Abstract

We show that optical absorption in thin-film photovoltaic cells can be enhanced by inserting a tuned two-component aperiodic dielectric stack into the device structure. These coatings are a generalization and unification of the concepts of an anti-reflection coating used in solar cells and high-reflectivity distributed Bragg mirror used in resonant cavity-enhanced narrowband photodetectors. Optimized two-component coatings approach the physically realizable limit and optimally redistribute the spectral photon density-of-states to enhance the absorption of the active layer across its absorption spectrum. Specific designs for thin-film organic solar cells increase the photocurrent under AM1.5 illumination, averaged over all incident angles and polarizations, by up to 40%.

© 2008 Optical Society of America

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2007 (1)

2006 (2)

B. O’Connor, K. H. An, K. Pipe, Y. Zhao, and M. Shtein, "Enhanced optical field intensity distribution in organic photovoltaic devices using external coatings," Appl. Phys. Lett. 89, 233502 (2006).
[CrossRef]

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Muller, "Silicon thin-film solar cells with rectangular-shaped grating couplers," Prog. Photovoltaics 14, 13-24 (2006).
[CrossRef]

2005 (4)

J. Xue, B. P. Rand, S. Uchida, and S. R. Forrest, "A hybrid planar-mixed molecular hetrojunction photovoltaic cell," Adv. Mater. 17, 66-71 (2005).
[CrossRef]

G. Li, V. Shrotriya, J. Huang, Y. Yao, T. Moriarty, K. Emery, and Y. Yang, "High-efficiency solution processable polymer photovoltaic cells by self-organization of polymer blends," Nat. Mater. 4, 864-868 (2005).
[CrossRef]

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, "Thermally stable, efficient polymer solar cells with nanoscale control of interpenetrating network morphology," Adv. Funct. Mater. 15, 1617-1622 (2005).
[CrossRef]

G. P. Ortiz and W. L. Mochan, "Nonadditivity of Poynting vector within opaque media," J. Opt. Soc. Am. A 22, 2827-2837 (2005).
[CrossRef]

2004 (1)

S. R. Forrest, "The path to ubiquitous and low-cost organic electronic appliances on plastic," Nature 428, 911-918 (2004).
[CrossRef] [PubMed]

2003 (2)

P. Peumans, A. Yakimov, and S. R. Forrest, "Small molecular weight organic thin-film photodetectors and solar cells," J. Appl. Phys. 93, 3693-3723 (2003).
[CrossRef]

P. Peumans, S. Uchida, and S. R. Forrest, "Efficient bulk heterojunction photovoltaic cells using small-molecular-weight organic thin films," Nature 425, 158-162 (2003).
[CrossRef] [PubMed]

2001 (1)

P. Peumans and S. R. Forrest, "Very-high-efficiency double-hetrostructure copper pthalocyanine/C60 photovoltaic cells," Appl. Phys. Lett. 79, 126-128 (2001).
[CrossRef]

2000 (1)

L. S. Roman, O. Inganas, T. Granlund, T. Nyberg, M. Svensson, M. R. Andersson, and J. C. Hummelen, "Trapping light in polymer photodiodes with soft embossed gratings," Adv. Mater. 12, 189-195 (2000).
[CrossRef]

1999 (2)

R. R. Bilyalov, L. Stalmans, L. Schirone, and C. Levy-Clement, "Use of porous silicon antireflection coating in multicrystalline silicon solar cell processing," IEEE Trans. Electron. Devices 46, 2035-2040 (1999).
[CrossRef]

L. A. A. Pettersson, L. S. Roman, and O. Inganas, "Modeling photocurrent action spectra of photovoltaic devices based on organic thin film," J. Appl. Phys. 86, 487-496 (1999).
[CrossRef]

1998 (1)

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

1997 (1)

1996 (2)

1995 (1)

M. S. Unlu and S. Strite, "Resonant cavity enhanced photonic devices," J. Appl. Phys. 78, 607-639 (1995).
[CrossRef]

1994 (1)

1993 (1)

1991 (2)

K. Kishino, M. S. Unlu, J. Chyi, J. Reed, L. Arsenault, and H. Morkoc, "Resonant cavity-enhanced photodetector," IEEE J. Quantum Electron. 27, 2025-2034 (1991).
[CrossRef]

J. Zhao and M. A. Green, "Optimized antireflection coatings for high-efficiency silicon solar cells," IEEE Trans. Electron. Devices 38, 1925-1934 (1991).
[CrossRef]

1987 (1)

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

1986 (1)

C. W. Tang, "Two layer organic photovoltaic cell," Appl. Phys. Lett. 48, 183-185 (1986).
[CrossRef]

1984 (1)

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]

1983 (1)

P. Sheng, A. N. Bloch, and R. S. Stepleman, "Wavelength-selective absorption enhancement in thin-film solar cells," Appl. Phys. Lett. 43, 579-581 (1983).
[CrossRef]

1982 (1)

E. Yablonovitch, "Statistical ray optics," J. Opt. Soc. Amer. 72, 899-907 (1982).
[CrossRef]

1974 (1)

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

1971 (1)

R. K. Ahrenkiel, "Modified Kramers-Kronig analysis of optical spectra," J. Opt. Soc. Am,  61, 1651-1655 (1971).
[CrossRef]

1969 (1)

R. J. Vernon and S. R. Seshadri, "Reflection coefficient and reflected power on a lossy transmission line," Proc. IEEE  57, 101-102 (1969).
[CrossRef]

1967 (1)

C. A. Emeis, L. J. Oosterhoff, and G. de Vries, "Numerical evaluation of Kramers-Kronig Relations," Proc. R. Soc. Lond. A 297, 54-65 (1967).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, "Simplex method for function minimization," Comput. J. 7, 308-313 (1965).

