Abstract

A directionally selective multilayer filter is applied to a hydrogenated amorphous silicon solar cell to improve the light trapping. The filter prevents non-absorbed long-wavelength photons from leaving the cell under oblique angles leading to an enhancement of the total optical path length for weakly absorbed light within the device by a factor of κr = 3.5. Parasitic absorption in the contact layers limits the effective path length improvement for the photovoltaic quantum efficiency to a factor of κEQE = 1.5. The total short-circuit current density increases by ΔJ sc = 0.2 mAcm−2 due to the directional selectivity of the Bragg-like filter.

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References

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  1. T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
    [CrossRef]
  2. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
    [CrossRef] [PubMed]
  3. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982).
    [CrossRef]
  4. J. C. Miñano, “Optical confinement in photovoltaics,“ in Physical Limitations to the Photovoltaic Solar Energy Conversion, A. Luque and G. L. Araújo, eds. (Hilger, Bristol, UK,1990), p. 55.
  5. M. A. Green, “High efficiency solar cells,” (Trans Tech Publications, Switzerland, 1987), p. 80.
  6. R. Brendel, “Thin-film crystalline silicon solar cells,” (Wiley-VCH, Weinh., Germany, 2003), pp. 193–199.
  7. V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005).
    [CrossRef]
  8. C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
    [CrossRef]
  9. C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
    [CrossRef]
  10. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
    [CrossRef]
  11. G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
    [CrossRef]
  12. M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
    [CrossRef]
  13. J. Turunen, and F. Wyrowski, Diffractive Optics for industrial and commercial applications (Akademie Verlag, Berlin, Germany, 1997), Chap. 12.4.
  14. A. Löffl, S. Wieder, B. Rech, O. Kluth, C. Beneking, and H. Wagner, “Al-doped ZnO films for thin-film solar cells with very low sheet resistance and controlled texture,” Proc. 14th Europ. PV Sol. En. Conf., Barcelona, 1997, p. 2089.
  15. R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985).
    [CrossRef]
  16. H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
    [CrossRef]

2010 (1)

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

2009 (1)

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

2008 (2)

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

2005 (1)

V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005).
[CrossRef]

1994 (1)

G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
[CrossRef]

1985 (1)

R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985).
[CrossRef]

1983 (2)

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[CrossRef]

1982 (1)

1961 (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

Abeles, B.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[CrossRef]

Araújo, G.

G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
[CrossRef]

Atwater, H. A.

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

Badescu, V.

V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005).
[CrossRef]

Bird, R.

R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985).
[CrossRef]

Bläsi, B.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

Cebulka, J. M.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[CrossRef]

Deckman, H. W.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Fahr, S.

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

Goldschmidt, J. C.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Gombert, A.

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

Hulstrom, R.

R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985).
[CrossRef]

Kirchartz, T.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Lederer, F.

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

Löper, P.

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Martí, A.

G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
[CrossRef]

Pelz, J.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[CrossRef]

Peters, M.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Polman, A.

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

Queisser, H. J.

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

Rau, U.

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

Riordan, C.

R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985).
[CrossRef]

Rockstuhl, C.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Shockley, W.

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

Tiedje, T.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[CrossRef]

Ulbrich, C.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Üpping, J.

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

Wehrspohn, R.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Witzke, H.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Wronski, C. R.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Yablonovitch, E.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

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

Appl. Phys. Lett. (2)

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[CrossRef]

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

J. Appl. Phys. (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. D Appl. Phys. (1)

V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005).
[CrossRef]

Nat. Mater. (1)

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

Phys. Status Solidi., A Appl. Mater. Sci. (1)

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008).
[CrossRef]

Proc. SPIE (1)

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008).
[CrossRef]

Sol. Energy Mater. Sol. Cells (2)

G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
[CrossRef]

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

Solar Cells (1)

R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985).
[CrossRef]

Other (5)

J. Turunen, and F. Wyrowski, Diffractive Optics for industrial and commercial applications (Akademie Verlag, Berlin, Germany, 1997), Chap. 12.4.

