Abstract

We report in this work that quantum efficiency can be significantly enhanced in an ultra-thin silicon solar cell coated by a fractal-like pattern of silver nano cuboids. When sunlight shines this solar cell, multiple antireflection bands are achieved mainly due to the self-similarity in the fractal-like structure. Actually, several kinds of optical modes exist in the structure. One is cavity modes, which come from Fabry-Perot resonances at the longitudinal and transverse cavities, respectively; the other is surface plasmon (SP) modes, which propagate along the silicon-silver interface. Due to the fact that several feature sizes distribute in a fractal-like structure, both low-index and high-index SP modes are simultaneously excited. As a whole effect, broadband absorption is achieved in this solar cell. Further by considering the ideal process that the lifetime of carriers is infinite and the recombination loss is ignored, we demonstrate that external quantum efficiency of the solar cell under this ideal condition is significantly enhanced. This theoretical finding contributes to high-performance plasmonic solar cells and can be applied to designing miniaturized compact photovoltaic devices.

© 2013 OSA

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2012 (4)

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

H. P. Wang, K. T. Tsai, K. Y. Lai, T. C. Wei, Y. L. Wang, J. H. He, “Periodic Si nanopillar arrays by anodic aluminum oxide template and catalytic etching for broadband and omnidirectional light harvesting,” Opt. Express 20(S1), A94–A103 (2012).
[CrossRef] [PubMed]

E. Battal, T. A. Yogurt, L. E. Aygun, A. K. Okyay, “Triangular metallic gratings for large absorption enhancement in thin film Si solar cells,” Opt. Express 20(9), 9458–9464 (2012).
[CrossRef] [PubMed]

A. Abass, K. Q. Le, A. Alu, M. Burgelman, B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012).
[CrossRef]

2011 (10)

Y. H. Kuang, K. H. M. van der Werf, Z. S. Houweling, R. E. I. Schropp, “Nanorod solar cell with an ultrathin a-Si:H absorber layer,” Appl. Phys. Lett. 98(11), 113111 (2011).
[CrossRef]

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011).
[CrossRef]

C. A. Keasler, E. Bellotti, “A numerical study of broadband absorbers for visible to infrared detectors,” Appl. Phys. Lett. 99(9), 091109 (2011).
[CrossRef]

S. Fahr, T. Kirchartz, C. Rockstuhl, F. Lederer, “Approaching the Lambertian limit in randomly textured thin-film solar cells,” Opt. Express 19(14, S4), A865–A874 (2011).
[CrossRef] [PubMed]

G. Volpe, G. Volpe, R. Quidant, “Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet,” Opt. Express 19(4), 3612–3618 (2011).
[CrossRef] [PubMed]

D. Li, L. Qin, X. Xiong, R. W. Peng, Q. Hu, G. B. Ma, H. S. Zhou, M. Wang, “Exchange of electric and magnetic resonances in multilayered metal/dielectric nanoplates,” Opt. Express 19(23), 22942–22949 (2011).
[CrossRef] [PubMed]

M. Yang, Z. P. Fu, F. Lin, X. Zhu, “Incident angle dependence of absorption enhancement in plasmonic solar cells,” Opt. Express 19(S4), A763–A771 (2011).
[CrossRef] [PubMed]

J. N. Munday, H. A. Atwater, “Large Integrated Absorption Enhancement in Plasmonic Solar Cells by Combining Metallic Gratings and Antireflection Coatings,” Nano Lett. 11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, C. M. de Sterke, R. C. McPhedran, “Modal analysis of enhanced absorption in silicon nanowire arrays,” Opt. Express 19(S5), A1067–A1081 (2011).
[CrossRef] [PubMed]

2010 (2)

2009 (1)

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

2008 (2)

S. Chhajed, M. F. Schubert, J. K. Kim, E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008).
[CrossRef]

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

2007 (2)

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

2006 (1)

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

2004 (1)

M. A. Green, “Recent developments in photovoltaics,” Sol. Energy 76(1–3), 3–8 (2004).
[CrossRef]

2003 (3)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

R. W. Peng, M. Mazzer, K. W. J. Barnham, “Efficiency enhancement of ideal photovoltaic solar cells by photonic excitations in multi-intermediate band structures,” Appl. Phys. Lett. 83(4), 770–772 (2003).
[CrossRef]

2000 (1)

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

1990 (1)

A. Wang, J. Zhao, M. A. Green, “24% efficient silicon solar cells,” Appl. Phys. Lett. 57(6), 602–604 (1990).
[CrossRef]

1961 (1)

W. Shockley, H. J. Queisser, “Detailed balance limit of efficiency of pn junction solar cells,” J. Appl. Phys. 32(3), 510 (1961).
[CrossRef]

Abass, A.

