Abstract

A simulation method is presented and evaluated for simulating two- and three dimensional wave optical effects in crystalline silicon solar cells. Due to a thickness in the 100 µm range, optical properties of these solar cells typically are simulated, primarily through the use of ray-tracing. Recently, diffractive elements such as gratings or photonic crystals have been investigated for their application in crystalline silicon solar cells, making it necessary to consider two- and three dimensional wave optical effects. The presented approach couples a rigorous wave optical simulation to a semiconductor device simulation. In a first step, characteristic parameters, simulated for a reference setup using the electro-optical method and the standard procedure are compared. Occurring differences provide a measure to quantify the errors of the electro-optical method. These errors are below 0.4% relative. In a second step the electro-optical method is used to simulate a crystalline silicon solar cell with a back side diffractive grating. It is found that the grating enhances to short circuit current density jSC of the solar cell by more than 1 mA/cm2.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. 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. Stat. Solidi A 205(12), 2831–2843 (2008).
    [CrossRef]
  4. 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]
  5. K. Tvingstedt, S. Dal Zilio, O. Inganäs, and M. Tormen, “Trapping light with micro lenses in thin film organic photovoltaic cells,” Opt. Express 16(26), 21608–21615 (2008).
    [CrossRef] [PubMed]
  6. A. Macleod, Thin Film Optical Filters 3rd Ed (Institute of Physics Publishing, Bristol and Philadelphia, 2001)
  7. 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]
  8. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995).
    [CrossRef] [PubMed]
  9. O. Isabella, A. Campa, M. C. Heijna, W. Soppe, R. van Erwen, R. H. Franken, H. Borg, and M. Zeman, “Diffraction Gratings for Light Trapping in Thin-Film Silicon Solar Cells” in Proceedings of the 23rd European Photovoltaic Solar energy Conference, (Valencia, Spain, 2008), pp. 2320 – 2324.
  10. M. Niggemann, B. Bläsi, A. Gombert, A. Hinsch, H. Hoppe, P. Lalanne, D. Meissner, and V. Wittwer, “Trapping Light in Organic Plastic Solar Cells with Integrated Diffraction Grating,” presented at the 17th European Photovoltaic Solar energy Conference, Munich, Germany, 22 – 26 oct. 2001.
  11. 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]
  12. P. Voisin, M. Peters, H. Hauser, C. Helgert, E. B. Kley, T. Pertsch, B. Bläsi, M. Hermle, and S. W. Glunz, “Nanostructured Back Side Silicon Solar Cells,” in Proceedings of the 24th European European Photovoltaic Solar energy Conference, (Hamburg., Germany, 2009), pp. 1997 - 2000.
  13. S. Janz, M. Peters, D. Suwito, M. Hermle, and S. W. Glunz, “Photonic crystals as rear-side diffusers and reflectors for high efficiency silicon solar cells,” in Proceedings of the 24th European European Photovoltaic Solar energy Conference, (Hamburg., Germany, 2009), pp. 1529 - 1533.
  14. C. B. Burcardt, “Diffraction of a Plane Wave at a Sinusoidally Stratified Dielectric Grating,” J. Opt. Soc. Am. 56(11), 1502–1509 (1966).
    [CrossRef]
  15. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  16. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
    [CrossRef]
  17. P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for TM polarization,” J. Mod. Opt. 45, 1357–1374 (1998).
    [CrossRef]
  18. P. Kailuweit, R. Kellenbenz, M. Peters, and F. Dimroth, “Optical modelling of nanostructured III-V multi-junction solar cells”, Proceedings of SPIE Photonics West (page unknown) (2010)
  19. G. Létay, “Modellierung von III-V Solarzellen”, Dissertation, University of Constance (2003) http://www.ub.uni-konstanz.de/kops/volltexte/2003/1118/
  20. M. Peters, “Photonic Concepts for Solar Cells,” Dissertation at the University of Freiburg (2009). http://www.freidok.uni-freiburg.de/volltexte/6768/
  21. J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Phil. Trans. 175(0), 343–361 (1884).
    [CrossRef]

2010 (1)

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

2008 (3)

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. Stat. Solidi A 205(12), 2831–2843 (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 cells,” Opt. Express 16(26), 21608–21615 (2008).
[CrossRef] [PubMed]

2007 (1)

2002 (1)

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]

1998 (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for TM polarization,” J. Mod. Opt. 45, 1357–1374 (1998).
[CrossRef]

1995 (2)

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]

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1966 (1)

1884 (1)

J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Phil. Trans. 175(0), 343–361 (1884).
[CrossRef]

Bermel, P.

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]

Burcardt, C. B.

Dal Zilio, S.

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

Garnett, E.

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

Gaylord, T. K.

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.

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]

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

Grann, E. B.

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]

Heine, C.

Inganäs, O.

Joannopoulos, J. D.

Jurek, M. P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for TM polarization,” J. Mod. Opt. 45, 1357–1374 (1998).
[CrossRef]

Kimerling, L. C.

Kirchartz, T.

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

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lalanne, P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for TM polarization,” J. Mod. Opt. 45, 1357–1374 (1998).
[CrossRef]

Lederer, F.

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. Stat. Solidi A 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]

Luo, C.

Moharam, M. G.

Morf, R. H.

Peters, M.

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

Pommet, D. A.

Poynting, J. H.

J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Phil. Trans. 175(0), 343–361 (1884).
[CrossRef]

Rau, U.

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. Stat. Solidi A 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. Stat. Solidi A 205(12), 2831–2843 (2008).
[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]

Stepleman, R. S.

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]

Tormen, M.

Tvingstedt, K.

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. Stat. Solidi A 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. Stat. Solidi A 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. Stat. Solidi A 205(12), 2831–2843 (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]

Zeng, L.

