Abstract

We suggest a design for a coating that could be applied on top of any solar cell having at least one diffusing surface. This coating acts as an angle and wavelength selective filter, which increases the average path length and absorptance at long wavelengths without altering the solar cell performance at short wavelengths. The filter design is based on a continuous variation of the refractive index in order to minimize undesired reflection losses. Numerical procedures are used to optimize the filter for a 10 µm thick monocrystalline silicon solar cell, which lifts the efficiency above the Auger limit for unconcentrated illumination. The feasibility to fabricate such filters is also discussed, considering a finite available refractive index range.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510-519 (1961).
    [CrossRef]
  2. M. J. Kerr, A. Cuevas, and P. Campbell, "Limiting Efficiency of Crystalline Silicon Solar Cells Due to Coulomb-Enhanced Auger Recombination," Prog. Photovoltaics 11, 97-104 (2002).
    [CrossRef]
  3. D. Redfield, "Multiple-pass thin-film silicon solar cell," Appl. Phys. Lett. 25, 647-648 (1974).
    [CrossRef]
  4. E. Yablonovitch, "Statistical ray optics," J. Opt. Soc. Am. 72, 899-907 (1982).
    [CrossRef]
  5. M. A. Green, "Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions," Prog. Photovoltaics 10, 235-241 (2002).
    [CrossRef]
  6. 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, 16986-17000 (2007).
    [CrossRef] [PubMed]
  7. 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, 111111 (2006).
    [CrossRef]
  8. P. Campbell, "Enhancement of light absorption from randomizing and geometric textures," J. Opt. Soc. Am. B 10, 2410-2415 (1993).
    [CrossRef]
  9. P. Campbell and M. A. Green, "Light trapping properties of pyramidally textured surfaces," J. Appl. Phys. 62, 243-249 (1987).
    [CrossRef]
  10. S. Fahr, C. Rockstuhl, and F. Lederer, "Engineering the randomness for enhanced absorption in solar cells," Appl. Phys. Lett. 92, 171114 (2008).
    [CrossRef]
  11. C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
    [CrossRef]
  12. J. C. Minano, Physical Limitations to Photovoltaic Energy Conversion, chap. Optical confinement in photovoltaics, (Adam Hilger, Bristol, 1990) pp. 50-83 .
  13. D. Buie and A. G. Monger, "The effect of circumsolar radiation on a solar concentrating system," Sol. Energy 76, 181-185 (2004).
    [CrossRef]
  14. C. Ulbrich, S. Fahr, M. Peters, J. Upping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Loper, R.Wehrspohn, A. Gombert, F. Lederer, and U. Rau, "Directional selectivity and light-trapping in solar cells," Photonics for Solar Energy Systems II 7002, 70020A (2008).
  15. J. A. Dobrowolski and D. G. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
    [CrossRef] [PubMed]
  16. P. Baumeister, "Design of multilayer filters by successive approximations," J. Opt. Soc. Am. (1917-1983) 48, 955-958 (1958).
    [CrossRef]
  17. P. G. Verly, A. V. Tikhonravov, and M. K. Trubetskov, "Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings," Appl. Opt. 36, 1487-1495 (1997).
    [CrossRef] [PubMed]
  18. J.-M. Yang and C.-Y. Kao, "An Evolutionary Algorithm for the Synthesis of Multilayer Coatings at Oblique Light Incidence," J. Lightwave Technol. 19, 559-570 (2001).
    [CrossRef]
  19. S. Kirkpatrick, J. Gelatt, C. D. and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
    [CrossRef] [PubMed]
  20. M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, "Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm," Opt. Express 16, 5290-5298 (2008).
    [CrossRef] [PubMed]
  21. W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
    [CrossRef] [PubMed]
  22. R. Jacobsson, "Inhomogeneous and coevaporated homogeneous films for optical applications," Phys. Thin Films 8, 51-98 (1975).
  23. E. Lorenzo, C. J. Oton, N. E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, and L. Pavesi, "Porous silicon-based rugate filters," Appl. Opt. 44, 5415-5421 (2005).
    [CrossRef] [PubMed]
  24. G. Boivin and D. St.-Germain, "Synthesis of gradient-index profiles corresponding to spectral reflectance derived by inverse Fourier transform," Appl. Opt. 26, 4209-4213 (1987).
    [CrossRef] [PubMed]
  25. B. G. Bovard, "Rugate filter theory: an overview," Appl. Opt. 32, 5427-5442 (1993).
    [CrossRef] [PubMed]
  26. W. H. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
    [CrossRef] [PubMed]
  27. W. Southwell, "Using apodization functions to reduce sidelobes in rugate filters," Appl. Opt. 28, 5091-5094 (1989).
    [CrossRef] [PubMed]
  28. M. J. Minot, "The angular reflectance of single-layer gradient refractive-index films," J. Opt. Soc. Am. 67, 1046- 1050 (1977).
    [CrossRef]
  29. W. Southwell, "Omnidirectional Mirror DesignWith Quarter-Wave Dielectric Stacks," Appl. Opt. 38, 5464-5467 (1999).
    [CrossRef]
  30. P. A. Basore and D. A. Clugston, "PC1D Version 5.1" (1997).
  31. M. J. Kerr and A. Cuevas, "General parameterization of Auger recombination in crystalline silicon," J. Appl. Phys. 91, 2473-2480 (2002).
    [CrossRef]
  32. J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Comput. J. 7, 308-313 (1965).
  33. J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).
  34. W. J. Gunning, R. L. Hall, F. J. Woodberry, W. H. Southwell, and N. S. Gluck, "Codeposition of continuous composition rugate filters," Appl. Opt. 28, 2945-2948 (1989).
    [CrossRef] [PubMed]

