Abstract

This paper aims at modeling bi-periodic micro-structured silicon surfaces exhibiting broadband antireflection properties in the infrared range using Rigorous Coupled-Wave Analysis (RCWA). These structures of pyramidal shape, which typical dimensions are smaller than the wavelength, are not in the Effective Medium Theory (EMT) validity domain. The influence of various opto-geometrical parameters such as period, depth, shape of the pattern is examined. The antireflective properties of such biperiodic patterned surfaces are then discussed using the photonic crystal theory and photonic band diagrams description. Correlations between the density of Bloch modes, their localizations with respect to the incident medium light line and the surface reflectance are presented.

© 2008 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  14. C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.
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2008 (1)

2007 (1)

E. F. Schubert, J. K. Kim, and J. Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244, 3002–3008 (2007).
[Crossref]

2006 (2)

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

2005 (1)

2003 (2)

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

P. Lalanne and M. Hutley, “Artificial media optical properties - subwavelength scale,” Encyclopedia of Optical Engineering, 62′71 (2003).

1999 (1)

1998 (1)

1995 (1)

1986 (1)

1981 (1)

1973 (1)

P. H. Clapham and M. C. Hutley, “Reduction of Lens Reflexion by the ′Moth Eye′ Principle,” Nature 244, 281–282 (1973).
[Crossref]

Arafune, K.

H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Progress in Photovoltaics: Research and Applications15, 415′423 (2007).
[Crossref]

Auslender, M.

Berginc, G.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1980), 705′708.

Campbell, J. C.

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Carey, J. E.

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Clapham, P. H.

P. H. Clapham and M. C. Hutley, “Reduction of Lens Reflexion by the ′Moth Eye′ Principle,” Nature 244, 281–282 (1973).
[Crossref]

Clausnitzer, T.

Drouard, E.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Escoubas, L.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Flory, F.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Fourmond, E.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Gaylord, T. K.

Giovannini, H.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Grann, E.

Guo, X.

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Hane, K.

Hava, S.

Huang, Z.

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Hutley, M.

P. Lalanne and M. Hutley, “Artificial media optical properties - subwavelength scale,” Encyclopedia of Optical Engineering, 62′71 (2003).

Hutley, M. C.

P. H. Clapham and M. C. Hutley, “Reduction of Lens Reflexion by the ′Moth Eye′ Principle,” Nature 244, 281–282 (1973).
[Crossref]

Kaiser, N.

Kaminski, A.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Kämpfe, T.

Kanamori, Y.

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

H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Progress in Photovoltaics: Research and Applications15, 415′423 (2007).
[Crossref]

Kim, J. K.

E. F. Schubert, J. K. Kim, and J. Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244, 3002–3008 (2007).
[Crossref]

Kley, E. B.

Lalanne, P.

P. Lalanne and M. Hutley, “Artificial media optical properties - subwavelength scale,” Encyclopedia of Optical Engineering, 62′71 (2003).

Leitel, R.

Lemiti, M.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Letartre, X.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Levy, D.

Liu, M.

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Liu, Z.

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Loli, M.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Mazur, E.

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Moharam, M.

Moharam, M. G.

Moore, D. T.

Ohshita, Y.

H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Progress in Photovoltaics: Research and Applications15, 415′423 (2007).
[Crossref]

Park, Y.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Parriaux, O.

Peschel, U.

Pickering, M. A.

Pommet, D.

Sai, H.

H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Progress in Photovoltaics: Research and Applications15, 415′423 (2007).
[Crossref]

Sasaki, M.

Schubert, E. F.

E. F. Schubert, J. K. Kim, and J. Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244, 3002–3008 (2007).
[Crossref]

Schulz, U.

Seassal, C.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Shao, H.

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Simon, J. J.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Tavlove, A.

A. Tavlove, Computationel Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 1995).

Taylor, R. L.

Tishchenko, A. V.

Tünnermann, A.

Viktorovitch, P.

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1980), 705′708.

Xi, J. Q.

E. F. Schubert, J. K. Kim, and J. Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244, 3002–3008 (2007).
[Crossref]

Xie, G.

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Yamaguchi, M.

H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Progress in Photovoltaics: Research and Applications15, 415′423 (2007).
[Crossref]

Zhang, G.

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Zhang, J.

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

Z. Huang, J. E. Carey, M. Liu, X. Guo, E. Mazur, and J. C. Campbell, “Microstructured silicon photodetector,” Appl. Phys. Lett. 89, 033506 (2006).
[Crossref]

Encyclopedia of Optical Engineering (1)

P. Lalanne and M. Hutley, “Artificial media optical properties - subwavelength scale,” Encyclopedia of Optical Engineering, 62′71 (2003).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (1)

P. H. Clapham and M. C. Hutley, “Reduction of Lens Reflexion by the ′Moth Eye′ Principle,” Nature 244, 281–282 (1973).
[Crossref]

Opt. Commun. (1)

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81′88 (2003).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Status Solidi B (1)

E. F. Schubert, J. K. Kim, and J. Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244, 3002–3008 (2007).
[Crossref]

Small (1)

G. Zhang, J. Zhang, G. Xie, Z. Liu, and H. Shao, “Cicada wings: a stamp from Nature for nanoimprint lithography,” Small 2, 1440′1443 (2006).
[Crossref] [PubMed]

Other (4)

M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1980), 705′708.

A. Tavlove, Computationel Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 1995).

H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Progress in Photovoltaics: Research and Applications15, 415′423 (2007).
[Crossref]

C. Seassal, Y. Park, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” presented at SPIE Photonics Europe, Strasbourg, France, April 2008.

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Figures (4)

Fig. 1.
Fig. 1.

(a). Atomic Force Microscopy (AFM) image of the microstructured surface. (b). Scheme of the pyramid pattern and its various parameters (P, T, M).

Fig. 2.
Fig. 2.

Reflectance R versus the wavelength for various values of the pyramid height (0.5µm ≤ T ≤ 1µm), 2 top flat sizes (M=0µm and M=0.25µm). The period (P) equals 1µm. Unit in the legend is µm.

Fig. 3.
Fig. 3.

Reflectance R versus the wavelength for two values of M (M=0µm and M=0.25µm). The other parameters of the pattern are fixed: the period (P) equals 1µm, and the height (T) equals 1µm. Unit in the legend is µm.

Fig. 4.
Fig. 4.

(a). Band diagram computed using plane waves theory of a structured silicon surface such as that of Fig 1a with pyramids (P=1µm, T=1µm, M=0 µm). (b)-(c)-(d) Band diagrams computed using the plane waves theory (between Γ and X wave vector directions) and reflectance curves (R) versus the same frequency scale (µm-1). Patterns parameters are P=1µm, T=1µm, and M=0 µm (b), M=0.25 µm (c), M=0.5 µm (d).

Tables (1)

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Table 1. Range of explored parameters (min − max) and variation step in each case.

Equations (1)

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P λ n sub + n inc sin θ inc

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