Abstract

Restricting the angular range in which a photovoltaic system emits light, is a promising but rather unexplored approach to enhance conversion efficiency. In this paper we analyze and discuss the effect of a directionally selective filter on the absorption of light and the generation of charge carriers in a germanium solar cell. A directionally selective filter transmits photons of perpendicular incidence and reflects photons under oblique incidence in a given spectral range. To investigate its effect on light trapping, we perform reflection and quantum efficiency measurements. The reflection measurements show that a wavelength dependent absorption enhancement is induced by the application of the directionally selective filter. We calculate a maximum absorption enhancement of 45% at λ ≈ 1900 nm. We show that the absorption enhancement is caused by light trapping of non-absorbed and scattered light and is not due to a suppression of radiative processes. A trapping of photons generated by radiative recombination could not be detected. Measurements of the quantum efficiency confirm the results of the reflection measurements. The generation of charge carriers is increased by up to 33% at λ ≈1900 nm. A comparison of path length enhancement factors calculated from reflection and quantum efficiency measurements indicates a low parasitic absorption in the solar cell device.

© 2011 OSA

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  1. A. Goetzberger, J. C. Goldschmidt, M. Peters, and P. Löper, “Light trapping, a new approach to spectrum splitting,” Sol. Energy Mater. Sol. Cells 92(12), 1570–1578 (2008).
    [CrossRef]
  2. E. Garnett and P. Yang, “Light Trapping in Silicon Nanowire Solar Cells,” Nano Lett. 10(3), 1082–1087 (2010).
    [CrossRef] [PubMed]
  3. M. Green, “Lambertian Light Trapping in Textured Solar Cells and Light-Emitting Diodes: Analytical Solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
    [CrossRef]
  4. K. Tvingstedt, S. Dal Zilio, O. Inganäs, and M. Tormen, “Trapping light with micro lenses in thin film organic photovoltaic sells,” Opt. Express 16(26), 21608–21615 (2008).
    [CrossRef] [PubMed]
  5. J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
    [CrossRef]
  6. J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
    [CrossRef]
  7. G. L. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
    [CrossRef]
  8. 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 205(12), 2831–2843 (2008).
    [CrossRef]
  9. M. Peters, J. C. Goldschmidt, and B. Bläsi, “Angular confinement and concentration in photovoltaic converters,” Sol. Energy Mater. Sol. Cells 94(8), 1393–1398 (2010).
    [CrossRef]
  10. G. L. Araujo and A. Marti, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994).
    [CrossRef]
  11. T. Markvart, “Thermodynamics of losses in photovoltaic conversion,” Appl. Phys. Lett. 91(6), 064102 (2007).
    [CrossRef]
  12. P. T. Landsberg and V. Badescu, “Solar cell thermodynamics including multiple impact ionization and concentration of radiation,” J. Phys. D 35(11), 1236–1240 (2002).
    [CrossRef]
  13. V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D 38(13), 2166–2172 (2005).
    [CrossRef]
  14. S. Shevchenko, “Dislocation photoluminescence in silicone and germanium,” Solid State Phenom. 131, 583–588 (2008).
    [CrossRef]
  15. 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]
  16. C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
    [CrossRef]
  17. S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
    [CrossRef] [PubMed]
  18. G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
    [CrossRef]

2010

E. Garnett and P. Yang, “Light Trapping in Silicon Nanowire Solar Cells,” Nano Lett. 10(3), 1082–1087 (2010).
[CrossRef] [PubMed]

M. Peters, J. C. Goldschmidt, and B. Bläsi, “Angular confinement and concentration in photovoltaic converters,” Sol. Energy Mater. Sol. Cells 94(8), 1393–1398 (2010).
[CrossRef]

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[CrossRef]

2009

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]

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[CrossRef]

2008

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

A. Goetzberger, J. C. Goldschmidt, M. Peters, and P. Löper, “Light trapping, a new approach to spectrum splitting,” Sol. Energy Mater. Sol. Cells 92(12), 1570–1578 (2008).
[CrossRef]

K. Tvingstedt, S. Dal Zilio, O. Inganäs, and M. Tormen, “Trapping light with micro lenses in thin film organic photovoltaic sells,” Opt. Express 16(26), 21608–21615 (2008).
[CrossRef] [PubMed]

S. Shevchenko, “Dislocation photoluminescence in silicone and germanium,” Solid State Phenom. 131, 583–588 (2008).
[CrossRef]

S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

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 205(12), 2831–2843 (2008).
[CrossRef]

2007

T. Markvart, “Thermodynamics of losses in photovoltaic conversion,” Appl. Phys. Lett. 91(6), 064102 (2007).
[CrossRef]

2005

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

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

2002

P. T. Landsberg and V. Badescu, “Solar cell thermodynamics including multiple impact ionization and concentration of radiation,” J. Phys. D 35(11), 1236–1240 (2002).
[CrossRef]

M. Green, “Lambertian Light Trapping in Textured Solar Cells and Light-Emitting Diodes: Analytical Solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

1994

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

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

Araujo, G. L.