A. Abass, K. Q. Le, A. Alu, M. Burgelman, B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012).
[CrossRef]

Alu, A.

A. Abass, K. Q. Le, A. Alu, M. Burgelman, B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012).
[CrossRef]

Asatryan, A. A.

Atwater, H. A.

J. N. Munday, H. A. Atwater, “Large Integrated Absorption Enhancement in Plasmonic Solar Cells by Combining Metallic Gratings and Antireflection Coatings,” Nano Lett. 11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(13, S2), A237–A245 (2010).
[CrossRef] [PubMed]

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Aygun, L. E.

Bao, Y. J.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Barnham, K. W. J.

R. W. Peng, M. Mazzer, K. W. J. Barnham, “Efficiency enhancement of ideal photovoltaic solar cells by photonic excitations in multi-intermediate band structures,” Appl. Phys. Lett. 83(4), 770–772 (2003).
[CrossRef]

Battal, E.

Bellotti, E.

C. A. Keasler, E. Bellotti, “A numerical study of broadband absorbers for visible to infrared detectors,” Appl. Phys. Lett. 99(9), 091109 (2011).
[CrossRef]

Botten, L. C.

Brongersma, M. L.

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

Burgelman, M.

A. Abass, K. Q. Le, A. Alu, M. Burgelman, B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012).
[CrossRef]

Carius, R.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Chhajed, S.

S. Chhajed, M. F. Schubert, J. K. Kim, E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008).
[CrossRef]

de Sterke, C. M.

Dereux, A.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ding, X. M.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Dossou, K. B.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Emery, K.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011).
[CrossRef]

Fahr, S.

Ferry, V. E.

Finger, F.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Fu, Z. P.

Ge, J.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Green, M. A.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011).
[CrossRef]

M. A. Green, “Recent developments in photovoltaics,” Sol. Energy 76(1–3), 3–8 (2004).
[CrossRef]

A. Wang, J. Zhao, M. A. Green, “24% efficient silicon solar cells,” Appl. Phys. Lett. 57(6), 602–604 (1990).
[CrossRef]

Gu, M.

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Hao, X. P.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Hapke, P.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Hassani-Afshar, A.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

He, J. H.

Hishikawa, Y.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011).
[CrossRef]

Ho, J. J.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Hou, X. Y.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Houben, L.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Houweling, Z. S.

Y. H. Kuang, K. H. M. van der Werf, Z. S. Houweling, R. E. I. Schropp, “Nanorod solar cell with an ultrathin a-Si:H absorber layer,” Appl. Phys. Lett. 98(11), 113111 (2011).
[CrossRef]

Hsu, J. W. P.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Hu, Q.

Jia, B. H.

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Jiang, N.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Keasler, C. A.

C. A. Keasler, E. Bellotti, “A numerical study of broadband absorbers for visible to infrared detectors,” Appl. Phys. Lett. 99(9), 091109 (2011).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Kim, J. K.

S. Chhajed, M. F. Schubert, J. K. Kim, E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008).
[CrossRef]

Kim, S.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Kirchartz, T.

Kluth, O.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Kuang, Y. H.

Y. H. Kuang, K. H. M. van der Werf, Z. S. Houweling, R. E. I. Schropp, “Nanorod solar cell with an ultrathin a-Si:H absorber layer,” Appl. Phys. Lett. 98(11), 113111 (2011).
[CrossRef]

Lai, K. Y.

Lambertz, A.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Le, K. Q.

A. Abass, K. Q. Le, A. Alu, M. Burgelman, B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012).
[CrossRef]

Lederer, F.

Lee, Y. J.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Li, D.

Li, H. B. T.

Li, Z. F.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Lin, F.

Liu, J.

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

Lu, W.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Lu, X.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Ma, G. B.

