Abstract

Absorption enhancement in thin metal-backed solar cells caused by dipole scatterers embedded in the absorbing layer is studied using a semi-analytical approach. The method accounts for changes in the radiation rate produced by layers above and below the dipole, and treats incoherently the subsequent scattering of light in guided modes from other dipoles. We find large absorption enhancements for strongly coupled dipoles, exceeding the ergodic limit in some configurations involving lossless dipoles. An antireflection-coated 100-nm layer of a-Si:H on Ag absorbs up to 87% of incident above-gap light. Thin layers of both strong and weak absorbers show similar strongly enhanced absorption.

© 2009 Optical Society of America

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  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. C. H. Henry, "Limiting efficiencies of ideal single and multiple energy-gap terrestrial solar-cells," J. Appl. Phys. 51, 4494-4500 (1980).
    [CrossRef]
  3. K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
    [CrossRef]
  4. P. Campbell and M. A. Green, "Light trapping properties of pyramidally textured surfaces," J. Appl. Phys. 62, 243-249 (1987).
    [CrossRef]
  5. S. S. Hegedus and X. Deng, "Analysis of optical enhancement in a-si n-i-p solar cells using a detachable back reflector," Conference Record of the 25th IEEE Photovoltaic Specialists Conference pp. 1061-1064 (1996).
  6. H. R. Stuart and D. G. Hall, "Thermodynamic limit to light trapping in thin planar structures," J. Opt. Soc. Am. A 14, 3001-3008 (1997).
    [CrossRef]
  7. H. Stuart and D. G. Hall, "Island size effects in nanoparticle-enhanced photodetectors," Appl. Phys. Lett. 73, 3815-3817 (1998).
    [CrossRef]
  8. B. Soller and D. G. Hall, "Energy transfer at optical frequencies to silicon-based waveguiding structures," J. Opt. Soc. Am. A 18, 2577-2584 (2001).
    [CrossRef]
  9. D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
    [CrossRef]
  10. K. Nakayama, K. Tanabe, and H. Atwater, "Plasmonic nanoparticle enhanced light absorption in GaAs solar cells," Appl. Phys. Lett. 93, 121904 (2008).
    [CrossRef]
  11. K. R. Catchpole and S. Pillai, "Absorption enhancement due to scattering by dipoles into silicon waveguides," J. Appl. Phys. 100, 044504 (2006).
    [CrossRef]
  12. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
    [CrossRef]
  13. F. J. Beck, A. Polman, and K. R. Catchpole, "Tunable light trapping for solar cells using localized surface plasmons," J. Appl. Phys. 105, 114310 (2009).
    [CrossRef]
  14. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
    [CrossRef]
  15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, A Wiley-Interscience publication (Wiley, 1983).
  16. The law of refraction is usually attributed (in English-speaking countries) to the Dutch astronomer and mathematician Willebrord Snel van Royen, which he enunciated in 1621, although some scholars argue that the law was first discovered by Ibn Sahl in 984.
  17. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge University Press, 1999).
  18. E. Yablonovitch and G. D. Cody, "Intensity enhancement in textured optical sheets for solar-cells," IEEE Trans. Electron. Devices 29, 300-305 (1982).
    [CrossRef]
  19. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
    [CrossRef]
  20. P. Sheng, "Optical absorption of thin film on a Lambertian reflector substrate," IEEE Trans. Electron. Devices ED-31, 634-636 (1984).
    [CrossRef]
  21. J. E. Sipe, "The dipole antenna problem in surface physics: a new approach," Surf. Sci. 105, 498-504 (1981).
    [CrossRef]
  22. G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rpt. 113, 195-287 (1984).
    [CrossRef]
  23. H. Benisty, R. Stanley, and M. Mayer, "Method of source terms for dipole emission modification in modes of arbitrary planar structures," J. Opt. Soc. Am. A 15, 1192-1201 (1998).
    [CrossRef]
  24. W. L. Barnes, "Fluorescence near interfaces: The role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
    [CrossRef]
  25. J. C. Mertz, "Radiative absorption, fluorescence, and scattering of a classical dipole near a lossless interface: a unified description," J. Opt. Soc. Am. B 17, 1906-1913 (2000).
    [CrossRef]
  26. A. C. Hryciw, Y. C. Jun, and M. L. Brongersma, "Plasmon-enhanced emission from optically-doped MOS light sources," Opt. Express 17, 185-192 (2009).
    [CrossRef] [PubMed]
  27. F. Leblanc, J. Perrin, and J. Schmitt, "Numerical modeling of the optical properties of hydrogenated amorphoussilicon-based p-i-n solar cells deposited on rough transparent conducting oxide substrates," J. Appl. Phys. 75, 1074-1087 (1994).
    [CrossRef]
  28. D. Poitras and J. Dobrowolski, "Toward perfect antireflection coatings. 2. Theory," Appl. Opt. 43, 1286-1295 (2004).
    [CrossRef] [PubMed]
  29. M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, L. K. Kim, E. F. Schubert, and S.-Y. Lin, "Realization of a near-perfect antireflection coating for silicon solar energy utilization," Opt. Lett. 33, 2527-2529 (2008).
    [CrossRef] [PubMed]
  30. ASTM G-173-03 (accessed 30 September 2008).http://rredc.nrel.gov/solar/spectra/ am1.5/.

