Abstract

Nanophotonic light trapping offers a promising approach to increased efficiency in thin-film organic photovoltaics. In this paper, an extension of the direct-binary-search algorithm was adopted to optimize dielectric nanophotonic structures for increasing power output of ultra-thin organic solar cells. The optimized devices were comprised of an absorber layer sandwiched between two patterned, transparent, conducting cladding layers. Light trapping in such devices with an absorber thickness of only 10nm increases power output by a factor of 16 when compared to a flat reference device. We further show that even under oblique illumination with angles ranging from 0 to 60degrees, such a device could produce over 7 times more power compared to a flat reference device. Finally, we also performed a spectral and parametric analysis of the optimized design, and show that the increase is primarily due to guided-mode resonances. Our simulations indicate that this new design approach has the potential to significantly increase the performance of ultra-thin solar cells in realistic scenarios.

© 2013 OSA

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    [CrossRef] [PubMed]

2012

M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
[CrossRef] [PubMed]

Z. Pan, H. Gu, M. T. Wu, Y. Li, and Y. Chen, “Graphene-based functional materials for organic solar cells,” Opt. Mater. Express2(6), 814–824 (2012).
[CrossRef]

L. Song and A. Uddin, “Design of high efficiency organic solar cell with light trapping,” Opt. Express20(S5Suppl 5), A606–A621 (2012).
[CrossRef] [PubMed]

P. Zilio, D. Sammito, G. Zacco, M. Mazzeo, G. Gigli, and F. Romanato, “Light absorption enhancement in heterostructure organic solar cells through the integration of 1-D plasmonic gratings,” Opt. Express20(S4Suppl 4), A476–A488 (2012).
[CrossRef] [PubMed]

R. B. Dunbar, T. Pfadler, and L. Schmidt-Mende, “Highly absorbing solar cells--a survey of plasmonic nanostructures,” Opt. Express20(S2Suppl 2), A177–A189 (2012).
[CrossRef] [PubMed]

P. Wang and R. Menon, “Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping,” Opt. Express20(2), 1849–1855 (2012).
[CrossRef] [PubMed]

G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express20(3), 2814–2823 (2012).
[CrossRef] [PubMed]

P. Wang and R. Menon, “Simulation and analysis of the angular response of 1D dielectric nanophotonic light-trapping structures in thin-film photovoltaics,” Opt. Express20(S4Suppl 4), A545–A553 (2012).
[CrossRef] [PubMed]

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[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]

A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012).
[CrossRef] [PubMed]

2011

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

M. A. Green, “Enhanced evanescent mode light trapping in organic solar cells and other low index optoelectronic devices,” Prog. Photovolt. Res. Appl.19(4), 473–477 (2011).
[CrossRef]

N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett.107(20), 205501 (2011).
[CrossRef] [PubMed]

A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys.384(1-3), 44–51 (2011).
[CrossRef]

M. Leclerc and A. Najari, “Organic thermoelectrics: Green energy from a blue polymer,” Nat. Mater.10(6), 409–410 (2011).
[CrossRef] [PubMed]

H. Shen and B. Maes, “Combined plasmonic gratings in organic solar cells,” Opt. Express19(S6Suppl 6), A1202–A1210 (2011).
[CrossRef] [PubMed]

A. Raman, Z. Yu, and S. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express19(20), 19015–19026 (2011).
[CrossRef] [PubMed]

A. Tada, Y. Geng, Q. Wei, K. Hashimoto, and K. Tajima, “Tailoring organic heterojunction interfaces in bilayer polymer photovoltaic devices,” Nat. Mater.10(6), 450–455 (2011).
[CrossRef] [PubMed]

2010

W. H. Lee, S. Y. Chuang, H. L. Chen, W. F. Su, and C. H. Lin, “Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode,” Thin Solid Films518(24), 7450–7454 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107(41), 17491–17496 (2010).
[CrossRef] [PubMed]

2009

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science324(5929), 917–921 (2009).
[CrossRef] [PubMed]