Ma, L. L.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Maes, B.

A. Abass, K. Q. Le, A. Alu, M. Burgelman, B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012).
[CrossRef]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Mazzer, M.

R. W. Peng, M. Mazzer, K. W. J. Barnham, “Efficiency enhancement of ideal photovoltaic solar cells by photonic excitations in multi-intermediate band structures,” Appl. Phys. Lett. 83(4), 770–772 (2003).
[CrossRef]

McKenzie, B. B.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

McPhedran, R. C.

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Ming, N. B.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Muck, A.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Munday, J. N.

J. N. Munday, H. A. Atwater, “Large Integrated Absorption Enhancement in Plasmonic Solar Cells by Combining Metallic Gratings and Antireflection Coatings,” Nano Lett. 11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

Okyay, A. K.

Ouyang, Z.

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

Peng, R. W.

D. Li, L. Qin, X. Xiong, R. W. Peng, Q. Hu, G. B. Ma, H. S. Zhou, M. Wang, “Exchange of electric and magnetic resonances in multilayered metal/dielectric nanoplates,” Opt. Express 19(23), 22942–22949 (2011).
[CrossRef] [PubMed]

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

R. W. Peng, M. Mazzer, K. W. J. Barnham, “Efficiency enhancement of ideal photovoltaic solar cells by photonic excitations in multi-intermediate band structures,” Appl. Phys. Lett. 83(4), 770–772 (2003).
[CrossRef]

Peters, D. W.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Polman, A.

Poulton, C. G.

Qin, L.

Queisser, H. J.

W. Shockley, H. J. Queisser, “Detailed balance limit of efficiency of pn junction solar cells,” J. Appl. Phys. 32(3), 510 (1961).
[CrossRef]

Quidant, R.

Rech, B.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef] [PubMed]

Rockstuhl, C.

Ruby, D. S.

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Schropp, R. E. I.

Y. H. Kuang, K. H. M. van der Werf, Z. S. Houweling, R. E. I. Schropp, “Nanorod solar cell with an ultrathin a-Si:H absorber layer,” Appl. Phys. Lett. 98(11), 113111 (2011).
[CrossRef]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(13, S2), A237–A245 (2010).
[CrossRef] [PubMed]

Schubert, E. F.

S. Chhajed, M. F. Schubert, J. K. Kim, E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008).
[CrossRef]

Schubert, M. F.

S. Chhajed, M. F. Schubert, J. K. Kim, E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008).
[CrossRef]

Shao, J.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Shen, H. J.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Shi, Z. R.

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Shockley, W.

W. Shockley, H. J. Queisser, “Detailed balance limit of efficiency of pn junction solar cells,” J. Appl. Phys. 32(3), 510 (1961).
[CrossRef]

Si, J. W.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Stokes, N.

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Sturmberg, B. C. P.

Sun, W. H.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Tang, Z. H.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Tsai, K. T.

van der Werf, K. H. M.

Y. H. Kuang, K. H. M. van der Werf, Z. S. Houweling, R. E. I. Schropp, “Nanorod solar cell with an ultrathin a-Si:H absorber layer,” Appl. Phys. Lett. 98(11), 113111 (2011).
[CrossRef]

Verhagen, E.

Verschuuren, M. A.

Vetterl, O.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Volpe, G.

Wagner, H.

O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Muck, B. Rech, H. Wagner, “Intrinsic microcrystalline silicon: A new material for photovoltaics,” Sol. Energy Mater. Sol. Cells 62(1–2), 97–108 (2000).
[CrossRef]

Walters, R. J.

Wang, A.

A. Wang, J. Zhao, M. A. Green, “24% efficient silicon solar cells,” Appl. Phys. Lett. 57(6), 602–604 (1990).
[CrossRef]

Wang, H. P.

Wang, K. L.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Wang, M.

D. Li, L. Qin, X. Xiong, R. W. Peng, Q. Hu, G. B. Ma, H. S. Zhou, M. Wang, “Exchange of electric and magnetic resonances in multilayered metal/dielectric nanoplates,” Opt. Express 19(23), 22942–22949 (2011).
[CrossRef] [PubMed]

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Wang, Q. J.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Wang, Y. L.

Wang, Z.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Warta, W.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011).
[CrossRef]

Wei, T. C.

