Abstract

For ultrathin (~10 nm) nanocomposite films of plasmonic materials and semiconductors, the absorptance of normal incident light is typically limited to about 50%. However, through addition of a non-absorbing spacer with a highly reflective backside to such films, close to 100% absorptance can be achieved at a targeted wavelength. Here, a simple analytic model useful in the long wavelength limit is presented. It shows that the spectral response can largely be characterized in terms of two wavelengths, associated with the absorber layer itself and the reflective support, respectively. These parameters influence both absorptance peak position and shape. The model is employed to optimize the system towards broadband solar energy conversion, with the spectrally integrated plasmon induced semiconductor absorptance as a figure of merit. Geometries optimized in this regard are then evaluated in full finite element calculations which demonstrate conversion efficiencies of up to 64% of the Shockley-Queisser limit. This is achieved using only the equivalence of about 10 nanometer composite material, comprising Ag and a thin film solar cell layer of a-Si, CuInSe2 or the organic semiconductor MDMO-PPV. A potential for very resource efficient solar energy conversion based on plasmonics is thus demonstrated.

© 2010 OSA

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2010

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

2009

E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

C. Hägglund and B. Kasemo, “Nanoparticle plasmonics for 2D-photovoltaics: mechanisms, optimization, and limits,” Opt. Express 17(14), 11944–11957 (2009).
[CrossRef] [PubMed]

J. Le Perchec, Y. Desieres, and R. E. de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett. 94(18), 181104 (2009).
[CrossRef]

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

S. D. Standridge, G. C. Schatz, and J. T. Hupp, “Distance dependence of plasmon-enhanced photocurrent in dye-sensitized solar cells,” J. Am. Chem. Soc. 131(24), 8407–8409 (2009).
[CrossRef] [PubMed]

M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovoltaics 17(5), 320–326 (2009).
[CrossRef]

2008

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92(1), 013113 (2008).
[CrossRef]

C. Hägglund, M. Zäch, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. S. Cai, and V. M. Shalaev, “The Ag dielectric function in plasmonic metamaterials,” Opt. Express 16(2), 1186–1195 (2008).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

N. C. Lindquist, W. A. Luhman, S.-H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett. 93(12), 123308 (2008).
[CrossRef]

2007

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

2004

Y. S. Jung, “Spectroscopic ellipsometry studies on the optical constants of indium tin oxide films deposited under various sputtering conditions,” Thin Solid Films 467(1-2), 36–42 (2004).
[CrossRef]

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

2003

E. A. Coronado and G. C. Schatz, “Surface plasmon broadening for arbitrary shape nanoparticles: A geometrical probability approach,” J. Chem. Phys. 119(7), 3926–3934 (2003).
[CrossRef]

2002

H. Hoppe, N. S. Sariciftci, and D. Meissner, “Optical constants of conjugated polymer/fullerene based bulk-heterojunction organic solar cells,” Mol. Cryst. Liquid Cryst. 385(1), 233–239 (2002).
[CrossRef]

H. J. Queisser, “Photovoltaic conversion at reduced dimensions,” Physica E 14(1-2), 1–10 (2002).
[CrossRef]

2001

M. I. Alonso, K. Wakita, J. Pascual, M. Garriga, and N. Yamamoto, “Optical functions and electronic structure of CuInSe2, CuGaSe2, CuInS2, and CuGaS2,” Phys. Rev. B 63(7), 075203 (2001).
[CrossRef]

1990

J. R. Bolton and M. D. Archer, “Requirements for ideal performance of photochemical and photovoltaic solar energy converters,” J. Phys. Chem. 94(21), 8028–8036 (1990).
[CrossRef]

1973

J. Vlieger, “Reflection and transmission of light by a square nonpolar llattice,” Physica 64(1), 63–81 (1973).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1961

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

Alonso, M. I.

M. I. Alonso, K. Wakita, J. Pascual, M. Garriga, and N. Yamamoto, “Optical functions and electronic structure of CuInSe2, CuGaSe2, CuInS2, and CuGaS2,” Phys. Rev. B 63(7), 075203 (2001).
[CrossRef]

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Archer, M. D.

J. R. Bolton and M. D. Archer, “Requirements for ideal performance of photochemical and photovoltaic solar energy converters,” J. Phys. Chem. 94(21), 8028–8036 (1990).
[CrossRef]

Atwater, H. A.

