Abstract

Broadband omnidirectional antireflection (AR) coatings for solar cells optimized using simulated annealing (SA) algorithm incorporated with the solar (irradiance) spectrum at Earth’s surface (AM1.57 radiation) are described. Material dispersions and reflections from the planar backside metal are considered in the rigorous electromagnetic calculations. Optimized AR coatings for bulk crystalline Si and thin-film CuIn1–xGaxSe2 (CIGS) solar cells as two representative cases are presented and the effect of solar spectrum in the AR coating designs is investigated. In general, the angle-averaged reflectance of a solar-spectrum-incorporated AR design is shown to be smaller and more uniform in the spectral range with relatively stronger solar irradiance. By incorporating the transparent conductive and buffer layers as part of the AR coating in CIGS solar cells (2μm-thick CIGS layer), a single MgF2 layer could provide an average reflectance of 8.46% for wavelengths ranging from 350 nm to 1200 nm and incident angles from 0° to 80°.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
    [CrossRef]
  2. C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
    [CrossRef]
  3. S. Wang, X. Z. Yu, and H. T. Fan, “Simple lithographic approach for subwavelength structure antireflection,” Appl. Phys. Lett. 91, 061105 (2007).
    [CrossRef]
  4. V. M. Aroutiounian, Kh. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D 39, 1623–1625 (2006).
    [CrossRef]
  5. J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
    [CrossRef]
  6. Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
    [CrossRef]
  7. 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(8), 5290–5298 (2008).
    [CrossRef] [PubMed]
  8. S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93, 251108 (2008).
    [CrossRef]
  9. M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S.-Y. Lin, “Realization of a near-perfect antireflection coating for silicon solar energy utilization,” Opt. Lett. 33(21), 2527–2529 (2008).
    [CrossRef] [PubMed]
  10. D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009).
    [CrossRef] [PubMed]
  11. J. S. Cramer, Econometric Application of Maximum Likelihood Methods (Cambridge University Press, 1986).
    [CrossRef]
  12. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
    [CrossRef] [PubMed]
  13. A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
    [CrossRef]
  14. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).
  15. N. Imam, E. N. Glytsis, and T. K. Gaylord, “Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm,” Supperlattices Microstruct. 30(1), 29–43 (2001).
    [CrossRef]
  16. S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra , 2nd ed. (Prentice-Hall, 1992).
  17. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
    [CrossRef]
  18. E. H. L. Aarts and P. J. M. Van Laarhoven, “Statistical cooling: a general approach to combinatorial optimization problems,” Philips J. Res. 40(4), 193–226 (1985).
  19. T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14(5), 914–927 (1996).
    [CrossRef]
  20. Y.-J. Chang and Y.-C. Liu, “Polarization-insensitive subwavelength sharp bends in asymmetric metal/multi-insulator configuration,” Opt. Express 19(4), 3063–3076 (2011).
    [CrossRef] [PubMed]
  21. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1997).
  22. R. E. Bird, R. L. Hulstrom, A. W. Kliman, and H. G. Eldering, “Solar spectral measurements in the terrestrial environment,” Appl. Opt. 21(8), 1430–1436 (1982).
    [CrossRef] [PubMed]
  23. J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).
  24. S.-D. Mo and W. Y. Ching, “Electronic and optical properties of three phses of titanium dioxide: rutile, anatase, and brookite,” Phys. Rev. B 51(19), 13023–13032 (1995).
    [CrossRef]
  25. M. Pagliaro, G. Palmisano, and R. Ciriminna, Flexible Solar Cells (Wiley-VCH, 2008).
    [CrossRef]
  26. K. Ellmer, A. Klein, and B. Rech, ed., Transparent Conductive Zinc Oxide: Basics and Applications in Thin Film Solar Cells (Springer, 2010).
  27. J. Li, J. Chen, M. N. Sestak, C. Thornberry, and R. W. Collins, “Spectroscopic ellipsometry studies of thin film CdTe and CdS: From dielectric functions to solar cell structures,” in 34th IEEE Photovoltaic Specialists Conf. pp. 001982–001987 (2009).
  28. P. D. Paulson, R. W. Birkmire, and W. N. Shafarmana, “Optical characterization of CuIn1–xGaxSe2 alloy thin films by spectroscopic ellipsometry,” J. Appl. Phys. 94(2), 879–888 (2003).
    [CrossRef]
  29. Y. Hamakawa, ed., Thin-Film Solar Cells: Next Generation Photovoltaics and its Applications (Springer, 2010).
  30. T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).
  31. R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
    [CrossRef]
  32. S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
    [CrossRef]
  33. M. J. Dodge, “Refractive properties of magnesium fluoride,” Appl. Opt. 23(12), 1980–1985 (1984).
    [CrossRef] [PubMed]

