Abstract

We analytically investigate the light trapping performance in plasmonic solar cells with Si/metallic structures. We consider absorption enhancements for surface plasmon polaritons (SPPs) at planar Si/metal interfaces and localized surface plasmon resonances (LSPRs) for metallic spheres in a Si matrix. We discover that the enhancement factors at Si/metal interfaces are not bound to the conventional Lambertian limit, and strong absorption can be achieved around plasmonic resonant frequencies. In addition, those enhancements are greatly reduced as the fields decay away from the Si/metal interfaces. Therefore, localized plasmonic resonances can be used as efficient light trapping schemes for ultrathin Si solar cells (< 50 nm), while photonic guided mode enhancement is more appropriate for thicker films.

© 2012 OSA

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Corrections

Xing Sheng, Juejun Hu, Jurgen Michel, and Lionel C. Kimerling, "Light trapping limits in plasmonic solar cells: an analytical investigation: errata," Opt. Express 20, 24699-24700 (2012)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-20-22-24699

References

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  1. R. Brendel, Thin-Film Crystalline Silicon Solar Cells: Physics and Technology (Wiley-VCH Verlag GmbH & Co. KGaA, 2003).
  2. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
    [CrossRef] [PubMed]
  3. H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
    [CrossRef]
  4. X. Sheng, J. Liu, I. Kozinsky, A. M. Agarwal, J. Michel, and L. C. Kimerling, “Design and non-lithographic fabrication of light trapping structures for thin film silicon solar cells,” Adv. Mater. (Deerfield Beach Fla.)23(7), 843–847 (2011).
    [CrossRef] [PubMed]
  5. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93(19), 191113 (2008).
    [CrossRef]
  6. 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(12), 4391–4397 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. E. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
  16. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Verlag, 2007).
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  18. L. Hu, X. Chen, and G. Chen, “Surface-plasmon enhanced near-bandgap light absorption in silicon photovoltaics,” J. Comput. Theor. Nanosci.5(11), 2096–2101 (2008).
    [CrossRef]
  19. J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett.11(6), 2195–2201 (2011).
    [CrossRef] [PubMed]

2012 (2)

D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar cell light trapping beyond the ray optic limit,” Nano Lett.12(1), 214–218 (2012).
[CrossRef] [PubMed]

J. N. Munday, D. M. Callahan, and H. A. Atwater, “Light trapping beyond the 4n2 limit in thin waveguides,” Appl. Phys. Lett.100(12), 121121 (2012).
[CrossRef]

2011 (3)

E. A. Schiff, “Thermodynamic limit to photonic-plasmonic light-trapping in thin films on metals,” J. Appl. Phys.110(10), 104501 (2011).
[CrossRef]

J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett.11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

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

2010 (2)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

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

2009 (1)

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

2008 (3)

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93(19), 191113 (2008).
[CrossRef]

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(12), 4391–4397 (2008).
[CrossRef] [PubMed]

L. Hu, X. Chen, and G. Chen, “Surface-plasmon enhanced near-bandgap light absorption in silicon photovoltaics,” J. Comput. Theor. Nanosci.5(11), 2096–2101 (2008).
[CrossRef]

1999 (1)

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

1997 (1)

1982 (1)

1971 (1)

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys.241(4), 313–324 (1971).
[CrossRef]

Agarwal, A. M.

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

Atwater, H. A.

D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar cell light trapping beyond the ray optic limit,” Nano Lett.12(1), 214–218 (2012).
[CrossRef] [PubMed]

J. N. Munday, D. M. Callahan, and H. A. Atwater, “Light trapping beyond the 4n2 limit in thin waveguides,” Appl. Phys. Lett.100(12), 121121 (2012).
[CrossRef]

J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett.11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[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(12), 4391–4397 (2008).
[CrossRef] [PubMed]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

Brongersma, M. L.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

Callahan, D. M.

D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar cell light trapping beyond the ray optic limit,” Nano Lett.12(1), 214–218 (2012).
[CrossRef] [PubMed]

J. N. Munday, D. M. Callahan, and H. A. Atwater, “Light trapping beyond the 4n2 limit in thin waveguides,” Appl. Phys. Lett.100(12), 121121 (2012).
[CrossRef]

Catchpole, K. R.

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93(19), 191113 (2008).
[CrossRef]

Chen, G.

L. Hu, X. Chen, and G. Chen, “Surface-plasmon enhanced near-bandgap light absorption in silicon photovoltaics,” J. Comput. Theor. Nanosci.5(11), 2096–2101 (2008).
[CrossRef]

Chen, X.

L. Hu, X. Chen, and G. Chen, “Surface-plasmon enhanced near-bandgap light absorption in silicon photovoltaics,” J. Comput. Theor. Nanosci.5(11), 2096–2101 (2008).
[CrossRef]

Fan, S.

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

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(12), 4391–4397 (2008).
[CrossRef] [PubMed]

Fischer, D.

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

Hall, D. G.

Hu, L.

L. Hu, X. Chen, and G. Chen, “Surface-plasmon enhanced near-bandgap light absorption in silicon photovoltaics,” J. Comput. Theor. Nanosci.5(11), 2096–2101 (2008).
[CrossRef]

Keppner, H.

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

Kimerling, L. C.

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

Kozinsky, I.

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

Kretschmann, E.

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys.241(4), 313–324 (1971).
[CrossRef]

Liu, J.