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

Bolton, J. R.

J. R. Bolton and M. D. Archer, “Requirements for ideal performance of photochemical and photovoltaic solar energy converters,” J. Phys. Chem. 94(21), 8028–8036 (1990).
[CrossRef]

Braakman, F. R.

E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

Cai, W. S.

Carius, R.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Catchpole, K. R.

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Coronado, E. A.

E. A. Coronado and G. C. Schatz, “Surface plasmon broadening for arbitrary shape nanoparticles: A geometrical probability approach,” J. Chem. Phys. 119(7), 3926–3934 (2003).
[CrossRef]

de Dood, M. J. A.

E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

de Lamaestre, R. E.

J. Le Perchec, Y. Desieres, and R. E. de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett. 94(18), 181104 (2009).
[CrossRef]

Desieres, Y.

J. Le Perchec, Y. Desieres, and R. E. de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett. 94(18), 181104 (2009).
[CrossRef]

Dorenbos, S. N.

E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

Drachev, V. P.

Driessen, E. F. C.

E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

Emery, K.

M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovoltaics 17(5), 320–326 (2009).
[CrossRef]

Engheta, N.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Forrest, S. R.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

Garriga, M.

M. I. Alonso, K. Wakita, J. Pascual, M. Garriga, and N. Yamamoto, “Optical functions and electronic structure of CuInSe2, CuGaSe2, CuInS2, and CuGaS2,” Phys. Rev. B 63(7), 075203 (2001).
[CrossRef]

Green, M. A.

M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovoltaics 17(5), 320–326 (2009).
[CrossRef]

Hägglund, C.

C. Hägglund and B. Kasemo, “Nanoparticle plasmonics for 2D-photovoltaics: mechanisms, optimization, and limits,” Opt. Express 17(14), 11944–11957 (2009).
[CrossRef] [PubMed]

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92(1), 013113 (2008).
[CrossRef]

C. Hägglund, M. Zäch, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

Hishikawa, Y.

M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovoltaics 17(5), 320–326 (2009).
[CrossRef]

Holmes, R. J.

N. C. Lindquist, W. A. Luhman, S.-H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett. 93(12), 123308 (2008).
[CrossRef]

Hoppe, H.

H. Hoppe, N. S. Sariciftci, and D. Meissner, “Optical constants of conjugated polymer/fullerene based bulk-heterojunction organic solar cells,” Mol. Cryst. Liquid Cryst. 385(1), 233–239 (2002).
[CrossRef]

Hupp, J. T.

S. D. Standridge, G. C. Schatz, and J. T. Hupp, “Distance dependence of plasmon-enhanced photocurrent in dye-sensitized solar cells,” J. Am. Chem. Soc. 131(24), 8407–8409 (2009).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Jung, Y. S.

Y. S. Jung, “Spectroscopic ellipsometry studies on the optical constants of indium tin oxide films deposited under various sputtering conditions,” Thin Solid Films 467(1-2), 36–42 (2004).
[CrossRef]

Kasemo, B.

C. Hägglund and B. Kasemo, “Nanoparticle plasmonics for 2D-photovoltaics: mechanisms, optimization, and limits,” Opt. Express 17(14), 11944–11957 (2009).
[CrossRef] [PubMed]

C. Hägglund, M. Zäch, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92(1), 013113 (2008).
[CrossRef]

Kildishev, A. V.

Kirchhoff, J.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Le Perchec, J.

J. Le Perchec, Y. Desieres, and R. E. de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett. 94(18), 181104 (2009).
[CrossRef]

Lindquist, N. C.

N. C. Lindquist, W. A. Luhman, S.-H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett. 93(12), 123308 (2008).
[CrossRef]

Luhman, W. A.

N. C. Lindquist, W. A. Luhman, S.-H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett. 93(12), 123308 (2008).
[CrossRef]

Luo, P. Q.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Meissner, D.

H. Hoppe, N. S. Sariciftci, and D. Meissner, “Optical constants of conjugated polymer/fullerene based bulk-heterojunction organic solar cells,” Mol. Cryst. Liquid Cryst. 385(1), 233–239 (2002).
[CrossRef]

Moulin, E.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Muller, T.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Oh, S.-H.

