Abstract

We apply a Fourier-scattering model to describe light scattering in solar cells with textured surfaces. For the size and inclination angle of typical micro-textures, scattering may occur into large angles. This makes the model prone to paraxial errors. We present a non-paraxial formulation and discuss the transition from the domain of refraction at large facets to scattering at small features.

© 2017 Optical Society of America

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References

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  1. P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987).
    [Crossref]
  2. P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
    [Crossref]
  3. E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
    [Crossref]
  4. J. Goodman, Introduction to Fourier optics (Roberts & Company Publishers, 2005).
  5. D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
    [Crossref]
  6. J. E. Harvey, A. Krywonos, and D. Bogunovic, “Nonparaxial scalar treatment of sinusoidal phase gratings,” J. Opt. Soc. Am. A 23(4), 858–865 (2006).
    [Crossref] [PubMed]
  7. F. J. Haug, C. Battaglia, D. Domine, and C. Ballif, “Light scattering at nano-textured surfaces in thin film silicon solar cells,” in 35 IEEE PVSC (IEEE, 2010), pp. 754–759.
  8. K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
    [Crossref]
  9. Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
    [Crossref]
  10. A. Krywonos, J. E. Harvey, and N. Choi, “Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles,” J. Opt. Soc. Am. A 28(6), 1121–1138 (2011).
    [Crossref] [PubMed]
  11. J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
    [Crossref]
  12. S. Manzoor, “Light trapping in monocrystalline silicon solar cells using random upright pyramids,” (Arizona State University, 2014).

2013 (1)

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

2011 (3)

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

A. Krywonos, J. E. Harvey, and N. Choi, “Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles,” J. Opt. Soc. Am. A 28(6), 1121–1138 (2011).
[Crossref] [PubMed]

2010 (1)

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[Crossref]

2006 (2)

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

J. E. Harvey, A. Krywonos, and D. Bogunovic, “Nonparaxial scalar treatment of sinusoidal phase gratings,” J. Opt. Soc. Am. A 23(4), 858–865 (2006).
[Crossref] [PubMed]

1999 (1)

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

1987 (1)

P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987).
[Crossref]

Ballif, C.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[Crossref]

Battaglia, C.

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[Crossref]

Beckers, T.

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

Bittkau, K.

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

Bogunovic, D.

Campbell, P.

P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987).
[Crossref]

Carius, R.

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

Chaumartin, A.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Choi, N.

De Clercq, K.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

De Wolf, S.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

Descoeudres, A.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

Dominé, D.

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[Crossref]

Einhaus, R.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Escarré, J.

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

Fave, A.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Filipic, M.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

Green, M.

P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987).
[Crossref]

Harvey, J. E.

Haug, F. J.

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[Crossref]

Holman, Z. C.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

Kaminski, A.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Klein, M.

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

Kraiem, J.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Krywonos, A.

Lelievre, J.-F.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Lemiti, M.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Nichiporuk, O.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Nijs, J.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Papet, P.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Poortmans, J.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Rozier, Y.

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

Said, K.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Schulte, M.

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

Smole, F.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

Söderström, K.

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

Szlufcik, J.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Topic, M.

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

Van Kerschaver, E.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Vazsonyi, E.

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

J. Appl. Phys. (3)

P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987).
[Crossref]

Z. C. Holman, M. Filipic, A. Descoeudres, S. De Wolf, F. Smole, M. Topic, and C. Ballif, “Infrared light management in high-efficiency silicon heterojunction and rear-passivated solar cells,” J. Appl. Phys. 113(1), 013107 (2013).
[Crossref]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modelling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[Crossref]

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

Sol. Energy Mater. Sol. Cells (3)

J. Escarré, K. Söderström, C. Battaglia, F. J. Haug, and C. Ballif, “High fidelity transfer of nanometric random textures by UV embossing for thin film solar cells applications,” Sol. Energy Mater. Sol. Cells 95(3), 881–886 (2011).
[Crossref]

P. Papet, O. Nichiporuk, A. Kaminski, Y. Rozier, J. Kraiem, J.-F. Lelievre, A. Chaumartin, A. Fave, and M. Lemiti, “Pyramidal texturing of silicon solar cell with TMAH chemical anisotropic etching,” Sol. Energy Mater. Sol. Cells 90(15), 2319–2328 (2006).
[Crossref]

