Abstract

We propose a new figure of merit to assess the performance of light trapping nanostructures for solar cells, which we call the light trapping efficiency (LTE). The LTE has a target value of unity to represent the performance of an ideal Lambertian scatterer, although this is not an absolute limit but rather a benchmark value. Since the LTE aims to assess the nanostructure itself, it is, in principle, independent of the material, fabrication method or technology used. We use the LTE to compare numerous proposals in the literature and to identify the most promising light trapping strategies. We find that different types of photonic structures allow approaching the Lambertian limit, which shows that the light trapping problem can be approached from multiple directions. The LTE of theoretical structures significantly exceeds that of experimental structures, which highlights the need for theoretical descriptions to be more comprehensive and to take all relevant electro-optic effects into account.

© 2014 Optical Society of America

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2013 (6)

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013).
[CrossRef]

D. Lockau, T. Sontheimer, C. Becker, E. Rudigier-Voigt, F. Schmidt, and B. Rech, “Nanophotonic light trapping in 3-dimensional thin-film silicon architectures,” Opt. Express 21(S1), A42–A52 (2013).
[CrossRef] [PubMed]

N. T. Fofang, T. S. Luk, M. Okandan, G. N. Nielson, and I. Brener, “Substrate-modified scattering properties of silicon nanostructures for solar energy applications,” Opt. Express 21(4), 4774–4782 (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(S2), A295–A304 (2013).
[CrossRef] [PubMed]

2012 (5)

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(S2Suppl 2), A224–A244 (2012).
[CrossRef] [PubMed]

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(9), 094504 (2012).
[CrossRef]

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

2011 (2)

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

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

2010 (2)

S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010).
[CrossRef] [PubMed]

S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010).
[CrossRef] [PubMed]

2009 (1)

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[CrossRef]

2008 (1)

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

2007 (1)

2006 (1)

C. Haase and H. Stiebig, “Optical Properties of Thin-film Silicon Solar Cells with Grating Couplers,” Prog. Photovolt. Res. Appl. 14(7), 629–641 (2006).
[CrossRef]

2004 (1)

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

2002 (1)

M. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: Analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

1996 (1)

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

1995 (1)

M. A. Green and M. J. Keevers, “Optical Properties of Intrinsic Silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

1987 (1)

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

1984 (1)

T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984).
[CrossRef]

1982 (1)

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

Agrawal, M.

Altermatt, P. P.

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

Andreani, L. C.

Ballif, 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(9), 094504 (2012).
[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(9), 094504 (2012).
[CrossRef]

Becker, C.

Benick, J.

Berginski, M.

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

Bermel, P.

Bläsi, B.

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(9), 094504 (2012).
[CrossRef]

Bozzola, A.

Brendel, R.

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

Brener, I.

Broderick, L. Z.

X. Sheng, L. Z. Broderick, and L. C. Kimerling, “Photonic crystal structures for light trapping in thin-film Si solar cells: Modeling, process and optimizations,” Opt. Commun.in press.

Brooks, B.

T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984).
[CrossRef]

Campbell, P.

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

Chen, G.

S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010).
[CrossRef] [PubMed]

Chen, Z.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Cody, G.

T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984).
[CrossRef]

Cody, G. D.

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

Cui, Y.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

Depauw, V.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

Dewan, R.

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[CrossRef]

Eisenlohr, J.

El Daif, O.

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

Fan, S.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

Fofang, N. T.

Gjessing, J.

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

Goetzberger, A.

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

Gordijn, A.

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

Gordon, I.

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

Green, M.

M. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: Analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

Green, M. A.

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

M. A. Green and M. J. Keevers, “Optical Properties of Intrinsic Silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

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

Guttowski, A.

Haase, C.

C. Haase and H. Stiebig, “Optical Properties of Thin-film Silicon Solar Cells with Grating Couplers,” Prog. Photovolt. Res. Appl. 14(7), 629–641 (2006).
[CrossRef]

Haase, F.

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

Han, S. E.

S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010).
[CrossRef] [PubMed]

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(9), 094504 (2012).
[CrossRef]

Hauser, H.

Hozuki, N.

H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013).
[CrossRef]

Hüpkes, J.

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

Jäger-Waldau, A.

A. Jäger-Waldau, JRC PV Status Report2013, http://iet.jrc.ec.europa.eu/remea/pv-status-report-2013 .

Joannopoulos, J. D.

