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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 15908–15918
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Optical design of organic solar cell with hybrid plasmonic system

Wei E. I. Sha, Wallace C. H. Choy, Yongpin P. Chen, and Weng Cho Chew  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 15908-15918 (2011)
http://dx.doi.org/10.1364/OE.19.015908


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Abstract

We propose a novel optical design of organic solar cell with a hybrid plasmonic system, which comprises a plasmonic cavity coupled with a dielectric core-metal shell nanosphere. From a rigorous solution of Maxwell’s equations, called volume integral equation method, optical absorption of the active polymer material has a four-fold increase. The significant enhancement mainly attributes to the coupling of symmetric surface wave modes supported by the cavity resonator. The dispersion relation of the plasmonic cavity is characterized by solving an 1D eigenvalue problem of the air/metal/polymer/metal/air structure with finite thicknesses of metal layers. We demonstrate that the optical enhancement strongly depends on the decay length of surface plasmon waves penetrated into the active material. Furthermore, the coherent interplay between the cavity and the dielectric core-metal shell nanosphere is undoubtedly confirmed by our theoretical model. The work offers detailed physical explanations to the hybrid plasmonic cavity device structure for enhancing the optical absorption of organic photovoltaics.

© 2011 OSA

1. Introduction

Critically different from the thin-film polycrystalline or amorphous silicon solar cells (SCs) with active layer thickness of a few microns [1

1. K. L. Chopra, P. D. Paulson, and V. Dutta, “Thin-film solar cells: an overview,” Prog. Photovoltaics 12, 69–92 (2004). [CrossRef]

], the active polymer layer of thin-film organic solar cells (OSCs) only has few hundreds nanometers or even thinner thickness due to an extreme short exciton diffusion length [2

2. H. Hoppe and N. S. Sariciftci, “Organic solar cells: an overview,” J. Mater. Res. 19, 1924–1945 (2004). [CrossRef]

]. Such thin active layer with low refractive index (n ≈ 1.8) induces not only the weak optical absorption of OSCs but also fundamental (half-wavelength) limits of the optical design. On one hand, the strong Fabry-Pérot photonic mode or waveguide mode [3

3. 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. 21, 3504–3509 (2009). [CrossRef]

, 4

4. W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “A comprehensive study for the plasmonic thin-film solar cell with periodic structure,” Opt. Express 18, 5993–6007 (2010). [CrossRef] [PubMed]

] cannot be expected in the ultra-thin active layer. On the other hand, the physical mechanism of near-field concentration (not far-field scattering) should be taken into account in the design. Having unique features of tunable subwavelength resonance and engineered near-field concentration, plasmon is an enabling technique for light manipulation and management [5

5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

7

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

]. Plasmonic effects allow us to unprecedentedly improve the optical absorption of thin-film OSCs [8

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

] and promote emerging SC technology meeting clean energy demands. Plasmonic nanostructures can offer three principles to enhance the optical absorption of OSCs. The first one is surface plasmon resonance by metal gratings fabricated on the top or bottom of the active layer [9

9. A. J. Morfa, K. L. Rowlen, T. H. Reilly, M. J. Romero, and J. van de Lagemaat, “Plasmon-enhanced solar energy conversion in organic bulk heterojunction photovoltaics,” Appl. Phys. Lett. 92, 013504 (2008). [CrossRef]

13

13. W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “Angular response of thin-film organic solar cells with periodic metal back nanostrips,” Opt. Lett. 36, 478–480 (2011). [CrossRef] [PubMed]

]. The second one is local plasmon resonance by metal particles incorporated into or near the active layer [14

14. D. Duche, P. Torchio, L. Escoubas, F. Monestier, J. J. Simon, F. Flory, and G. Mathian, “Improving light absorption in organic solar cells by plasmonic contribution,” Sol. Energy Mater. Sol. Cells 93, 1377–1382 (2009). [CrossRef]

18

18. J. Jung, T. Sondergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83, 085419 (2011). [CrossRef]

]. The third one is plasmon coupling and hybridization, such as surface plasmon resonance coupled with local plasmon resonance or plasmon resonance coupled with photonic resonance [19

19. 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]

].

In the paper, we propose a novel optical design of OSC with a hybrid plasmonic system, which comprises a plasmonic cavity coupled with a dielectric core-metal shell nanosphere. It has been investigated that optical absorption of the active polymer material has a four-fold increase. With the help of rigorous electrodynamic approaches, we unveil the fundamental physics of the significant enhancement, which mainly attributes to the coupling of symmetric surface wave modes supported by the cavity resonator with a long penetration length. Moreover, coherent interaction between the cavity and the dielectric core-metal shell nanosphere is definitely confirmed by our theoretical model. A distribution of polarization charges on the surface of the cavity indicates a bonding and antibonding coupling modes in the hybrid plasmonic system. The work introduces a new hybrid plasmonic cavity device structure to enhance the optical absorption of organic photovoltaics with detailed physical explanations.