2009 (2)

F. J. Beck, A. Polman, and K. R. Catchpole, "Tunable light trapping for solar cells using localized surface plasmons," J. Appl. Phys. 105, 114310 (2009).
[CrossRef]

A. C. Hryciw, Y. C. Jun, and M. L. Brongersma, "Plasmon-enhanced emission from optically-doped MOS light sources," Opt. Express 17, 185-192 (2009).
[CrossRef] [PubMed]

2008 (3)

M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, L. K. Kim, E. F. Schubert, and S.-Y. Lin, "Realization of a near-perfect antireflection coating for silicon solar energy utilization," Opt. Lett. 33, 2527-2529 (2008).
[CrossRef] [PubMed]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
[CrossRef]

K. Nakayama, K. Tanabe, and H. Atwater, "Plasmonic nanoparticle enhanced light absorption in GaAs solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

2007 (1)

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

2006 (2)

K. R. Catchpole and S. Pillai, "Absorption enhancement due to scattering by dipoles into silicon waveguides," J. Appl. Phys. 100, 044504 (2006).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

2004 (1)

2001 (1)

2000 (1)

1998 (3)

H. Benisty, R. Stanley, and M. Mayer, "Method of source terms for dipole emission modification in modes of arbitrary planar structures," J. Opt. Soc. Am. A 15, 1192-1201 (1998).
[CrossRef]

W. L. Barnes, "Fluorescence near interfaces: The role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
[CrossRef]

H. Stuart and D. G. Hall, "Island size effects in nanoparticle-enhanced photodetectors," Appl. Phys. Lett. 73, 3815-3817 (1998).
[CrossRef]

1997 (1)

1994 (1)

F. Leblanc, J. Perrin, and J. Schmitt, "Numerical modeling of the optical properties of hydrogenated amorphoussilicon-based p-i-n solar cells deposited on rough transparent conducting oxide substrates," J. Appl. Phys. 75, 1074-1087 (1994).
[CrossRef]

1992 (1)

K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
[CrossRef]

1987 (1)

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

1984 (3)

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rpt. 113, 195-287 (1984).
[CrossRef]

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
[CrossRef]

P. Sheng, "Optical absorption of thin film on a Lambertian reflector substrate," IEEE Trans. Electron. Devices ED-31, 634-636 (1984).
[CrossRef]

1982 (1)

E. Yablonovitch and G. D. Cody, "Intensity enhancement in textured optical sheets for solar-cells," IEEE Trans. Electron. Devices 29, 300-305 (1982).
[CrossRef]

1981 (1)

J. E. Sipe, "The dipole antenna problem in surface physics: a new approach," Surf. Sci. 105, 498-504 (1981).
[CrossRef]

1980 (1)

C. H. Henry, "Limiting efficiencies of ideal single and multiple energy-gap terrestrial solar-cells," J. Appl. Phys. 51, 4494-4500 (1980).
[CrossRef]

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]

Atwater, H.

