Abstract

Laterally structured antireflective sub-wavelength structures show unique properties with respect to broadband performance, damage threshold and thermal stability. Thus they are superior to classical layer based antireflective coatings for a number of applications. Dependent on the selected fabrication technology the local topography of the periodic structure may deviate from the perfect repetition of a sub-wavelength unit cell. We used rigorous coupled-wave analysis (RCWA) to simulate the efficiency losses due to scattering effects based on height and displacement variations between the individual protuberances. In these simulations we chose conical and Super-Gaussian shapes to approximate the real profile of structures fabricated in fused silica. The simulation results are in accordance with the experimentally determined optical properties of sub-wavelength structures over a broad wavelength range. Especially the transmittance reduction in the deep-UV could be ascribed to these variations in the sub-wavelength structures.

© 2010 Optical Society of America

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References

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  1. P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature 244, 281–282 (1973).
    [Crossref]
  2. A. R. Parker, “515 million years of structural colors,” J. Opt. A: Pure Appl. Opt. 2, R15–R28 (2000).
    [Crossref]
  3. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
    [Crossref]
  4. M. E. Motamedi, W. H. Southwell, and W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31(22), 4371–4376 (1993).
    [Crossref]
  5. A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
    [Crossref] [PubMed]
  6. Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
    [Crossref]
  7. M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
    [Crossref]
  8. L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
    [Crossref]
  9. K. Asakawa and T. Hiraoka, “Nanopatterning with microdomains of Block Copolymers using reactive-ion etching selectivity,” Jpn. J. Appl. Phys. 41, 6112–6118 (2002).
    [Crossref]
  10. J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
    [Crossref]
  11. R. Glass, M. Möller, and J. P. Spatz, “Block copolymer micelle nanolithography,” Nanotechnology 14(10), 1153–1160 (2003).
    [Crossref]
  12. T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
    [Crossref] [PubMed]
  13. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995).
    [Crossref]
  14. S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93, 133108 (2008).
    [Crossref]
  15. M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
    [Crossref]
  16. K. Hehl, “Unigit - versatile rigorous grating solver,” Jena, Germany, web site: http://www.unigit.com/ .
  17. J. Bischoff, “Formulation of the normal vector RCWA for symmetric crossed gratings in symmetric mountings,” J. Opt. Soc. Am. A 27(5), 1024–1031 (2010).
    [Crossref]
  18. R. Bräuer and O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Applied Optics 33(34), 7875–7882 (1994).
    [Crossref] [PubMed]

2010 (1)

2008 (2)

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93, 133108 (2008).
[Crossref]

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

2003 (2)

R. Glass, M. Möller, and J. P. Spatz, “Block copolymer micelle nanolithography,” Nanotechnology 14(10), 1153–1160 (2003).
[Crossref]

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

2002 (1)

K. Asakawa and T. Hiraoka, “Nanopatterning with microdomains of Block Copolymers using reactive-ion etching selectivity,” Jpn. J. Appl. Phys. 41, 6112–6118 (2002).
[Crossref]

2001 (1)

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

2000 (2)

J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
[Crossref]

A. R. Parker, “515 million years of structural colors,” J. Opt. A: Pure Appl. Opt. 2, R15–R28 (2000).
[Crossref]

1999 (1)

1998 (1)

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

1997 (1)

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

1995 (2)

E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995).
[Crossref]

M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
[Crossref]

1994 (1)

R. Bräuer and O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Applied Optics 33(34), 7875–7882 (1994).
[Crossref] [PubMed]

1993 (1)

1973 (1)

P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature 244, 281–282 (1973).
[Crossref]

Adamson, D. H.

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

Asakawa, K.

K. Asakawa and T. Hiraoka, “Nanopatterning with microdomains of Block Copolymers using reactive-ion etching selectivity,” Jpn. J. Appl. Phys. 41, 6112–6118 (2002).
[Crossref]

Bagnall, D. M.

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93, 133108 (2008).
[Crossref]

Banhart, F.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Bischoff, J.

Bläsi, B.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Boden, S. A.

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93, 133108 (2008).
[Crossref]

Bräuer, R.

R. Bräuer and O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Applied Optics 33(34), 7875–7882 (1994).
[Crossref] [PubMed]

Brunner, R.

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

Bryngdahl, O.

R. Bräuer and O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Applied Optics 33(34), 7875–7882 (1994).
[Crossref] [PubMed]

Cao, L.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Chaikin, P. M.