White, J.

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

Wu, X.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Wu, Z.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Xiong, X.

Xue, M.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Yang, M.

Yogurt, T. A.

Zeng, B. Q.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Zhang, B.

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

Zhang, Y. N.

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Zhang, Z. J.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007).
[CrossRef]

Zhao, J.

A. Wang, J. Zhao, M. A. Green, “24% efficient silicon solar cells,” Appl. Phys. Lett. 57(6), 602–604 (1990).
[CrossRef]

Zhou, H. S.

Zhou, Y. C.

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

Zhu, J. F.

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Zhu, X.

Adv. Mater. (1)

R. A. Pala, J. White, E. Barnard, J. Liu, M. L. Brongersma, “Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements,” Adv. Mater. 21(34), 3504–3509 (2009).
[CrossRef]

Appl. Phys. Lett. (9)

S. Chhajed, M. F. Schubert, J. K. Kim, E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008).
[CrossRef]

J. F. Zhu, M. Xue, H. J. Shen, Z. Wu, S. Kim, J. J. Ho, A. Hassani-Afshar, B. Q. Zeng, K. L. Wang, “Plasmonic effects for light concentration in organic photovoltaic thin films induced by hexagonal periodic metallic nanospheres,” Appl. Phys. Lett. 98(15), 151110 (2011).
[CrossRef]

Y. N. Zhang, Z. Ouyang, N. Stokes, B. H. Jia, Z. R. Shi, M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012).
[CrossRef]

Y. H. Kuang, K. H. M. van der Werf, Z. S. Houweling, R. E. I. Schropp, “Nanorod solar cell with an ultrathin a-Si:H absorber layer,” Appl. Phys. Lett. 98(11), 113111 (2011).
[CrossRef]

L. L. Ma, Y. C. Zhou, N. Jiang, X. Lu, J. Shao, W. Lu, J. Ge, X. M. Ding, X. Y. Hou, “Wide-band “black silicon” based on porous silicon,” Appl. Phys. Lett. 88(17), 171907 (2006).
[CrossRef]

C. A. Keasler, E. Bellotti, “A numerical study of broadband absorbers for visible to infrared detectors,” Appl. Phys. Lett. 99(9), 091109 (2011).
[CrossRef]

Y. J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, J. Shao, Z. F. Li, X. P. Hao, N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007).
[CrossRef]

R. W. Peng, M. Mazzer, K. W. J. Barnham, “Efficiency enhancement of ideal photovoltaic solar cells by photonic excitations in multi-intermediate band structures,” Appl. Phys. Lett. 83(4), 770–772 (2003).
[CrossRef]

A. Wang, J. Zhao, M. A. Green, “24% efficient silicon solar cells,” Appl. Phys. Lett. 57(6), 602–604 (1990).
[CrossRef]

J. Appl. Phys. (1)

W. Shockley, H. J. Queisser, “Detailed balance limit of efficiency of pn junction solar cells,” J. Appl. Phys. 32(3), 510 (1961).
[CrossRef]

Nano Lett. (2)

J. N. Munday, H. A. Atwater, “Large Integrated Absorption Enhancement in Plasmonic Solar Cells by Combining Metallic Gratings and Antireflection Coatings,” Nano Lett. 11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008).
[CrossRef] [PubMed]

Nat. Mater. (2)

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

The schematic ultra-thin silicon solar cell with a plasmonic fractal, which consists of a silver (Ag) fractal-like pattern (thickness d1) coated on the top, a crystalline silicon (c-Si) absorb layer (thickness d2) in the middle and a silver (Ag) back reflector (thickness d3) on the bottom. The inset on top left is the front view of the pattern.

Fig. 2
Fig. 2

(a)-(c) Calculated reflectance spectra of three silicon solar cells with base-periodicity patterns: (a) P1 = 100nm, and W1 = 25nm; (b) P2 = 200nm, and W2 = 100nm; (c) P3 = 400nm, and W3 = 200nm, respectively. The insets show the related schematic patterns. (d)-(f) Dispersion maps of these three silicon solar cells, k// is the in-plane wave vector, and kg = 2π / P3 for normalization. Black dotted lines are the light cone lines. Color bar shows the calculated reflection intensity. In all three solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively.