K. Nakayama, K. Tanabe, and H. Atwater, "Plasmonic nanoparticle enhanced light absorption in GaAs solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Atwater, H. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
[CrossRef]

Barnes, W. L.

W. L. Barnes, "Fluorescence near interfaces: The role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
[CrossRef]

Beck, F. J.

F. J. Beck, A. Polman, and K. R. Catchpole, "Tunable light trapping for solar cells using localized surface plasmons," J. Appl. Phys. 105, 114310 (2009).
[CrossRef]

Benisty, H.

Brongersma, M. L.

Brooks, B. G.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
[CrossRef]

Campbell, P.

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

Catchpole, K. R.

F. J. Beck, A. Polman, and K. R. Catchpole, "Tunable light trapping for solar cells using localized surface plasmons," J. Appl. Phys. 105, 114310 (2009).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

K. R. Catchpole and S. Pillai, "Absorption enhancement due to scattering by dipoles into silicon waveguides," J. Appl. Phys. 100, 044504 (2006).
[CrossRef]

Cody, G. D.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
[CrossRef]

E. Yablonovitch and G. D. Cody, "Intensity enhancement in textured optical sheets for solar-cells," IEEE Trans. Electron. Devices 29, 300-305 (1982).
[CrossRef]

Daub, E.

K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
[CrossRef]

Derkacs, D.

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Dobrowolski, J.

Ferry, V. E.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
[CrossRef]

Finkbeiner, S.

K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
[CrossRef]

Ford, G. W.

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rpt. 113, 195-287 (1984).
[CrossRef]

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

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

Hall, D. G.

Henry, C. H.

C. H. Henry, "Limiting efficiencies of ideal single and multiple energy-gap terrestrial solar-cells," J. Appl. Phys. 51, 4494-4500 (1980).
[CrossRef]

Hryciw, A. C.

Jun, Y. C.

Kim, L. K.

Kim, Y. S.

Kuo, M.-L.

Leblanc, F.

F. Leblanc, J. Perrin, and J. Schmitt, "Numerical modeling of the optical properties of hydrogenated amorphoussilicon-based p-i-n solar cells deposited on rough transparent conducting oxide substrates," J. Appl. Phys. 75, 1074-1087 (1994).
[CrossRef]

Lim, S. H.

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Lin, S.-Y.

Mar, W.

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Matheu, P.

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Mayer, M.

Mertz, J. C.

Mont, F. W.

Nakayama, K.

K. Nakayama, K. Tanabe, and H. Atwater, "Plasmonic nanoparticle enhanced light absorption in GaAs solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Pacifici, D.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
[CrossRef]

Perrin, J.

F. Leblanc, J. Perrin, and J. Schmitt, "Numerical modeling of the optical properties of hydrogenated amorphoussilicon-based p-i-n solar cells deposited on rough transparent conducting oxide substrates," J. Appl. Phys. 75, 1074-1087 (1994).
[CrossRef]

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

K. R. Catchpole and S. Pillai, "Absorption enhancement due to scattering by dipoles into silicon waveguides," J. Appl. Phys. 100, 044504 (2006).
[CrossRef]

Poitras, D.

Polman, A.

F. J. Beck, A. Polman, and K. R. Catchpole, "Tunable light trapping for solar cells using localized surface plasmons," J. Appl. Phys. 105, 114310 (2009).
[CrossRef]

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]

Schick, K.

K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
[CrossRef]

Schmitt, J.

F. Leblanc, J. Perrin, and J. Schmitt, "Numerical modeling of the optical properties of hydrogenated amorphoussilicon-based p-i-n solar cells deposited on rough transparent conducting oxide substrates," J. Appl. Phys. 75, 1074-1087 (1994).
[CrossRef]

Schubert, E. F.

Sheng, P.

P. Sheng, "Optical absorption of thin film on a Lambertian reflector substrate," IEEE Trans. Electron. Devices ED-31, 634-636 (1984).
[CrossRef]

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]

Sipe, J. E.