J. L. Brédas, J. E. Norton, J. Cornil, and V. Coropceanu, “Molecular understanding of organic solar cells: the challenges,” Acc. Chem. Res.42(11), 1691–1699 (2009).
[CrossRef] [PubMed]

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

2008

S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett.93(7), 073307 (2008).
[CrossRef]

2007

A. C. Mayer, S. R. Scully, B. E. Hardin, M. W. Rowell, and M. D. McGehee, “Polymer-based solar cells,” Mater. Today10(11), 28–33 (2007).
[CrossRef]

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
[CrossRef]

2006

Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510(1-2), 95–101 (2006).
[CrossRef]

S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express14(6), 2300–2308 (2006).
[CrossRef] [PubMed]

T. L. Benanti and D. Venkataraman, “Organic solar cells: an overview focusing on active layer morphology,” Photosynth. Res.87(1), 73–81 (2006).
[CrossRef] [PubMed]

2004

H. Hoppe and N. S. Sariciftci, “Organic solar cells: An overview,” J. Mater. Res.19(07), 1924–1945 (2004).
[CrossRef]

L. J. Guo, “Recent progress in nanoimprint technology and its applications,” J. Phys. D Appl. Phys.37(11), R123–R141 (2004).
[CrossRef]

2002

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002).
[CrossRef]

L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron.3(3-4), 143–148 (2002).
[CrossRef]

J. Nelson, “Organic photovoltaic films,” Curr. Opin. Solid St. Mat.6(1), 87–95 (2002).
[CrossRef]

2000

T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature406(6799), 1027–1031 (2000).
[CrossRef] [PubMed]

1987

Allebach, J. P.

Andrew, T. L.

N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett.107(20), 205501 (2011).
[CrossRef] [PubMed]

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science324(5929), 917–921 (2009).
[CrossRef] [PubMed]

Ballif, C.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Barraud, L.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Battaglia, C.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Bauer, S.

M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
[CrossRef] [PubMed]

Bazan, G. C.

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Beaupre, S.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Benanti, T. L.

T. L. Benanti and D. Venkataraman, “Organic solar cells: an overview focusing on active layer morphology,” Photosynth. Res.87(1), 73–81 (2006).
[CrossRef] [PubMed]

Billet, A.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Boccard, M.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Branham, M. S.

A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012).
[CrossRef] [PubMed]

Brédas, J. L.

J. L. Brédas, J. E. Norton, J. Cornil, and V. Coropceanu, “Molecular understanding of organic solar cells: the challenges,” Acc. Chem. Res.42(11), 1691–1699 (2009).
[CrossRef] [PubMed]

Bremel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Brimhall, N.

N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett.107(20), 205501 (2011).
[CrossRef] [PubMed]

Brongersma, M. L.

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[CrossRef] [PubMed]

Bugnon, G.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Chen, B. J.

Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510(1-2), 95–101 (2006).
[CrossRef]

Chen, G.

A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012).
[CrossRef] [PubMed]

Chen, H. L.

W. H. Lee, S. Y. Chuang, H. L. Chen, W. F. Su, and C. H. Lin, “Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode,” Thin Solid Films518(24), 7450–7454 (2010).
[CrossRef]

Chen, T. P.

Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510(1-2), 95–101 (2006).
[CrossRef]

Chen, Y.

Cho, S.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Chuang, S. Y.

W. H. Lee, S. Y. Chuang, H. L. Chen, W. F. Su, and C. H. Lin, “Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode,” Thin Solid Films518(24), 7450–7454 (2010).
[CrossRef]

Coates, N.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Coates, N. E.

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Cornil, J.

J. L. Brédas, J. E. Norton, J. Cornil, and V. Coropceanu, “Molecular understanding of organic solar cells: the challenges,” Acc. Chem. Res.42(11), 1691–1699 (2009).
[CrossRef] [PubMed]

Coropceanu, V.