1956 (1)

J. S. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Adv. Funct. Mater. (1)

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, "Thermally stable, efficient polymer solar cells with nanoscale control of interpenetrating network morphology," Adv. Funct. Mater. 15, 1617-1622 (2005).
[CrossRef]

Adv. Mater. (2)

J. Xue, B. P. Rand, S. Uchida, and S. R. Forrest, "A hybrid planar-mixed molecular hetrojunction photovoltaic cell," Adv. Mater. 17, 66-71 (2005).
[CrossRef]

L. S. Roman, O. Inganas, T. Granlund, T. Nyberg, M. Svensson, M. R. Andersson, and J. C. Hummelen, "Trapping light in polymer photodiodes with soft embossed gratings," Adv. Mater. 12, 189-195 (2000).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (5)

C. W. Tang, "Two layer organic photovoltaic cell," Appl. Phys. Lett. 48, 183-185 (1986).
[CrossRef]

P. Peumans and S. R. Forrest, "Very-high-efficiency double-hetrostructure copper pthalocyanine/C60 photovoltaic cells," Appl. Phys. Lett. 79, 126-128 (2001).
[CrossRef]

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

P. Sheng, A. N. Bloch, and R. S. Stepleman, "Wavelength-selective absorption enhancement in thin-film solar cells," Appl. Phys. Lett. 43, 579-581 (1983).
[CrossRef]

B. O’Connor, K. H. An, K. Pipe, Y. Zhao, and M. Shtein, "Enhanced optical field intensity distribution in organic photovoltaic devices using external coatings," Appl. Phys. Lett. 89, 233502 (2006).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, "Simplex method for function minimization," Comput. J. 7, 308-313 (1965).

IEEE J. Quantum Electron. (2)

K. Kishino, M. S. Unlu, J. Chyi, J. Reed, L. Arsenault, and H. Morkoc, "Resonant cavity-enhanced photodetector," IEEE J. Quantum Electron. 27, 2025-2034 (1991).
[CrossRef]

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

IEEE Trans. Electron. Devices (3)

J. Zhao and M. A. Green, "Optimized antireflection coatings for high-efficiency silicon solar cells," IEEE Trans. Electron. Devices 38, 1925-1934 (1991).
[CrossRef]

R. R. Bilyalov, L. Stalmans, L. Schirone, and C. Levy-Clement, "Use of porous silicon antireflection coating in multicrystalline silicon solar cell processing," IEEE Trans. Electron. Devices 46, 2035-2040 (1999).
[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]

J. Appl. Phys. (4)

P. Peumans, A. Yakimov, and S. R. Forrest, "Small molecular weight organic thin-film photodetectors and solar cells," J. Appl. Phys. 93, 3693-3723 (2003).
[CrossRef]

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

L. A. A. Pettersson, L. S. Roman, and O. Inganas, "Modeling photocurrent action spectra of photovoltaic devices based on organic thin film," J. Appl. Phys. 86, 487-496 (1999).
[CrossRef]

M. S. Unlu and S. Strite, "Resonant cavity enhanced photonic devices," J. Appl. Phys. 78, 607-639 (1995).
[CrossRef]

J. Opt. Soc. Am (1)

R. K. Ahrenkiel, "Modified Kramers-Kronig analysis of optical spectra," J. Opt. Soc. Am,  61, 1651-1655 (1971).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Amer. (1)

E. Yablonovitch, "Statistical ray optics," J. Opt. Soc. Amer. 72, 899-907 (1982).
[CrossRef]

Nat. Mater. (1)

G. Li, V. Shrotriya, J. Huang, Y. Yao, T. Moriarty, K. Emery, and Y. Yang, "High-efficiency solution processable polymer photovoltaic cells by self-organization of polymer blends," Nat. Mater. 4, 864-868 (2005).
[CrossRef]

Nature (2)

P. Peumans, S. Uchida, and S. R. Forrest, "Efficient bulk heterojunction photovoltaic cells using small-molecular-weight organic thin films," Nature 425, 158-162 (2003).
[CrossRef] [PubMed]

S. R. Forrest, "The path to ubiquitous and low-cost organic electronic appliances on plastic," Nature 428, 911-918 (2004).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. (1)

J. S. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Proc. IEEE (1)

R. J. Vernon and S. R. Seshadri, "Reflection coefficient and reflected power on a lossy transmission line," Proc. IEEE  57, 101-102 (1969).
[CrossRef]

