Abstract

In this paper, we introduce a simulation formalism for determining the Optical Properties of Textured Optical Sheets (OPTOS). Our matrix-based method allows for the computationally-efficient calculation of non-coherent light propagation and absorption in thick textured sheets, especially solar cells, featuring different textures on front and rear side that may operate in different optical regimes. Within the simulated system, the angular power distribution is represented by a vector. This light distribution is modified by interaction with the surfaces of the textured sheets, which are described by redistribution matrices. These matrices can be calculated for each individual surface texture with the most appropriate technique. Depending on the feature size of the texture, for example, either ray- or wave-optical methods can be used. The comparison of the simulated absorption in a sheet of silicon for a variety of surface textures, both with the results from other simulation techniques and experimentally measured data, shows very good agreement. To demonstrate the versatility of this newly-developed approach, the absorption in silicon sheets with a large-scale structure (V-grooves) at the front side and a small-scale structure (diffraction grating) at the rear side is calculated. Moreover, with minimal computational effort, a thickness parameter variation is performed.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
3D optical simulation formalism OPTOS for textured silicon solar cells

Nico Tucher, Johannes Eisenlohr, Peter Kiefel, Oliver Höhn, Hubert Hauser, Marius Peters, Claas Müller, Jan Christoph Goldschmidt, and Benedikt Bläsi
Opt. Express 23(24) A1720-A1734 (2015)

Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS

Nico Tucher, Johannes Eisenlohr, Habtamu Gebrewold, Peter Kiefel, Oliver Höhn, Hubert Hauser, Jan Christoph Goldschmidt, and Benedikt Bläsi
Opt. Express 24(14) A1083-A1093 (2016)

Optical modeling of structured silicon-based tandem solar cells and module stacks

Nico Tucher, Oliver Höhn, Jan Christoph Goldschmidt, and Benedikt Bläsi
Opt. Express 26(18) A761-A768 (2018)

References

  • View by:
  • |
  • |
  • |

  1. A. Gombert and B. Bläsi, “The Moth-Eye Effect — From Fundamentals to Commercial Exploitation,” in Functional Properties of Bio-Inspired Surfaces: Characterization and Technological Applications, E. A. Favret and N. O. Fuentes, eds. (World Scientific, 2009), pp. 79–102.
  2. M. A. Green, Silicon Solar Cells: Advanced Principles and Practice (Centre for Photovoltaic Devises and Systems UNSW, 1995), p. 366.
  3. P. Würfel, Physics of Solar Cells - from Basic Principles to Advanced Concepts, 2nd ed. (Wiley-VCH, 2009), p. 256.
  4. S. C. Tang, “Brightness enhancement film,” (Google Patents, 2001).
  5. A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
    [Crossref]
  6. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
    [Crossref] [PubMed]
  7. A. W. Smith and A. Rohatgi, “Ray tracing analysis of the inverted pyramid texturing geometry for high efficiency silicon solar cells,” Sol. Energy Mater. Sol. Cells 29(1), 37–49 (1993).
    [Crossref]
  8. S. C. Baker-Finch and K. R. McIntosh, “Reflection of normally incident light from silicon solar cells with pyramidal texture,” Prog. Photovolt. Res. Appl. 19(4), 406–416 (2011).
    [Crossref]
  9. S. C. Baker-Finch, K. R. McIntosh, and M. L. Terry, “Isotextured silicon solar cell analysis and modeling 1: Optics,” IEEE J. Photovolt. 2(4), 457–464 (2012).
    [Crossref]
  10. H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
    [Crossref]
  11. 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.
  12. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
    [Crossref]
  13. D. Domine, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107, 044504–044504–044508 (2010).
    [Crossref]
  14. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [Crossref]
  15. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., Artech House Antennas and Propagation Library (Artech House, 2005).
  16. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
    [Crossref]
  17. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
    [Crossref]
  18. R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).
  19. A. Mellor, I. Tobías, A. Martí, 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]
  20. A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
    [Crossref]
  21. D. Werner, Funktionalanalysis, 7. Auflage (2011).
  22. P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
    [Crossref]
  23. J. P. Hugonin and P. Lalanne, “RETICOLO CODE 2D for the diffraction by stacks of lamellar 2D crossed gratings,” Institut d'Optique, Orsay (2005).
  24. A. Mellor, “Photon Management Structures For Absorption Enhancement in Intermediate Band Solar Cells and Crystalline Silicon Solar Cells,” Tesis Doctoral (Universidad Politecnica de Madrid, 2013).
  25. B. Harbecke, “Coherent and incoherent reflection and transmission of multilayer structures,” Appl. Phys. B 39(3), 165–170 (1986).
    [Crossref]
  26. P. Berger, H. Hauser, D. Suwito, S. Janz, M. Peters, B. Bläsi, and M. Hermle, “Realization and evaluation of diffractive systems on the back side of silicon solar cells,” in Photonics Europe, April 12–16, R. B. G. Wehrspohn, A., ed. (SPIE, Brussels, Belgium, 2010).
  27. A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
    [Crossref]
  28. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982).
    [Crossref]