J. L. Brédas, J. E. Norton, J. Cornil, and V. Coropceanu, “Molecular understanding of organic solar cells: the challenges,” Acc. Chem. Res.42(11), 1691–1699 (2009).
[CrossRef] [PubMed]

Cui, Y.

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]

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[CrossRef] [PubMed]

De Wolf, S.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Dennler, G.

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

Despeisse, M.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Ding, L.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Domínguez-Caballero, J. A.

Dunbar, R. B.

Erni, L.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Escarré, J.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Fan, S.

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[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]

A. Raman, Z. Yu, and S. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express19(20), 19015–19026 (2011).
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107(41), 17491–17496 (2010).
[CrossRef] [PubMed]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002).
[CrossRef]

Garnett, E. C.

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[CrossRef] [PubMed]

Geng, Y.

A. Tada, Y. Geng, Q. Wei, K. Hashimoto, and K. Tajima, “Tailoring organic heterojunction interfaces in bilayer polymer photovoltaic devices,” Nat. Mater.10(6), 450–455 (2011).
[CrossRef] [PubMed]

Ghosh, S.

L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron.3(3-4), 143–148 (2002).
[CrossRef]

Gigli, G.

Glatthaar, M.

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

Glowacki, E. D.

M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
[CrossRef] [PubMed]

Gorishnyy, T.

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
[CrossRef]

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M. A. Green, “Enhanced evanescent mode light trapping in organic solar cells and other low index optoelectronic devices,” Prog. Photovolt. Res. Appl.19(4), 473–477 (2011).
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Guo, L. J.

L. J. Guo, “Recent progress in nanoimprint technology and its applications,” J. Phys. D Appl. Phys.37(11), R123–R141 (2004).
[CrossRef]

Han, S. E.

A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012).
[CrossRef] [PubMed]

Hardin, B. E.

A. C. Mayer, S. R. Scully, B. E. Hardin, M. W. Rowell, and M. D. McGehee, “Polymer-based solar cells,” Mater. Today10(11), 28–33 (2007).
[CrossRef]

Hashimoto, K.

A. Tada, Y. Geng, Q. Wei, K. Hashimoto, and K. Tajima, “Tailoring organic heterojunction interfaces in bilayer polymer photovoltaic devices,” Nat. Mater.10(6), 450–455 (2011).
[CrossRef] [PubMed]

Haug, F. J.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011).
[CrossRef] [PubMed]

Heeger, A. J.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Hoppe, H.

H. Hoppe and N. S. Sariciftci, “Organic solar cells: An overview,” J. Mater. Res.19(07), 1924–1945 (2004).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Inganas, O.

L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron.3(3-4), 143–148 (2002).
[CrossRef]

Ito, T.

T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature406(6799), 1027–1031 (2000).
[CrossRef] [PubMed]

Jang, J.

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
[CrossRef]

Jeon, S.

Jeong, S.

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[CrossRef] [PubMed]

Jo, J.

S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett.93(7), 073307 (2008).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Kaltenbrunner, M.

M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
[CrossRef] [PubMed]

Kariis, H.

A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys.384(1-3), 44–51 (2011).
[CrossRef]

Kim, D.

S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett.93(7), 073307 (2008).
[CrossRef]

Kim, G.

Kim, J. Y.

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Kim, S.

S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett.93(7), 073307 (2008).
[CrossRef]

Koh, C. Y.

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
[CrossRef]

Kooi, S.

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
[CrossRef]

Leclerc, M.

M. Leclerc and A. Najari, “Organic thermoelectrics: Green energy from a blue polymer,” Nat. Mater.10(6), 409–410 (2011).
[CrossRef] [PubMed]

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Lee, K.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Lee, W. H.

W. H. Lee, S. Y. Chuang, H. L. Chen, W. F. Su, and C. H. Lin, “Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode,” Thin Solid Films518(24), 7450–7454 (2010).
[CrossRef]

Lenz, A.

A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys.384(1-3), 44–51 (2011).
[CrossRef]

Li, Y.

Lin, C. H.