E. Vazsonyi, K. De Clercq, R. Einhaus, E. Van Kerschaver, K. Said, J. Poortmans, J. Szlufcik, and J. Nijs, “Improved anisotropic etching process for industrial texturing of silicon solar cells,” Sol. Energy Mater. Sol. Cells 57(2), 179–188 (1999).
[Crossref]

Thin Solid Films (1)

K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films 519(19), 6538–6543 (2011).
[Crossref]

Other (3)

F. J. Haug, C. Battaglia, D. Domine, and C. Ballif, “Light scattering at nano-textured surfaces in thin film silicon solar cells,” in 35 IEEE PVSC (IEEE, 2010), pp. 754–759.

J. Goodman, Introduction to Fourier optics (Roberts & Company Publishers, 2005).

S. Manzoor, “Light trapping in monocrystalline silicon solar cells using random upright pyramids,” (Arizona State University, 2014).

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Figures (9)

Fig. 1
Fig. 1 Illustration of scattering at a surface texture; refraction at a facet is shown to the left, diffraction of partial waves by periodic repetition of a profile with length L is illustrated in the middle, and definition of the phase-change introduced by the texture is shown to the right.
Fig. 2
Fig. 2 Variation of the refracted angle δ tr upon perpendicular incidence on facets inclined by an angle φ w.r. to the surface plane (c.f. left panel of Fig. 1). Lines are according to Snell’s law, circles are modeled with the paraxial approach according to Eq. (1), squares after non-paraxial correction according to Eq. (3). Dashed lines and open symbols refer to incidence on a polymer, full lines and symbols refer to incidence on silicon.
Fig. 3
Fig. 3 The 2D radiance pattern of an idealized facet (dashed lines), assembled from ten diffraction patterns. Each of the patterns contributes only in an angular domain as illustrated by the by the dashed lines. The pattern extends over a domain of [11]×[11] in cosine-space, the outermost line represents the unit circle which separates propagating from evanescent modes. The data within the dashed box and its assembly is illustrated in Fig. 4.
Fig. 4
Fig. 4 Assembly of the ARS from the diffraction intensity of 10 provisionally calculated diffraction patterns. For the sake of clarity, only five spectra, corresponding to lowest angular domains, are shown in the graph. Depending on rounding, each one contributes 5 or 6 points to the assembled curve.
Fig. 5
Fig. 5 Panel a) shows an AFM topography of a replica of the pyramids etched into a Si-100 surface (image size 15 µm x 15 µm). Panels b) and c) show corresponding 2D scattering patterns obtained with ray tracing and with the modified Fourier model, respectively. The arrows illustrate the direction of data extraction for Fig. 6.
Fig. 6
Fig. 6 Measurement of the angle-resolved scattering intensity (thick red line), using the geometry shown in the inset. The open squares denote results modeled with the modified Fourier method (adjacent average of the full data shown by the thin gray line), full and open circles with drop-lines represent results of ray tracing for direct incidence and the second rebound, respectively.
Fig. 7
Fig. 7 Measurement of the angle-resolved scattering intensity upon outcoupling into air for three different angles of incidence (thick lines), using the illustrated geometry. Small open squares denote again a 5pt average over the Fourier model, whereas full and open circles with drop-lines denote results of ray tracing.
Fig. 8
Fig. 8 Panels a) and d) show AFM topographies of two differently etched Si-100 wafers on an area of 20 µm x 20 µm. Panels b) and e) denote corresponding 2D refraction patterns obtained by ray tracing, and panels c) and f) show corresponding data obtained with the modified Fourier model. The AFM image d) with the small pyramids was taken from ref [12], the arrow in panel f) illustrates the extraction of azimuthal data through the maxima which is shown in Fig. 9.
Fig. 9
Fig. 9 Cuts through the 2D data of Fig. 8 for a polar angle of 40°. Full and dashed lines correspond to Fourier modelling of large and small facets, respectively, Full and open symbols with drop-lines denote corresponding results of ray tracing (shifted vertically for clarity).

Equations (3)

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f q = 1 N p=1 N e i k 0 ζ(p/L)( n 1 n 2 ) U t e 2πipq/N
sin δ q,r = γ q,r = (1 α q 2 β r 2 ) 1/2
U t = e i k 0 ζ(p/L)( n 1 cos δ inc n 2 cos δ q

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