Jovanov, V.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

Keevers, M. J.

M. A. Green and M. J. Keevers, “Optical Properties of Intrinsic Silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

Kimerling, L. C.

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007).
[CrossRef] [PubMed]

X. Sheng, L. Z. Broderick, and L. C. Kimerling, “Photonic crystal structures for light trapping in thin-film Si solar cells: Modeling, process and optimizations,” Opt. Commun.in press.

Knipp, D.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[CrossRef]

Kondo, M.

H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013).
[CrossRef]

Krauss, T. F.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Li, J.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Liscidini, M.

Liu, V.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

Liu, Y.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Lockau, D.

Luk, T. S.

Luo, C.

Luque, A.

Magnus, P.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

Mallick, S. B.

Marstein, E. S.

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

Marti, A.

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

Martí, A.

Martins, E. R.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Mellor, A.

Müller, J.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Nielson, G. N.

Okandan, M.

Petermann, J. H.

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

Peters, M.

Peumans, P.

Planchoke, U.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

Poortmans, J.

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

Rech, B.

D. Lockau, T. Sontheimer, C. Becker, E. Rudigier-Voigt, F. Schmidt, and B. Rech, “Nanophotonic light trapping in 3-dimensional thin-film silicon architectures,” Opt. Express 21(S1), A42–A52 (2013).
[CrossRef] [PubMed]

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Reetz, W.

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

Rojas, E. G.

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

Rudigier-Voigt, E.

Sai, H.

H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013).
[CrossRef]

Saito, K.

H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013).
[CrossRef]

Schmidt, F.

Schmidt, J.

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

Sheng, X.

X. Sheng, L. Z. Broderick, and L. C. Kimerling, “Photonic crystal structures for light trapping in thin-film Si solar cells: Modeling, process and optimizations,” Opt. Commun.in press.

Sontheimer, T.

Springer, J.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Stiebig, H.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

C. Haase and H. Stiebig, “Optical Properties of Thin-film Silicon Solar Cells with Grating Couplers,” Prog. Photovolt. Res. Appl. 14(7), 629–641 (2006).
[CrossRef]

Sudbø, A. S.

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

Tiedje, T.

T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984).
[CrossRef]

Tobias, I.

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

Tobías, I.

Trompoukis, C.

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

Vanecek, M.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Wang, A.

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

Wang, K. X.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

Wätjen, T.

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

Wellens, C.

Wenham, S. R.

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

Wuttig, M.

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

Yablonovitch, E.

T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984).
[CrossRef]

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

Yu, Z.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

Zeng, L.

Zhao, J.

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

Zhou, J.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Zielke, D.

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

Appl. Phys. Lett. (2)

H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013).
[CrossRef]

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012).
[CrossRef]

IEEE Trans. Electron. Dev. (2)

T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984).
[CrossRef]

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

J. Appl. Phys. (4)

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[CrossRef]

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

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(9), 094504 (2012).
[CrossRef]

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

Nano Lett. (2)

S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010).
[CrossRef] [PubMed]

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012).
[CrossRef] [PubMed]

Nat Commun (1)

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013).
[CrossRef] [PubMed]

Opt. Express (6)

Prog. Photovolt. Res. Appl. (4)

C. Haase and H. Stiebig, “Optical Properties of Thin-film Silicon Solar Cells with Grating Couplers,” Prog. Photovolt. Res. Appl. 14(7), 629–641 (2006).
[CrossRef]

J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012).
[CrossRef]

M. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: Analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

M. A. Green and M. J. Keevers, “Optical Properties of Intrinsic Silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

Sol. Energy (1)

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Sol. Energy Mater. Sol. Cells (4)

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

J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996).
[CrossRef]

M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008).
[CrossRef]

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

Other (11)

V. Depauw, X. Meng, O. El Daif, G. Gomard, L. Lalouat, E. Drouard, C. Trompoukis, A. Fave, C. Seassal, and I. Gordon, “Micrometer-Thin Crystalline-Silicon Solar Cells Integrating Numerically Optimized 2-D Photonic Crystals,” IEEE J Phot., in press (2013).