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

Araújo, G. L.

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

Badescu, V.

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

P. T. Landsberg and V. Badescu, “Solar cell thermodynamics including multiple impact ionization and concentration of radiation,” J. Phys. D 35(11), 1236–1240 (2002).
[CrossRef]

Bläsi, B.

M. Peters, J. C. Goldschmidt, and B. Bläsi, “Angular confinement and concentration in photovoltaic converters,” Sol. Energy Mater. Sol. Cells 94(8), 1393–1398 (2010).
[CrossRef]

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[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]

Bosch, A.

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[CrossRef]

Bösch, A.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

Dal Zilio, S.

Dimroth, F.

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[CrossRef]

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

Fahr, S.

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 205(12), 2831–2843 (2008).
[CrossRef]

S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

Gajiev, G. M.

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Garnett, E.

E. Garnett and P. Yang, “Light Trapping in Silicon Nanowire Solar Cells,” Nano Lett. 10(3), 1082–1087 (2010).
[CrossRef] [PubMed]

Gerber, A.

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[CrossRef]

Glunz, S.

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[CrossRef]

Glunz, S. W.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

Goetzberger, A.

A. Goetzberger, J. C. Goldschmidt, M. Peters, and P. Löper, “Light trapping, a new approach to spectrum splitting,” Sol. Energy Mater. Sol. Cells 92(12), 1570–1578 (2008).
[CrossRef]

Goldschmidt, J. C.

M. Peters, J. C. Goldschmidt, and B. Bläsi, “Angular confinement and concentration in photovoltaic converters,” Sol. Energy Mater. Sol. Cells 94(8), 1393–1398 (2010).
[CrossRef]

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[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]

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

A. Goetzberger, J. C. Goldschmidt, M. Peters, and P. Löper, “Light trapping, a new approach to spectrum splitting,” Sol. Energy Mater. Sol. Cells 92(12), 1570–1578 (2008).
[CrossRef]

Golubev, V. G.

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Gombert, A.

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 205(12), 2831–2843 (2008).
[CrossRef]

Green, M.

M. Green, “Lambertian Light Trapping in Textured Solar Cells and Light-Emitting Diodes: Analytical Solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

Helmers, H.

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[CrossRef]

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

Inganäs, O.

Kirchartz, T.

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[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]

S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

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 205(12), 2831–2843 (2008).
[CrossRef]

Kurdyukov, D. A.

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Landsberg, P. T.

P. T. Landsberg and V. Badescu, “Solar cell thermodynamics including multiple impact ionization and concentration of radiation,” J. Phys. D 35(11), 1236–1240 (2002).
[CrossRef]

Lederer, F.

S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

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 205(12), 2831–2843 (2008).
[CrossRef]

Löper, P.

A. Goetzberger, J. C. Goldschmidt, M. Peters, and P. Löper, “Light trapping, a new approach to spectrum splitting,” Sol. Energy Mater. Sol. Cells 92(12), 1570–1578 (2008).
[CrossRef]

Markvart, T.

T. Markvart, “Thermodynamics of losses in photovoltaic conversion,” Appl. Phys. Lett. 91(6), 064102 (2007).
[CrossRef]

Marti, A.

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

Martí, A.

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

Medvedev, A. V.

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Peters, M.

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[CrossRef]

M. Peters, J. C. Goldschmidt, and B. Bläsi, “Angular confinement and concentration in photovoltaic converters,” Sol. Energy Mater. Sol. Cells 94(8), 1393–1398 (2010).
[CrossRef]

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[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]

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

A. Goetzberger, J. C. Goldschmidt, M. Peters, and P. Löper, “Light trapping, a new approach to spectrum splitting,” Sol. Energy Mater. Sol. Cells 92(12), 1570–1578 (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 205(12), 2831–2843 (2008).
[CrossRef]

Pevtsov, A. B

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Rau, U.

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[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 205(12), 2831–2843 (2008).
[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 205(12), 2831–2843 (2008).
[CrossRef]

S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

Sel’kin, A. V.

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Shevchenko, S.

S. Shevchenko, “Dislocation photoluminescence in silicone and germanium,” Solid State Phenom. 131, 583–588 (2008).
[CrossRef]

Tormen, M.

Travnikov, V. V.