2013 (2)

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

2012 (4)

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

S. C. Baker-Finch, K. R. McIntosh, and M. L. Terry, “Isotextured silicon solar cell analysis and modeling 1: Optics,” IEEE J. Photovolt. 2(4), 457–464 (2012).
[Crossref]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

2011 (3)

S. C. Baker-Finch and K. R. McIntosh, “Reflection of normally incident light from silicon solar cells with pyramidal texture,” Prog. Photovolt. Res. Appl. 19(4), 406–416 (2011).
[Crossref]

A. Mellor, I. Tobías, A. Martí, 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]

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

2004 (1)

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

1998 (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

1997 (1)

1993 (1)

A. W. Smith and A. Rohatgi, “Ray tracing analysis of the inverted pyramid texturing geometry for high efficiency silicon solar cells,” Sol. Energy Mater. Sol. Cells 29(1), 37–49 (1993).
[Crossref]

1986 (1)

B. Harbecke, “Coherent and incoherent reflection and transmission of multilayer structures,” Appl. Phys. B 39(3), 165–170 (1986).
[Crossref]

1982 (1)

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Altermatt, P. P.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Baker-Finch, S. C.

S. C. Baker-Finch, K. R. McIntosh, and M. L. Terry, “Isotextured silicon solar cell analysis and modeling 1: Optics,” IEEE J. Photovolt. 2(4), 457–464 (2012).
[Crossref]

S. C. Baker-Finch and K. R. McIntosh, “Reflection of normally incident light from silicon solar cells with pyramidal texture,” Prog. Photovolt. Res. Appl. 19(4), 406–416 (2011).
[Crossref]

Bläsi, B.

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Bothe, K.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Brendel, R.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Bühler, C.

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Fromherz, T.

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

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.

Gombert, A.

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Harbecke, B.

B. Harbecke, “Coherent and incoherent reflection and transmission of multilayer structures,” Appl. Phys. B 39(3), 165–170 (1986).
[Crossref]

Hauser, H.

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

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,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

Hingerl, K.

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

Höhn, O.

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

Holst, H.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Hoßfeld, W.

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Jantsch, W.

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

Jurek, M. P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

Köntges, M.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Kübler, V.

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

Lalanne, P.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

Li, L.

Luque, A.

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

A. Mellor, I. Tobías, A. Martí, 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.

A. Mellor, I. Tobías, A. Martí, 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]

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

McIntosh, K. R.

S. C. Baker-Finch, K. R. McIntosh, and M. L. Terry, “Isotextured silicon solar cell analysis and modeling 1: Optics,” IEEE J. Photovolt. 2(4), 457–464 (2012).
[Crossref]

S. C. Baker-Finch and K. R. McIntosh, “Reflection of normally incident light from silicon solar cells with pyramidal texture,” Prog. Photovolt. Res. Appl. 19(4), 406–416 (2011).
[Crossref]

Meinhardt, G.

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

Mellor, A.

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

A. Mellor, I. Tobías, A. Martí, 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]

Mendes, M. J.