W. H. Lee, S. Y. Chuang, H. L. Chen, W. F. Su, and C. H. Lin, “Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode,” Thin Solid Films518(24), 7450–7454 (2010).
[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]

Lungenschmied, C.

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

Ma, W. L.

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Maes, B.

Maldovan, M.

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
[CrossRef]

Malyarchuk, V.

Manthena, R. V.

N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett.107(20), 205501 (2011).
[CrossRef] [PubMed]

Mavrokefalos, A.

A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012).
[CrossRef] [PubMed]

Mayer, A. C.

A. C. Mayer, S. R. Scully, B. E. Hardin, M. W. Rowell, and M. D. McGehee, “Polymer-based solar cells,” Mater. Today10(11), 28–33 (2007).
[CrossRef]

Mazzeo, M.

McGehee, M. D.

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
[CrossRef] [PubMed]

A. C. Mayer, S. R. Scully, B. E. Hardin, M. W. Rowell, and M. D. McGehee, “Polymer-based solar cells,” Mater. Today10(11), 28–33 (2007).
[CrossRef]

Menon, R.

G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express20(3), 2814–2823 (2012).
[CrossRef] [PubMed]

P. Wang and R. Menon, “Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping,” Opt. Express20(2), 1849–1855 (2012).
[CrossRef] [PubMed]

P. Wang and R. Menon, “Simulation and analysis of the angular response of 1D dielectric nanophotonic light-trapping structures in thin-film photovoltaics,” Opt. Express20(S4Suppl 4), A545–A553 (2012).
[CrossRef] [PubMed]

N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett.107(20), 205501 (2011).
[CrossRef] [PubMed]

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science324(5929), 917–921 (2009).
[CrossRef] [PubMed]

Meyer, A.

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

Meyer, T.

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

Moon, J. S.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Moses, D.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Na, S.

S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett.93(7), 073307 (2008).
[CrossRef]

Nah, Y.

S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett.93(7), 073307 (2008).
[CrossRef]

Najari, A.

M. Leclerc and A. Najari, “Organic thermoelectrics: Green energy from a blue polymer,” Nat. Mater.10(6), 409–410 (2011).
[CrossRef] [PubMed]

Nelson, J.

J. Nelson, “Organic photovoltaic films,” Curr. Opin. Solid St. Mat.6(1), 87–95 (2002).
[CrossRef]

Neugebauer, H.

C. Lungenschmied, G. Dennler, H. Neugebauer, S. N. Sariciftci, M. Glatthaar, T. Meyer, and A. Meyer, “Flexible, long-lived, large-area, organic solar cells,” Sci. Energy Mater. Sci. Cell91, 379–384 (2007).

Norton, J. E.

J. L. Brédas, J. E. Norton, J. Cornil, and V. Coropceanu, “Molecular understanding of organic solar cells: the challenges,” Acc. Chem. Res.42(11), 1691–1699 (2009).
[CrossRef] [PubMed]

Ojamae, L.

A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys.384(1-3), 44–51 (2011).
[CrossRef]

Okazaki, S.

T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature406(6799), 1027–1031 (2000).
[CrossRef] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Pan, Z.

Park, S. H.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Peet, J.

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007).
[CrossRef] [PubMed]

Persson, P.

A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys.384(1-3), 44–51 (2011).
[CrossRef]

Pettersson, L. A. A.

L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron.3(3-4), 143–148 (2002).
[CrossRef]

Pfadler, T.

Pohl, A.

A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys.384(1-3), 44–51 (2011).
[CrossRef]

Raman, A.

A. Raman, Z. Yu, and S. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express19(20), 19015–19026 (2011).
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107(41), 17491–17496 (2010).
[CrossRef] [PubMed]

Rogers, J. A.

Romanato, F.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Rowell, M. W.

A. C. Mayer, S. R. Scully, B. E. Hardin, M. W. Rowell, and M. D. McGehee, “Polymer-based solar cells,” Mater. Today10(11), 28–33 (2007).
[CrossRef]

Roy, A.

