Abstract

We use a rigorous electromagnetic approach to analyze the fundamental limit of light-trapping enhancement in grating structures. This limit can exceed the bulk limit of 4n 2, but has significant angular dependency. We explicitly show that 2D gratings provide more enhancement than 1D gratings. We also show the effects of the grating profile’s symmetry on the absorption enhancement limit. Numerical simulations are applied to support the theory. Our findings provide general guidance for the design of grating structures for light-trapping solar cells.

© 2010 OSA

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2010 (5)

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

E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010).
[CrossRef] [PubMed]

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010).
[CrossRef] [PubMed]

J. Zhu, C.-M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010).
[CrossRef]

2009 (7)

Y. Park, E. Drouard, O. El Daif, X. Letartre, P. Viktorovitch, A. Fave, A. Kaminski, M. Lemiti, and C. Seassal, “Absorption enhancement using photonic crystals for silicon thin film solar cells,” Opt. Express 17(16), 14312–14321 (2009).
[CrossRef] [PubMed]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17(23), 20975–20990 (2009).
[CrossRef] [PubMed]

C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express 17(22), 19371–19381 (2009).
[CrossRef] [PubMed]

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009).
[CrossRef]

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

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

2008 (7)

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78(2), 023825–023815 (2008).
[CrossRef]

I. Tobías, A. Luque, and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys. 104(3), 034502 (2008).
[CrossRef]

L. Tsakalakos, “Nanostructures for photovoltaics,” Mater. Sci. Eng. Rep. 62(6), 175–189 (2008).
[CrossRef]

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Opt. Express 16(19), 15238–15248 (2008).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103(9), 093102 (2008).
[CrossRef]

2007 (2)

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007).
[CrossRef] [PubMed]

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

2006 (1)

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

2005 (1)

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

2004 (1)

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

2003 (2)

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

2002 (3)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).
[CrossRef]

M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovoltaics 10(4), 235–241 (2002).
[CrossRef]

2001 (1)

C. Eisele, C. E. Nebel, and M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

1995 (1)

1986 (1)

P. Campbell and M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

1983 (1)

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983).
[CrossRef]

1982 (2)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. A 72(7), 899–907 (1982).
[CrossRef]

Abrams, N.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Agrawal, M.

Alamariu, B. A.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Atwater, H. A.

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

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17(23), 20975–20990 (2009).
[CrossRef] [PubMed]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Barnard, E.

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

Barnett, A.

Beck, F. J.

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009).
[CrossRef]

Benkstein, K. D.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Bermel, P.

Biswas, R.

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103(9), 093102 (2008).
[CrossRef]

Bloch, A. N.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983).
[CrossRef]

Boettcher, S. W.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Brammer, T.

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

Briggs, R. M.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Brongersma, M. L.

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

Bunte, E.

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

Burkhard, G. F.

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Campbell, P.

P. Campbell and M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

Catchpole, K. R.

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009).
[CrossRef]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

Chen, C.

Chutinan, A.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78(2), 023825–023815 (2008).
[CrossRef]

Cody, G. D.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Connor, S. T.

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Creazzo, T.

Cui, Y.

J. Zhu, C.-M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010).
[CrossRef]

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

DeSimone, J. M.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Drouard, E.

Duan, X.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Eisele, C.

C. Eisele, C. E. Nebel, and M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

El Daif, O.

Fan, S.

J. Zhu, C.-M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010).
[CrossRef]

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Fang, Y.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Fave, A.

Feng, B.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Feng, N.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Ferry, V. E.

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17(23), 20975–20990 (2009).
[CrossRef] [PubMed]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Frank, A. J.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Garnett, E.

E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010).
[CrossRef] [PubMed]

Gippius, N. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).
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Green, M. A.

M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovoltaics 10(4), 235–241 (2002).
[CrossRef]

P. Campbell and M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

Halaoui, L. I.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Heine, C.

Hong, C.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Honsberg, C.

Hsu, C.-M.

J. Zhu, C.-M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010).
[CrossRef]

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Huang, J.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Ishihara, T.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).
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Joannopoulos, J. D.

John, S.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78(2), 023825–023815 (2008).
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Kaminski, A.

