Abstract

We analyze the enhancement in optical absorption of an absorbing medium when spherical metal nanoparticles are embedded in it. Our analysis uses generalized Mie theory to calculate the absorbed optical power as a function of the distance from the metal nanoparticle. This analysis is used to evaluate the potential of enhancing optical absorption in thin-film solar cells by embedding spherical metal nanoparticles. We consider the trade-off between maximizing overall optical absorption and ensuring that a large fraction of the incident optical power is dissipated in the absorbing host medium rather than in the metal nanoparticle. We show that enhanced optical absorption results from strong scattering by the metal nanoparticle which locally enhances the optical electric fields. We also discuss the effect of a thin dielectric encapsulation of the metal nanoparticles.

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References

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  1. D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
    [CrossRef]
  2. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
    [CrossRef]
  3. H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
    [CrossRef]
  4. B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
    [CrossRef]
  5. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
    [CrossRef]
  6. S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
    [CrossRef]
  7. S. Fujimori, R. Dinyari, J.-Y. Lee, and P. Peumans, “Plasmonic light concentration in organic solar cells,” accepted in Nano Lett. (2009).
  8. A. Luque, and S. Hegedus, eds., Handbook of Photovoltaic Science and Engineering (John Wiley & Sons, Ltd, 2003).
  9. P. Peumans, V. Bulovic, and S. R. Forrest, “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Appl. Phys. Lett. 76(19), 2650–2652 (2000).
    [CrossRef]
  10. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
    [CrossRef]
  11. J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
    [CrossRef]
  12. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  13. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 330(3), 377–445 (1908).
    [CrossRef]
  14. Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40(9), 1354–1361 (2001).
    [CrossRef]
  15. I. W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18(6), 1275–1278 (2001).
    [CrossRef]
  16. COMSOL AB, 1 New England Executive Park Suite 350, Burlington, MA 01803, (2007).

2008

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

2007

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
[CrossRef]

2006

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

2005

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

2004

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

2001

2000

P. Peumans, V. Bulovic, and S. R. Forrest, “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Appl. Phys. Lett. 76(19), 2650–2652 (2000).
[CrossRef]

1996

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

1982

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 330(3), 377–445 (1908).
[CrossRef]

Bulovic, V.

P. Peumans, V. Bulovic, and S. R. Forrest, “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Appl. Phys. Lett. 76(19), 2650–2652 (2000).
[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]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

Chylek, P.

Cody, G. D.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Feng, B.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Forrest, S. R.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

P. Peumans, V. Bulovic, and S. R. Forrest, “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Appl. Phys. Lett. 76(19), 2650–2652 (2000).
[CrossRef]

Fu, Q.

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

Hall, D. G.

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 330(3), 377–445 (1908).
[CrossRef]

Müller, J.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Peumans, P.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

P. Peumans, V. Bulovic, and S. R. Forrest, “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Appl. Phys. Lett. 76(19), 2650–2652 (2000).
[CrossRef]

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

Polman, A.

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

Rand, B. P.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

Rech, B.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Schaadt, D. M.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Springer, J.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Stuart, H. R.

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

Sudiarta, I. W.

Sun, W.

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

Vanecek, M.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Yu, E. T.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Zhang, G.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

Zhao, J.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

Annalen der Physik

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 330(3), 377–445 (1908).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

P. Peumans, V. Bulovic, and S. R. Forrest, “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Appl. Phys. Lett. 76(19), 2650–2652 (2000).
[CrossRef]

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

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

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light-emitting diodes using surface plasmons,” Appl. Phys. Lett. 88(16), 161102–161103 (2006).
[CrossRef]

IEEE Trans. Electron. Dev.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

J. Appl. Phys.

B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105–093108 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Sol. Energy

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004).
[CrossRef]

Other

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

COMSOL AB, 1 New England Executive Park Suite 350, Burlington, MA 01803, (2007).

S. Fujimori, R. Dinyari, J.-Y. Lee, and P. Peumans, “Plasmonic light concentration in organic solar cells,” accepted in Nano Lett. (2009).

A. Luque, and S. Hegedus, eds., Handbook of Photovoltaic Science and Engineering (John Wiley & Sons, Ltd, 2003).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of a photovoltaic cell with MNPs placed on the surface of the cell. Enhancement of optical absorption is a far-field effect caused by the redirection of light into guided or trapped modes. (b) Schematic of a photovoltaic cell with MNPs embedded in the active layer. In this case, enhancement of optical absorption can results from near-field coupling which exploits the locally enhanced optical electric fields.