J. E. Sipe, "The dipole antenna problem in surface physics: a new approach," Surf. Sci. 105, 498-504 (1981).
[CrossRef]

Soller, B.

Stanley, R.

Stuart, H.

H. Stuart and D. G. Hall, "Island size effects in nanoparticle-enhanced photodetectors," Appl. Phys. Lett. 73, 3815-3817 (1998).
[CrossRef]

Stuart, H. R.

Sweatlock, L. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
[CrossRef]

Tanabe, K.

K. Nakayama, K. Tanabe, and H. Atwater, "Plasmonic nanoparticle enhanced light absorption in GaAs solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Tiedje, T.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
[CrossRef]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

W¨urfel, P.

K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
[CrossRef]

Weber, W. H.

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rpt. 113, 195-287 (1984).
[CrossRef]

Yablonovitch, E.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
[CrossRef]

E. Yablonovitch and G. D. Cody, "Intensity enhancement in textured optical sheets for solar-cells," IEEE Trans. Electron. Devices 29, 300-305 (1982).
[CrossRef]

Yu, E. T.

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A: Mat. Sci. Proc. (1)

K. Schick, E. Daub, S. Finkbeiner, and P. W¨urfel, "Verification of a generalized Planck law for luminescence radiation from silicon solar cells," Appl. Phys. A: Mat. Sci. Proc. 54, 109-114 (1992).
[CrossRef]

Appl. Phys. Lett. (3)

D. Derkacs, S. H. Lim, P. Matheu,W. Mar, and E. T. Yu, "Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles," Appl. Phys. Lett. 89, 093103 (2006).
[CrossRef]

K. Nakayama, K. Tanabe, and H. Atwater, "Plasmonic nanoparticle enhanced light absorption in GaAs solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

H. Stuart and D. G. Hall, "Island size effects in nanoparticle-enhanced photodetectors," Appl. Phys. Lett. 73, 3815-3817 (1998).
[CrossRef]

IEEE Trans. Electron. Devices (3)

E. Yablonovitch and G. D. Cody, "Intensity enhancement in textured optical sheets for solar-cells," IEEE Trans. Electron. Devices 29, 300-305 (1982).
[CrossRef]

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, "Limiting efficiency of silicon solar cells," IEEE Trans. Electron. Devices ED-31, 711-716 (1984).
[CrossRef]

P. Sheng, "Optical absorption of thin film on a Lambertian reflector substrate," IEEE Trans. Electron. Devices ED-31, 634-636 (1984).
[CrossRef]

J. Appl. Phys. (7)

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]

C. H. Henry, "Limiting efficiencies of ideal single and multiple energy-gap terrestrial solar-cells," J. Appl. Phys. 51, 4494-4500 (1980).
[CrossRef]

K. R. Catchpole and S. Pillai, "Absorption enhancement due to scattering by dipoles into silicon waveguides," J. Appl. Phys. 100, 044504 (2006).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

F. J. Beck, A. Polman, and K. R. Catchpole, "Tunable light trapping for solar cells using localized surface plasmons," J. Appl. Phys. 105, 114310 (2009).
[CrossRef]

F. Leblanc, J. Perrin, and J. Schmitt, "Numerical modeling of the optical properties of hydrogenated amorphoussilicon-based p-i-n solar cells deposited on rough transparent conducting oxide substrates," J. Appl. Phys. 75, 1074-1087 (1994).
[CrossRef]

J. Mod. Opt. (1)

W. L. Barnes, "Fluorescence near interfaces: The role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Nano Lett. (1)

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 4391-4397 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rpt. (1)

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rpt. 113, 195-287 (1984).
[CrossRef]

Surf. Sci. (1)

J. E. Sipe, "The dipole antenna problem in surface physics: a new approach," Surf. Sci. 105, 498-504 (1981).
[CrossRef]

Other (5)

S. S. Hegedus and X. Deng, "Analysis of optical enhancement in a-si n-i-p solar cells using a detachable back reflector," Conference Record of the 25th IEEE Photovoltaic Specialists Conference pp. 1061-1064 (1996).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, A Wiley-Interscience publication (Wiley, 1983).

