Abstract

The optical response of periodically nanotextured layer stacks with dimensions comparable to the wavelength of the incident light can be computed with rigorous Maxwell solvers, such as the finite element method (FEM). Experimentally, such layer stacks are often prepared on glass superstrates with a thickness, which is orders of magnitude larger than the wavelength. For many applications, light in these thick superstrates can be treated incoherently. The front side of thick superstrate is located far away from the computational domain of the Maxwell solvers. Nonetheless, it has to be considered in order to achieve accurate results. In this contribution, we discuss how solutions of rigorous Maxwell solvers can be corrected for flat front sides of the superstrates with an incoherent a posteriori approach. We test these corrections for hexagonal sinusoidal nanotextured silica-silicon interfaces, which are applied in certain silicon thin-film solar cells. These corrections are determined via a scattering matrix, which contains the full scattering information of the periodically nanotextured structure. A comparison with experimental data reveals that higher-order corrections can predict the measured reflectivity of the samples much better than an often-applied zeroth-order correction.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  23. C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
    [Crossref]
  24. M. Verschuuren and H. van Sprang, “3D Photonic Structures by Sol-Gel Imprint Lithography,” Mater. Res. Soc. Symp. Proc. 1002, 1002 (2007).
    [Crossref]
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    [Crossref]
  26. C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
    [Crossref]

2018 (1)

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

2017 (3)

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

2016 (5)

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

G. Köppel, B. Rech, and C. Becker, “Sinusoidal nanotextures for light management in silicon thin-film solar cells,” Nanoscale 8, 8722–8728 (2016).
[Crossref] [PubMed]

N. Tucher, J. Eisenlohr, H. Gebrewold, P. Kiefel, O. Höhn, H. Hauser, J. C. Goldschmidt, and B. Bläsi, “Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism optos,” Opt. Express 24, A1083–A1093 (2016).
[Crossref] [PubMed]

J. Haschke, D. Amkreutz, and B. Rech, “Liquid phase crystallized silicon on glass: Technology, material quality and back contacted heterojunction solar cells, ” Jpn. J. Appl. Phys. 55, 04EA04 (2016).
[Crossref]

2015 (1)

2014 (1)

A. Herman, M. Sarrazin, and O. Deparis, “The fundamental problem of treating light incoherence in photovoltaics and its practical consequences,” New J. Phys. 16, 013022 (2014).
[Crossref]

2013 (4)

R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013).
[Crossref] [PubMed]

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, A295–A304 (2013).
[Crossref] [PubMed]

A. Campa, J. Krc, and M. Topic, “Two approaches for incoherent propagation of light in rigorous numerical simulations,” Progress In Electromagnetics Research 137, 187–202 (2013).
[Crossref]

O. Isabella, S. Solntsev, D. Caratelli, and M. Zeman, “3-D optical modeling of thin-film silicon solar cells on diffraction gratings,” Prog. Photovolt: Res. Appl. 21, 94–108 (2013).
[Crossref]

2011 (2)

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

2010 (1)

2007 (3)

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[Crossref]

M. Verschuuren and H. van Sprang, “3D Photonic Structures by Sol-Gel Imprint Lithography,” Mater. Res. Soc. Symp. Proc. 1002, 1002 (2007).
[Crossref]

2004 (1)

Agarwal, G. S.

Amkreutz, D.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

J. Haschke, D. Amkreutz, and B. Rech, “Liquid phase crystallized silicon on glass: Technology, material quality and back contacted heterojunction solar cells, ” Jpn. J. Appl. Phys. 55, 04EA04 (2016).
[Crossref]

Ballif, C.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Barth, C.

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

Battaglia, C.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Becker, C.

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

G. Köppel, B. Rech, and C. Becker, “Sinusoidal nanotextures for light management in silicon thin-film solar cells,” Nanoscale 8, 8722–8728 (2016).
[Crossref] [PubMed]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

K. Jäger, M. Hammerschmidt, G. Köppel, S. Burger, and C. Becker, “On accurate simulations of thin-film solar cells with a thick glass superstrate,” in “Light, Energy and the Environment,” (Optical Society of America, 2016), p. PM3B.5.
[Crossref]

Benick, J.