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

Mick, J.

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Niggemann, M.

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Nitz, P.

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Peters, M.

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

Polman, A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Rohatgi, A.

A. W. Smith and A. Rohatgi, “Ray tracing analysis of the inverted pyramid texturing geometry for high efficiency silicon solar cells,” Sol. Energy Mater. Sol. Cells 29(1), 37–49 (1993).
[Crossref]

Rothemund, R.

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

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,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

Smith, A. W.

A. W. Smith and A. Rohatgi, “Ray tracing analysis of the inverted pyramid texturing geometry for high efficiency silicon solar cells,” Sol. Energy Mater. Sol. Cells 29(1), 37–49 (1993).
[Crossref]

Spinelli, P.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Terry, M. L.

S. C. Baker-Finch, K. R. McIntosh, and M. L. Terry, “Isotextured silicon solar cell analysis and modeling 1: Optics,” IEEE J. Photovolt. 2(4), 457–464 (2012).
[Crossref]

Tobías, I.

A. Mellor, I. Tobías, A. Martí, 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]

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

Umundum, T.

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

Verschuuren, M. A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Vogt, M. R.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Walk, C.

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

Winter, M.

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

Wolf, A. J.

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

Yablonovitch, E.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Appl. Phys. B (1)

B. Harbecke, “Coherent and incoherent reflection and transmission of multilayer structures,” Appl. Phys. B 39(3), 165–170 (1986).
[Crossref]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

Energy Procedia (1)

H. Holst, M. Winter, M. R. Vogt, K. Bothe, M. Köntges, R. Brendel, and P. P. Altermatt, “Application of a new ray tracing framework to the analysis of extended regions in Si solar cell modules,” Energy Procedia 38, 86–93 (2013).
[Crossref]

IEEE J. Photovolt. (1)

S. C. Baker-Finch, K. R. McIntosh, and M. L. Terry, “Isotextured silicon solar cell analysis and modeling 1: Optics,” IEEE J. Photovolt. 2(4), 457–464 (2012).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

J. Mod. Opt. (1)

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45(7), 1357–1374 (1998).
[Crossref]

J. Opt. Soc. Am. (1)

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

Microelectron. Eng. (1)

A. J. Wolf, H. Hauser, V. Kübler, C. Walk, O. Höhn, and B. Bläsi, “Origination of nano- and microstructures on large areas by interference lithography,” Microelectron. Eng. 98, 293–296 (2012).
[Crossref]

Nat. Commun. (1)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Opt. Eng. (1)

A. Gombert, B. Bläsi, C. Bühler, P. Nitz, J. Mick, W. Hoßfeld, and M. Niggemann, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43(11), 2525–2533 (2004).
[Crossref]

Prog. Photovolt. Res. Appl. (4)

S. C. Baker-Finch and K. R. McIntosh, “Reflection of normally incident light from silicon solar cells with pyramidal texture,” Prog. Photovolt. Res. Appl. 19(4), 406–416 (2011).
[Crossref]

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Prog. Photovolt. Res. Appl. 20(7), 862–873 (2012).
[Crossref]

R. Rothemund, T. Umundum, G. Meinhardt, K. Hingerl, T. Fromherz, and W. Jantsch, “Light trapping in pyramidally textured crystalline silicon solar cells using back-side diffractive gratings,” Prog. Photovolt. Res. Appl. 21, 747–753 (2013).

A. Mellor, I. Tobías, A. Martí, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt. Res. Appl. 19(6), 676–687 (2011).
[Crossref]

Sol. Energy Mater. Sol. Cells (2)

A. Mellor, I. Tobías, A. Martí, 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]

A. W. Smith and A. Rohatgi, “Ray tracing analysis of the inverted pyramid texturing geometry for high efficiency silicon solar cells,” Sol. Energy Mater. Sol. Cells 29(1), 37–49 (1993).
[Crossref]

Other (11)

A. Gombert and B. Bläsi, “The Moth-Eye Effect — From Fundamentals to Commercial Exploitation,” in Functional Properties of Bio-Inspired Surfaces: Characterization and Technological Applications, E. A. Favret and N. O. Fuentes, eds. (World Scientific, 2009), pp. 79–102.

