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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References

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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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2008

2007

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]

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 Applications 15, 415 - 423 (2007).
[CrossRef]

2006

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]

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]

2005

2003

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]

1999

1998

1995

1986

1981

1973

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 Applications 15, 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]

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. 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.

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 Applications 15, 415 - 423 (2007).
[CrossRef]

Y. Kanamori, M. Sasaki and K. Hane, "Broadband antireflection gratings fabricated upon silicon substrates," Opt. Lett. 24,1422 - 1424 (1999).
[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.

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 Applications 15, 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 Applications 15, 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]

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.

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 Applications 15, 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.

Appl. Phys. Lett.

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]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

P. H. Clapham and M. C. Hutley, "Reduction of Lens Reflexion by the 'Moth Eye' Principle," Nature 244, 281 - 282 (1973).
[CrossRef]

Opt. Commun.

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

Opt. Lett.

Phys. Status Solidi B

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]

Progress in Photovoltaics: Research and Applications

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 Applications 15, 415 - 423 (2007).
[CrossRef]

Small

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

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

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

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.

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

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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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