Bläsi, B.

Burger, S.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[Crossref]

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

K. Jäger, M. Hammerschmidt, G. Köppel, S. Burger, and C. Becker, “On accurate simulations of thin-film solar cells with a thick glass superstrate,” in “Light, Energy and the Environment,” (Optical Society of America, 2016), p. PM3B.5.
[Crossref]

Campa, A.

A. Campa, J. Krc, and M. Topic, “Two approaches for incoherent propagation of light in rigorous numerical simulations,” Progress In Electromagnetics Research 137, 187–202 (2013).
[Crossref]

Caratelli, D.

O. Isabella, S. Solntsev, D. Caratelli, and M. Zeman, “3-D optical modeling of thin-film silicon solar cells on diffraction gratings,” Prog. Photovolt: Res. Appl. 21, 94–108 (2013).
[Crossref]

Charrière, M.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Chen, D.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

Deparis, O.

A. Herman, M. Sarrazin, and O. Deparis, “The fundamental problem of treating light incoherence in photovoltaics and its practical consequences,” New J. Phys. 16, 013022 (2014).
[Crossref]

Despeisse, M.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Divitt, S.

Eisenhauer, D.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

Eisenlohr, J.

Escarré, J.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Gbur, G.

Gebrewold, H.

Goldschmidt, J. C.

Guttowski, A.

Hammerschmidt, M.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

K. Jäger, M. Hammerschmidt, G. Köppel, S. Burger, and C. Becker, “On accurate simulations of thin-film solar cells with a thick glass superstrate,” in “Light, Energy and the Environment,” (Optical Society of America, 2016), p. PM3B.5.
[Crossref]

Haschke, J.

J. Haschke, D. Amkreutz, and B. Rech, “Liquid phase crystallized silicon on glass: Technology, material quality and back contacted heterojunction solar cells, ” Jpn. J. Appl. Phys. 55, 04EA04 (2016).
[Crossref]

Haug, F.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Hauser, H.

Hecht, E.

E. Hecht, Optics (Pearson Higher Education, Harlow, England, 2016), 5th ed.

Herman, A.

A. Herman, M. Sarrazin, and O. Deparis, “The fundamental problem of treating light incoherence in photovoltaics and its practical consequences,” New J. Phys. 16, 013022 (2014).
[Crossref]

Herrmann, S.

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

Höhn, O.

Isabella, O.

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

O. Isabella, S. Solntsev, D. Caratelli, and M. Zeman, “3-D optical modeling of thin-film silicon solar cells on diffraction gratings,” Prog. Photovolt: Res. Appl. 21, 94–108 (2013).
[Crossref]

Jäger, K.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

K. Jäger, M. Hammerschmidt, G. Köppel, S. Burger, and C. Becker, “On accurate simulations of thin-film solar cells with a thick glass superstrate,” in “Light, Energy and the Environment,” (Optical Society of America, 2016), p. PM3B.5.
[Crossref]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, 2002).

Kiefel, P.

Klose, R.

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

Koizumi, G.

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

Köppel, G.

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

G. Köppel, B. Rech, and C. Becker, “Sinusoidal nanotextures for light management in silicon thin-film solar cells,” Nanoscale 8, 8722–8728 (2016).
[Crossref] [PubMed]

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, M. Hammerschmidt, G. Köppel, S. Burger, and C. Becker, “On accurate simulations of thin-film solar cells with a thick glass superstrate,” in “Light, Energy and the Environment,” (Optical Society of America, 2016), p. PM3B.5.
[Crossref]

Krc, J.

A. Campa, J. Krc, and M. Topic, “Two approaches for incoherent propagation of light in rigorous numerical simulations,” Progress In Electromagnetics Research 137, 187–202 (2013).
[Crossref]

Lockau, D.