M. A. Green, Silicon Solar Cells: Advanced Principles and Practice (Centre for Photovoltaic Devises and Systems UNSW, 1995), p. 366.

P. Würfel, Physics of Solar Cells - from Basic Principles to Advanced Concepts, 2nd ed. (Wiley-VCH, 2009), p. 256.

S. C. Tang, “Brightness enhancement film,” (Google Patents, 2001).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., Artech House Antennas and Propagation Library (Artech House, 2005).

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.

D. Domine, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107, 044504–044504–044508 (2010).
[Crossref]

D. Werner, Funktionalanalysis, 7. Auflage (2011).

J. P. Hugonin and P. Lalanne, “RETICOLO CODE 2D for the diffraction by stacks of lamellar 2D crossed gratings,” Institut d'Optique, Orsay (2005).

A. Mellor, “Photon Management Structures For Absorption Enhancement in Intermediate Band Solar Cells and Crystalline Silicon Solar Cells,” Tesis Doctoral (Universidad Politecnica de Madrid, 2013).

P. Berger, H. Hauser, D. Suwito, S. Janz, M. Peters, B. Bläsi, and M. Hermle, “Realization and evaluation of diffractive systems on the back side of silicon solar cells,” in Photonics Europe, April 12–16, R. B. G. Wehrspohn, A., ed. (SPIE, Brussels, Belgium, 2010).

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 (9)

Fig. 1
Fig. 1 Light propagation in a continuous medium with textured surfaces on both sides. Incoming light is divided into different channels as depicted in (a). The power fractions in these channels are described by a vector v ' 0 . Before the reflection (and redistribution) at the rear side it is called v1, after reflection v ' 1 and so on. The reflectance and redistribution at the surfaces is described by the matrices (B) and (C). The bulk propagation, where no redistribution but only absorption occurs, is described by the propagation matrix (D).
Fig. 2
Fig. 2 Redistribution matrices for two different structures at a wavelength of 1100 nm using sin(θ) binning and averaged polarization. The colour scales are a measure of the diffraction or scattering intensity into the respective channels. (a) shows a planar silicon-air interface. Due to the specular reflection only diagonal entries appear. For all angles outside the loss cone the values are one. (b) shows V-grooves with dimensions that allow a treatment with ray tracing.
Fig. 3
Fig. 3 Redistribution matrices for two different structures at a wavelength of 1100 nm using sin(θ) binning and averaged polarization. (a) shows a linear grating at a silicon-air interface. (b) shows a 2D representation of a 3D Lambertian scatterer with 100% reflection. For all incoming angles a Lambertian light distribution is created. The values increase for increasing values of θout because of integration over the azimuth angles φ. In a fully 3D-description with appropriate angle discretization the representation of the Lambertian matrix would be single-valued.
Fig. 4
Fig. 4 Calculated absorption for a silicon wafer with a thickness of 40 µm. The black line shows the absorption of a planar reference wafer calculated by a transfer matrix method (TMM) corresponding to [25]. The orange triangles show the results for the same system obtained by the OPTOS method. The orange circles and rhombs are OPTOS calculations for systems with planar front and line grating rear side. Grating 1 has a period of 990 nm and a grating depth of 160 nm, grating 2 a period of 350 nm and a depth of 180 nm. The results are compared to calculations of Mellor, where the diffraction orders of the gratings are directly used as angle channels [24] (blue and green line). The OPTOS formalism shows excellent agreement with the results obtained using other simulation techniques.
Fig. 5
Fig. 5 Calculated and measured absorption for a silicon wafer with a thickness of 250 µm and a binary line grating on the rear side. The measured absorption is in accordance to the absorption calculated using OPTOS.
Fig. 6
Fig. 6 Calculated absorption for a 100 µm thick silicon wafer with planar front and Lambertian rear. The simulation result of the OPTOS formalism (orange) and the Yablonovitch limit (green) agree very well. For comparison the absorption of a planar-planar reference wafer is shown (black).
Fig. 7
Fig. 7 Calculated absorption for a 100 µm thick silicon wafer with additional V-groove front (groove height 3.536 µm) and planar rear. The lines with symbols are the results of the OPTOS formalism for TE polarization (orange), TM polarization (green) and the averaged values (blue). The latter agree very well with results of a ray tracing simulation with the same texture and sheet parameters that was run based on the PV-Lighthouse wafer ray tracer (black).
Fig. 8
Fig. 8 Absorption in a 100 µm thick silicon wafer with V-groove front and planar rear (black) and with V-groove front and line grating rear (orange). Although the presented case is only two-dimensional and no additional rear reflector has been considered, the result is a hint, that additional redistribution of light at the rear surface can further improve the overall light trapping properties also for three-dimensional, pyramidal front side textures.
Fig. 9
Fig. 9 Sheet thickness variation of an OPTOS calculation for a silicon wafer with V-grooves front and line grating rear. The simulation results show the expected absorption increase for larger sheet thicknesses. The computation is remarkably efficient, requiring only several minutes for this thickness variation.

