Abstract

Reflectance, reduction, and light trapping enhancement are essential to maximize the absorption of silicon solar cells. The industrial state of the art method to improve the solar cell optics is wet chemical texturization of the front surface in combination with the deposition of antireflection coatings. This work analyzes an alternative route, namely a TiO2 pillar structure on the front side of a planar silicon solar cell encapsulated in ethylene vinyl acetate (EVA) and glass. It focuses on parameter variations of the structured TiO2 layer while taking the module encapsulation into account. It is shown that internal reflections at the front interface of the module play a crucial role for the structure design. This leads to optimized structures working in a different optical regime. While state of the art structures optimized for a half infinite encapsulation act as effective media, structures optimized for the full module show an improved performance by making use of diffractive effects. It could be shown that weighted reflectance of 4.7% can be reached for a solar module with TiO2 pillar structure on top of the silicon surface compared to 5.5% for a two-layer ARC with a TiO2 bottom layer and 2.3% for an isotexture, which is the state of the art structure for multicrystalline silicon cells.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]

2018 (2)

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

2017 (3)

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

2016 (4)

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
[Crossref] [PubMed]

D. A. Goldman, J. Murray, and J. N. Munday, “Nanophotonic resonators for InP solar cells,” Opt. Express 24(10), A925–A934 (2016).
[Crossref] [PubMed]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

2015 (3)

P. Spinelli, F. Lenzmann, A. Weeber, and A. Polman, “Effect of EVA Encapsulation on Antireflection Properties of Mie Nanoscatterers for c-Si Solar Cells,” IEEE J. Photovoltaics 5(2), 559–564 (2015).
[Crossref]

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

A. Ingenito, O. Isabella, and M. Zeman, “Nano-cones on micro-pyramids. Modulated surface textures for maximal spectral response and high-efficiency solar cells,” Prog. Photovolt. Res. Appl. 23(11), 1649–1659 (2015).
[Crossref]

2014 (1)

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

2013 (3)

J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE J. Photovoltaics 3(2), 709–715 (2013).
[Crossref]

A. Richter, J. Benick, and M. Hermle, “Boron Emitter Passivation With Al2O3 and Al2O3/SiN x Stacks Using ALD Al2O3,” IEEE J. Photovolt 3(1), 236–245 (2013).
[Crossref]

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

2012 (4)

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

2007 (1)

A. Garahan, L. Pilon, J. Yin, and I. Saxena, “Effective optical properties of absorbing nanoporous and nanocomposite thin films,” J. Appl. Phys. 101(1), 014320 (2007).
[Crossref]

2006 (1)

M. M. Braun and L. Pilon, “Effective optical properties of non-absorbing nanoporous thin films,” Thin Solid Films 496(2), 505–514 (2006).
[Crossref]

2005 (1)

P. Panek, M. Lipinski, and J. Dutkiewicz, “Texturization of multicrystalline silicon by wet chemical etchinh for silicon solar cells,” J. Mater. Sci. 40(6), 1459–1463 (2005).
[Crossref]

2004 (2)

O. Schultz, S. W. Glunz, and G. P. Willeke, “Multicrystalline silicon solar cells exceeding 20% efficiency,” Prog. Photovolt. Res. Appl. 12(7), 553–558 (2004).
[Crossref]

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[Crossref]

1982 (1)

1978 (1)

D. J. Bergman, “The dielectric constant of a composite material-A problem in classical physics,” Phys. Rep. 43377–407 (1978.).

1974 (1)

J. R. Birchak, C. G. Gardner, J. E. Hipp, and J. M. Victor, “High dielectric constant microwave probes for sensing soil moisture,” Proc. IEEE 62(1), 93–98 (1974).
[Crossref]

1969 (1)

D. B. Lee, “Anisotropic Etching of Silicon,” J. Appl. Phys. 40(11), 4569–4574 (1969).
[Crossref]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

Alcubilla, R.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Álvaro, R.

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
[Crossref] [PubMed]

Arimoto, S.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Ballif, C.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[Crossref]

Becker, C.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
[Crossref]

Benick, J.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

A. Richter, J. Benick, and M. Hermle, “Boron Emitter Passivation With Al2O3 and Al2O3/SiN x Stacks Using ALD Al2O3,” IEEE J. Photovolt 3(1), 236–245 (2013).
[Crossref]

Bergman, D. J.