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

Lupini, A. R.

Luque, A.

Martí, A.

Meguro, T.

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

Mellor, A.

Muske, M.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

Novotny, L.

Peters, M.

Pomplun, J.

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[Crossref]

Preissler, N.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

Rech, B.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

G. Köppel, B. Rech, and C. Becker, “Sinusoidal nanotextures for light management in silicon thin-film solar cells,” Nanoscale 8, 8722–8728 (2016).
[Crossref] [PubMed]

J. Haschke, D. Amkreutz, and B. Rech, “Liquid phase crystallized silicon on glass: Technology, material quality and back contacted heterojunction solar cells, ” Jpn. J. Appl. Phys. 55, 04EA04 (2016).
[Crossref]

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

Ruske, F.

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

Sabau, A. S.

Santbergen, R.

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013).
[Crossref] [PubMed]

Sarrazin, M.

A. Herman, M. Sarrazin, and O. Deparis, “The fundamental problem of treating light incoherence in photovoltaics and its practical consequences,” New J. Phys. 16, 013022 (2014).
[Crossref]

Schädle, A.

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

Schlatmann, R.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

Schmidt, F.

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

K. Jäger, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells,” Opt. Express 24, A569–A580 (2016).
[Crossref] [PubMed]

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[Crossref]

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

Smets, A. H. M.

Söderström, K.

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

Solntsev, S.

O. Isabella, S. Solntsev, D. Caratelli, and M. Zeman, “3-D optical modeling of thin-film silicon solar cells on diffraction gratings,” Prog. Photovolt: Res. Appl. 21, 94–108 (2013).
[Crossref]

Sonntag, P.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

Suezaki, T.

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

Swaaij, R. V.

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

Tobías, I.

Topic, M.

A. Campa, J. Krc, and M. Topic, “Two approaches for incoherent propagation of light in rigorous numerical simulations,” Progress In Electromagnetics Research 137, 187–202 (2013).
[Crossref]

Trahms, M.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

Trinh, C. T.

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

Troparevsky, M. C.

Tucher, N.

van Sprang, H.

M. Verschuuren and H. van Sprang, “3D Photonic Structures by Sol-Gel Imprint Lithography,” Mater. Res. Soc. Symp. Proc. 1002, 1002 (2007).
[Crossref]

Verdet, M. E.

M. E. Verdet, Leçons d’Optique Physique (L’Imprimerie Impériale, 1869).

Verschuuren, M.

M. Verschuuren and H. van Sprang, “3D Photonic Structures by Sol-Gel Imprint Lithography,” Mater. Res. Soc. Symp. Proc. 1002, 1002 (2007).
[Crossref]

Wellens, C.

Wolf, E.

Yamamoto, K.

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

Yang, G.

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

Zeman, M.

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

O. Isabella, S. Solntsev, D. Caratelli, and M. Zeman, “3-D optical modeling of thin-film silicon solar cells on diffraction gratings,” Prog. Photovolt: Res. Appl. 21, 94–108 (2013).
[Crossref]

R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013).
[Crossref] [PubMed]

Zhang, Z.

Zschiedrich, L.

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[Crossref]

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

IEEE J. Photovolt. (2)

R. Santbergen, T. Meguro, T. Suezaki, G. Koizumi, K. Yamamoto, and M. Zeman, “GenPro4 Optical Model for Solar Cell Simulation and Its Application to Multijunction Solar Cells,” IEEE J. Photovolt. 7, 919–926 (2017).
[Crossref]

G. Köppel, D. Amkreutz, P. Sonntag, G. Yang, R. V. Swaaij, O. Isabella, M. Zeman, B. Rech, and C. Becker, “Periodic and Random Substrate Textures for Liquid-Phase Crystallized Silicon Thin-Film Solar Cells,” IEEE J. Photovolt. 7, 85–90 (2017).
[Crossref]

