Abstract

Enhanced absorption of near infrared light in silicon solar cells is important for achieving high conversion efficiencies while reducing the solar cell’s thickness. Hexagonal gratings on the rear side of solar cells can achieve such absorption enhancement. Our wave optical simulations show photocurrent density gains of up to 3 mA/cm2 for solar cells with a thickness of 40 µm and a planar front side. Hexagonal sphere gratings have been fabricated and optical measurements confirm the predicted absorption enhancement. The measured absorption enhancement corresponds to a photocurrent density gain of 1.04 mA/cm2 for planar wafers with a thickness of 250 µm and 1.49 mA/cm2 for 100 µm.

© 2013 Optical Society of America

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References

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  1. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982).
    [CrossRef]
  2. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
    [CrossRef]
  3. I. M. Peters, “Photonic Concepts for Solar Cells”, PhD thesis (Universität Freiburg, Freiburg, Germany, 2009).
  4. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010).
    [CrossRef] [PubMed]
  5. 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]
  6. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995).
    [CrossRef] [PubMed]
  7. 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]
  8. J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
    [CrossRef]
  9. 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]
  10. IEC, Photovoltaic Devices - Part 3: Measurement Principles for Terrestrial Photovoltaic (PV) Solar Devices with Reference Spectral Irradiance Data., 2nd ed., International Standard, IEC 60904–3 (International Electrotechnical Commission, 2008).
  11. D. Kray, “Hocheffiziente Solarzellenstrukturen für Kristallines Silicium-Material Industrieller Qualität,” PhD thesis (Universität Konstanz, Konstanz, 2004).
  12. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).
  13. A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011).
    [CrossRef]
  14. J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011).
    [CrossRef]
  15. S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.
  16. 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 Solar Energy Conference,2009, 1997–2000.
  17. P. Berger, H. Hauser, D. Suwito, S. Janz, M. Peters, B. Bläsi, and M. Hermle,R. B. Wehrspohn and A. Gombert, eds., “Realization and Evaluation of Diffractive Systems on the Back Side of Silicon Solar Cells,” in Proceedings of SPIE, R. B. Wehrspohn and A. Gombert, eds. (2010), p. 772504.
    [CrossRef]
  18. J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Philos. Trans. R. Soc. Lond. 175(0), 343–361 (1884).
    [CrossRef]
  19. K.-H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Opt. Express 18(10), 10369–10376 (2010).
    [CrossRef] [PubMed]
  20. A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2Suppl 2), A295–A304 (2013).
    [CrossRef] [PubMed]
  21. A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” in Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981, 867–870.

2013 (1)

2011 (3)

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011).
[CrossRef]

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011).
[CrossRef]

2010 (2)

2008 (1)

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

2007 (1)

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]

1982 (2)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

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

1884 (1)

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

Benick, J.

Bermel, P.

Bläsi, B.

A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2Suppl 2), A295–A304 (2013).
[CrossRef] [PubMed]

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

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 Solar Energy Conference,2009, 1997–2000.

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]

Brendel, R.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

Brenner, K.-H.

Cody, G. D.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Eisenlohr, J.

Fan, S.

Gaylord, T. K.

Gjessing, J.

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011).
[CrossRef]

Glunz, S. W.

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 Solar Energy Conference,2009, 1997–2000.

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

Goetzberger, A.

A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” in Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981, 867–870.

Grann, E. B.

Guttowski, A.

Hauser, H.

A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2Suppl 2), A295–A304 (2013).
[CrossRef] [PubMed]

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

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 Solar Energy Conference,2009, 1997–2000.

Heine, C.

Helgert, C.

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 Solar Energy Conference,2009, 1997–2000.

Hermle, M.

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

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 Solar Energy Conference,2009, 1997–2000.

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

Hoex, B.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

Janz, S.

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

Joannopoulos, J. D.

Kessels, W. M. M.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

Kimerling, L. C.

Kley, E.-B.

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 Solar Energy Conference,2009, 1997–2000.

Luo, C.

Luque, A.

Marstein, E. S.

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011).
[CrossRef]

Marti, A.

A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011).
[CrossRef]

Martí, A.

Mellor, A.

Merkle, A.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

Moharam, M. G.

Morf, R. H.

Pertsch, T.

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 Solar Energy Conference,2009, 1997–2000.

Peters, M.

A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2Suppl 2), A295–A304 (2013).
[CrossRef] [PubMed]

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

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 Solar Energy Conference,2009, 1997–2000.

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

Pommet, D. A.

Poynting, J. H.

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

Raman, A.

Rüdiger, M.

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

Schmidt, J.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (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]

Sudbø, A. S.

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011).
[CrossRef]

Suwito, D.

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

Tobias, I.

A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011).
[CrossRef]

Tobías, I.

van de Sanden, M. C. M.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

Voisin, P.

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 Solar Energy Conference,2009, 1997–2000.

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

Wellens, C.

Yablonovitch, E.

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

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Yu, Z.

