Abstract

This numerical study investigates the influence of rectangular backside diffraction gratings on the efficiency of silicon solar cells. Backside gratings are used to diffract incident light to large propagation angles beyond the angle of total internal reflection, which can significantly increase the interaction length of long wavelength photons inside the silicon layer and thus enhance the efficiency. We investigate the influence of the silicon thickness on the optimum grating period and modulation depth by a simulation method which combines a 2D ray tracing algorithm with rigorous coupled wave analysis (RCWA) for calculating the grating diffraction efficiencies. The optimization was performed for gratings with period lengths ranging from 0.25 µm to 1.5 µm and modulation depths ranging from 25 nm to 400 nm under the assumption of normal light incidence. This study shows that the achievable efficiency improvement of silicon solar cells by means of backside diffraction gratings strongly depends on the proper choice of the grating parameters for a given silicon thickness. The relationship between the optimized grating parameters resulting in maximum photocurrent densities and the silicon thickness is determined. Moreover, the thicknesses of silicon solar cells with and without optimized backside diffraction gratings providing the same photocurrent densities are compared.

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References

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  1. A. Goetzberger, J. Knobloch, and B. Voss, Crystalline silicon solar cells (John Wiley & Sons, 1998).
  2. M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulomb-enhanced Auger recombination,” Prog. Photovolt. Res. Appl.11(2), 97–104 (2003).
    [CrossRef]
  3. K. Taretto and U. Rau, “Modeling extremely thin absorber solar cells for optimized design,” Prog. Photovolt. Res. Appl.12(8), 573–591 (2004).
    [CrossRef]
  4. 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]
  5. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt.34(14), 2476–2482 (1995).
    [CrossRef] [PubMed]
  6. R. H. Morf, H. Kiess, and C. Heine, Diffractive optics for solar cells,“ in Diffractive Optics for Industrial and Commercial Applications edited by J. Turunen and F. Wyrowski, 361-389 (Akademie Verlag, 1997).
  7. R. H. Morf and J. Gobrecht, “Optimized diffractive structures for light trapping in thin silicon solar cells,” Proc. of the 10th Workshop on Quantum Solar Energy Conversion (1998).
  8. 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,” 24th European PV Solar Energy Conference and Exhibition, paper 2DV.1.4. (2009).
  9. M. Peters, M. Rüdiger, D. Pelzer, H. Hauser, M. Hermle, and B. Bläsi, “Electro-optical modelling of solar cells with photonic structures,” 25th European PV Solar Energy Conference and Exhibition, 87–91 (2010).
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    [CrossRef] [PubMed]
  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. Express15(25), 16986–17000 (2007).
    [CrossRef] [PubMed]
  12. J. G. Mutitu, S. Shi, A. Barnett, and D. W. Prather, “Light trapping enhancement in thin silicon solar cells using photonic crystals,” 35th IEEE Photovoltaic Spec. Conf. (IEEE,2010), pp. 2208–2212.
  13. M. Wellenzohn and R. Hainberger, “A 2D numerical study of the photo current density enhancement in silicon solar cells with optimized backside gratings,” 37th IEEE Photovoltaic Spec. Conf. (IEEE, 2011), paper 836.
  14. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
    [CrossRef]
  15. K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” Solid-State Electron.22(9), 793–795 (1979).
    [CrossRef]
  16. M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl.3(3), 189–192 (1995).
    [CrossRef]
  17. M. O. D. Diffract, www.rsoftdesign.com
  18. S. H. Zaidi, J. M. Gee, and D. S. Ruby, Diffraction grating structures in solar cells,” in Conference Record of the Twenty-Eighth IEEE Photovoltaic Specialists Conference (IEEE, 2000), pp. 395–398.
  19. D. Abou-Ras, T. Kirchartz, and U. Rau, Advanced Characterization Techniques for Thin Film Solar Cells (Wiley-VCH, 2011).

2010 (1)

2007 (1)

2004 (1)

K. Taretto and U. Rau, “Modeling extremely thin absorber solar cells for optimized design,” Prog. Photovolt. Res. Appl.12(8), 573–591 (2004).
[CrossRef]

2003 (1)

M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulomb-enhanced Auger recombination,” Prog. Photovolt. Res. Appl.11(2), 97–104 (2003).
[CrossRef]

1998 (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

1995 (2)

C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt.34(14), 2476–2482 (1995).
[CrossRef] [PubMed]

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl.3(3), 189–192 (1995).
[CrossRef]

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]

1979 (1)

K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” Solid-State Electron.22(9), 793–795 (1979).
[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]

Campbell, P.

M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulomb-enhanced Auger recombination,” Prog. Photovolt. Res. Appl.11(2), 97–104 (2003).
[CrossRef]

Cuevas, A.

M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulomb-enhanced Auger recombination,” Prog. Photovolt. Res. Appl.11(2), 97–104 (2003).
[CrossRef]

Gjessing, J.

Green, M. A.

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl.3(3), 189–192 (1995).
[CrossRef]

Heine, C.

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

Joannopoulos, J. D.

Johs, B.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

Keevers, M. J.

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl.3(3), 189–192 (1995).
[CrossRef]

Kerr, M. J.

M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulomb-enhanced Auger recombination,” Prog. Photovolt. Res. Appl.11(2), 97–104 (2003).
[CrossRef]

Kimerling, L. C.

Luo, C.

Marstein, E. S.

McGahan, W. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

Morf, R. H.

Paulson, W.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

Rajkanan, K.

