Abstract

We present and experimentally validate a computational model for the light propagation in thin-film solar cells that integrates non-paraxial scalar diffraction theory with non-sequential ray-tracing. The model allows computing the spectral layer absorbances of solar cells with micro- and nano-textured interfaces directly from measured surface topographies. We can thus quantify decisive quantities such as the parasitic absorption without relying on heuristic scattering intensity distributions. In particular, we find that the commonly used approximation of Lambertian scattering intensity distributions for internal light propagation is violated even for solar cells on rough textured substrates. More importantly, we demonstrate how both scattering and parasitic absorption must be controlled to maximize photocurrent.

© 2015 Optical Society of America

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References

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  1. International Energy Agency, “Tracking clean energy progress 2014,” http://www.iea.org/publications/freepublications/publication/tracking-clean-energy-progress-2014.html .
  2. P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37, 4868–4870 (2012).
    [Crossref] [PubMed]
  3. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20, A224–A244 (2012).
    [Crossref] [PubMed]
  4. T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
    [Crossref]
  5. A. Bozzola, P. Kowalczewski, and L. C. Andreani, “Towards high efficiency thin-film crystalline silicon solar cells: The roles of light trapping and non-radiative recombinations,” J. Appl. Phys. 115, 094501 (2014).
    [Crossref]
  6. K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
    [Crossref]
  7. M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
    [Crossref]
  8. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. A 72, 899–907 (1982).
    [Crossref]
  9. H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
    [Crossref]
  10. C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
    [Crossref]
  11. C. S. Schuster, A. Bozzola, L. C. Andreani, and T. F. Krauss, “How to assess light trapping structures versus a lambertian scatterer for solar cells?” Opt. Express 22, A542–A551 (2014).
    [Crossref] [PubMed]
  12. T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
    [Crossref]
  13. J. E. Harvey, C. L. Vernold, A. Krywonos, and P. L. Thompson, “Diffracted radiance: A fundamental quantity in nonparaxial scalar diffraction theory,” Appl. Opt. 38, 6469–6481 (1999).
    [Crossref]
  14. D. Domine, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107, 044504 (2010).
    [Crossref]
  15. J. E. Harvey, A. Krywonos, and D. Bogunovic, “Nonparaxial scalar treatment of sinusoidal phase gratings,” J. Opt. Soc. Am. A 23, 858–865 (2006).
    [Crossref]
  16. A. V. Gitin, “Huygens-Feynman-Fresnel principle as the basis of applied optics,” Appl. Opt. 52, 7419–7434 (2013).
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  17. Fluxim Inc., www.fluxim.com .
  18. S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
    [Crossref]
  19. D. Dominé, “The role of front electrodes and intermediate reflectors in the optoelectronic properties of high-efficiency micromorph solar cells,” Ph.D. thesis, Université de Neuchâtel (2009).
  20. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [Crossref]

2014 (4)

A. Bozzola, P. Kowalczewski, and L. C. Andreani, “Towards high efficiency thin-film crystalline silicon solar cells: The roles of light trapping and non-radiative recombinations,” J. Appl. Phys. 115, 094501 (2014).
[Crossref]

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

C. S. Schuster, A. Bozzola, L. C. Andreani, and T. F. Krauss, “How to assess light trapping structures versus a lambertian scatterer for solar cells?” Opt. Express 22, A542–A551 (2014).
[Crossref] [PubMed]

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

2013 (1)

2012 (6)

C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
[Crossref]

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37, 4868–4870 (2012).
[Crossref] [PubMed]

A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20, A224–A244 (2012).
[Crossref] [PubMed]

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
[Crossref]

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

2011 (1)

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
[Crossref]

2010 (1)

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

2006 (1)

1999 (1)

1982 (1)

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

1975 (1)

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

Altazin, S.

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

Andreani, L. C.

Baik, S.

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

Ballif, C.

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
[Crossref]

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
[Crossref]

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

Battaglia, C.

C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
[Crossref]

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
[Crossref]

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

Boccard, M.

C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
[Crossref]

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

Bogunovic, D.

Bozzola, A.

Despeisse, M.

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

Domine, D.

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

Dominé, D.

D. Dominé, “The role of front electrodes and intermediate reflectors in the optoelectronic properties of high-efficiency micromorph solar cells,” Ph.D. thesis, Université de Neuchâtel (2009).

Fang, L.

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

Fischer, M.

K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
[Crossref]

Gitin, A. V.

Guha, S.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Harvey, J. E.

Haug, F. J.

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

Haug, F.-J.

C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
[Crossref]

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

Jager, K.

K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
[Crossref]

Kirsch, C.

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

Knaack, R.

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

Kowalczewski, P.

A. Bozzola, P. Kowalczewski, and L. C. Andreani, “Towards high efficiency thin-film crystalline silicon solar cells: The roles of light trapping and non-radiative recombinations,” J. Appl. Phys. 115, 094501 (2014).
[Crossref]

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37, 4868–4870 (2012).
[Crossref] [PubMed]

Krauss, T. F.

Krywonos, A.

Lanz, T.

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
[Crossref]

Lapagna, K.

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

Lim, K.

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

Liscidini, M.

Ozturk, B.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Phong, B. T.