G. M. Gajiev, V. G. Golubev, D. A. Kurdyukov, A. V. Medvedev, A. B Pevtsov, A. V. Sel’kin, and V. V. Travnikov, “Bragg reflection spectroscopy of opal-like photonic crystals,” Phys. Rev. B 72, 205115 1–9 (2005).
[CrossRef]

Tvingstedt, K.

Ulbrich, C.

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Express 18(S2), 133–138 (2010).
[CrossRef]

S. Fahr, C. Ulbrich, T. Kirchartz, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

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 205(12), 2831–2843 (2008).
[CrossRef]

Üpping, J.

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 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 205(12), 2831–2843 (2008).
[CrossRef]

Willeke, G.

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009).
[CrossRef]

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies,” Phys. Stat. Solidi A 205(12), 2811–2821 (2008).
[CrossRef]

Yang, P.

E. Garnett and P. Yang, “Light Trapping in Silicon Nanowire Solar Cells,” Nano Lett. 10(3), 1082–1087 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett.

T. Markvart, “Thermodynamics of losses in photovoltaic conversion,” Appl. Phys. Lett. 91(6), 064102 (2007).
[CrossRef]

J. Phys. D

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Phys. Stat. Solidi A

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Figures (7)

Fig. 1
Fig. 1

Sketch of the light trapping induced by a directionally selective filter. The filter is characterized by an angle θc defining the acceptance range. Within the acceptance range light passes the filter, outside the acceptance range it is reflected. Light emitted or scattered within the solar cell is either totally internally reflected (i), leaves the system through the acceptance range of the filter and is lost (ii) or is reflected by the filter (iii). Light taking path (iii) is trapped inside the system and causes additional absorption which eventually results in the generation of additional electron hole pairs.

Fig. 2
Fig. 2

Reflection characteristics of the used edge filter. Figure 2a shows the measured reflection characteristic of the filter for normal incident light and the quantum efficiency of the used germanium solar cell. Figure 2b shows the simulated angular dependent reflection characteristic of the same filter. According to Braggs’ equation (Eq. (1)), the reflection edge of the filter shifts towards shorter wavelength. This blue shift provides directional selectivity for all wavelengths λ close to the reflection edge λedge for normal incidence. Below an angle θc0) the filter is transparent. Above θc0) the filter shows specular reflection. This is exactly the desired characteristic of a directionally selective filter.

Fig. 3
Fig. 3

Measurement setups for reflection measurements with an integrating sphere. Figure 3a shows the setup used to measure the total (diffuse + specular) reflection. The sample is tilted by 4° so that the specularly reflected light hits the surface of the integrating sphere, is scattered and detected. Light scattered at the solar cell surface and light emitted by the solar cell is detected as well. Figure 3b shows the setup for a measurement of diffuse light. The sample is not tilted and the specularly reflected light leaves the integrating sphere through the entrance opening undetected.

Fig. 4
Fig. 4

Difference (a) and ratio (b) of the total absorption of a germanium solar cell with and without directionally selective filter on top (green dots). Also given is the transmission of the filter for normal incidence (blue line). The filter causes reflection losses that result in a reduced solar cell absorption which can be observed for wavelengths below λ = 1750 nm. Above λ = 1750 nm an absorption enhancement due to directional selectivity is found. Shown are the results from two measurements (dark and light green) at different positions of the same sample. These results mark the variation occurring within this method.

Fig. 5
Fig. 5

Measured diffuse reflection (a) and difference (b) between the diffuse reflections of a solar cell with a glass plate and with directionally selective filter. In the spectral range between λ = 1000 nm and λ = 1500 nm the angularly selective filter induces no effect on the diffuse reflection. For light emitted by radiative recombination this would have been expected though.

Fig. 6
Fig. 6

Difference (a) and ratio (b) of quantum efficiency measurements of a germanium solar cell with and without directionally selective filter on top (green circles). Also shown is the transmission characteristic of the used filter for normal incidence (blue line). Between λ = 1650 nm and λ = 1900 nm, a light trapping effect induced by the filter occurs.

Fig. 7
Fig. 7

Calculated path length enhancement factors caused by the directionally selective filter obtained from measurements of the total reflection (cf. Fig. 4, red & brown triangles) and quantum efficiency measurements (green dots). Outside the range of directional selectivity, reflection losses occur that lead to values of κ below unity. Results obtained with both methods are in good qualitative agreement. Also shown is the filter transmission for normal incidence (blue line).

Equations (4)

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λ 0 ( θ ) = λ 0 ( 0 ) 1 sin ( θ ) 2 n 2
A = 1 R
κ R ( λ ) = ln [ R w i t h ( λ ) ] ln [ R w i t h o u t ( λ ) ]
κ E Q E ( λ ) = ln [ 1 E Q E w i t h ( λ ) ] ln [ 1 E Q E w i t h o u t ( λ ) ]

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