or cause straylight in optical systems. On the other hand, the high sensitivity towards small imperfections and inhomogeneities makes light scattering measurements a powerful inspection tool. Measured light scattering is a good indicator of the surface quality and can be used to characterize the surface roughness or local defects. After an introduction of the main scattering quantities as well as their standardization, this chapter will focus on the instrumentation used to characterize light scattering and provide various application examples ranging from the light scattering based roughness characterization of supersmooth substrates to the roughness evolution of different multilayer coatings and its impact on the scattering properties.

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References

  1. V. Džimbeg-Malcic, Ž. Barbaric-Mikocevic, K. Itric, Kubelka-Munk theory indescribing optical properties of paper (I). Tehn. vjesn. 18, 117–124 (2011)

    Google Scholar 

  2. M.A. Hubbe, J.J. Pawlak, A.A. Koukoulas, Paper’s appearance: a review. BioResour. 3, 627–665 (2008)

    Google Scholar 

  3. E. Yablonovitch, G.D. Cody, Intensity enhancement in textured optical sheets for solar cells. IEEE Trans. Electron. Dev. 29, 300–305 (1982)

    Article  ADS  Google Scholar 

  4. M.A. Green, Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions. Prog. Photovoltaics: Res. Appl. 10, 235–241 (2002)

    Article  Google Scholar 

  5. R.P. Breault, Control of stray light, in Handbook of Optics Volume I Fundamentals, Techniques, and Design, ed. by M. Bass (1995), pp. 38.1–38.35

    Google Scholar 

  6. J.M. Bennett, L. Mattsson, in Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, 1989)

    Google Scholar 

  7. J.C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE Press, Bellingham, 2012)

    Google Scholar 

  8. M.G. Dittman, Contamination scatter functions for stray-light analysis. Proc. SPIE 4774, 99–110 (2002)

    Article  ADS  Google Scholar 

  9. P.A. Bobbert, J. Vlieger, Light scattering by a sphere on a substrate. Physica 137A, 209–242 (1986)

    Article  ADS  Google Scholar 

  10. T. Herffurth, S. Schröder, M. Trost, A. Duparré, A. Tünnermann, Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor. Appl. Opt. 52, 3279–3287 (2013)

    Article  ADS  Google Scholar 

  11. T.A. Germer, Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness. Appl. Opt. 36, 8798–8805 (1997)

    Article  ADS  Google Scholar 

  12. M. Trost, T. Herffurth, D. Schmitz, S. Schröder, A. Duparré, A. Tünnermann, Evaluation of subsurface damage by light scattering techniques. Appl. Opt. 52, 6579–6588 (2013)

    Article  ADS  Google Scholar 

  13. E.L. Church, P.Z. Takacs, Surface scattering, in Handbook of Optics: Fundamentals, Techniques, and Design, ed. by M. Bass, 2nd ed. (McGraw-Hill, Inc., New York, 1995), pp. 7.1–7.14

    Google Scholar 

  14. A. Sentenac, H. Giovannini, M. Saillard, Scattering from rough inhomogeneous media: splitting of surface and volume scattering. J. Opt. Soc. Am. A 19, 727–736 (2002)

    Article  ADS  Google Scholar 

  15. P. Bousquet, F. Flory, P. Roche, Scattering from multilayer thin films: theory and experiment. J. Opt. Soc. Am. 71, 1115–1123 (1981)

    Article  ADS  Google Scholar 

  16. C. Amra, Light scattering from multilayer optics. I. Tools of investigation. J. Opt. Soc. Am. A 11, 197–210 (1994)

    Article  ADS  Google Scholar 

  17. J.M. Elson, J.P. Rahn, J.M. Bennett, Light scattering from multilayer optics: comparison of theory and experiment. Appl. Opt. 19, 669–679 (1980)

    Article  ADS  Google Scholar 

  18. P. Bussemer, K. Hehl, S. Kassam, Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack. Waves Random Media 1, 207–221 (1991)