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

Ruhstaller, B.

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
[Crossref]

Schiff, E.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Schuster, C. S.

Sivec, L.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Thompson, P. L.

van Swaaij, R. A. C. M. M.

K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
[Crossref]

Vernold, C. L.

Yablonovitch, E.

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

Yan, B.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Yang, J.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Zeman, M.

K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
[Crossref]

Zhao, H.

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M. Boccard, C. Battaglia, F.-J. Haug, M. Despeisse, and C. Ballif, “Light trapping in solar cells: Analytical modeling,” Appl. Phys. Lett. 101, 151105 (2012).
[Crossref]

Commun. ACM (1)

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

J. Appl. Phys. (5)

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

A. Bozzola, P. Kowalczewski, and L. C. Andreani, “Towards high efficiency thin-film crystalline silicon solar cells: The roles of light trapping and non-radiative recombinations,” J. Appl. Phys. 115, 094501 (2014).
[Crossref]

K. Jager, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111, 083108 (2012).
[Crossref]

C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112, 094504 (2012).
[Crossref]

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys. 110, 033111 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Express (2)

Opt. Lett. (1)

SID Int. Symp. Dig. Tec. (1)

S. Altazin, K. Lapagna, T. Lanz, C. Kirsch, R. Knaack, and B. Ruhstaller, “40.4: Design tool for light scattering enhancement in OLEDs,” SID Int. Symp. Dig. Tec. 45, 576–579 (2014).
[Crossref]

Sol. Energ. Mat. Sol. Cells (2)

H. Zhao, B. Ozturk, E. Schiff, L. Sivec, B. Yan, J. Yang, and S. Guha, “Backreflector morphology effects and thermodynamic light-trapping in thin-film silicon solar cells,” Sol. Energ. Mat. Sol. Cells 129, 104–114 (2014).
[Crossref]

T. Lanz, L. Fang, S. Baik, K. Lim, and B. Ruhstaller, “Photocurrent increase in amorphous Si solar cells by increased reflectivity of LiF/Al electrodes,” Sol. Energ. Mat. Sol. Cells 107, 259–262 (2012).
[Crossref]

Other (3)

Fluxim Inc., www.fluxim.com .

International Energy Agency, “Tracking clean energy progress 2014,” http://www.iea.org/publications/freepublications/publication/tracking-clean-energy-progress-2014.html .

D. Dominé, “The role of front electrodes and intermediate reflectors in the optoelectronic properties of high-efficiency micromorph solar cells,” Ph.D. thesis, Université de Neuchâtel (2009).

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Figures (7)

Fig. 1
Fig. 1 Illustration for the case of reflection: the plane of incidence Γ0, a plane Γϕ, the hemisphere and its coordinates on which the angle resolved scattering (ARS) is defined. The red arrow illustrates oblique incidence, the blue arrow the specular part of the reflected light.
Fig. 2
Fig. 2 Atomic force microscopy (AFM) measurements of the two analyzed ZnO substrates. The dimensions of the scans are 10 by 10 μm2 and the root-mean-square (RMS) roughnesses of the substrates are 150 nm (a) and 120 nm (b).
Fig. 3
Fig. 3 Illustration of the computed diffracted radiance for scattering from the ZnO/silicon interface (RMS roughness 120 nm) into silicon. (a) Perpendicular incidence; (b) oblique incidence. The red circles denote (α2 + β2)1/2 = 1, only modes within this unit circle are propagating.
Fig. 4
Fig. 4 Angular resolved transmission through the two ZnO surfaces: (a) σRMS = 150 nm, (b) σRMS = 120 nm into air for monochromatic light with a wavelength of 543 nm at normal and oblique incidence. Solid lines represent calculations, dotted lines measurements. The inset gives the root-mean-square roughness and the correlation length of the two substrate textures.
Fig. 5
Fig. 5 EQE and 1-R curves for μc-Si solar cells deposited on the two substrates with intrinsic layer thicknesses of 1 μm. The dashed curves represent the calculations. The shaded area in the figures represents the parasitic absorption in the electrodes, quantified by an equivalent current. The inset gives the root-mean-square roughness and the correlation length of the two substrate textures. Also given are the computed photocurrents.
Fig. 6
Fig. 6 ARSϕ̄ for a wavelength of 700 nm for the two substrates: (a) σRMS = 150 nm, (b) σRMS = 120 nm. The initial transmission into silicon (solid blue), the equilibrated distribution containing all propagating modes (dotted blue) and a Lambertian scatterer (solid black). The inset gives the root-mean-square roughness and the correlation length of the two substrate textures.
Fig. 7
Fig. 7 (a) Parametric variation of the specularity of the scattered light, parametrized by the Phong Factor. (b) ARSϕ̄ for a wavelength of 700 nm for Phong factor 1.5. The initial transmission into silicon (solid blue), the equilibrated distribution containing all propagating modes (dotted blue) and a Lambertian scatterer (solid black).

Equations (2)

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

L ( α , β β 0 ) = λ 2 A s | { U 0 ( x ^ , y ^ ) exp ( i 2 π β 0 y ^ ) } | 2 .
ARS ( ϕ , θ ) = cos ( θ ) L ( α , β ) A s .

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