Equations (14)

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

v = ( p ( θ 1 , φ 1 ) p ( θ 1 , φ 2 ) p ( θ 1 , φ m ) p ( θ 2 , φ 1 ) p ( θ 2 , φ 2 ) p ( θ n , φ m ) )
D = ( e α d / cos θ 1 0 0 e α d / cos θ n )
B , C = ( ( θ 1 , φ 1 ) ( θ 1 , φ 1 ) ) ( θ n , φ m ) ( θ 1 , φ 1 ) ( θ 1 , φ 1 ) ( θ 1 , φ 2 ) ( θ 1 , φ 1 ) ( θ 1 , φ 1 ) ( θ 1 , φ 1 ) ( θ n , φ m ) ( θ 1 , φ 1 ) ( θ 1 , φ 1 ) )
v ' 2 i = ( B D C D ) i v ' 0 v ' 2 i + 1 = ( C D B D ) i C D v ' 0 P ' i = j ( v ' i ) j v 2 = D C D v ' 0 v 2 i = ( D C D B ) i 1 v 2 v 2 i + 1 = ( D B D C ) i D v ' 0 P i = j ( v i ) j
A b s = A b s down + A b s up = ( i = 0 i max ( P ' 2 i P 2 i + 1 ) ) + ( i = 1 i max ( P ' 2 i 1 P 2 i ) )
A b s = P 0 P 1 + P ' 1 P 2 + P ' 2 P 3 + P ' 3 P 4 + ... = j ( i = 0 ( B D C D ) i v 0 i = 0 ( D B D C ) i D v 0 + i = 0 ( C D B D ) i C D v 0 i = 0 ( D C D B ) i D C D v 0 ) j = j ( ( I B D C D ) 1 v 0 ( I D B D C ) 1 D v 0 + ( I C D B D ) 1 C D v 0 ( I D C D B ) 1 D C D v 0 ) j
D ( z ) = ( e α z / cos θ 1 0 0 e α z / cos θ n )
A down ( z ) = ( 1 e α z / cos θ 1 0 0 1 e α z / cos θ n )
A up ( z ) = ( 1 e α ( d z ) / cos θ 1 0 0 1 e α ( d z ) / cos θ n )
A b s down ( z ) = j ( i = 0 i max A down ( z ) v ' 2 i ) j = j ( A down ( z ) i = 0 i max v ' 2 i ) j
A b s up ( z ) = j ( i = 0 i max A up ( z ) v ' 2 i + 1 ) j = j ( A up ( z ) i = 0 i max v ' 2 i + 1 ) j
A b s ( z ) = A b s down ( z ) + A b s up ( 0 ) A b s up ( z )
sin ( θ i ) = 2 i 2 r 1
C k + 2 , j = 1 π Δ Ω cos ( θ ) d Ω = 1 π 0 2 π θ k θ k + 1 cos ( θ ) sin ( θ ) d θ d φ = 8 k + 1 ( 2 r 1 ) 2

Metrics