Kelzenberg, M. D.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Kempa, T. J.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Kimerling, L. C.

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007).
[CrossRef] [PubMed]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Ko, D.-H.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Krause, M.

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

Lemiti, M.

Letartre, X.

Lewis, B. A.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Lewis, N. S.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Lieber, C. M.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Lin, C.

Liu, J.

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

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Lopez, R.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Luo, C.

Luque, A.

I. Tobías, A. Luque, and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys. 104(3), 034502 (2008).
[CrossRef]

Mallick, S. B.

Mallouk, T. E.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Marti, A.

I. Tobías, A. Luque, and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys. 104(3), 034502 (2008).
[CrossRef]

McGehee, M.

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Mokkapati, S.

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009).
[CrossRef]

Morf, R. H.

Muljarov, E. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).
[CrossRef]

Müller, J.

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

Munday, J. N.

Mutitu, J. G.

Nebel, C. E.

C. Eisele, C. E. Nebel, and M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

Nishimura, S.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Pacifici, D.

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17(23), 20975–20990 (2009).
[CrossRef] [PubMed]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Pala, R. A.

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

Park, Y.

Petykiewicz, J. A.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Peumans, P.

Polman, A.

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

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009).
[CrossRef]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

Povinelli, M. L.

Prather, D. W.

Putnam, M. C.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

Saeta, P. N.

Samulski, E. T.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Schaadt, D. M.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Seassal, C.

Senoussaoui, N.

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

Sheng, P.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983).
[CrossRef]

Shi, S.

Spurgeon, J. M.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

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P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983).
[CrossRef]

Stiebig, H.

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films 451–452, 397–401 (2004).
[CrossRef]

Stutzmann, M.

C. Eisele, C. E. Nebel, and M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

Suh, W.

Sweatlock, L. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Tian, B.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Tikhodeev, S. G.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).
[CrossRef]

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I. Tobías, A. Luque, and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys. 104(3), 034502 (2008).
[CrossRef]

Tsakalakos, L.

L. Tsakalakos, “Nanostructures for photovoltaics,” Mater. Sci. Eng. Rep. 62(6), 175–189 (2008).
[CrossRef]

Tumbleston, J. R.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Turner-Evans, D. B.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

van de Lagemaat, J.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

Viktorovitch, P.

Wang, Q.

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Warren, E. L.

M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[CrossRef] [PubMed]

White, J.

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

Williams, S.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Xu, Y.

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
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E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. A 72(7), 899–907 (1982).
[CrossRef]

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Yablonskii, A. L.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).
[CrossRef]

Yang, P.

E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010).
[CrossRef] [PubMed]

Yi, Y.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Yu, E. T.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Yu, G.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Yu, N.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Yu, Z.

J. Zhu, C.-M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010).
[CrossRef]

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Zeng, L.

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007).
[CrossRef] [PubMed]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

Zhang, L.

D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Photonic crystal geometry for organic solar cells,” Nano Lett. 9(7), 2742–2746 (2009).
[CrossRef] [PubMed]

Zheng, X.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Zhou, D.

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103(9), 093102 (2008).
[CrossRef]

Zhu, J.

J. Zhu, C.-M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010).
[CrossRef]

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

Adv. Mater. (1)

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

Appl. Opt. (1)

Appl. Phys. Lett. (5)

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983).
[CrossRef]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009).
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006).
[CrossRef]

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

IEEE Trans. Electron. Dev. (2)

P. Campbell and M. A. Green, “The limiting efficiency of silicon solar-cells under concentrated sunlight,” IEEE Trans. Electron. Dev. 33(2), 234–239 (1986).
[CrossRef]

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

J. Am. Chem. Soc. (1)

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125(20), 6306–6310 (2003).
[CrossRef] [PubMed]

J. Appl. Phys. (3)

I. Tobías, A. Luque, and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys. 104(3), 034502 (2008).
[CrossRef]

C. Eisele, C. E. Nebel, and M. Stutzmann, “Periodic light coupler gratings in amorphous thin film solar cells,” J. Appl. Phys. 89(12), 7722–7726 (2001).
[CrossRef]