2008 (3)

S. Fahr, C. Rockstuhl, and F. Lederer, "Engineering the randomness for enhanced absorption in solar cells," Appl. Phys. Lett. 92, 171114 (2008).
[CrossRef]

C. Ulbrich, S. Fahr, M. Peters, J. Upping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Loper, R.Wehrspohn, A. Gombert, F. Lederer, and U. Rau, "Directional selectivity and light-trapping in solar cells," Photonics for Solar Energy Systems II 7002, 70020A (2008).

M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, "Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm," Opt. Express 16, 5290-5298 (2008).
[CrossRef] [PubMed]

2007 (3)

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
[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, 16986-17000 (2007).
[CrossRef] [PubMed]

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, 111111 (2006).
[CrossRef]

2005 (1)

2004 (1)

D. Buie and A. G. Monger, "The effect of circumsolar radiation on a solar concentrating system," Sol. Energy 76, 181-185 (2004).
[CrossRef]

2002 (3)

M. A. Green, "Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions," Prog. Photovoltaics 10, 235-241 (2002).
[CrossRef]

M. J. Kerr, A. Cuevas, and P. Campbell, "Limiting Efficiency of Crystalline Silicon Solar Cells Due to Coulomb-Enhanced Auger Recombination," Prog. Photovoltaics 11, 97-104 (2002).
[CrossRef]

M. J. Kerr and A. Cuevas, "General parameterization of Auger recombination in crystalline silicon," J. Appl. Phys. 91, 2473-2480 (2002).
[CrossRef]

2001 (1)

1999 (1)

1997 (2)

1993 (2)

1989 (2)

1987 (2)

1983 (2)

S. Kirkpatrick, J. Gelatt, C. D. and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
[CrossRef] [PubMed]

1982 (1)

1978 (1)

1977 (1)

1975 (1)

R. Jacobsson, "Inhomogeneous and coevaporated homogeneous films for optical applications," Phys. Thin Films 8, 51-98 (1975).

1974 (1)

D. Redfield, "Multiple-pass thin-film silicon solar cell," Appl. Phys. Lett. 25, 647-648 (1974).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Comput. J. 7, 308-313 (1965).

1961 (1)

W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510-519 (1961).
[CrossRef]

Alamariu, B. A.

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, 111111 (2006).
[CrossRef]

Bermel, P.

Bittkau, K.

C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
[CrossRef]

Boivin, G.

Bovard, B. G.

Buie, D.

D. Buie and A. G. Monger, "The effect of circumsolar radiation on a solar concentrating system," Sol. Energy 76, 181-185 (2004).
[CrossRef]

Campbell, P.