2011

2010

J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
[CrossRef]

2009

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009).
[CrossRef] [PubMed]

2008

2007

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

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[CrossRef]

S. Wang, X. Z. Yu, and H. T. Fan, “Simple lithographic approach for subwavelength structure antireflection,” Appl. Phys. Lett. 91, 061105 (2007).
[CrossRef]

2006

V. M. Aroutiounian, Kh. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D 39, 1623–1625 (2006).
[CrossRef]

2003

P. D. Paulson, R. W. Birkmire, and W. N. Shafarmana, “Optical characterization of CuIn1–xGaxSe2 alloy thin films by spectroscopic ellipsometry,” J. Appl. Phys. 94(2), 879–888 (2003).
[CrossRef]

2001

N. Imam, E. N. Glytsis, and T. K. Gaylord, “Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm,” Supperlattices Microstruct. 30(1), 29–43 (2001).
[CrossRef]

1999

R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
[CrossRef]

Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
[CrossRef]

1996

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14(5), 914–927 (1996).
[CrossRef]

1995

S.-D. Mo and W. Y. Ching, “Electronic and optical properties of three phses of titanium dioxide: rutile, anatase, and brookite,” Phys. Rev. B 51(19), 13023–13032 (1995).
[CrossRef]

1987

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
[CrossRef]

1985

E. H. L. Aarts and P. J. M. Van Laarhoven, “Statistical cooling: a general approach to combinatorial optimization problems,” Philips J. Res. 40(4), 193–226 (1985).

1984

1983

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

1982

1953

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

Aarts, E. H. L.

E. H. L. Aarts and P. J. M. Van Laarhoven, “Statistical cooling: a general approach to combinatorial optimization problems,” Philips J. Res. 40(4), 193–226 (1985).

Aroutiounian, V. M.

V. M. Aroutiounian, Kh. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D 39, 1623–1625 (2006).
[CrossRef]

Batchelor, W.

R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
[CrossRef]

Bhattacharya, R. N.

R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
[CrossRef]

Bird, R. E.

Birkmire, R. W.

P. D. Paulson, R. W. Birkmire, and W. N. Shafarmana, “Optical characterization of CuIn1–xGaxSe2 alloy thin films by spectroscopic ellipsometry,” J. Appl. Phys. 94(2), 879–888 (2003).
[CrossRef]

Chang, Y.-J.

Chen, L.

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[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 thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Chhajed, S.

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93, 251108 (2008).
[CrossRef]

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(8), 5290–5298 (2008).
[CrossRef] [PubMed]

Ching, W. Y.

S.-D. Mo and W. Y. Ching, “Electronic and optical properties of three phses of titanium dioxide: rutile, anatase, and brookite,” Phys. Rev. B 51(19), 13023–13032 (1995).
[CrossRef]

Ciriminna, R.

M. Pagliaro, G. Palmisano, and R. Ciriminna, Flexible Solar Cells (Wiley-VCH, 2008).
[CrossRef]

Corana, A.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
[CrossRef]

Cramer, J. S.

J. S. Cramer, Econometric Application of Maximum Likelihood Methods (Cambridge University Press, 1986).
[CrossRef]

Dodge, M. J.

Eldering, H. G.

Fan, H. T.

S. Wang, X. Z. Yu, and H. T. Fan, “Simple lithographic approach for subwavelength structure antireflection,” Appl. Phys. Lett. 91, 061105 (2007).
[CrossRef]

Fons, P.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Foss, S. E.

J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
[CrossRef]

Friedberg, S. H.

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra , 2nd ed. (Prentice-Hall, 1992).

Gaylord, T. K.

N. Imam, E. N. Glytsis, and T. K. Gaylord, “Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm,” Supperlattices Microstruct. 30(1), 29–43 (2001).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Glytsis, E. N.

N. Imam, E. N. Glytsis, and T. K. Gaylord, “Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm,” Supperlattices Microstruct. 30(1), 29–43 (2001).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

Guo, L. Q.