A. Löffl, S. Wieder, B. Rech, O. Kluth, C. Beneking, and H. Wagner, “Al-doped ZnO films for thin-film solar cells with very low sheet resistance and controlled texture,” Proc. 14th Europ. PV Sol. En. Conf., Barcelona, 1997, p. 2089.

J. C. Miñano, “Optical confinement in photovoltaics,“ in Physical Limitations to the Photovoltaic Solar Energy Conversion, A. Luque and G. L. Araújo, eds. (Hilger, Bristol, UK,1990), p. 55.

M. A. Green, “High efficiency solar cells,” (Trans Tech Publications, Switzerland, 1987), p. 80.

R. Brendel, “Thin-film crystalline silicon solar cells,” (Wiley-VCH, Weinh., Germany, 2003), pp. 193–199.

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Figures (4)

Fig. 1
Fig. 1

The investigated solar cells consist of a glass superstrate, a transparent conductive oxide (TCO) layer, a pin-absorber of hydrogenated amorphous silicon (a-Si:H), and a back contact of TCO and silver (Ag). The Bragg filter is applied on top of the front glass after a first characterization of the cell without filter. The filter reflects light with incidence angles θ > θth in the respective wavelength range. (Thicknesses are not to scale.)

Fig. 2
Fig. 2

(a) The total reflectance (r 0/r fi, without/with filter, black/orange line) of a 322 nm thick a-Si:H solar cell prepared on ZnO:Al on Corning glass increases for wavelengths λ > 600 nm because non-absorbed light is re-emitted from the cell. The filter increases the reflectance at wavelengths λ < 350 nm and λ > 770 nm but suppresses the re-emission of photons for 650 nm < λ < 770 nm. (b) The difference Δr = r fi-r 0 is reduced due to enhanced light trapping to a minimum of −40% at λ < 764 nm. (c) The external quantum efficiency EQE of the same solar cell measured with and without filter and (d) the difference ΔEQE=EQE fi-EQE 0 show that the filter acts as antireflective coating for 350 nm < λ < 600 nm and increases the light trapping for 650 nm < λ < 770 nm.

Fig. 3
Fig. 3

(a) The optical path length improvement κr calculated from the data in Fig. 2(a) demonstrates the enhanced light trapping in the device for wavelengths 650 nm < λ < 770 nm. In the range 350 nm < λ < 650 nm the improvement is not due to the spectral selectivity, but rather to the anti reflective properties of the filter. The effective path length improvement κEQE shows the same wavelength dependence but a weaker increase than κr. (b) The maximum values of the improvement factors κ ¯ r and κ ¯ EQE depend on absorber layer thickness and the used superstrate (dots: AsahiU, squares: Corning glass). The error bars represent the standard deviation of the 5-12 investigated samples for each data point.

Fig. 4
Fig. 4

(a) The dependence of the external quantum efficiency EQE fi of a 414 nm thick a-Si:H solar cell (prepared on Corning glass) on the angle of incidence θ is used to characterize the Bragg filter. (b) The effect of the filter is visualized by dividing EQE fi by EQE 0 obtained from a sample without filter prepared in the same run. The dashed line is calculated from Eq. (3) using λ0 = 767 nm and λ1 = 600 nm.

Equations (7)

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w opt = k w = 4 n 2 w ,
w opt = k w = 4 n 2 w / sin 2 ( θ th ) .
λ th ( θ ) = 2 d n 2 sin 2 ( θ ) = λ 0 2 ( λ 0 2 λ 1 2 ) sin 2 θ .
r ( λ ) = e α ( λ ) w opt ( λ) .
k 0/fi ( λ ) = ln ( r 0/fi ( λ ) ) / ( w α ( λ ) ) .
κ r ( λ ) : = k fi ( λ ) k 0 ( λ ) = ln ( r fi ( λ ) ) / ln ( r 0 ( λ ) )
κ EQE ( λ ) : = ln [ 1 E Q E fi ( λ ) ] ln [ 1 E Q E 0 ( λ ) ] .

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