    Article  ADS  Google Scholar 

  19. S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, A. Duparré, Spectral angle resolved scattering of thin film coatings. Appl. Opt. 53, A35–A41 (2014)

    Article  Google Scholar 

  20. M. Trost, T. Herffurth, S. Schröder, A. Duparré, A. Tünnermann, Scattering reduction through oblique multilayer deposition. Appl. Opt. 53, A197–A204 (2014)

    Article  Google Scholar 

  21. T. Herffurth, M. Trost, S. Schröder, K. Täschner, H. Bartzsch, P. Frach, A. Duparré, A. Tünnermann, Roughness and optical losses of rugate coatings. Appl. Opt. 53, A351–A359 (2014)

    Article  Google Scholar 

  22. S. Schröder, A. Duparré, Measurement of light scattering, transmittance, and reflectance, in Laser-Induced Damage in Optical Materials, ed. by D. Ristau. (CRC Press/Taylor & Francis Group, 2014), pp. 213–245

    Google Scholar 

  23. M. Trost, T. Herffurth, S. Schröder, A. Duparré, M. Beier, S. Risse, A. Tünnermann, N. Böwering, In situ and ex situ characterization of optical surfaces by light scattering techniques. Opt. Eng. 53, 092013 (2014)

    Article  ADS  Google Scholar 

  24. V. Rehn, V.O. Jones, J.M. Elson, J.M. Bennett, The role of surface topography in predicting scattering at grazing incidence from optical surfaces. Nucl. Instrum. Methods 172, 307–314 (1980)

    Article  ADS  Google Scholar 

  25. F.E. Nicodemus, J.C. Richmond, J.J. Hsia, I.W. Ginsberg, T. Limperis, Geometrical considerations and nomenclature for reflectance. Natl. Bur. Stand. Monogr. 160, 1–52 (1977)

    Google Scholar 

  26. ASTM E 1392-90, Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces (American Society for Testing and Materials, Philadelphia, 1990)

    Google Scholar 

  27. T.A. Leonard, M. Pantoliano, J. Reilly, Results of a CO2 BRDF round robin. Proc. SPIE 1165, 444–449 (1989)

    Article  ADS  Google Scholar 

  28. T.A. Leonard, P. Rudolph, BRDF round robin test of ASTM E1392. Proc. SPIE 1995, 285–293 (1993)

    Article  ADS  Google Scholar 

  29. ASTM E 2387-5, Standard Practice for Goniometric Optical Scatter Measurements (American Society for Testing and Materials, Philadelphia, 2011)

    Google Scholar 

  30. ISO 13696, Optics and Photonics – Lasers and Laser Related Equipment – Test Methods for Radiation Scattered by Optical Components (International Organization for Standardization, Geneva, Switzerland, 2002)

    Google Scholar 

  31. ASTM F 1048-87, Standard Test Method for Measuring the Effective Surface Roughness of Optical Components by Total Integrated Scattering (American Society for Testing and Materials, Philadelphia, 1999)

    Google Scholar 

  32. S.O. Rice, Reflection of electromagnetic waves from slightly rough surfaces. Commun. Pure Appl. Math. 4, 351–378 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  33. E.L. Church, H.A. Jenkinson, J.M. Zavada, Relationship between surface scattering and microtopographic features. Opt. Eng. 18, 125–136 (1979)

    Article  ADS  Google Scholar 

  34. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon Press, Oxford, 1963)

    MATH  Google Scholar 

  35. Lord Rayleigh, On the dynamical theory of gratings. Proc. R. Soc. Lond. Ser. A 79, 399–416 (1907)

    Article  ADS  MATH  Google Scholar 

  36. J.C. Stover, Experimental confirmation of the Rayleigh-Rice obliquity factor. Proc. SPIE 7792, 77920J (2010)

    Article  ADS  Google Scholar 

  37. N. Choi, J.E. Harvey, Numerical validation of the generalized Harvey-Shack surface scatter theory. Opt. Eng. 52, 115103 (2013)