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

Hane, K.

Hiltner, J. F.

R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
[CrossRef]

Hulstrom, R. L.

Imam, N.

N. Imam, E. N. Glytsis, and T. K. Gaylord, “Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm,” Supperlattices Microstruct. 30(1), 29–43 (2001).
[CrossRef]

Insel, A. J.

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra , 2nd ed. (Prentice-Hall, 1992).

Ishizaki, H.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Ishizuka, S.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Jiang, B.

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[CrossRef]

Jianga, P.

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[CrossRef]

Kanamori, Y.

Kanda, Y.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Kijima, S.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Kim, J. K.

Kim, Y. S.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Kliman, A. W.

Komiya, Y.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Kuo, M.-L.

Lin, S.-Y.

M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S.-Y. Lin, “Realization of a near-perfect antireflection coating for silicon solar energy utilization,” Opt. Lett. 33(21), 2527–2529 (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 thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Linn, N. C.

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[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 thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Liu, Y.-C.

Marchesi, M.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
[CrossRef]

Marstein, E. S.

J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
[CrossRef]

Martini, C.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
[CrossRef]

Martirosyan, Kh.

V. M. Aroutiounian, Kh. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D 39, 1623–1625 (2006).
[CrossRef]

Matsubara, K.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Metropolis, N.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

Min, W.-L.

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[CrossRef]

Mo, S.-D.

S.-D. Mo and W. Y. Ching, “Electronic and optical properties of three phses of titanium dioxide: rutile, anatase, and brookite,” Phys. Rev. B 51(19), 13023–13032 (1995).
[CrossRef]

Mont, F. W.

Nakada, T.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Niki, S.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Ohmori, D.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Pagliaro, M.

M. Pagliaro, G. Palmisano, and R. Ciriminna, Flexible Solar Cells (Wiley-VCH, 2008).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1997).

Palmisano, G.

M. Pagliaro, G. Palmisano, and R. Ciriminna, Flexible Solar Cells (Wiley-VCH, 2008).
[CrossRef]

Paulson, P. D.

P. D. Paulson, R. W. Birkmire, and W. N. Shafarmana, “Optical characterization of CuIn1–xGaxSe2 alloy thin films by spectroscopic ellipsometry,” J. Appl. Phys. 94(2), 879–888 (2003).
[CrossRef]

Poxson, D. J.

Ridella, S.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
[CrossRef]

Rosenbluth, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

Rosenbluth, M.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

Sakurai, K.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Sasaki, M.

Schubert, E. F.

Schubert, M. F.

D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009).
[CrossRef] [PubMed]

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(8), 5290–5298 (2008).
[CrossRef] [PubMed]

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93, 251108 (2008).
[CrossRef]

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

Selj, J. H.

J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
[CrossRef]

Shafarmana, W. N.

P. D. Paulson, R. W. Birkmire, and W. N. Shafarmana, “Optical characterization of CuIn1–xGaxSe2 alloy thin films by spectroscopic ellipsometry,” J. Appl. Phys. 94(2), 879–888 (2003).
[CrossRef]

Shibata, H.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Sites, J. R.

R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
[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 thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Soukiassian, P.

V. M. Aroutiounian, Kh. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D 39, 1623–1625 (2006).
[CrossRef]

Spence, L. E.

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra , 2nd ed. (Prentice-Hall, 1992).

Sun, C.-H.

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[CrossRef]

Tamir, T.

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14(5), 914–927 (1996).
[CrossRef]

Tao, M.

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

Teller, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

Thogersen, A.

J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
[CrossRef]

Tummala, R.

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

Van Laarhoven, P. J. M.

E. H. L. Aarts and P. J. M. Van Laarhoven, “Statistical cooling: a general approach to combinatorial optimization problems,” Philips J. Res. 40(4), 193–226 (1985).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Wang, S.

S. Wang, X. Z. Yu, and H. T. Fan, “Simple lithographic approach for subwavelength structure antireflection,” Appl. Phys. Lett. 91, 061105 (2007).
[CrossRef]

Wang, Y.

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

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 thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Yamada, A.

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

Yamada, N.

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

Yu, X. Z.

S. Wang, X. Z. Yu, and H. T. Fan, “Simple lithographic approach for subwavelength structure antireflection,” Appl. Phys. Lett. 91, 061105 (2007).
[CrossRef]

Zhang, S.