D. J. Bergman, “The dielectric constant of a composite material-A problem in classical physics,” Phys. Rep. 43377–407 (1978.).

Bett, A. W.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

Beutel, P.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Birchak, J. R.

J. R. Birchak, C. G. Gardner, J. E. Hipp, and J. M. Victor, “High dielectric constant microwave probes for sensing soil moisture,” Proc. IEEE 62(1), 93–98 (1974).
[Crossref]

Biro, D.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Bläsi, B.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
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Borchert, D.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
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M. M. Braun and L. Pilon, “Effective optical properties of non-absorbing nanoporous thin films,” Thin Solid Films 496(2), 505–514 (2006).
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M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935).
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Bruton, T. M.

A. Hauser, I. Melnyk, P. Fath, S. Narayanan, S. Roberts, and T. M. Bruton, “A simplified process for isotropic texturing of mc-Si,” in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion (2003), pp. 1447–1450.

Buencuerpo, J.

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
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Burger, S.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
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Calle, E.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Cariou, R.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Chen, D.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
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Cui, Y.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Dicker, J.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[Crossref]

Dimroth, F.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Dotor, M. L.

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
[Crossref] [PubMed]

Dutkiewicz, J.

P. Panek, M. Lipinski, and J. Dutkiewicz, “Texturization of multicrystalline silicon by wet chemical etchinh for silicon solar cells,” J. Mater. Sci. 40(6), 1459–1463 (2005).
[Crossref]

Eisenhauer, D.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
[Crossref]

Eisenlohr, J.

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

Ernst, M.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Fan, S.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Fath, P.

A. Hauser, I. Melnyk, P. Fath, S. Narayanan, S. Roberts, and T. M. Bruton, “A simplified process for isotropic texturing of mc-Si,” in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion (2003), pp. 1447–1450.

Feldmann, F.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

Foss, S. E.

J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE J. Photovoltaics 3(2), 709–715 (2013).
[Crossref]

Fujioka, H.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Garahan, A.

A. Garahan, L. Pilon, J. Yin, and I. Saxena, “Effective optical properties of absorbing nanoporous and nanocomposite thin films,” J. Appl. Phys. 101(1), 014320 (2007).
[Crossref]

Gardner, C. G.

J. R. Birchak, C. G. Gardner, J. E. Hipp, and J. M. Victor, “High dielectric constant microwave probes for sensing soil moisture,” Proc. IEEE 62(1), 93–98 (1974).
[Crossref]

Garín, M.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Gaylord, T. K.

Gebrewold, H.

Geisemeyer, I.

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

Gjessing, J.

J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE J. Photovoltaics 3(2), 709–715 (2013).
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Glover, W.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Glunz, S. W.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
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O. Schultz, S. W. Glunz, and G. P. Willeke, “Multicrystalline silicon solar cells exceeding 20% efficiency,” Prog. Photovolt. Res. Appl. 12(7), 553–558 (2004).
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Goldman, D. A.

Goldschmidt, J. C.

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

Graf, M.

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

Hädrich, I.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Hammerschmidt, M.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
[Crossref]

Hauser, A.

A. Hauser, I. Melnyk, P. Fath, S. Narayanan, S. Roberts, and T. M. Bruton, “A simplified process for isotropic texturing of mc-Si,” in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion (2003), pp. 1447–1450.

Hauser, H.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

Hermle, M.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

A. Richter, J. Benick, and M. Hermle, “Boron Emitter Passivation With Al2O3 and Al2O3/SiN x Stacks Using ALD Al2O3,” IEEE J. Photovolt 3(1), 236–245 (2013).
[Crossref]

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

Hipp, J. E.

J. R. Birchak, C. G. Gardner, J. E. Hipp, and J. M. Victor, “High dielectric constant microwave probes for sensing soil moisture,” Proc. IEEE 62(1), 93–98 (1974).
[Crossref]

Hofmann, T.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[Crossref]

Hohl-Ebinger, J.