Proc. R. Soc. Lond. A (1)

C. A. Emeis, L. J. Oosterhoff, and G. de Vries, "Numerical evaluation of Kramers-Kronig Relations," Proc. R. Soc. Lond. A 297, 54-65 (1967).
[CrossRef]

Prog. Photovoltaics (1)

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Muller, "Silicon thin-film solar cells with rectangular-shaped grating couplers," Prog. Photovoltaics 14, 13-24 (2006).
[CrossRef]

Other (8)

L. Brillouin, Wave Propagation and Group Velocity (Academic Press, 1960).

K. Tvingstedt, V. Andersson, F. Zhang, and Olle Inganas, "Folded reflective tandem polymer solar cell doubles efficiency," Appl. Phys. Lett. 91, 123514-1-123514-3 (2007).
[CrossRef]

M. Agrawal, Y. Sun, S. R. Forrest, and P. Peumans, "Enhanced outcoupling from organic light-emitting diodes using aperiodic dielectric mirrors," Appl. Phys. Lett. 90, 241112-1-241112-3 (2007).
[CrossRef]

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1998).

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972).

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical MaterialsRresearch, (Springer, 2005).

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford, 1948).

Matlab 7.0, The Mathworks Inc., Apple Hill Drive, Natick, MA 01760.

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Figures (5)

Fig. 1.
Fig. 1.

Simplified schematics of thin film PV cells (a) with Lambertian scattering at the transparent electrode interface, (b) without an ARC, (c) with an ARC over the transparent electrode, and (d) with a high-reflectivity mirror over the transparent electrode in the RCE configuration.

Fig. 2.
Fig. 2.

Schematic of a thin-film organic PV cell with an aperiodic dielectric stack between the glass substrate and transparent ITO anode.

Fig. 3.
Fig. 3.

(a). Absorbance as a function of wavelength is shown for a device with 15nm thick active layer (control structure) without a multilayer mirror (dashed line). Also shown are the spectrally-selective upper bound of absorbance (solid line) and the absorbance of devices with optimal causal top mirror such that the AM 1.5 weighted average EQE over different target wavelength bandwidths (BW) is maximized (squares: BW=20nm, circles: BW=60nm, triangles: BW=150nm, stars: BW=400nm). (b) shows the corresponding amplitude of reflectance of the top mirror and (c) shows the corresponding phase of reflectance of the top mirror to achieve the spectrally selective-upper bound (solid line). The desired amplitude and phase of reflectance for causal top mirrors designed for broadband (BW=400nm, stars) and narrowband (BW=20nm, squares) response are also shown.

Fig. 4.
Fig. 4.

(a). AM1.5-weighted average EQE for the control BHJ device (open triangles) and a BHJ device with an optimal causal top mirror (filled triangles) for different charge collection lengths (Lc =20nm and 40nm) as a function of the thickness of active layer. Also shown is the broadband improvement achieved through coherent light trapping as a function of the active layer thickness. (b). Optimal causal limit of absorbance averaged over the spectral range λ=425nm-825nm that is achievable as a function of the targeted bandwidth for a device with 15nm-thick active layer. Inset: Example of an absorbance spectrum without stack (open squares) and with stack (solid squares) optimized for a bandwidth of 150nm.

Fig. 5.
Fig. 5.

(a). External quantum efficiency for the bilayer (squares) and the BHJ (triangles) 15nm-thick cells with (filled symbols) and without (open symbols) an optimized dielectric stack between the substrate and ITO layer. (b) Normalized short-circuit current as a function of angle of incidence of the illumination for a 15nm-thick bilayer device with (filled squares) and without (open squares) an optimized dielectric stack. The short circuit current at normal incidence is normalized to 1. The enhancement in short-circuit current density by insertion of the optimized dielectric stack is also shown for the bilayer (circles) and the BHJ (triangles) devices.

Tables (1)

Tables Icon

Table 1. The refractive indices of all materials at λ=600nm in the multilayer BHJ and bilayer cell designs.

Equations (7)

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

2 n N ω L c + ϕ 1 + ϕ 2 = 2 m π
j exciton ( θ ) = s , p 0 0 L G s , p ( z , ω , θ ) f ( z ) dzd ω
G s , p ( z , ω , θ ) = n N ( ω ) α N ( ω ) n 1 ( ω ) ћ ω I ( ω , θ ) E s , p ( z , ω , θ ) 2
E s ( z , ω , θ ) = t 1 N exp ( ik zN z ) + r NM t 1 N exp ( 2 ik zN L z ) 1 r N 1 r NM exp ( 2 i k zN L ) e ̂ s
E p ( z , ω , θ ) = k N ε N ω t 1 N exp ( ik zN z ) e ̂ p , + + r NM t 1 N exp ( 2 ik zN L z ) e ̂ p , 1 r N 1 r NM exp ( 2 i k zN L )
η s , p ( ω ) = ћ ω I ( ω , θ ) 0 L G s , p ( z , ω , θ ) dz
ϕ ( ω ) = 2 ω π 0 log ( R ( ω ) ) ω 2 ω 2 d ω + ϕ ( 0 )

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