S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics3(5), 297–302 (2009).
[CrossRef]

Sammito, D.

Sariciftci, N. S.

M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
[CrossRef] [PubMed]

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M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
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Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510(1-2), 95–101 (2006).
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J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007).
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T. L. Benanti and D. Venkataraman, “Organic solar cells: an overview focusing on active layer morphology,” Photosynth. Res.87(1), 73–81 (2006).
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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).
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S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012).
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Nat Commun

M. Kaltenbrunner, M. S. White, E. D. Głowacki, T. Sekitani, T. Someya, N. S. Sariciftci, and S. Bauer, “Ultrathin and lightweight organic solar cells with high flexibility,” Nat Commun3, 770 (2012).
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Nat. Mater.

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[CrossRef]

Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510(1-2), 95–101 (2006).
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Figures (6)

Fig. 1
Fig. 1

Schematics of the simulation models. (a) Ultra-thin absorber layer sandwiched between two nanostructured light-trapping layers. (b) First reference cell with bare, unpatterned surface. The incident angle is defined as θ . (c) Second reference cell with an optimal anti-reflection coating.

Fig. 2
Fig. 2

Results of the optimized device with 10-nm thick absorber. (a) Evolution of the enhancement factors as a function of the iteration number. The optimized design is shown in the inset. (b) Calculated J-V and P-V curves for both the optimized device and the reference device (inset). (c) Enhancement spectrum analysis (inset: electric-field-intensity distributions inside the active layer at the peaks of the TE and TM polarizations). (d) Angular response analysis of the optimal design (inset: spectral-angular analysis).

Fig. 3
Fig. 3

Results of the optimized device with 30-nm thick absorber. (a) Evolution of the enhancement factors as a function of the iteration number. The optimized design is shown in the inset. (b) Calculated J-V and P-V curves for both the optimized device and the reference device (inset). (c) Enhancement spectrum analysis (inset: electric-field-intensity distributions inside the active layer at the peaks of the TE and TM polarizations). (d) Angular response analysis of the optimal design (inset: spectral-angular analysis).

Fig. 4
Fig. 4

Results of the optimized device with 50-nm thick absorber. (a) Evolution of the enhancement factors as a function of the iteration number. The optimized design is shown in the inset. (b) Calculated J-V and P-V curves for both the optimized device and the reference device. (c) Enhancement spectrum analysis (inset: electric-field-intensity distributions inside the active layer at the peaks of the TE and TM polarizations). (d) Angular response analysis of the optimal design (inset: spectral-angular analysis).

Fig. 5
Fig. 5

Parametric analysis of the optimized device with an active-layer thickness of 10nm. (a) (E) vs. Λ; (b) Enhancement spectrum vs. Λ; (c) (E) vs. s; (d) Enhancement spectrum vs. s; (e) (E) vs. ff1; (f) Enhancement spectrum vs. ff1; (g) (E) vs. ts; (h) Enhancement spectrum vs. ts; (i) (E) vs. ff2; (j) Enhancement spectrum vs. ff2; (l) (E) vs. tb; (l) Enhancement spectrum vs. tb; (m) (E) vs. tc1; (n) Enhancement spectrum vs. tc1; (o) (E) vs. tc2; (p) Enhancement spectrum vs. tc2.

Fig. 6
Fig. 6

Power-enhancement factor, (E) of the optimized devices vs. thickness of the active layer, compared to both bare reference and reference device with ARC. The comparison is made for both normal incidence and averaged over a range of incident angles from 0° to 60°. The enhancement factor, (E) is plotted in log scale.

Tables (1)

Tables Icon

Table 1 Ranges and unit perturbations of geometric parameters for optimization

Equations (3)

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j sc = q t a Λ active ( λ min λ max Φ λ (x,y,λ)IQE(λ)dλ )dxdy ,
j( V )= j sc j 0 ( exp( qV k B T )1 ),
P( V )=j(V)V.

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