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14(5), 914–927 (1996).
[CrossRef]

Zhou, W.

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

ACM. Trans. Math. Softw.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continous variables with the “Simulated Annealing” algorithm,” ACM. Trans. Math. Softw. 13(3), 262–280 (1987).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. N. Bhattacharya, W. Batchelor, J. F. Hiltner, and J. R. Sites, “Thin-film CuIn1–xGaxSe2 photovoltaic cells from solution-based precursor layers,” Appl. Phys. Lett. 75, 1431 (1999).
[CrossRef]

S. Ishizuka, H. Shibata, A. Yamada, P. Fons, K. Sakurai, K. Matsubara, and S. Niki, “Growth of polycrystalline Cu(In,Ga)Se2 thin films using a radio frequency-cracked Se-radical beam source and application for photovoltaic devices,” Appl. Phys. Lett. 91, 041902 (2007).
[CrossRef]

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93, 251108 (2008).
[CrossRef]

C.-H. Sun, W.-L. Min, N. C. Linn, P. Jianga, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91, 231105 (2007).
[CrossRef]

S. Wang, X. Z. Yu, and H. T. Fan, “Simple lithographic approach for subwavelength structure antireflection,” Appl. Phys. Lett. 91, 061105 (2007).
[CrossRef]

J. Appl. Phys.

J. H. Selj, A. Thogersen, S. E. Foss, and E. S. Marstein, “Optimization of multilayer porous silicon antireflection coatings for silicon solar cells,” J. Appl. Phys. 107, 074904 (2010).
[CrossRef]

Y. Wang, R. Tummala, L. Chen, L. Q. Guo, W. Zhou, and M. Tao, “Solution-processed omnidirectional antireflection coatings on amorphous silicon solar cells,” J. Appl. Phys. 105, 103501 (2009).
[CrossRef]

P. D. Paulson, R. W. Birkmire, and W. N. Shafarmana, “Optical characterization of CuIn1–xGaxSe2 alloy thin films by spectroscopic ellipsometry,” J. Appl. Phys. 94(2), 879–888 (2003).
[CrossRef]

J. Chem. Phys.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1090 (1953).
[CrossRef]

J. Lightwave Technol.

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14(5), 914–927 (1996).
[CrossRef]

J. Phys. D

V. M. Aroutiounian, Kh. Martirosyan, and P. Soukiassian, “Almost zero reflectance of a silicon oxynitride/porous silicon double layer antireflection coating for silicon photovoltaic cells,” J. Phys. D 39, 1623–1625 (2006).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Philips J. Res.

E. H. L. Aarts and P. J. M. Van Laarhoven, “Statistical cooling: a general approach to combinatorial optimization problems,” Philips J. Res. 40(4), 193–226 (1985).

Phys. Rev. B

S.-D. Mo and W. Y. Ching, “Electronic and optical properties of three phses of titanium dioxide: rutile, anatase, and brookite,” Phys. Rev. B 51(19), 13023–13032 (1995).
[CrossRef]

Science

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Supperlattices Microstruct.

N. Imam, E. N. Glytsis, and T. K. Gaylord, “Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm,” Supperlattices Microstruct. 30(1), 29–43 (2001).
[CrossRef]

Other

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra , 2nd ed. (Prentice-Hall, 1992).

J. S. Cramer, Econometric Application of Maximum Likelihood Methods (Cambridge University Press, 1986).
[CrossRef]

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

M. Pagliaro, G. Palmisano, and R. Ciriminna, Flexible Solar Cells (Wiley-VCH, 2008).
[CrossRef]

K. Ellmer, A. Klein, and B. Rech, ed., Transparent Conductive Zinc Oxide: Basics and Applications in Thin Film Solar Cells (Springer, 2010).

J. Li, J. Chen, M. N. Sestak, C. Thornberry, and R. W. Collins, “Spectroscopic ellipsometry studies of thin film CdTe and CdS: From dielectric functions to solar cell structures,” in 34th IEEE Photovoltaic Specialists Conf. pp. 001982–001987 (2009).

