Abstract

We numerically investigate the light-absorption behavior of thin-film silicon for normal-incident light, using surface textures to enhance absorption. We consider a variety of texture designs, such as simple periodic gratings and commercial random textures, and examine arbitrary irregular periodic textures designed by multi-parameter optimization. Deep and high-index-contrast textures exhibit strong anisotropic scattering that is outside the regime of validity of the Lambertian models commonly used to describe texture-induced absorption enhancement for normal incidence. Over a 900–1100 nm wavelength range, our optimized surface texture in two dimensions (2D) enhances absorption by a factor of 2.7πn, considerably larger than the original πn Lambertian result and exceeding by almost 50% a recent generalization of Lambertian model for periodic structures in finite spectral range. However, the πn Lambertian limit still applies for isotropic incident light, and our structure obeys this limit when averaged over all the angles. Therefore, our design can be thought of optimizing the angle/enhancement tradeoff for periodic textures.

© 2011 OSA

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2011 (3)

A. Naqavi, K. Soderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19(1), 128–140 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-1-128 .
[CrossRef] [PubMed]

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

Z. Yu and S. Fan, “Angular constraint on light-trapping absorption enhancement in solar cells,” Appl. Phys. Lett. 98(1), 011106 (2011), http://link.aip.org/link/doi/10.1063/1.3532099 .
[CrossRef]

2010 (7)

J. Wang, J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Cavity-enhanced multispectral photodetector using phase-tuned propagation: theory and design,” Opt. Lett. 35(5), 742–744 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-5-742 .
[CrossRef] [PubMed]

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
[CrossRef]

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-6-5691 .
[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), http://dx.doi.org/10.1021/nl1029804 .
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010), http://dx.doi.org/10.1073/pnas.1008296107 .
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S3-A366 .
[CrossRef] [PubMed]

C. Lin and M. L. Povinelli, “The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays,” Appl. Phys. Lett. 97(7), 071110 (2010), http://link.aip.org/link/doi/10.1063/1.3475484 .
[CrossRef]

2009 (4)

2008 (4)

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Opt. Express 16(19), 15238–15248 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-19-15238 .
[CrossRef] [PubMed]

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008), http://dx.doi.org/10.1016/j.solmat.2008.07.021 .
[CrossRef]

2007 (2)

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-16986 .
[CrossRef] [PubMed]

C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116–061119 (2007), http://link.aip.org/link/doi/10.1063/1.2768882 .
[CrossRef]

2006 (1)

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

2005 (2)

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81(2-3), 235–244 (2005), http://dx.doi.org/10.1007/s00340-005-1877-3 .
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86(11), 111114 (2005), http://link.aip.org/link/doi/10.1063/1.1885170 .
[CrossRef]

2004 (1)

1999 (1)

D. C. Dobson and S. J. Cox, “Maximizing Band Gaps in Two-Dimensional Photonic Crystals,” SIAM J. Appl. Math. 59(6), 2108–2120 (1999), http://dx.doi.org/10.1137/S0036139998338455 .
[CrossRef]

1998 (1)

M. J. D. Powell, “Direct search algorithms for optimization calculations,” Acta. Numerica 7, 287–336 (1998), http://dx.doi.org/10.1017/S0962492900002841 .
[CrossRef]

1997 (1)

1995 (1)

1992 (1)

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

1983 (1)

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983), http://link.aip.org/link/doi/10.1063/1.94432 .
[CrossRef]

1982 (1)

Adachi, K.

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

Agarwal, A.

Agarwal, A. M.

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

Agrawal, M.

Alamariu, B. A.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Atwater, H. A.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
[CrossRef]

Avniel, Y.

Ballif, C.

Barnett, A.

Bermel, P.

Bloch, A. N.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983), http://link.aip.org/link/doi/10.1063/1.94432 .
[CrossRef]

Borel, P.

Broderick, K. A.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

Chen, C.

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), http://dx.doi.org/10.1021/nl1029804 .
[CrossRef] [PubMed]

Chutinan, A.

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

Cox, S. J.

D. C. Dobson and S. J. Cox, “Maximizing Band Gaps in Two-Dimensional Photonic Crystals,” SIAM J. Appl. Math. 59(6), 2108–2120 (1999), http://dx.doi.org/10.1137/S0036139998338455 .
[CrossRef]

Creazzo, T.

Cui, Y.

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
[CrossRef]

Dewan, R.

Dobson, D. C.

D. C. Dobson and S. J. Cox, “Maximizing Band Gaps in Two-Dimensional Photonic Crystals,” SIAM J. Appl. Math. 59(6), 2108–2120 (1999), http://dx.doi.org/10.1137/S0036139998338455 .
[CrossRef]

Duan, X.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Fan, S.