O. Isabella, A. Ingenito, D. Linssen, and M. Zeman, “Front/Rear Decoupled Texturing in Refractive and Diffractive Regimes for Ultra-Thin Silicon-Based Solar Cells,” Renewable Energy and the Environment, OSA Technical Digest, paper PM4C.2 (2013).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, 1985).

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X. Sheng, L. Z. Broderick, and L. C. Kimerling, “Photonic crystal structures for light trapping in thin-film Si solar cells: Modeling, process and optimizations,” Opt. Commun.in press.

F. Feldmann, M. Bivour, C. Reichel, M. Hermle, and S.W. Glunz, “A Passivated Rear Contact for High-Efficiency n-Type Si Solar Cells Enabling High Voc's and FF>82%,” 28th EU PVSEC, 2CO.4.4 (2013).

L. Wang, J. Han, A. Lochtefeld, A. Gerger, M. Carroll, D. Stryker, S. Bengtson, M. Curtin, H. Li, Y. Yao, D. Lin, J. Ji, A.J. Lennon, R.L. Opila, and A. Barnett, “16.8% Efficient Ultra-Thin Silicon Solar Cells on Steel,” 28th EU PVSEC, 3DV.1.12 (2013).

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Figures (4)

Fig. 1
Fig. 1

Short-circuit currents as a function of the absorber thickness. The JMB and Jmin graphs correspond to currents generated by a double pass traversal of light in the absorber layer with (blue solid) and without (black dotted) perfect anti-reflection coating, respectively. The JLL refers to devices textured with an ideal Lambertian scatterer and perfect anti-reflection coating (red-dashed line). All devices have a perfect mirror on the back.

Fig. 2
Fig. 2

The performance of a scatterer relies on the refractive index contrast and thus on the materials between the structures. Therefore, the LTE is defined for the total thickness ttot of the absorber material that includes the scattering layer.

Fig. 3
Fig. 3

The calculated light trapping efficiency (LTE) of proposed c-Si structures in literature. All µc-Si:H data points were also qualitatively assessed with the optical constants of c-Si [17]. While the LTE is, in principle, independent of absorber thickness, we note that the highest performing structures operate in the 1µm - 5µm range, which we believe is motivated by the fact that the benefit of light trapping is maximum in this thickness range. We also note that solar cells with the highest efficiency (e.g. the PERL cell of [18]) are not necessarily the best light trapping structures, which highlights the difference between the LTE and the absolute efficiency as well as the importance of anti-reflection coating, as already shown in Fig. 1.

Fig. 4
Fig. 4

When randomization of light at the scattering layer allows to neglect coherent effects, the propagation of an average light ray in a lossy waveguide is described by the external reflection Rext, the internal effective reflectances Rf and Rb and the attenuated transmissions T+ and T respective to a single-pass traversal Tsp.

Tables (3)

Tables Icon

Table 1 Experimental structures using c-Si.

Tables Icon

Table 2 Experimental structures using µc-Si:H (qualitatively assessed with c-Si [17]).

Tables Icon

Table 3 Numerical structures using c-Si (considering the best proposal in each reference).

Equations (9)

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

J LL ( t tot )= J sun e hc 300nm 1200nm λ 1+ n 2 ( 1 T r 2 T r 2 ) d I sun dλ dλ.
T r ( t tot )=exp( α eff t tot )=2 0 π/2 cosθexp(α t tot /cosθ) sinθdθ.
J MB ( t tot )= J sun e hc 300nm 1200nm λ d I sun dλ exp(2α t tot )dλ .
J min ( t tot )= J sun e hc 300nm 1200nm ( n1 n+1 ) 2 λ d I sun dλ exp(2α t tot )dλ.
LTE= J max J ref J LL J MB .
η C a r n o t = T a b s T 0 T a b s 0 ,
A=1RT =1[ R ext +(1 R ext )(1 R f ) R b T T + m=0 ( R b R f T T + ) m ] [ (1 R ext )(1 R b )T m=0 ( R b R f T T + ) m ] =(1 R ext ) (1T)+ R b T[ 1 T + + R f ( 1 T /T ) T + ] 1 R b R f T T +
A = ( 1 R ext ) ( 1 T r )( 1+ R b T r ) 1 R b R f T r 2 .                 
A=(1 R ext ) 1 T r 2 + T r 2 / n 2 T r 2 / n 2 1(11/ n 2 ) T r 2 =1 1 1+ (1 T r 2 ) T r 2 n 2 .

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