Abstract

We theoretically study the angular response of thin-film organic solar cells with periodic Au back nanostrips. In particular, the equation of the generalized Lambert’s cosine law for arbitrary periodic nanostructure is formulated. We show that the periodic strip structure achieves wide-angle absorption enhancement compared with the planar nonstrip structure for both the s- and p-polarized light, which is mainly attributed to the resonant Wood’s anomalies and surface plasmon resonances, respectively. The work is important for designing and optimizing high-efficiency photovoltaic cells.

© 2011 Optical Society of America

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2010 (4)

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

W. E. I. Sha, W. C. H. Choy, and W. C. Chew, Opt. Express 18, 5993 (2010).
[CrossRef] [PubMed]

2009 (1)

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

2008 (2)

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

W. C. H. Choy and H. H. Fong, J. Phys. D 41, 155109 (2008).
[CrossRef]

2007 (1)

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

2005 (1)

J. L. Balenzategui and F. Chenlo, Sol. Energy Mater. Sol. Cells 86, 53 (2005).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

1965 (1)

Atwater, H. A.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

Balenzategui, J. L.

J. L. Balenzategui and F. Chenlo, Sol. Energy Mater. Sol. Cells 86, 53 (2005).
[CrossRef]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Brongersma, M. L.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Brown, T. M.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

Chenlo, F.

J. L. Balenzategui and F. Chenlo, Sol. Energy Mater. Sol. Cells 86, 53 (2005).
[CrossRef]

Chew, W. C.

Cheyns, D.

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

Choy, W. C. H.

Colonna, D.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

Di Carlo, A.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

Djurisic, A. B.

Dominici, L.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

Elazar, J. M.

Fan, S. H.

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Fong, H. H.

W. C. H. Choy and H. H. Fong, J. Phys. D 41, 155109 (2008).
[CrossRef]

Garg, H. P.

H. P. Garg, Treatise on Solar Energy: Fundamentals of Solar Energy (Wiley, 1982).

Gaylord, T. K.

Genoe, J.

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

Grann, E. B.

Heremans, P.

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

Hessel, A.

Lee, J. Y.

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Li, J.

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Liu, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Majewski, M. L.

McGehee, M. D.

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

Michelotti, F.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

Min, C. J.

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Moharam, M. G.

Oliner, A. A.

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Peumans, P.

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

Pommet, D. A.

Poortmans, J.

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

Rakic, A. D.

Rand, B. P.

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

Reale, A.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

Rim, S. B.

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

Scully, S. R.

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

Sha, W. E. I.

Tamir, T.

Veronis, G.

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Verreet, B.

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

Vesce, L.

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

White, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Zhang, S. Z.

Zhao, S.

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

Adv. Mater. (1)

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

S. B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, and P. Peumans, Appl. Phys. Lett. 91, 243501 (2007).
[CrossRef]

D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans, and P. Heremans, Appl. Phys. Lett. 92, 243310 (2008).
[CrossRef]

L. Dominici, L. Vesce, D. Colonna, F. Michelotti, T. M. Brown, A. Reale, and A. Di Carlo, Appl. Phys. Lett. 96, 103302 (2010).
[CrossRef]

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

J. Phys. D (1)

W. C. H. Choy and H. H. Fong, J. Phys. D 41, 155109 (2008).
[CrossRef]

Nat. Mater. (1)

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

Opt. Express (1)

Sol. Energy Mater. Sol. Cells (1)

J. L. Balenzategui and F. Chenlo, Sol. Energy Mater. Sol. Cells 86, 53 (2005).
[CrossRef]

Other (1)

H. P. Garg, Treatise on Solar Energy: Fundamentals of Solar Energy (Wiley, 1982).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic structure of the unit cell of the OSC. The structural parameters are t 1 = 100 nm , t 2 = 10 nm , t 3 = 40 nm , t 4 = 30 nm , t 5 = 30 nm , t 6 = 100 nm , w = 100 nm , and P = 200 nm . (b) Absorption coefficients of CuPc and C 60 . The inset is the Sun irradiance spectrum of an air mass of 1.5 (AM1.5).

Fig. 2
Fig. 2

Absorption of the periodic strip structure is compared to that of the nonstrip structure, replacing the laterally periodic Au-PEDOT:PSS-Au pattern with the planar PEDOT:PSS layer. The near-field profiles of the absorption peaks pointed by the arrows are shown in Fig. 3. (a) Absorption enhancement factor for the s polarization. The inset shows the averaged power density of the Au-PEDOT:PSS-Au pattern along the x direction. The negative power density peak due to the opposite propagation direction coincides with the absorption peak at θ = 40 ° with the wavelength 460 nm . (b) Absorption enhancement factor for the p polarization.

Fig. 3
Fig. 3

(a)  E z field profile of the s polarization at θ = 80 ° with 435 nm . (b)  H z field profile of the p polarization at θ = 80 ° with 755 nm .

Fig. 4
Fig. 4

Total absorptivity as a function of the incident angle θ. The generalized Lambert’s cosine law (straight–dotted and dash–dotted curves) are calculated by A 0 t cos θ , where A 0 t is the total absorptivity under the vertical incidence condition. (a) s polarization; (b) p polarization.

Equations (2)

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[ 1 L ( θ ) ] · 1 2 Re [ E i × H i * ] · d S = n r n i ω ϵ 0 | E | 2 d V ,
I = 1 2 Re [ E i × H i * ] · n = | E i | 2 2 Z cos θ ,

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