M. J. Kerr, A. Cuevas, and P. Campbell, "Limiting Efficiency of Crystalline Silicon Solar Cells Due to Coulomb-Enhanced Auger Recombination," Prog. Photovoltaics 11, 97-104 (2002).
[CrossRef]

P. Campbell, "Enhancement of light absorption from randomizing and geometric textures," J. Opt. Soc. Am. B 10, 2410-2415 (1993).
[CrossRef]

P. Campbell and M. A. Green, "Light trapping properties of pyramidally textured surfaces," J. Appl. Phys. 62, 243-249 (1987).
[CrossRef]

Capuj, N. E.

Carius, R.

C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
[CrossRef]

Chen, M.

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Chhajed, S.

Cuevas, A.

M. J. Kerr and A. Cuevas, "General parameterization of Auger recombination in crystalline silicon," J. Appl. Phys. 91, 2473-2480 (2002).
[CrossRef]

M. J. Kerr, A. Cuevas, and P. Campbell, "Limiting Efficiency of Crystalline Silicon Solar Cells Due to Coulomb-Enhanced Auger Recombination," Prog. Photovoltaics 11, 97-104 (2002).
[CrossRef]

Dobrowolski, J. A.

Duan, X.

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, 111111 (2006).
[CrossRef]

Fahr, S.

C. Ulbrich, S. Fahr, M. Peters, J. Upping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Loper, R.Wehrspohn, A. Gombert, F. Lederer, and U. Rau, "Directional selectivity and light-trapping in solar cells," Photonics for Solar Energy Systems II 7002, 70020A (2008).

S. Fahr, C. Rockstuhl, and F. Lederer, "Engineering the randomness for enhanced absorption in solar cells," Appl. Phys. Lett. 92, 171114 (2008).
[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, 111111 (2006).
[CrossRef]

Gaburro, Z.

Gelatt, J.

S. Kirkpatrick, J. Gelatt, C. D. and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Ghulinyan, M.

Gluck, N. S.

Green, M. A.

M. A. Green, "Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions," Prog. Photovoltaics 10, 235-241 (2002).
[CrossRef]

P. Campbell and M. A. Green, "Light trapping properties of pyramidally textured surfaces," J. Appl. Phys. 62, 243-249 (1987).
[CrossRef]

Gunning, W. J.

Hall, R. L.

Hong, C.

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, 111111 (2006).
[CrossRef]

Jacobsson, R.

R. Jacobsson, "Inhomogeneous and coevaporated homogeneous films for optical applications," Phys. Thin Films 8, 51-98 (1975).

Joannopoulos, J. D.

Kao, C.-Y.

Kerr, M. J.

M. J. Kerr and A. Cuevas, "General parameterization of Auger recombination in crystalline silicon," J. Appl. Phys. 91, 2473-2480 (2002).
[CrossRef]

M. J. Kerr, A. Cuevas, and P. Campbell, "Limiting Efficiency of Crystalline Silicon Solar Cells Due to Coulomb-Enhanced Auger Recombination," Prog. Photovoltaics 11, 97-104 (2002).
[CrossRef]

Kim, J. K.

M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, "Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm," Opt. Express 16, 5290-5298 (2008).
[CrossRef] [PubMed]

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

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, 16986-17000 (2007).
[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, 111111 (2006).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, J. Gelatt, C. D. and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Lederer, F.

S. Fahr, C. Rockstuhl, and F. Lederer, "Engineering the randomness for enhanced absorption in solar cells," Appl. Phys. Lett. 92, 171114 (2008).
[CrossRef]

C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
[CrossRef]

Lin, S.-Y.

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Liu, J.

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, 111111 (2006).
[CrossRef]

Liu, W.

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Lorenzo, E.

Lowe, D. G.

Luo, C.

Mead, R.

J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Comput. J. 7, 308-313 (1965).

Minot, M. J.

Monger, A. G.

D. Buie and A. G. Monger, "The effect of circumsolar radiation on a solar concentrating system," Sol. Energy 76, 181-185 (2004).
[CrossRef]

Mont, F. W.

Navarro-Urrios, D.

Nelder, J. A.

J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Comput. J. 7, 308-313 (1965).

Oton, C. J.

Pavesi, L.