The law of refraction is usually attributed (in English-speaking countries) to the Dutch astronomer and mathematician Willebrord Snel van Royen, which he enunciated in 1621, although some scholars argue that the law was first discovered by Ibn Sahl in 984.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge University Press, 1999).

ASTM G-173-03 (accessed 30 September 2008).http://rredc.nrel.gov/solar/spectra/ am1.5/.

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Figures (8)

Fig. 1.
Fig. 1.

A multilayer structure with an antireflection-coated silicon absorbing layer on top of an optically thick layer of silver. Absorption in each layer is determined by integrating the power flux through the x=0 plane and through the constant-z interfaces between layers. The illustrated modes have been calculated for a 500-nm Si layer on Ag, with a 56-nm TiO2 layer on top, at λ=1100 nm.

Fig. 2.
Fig. 2.

Absorption enhancement η in a silicon layer on silver compared to a single pass at normal incidence for TM modes (left panel) and TE modes (right panel) as a function of the fraction of energy absorbed in the silicon layer. The marker size shows the thickness of the silicon layer from 100 to 1000 nm and color indicates the wavelength. The SPP mode shows significantly smaller enhancement than other modes, decreasing with increasing layer thickness. For the photonic modes, the absorption enhancement tends to rise with layer thickness. Note that the calculation here assumes that light does not scatter out of the mode.

Fig. 3.
Fig. 3.

Normalized decay rate at λ=1100 nm for a dipole in a d=1-µm silicon layer a distance d =50 nm from a silver substrate (solid traces) and 200 nm from the silver layer (dotted traces) as a function of the normalized wave vector component parallel to the surface. The inset illustrates the structure.

Fig. 4.
Fig. 4.

Diffusion model of light propagation inside the multilayer structure. Light is scattered by the dipole on the left into the escape cone, with fraction ρ 0, and into guided modes with fractions ρj . Each guided mode propagates a distance L to the next dipole, with loss in each absorbing layer dependent on the mode. At the next dipole, a fraction Λρj of the remaining light scatters. Its power is added to the unscattered light in each mode.

Fig. 5.
Fig. 5.

Band-edge absorption enhancement (η, left axis) of light leaving a dipole a distance d from the Ag/Si interface, compared to single-pass absorption for a 200-nm Si layer on Ag, as a function of coupling coefficient Λ (L=1 µm, λ=1100 nm). The product Λη (right axis) scales the curves assuming that the initial scattering is also Λ.

Fig. 6.
Fig. 6.

Absorption enhancement of light near the band edge caused by dipoles parallel to the surface of an 800-nm Si layer on Ag. The silicon is covered with a perfect antireflection coating, Λ=1, and L=1 µm. The dashed line shows the ergodic limit for λ=1100 nm in a thick silicon layer. Note that a higher density of points has been computed for d <400 nm.

Fig. 7.
Fig. 7.

TM (left) and TE (right) modes of an 800-nm Si layer on Ag at λ=1100 nm. The shaded curves show the magnitude squared of the parallel component of electric field, and have equal area. The black numbers in each layer show for each guided mode the fraction absorbed in the layer (e.g., for the SPP mode at the lower left, 0.35% is absorbed in the silicon and 99.65% is absorbed in the silver). The fraction of light coupled into each mode for a parallel dipole positions 200 nm (300 nm) from the Ag layer is shown in red (green) at the right of each figure; the fraction coupled into the escape cone is shown at the top.

Fig. 8.
Fig. 8.

Limiting integrated absorption efficiency (IAE) for thin layers of silicon, germanium, amorphous silicon, and gallium arsenide on optically thick Ag layers illuminated with the AM1.5G spectrum [30]. The squares show the IAE for the spectral range near the band edge ( ( 3 4 λ g λ λ g ) ), whereas the circles show the IAE for the same spectral range in the absence of dipole scatterers. The diamonds show IAE for the full spectrum (λ UVλλg ). The semiconductor layers are covered with a perfect antireflection coating. The dipoles are separated by 500 nm for the filled symbols and by 1000 nm for the open symbols.