    Article  ADS  Google Scholar 

  38. S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D.H. Penalver, J.E. Harvey, Modeling of light scattering in different regimes of surface roughness. Opt. Express 19, 9820–9835 (2011)

    Article  ADS  Google Scholar 

  39. J.M. Elson, J.M. Bennett, Calculation of the power spectral density from surface profile data. Appl. Opt. 34, 201–208 (1995)

    Article  ADS  Google Scholar 

  40. A. Duparré, J. Ferré-Borrull, S. Gliech, G. Notni, J. Steinert, J.M. Bennett, Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components. Appl. Opt. 41, 154–171 (2002)

    Article  ADS  Google Scholar 

  41. E.L. Church, H.A. Jenkinson, J.M. Zavada, Measurement of the finish of diamond-turned metal surfaces by differential light scattering. Opt. Eng. 16, 360–374 (1977)

    Article  ADS  Google Scholar 

  42. C. Amra, From light scattering to the microstructure of thin-film multilayers. Appl. Opt. 32, 5481–5491 (1993)

    Article  ADS  Google Scholar 

  43. H. Davies, The reflection of electromagnetic waves from a rough surface. Proc. IEEE 101, 209–214 (1954)

    Google Scholar 

  44. H.E. Bennett, J.O. Porteus, Relation between surface roughness and specular reflectance at normal incidence. J. Opt. Soc. Am. 51, 123–129 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  45. J.C. Stover, S. Schröder, T.A. Germer, Upper roughness limitations on the TIS/RMS relationship. Proc. SPIE 8495, 849503 (2012)

    Article  Google Scholar 

  46. J.V. Grishchenko, M.L. Zanaveskin, Investigation into the correlation factor of substrate and multilayer film surfaces by atomic force microscopy. Crystallogr. Rep. 58, 493–497 (2013)

    Article  ADS  Google Scholar 

  47. S. Schröder, A. Duparré, A. Tünnermann, Roughness evolution and scatter losses of multilayers for 193 nm optics. Appl. Opt. 47, C88–C97 (2008)

    Article  Google Scholar 

  48. W.M. Tong, R.S. Williams, Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothing and roughening. Annu. Rev. Phys. Chem. 45, 401–438 (1994)

    Article  ADS  Google Scholar 

  49. M. Kardar, G. Parisi, Y.-C. Zhang, Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892 (1986)

    Article  ADS  MATH  Google Scholar 

  50. D.G. Stearns, Stochastic model for thin film growth and erosion. Appl. Phys. Lett. 62, 1745–1747 (1993)

    Article  ADS  Google Scholar 

  51. J. Ebert, H. Pannhorst, H. Küster, H. Welling, Scatter losses of broadband interference coatings. Appl. Opt. 18, 818–822 (1979)

    Article  ADS  Google Scholar 

  52. S. Schröder, H. Uhlig, A. Duparré, N. Kaiser, Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components. Proc. SPIE 5963, 59630R (2005)

    Article  Google Scholar 

  53. K.H. Guenther, Revisiting structure zone models for thin film growth. Proc. SPIE 1324, 2–12 (1990)

    Article  ADS  Google Scholar 

  54. S. Schröder, T. Feigl, A. Duparré, A. Tünnermann, EUV reflectance and scattering of Mo/Si multilayers on differently polished substrates. Opt. Express 15, 13997–14012 (2007)

    Article  ADS  Google Scholar 

  55. R. Canestrari, D. Spiga, G. Pareschi, Analysis of microroughness evolution in X-ray astronomical multilayer mirrors by surface topography with the MPES program and by X-ray scattering. Proc. SPIE 6266, 626613 (2006)