J. Comput. Phys. (1)

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: Scattering off periodic structures,” J. Comput. Phys. 226, 477–493 (2007).
[Crossref]

Jpn. J. Appl. Phys. (1)

J. Haschke, D. Amkreutz, and B. Rech, “Liquid phase crystallized silicon on glass: Technology, material quality and back contacted heterojunction solar cells, ” Jpn. J. Appl. Phys. 55, 04EA04 (2016).
[Crossref]

Mater. Res. Soc. Symp. Proc. (1)

M. Verschuuren and H. van Sprang, “3D Photonic Structures by Sol-Gel Imprint Lithography,” Mater. Res. Soc. Symp. Proc. 1002, 1002 (2007).
[Crossref]

Nanoscale (1)

G. Köppel, B. Rech, and C. Becker, “Sinusoidal nanotextures for light management in silicon thin-film solar cells,” Nanoscale 8, 8722–8728 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

C. Battaglia, J. Escarré, K. Söderström, M. Charrière, M. Despeisse, F. Haug, and C. Ballif, “Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells,” Nat. Photonics 5, 535 (2011).
[Crossref]

New J. Phys. (1)

A. Herman, M. Sarrazin, and O. Deparis, “The fundamental problem of treating light incoherence in photovoltaics and its practical consequences,” New J. Phys. 16, 013022 (2014).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Optica (1)

Phys. Status Solidi B (1)

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[Crossref]

Proc. SPIE (3)

K. Jäger, G. Köppel, C. Barth, M. Hammerschmidt, S. Herrmann, S. Burger, F. Schmidt, and C. Becker, “Sinusoidal gratings for optimized light management in c-Si thin-film solar cells,” Proc. SPIE 9898, 989808 (2016).
[Crossref]

D. Lockau, L. Zschiedrich, S. Burger, F. Schmidt, F. Ruske, and B. Rech, “Rigorous optical simulation of light management in crystalline silicon thin film solar cells with rough interface textures,” Proc. SPIE 7933, 79330M (2011).
[Crossref]

K. Jäger, G. Köppel, D. Eisenhauer, D. Chen, M. Hammerschmidt, S. Burger, and C. Becker, “Optical simulations of advanced light management for liquid-phase crystallized silicon thin-film solar cells,” Proc. SPIE 10356, 103560F (2017).

Prog. Photovolt: Res. Appl. (1)

O. Isabella, S. Solntsev, D. Caratelli, and M. Zeman, “3-D optical modeling of thin-film silicon solar cells on diffraction gratings,” Prog. Photovolt: Res. Appl. 21, 94–108 (2013).
[Crossref]

Progress In Electromagnetics Research (1)

A. Campa, J. Krc, and M. Topic, “Two approaches for incoherent propagation of light in rigorous numerical simulations,” Progress In Electromagnetics Research 137, 187–202 (2013).
[Crossref]

Sol. Energ. Mat. Sol. C. (1)

C. T. Trinh, N. Preissler, P. Sonntag, M. Muske, K. Jäger, M. Trahms, R. Schlatmann, B. Rech, and D. Amkreutz, “Potential of interdigitated back-contact silicon heterojunction solar cells for liquid phase crystallized silicon on glass with efficiency above 14%,” Sol. Energ. Mat. Sol. C. 174, 187–195 (2018).
[Crossref]

Other (4)

M. E. Verdet, Leçons d’Optique Physique (L’Imprimerie Impériale, 1869).

E. Hecht, Optics (Pearson Higher Education, Harlow, England, 2016), 5th ed.

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, 2002).