Peters, M.

C. Ulbrich, S. Fahr, M. Peters, J. Upping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Loper, R.Wehrspohn, A. Gombert, F. Lederer, and U. Rau, "Directional selectivity and light-trapping in solar cells," Photonics for Solar Energy Systems II 7002, 70020A (2008).

Poxson, D. J.

Queisser, H. J.

W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510-519 (1961).
[CrossRef]

Redfield, D.

D. Redfield, "Multiple-pass thin-film silicon solar cell," Appl. Phys. Lett. 25, 647-648 (1974).
[CrossRef]

Rockstuhl, C.

S. Fahr, C. Rockstuhl, and F. Lederer, "Engineering the randomness for enhanced absorption in solar cells," Appl. Phys. Lett. 92, 171114 (2008).
[CrossRef]

C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
[CrossRef]

Schubert, E. F.

M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, "Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm," Opt. Express 16, 5290-5298 (2008).
[CrossRef] [PubMed]

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Schubert, M. F.

M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, "Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm," Opt. Express 16, 5290-5298 (2008).
[CrossRef] [PubMed]

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Shockley, W.

W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510-519 (1961).
[CrossRef]

Smart, J. A.

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Southwell, W.

Southwell, W. H.

St.-Germain, D.

Tikhonravov, A. V.

Trubetskov, M. K.

Ulbrich, C.

C. Ulbrich, S. Fahr, M. Peters, J. Upping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Loper, R.Wehrspohn, A. Gombert, F. Lederer, and U. Rau, "Directional selectivity and light-trapping in solar cells," Photonics for Solar Energy Systems II 7002, 70020A (2008).

Verly, P. G.

Woodberry, F. J.

Xi, J. Q.

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Yablonovitch, E.

Yang, J.-M.

Yi, Y.

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, 111111 (2006).
[CrossRef]

Zeng, L.

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, 16986-17000 (2007).
[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, 111111 (2006).
[CrossRef]

Appl. Opt. (9)

Appl. Phys. Lett. (4)

S. Fahr, C. Rockstuhl, and F. Lederer, "Engineering the randomness for enhanced absorption in solar cells," Appl. Phys. Lett. 92, 171114 (2008).
[CrossRef]

C. Rockstuhl, F. Lederer, K. Bittkau, and R. Carius, "Light localization at randomly textured surfaces for solarcell applications," Appl. Phys. Lett. 91, 1104-1106 (2007).
[CrossRef]

D. Redfield, "Multiple-pass thin-film silicon solar cell," Appl. Phys. Lett. 25, 647-648 (1974).
[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, 111111 (2006).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Comput. J. 7, 308-313 (1965).

J. Appl. Phys. (3)

M. J. Kerr and A. Cuevas, "General parameterization of Auger recombination in crystalline silicon," J. Appl. Phys. 91, 2473-2480 (2002).
[CrossRef]

P. Campbell and M. A. Green, "Light trapping properties of pyramidally textured surfaces," J. Appl. Phys. 62, 243-249 (1987).
[CrossRef]

W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510-519 (1961).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (2)

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

Nat. Photonics (1)

J. Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thinfilm materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Opt. Express (2)

Opt. Lett. (1)

Photonics for Solar Energy Systems II (1)

C. Ulbrich, S. Fahr, M. Peters, J. Upping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Loper, R.Wehrspohn, A. Gombert, F. Lederer, and U. Rau, "Directional selectivity and light-trapping in solar cells," Photonics for Solar Energy Systems II 7002, 70020A (2008).

Phys. Thin Films (1)

R. Jacobsson, "Inhomogeneous and coevaporated homogeneous films for optical applications," Phys. Thin Films 8, 51-98 (1975).

Prog. Photovoltaics (2)

M. A. Green, "Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions," Prog. Photovoltaics 10, 235-241 (2002).
[CrossRef]

M. J. Kerr, A. Cuevas, and P. Campbell, "Limiting Efficiency of Crystalline Silicon Solar Cells Due to Coulomb-Enhanced Auger Recombination," Prog. Photovoltaics 11, 97-104 (2002).
[CrossRef]

Science (1)

S. Kirkpatrick, J. Gelatt, C. D. and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Sol. Energy (1)

D. Buie and A. G. Monger, "The effect of circumsolar radiation on a solar concentrating system," Sol. Energy 76, 181-185 (2004).
[CrossRef]

Other (3)

J. C. Minano, Physical Limitations to Photovoltaic Energy Conversion, chap. Optical confinement in photovoltaics, (Adam Hilger, Bristol, 1990) pp. 50-83 .