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

Höhn, O.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

Ingenito, A.

A. Ingenito, O. Isabella, and M. Zeman, “Nano-cones on micro-pyramids. Modulated surface textures for maximal spectral response and high-efficiency solar cells,” Prog. Photovolt. Res. Appl. 23(11), 1649–1659 (2015).
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Isabella, O.

A. Ingenito, O. Isabella, and M. Zeman, “Nano-cones on micro-pyramids. Modulated surface textures for maximal spectral response and high-efficiency solar cells,” Prog. Photovolt. Res. Appl. 23(11), 1649–1659 (2015).
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Ishihara, T.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Jäger, K.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
[Crossref]

Jakob, P.

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

Jin, H.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Katsura, T.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Kessels, W. M. M.

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

Kiefel, P.

Köppel, G.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” in Proc. of SPIE, 10356 of Proceedings of SPIE (SPIE, 2017), p. 14.
[Crossref]

Krenckel, P.

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

Kübler, V.

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

Lackner, D.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Lee, D. B.

D. B. Lee, “Anisotropic Etching of Silicon,” J. Appl. Phys. 40(11), 4569–4574 (1969).
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Lenzmann, F.

P. Spinelli, F. Lenzmann, A. Weeber, and A. Polman, “Effect of EVA Encapsulation on Antireflection Properties of Mie Nanoscatterers for c-Si Solar Cells,” IEEE J. Photovoltaics 5(2), 559–564 (2015).
[Crossref]

Lipinski, M.

P. Panek, M. Lipinski, and J. Dutkiewicz, “Texturization of multicrystalline silicon by wet chemical etchinh for silicon solar cells,” J. Mater. Sci. 40(6), 1459–1463 (2005).
[Crossref]

Liu, V.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Llorens, J. M.

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
[Crossref] [PubMed]

Macco, B.

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

Macdonald, D.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Marstein, E. S.

J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE J. Photovoltaics 3(2), 709–715 (2013).
[Crossref]

Matsuno, S.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Melnyk, I.

A. Hauser, I. Melnyk, P. Fath, S. Narayanan, S. Roberts, and T. M. Bruton, “A simplified process for isotropic texturing of mc-Si,” in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion (2003), pp. 1447–1450.

Michl, B.

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

Moharam, M. G.

Morikawa, H.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Muller, B.

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

Müller, B.

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

Müller, C.

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

Müller, R.

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

Munday, J. N.

Murray, J.

Narayanan, S.

A. Hauser, I. Melnyk, P. Fath, S. Narayanan, S. Roberts, and T. M. Bruton, “A simplified process for isotropic texturing of mc-Si,” in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion (2003), pp. 1447–1450.

Nievendick, J.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Niinobe, D.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Nishimura, K.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Okamoto, T.

D. Niinobe, K. Nishimura, S. Matsuno, H. Fujioka, T. Katsura, T. Okamoto, T. Ishihara, H. Morikawa, and S. Arimoto, “Honeycomb-structured mulit-crystalline silicon solar cells with 18,6% efficiency via industrially applicable laser process,” in Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2008).

Ortega, P.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Panek, P.

P. Panek, M. Lipinski, and J. Dutkiewicz, “Texturization of multicrystalline silicon by wet chemical etchinh for silicon solar cells,” J. Mater. Sci. 40(6), 1459–1463 (2005).
[Crossref]

Peters, I. M.

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

Pilon, L.

A. Garahan, L. Pilon, J. Yin, and I. Saxena, “Effective optical properties of absorbing nanoporous and nanocomposite thin films,” J. Appl. Phys. 101(1), 014320 (2007).
[Crossref]

M. M. Braun and L. Pilon, “Effective optical properties of non-absorbing nanoporous thin films,” Thin Solid Films 496(2), 505–514 (2006).
[Crossref]

Polman, A.

P. Spinelli, F. Lenzmann, A. Weeber, and A. Polman, “Effect of EVA Encapsulation on Antireflection Properties of Mie Nanoscatterers for c-Si Solar Cells,” IEEE J. Photovoltaics 5(2), 559–564 (2015).
[Crossref]

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

Razek, N.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Rentsch, J.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Repo, P.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Richter, A.