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

Clapham, P. B.

P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature 244, 281–282 (1973).
[Crossref]

Gaylord, T. K.

M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
[Crossref]

Glass, R.

R. Glass, M. Möller, and J. P. Spatz, “Block copolymer micelle nanolithography,” Nanotechnology 14(10), 1153–1160 (2003).
[Crossref]

Gombert, A.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Grann, E. B.

M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
[Crossref]

E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995).
[Crossref]

Gunning, W. J.

Hane, K.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
[Crossref]

Harrison, C.

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

Hartmann, C.

J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
[Crossref]

Heinzel, A.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Helgert, M.

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

Hiraoka, T.

K. Asakawa and T. Hiraoka, “Nanopatterning with microdomains of Block Copolymers using reactive-ion etching selectivity,” Jpn. J. Appl. Phys. 41, 6112–6118 (2002).
[Crossref]

Horbelt, W.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Hutley, M. C.

P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature 244, 281–282 (1973).
[Crossref]

Kanamori, Y.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
[Crossref]

Lohmüller, T.

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

Manners, I.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Massey, J. A.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Moharam, M. G.

Moharam, M.G.

M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
[Crossref]

Möller, M.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

R. Glass, M. Möller, and J. P. Spatz, “Block copolymer micelle nanolithography,” Nanotechnology 14(10), 1153–1160 (2003).
[Crossref]

J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
[Crossref]

Mössmer, S.

J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
[Crossref]

Motamedi, M. E.

Park, M.

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

Parker, A. R.

A. R. Parker, “515 million years of structural colors,” J. Opt. A: Pure Appl. Opt. 2, R15–R28 (2000).
[Crossref]

Pommet, D. A.

M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
[Crossref]

E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995).
[Crossref]

Register, R. A.

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

Riethmüller, S.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Rose, K.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Sai, H.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Sasaki, M.

Southwell, W. H.

Spatz, J. P.

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

R. Glass, M. Möller, and J. P. Spatz, “Block copolymer micelle nanolithography,” Nanotechnology 14(10), 1153–1160 (2003).
[Crossref]

J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
[Crossref]

Sundermann, M.

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

Winnik, M. A.

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Wittwer, V.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Yugami, H.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Zanke, Ch.

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Adv. Funct. Mater. (1)

L. Cao, J. A. Massey, M. A. Winnik, I. Manners, S. Riethmüller, F. Banhart, J. P. Spatz, and M. Möller, “Reactive ion etching of cylindrical polyferrocenylsilane block copolymer micelles: Fabrication of ceramic nanolines on semiconducting substrates,” Adv. Funct. Mater. 13(4), 271–276 (2003).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93, 133108 (2008).
[Crossref]

Applied Optics (1)

R. Bräuer and O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Applied Optics 33(34), 7875–7882 (1994).
[Crossref] [PubMed]

J. Opt. A: Pure Appl. Opt. (1)

A. R. Parker, “515 million years of structural colors,” J. Opt. A: Pure Appl. Opt. 2, R15–R28 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

M.G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. 12(5), 1077–1085 (1995).
[Crossref]

J. Opt. Soc. Am. A (2)

Jpn. J. Appl. Phys. (1)

K. Asakawa and T. Hiraoka, “Nanopatterning with microdomains of Block Copolymers using reactive-ion etching selectivity,” Jpn. J. Appl. Phys. 41, 6112–6118 (2002).
[Crossref]

Langmuir (1)

J. P. Spatz, S. Mössmer, C. Hartmann, and M. Möller, “Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films,” Langmuir 16(2), 407–415 (2000).
[Crossref]

Nano Lett. (1)

T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008).
[Crossref] [PubMed]

Nanotechnology (1)

R. Glass, M. Möller, and J. P. Spatz, “Block copolymer micelle nanolithography,” Nanotechnology 14(10), 1153–1160 (2003).
[Crossref]

Nature (1)

P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature 244, 281–282 (1973).
[Crossref]

Opt. Lett. (1)

Science (1)

M. Park, C. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, “Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter,” Science 276(5317), 1401–1404 (1997).
[Crossref]

Solar Energy Materials & Solars Cells (1)

A. Gombert, K. Rose, A. Heinzel, W. Horbelt, Ch. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Solar Energy Materials & Solars Cells 54(1–4), 333–342 (1998).
[Crossref] [PubMed]