P. Baumeister, "Design of multilayer filters by successive approximations," J. Opt. Soc. Am. (1917-1983) 48, 955-958 (1958).
[CrossRef]

P. A. Basore and D. A. Clugston, "PC1D Version 5.1" (1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Schematic drawing of the solar cell considered throughout this paper.

Fig. 2.
Fig. 2.

Transmission of unpolarized light of the ideal wavelength and angle selective filter considered in this paper.

Fig. 3.
Fig. 3.

a) A 1 µm thick quintic continuous refractive index profile going from 1.0 to 3.5. b) The corresponding angle and wavelength dependent transmission of unpolarized light. The structure shows nearly perfect transmission for wavelength to AR-coating thickness ratios smaller than 1.0. The white region corresponds to more than 99% transmission.

Fig. 4.
Fig. 4.

a) Four periods of a binary (dotted), a sinusoidal (dash-dot) and an exponential sinusoidal (solid) refractive index profile for n min=1.0 and n max=3.5 at a design wavelength of λ 0=1.0 µm. b) The corresponding wavelength dependent reflection of each filter.

Fig. 5.
Fig. 5.

a) Exponential sinusoidal refractive index profile (solid line) with quintic amplitude function (dotted line). The dash-dotted line represents the averaged refractive index. b) The angle resolved transmission spectrum shows the desired blue shift of the stop band when tilting the angle of incidence.

Fig. 6.
Fig. 6.

Refractive index profile versus optical thickness for t tot=5 µm, λ 0=1 µm, t apo=0.25×t tot, A max=0.7, n inc=1.0, and n sub=3.5.

Fig. 7.
Fig. 7.

a) Optimized refractive index profile, values were allowed to lie between 1.0 and 3.5. b) Angle resolved transmission spectrum leads to an efficiency of 30.1%.

Fig. 8.
Fig. 8.

a) Quintic refractive index profile and b) angle resolved transmission spectrum for limited refractive index values The parameter n 1 was set to 1.5 and n 2 to 2.0. η=26.1%.

Fig. 9.
Fig. 9.

a) Optimized refractive index profile and b) angle resolved transmission spectrum for limited refractive index values. n min,a was set to 1.5 and n max,a to 2.0. η=26.9%.

Fig. 10.
Fig. 10.

Mean calculated efficiencies (solid black curve) versus relative standard deviation σ of individual layer thickness for the filter shown in (a) Fig. 7 and (b) Fig. 9. The dotted red curves represent the standard deviation corridor of 100 filter modifications.

Tables (1)

Tables Icon

Table 1. Parameters of several filters discussed in this paper.

Equations (11)

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

n ( t n ) = n 1 + ( n 2 n 1 ) ( 6 t n 5 15 t n 4 + 10 t n 3 ) ,
n ( t ) = n min + n max n min 2 [ 1 + sin ( 4 π λ 0 t π 2 ) ] ,
n ( t ) = n min n max exp [ ln ( n max n min ) 2 sin ( 4 π λ 0 t π 2 ) ] .
n min , II = n sub + n inc 2 A max n sub n inc 2
n max , II = n sub + n inc 2 + A max n sub n inc 2 ,
n min , I ( t n , I ) = n inc + ( n min , II n inc ) Q ( t n , I )
n max , I ( t n , I ) = n inc + ( n max , II n inc ) Q ( t n , I ) ,
Q ( x ) = ( 6 x 5 15 x 4 + 10 x 3 )
n min , III ( t n , III ) = n min , II + ( n sub n min , II ) Q ( t n , III )
n max , III ( t n , III ) = n max , II + ( n sub n max , II ) Q ( t n , III ) ,
n ( t ) = n min n max exp [ ln ( n max n min ) 2 sin ( 4 π exp ( Ct t tot C 2 ) λ 0 t π 2 ) ] .

Metrics