Appl. Opt. (1)

Appl. Phys. Lett. (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]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Mod. Opt. (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for TM polarization,” J. Mod. Opt. 45, 1357–1374 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

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

Opt. Express (2)

Phil. Trans. (1)

J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Phil. Trans. 175(0), 343–361 (1884).
[CrossRef]

Phys. Stat. Solidi A (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. Stat. Solidi A 205(12), 2831–2843 (2008).
[CrossRef]

Prog. Photovolt. Res. Appl. (1)

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]

Sol. Energy Mater. Sol. Cells (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]

Other (8)

A. Macleod, Thin Film Optical Filters 3rd Ed (Institute of Physics Publishing, Bristol and Philadelphia, 2001)

O. Isabella, A. Campa, M. C. Heijna, W. Soppe, R. van Erwen, R. H. Franken, H. Borg, and M. Zeman, “Diffraction Gratings for Light Trapping in Thin-Film Silicon Solar Cells” in Proceedings of the 23rd European Photovoltaic Solar energy Conference, (Valencia, Spain, 2008), pp. 2320 – 2324.

M. Niggemann, B. Bläsi, A. Gombert, A. Hinsch, H. Hoppe, P. Lalanne, D. Meissner, and V. Wittwer, “Trapping Light in Organic Plastic Solar Cells with Integrated Diffraction Grating,” presented at the 17th European Photovoltaic Solar energy Conference, Munich, Germany, 22 – 26 oct. 2001.

P. Voisin, M. Peters, H. Hauser, C. Helgert, E. B. Kley, T. Pertsch, B. Bläsi, M. Hermle, and S. W. Glunz, “Nanostructured Back Side Silicon Solar Cells,” in Proceedings of the 24th European European Photovoltaic Solar energy Conference, (Hamburg., Germany, 2009), pp. 1997 - 2000.

S. Janz, M. Peters, D. Suwito, M. Hermle, and S. W. Glunz, “Photonic crystals as rear-side diffusers and reflectors for high efficiency silicon solar cells,” in Proceedings of the 24th European European Photovoltaic Solar energy Conference, (Hamburg., Germany, 2009), pp. 1529 - 1533.

P. Kailuweit, R. Kellenbenz, M. Peters, and F. Dimroth, “Optical modelling of nanostructured III-V multi-junction solar cells”, Proceedings of SPIE Photonics West (page unknown) (2010)

G. Létay, “Modellierung von III-V Solarzellen”, Dissertation, University of Constance (2003) http://www.ub.uni-konstanz.de/kops/volltexte/2003/1118/

M. Peters, “Photonic Concepts for Solar Cells,” Dissertation at the University of Freiburg (2009). http://www.freidok.uni-freiburg.de/volltexte/6768/

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 3
Fig. 3

Absorption profiles calculated with SD and RCWA. Figure 3a shows the absorption profile calculated with SD. The generated short circuit current density is jSC = 11.40 mA/cm2 . Figure 3b shows the result obtained with a single RCWA calculation. Strong interference effects are noticeable. The current density here is jSC = 11.45 mA/cm2 . Figure 3c shows the average over nine RCWA simulations with a small variation of the silicon thickness. Coherent effects are reduced, jSC = 11.40mA/cm2. Figure 3d shows the result of an additional exponential fit; jSC = 11.40 mA/cm2 . Note that the z-axes are scaled non-linearly. The absorption is given in relation to 100% incident light for each wavelength.

Fig. 1
Fig. 1

Sketch of the solar cell geometries investigated in this paper. Figure 1a shows the solar cell geometry used for evaluating the substitution of optical simulation tools and used as a reference for the investigation of grating effects. Figure 1b shows the solar cell geometry used to simulate the effects of a diffractive grating in a crystalline silicon solar cell.

Fig. 2
Fig. 2

Absorption spectra simulated using SD and RCWA. Also given are the photocurrent densities corresponding to each spectrum. Figure 2a shows the reference spectrum calculated with SD. Figure 2b shows the spectrum for the same system calculated with RCWA by a single simulation. Strong interference effects are noticeable. In Fig. 2c interference effects have been eliminated by averaging over several calculations for which the silicon thickness has been varied.

Fig. 4
Fig. 4

Electrical characteristics of a solar cell simulated using the coupled method (lines) and the standard procedure with SD (circles). Shown are the current voltage relation (orange / brown) and the power voltage relation (cyan / blue). Small deviations in the characteristics occur that are caused by differences in the total absorption. The significant deviations occur for jSC; ΔjSC = 0.11 mA/cm2 and for efficiency Δη = 0.06% absolute.

Fig. 5
Fig. 5

Figure 5a shows the absorption spectra for a crystalline silicon solar cell with and without grating (blue and cyan line) as well as the difference between these spectra (brown circles). The grating causes an increase in absorption of up to 20% around λ = 990 nm resulting in an increase in photocurrent density of Δjph = 1.2( ± 0.1) mA/cm2 . Figure 5b shows the difference of the corresponding absorption profiles (cf. Figure 3).

Fig. 6
Fig. 6

Electrical characteristics for a crystalline silicon solar cell with (lines) and without (circles) grating. Given are the current voltage relation (brown / orange) and the power voltage relation (blue / cyan). The grating induces an increase in short circuit current density of ΔjSC = 1.02 ( ± 0.11) mA/cm2 and an increase inefficiency of Δη = 0.55 ( ± 0.06) % absolute.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

j p h = e 0 d λ a b s ( λ ) Φ A M 1.5 g ( λ )
A b s ( r , ω ) = 1 2 ω ε 0 ε ( ω ) | E ( r , ω ) | 2

Metrics