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

A. Richter, J. Benick, and M. Hermle, “Boron Emitter Passivation With Al2O3 and Al2O3/SiN x Stacks Using ALD Al2O3,” IEEE J. Photovolt 3(1), 236–245 (2013).
[Crossref]

Riepe, S.

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

Ripalda, J. M.

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
[Crossref] [PubMed]

Roberts, S.

A. Hauser, I. Melnyk, P. Fath, S. Narayanan, S. Roberts, and T. M. Bruton, “A simplified process for isotropic texturing of mc-Si,” in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion (2003), pp. 1447–1450.

Rüdiger, M.

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

Savin, H.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Saxena, I.

A. Garahan, L. Pilon, J. Yin, and I. Saxena, “Effective optical properties of absorbing nanoporous and nanocomposite thin films,” J. Appl. Phys. 101(1), 014320 (2007).
[Crossref]

Schindler, F.

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

Schubert, M. C.

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

Schultz, O.

O. Schultz, S. W. Glunz, and G. P. Willeke, “Multicrystalline silicon solar cells exceeding 20% efficiency,” Prog. Photovolt. Res. Appl. 12(7), 553–558 (2004).
[Crossref]

Schwarzkopf, S.

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

Siefer, G.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Specht, J.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Spinelli, P.

P. Spinelli, F. Lenzmann, A. Weeber, and A. Polman, “Effect of EVA Encapsulation on Antireflection Properties of Mie Nanoscatterers for c-Si Solar Cells,” IEEE J. Photovoltaics 5(2), 559–564 (2015).
[Crossref]

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

Steinkemper, H.

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

Stüwe, D.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Thomson, A.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Thorstensen, J.

J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE J. Photovoltaics 3(2), 709–715 (2013).
[Crossref]

Torné, L.

J. Buencuerpo, L. Torné, R. Álvaro, J. M. Llorens, M. L. Dotor, and J. M. Ripalda, “Nano-cones for broadband light coupling to high index substrates,” Sci. Rep. 6(1), 38682 (2016).
[Crossref] [PubMed]

Tucher, N.

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

N. Tucher, B. Müller, P. Jakob, J. Eisenlohr, O. Höhn, H. Hauser, J. C. Goldschmidt, M. Hermle, and B. Bläsi, “Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism,” Sol. Energy Mater. Sol. Cells 173, 66–71 (2017).
[Crossref]

J. Eisenlohr, N. Tucher, H. Hauser, M. Graf, J. Benick, B. Bläsi, J. C. Goldschmidt, and M. Hermle, “Efficiency increase of crystalline silicon solar cells with nanoimprinted rear side gratings for enhanced light trapping,” Sol. Energy Mater. Sol. Cells 155, 288–293 (2016).
[Crossref]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS,” Opt. Express 24(14), A1083–A1093 (2016).
[Crossref] [PubMed]

Verschuuren, M. A.

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

Victor, J. M.

J. R. Birchak, C. G. Gardner, J. E. Hipp, and J. M. Victor, “High dielectric constant microwave probes for sensing soil moisture,” Proc. IEEE 62(1), 93–98 (1974).
[Crossref]

von Gastrow, G.

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Wang, K. X.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Warta, W.

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

Weeber, A.

P. Spinelli, F. Lenzmann, A. Weeber, and A. Polman, “Effect of EVA Encapsulation on Antireflection Properties of Mie Nanoscatterers for c-Si Solar Cells,” IEEE J. Photovoltaics 5(2), 559–564 (2015).
[Crossref]

Willeke, G. P.

O. Schultz, S. W. Glunz, and G. P. Willeke, “Multicrystalline silicon solar cells exceeding 20% efficiency,” Prog. Photovolt. Res. Appl. 12(7), 553–558 (2004).
[Crossref]

Wimplinger, M.

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Yin, J.

A. Garahan, L. Pilon, J. Yin, and I. Saxena, “Effective optical properties of absorbing nanoporous and nanocomposite thin films,” J. Appl. Phys. 101(1), 014320 (2007).
[Crossref]

Yu, Z.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Zahner, L.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Zeman, M.