    Article  Google Scholar 

  56. M. Trost, S. Schröder, T. Feigl, A. Duparré, A. Tünnermann, Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers. Appl. Opt. 50, C148–C153 (2011)

    Article  Google Scholar 

  57. H.E. Bennett, Scattering characteristics of optical materials. Opt. Eng. 17, 480–488 (1978)

    Article  ADS  Google Scholar 

  58. K.H. Guenther, P.G. Wierer, J.M. Bennett, Surface roughness measurements of low-scatter mirrors and roughness standards. Appl. Opt. 23, 3820–3836 (1984)

    Article  ADS  Google Scholar 

  59. J.A. Detrio, S.M. Miner, Standardized total integrated scatter measurements of optical surfaces. Opt. Eng. 24, 419–422 (1985)

    Article  ADS  Google Scholar 

  60. D. Rönnow, E. Veszelei, Design review of an instrument for spectroscopic total integrated light scattering measurements in the visible wavelength region. Rev. Sci. Instrum. 65, 327–334 (1994)

    Article  ADS  Google Scholar 

  61. O. Kienzle, J. Staub, T. Tschudi, Description of an integrated scatter instrument for measuring scatter losses of “superpolished” optical surfaces. Meas. Sci. Technol. 5, 747–752 (1994)

    Article  ADS  Google Scholar 

  62. A. Duparré, S. Gliech, Non-contact testing of optical surfaces by multiple-wavelength light scattering measurement. Proc. SPIE 3110, 566–573 (1997)

    Article  ADS  Google Scholar 

  63. P. Kadkhoda, A. Mueller, D. Ristau, Total scatter losses of optical components in the DUV/VUV spectral range. Proc. SPIE 3902, 118–127 (2000)

    Article  ADS  Google Scholar 

  64. S. Gliech, J. Steinert, A. Duparré, Light-scattering measurements of optical thin-film components at 157 and 193 nm. Appl. Opt. 41, 3224–3235 (2002)

    Article  ADS  Google Scholar 

  65. M. Otani, R. Biro, C. Ouchi, Y. Suzuki, K. Sone, S. Niisaka, T. Saito, J. Saito, A. Tanaka, A. Matsumoto, Development of optical coatings for 157-nm lithography. II. Reflectance, absorption, and scatter measurement. Appl. Opt. 41, 3248–3255 (2002)

    Article  ADS  Google Scholar 

  66. S. Schröder, S. Gliech, A. Duparré, Measurement system to determine the total and angle-resolved light scattering of optical components in the deep-ultraviolet and vacuum-ultraviolet spectral regions. Appl. Opt. 44, 6093–6107 (2005)

    Article  ADS  Google Scholar 

  67. D.R. Cheever, F.M. Cady, K.A. Klicker, J.C. Stover, Design review of a unique complete angle scatter instrument (CASI). Proc. SPIE 818, 13–20 (1987)

    Article  ADS  Google Scholar 

  68. C.C. Asmail, C.L. Cromer, J.E. Proctor, J.J. Hsia, Instrumentation at the national institute of standards and technology for bidirectional reflectance distribution function (BRDF) measurements. Proc. SPIE 2260, 52–61 (1994)

    Article  ADS  Google Scholar 

  69. A. von Finck, T. Herffurth, S. Schröder, A. Duparré, S. Sinzinger, Characterization of optical coatings using a multisource table-top scatterometer. Appl. Opt. 53, A259–A269 (2014)

    Article  Google Scholar 

  70. A. von Finck, M. Trost, S. Schröder, A. Duparré, Parallelized multichannel BSDF measurements. Opt. Express 23, 33493–33505 (2015)

    Article  ADS  Google Scholar 

  71. C. Amra, D. Torricini, P. Roche, Multiwavelength (0.45–10.6 µm) angle-resolved scatterometer or how to extend the optical window. Appl. Opt. 32, 5462–5474 (1993)