Z. Yu and S. Fan, “Angular constraint on light-trapping absorption enhancement in solar cells,” Appl. Phys. Lett. 98(1), 011106 (2011), http://link.aip.org/link/doi/10.1063/1.3532099 .
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010), http://dx.doi.org/10.1073/pnas.1008296107 .
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S3-A366 .
[CrossRef] [PubMed]

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
[CrossRef]

Feng, N.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Ferry, V. E.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
[CrossRef]

Frandsen, L.

Frei, W. R.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86(11), 111114 (2005), http://link.aip.org/link/doi/10.1063/1.1885170 .
[CrossRef]

Ghebrebrhan, M.

Gotoh, Y.

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

Haase, C.

C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116–061119 (2007), http://link.aip.org/link/doi/10.1063/1.2768882 .
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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), http://dx.doi.org/10.1021/nl1029804 .
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Haug, F.-J.

Hayasahi, Y.

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

Heine, C.

Herzig, H. P.

Hong, C.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Honsberg, C.

Hsu, C. M.

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
[CrossRef]

Hu, J.

Jensen, J.

Joannopoulos, J. D.

John, S.

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

Johnson, H. T.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86(11), 111114 (2005), http://link.aip.org/link/doi/10.1063/1.1885170 .
[CrossRef]

Johnson, S. G.

Kao, C. Y.

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81(2-3), 235–244 (2005), http://dx.doi.org/10.1007/s00340-005-1877-3 .
[CrossRef]

Kherani, N. P.

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

Kimerling, L. C.

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
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[CrossRef]

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-16986 .
[CrossRef] [PubMed]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Knipp, D.

Kozinsky, I.

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

Kristensen, M.

Li, H. B. T.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
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A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008), http://dx.doi.org/10.1016/j.solmat.2008.07.021 .
[CrossRef]

Lin, C.

C. Lin and M. L. Povinelli, “The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays,” Appl. Phys. Lett. 97(7), 071110 (2010), http://link.aip.org/link/doi/10.1063/1.3475484 .
[CrossRef]

C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express 17(22), 19371–19381 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19371 .
[CrossRef] [PubMed]

Liu, J.

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Luo, C.

Mallick, S. B.

Marinkovic, M.

Michel, J.

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

Morf, R. H.

Mutitu, J. G.

Naqavi, A.

Nishimura, H.

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

Noriega, R.

O’Brien, P. G.

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

Osher, S.

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81(2-3), 235–244 (2005), http://dx.doi.org/10.1007/s00340-005-1877-3 .
[CrossRef]

Ozin, G. A.

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

Paeder, V.

Peumans, P.

Phadke, S.

Phillips, J.

A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008), http://dx.doi.org/10.1016/j.solmat.2008.07.021 .
[CrossRef]

Polman, A.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
[CrossRef]

Povinelli, M. L.

C. Lin and M. L. Povinelli, “The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays,” Appl. Phys. Lett. 97(7), 071110 (2010), http://link.aip.org/link/doi/10.1063/1.3475484 .
[CrossRef]

C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express 17(22), 19371–19381 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19371 .
[CrossRef] [PubMed]

Powell, M. J. D.

M. J. D. Powell, “Direct search algorithms for optimization calculations,” Acta. Numerica 7, 287–336 (1998), http://dx.doi.org/10.1017/S0962492900002841 .
[CrossRef]

Prather, D. W.

Raman, A.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010), http://dx.doi.org/10.1073/pnas.1008296107 .
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S3-A366 .
[CrossRef] [PubMed]

Salleo, A.

Sato, K.

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

Scharf, T.

Schropp, R. E. I.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
[CrossRef]

Sheng, P.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983), http://link.aip.org/link/doi/10.1063/1.94432 .
[CrossRef]

Sheng, X.

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

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Shi, S.

Sigmund, O.

Soderström, K.

Stepleman, R. S.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983), http://link.aip.org/link/doi/10.1063/1.94432 .
[CrossRef]

Stiebig, H.

C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116–061119 (2007), http://link.aip.org/link/doi/10.1063/1.2768882 .
[CrossRef]

Stuart, H. R.

Sun, X.

Tortorelli, D. A.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86(11), 111114 (2005), http://link.aip.org/link/doi/10.1063/1.1885170 .
[CrossRef]

Verschuuren, M. A.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
[CrossRef]

Wakayama, Y.

K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayasahi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).

Wang, J.

Yablonovitch, E.

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81(2-3), 235–244 (2005), http://dx.doi.org/10.1007/s00340-005-1877-3 .
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E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982), http://www.opticsinfobase.org/abstract.cfm?URI=josa-72-7-899 .
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L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Yu, Z.

Z. Yu and S. Fan, “Angular constraint on light-trapping absorption enhancement in solar cells,” Appl. Phys. Lett. 98(1), 011106 (2011), http://link.aip.org/link/doi/10.1063/1.3532099 .
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010), http://dx.doi.org/10.1073/pnas.1008296107 .
[CrossRef] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S3-A366 .
[CrossRef] [PubMed]

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
[CrossRef]

Zeng, L.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-16986 .
[CrossRef] [PubMed]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

Zhu, J.