K. Jäger, M. Hammerschmidt, G. Köppel, S. Burger, and C. Becker, “On accurate simulations of thin-film solar cells with a thick glass superstrate,” in “Light, Energy and the Environment,” (Optical Society of America, 2016), p. PM3B.5.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Cross section through a periodic unit cell (enclosed by the green box) with a sinusoidal interface [14] and the glass and silicon half spaces above and below the unit cell. The a posteriori corrections described in this paper account for the interaction of light, which is reflected from the unit cell back into the glass half space, with the glass-air interface, depicted in red. The intensities are named as in Section 2: I0, a and I0 are the incident intensities in air and glass, respectively, and Rg is the reflectivity of the air-glass interface; all three variables must be treated for both polarizations. I out j is the vector of all intensities emitted from the unit cell in the jth correction order. The glass-air interface reflects the intensities I in j back towards the unit cell. ρj is the contribution of the jth correction order to the total reflectivity. (b) The sinusoidal texture used in the simulations, which is generated according to Eq. (14). (c) Atomic force microscopy (AFM) measurements of a sinusoidally nanotextured sol-gel layer on glass with 750 nm pitch and about 150 nm texture height, hence an aspect ratio of about a = 20%.
Fig. 2
Fig. 2 Angles of the diffraction orders into which a hexagonal periodic structure with a pitch of (a) P = 500 nm and (b) P = 750 nm scatters light at normal incidence. The figure shows the angles in glass and in air. The zeroth diffraction order (θg = θa ≡ 0) is not shown. Experimental data is available in the wavelength range (350–600 nm) – this range is marked by the white boxes. In glass, the diffraction orders are present up to much longer wavelength than in air, which is also illustrated in (c). For P = 750 nm, also the 4th and 5th diffraction orders are present in glass at short wavelengths, but in (b) they are omitted for clarity.
Fig. 3
Fig. 3 Numerical and experimental 1 − R spectra for the nanotextured layer stacks illustrated in Fig. 1(a) with (a) 500 nm pitch and (b) 750 nm pitch. Numerical results were calculated with the 0th-order correction [Eq. (2)], the 1st-order correction [Eq. (13)], and iterated using the scattering matrix, until convergence was reached for the threshold τ = 10−4 [Eq. (12)]. The 0th-order correction differs strongly from the other curves because not all diffraction orders that are present in glass can propagate into air [see Fig. 2]. Simulation and experimental results are shown for θin = 8°.
Fig. 4
Fig. 4 The correction order required to reach convergence with τ = 10−4 [red line, see Eq. (12)] for a nanotexture with 750 nm pitch and 25% aspect ratio at normal incidence. Further, the number of directions N is shown, into which the nanotexture diffracts light in glass [cyan dots]. For three wavelengths, these directions are shown on the right. The numbers correspond to the polar angles. More information is given in [14].
Fig. 5
Fig. 5 Simulated and experimental mean 1 − R between 350 and 600 nm wavelength for a nanotexture pitch of (a) P = 500 nm and (b) 750 nm. All results are shown for θin = 8°.

Equations (14)

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

R p ( λ ) = 1 | E i , p g ( λ ) | 2 cos θ i g ( λ ) n | E n , p g ( λ ) | 2 cos θ n g ( λ ) ,
R p 0 ( λ ) = R p ( λ ) [ 1 R p g ( λ ) ] + R p g ( λ ) ,
G p q = p g 1 + p g 2 ,
g 1 = 4 π 3 P ( 1 2 , 3 2 ) , g 2 = 4 π 3 P ( 1 2 , + 3 2 ) .
| k p q , in | = | G p q O + k i | k i .
k p q , in = k i 2 | k p q , in | 2
S b a = | E b a g | 2 cos θ b cos θ a ,
I out j = S I in j 1 .
ρ j = I out j T ,
I in , a j = I out , a j R a .
R ( λ ) = j = 1 ρ j ( λ ) + 1 2 [ R p g ( λ ) + R s g ( λ ) ] .
ρ R 1 < τ ,
R 1 = 1 | E i a | 2 cos θ i a n [ ( t n s E s , n g ) 2 + ( t n p E p , n g ) 2 ] cos θ n a + R g .
f ( x , y ) = cos ( x ) cos [ 1 2 ( x + 3 y ) ] cos [ 1 2 ( x 3 y ) ] .

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