A. Ingenito, O. Isabella, and M. Zeman, “Nano-cones on micro-pyramids. Modulated surface textures for maximal spectral response and high-efficiency solar cells,” Prog. Photovolt. Res. Appl. 23(11), 1649–1659 (2015).
[Crossref]

Zhang, X.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Zheng, P.

I. Hädrich, M. Ernst, A. Thomson, P. Zheng, X. Zhang, H. Jin, and D. Macdonald, “How cell textures impact angular cell-to-module ratios and the annual yield of crystalline solar modules,” Sol. Energy Mater. Sol. Cells 183, 181–192 (2018).
[Crossref]

Zimmer, M.

J. Nievendick, J. Specht, M. Zimmer, L. Zahner, W. Glover, D. Stüwe, D. Biro, and J. Rentsch, “An industrially applicable honeycomb texture,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC) (2011), pp. 1722–1725.

Ann. Phys. (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935).
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Appl. Phys. Lett. (1)

P. Spinelli, B. Macco, M. A. Verschuuren, W. M. M. Kessels, and A. Polman, “Al2O3/TiO2 nano-pattern antireflection coating with ultralow surface recombination,” Appl. Phys. Lett. 102(23), 233902 (2013).
[Crossref]

IEEE J. Photovolt (1)

A. Richter, J. Benick, and M. Hermle, “Boron Emitter Passivation With Al2O3 and Al2O3/SiN x Stacks Using ALD Al2O3,” IEEE J. Photovolt 3(1), 236–245 (2013).
[Crossref]

IEEE J. Photovoltaics (5)

H. Hauser, B. Michl, S. Schwarzkopf, V. Kübler, C. Müller, M. Hermle, and B. Bläsi, “Honeycomb texturing of Silicon via nanoimprint lithography for solar cell applications,” IEEE J. Photovoltaics 2(2), 114–122 (2012).
[Crossref]

J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE J. Photovoltaics 3(2), 709–715 (2013).
[Crossref]

J. Benick, A. Richter, R. Müller, H. Hauser, F. Feldmann, P. Krenckel, S. Riepe, F. Schindler, M. C. Schubert, M. Hermle, A. W. Bett, and S. W. Glunz, “High-Efficiency n-Type HP mc Silicon Solar Cells,” IEEE J. Photovoltaics 7(5), 1171–1175 (2017).
[Crossref]

P. Spinelli, F. Lenzmann, A. Weeber, and A. Polman, “Effect of EVA Encapsulation on Antireflection Properties of Mie Nanoscatterers for c-Si Solar Cells,” IEEE J. Photovoltaics 5(2), 559–564 (2015).
[Crossref]

I. Geisemeyer, N. Tucher, B. Muller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert, and W. Warta, “Angle Dependence of Solar Cells and Modules. The Role of Cell Texturization,” IEEE J. Photovoltaics 7(1), 19–24 (2017).
[Crossref]

J. Appl. Phys. (2)

A. Garahan, L. Pilon, J. Yin, and I. Saxena, “Effective optical properties of absorbing nanoporous and nanocomposite thin films,” J. Appl. Phys. 101(1), 014320 (2007).
[Crossref]

D. B. Lee, “Anisotropic Etching of Silicon,” J. Appl. Phys. 40(11), 4569–4574 (1969).
[Crossref]

J. Mater. Sci. (1)

P. Panek, M. Lipinski, and J. Dutkiewicz, “Texturization of multicrystalline silicon by wet chemical etchinh for silicon solar cells,” J. Mater. Sci. 40(6), 1459–1463 (2005).
[Crossref]

J. Opt. Soc. Am. (1)

Nano Lett. (1)

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption Enhancement in Ultrathin Crystalline Silicon Solar Cells with Antireflection and Light-Trapping Nanocone Gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[Crossref] [PubMed]

Nat. Commun. (1)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

Nat. Energy (1)

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 17, 183 (2018).

Nat. Mater. (1)

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

H. Savin, P. Repo, G. von Gastrow, P. Ortega, E. Calle, M. Garín, and R. Alcubilla, “Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency,” Nat. Nanotechnol. 10(7), 624–628 (2015).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Rep. (1)

D. J. Bergman, “The dielectric constant of a composite material-A problem in classical physics,” Phys. Rep. 43377–407 (1978.).