K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” Solid-State Electron.22(9), 793–795 (1979).
[CrossRef]

Rau, U.

K. Taretto and U. Rau, “Modeling extremely thin absorber solar cells for optimized design,” Prog. Photovolt. Res. Appl.12(8), 573–591 (2004).
[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]

Shewchun, J.

K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” Solid-State Electron.22(9), 793–795 (1979).
[CrossRef]

Singh, R.

K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” Solid-State Electron.22(9), 793–795 (1979).
[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]

Sudbø, A.

Taretto, K.

K. Taretto and U. Rau, “Modeling extremely thin absorber solar cells for optimized design,” Prog. Photovolt. Res. Appl.12(8), 573–591 (2004).
[CrossRef]

Woollam, J. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

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]

J. Appl. Phys. (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys.83(6), 3323–3326 (1998).
[CrossRef]

Opt. Express (2)

Prog. Photovolt. Res. Appl. (3)

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl.3(3), 189–192 (1995).
[CrossRef]

M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulomb-enhanced Auger recombination,” Prog. Photovolt. Res. Appl.11(2), 97–104 (2003).
[CrossRef]

K. Taretto and U. Rau, “Modeling extremely thin absorber solar cells for optimized design,” Prog. Photovolt. Res. Appl.12(8), 573–591 (2004).
[CrossRef]

Solid-State Electron. (1)

K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” Solid-State Electron.22(9), 793–795 (1979).
[CrossRef]

Other (10)

A. Goetzberger, J. Knobloch, and B. Voss, Crystalline silicon solar cells (John Wiley & Sons, 1998).

R. H. Morf, H. Kiess, and C. Heine, Diffractive optics for solar cells,“ in Diffractive Optics for Industrial and Commercial Applications edited by J. Turunen and F. Wyrowski, 361-389 (Akademie Verlag, 1997).

R. H. Morf and J. Gobrecht, “Optimized diffractive structures for light trapping in thin silicon solar cells,” Proc. of the 10th Workshop on Quantum Solar Energy Conversion (1998).

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,” 24th European PV Solar Energy Conference and Exhibition, paper 2DV.1.4. (2009).

M. Peters, M. Rüdiger, D. Pelzer, H. Hauser, M. Hermle, and B. Bläsi, “Electro-optical modelling of solar cells with photonic structures,” 25th European PV Solar Energy Conference and Exhibition, 87–91 (2010).

M. O. D. Diffract, www.rsoftdesign.com

S. H. Zaidi, J. M. Gee, and D. S. Ruby, Diffraction grating structures in solar cells,” in Conference Record of the Twenty-Eighth IEEE Photovoltaic Specialists Conference (IEEE, 2000), pp. 395–398.

D. Abou-Ras, T. Kirchartz, and U. Rau, Advanced Characterization Techniques for Thin Film Solar Cells (Wiley-VCH, 2011).

J. G. Mutitu, S. Shi, A. Barnett, and D. W. Prather, “Light trapping enhancement in thin silicon solar cells using photonic crystals,” 35th IEEE Photovoltaic Spec. Conf. (IEEE,2010), pp. 2208–2212.

M. Wellenzohn and R. Hainberger, “A 2D numerical study of the photo current density enhancement in silicon solar cells with optimized backside gratings,” 37th IEEE Photovoltaic Spec. Conf. (IEEE, 2011), paper 836.

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Figures (8)

Fig. 1
Fig. 1

Investigated silicon solar cells structures a) without and b) with backside grating.

Fig. 2
Fig. 2

Absorption spectra calculated by the combined RCWA/ray tracing approach and by full RCWA simulations for 3-µm and 60-µm thick silicon solar cells with backside gratings. Results for TE and TM polarization are averaged. The dashed lines indicate results of the combined RCWA/ray tracing approach for structures without grating.

Fig. 3
Fig. 3

Increase of the photocurrent density ΔJph of solar cells with backside gratings as a function of the period ranging from 0.25 µm to 1.5 µm and modulation depth ranging from 25 nm to 400 nm in steps of 25 nm with respect to solar cells without grating for different silicon thicknesses.

Fig. 4
Fig. 4

Calculated photocurrent densities as function of grating period ranging from 0.25 µm to 1.25 µm and modulation depth ranging from 25 nm to 150 nm for different silicon thicknesses.

Fig. 5
Fig. 5

A detailed view of the increase of the photocurrent density of solar cells with backside gratings as a function of grating period ranging from 0.25 µm to 1.25 µm and modulation depth ranging from 25 nm to 150 nm with respect to solar cells without grating for different silicon thicknesses.

Fig. 6
Fig. 6

Optimized grating period Λ (solid circle) and modulation depth h (open diamond) as a function of the silicon thickness, and the corresponding maximum increase of the photocurrent density.

Fig. 7
Fig. 7

a) Absolute (solid circle) and relative increase (open diamond) of photocurrent density ΔJmax with optimed gratings as a function of silicon thickness; b) photocurrent densities of solar cells with backside gratings as a function of the silicon thickness in comparison with solar cells without backside gratings.

Fig. 8
Fig. 8

Double logarithmic plot of silicon thicknesses of solar cells with optimized grating and without providing the same photocurrent densities; the table gives the corresponding data of the silicon thicknesses as well as the resulting scaling factors.

Equations (2)

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J ph =e λ=300nm λ=1140nm A(λ)S(λ)dλ,
A(λ)=(1 R f (λ)) (1 e α(λ) d Si )(1+ R b (λ) e α(λ) d Si ) 1 R f (λ) R b (λ) e 2α(λ) d Si ,

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