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103(9), 093102 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Mater. Sci. Eng. Rep. (1)

L. Tsakalakos, “Nanostructures for photovoltaics,” Mater. Sci. Eng. Rep. 62(6), 175–189 (2008).
[CrossRef]

Nano Lett. (5)

J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009).
[CrossRef]

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Nat. Mater. (2)

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Figures (8)

Fig. 1
Fig. 1

a) Grating structure with periodicity L = 600nm. Brown ribbons are non-absorptive dielectric medium with index n2 = 12.5. The widths of three air slots are 4%, 12%, and 24% of the period respectively. The absorptive film (grey) is d = 3000nm thick. The whole structure is placed on a perfect mirror (yellow). b) and c) Absorption spectra obtained by numerical simulations for s (b) and p (c) polarized incident light. Light is incident from the normal direction. Red lines represent spectrally-averaged absorption in the presence of the grating and blue lines represent single-pass absorption in the absence of the grating.

Fig. 2
Fig. 2

a) Channels in 1D k-space. b) Resonances in a film with 1D grating. Dots represent resonances. c) Upper limit of absorption enhancement in 1D grating films without mirror symmetry.

Fig. 3
Fig. 3

a) 1D grating structure with mirror symmetry. Air slot width is 40% of the period. The film is the same as that in Fig. 1a. b) Limit of absorption enhancement in grating structures with mirror symmetry. c) and d) Absorption spectra obtained by numerical simulations for s and p polarization lights, respectively. Lights are incident from the normal direction.

Fig. 4
Fig. 4

Absorption spectra for off-normally incident light (averaged among s and p lights). Light incidence angle is 30° and incident plane is oriented at azimuthal angle 30°. a) for the asymmetrical structure in Fig. 1a. b) for the symmetrical structure in Fig. 3a.

Fig. 5
Fig. 5

a) Channels in 2D k-space. Blue and grey dots represent channels when the incident light comes in from normal and off-normal directions, respectively. The radius of the circle is k0 . b) Limit of absorption enhancement in 2D grating structures. c) Angular response of the average enhancement factor integrated over wavelength from 600nm to 1200nm. The periodicity of the grating is 600nm. d) the same as (c) except the periodicity is 3000nm.

Fig. 6
Fig. 6

a) The unit of cell of a 2D grating structure. Film thickness is the same as the structure in Fig. 1a. b) Absorption spectrum for normally incident light (averaged among two polarizations). c) Spectra of the running average enhancement factors. Blue: simulation result. Red: analytical theory. d. average enhancement factor for different incidence angles θ. The azimuthal angle is fixed at φ = 0 . Blue dots are simulation results and red is analytical theory.

Fig. 7
Fig. 7

a) Channels in 2D k-space for a grating with triangular lattice periodicity. The lattice constant is L. b) Upper limit of absorption enhancement for gratings with triangular lattice periodicity.

Fig. 8
Fig. 8

Absorption spectrum for structure shown in Fig. 6a. except that the film is replaced with crystalline silicon. Dashed line is single-pass absorption spectrum.

Equations (17)

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d d t a = ( j ω 0 N γ e + γ i 2 ) a + j γ e S
A ( ω ) = γ i γ e ( ω ω 0 ) 2 + ( γ i + N γ e ) 2 / 4
σ = A ( ω ) d ω
σ = 2 π γ i N + γ i / γ e
σ max = 2 π γ i N
A = σ max Δ ω = 2 π γ i Δ ω M N
F = A α d = 2 π γ i α d Δ ω M N
N = 2 k 0 2 π / L = 2 L λ
M = 2 n 2 π ω c 2 ( L 2 π ) ( d 2 π ) Δ ω
F = A d α = π n
N = 2 k 0 2 π / L + 1 = 2 L λ + 1
L > > λ / n d > > λ / n
M s y m = M / 2
S e v e n = 1 2 ( S k / / + S k / / ) S o d d = 1 2 ( S k / / S k / / )
M = 8 π n 3 ω 2 c 3 ( L 2 π ) 2 ( d 2 π ) Δ ω .
G m , n = m 2 π L x ^ + n 2 π L y ^ ,
k = k / / + G m , n   ,

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