Y. Hamakawa, ed., Thin-Film Solar Cells: Next Generation Photovoltaics and its Applications (Springer, 2010).

T. Nakada, Y. Kanda, S. Kijima, Y. Komiya, D. Ohmori, H. Ishizaki, and N. Yamada, “Bifacial CIGS thin film solar cells,” in Proc. 20th Eur. Photovoltaic Sol. Energy Conf. , pp. 1736–1739 (Fraunhofer ISE, 2005).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 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 (5)

Fig. 1
Fig. 1

Two-dimensional structure and the associated transmission-line network for the reflectance calculation of a general solar cell with a backside metal.

Fig. 2
Fig. 2

Calculated reflectance R(λ, θ) (averaged over TE and TM polarization) of a polished crystalline Si substrate with an SA-optimized three-layer AR coating given in Table 1 for (a) λ = [400, 750] nm, θ = [40°, 80°] and (b) λ = [400, 1100] nm, θ = [0°, 80°].

Fig. 3
Fig. 3

Calculated angle-averaged reflectance spectrum of an SA-optimized AR coating for metal-backed Si solar cells with (a) and without (b) the solar spectrum consideration. The Si layer is assumed 300 μm in thickness and the incident angle θ ranges from 0° to 80°. The electromagnetic model is shown as an inset; ARC: antireflection coating, PEC: perfect electric conductor.

Fig. 4
Fig. 4

Calculated angle-averaged (θ = [0°, 80°]) reflectance spectrum for CIGS solar cells with (a) and without (b) the solar spectrum consideration. The CIGS layer has a thickness of 2 μm. The electromagnetic model is shown as an inset; ARC: antireflection coating, PEC: perfect electric conductor.

Fig. 5
Fig. 5

The reflectance R(λ, θ) averaged over TE and TM polarization of (a) a single MgF2 layer and (b) a two-layer AR coating for CIGS solar cells. The CIGS structure is shown in the inset of Fig. 4.

Tables (4)

Tables Icon

Table 1 Comparisons Between Layer Thickness (in nm) and Average Reflectance R ave (Averaged over Incident Angles, Wavelengths, and Polarization) for a Three-Layer AR Coating on Top of a Polished Crystalline Si Substrate Obtained Using a Genetic Algorithm [8] and the Present SA Algorithm

Tables Icon

Table 2 Refractive Index n and Thickness t (in nm) of Individual Layers in SA-Optimized AR Coatings for Bulk Crystalline Si Solar Cells with Back Reflectors*

Tables Icon

Table 3 Layer Thickness (in nm) and Average Reflectance R ave of an SiO2/TiO2 Double-Layer AR Coating for Metal-Backed 300-μm-Thick Crystalline Si Solar Cells

Tables Icon

Table 4 Refractive Index n and Layer Thickness t (in nm) of Individual Layers in SA-Optimized AR Coatings for CuIn1−x Ga x Se2| x=0.31 Solar Cells*

Equations (11)

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

X _ k + 1 = X _ k + r V ͇ e _ u T ,
v u = { v u [ 1 + c u ( n acpt ( u ) / N S 0.6 0.4 ) ] if n acpt ( u ) > 0.6 N S , v u [ 1 + c u ( 0.4 n acpt ( u ) / N S 0.4 ) ] 1 if n acpt ( u ) > 0.4 N S , v u , otherwise ,
T 0 = Δ C ¯ ( + ) [ ln m 2 m 2 χ + ( χ 1 ) m 1 ] 1 ,
Z 0 , i = { ω μ 0 / κ i TE wave κ i / ( ω ɛ 0 ɛ i ) TM wave ,
κ i = 2 π λ ɛ i ɛ a sin 2 θ ,
Γ ( λ , θ ) = Z L , 0 + Z 0 , a Z L , 0 + + Z 0 , a ,
Z in , i = Z 0 , i ( 1 + Γ i , i + 1 e j 2 κ i t i 1 Γ i , i + 1 e j 2 κ i t i ) ,
Γ i , i + 1 = Z in , i + 1 Z 0 , i Z in , i + 1 + Z 0 , i .
C ( X _ ) = 1 2 Δ λ Δ θ Δ λ Δ θ w ( λ ) [ | Γ TE ( λ , θ ) | 2 + | Γ TM ( λ , θ ) | 2 ] d θ d λ
w ( λ ) = I λ / Δ λ I λ d λ ,
R θ ave ( λ ) = 1 2 Δ θ Δ θ [ | Γ TE ( λ , θ ) | 2 + | Γ TM ( λ , θ ) | 2 ] d θ ,

Metrics