N. C. Lindquist, W. A. Luhman, S.-H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett. 93(12), 123308 (2008).
[CrossRef]

Pascual, J.

M. I. Alonso, K. Wakita, J. Pascual, M. Garriga, and N. Yamamoto, “Optical functions and electronic structure of CuInSe2, CuGaSe2, CuInS2, and CuGaS2,” Phys. Rev. B 63(7), 075203 (2001).
[CrossRef]

Petersson, G.

C. Hägglund, M. Zäch, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

Peumans, P.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

Pieters, B.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Polman, A.

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

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

Queisser, H. J.

H. J. Queisser, “Photovoltaic conversion at reduced dimensions,” Physica E 14(1-2), 1–10 (2002).
[CrossRef]

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

Rand, B. P.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

Reetz, W.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Reiger, E. M.

E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

Royer, F. X.

E. Moulin, P. Q. Luo, B. Pieters, J. Sukmanowski, J. Kirchhoff, W. Reetz, T. Muller, R. Carius, F. X. Royer, and H. Stiebig, “Photoresponse enhancement in the near infrared wavelength range of ultrathin amorphous silicon photosensitive devices by integration of silver nanoparticles,” Appl. Phys. Lett. 95(3), 033505 (2009).
[CrossRef]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Sariciftci, N. S.

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S. D. Standridge, G. C. Schatz, and J. T. Hupp, “Distance dependence of plasmon-enhanced photocurrent in dye-sensitized solar cells,” J. Am. Chem. Soc. 131(24), 8407–8409 (2009).
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[CrossRef]

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[CrossRef]

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M. I. Alonso, K. Wakita, J. Pascual, M. Garriga, and N. Yamamoto, “Optical functions and electronic structure of CuInSe2, CuGaSe2, CuInS2, and CuGaS2,” Phys. Rev. B 63(7), 075203 (2001).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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E. F. C. Driessen, F. R. Braakman, E. M. Reiger, S. N. Dorenbos, V. Zwiller, and M. J. A. de Dood, “Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors,” Eur. Phys. J. Appl. Phys. 47(1), 10701 (2009).
[CrossRef]

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[CrossRef]

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[CrossRef]

Physica

J. Vlieger, “Reflection and transmission of light by a square nonpolar llattice,” Physica 64(1), 63–81 (1973).
[CrossRef]

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H. J. Queisser, “Photovoltaic conversion at reduced dimensions,” Physica E 14(1-2), 1–10 (2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Basic light absorbing structures under consideration. Light is assumed incident from the left in a dielectric medium of refractive index ni . In (a), a light absorbing, planar thin film (complex refractive index m, thickness d) is supported by a dielectric spacer (refractive index ns , thickness h) and an optically thick reflective substrate (to the right). In (b), the absorbing film is replaced by an array of identical, ellipsoidal shaped core/shell nanoparticles. The cores have a circular cross section of radius a in the array plane, and a semi-axis length c in the normal direction. The shells extend the core semi-axes by a fixed thickness. The array has an effective thickness de . Incident wave vectors and their normal components are represented by black arrows in (a), but it should be noted that their amplitudes are complex inside the film. In (b), the black arrows illustrate incident and specularly reflected fields for normal incidence of light. Scattered fields mediating lateral interactions between the particles in the array are shown as green, dashed arrows, while fields mediating interactions via the reflector are indicated by red, dashed arrows.

Fig. 2
Fig. 2

Angular responses for practically 2D thin films (δ ~10−4), maximizing the absorptance at normal incidence of TE- (solid lines) and TM-polarized light (dashed lines). The incident wavelength was λ = 840 nm and ni = 1.5. The center wavelength was either λc = λ = 840 nm (red, thick lines) or λc = 550 nm (black, thin lines). The refractive index of the spacer layer was in (a) ns = 1; in (b) ns = 1.5 and in (c), ns = 2. The dip in the TM-polarized case is at the critical angle between the external media, here occurring at 42, 90 and 90-46i° (complex angle), respectively. The influence of λc (and thus spacer thickness) is less dramatic.