Fig. 2
Fig. 2

(a) Schematic of a MNP embedded in a host material system. (b)-(d) Spectrally-resolved enhancement of absorbed optical power when a 10nm-diameter MNP is embedded integrated over the volume of a 0.1nm-thick shell concentric with the MNP as a function of shell radius. The colorscale is logarithmic. The calculation was performed for Ag (b), Au (c), and Al (d). The shell radius for at which the absorption is enhanced by 10% is indicated by a white dashed line

Fig. 3
Fig. 3

(a) Schematic showing the direction and polarization of incident light and where scattered fields are calculated. (b) |Escattered|2 as a function of polar angle (θ) for both φ=0 (blue solid line) and φ=90 (red dotted line) for λ = 460 nm. (c) Re(Etotal) at z = −6nm (blue cones), 0 (red cones), and 6nm (blue cones) planes for λ = 460 nm. |ETotal|2 is also plotted in the z = 0 nm plane as a colormap.

Fig. 4
Fig. 4

Enhancement in optical absorption efficiency in the region bound by r = 5 nm and r = 10 nm when a 10 nm-diameter Ag MNP is embedded as a function of imaginary part of refractive index of medium (real part is set as 1.8). (b) Difference of the scattered power entering the same region as in (a) at r = 5nm and exiting at r = 10 nm. The similarity with (a) indicates that the increased in optical absorption comes mostly from re-absorption by scattering.

Fig. 5
Fig. 5

(a) Absorption and scattering efficiency for a 10 nm-diameter Ag MNP in vacuum. (b) Absorption and scattering efficiency of 30 nm-diameter Ag MNP in vacuum.

Fig. 6
Fig. 6

Enhancement in optical absorption obtained by embedding Ag MNPs in the host medium. This enhancement is calculated as the ratio of optical power scattered by the MNPs over the optical that would be absorbed if the MNP were replaced by the host material.

Fig. 7
Fig. 7

(a) Absorption in Ag MNPs (green line) and CuPc host material (blue line) for a MNP concentration of 1/(15nm)3 and 10 nm film thickness. The total absorption (red line) and absorption for the case of a homogeneous CuPc film (black line) are also shown. (b) Absorption of the CuPc host material when 10 nm-diameter Ag MNPs are embedded for bare MNPs (red line), 1nm-thick silica-coated (n = 1.5) MNPs (blue line), and 1nm-thick titania-coated (n = 2.5) MNPs (green line) The absorption of CuPc in the absence of MNPs is plotted for reference (black line).

Fig. 8
Fig. 8

Comparison between analytical calculations (solid lines) and optical simulations (dotted lines) of the optical absorption in the host material and MNPs for a system consisting of 10 nm-diameter Ag MNPs embedded in CuPc.

Equations (16)

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

Wabs(R)=12Rer=R[(Ei+Es)×(Hi*+Hs*)]ds
=Rer=R12(Ei×Hi*)dsRer=R12(Es×Hs*)dsRer=R12(Ei×Hs*+Es×Hi*)ds
=WiWs+Wext
ψn(ρ)=ρjn(ρ),  ξn(ρ)=ρhn(1)(ρ),
Wi(R)=π|E0|2ωn(2n+1)Im(ψnψn'*ψn'ψn*kμ*),
Ws(R)=π|E0|2ωn(2n+1)Im(|an|2ξn'ξn*|bn|2ξnξn'*kμ*),
Wext(R)=π|E0|2ωn(2n+1)Im(an*ψn'ξn*bn*ψnξn'*+anξn'ψn*bnξnψn'*kμ*).
Wabs(R)=π|E0|2ωn(2n+1)Im(Ankμ*).
An=(anξn'ψn')(an*ξn*ψn*)+(bnξnψn)(bn*ξn'*ψn'*)
η=[Wabs(r+0.1nm)Wabs(r)]with metal NP[Wabs(r+0.1nm)Wabs(r)]without metal NP,
Es=n=1E0in2n+1n(n+1)(ianΝe1n(3)bnΜo1n(3))32E0a1Νe1n(3),
a1i2(mka)33mt2m2mt2+2m2,
|Νe1n(3)|1|mkr|3
ws=12ωε"|Es|2dvRe(m)Im(m)λ|mt2m2mt2+2m2|2dv
dI=Iα0(143πr3N)dzICaNdzICsNdz
I=I0exp(α0(143πr3N)(Ca+Cs)N)d

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