Other (1)

K. Hehl, “Unigit - versatile rigorous grating solver,” Jena, Germany, web site: http://www.unigit.com/ .

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Figures (13)

Fig. 1
Fig. 1 SEM images of fabricated antireflective sub-wavelength structures. (a) AR structure generated by interference lithography and reactive ion beam etching (lattice spacing: 139 nm). (b) AR structure manufactured by a combination of BCML and RIE according to Lohmüeller et al (lattice spacing: 80 nm). [12]

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Fig. 2
Fig. 2 Calculated reflectance for a conical shaped AR structure in dependency of structure height and number of Rayleigh orders. The wavelength of light was 325 nm (perpendicular incidence). The simulated lateral grating period was exemplary set to 150 nm.

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Fig. 3
Fig. 3 Different profile shapes used as an input for the rigorous simulation. From upper left to lower right: conical structure, Gaussian profile (w = 0.6), 2nd order Super-Gaussian profile (w = 0.7) and 3rd order Super-Gaussian profile (w = 0.75)

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Fig. 4
Fig. 4 Calculated reflectance for the selected profile geometries in dependency of structure height. Incidence wavelength was assumed to be 325 nm (perpendicular incidence).

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Fig. 5
Fig. 5 Calculated reflectance as a function of wavelength for different conical and 3rd order Super-Gaussian profiles. The structure heights are optimized for minimum reflectance at 325 nm (perpendicular incidence angle).

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Fig. 6
Fig. 6 Comparison of measured and calculated transmittance spectra. The fused silica substrate was structured on both sides with BCML and reactive ion etching. The half-width of the optimized 2nd order Super-Gaussian profile was reduced from w = 0.7 to w = 0.5 to fit the profile of the manufactured structure.

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Fig. 7
Fig. 7 Schematic transition from the perfect periodic structure to a height varied approach. Here 4 single protuberances are displayed. For the calculation 128 units were used.

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Fig. 8
Fig. 8 Calculated transmittance of a 1-dim grating with a Gaussian profile in dependence of the mean structure height (wavelength: 325 nm, grating period: 80 nm, direction of incidence: perpendicular to the surface). Left: Increasing number of sub-units and averaging of each data point over 10 single simulation steps. Right: With and without averaging over 10 simulation steps (N = 128).

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Fig. 9
Fig. 9 Calculated sum of reflectance and transmittance of a 1-dim AR grating with local height variations as function of the mean structure height. The data was calculated for different grating periods and smoothed before drawing. The dotted line represents an antireflection grating without height variations.

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Fig. 10
Fig. 10 Left: Reflectance spectrum for 1-dim AR structure with local height variations. A Gaussian profile with a structure height of 235 nm was assumed. Right: Sum of reflectance and transmittance in dependency on wavelength. The different curves are related to different standard deviations.

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Fig. 11
Fig. 11 Schematic transition from the perfect periodic structure to a statistical variation of the grating period. Here 4 single protuberances are displayed. For the calculation 128 units were used.

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Fig. 12
Fig. 12 Left: Reflectance spectrum for 1-dim AR structure with local displacement variations. A Gaussian profile with a structure height of 200 nm was assumed. Right: Sum of reflectance and transmittance in dependency on wavelength. The different curves are related to different standard deviations.

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Fig. 13
Fig. 13 Comparison of measured and calculated transmittance spectra. The fused silica substrate was structured on both sides with BCML and RIE (solid line). The transmittance was calculated for a 2nd order Super-Gaussian profile (w = 0.7, h = 235 nm, Λ0 = 80 nm) with perfect periodicity (dashed line) and was multiplicatively combined with the scattering (TIS) of a 1-dim Gaussian profile (σ = 15 %, h = 235 nm, Λ0 = 80 nm, σ = 15 %) (dash-dotted line).

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Equations (6)

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z ( x , y ) ∝ e − [ 2 ρ ( x 2 + y 2 ) ] Ω
w = 2 2 ln 2 ρ
f ( h ) = 1 σ 2 π e − 1 2 ( ( h − 1 ) σ ) 2
TIS = 1 − ( T + R )
f ( Δ x ) = 1 σ 2 π e − 1 2 ( Δ x σ ) 2
T scatterd ( λ ) = ( 1 − TIS 1 D ( λ ) ) ⋅ T 2 D ( λ )

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