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

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

Meier, J.

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

Michel, J.

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

Munday, J. N.

D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar cell light trapping beyond the ray optic limit,” Nano Lett.12(1), 214–218 (2012).
[CrossRef] [PubMed]

J. N. Munday, D. M. Callahan, and H. A. Atwater, “Light trapping beyond the 4n2 limit in thin waveguides,” Appl. Phys. Lett.100(12), 121121 (2012).
[CrossRef]

J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett.11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

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(12), 4391–4397 (2008).
[CrossRef] [PubMed]

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93(19), 191113 (2008).
[CrossRef]

Raman, A.

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

Schiff, E. A.

E. A. Schiff, “Thermodynamic limit to photonic-plasmonic light-trapping in thin films on metals,” J. Appl. Phys.110(10), 104501 (2011).
[CrossRef]

Shah, A.

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

Sheng, X.

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

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(12), 4391–4397 (2008).
[CrossRef] [PubMed]

Torres, P.

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

White, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

Yablonovitch, E.

Yu, Z.

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

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

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

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009.
[CrossRef]

Appl. Phys. Lett. (2)

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93(19), 191113 (2008).
[CrossRef]

J. N. Munday, D. M. Callahan, and H. A. Atwater, “Light trapping beyond the 4n2 limit in thin waveguides,” Appl. Phys. Lett.100(12), 121121 (2012).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

H. Keppner, J. Meier, P. Torres, D. Fischer, and A. Shah, “Microcrystalline silicon and micromorph tandem solar cells,” Appl. Phys., A Mater. Sci. Process.69(2), 169–177 (1999), .
[CrossRef]

J. Appl. Phys. (1)

E. A. Schiff, “Thermodynamic limit to photonic-plasmonic light-trapping in thin films on metals,” J. Appl. Phys.110(10), 104501 (2011).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

L. Hu, X. Chen, and G. Chen, “Surface-plasmon enhanced near-bandgap light absorption in silicon photovoltaics,” J. Comput. Theor. Nanosci.5(11), 2096–2101 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nano Lett. (3)

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(12), 4391–4397 (2008).
[CrossRef] [PubMed]

D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar cell light trapping beyond the ray optic limit,” Nano Lett.12(1), 214–218 (2012).
[CrossRef] [PubMed]

J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett.11(6), 2195–2201 (2011).
[CrossRef] [PubMed]

Nat. Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

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

Z. Phys. (1)

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys.241(4), 313–324 (1971).
[CrossRef]

Other (4)

R. Brendel, Thin-Film Crystalline Silicon Solar Cells: Physics and Technology (Wiley-VCH Verlag GmbH & Co. KGaA, 2003).

E. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Verlag, 2007).

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

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Figures (3)

Fig. 1
Fig. 1

Different light trapping mechanisms existing in a Si/metal composite solar cell structure. (1) Photonic guided modes induced by various optical scattering due to spatial inhomogeneity. (2) Propagating surface plasmon polaritons (SPPs) at planar Si/metal interface. (3) Localized surface plasmon resonances (LSPRs) induced by metal particles in the dielectric medium.

Fig. 2
Fig. 2

(a) Schematic device geometry illustrating the SPP mode at the Si/metal interface; (b) Absorption enhancement FSPP as a function of wavelength in the thin Si region (d ≈0); (c) Peak value of FSPP as a function of the layer thickness d. The traditional 4n2 limit is also indicated.

Fig. 3
Fig. 3

(a) Schematic device geometry illustrating a metal sphere in Si matrix, which can induce LSPR modes. Here we consider the near field enhancement in a thin Si shell (with a thickness d) with weak absorption. Plot the absorption enhancement factor FLSPR as a function of wavelength for different Si/metal systems, sphere radius (b) a = 10 nm and (c) a = 200 nm.

Equations (12)

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

for z>0, { H y =A e iβx e k 2 z E x =iA k 2 ω ε 0 ε 2 e iβx e k 2 z E z =A β ω ε 0 ε 2 e iβx e k 2 z
for z<0, { H y =A e iβx e k 1 z E x =iA k 1 ω ε 0 ε 1 e iβx e k 1 z E z =A β ω ε 0 ε 1 e iβx e k 1 z
β= k 0 ε 1 ε 2 ε 1 + ε 2
{ k 1 2 = β 2 k 0 2 ε 1 k 2 2 = β 2 k 0 2 ε 2
A SPP = Im( ε 2 ) 0 d | E | 2 dz Im( ε 1 ) 0 | E | 2 dz +Im( ε 2 ) 0 + | E | 2 dz
F SPP = A SPP αd
C abs = C ext C sca = 2π k 0 2 n=1 + (2n+1)[ Re( a n + b n ) | a n | 2 | b n | 2 ]
E 1 = n=1 + 2n+1 n(n+1) ( c n M o1n (1) i d n N e1n (1) )
E s = n=1 + 2n+1 n(n+1) ( i a n N e1n (3) b n M o1n (3) )
E i = n=1 + 2n+1 n(n+1) ( M o1n (1) i N e1n (1) )
A LSPR = Im( ε 2 ) a a+d | E s + E i | 2 r 2 dr Im( ε 1 ) 0 a | E 1 | 2 r 2 dr
F LSPR = A LSPR α 4 3 π (a+d) 3 4 3 π a 3 C abs

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