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
[CrossRef]

Zukotynski, S.

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

Acta. Numerica (1)

M. J. D. Powell, “Direct search algorithms for optimization calculations,” Acta. Numerica 7, 287–336 (1998), http://dx.doi.org/10.1017/S0962492900002841 .
[CrossRef]

Adv. Mater. (Deerfield Beach Fla.) (2)

P. G. O’Brien, N. P. Kherani, A. Chutinan, G. A. Ozin, S. John, and S. Zukotynski, “Silicon Photovoltaics Using Conducting Photonic Crystal Back-Reflectors,” Adv. Mater. (Deerfield Beach Fla.) 20(8), 1577–1582 (2008), http://dx.doi.org/10.1002/adma.200702219 .
[CrossRef]

X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.) 23(7), 843–847 (2011), http://dx.doi.org/10.1002/adma.201003217 .
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81(2-3), 235–244 (2005), http://dx.doi.org/10.1007/s00340-005-1877-3 .
[CrossRef]

Appl. Phys. Lett. (8)

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86(11), 111114 (2005), http://link.aip.org/link/doi/10.1063/1.1885170 .
[CrossRef]

Z. Yu and S. Fan, “Angular constraint on light-trapping absorption enhancement in solar cells,” Appl. Phys. Lett. 98(1), 011106 (2011), http://link.aip.org/link/doi/10.1063/1.3532099 .
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006), http://link.aip.org/link/doi/10.1063/1.2349845 .
[CrossRef]

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983), http://link.aip.org/link/doi/10.1063/1.94432 .
[CrossRef]

C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116–061119 (2007), http://link.aip.org/link/doi/10.1063/1.2768882 .
[CrossRef]

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008), http://link.aip.org/link/doi/10.1063/1.3039787 .
[CrossRef]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009), http://link.aip.org/link/doi/10.1063/1.3256187 .
[CrossRef]

C. Lin and M. L. Povinelli, “The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays,” Appl. Phys. Lett. 97(7), 071110 (2010), http://link.aip.org/link/doi/10.1063/1.3475484 .
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nano Lett. (2)

J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010), http://dx.doi.org/10.1021/nl9034237 .
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Figures (5)

Fig. 1
Fig. 1

(left) Schematic device structure for a thin-film Si solar cell with a textured Si / SiO2 interface. The averaged thicknesses for Si and SiO2 layers are 1.5 μm and 0.5 μm, respectively. (right) Different types of texture we investigate are symmetric triangular grating, asymmetric sawtooth grating and general periodic structures with Fourier series.

Fig. 2
Fig. 2

(a) Schematic device structure with symmetric triangular grating. (b) Plot of the absorption enhancement factor (F) as a function of the grating period Λ and thickness t. The arrow indicates the optimal parameters. (c) Absorption spectrum of the optimal structure (Λ = 920 nm and t = 520 nm), obtaining F = 1.26πn.

Fig. 3
Fig. 3

(a) Schematic device structure with asymmetric sawtooth grating. (b) Plot of the absorption enhancement factor (F) as a function of the grating period Λ and thickness t. The arrow indicates the optimal parameters. (c) Absorption spectrum of the optimal structure (Λ = 920 nm and t = 240 nm), obtaining F = 2.04πn.

Fig. 4
Fig. 4

Summary of the calculated maximum enhancement factors F in Section 3 and comparison with Yu’s model in Ref [24]. and commercial Asahi glass. The insets indicate the structures with the best performance achieved in our optimizations. (a) Asymmetric structures. (b) Symmetric structures.

Fig. 5
Fig. 5

Angular dependence of the optimized asymmetric structures obtained in Fig. 4a.

Tables (1)

Tables Icon

Table 1 Optimized Structural Parameters For Asymmetric Structures, With F = 2.70πn. The Units For A 1, B 1, A 2, B 2t ox And Λ Are nm. B 5 Is Set To A Constant 0.

Equations (6)

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F = 1 λ 2 λ 1 λ 1 λ 2 A ( λ ) d λ α d ,
H ( x ) = 500 + n = 1 ( A n sin ( 2 π n Λ x ) + B n cos ( 2 π n Λ x ) ) ,
F = F ( A 1 , B 1 , A 2 , B 2 , ... , Λ ) .
F ( Λ ) = 1 λ 2 λ 1 λ 1 λ 2 ( Λ λ Λ λ + 1 2 ) d λ π n for asymmetric structures
F ( Λ ) = 1 λ 2 λ 1 λ 1 λ 2 ( Λ λ Λ λ + 1 ) d λ π n for symmetric structures
F a v g = 1 2 π 2 π 2 F ( θ ) cos θ d θ

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