Proc. IEEE (1)

J. R. Birchak, C. G. Gardner, J. E. Hipp, and J. M. Victor, “High dielectric constant microwave probes for sensing soil moisture,” Proc. IEEE 62(1), 93–98 (1974).
[Crossref]

Prog. Photovolt. Res. Appl. (3)

I. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells-optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

A. Ingenito, O. Isabella, and M. Zeman, “Nano-cones on micro-pyramids. Modulated surface textures for maximal spectral response and high-efficiency solar cells,” Prog. Photovolt. Res. Appl. 23(11), 1649–1659 (2015).
[Crossref]

O. Schultz, S. W. Glunz, and G. P. Willeke, “Multicrystalline silicon solar cells exceeding 20% efficiency,” Prog. Photovolt. Res. Appl. 12(7), 553–558 (2004).
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Sci. Rep. (1)

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Figures (8)

Fig. 1
Fig. 1 3D-Plot and cross sectional sketch of simulated pillar structure. Parameter variations were performed for height, diameter, period and residual layer thickness.
Fig. 2
Fig. 2 Weighted reflectance for a system of a structured TiO2 layer with a fixed height of 80 nm as function of the filling factor. Left: System without a residual layer. The smallest weighted reflectance is reached for filling factors 0.9. Right: System with residual layer thickness of 60 nm. Small periods (100 nm and 200 nm) lead to the smallest reflectance.
Fig. 3
Fig. 3 Left: Comparison of the RCWA simulation results for a structure with period 200 nm, height 80 nm and residual layer thickness 60 nm with the results from the different effective medium models. The best agreement between the RCWA simulation results and an effective medium model was reached for the Bruggeman model. For small filling factors the simulation data fits perfectly to the Bruggeman model. Right: A near field analysis showing two periods of a structure with an height of 80 nm and residual layer thickness of 60 nm, a 5 nm thick passivation layer of Al2O3 for wavelength 500 nm. It is clear to see that the wave front passes nearly unperturbed through the structure.
Fig. 4
Fig. 4 Sketch of the modeled system of a sol-gel structured solar module. The structure is placed on a semi-infinite silicon substrate at the backside and at the front side an encapsulation with an interface to air. Incoming light is reflected at the structure. The encapsulation-air-interface leads to total internal reflection above the critical angle of ϑ < 41.8°, which could help to further decrease reflectance for the systems with a larger period.
Fig. 5
Fig. 5 The modeled weighted reflectance for a pillar structure with a residual layer thickness of 60 nm, periods of 500 nm, 600 nm and 700 nm (triangles). In squares the weighted reflectance for angles smaller than 41.8° is shown and in dots for angles greater than 41.8°. The minimum in the reflectance for angles smaller than 41.8° is reached for a structure with a period of 600 nm and of height of 110 nm.
Fig. 6
Fig. 6 Sketch of the module with multiple light interactions used in the OPTOS formalism. The EVA is covered with an ARC to reduce reflectance on the module front side.
Fig. 7
Fig. 7 Comparison between the simulation results of the RCWA and the OPTOS formalism. The RCWA first order correction used in the optimization above is close to the OPTOS results. If reflectance at the front glass is taken into account the corrected RCWA results fit very well to the OPTOS simulation.
Fig. 8
Fig. 8 Comparison of the sol-gel structure (OPTOS results) with a two-layer antireflection coating and an isotexture. The reflectance is shown in dependence of the wavelength. All results are determined in a module stack case. The lowest reflectance over the complete wavelength range is reached for the isotexture. The sol-gel structure has in the wavelength range from 450 nm to 1200 nm a smaller reflectance than the two-layer antireflection coating.

Tables (1)

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Table 1 Conclusion of the different structure types investigated in this work and their best results.

Equations (2)

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FF= A Ti O 2 A unitcell .
b=(3FF1) n 2 Ti O 2 +(23FF) n 2 EVA n effective = b+ 8 n 2 EVA n 2 Ti O 2 + b 2 4

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