    Article  ADS  Google Scholar 

  72. F.M. Cady, J.C. Stover, D.R. Bjork, M.L. Bernt, M.W. Knighton, D.J. Wilson, D.R. Cheever, A design review of a multiwavelength, three-dimensional scatterometer. Proc. SPIE 1331, 201–208 (1990)

    Article  ADS  Google Scholar 

  73. S. Schröder, T. Herffurth, M. Trost, A. Duparré, Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis. Appl. Opt. 49, 1503–1512 (2010)

    Article  ADS  Google Scholar 

  74. M.M. Barysheva, Y.A. Vainer, B.A. Gribkov, M.V. Zorina, A.E. Pestov, N.N. Salashchenko, N.I. Chkhalo, A.V. Shcherbakov, Investigation of supersmooth optical surfaces and multilayer elements using soft x-ray radiation. Tech. Phys. 58, 1371–1379 (2013)

    Google Scholar 

  75. M. Zerrad, M. Lequime, C. Amra, Multimodal scattering facilities and modelization tools for a comprehensive investigation of optical coatings. Proc. SPIE 8169, 81690K (2011)

    Article  ADS  Google Scholar 

  76. M. Lequime, M. Zerrad, C. Deumié, C. Amra, A goniometric light scattering instrument with high-resolution imaging. Opt. Commun. 282, 1265–1273 (2009)

    Article  ADS  Google Scholar 

  77. C.C. Cooksey, M.E. Nadal, D.W. Allen, K.-O. Hauer, A. Höpe, Bidirectional reflectance scale comparison between NIST and PTB. Appl. Opt. 54, 4006–4015 (2015)

    Article  ADS  Google Scholar 

  78. S. Schröder, T. Herffurth, H. Blaschke, A. Duparré, Angle-resolved scattering: an effective method for characterizing thin-film coatings. Appl. Opt. 50, C164–C171 (2011)

    Article  Google Scholar 

  79. C.C. Asmail, J. Hsia, A. Parr, J. Hoeft, Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements. Appl. Opt. 33, 6084–6091 (1994)

    Article  ADS  Google Scholar 

  80. C. Wagner, N. Harned, EUV lithography: lithography gets extreme. Nat. Photonics 4, 24–26 (2010)

    Article  ADS  Google Scholar 

  81. N.R. Böwering et al., Performance results of laser-produced plasma test and prototype light sources for EUV lithography. J. Micro/Nanolithogr. MEMS MOEMS 8, 041504 (2009)

    Article  Google Scholar 

  82. M. Trost, S. Schröder, A. Duparré, S. Risse, T. Feigl, U.D. Zeitner, A. Tünnermann, Structured Mo/Si multilayers for IR-suppression in laser-produced EUV light sources. Opt. Express 21, 27852–27864 (2013)

    Article  ADS  Google Scholar 

  83. M. Trost, S. Schröder, C.C. Lin, A. Duparré, A. Tünnermann, Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering. Proc. SPIE 8501, 85010F (2012)

    Article  Google Scholar 

  84. A. Duparré, D. Ristau, Optical interference coatings 2010 measurement problem. Appl. Opt. 50, C172–C177 (2011)

    Article  Google Scholar 

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Authors and Affiliations

  1. Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Albert-Einstein-Str. 7, 07745, Jena, Germany

    M. Trost & S. Schröder

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  1. M. Trost
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  2. S. Schröder
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Editors and Affiliations

  1. Abbe School of Photonics, Friedrich-Schiller-University Jena, Jena, Thüringen, Germany

    Olaf Stenzel

  2. Institute of Physical Engineering, Brno University of Technology, Brno, Czech Republic

    Miloslav Ohlídal

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Trost, M., Schröder, S. (2018). Roughness and Scatter in Optical Coatings. In: Stenzel, O., Ohlídal, M. (eds) Optical Characterization of Thin Solid Films. Springer Series in Surface Sciences, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-75325-6_14

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