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]

IEEE Trans. Electron. Dev. (1)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

J. Appl. Phys. (1)

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Express (4)

Philos. Trans. R. Soc. Lond. (1)

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

Prog. Photovolt. Res. Appl. (1)

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008).
[CrossRef]

Progr. Photovolt.: Res. Appl. (1)

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

Sol. Energy Mater. Sol. Cells (1)

A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011).
[CrossRef]

Other (7)

IEC, Photovoltaic Devices - Part 3: Measurement Principles for Terrestrial Photovoltaic (PV) Solar Devices with Reference Spectral Irradiance Data., 2nd ed., International Standard, IEC 60904–3 (International Electrotechnical Commission, 2008).

D. Kray, “Hocheffiziente Solarzellenstrukturen für Kristallines Silicium-Material Industrieller Qualität,” PhD thesis (Universität Konstanz, Konstanz, 2004).

S. Janz, P. Voisin, D. Suwito, M. Peters, 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 Solar Energy Conference, 2009, 1529–1533.

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 Solar Energy Conference,2009, 1997–2000.

P. Berger, H. Hauser, D. Suwito, S. Janz, M. Peters, B. Bläsi, and M. Hermle,R. B. Wehrspohn and A. Gombert, eds., “Realization and Evaluation of Diffractive Systems on the Back Side of Silicon Solar Cells,” in Proceedings of SPIE, R. B. Wehrspohn and A. Gombert, eds. (2010), p. 772504.
[CrossRef]

A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” in Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981, 867–870.

I. M. Peters, “Photonic Concepts for Solar Cells”, PhD thesis (Universität Freiburg, Freiburg, Germany, 2009).

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Figures (6)

Fig. 1
Fig. 1

Schematic sketch of the investigated structure. A hexagonally ordered sphere layer at the rear side of a silicon wafer causes diffraction and hence a light path length enhancement.

Fig. 2
Fig. 2

Photocurrent density gain induced by a hexagonally ordered layer of mono-disperse spheres (a), or a layer of cylinders (b), for different solar cell thicknesses depending on the sphere diameter or cylinder diameter, respectively. Maximum current gains could be achieved for sphere diameters between 1000 and 1200 nm. The potential current gains are higher for thinner solar cells and exceed 3.0 mA/cm2 for 40 µm solar cell thickness. For cylinders a maximum current gain is observed for diameters of around 2000 nm. For the different solar cell thicknesses, the dependence on the cylinder diameter shows the same features. For thicker solar cells, the different features occur for slightly larger diameters, as the spectral distribution of the photons reaching the diffractive structure is shifted to longer wavelengths. For all calculations the matrix material was assumed to be amorphous silicon, with the same refractive index than the silicon wafer.

Fig. 3
Fig. 3

Left: Average absorption distribution of light in the spectral region from 950 to 1200 nm in a 40 µm thick silicon wafer with a hexagonal sphere grating (sphere diameter 1100 nm, matrix material amorphous silicon) at the rear side calculated from RCWA near field data according to Eq. (2). Displayed is a cross section in the x-z-plane (with different scaling in x- and z-direction) and two periods in x-direction. Blue color indicates no absorption, red color strong absorption (in arbitrary units). The position of the spheres in the simulated volume has been indicated in black. No absorption within the spheres occurs in the simulation. The inserted sketch shows the simulated structure. The black rectangle indicates the area displayed in the absorption graph. Right: Absorption integrated over x-direction. The equally distributed absorption values for all depth values can be seen.

Fig. 4
Fig. 4

(a) A monolayer of silica spheres (diameter 922 nm) after the spin coating process. A characteristic part of a 4 inch wafer is shown. Hexagonal order is achieved over a range of a few µm. (b) A monolayer after the inversion process. Amorphous titaniumoxide has been successfully infiltrated into the voids between the spheres by atomic layer deposition. Very small voids remain due to the conformal deposition.

Fig. 5
Fig. 5

The left graph shows the absorption measurements of wafers with hexagonal rear side grating in comparison to flat reference wafers. The absorption enhancement (difference between samples with grating and planar reference) is shown on the right side. For thinner wafers, the maximum absorption enhancement occurs for shorter wavelengths, as expected from theory.

Fig. 6
Fig. 6

Measured absorption enhancement due to the hexagonal grating for a wafer thickness of 250 µm (left side) and 100 µm (right side) and comparison to simulation results. The observed absorption enhancement can be described by the combination of diffractive effects and scattering. Scattering was assumed to be wavelength-independent and to be leading to an effective solar cell thickness enhancement by a factor of 4. Scattering and diffraction were weighted equally. This approach leads to good accordance between the simulation and the measurement for both wafer thicknesses.

Equations (2)

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J p h = e 0 λ = 0 λ = 1200 n m d λ N A M 1.5 ( λ ) A ( λ ) ,
A ( r , ω ) = 1 2 ω ε 0 Im ( ε ( r , ω ) ) | E ( r , ω ) | 2 ,

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