Fig. 3
Fig. 3

(a) Model absorptance in a square Ag-core/CuInSe2-shell nanoparticle array, as a function of the normalized lattice constant Λ and the aspect ratio a/c of the cores. The target wavelength was λ 0 = 800 nm and the external medium refractive index ne = 2. The volume equivalent radii of the particle cores were 20 nm, the shell thicknesses 10 nm and the spacer thickness such that the center wavelength was λc = 800 nm. For very small aspect ratios, the requirement that the particles do not touch the back reflector limits the parameter space. The further condition that they should not touch each other bounds the parameter space from below. These limits are indicated by solid white lines to the far left and below the maxima. The vertical, dashed white line distinguish prolate (left) and oblate (right) particle shapes. Maximum absorptance of 100% is predicted at the white cross. The cross size represents ± 10% changes of the underlying variables, and ends above the 90% absorptance contour. This indicates a relatively high robustness of the optimum in this parameter space. In (b), the absorptance for the geometrical conditions at the cross in (a) are shown as a function of incident light wavelength. The model calculation is compared to calculations by FEM for the same set of parameters, including an ideal backside reflector. The black arrow indicates λc and the vertical line λ 0. In (c) and (d), the same conditions applies, except that the center wavelength λc of the support is offset to 550 nm. In (e) and (f), λc is offset to 1050 nm instead. The main effect of these offsets is a skewing of the absorptance peak shape about the maximum.

Fig. 4
Fig. 4

Optical constants of thin film solar cell materials considered. The approximate positions of the bandgap thresholds are indicated by the arrows.

Fig. 5
Fig. 5

Spectrally weighted plasmon induced absorptance [Φ, see Eq. (7)] as a function of the equivalent sphere radius of the core and the peak wavelength λ 0. In this map, the particle aspect ratios and the lattice constants were optimized to maximize the total absorptance for each value of ro and λ 0. The particle cores are assumed to be Ag, and the shells are CuInSe2 with a fixed thickness of 5 nm. The external medium refractive index is ne = 2. Particles are prolate to the left of the white dashed curve, and oblate to the right. Unphysical overlap of the particles occurs below the solid white line, which leads to an approximate position of the valid local maximum at the cross mark. At this point, the core aspect ratio is a/c ≈2.7 and the lattice constant Λ ≈38 nm. The cross arms have lengths corresponding to 10% of the underlying parameters, and show that the optimum is relatively robust to deviations also for these parameters.

Fig. 6
Fig. 6

Analytic model and FEM calculated absorptance for core/shell systems selected on merits of their high spectrally weighted plasmon induced absorptance. The spectral photon flux distribution of AM1.5G sunlight (light grey, in arbitrary units) is included for comparison. The particle cores consist of Ag and the shells of different solar cell materials. Identical systems are considered in the different types of calculations, except that a more realistic Al backside reflector is simulated in the FEM calculations instead of the perfect reflector assumed in the model. In (a) and (b), the PV shells consist of CuInSe2, with the difference that the RS center wavelength is chosen equal to the peak wavelength at 840 nm in (a), and to 550 nm in (b), respectively. In (c), the shell material is a-Si, and in (d), it is the organic semiconductor MDMO-PPV. The circular symbols show estimates for the shell absorption at maximum, based on the analytic model.

Tables (1)

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Table 1 Conditions and results for optimized Ag-core/semiconductor-shell nanoparticle arrays

Equations (9)

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r ˜ = r i r d γ 2 1 r i r d γ 2   ,
m 2 i n i n ˜ s δ = λ 2 π d [ i n i + n s cot ( π λ c 2 λ ) ]   .
r i = q i q m q i + q m   and   r d = i q s cot ( q s h ) q m i q s cot ( q s h ) + q m   ,
r i = n i 2 q m m 2 q i n i 2 q m + m 2 q i   and   r d = i n s 2 q m cot ( q s h ) m 2 q s i n s 2 q m cot ( q s h ) + m 2 q s   .
m e 2 = 2 n e F α ¯ δ e ( 1 f α ¯ )  ,
[ f 2 i n e n e n ˜ s F ] α ¯ = 1   .
Φ = 0 λ G w ( λ ) Δ A ( λ ) d λ   .
A s c ( λ 0 ) = Γ 0 A ( λ 0 )  ,
A s c = 0 λ G w ( λ ) A s c ( λ ) d λ  ,

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