Fig. 3
Fig. 3

Electric field distributions of three ultra-thin silicon solar cells with base-periodicity patterns. The cross sections are at the center of the silver nano cuboids (x-z plane, y = 0nm). C M is the longitudinal cavity mode in the left column, C M is the transverse cavity mode in the middle column, and SP is the surface plasmon mode in the right column, respectively. (a) For period P1 = 100nm, C M (1) and C M (1) are excited at λ = 430nm, 780nm. (b) For period P2 = 200nm, C M (2) , C M (2) and SP(2)(1,0) are excited at λ = 430nm, 754nm and 890nm. (c) For period P3 = 400nm, C M (3) , C M (3) , C M (3') , SP(3)(2,0), SP(3′)(5,0) are excited at λ = 430nm, 820nm, 875nm, 914nm, and 670nm, respectively.

Fig. 4
Fig. 4

Calculated absorbance spectra of the solar cells (i.e., the absorbance of 50nm thick Si film) and the absorbance spectra of Ag nano cuboids in the structures with different base-periodicity patterns, respectively. (a) and (d) P1 = 100nm and W1 = 25nm; (b) and (e) P2 = 200nm and W2 = 100nm; (c) and (f) P3 = 400nm and W3 = 200nm. In all three solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively. Besides, black-dotted and brown-dotted lines in Fig. 4(a) illustrate the absorbance spectra of ref-1 (free-standing 50nm-thick Si film) and ref-2 (50nm-thick Si film with a 250nm-thick Ag back reflector), and both of these references are without any plasmonic structures on the top.

Fig. 5
Fig. 5

(a) The schematic silicon solar cell with a plasmonic fractal, which contains 3 length-scales. (b) Dispersion map of this silicon solar cell with the fractal. k// is the in-plane wave vector, and kg = 2π / P3 for normalization. Black dotted lines are the light cone lines. Color bar shows the calculated reflection intensity. (c) Calculated reflectance spectrum of this silicon solar cell with the fractal. (d) Calculated absorbance spectrum of a silicon solar cell with this fractal (red line). Green, blue and orange lines are the absorbance spectra of silicon solar cells with base-periodicity patterns in Figs. 4(a)-4(c). In these solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively. (e) Calculated reflectance spectrum of this silicon solar cell with the fractal and a 100nm-thick SiO2 antireflection coating (ARC). (f) Calculated absorbance spectrum of this silicon solar cell with the fractal and a 100nm-thick SiO2 antireflection coating (ARC) (violet line).

Fig. 6
Fig. 6

Calculated quantum efficiencies of the 50nm-thick silicon solar cells: i) ref-1 (free-standing 50nm-thick Si film) and ref-2 (50nm-thick Si film with a 250nm-thick Ag back reflector). Both of these references are without any plasmonic structures on the top. ii) Three silicon solar cells with base-periodicity patterns (P1 = 100nm, P2 = 200nm, P3 = 400nm), and iii) the silicon solar cell with a plasmonic fractal and the one with a plasmonic fractal plus a dielectric ARC, respectively. The QEs are 3.16%, 6.55%, 7.46%, 8.05%, 9.27%, 12.05% and 14.22% respectively. In five plasmonic solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively. The dielectric ARC is a 100nm-thick SiO2 film, which deposits on Si film with the plasmonic fractal inside.

Fig. 7
Fig. 7

Calculated quantum efficiency of the silicon solar cells with plasmonic fractals for different base-units and duty ratios. The unit size (P) of fractals is defined as P = 4P1 = 2P2 = P3 and the duty ratio (f) of silver in the fractal patterns is defined as f = 2W1/P1 = W2/P2 = W3/P3. The period is varied from 400nm to 1000nm for every 100nm and duty ratio is varied from 0.3 to 0.7 for every 0.1. In all these solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(back Ag) = 250nm, respectively.

Equations (4)

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k SP = k 0 ε d ε m ε d + ε m ,
λ min = P i 2 + j 2 ε d ε m ε d + ε m .
A(λ)=ωIm(ε) | E | 2 dV,
QE= λ 1 λ 2 λ c A(λ)× I AM1.5G (λ) dλ λ 1 λ 2 λ c I AM1.5G (λ) dλ ,

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