Equations (28)

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( 2 + n 2 ω ˜ 2 ) E ( r , t ) = 0
E ( r , t ) = E exp [ i ( k · r ωt ) ]
u · u = n 2
u z , j = ( n j 2 u x 2 ) 1 2
E ± ( r , t ) = E ± exp [ i ω ˜ ( u x x ± u z z ) iωt ]
γ ̂ = γ γ free = 0 1 𝒫 free d 𝒫 du x du x
1 𝒫 free d 𝒫 du x = 3 2 n 3 Re { u x u z [ u x 2 r ˜ p cos 2 θ d + sin 2 θ d 2 ( n 2 r ˜ s + u z 2 r ˜ p ) ] }
r ˜ p = [ 1 + r p exp ( 2 ik z d ) ] [ 1 + r + p exp ( 2 ik z d + ) ] 1 r p r + p exp ( 2 ik z d )
r ˜ s = [ 1 + r s exp ( 2 ik z d ) ] [ 1 + r + s exp ( 2 ik z d + ) ] 1 r s r + s exp ( 2 ik z d )
r ˜ p = [ 1 r p exp ( 2 ik z d ) ] [ 1 r + p exp ( 2 ik z d + ) ] 1 r p r + p exp ( 2 ik z d )
A βj ( 0 ) = f βj ( 1 e α j L ) j ( 0 ) = f βj l j j ( 0 )
A β ( 0 ) = j = 1 N A βj ( 0 )
μ ij = Λ ρ i ρ j + δ ij ( 1 Λ ) ρ j
μ ij = Λ ρ i ρ j ( 1 g ̂ ) + δ ij ( 1 Λ ) ρ j
i ( 1 ) = j = 1 N ( 1 l j ) μ ij j ( 0 )
{ ( n ) } = [ F ] { ( n 1 ) } = [ F ] n { ( 0 ) }
{ A } = n = 0 { A ( n ) } = n = 0 [ f ] [ l ] [ F ] n { ( 0 ) } = [ f ] [ l ] ( [ F ] ) 1 { ( 0 ) }
E ( d + ) = E 0 te i ω ˜ nd +
E ( r , t ) = [ E + ( u z x ̂ + u x z ̂ n ) e ik z z + E ( u z x ̂ + u x z ̂ n ) e ik z z ] e i ( k x x ωt )
H ( r , t ) = ( E + e i k z z + E e i k z z ) n e i ( k x x ω t ) y ̂
Φ x TM = 0 d S x d z = c 16 π u x Re [ n * u x n { E + 2 ( 1 e 2 u z ϕ ) u z + E 2 ( e 2 u z ϕ 1 ) u z
+ 2 Im ( E + E * ) sin ( 2 u z ϕ ) u z + 2 Re ( E + E * ) [ cos ( 2 u z ϕ ) 1 ] u z } ]
Φ z TM ( z ) = 0 S z ( z ) d x = Re { c n * u z 16 π n [ E + 2 e 2 k z z E 2 e 2 k z z + 2 i Im ( E + E * e 2 i k z z ) ] }
E ( r , t ) = ( E + e i k z z + E e i k z z ) e i ( k x x ω t ) y ̂
H ( r , t ) = [ E + ( u z x ̂ + u x z ̂ ) e i k z z + E ( u z x ̂ + u x z ̂ ) e i k z z ] e i ( k z x ω t )
Φ x TE = c u x u z 16 π [ E + 2 ( 1 e 2 u z ϕ ) + E 2 ( e 2 u z ϕ 1 ) u z
+ 2 u z ( Re [ E + E * ] sin ( 2 u z ϕ ) Im [ E + E * ] [ 1 cos ( 2 u z ϕ ) ] ) ]
Φ z TE ( z ) = c 16 π [ u z ( E + 2 e 2 k z z E 2 e 2 k z z ) + 2 u z Im ( E + * E e 2 i k z z ) ]

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