2. Theoretical Model

As a rigorous solution to Maxwell’s equations, a volume integral equation (VIE) method is developed to characterize the optical absorption of OSCs. Considering non-magnetic optical materials with an arbitrary inhomogeneity profile, the VIE can be written as
Ei(r)=J(r)i0ω(ɛ(r)ɛ0)i0ωμ0vG¯(r,r)J(r)dr
(1)
where i 0 is the imaginary unit, ɛ 0 (μ 0) is the permittivity (permeability) of free space, E i(r) is the incident electric field of the light, ɛ(r) is the position-dependent permittivity of the inhomogeneous materials, J is the volumetric polarization current to be solved, and (r, r′) is the dyadic Green’s tensor in free space. The widely adopted approach for solving the VIE is the discrete dipole approximation (DDA) method [20

20. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]

]. Due to the hypersingularity of the Green’s tensor and spurious discontinuity of tangential E-field induced by the scalar (piecewise constant) basis functions, the DDA method cannot accurately characterize the subwavelength plasmonic physics [21

21. A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009). [CrossRef]

] and breaks down in the multilayer device structure with high-contrast metallic materials. Here, we develop an alternate algorithm to bypass the difficulties. In our model, the polarization currents are expanded using the roof-top vector basis functions [22

22. A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980). [CrossRef]

] and thus the continuity of normal current is naturally satisfied at the material interfaces. Furthermore, the hypersingular Green’s tensor is smoothened by using the finite-difference approximation.

From the VIE [Eq. (1)], the scattered electric field generated by the volumetric polarization current J can be written as
Es(r)=i0ωμ0vG¯(r,r)J(r)dr
(2)
Considering the Cartesian coordinate system, we use the short notation (u 1, u 2, u 3) substituting for (x,y,z), then we have
[E1sE2sE3s]=[L11L12L13L21L22L23L31L32L33][J1J2J3]
(3)
where
Lij={Liic+Liiq,i=jLijq,ij
(4)
LiicJi=i0ωμ0vg(r,r)Ji(r)dr
(5)
LijqJj=i0ωɛ0uivg(r,r)Jj(r)ujdr
(6)
where g(r,r)=exp(i0K0|rr|)4π|rr| is the scalar green’s function, G¯(r,r)=[I¯+K02]g(r,r), and K 0 is the wave number of free space.

Using the rooftop basis functions to expand the unknown currents, we have
J(r)=i=13uik,m,nJiD(k,m,n)Tk,m,ni
(7)
where Tk,m,n1, Tk,m,n2, and Tk,m,n3 are the volumetric rooftop functions given by
Tk,m,n1=Λk(u1)Πm(u2)Πn(u3)Tk,m,n2=Πk(u1)Λm(u2)Πn(u3)Tk,m,n3=Πk(u1)Πm(u2)Λn(u3)
(8)
The functions Λk(u 1) and Πm(u 2) are defined by
Λk(u1)={1|u1kΔu1|Δu1,|u1kΔu1|Δu10,elseΠm(u2)={1,|u2(m12)Δu2|<Δu220,else
(9)
The cuboid cells are employed to discretize the structure to be modeled. Here, Δu 1 and Δu 2 are the grid sizes of each small cuboid along x and y directions, respectively. Other functions in Eq. (8) can be defined in the same way.

As a result, the discretized form for the operator Liic in Eq. (5) can be written as
LiiD,cJiD=i0ωμ0gDJiD
(10)
where ⊗ denotes the discrete convolution
gDJiD=k,m,ngD(kk,mm,nn)JiD(k,m,n)
(11)
and
gD(k,m,n)=0Δu10Δu20Δu3g(u1,ku1,u2,mu2,u3,nu3)du1du2du3
(12)
Likewise, the operator L12D,q in Eq. (6) can be discretized as
L12D,qJ2D=i0ωɛ0Δu1Δu2[gD(k+1,m,n)gD(k,m,n)[J2D(k,m,n)J2D(k,m1,n)]=i0ωɛ0Δu1Δu2{[gD(k+1,m,n)gD(k,m,n)][gD(k+1,m1,n)gD(k,m1,n)]}J2D(k,m,n)
(13)
where the finite-difference method is used for the smooth approximation of the dyadic Green’s function.

The computations of the discrete convolutions can be performed efficiently by means of cyclic convolutions and fast Fourier transform (FFT) [23

23. M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform,” IEEE Trans. Antennas Propag. 37, 528–537 (1989). [CrossRef]

], which is similar to the DDA method. As a traditional iterative solver of the resulting VIE matrix equation, the conjugate-gradient method converges very slowly and will produce the non-physical random errors in the calculation of optical absorption. To tackle the problem, we employ the fast and smoothly converging biconjugate gradient stabilized (BI-CGSTAB) method [24

24. H. A. Vandervorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992). [CrossRef]

]. The FFT is adopted to accelerate the matrix-vector multiplications encountered in the BI-CGSTAB solver with computational complexity of O(N logN) and memory of O(N).

Through the rigorous VIE solution to Maxwell’s equations, we can access some important physical quantities to reveal the physical mechanism of plasmonic effects in OSCs and optimize device performances. The absorption spectrum of OSCs is calculated by
SA(λ)=vnr(λ)ki(λ)2πc0λɛ0|E|2dV
(14)
where E=Ji0ω(ɛɛ0) is the total electric field, nc = nr + i 0 ki is the complex refractive index of the active material, λ is the incident wavelength, and c 0 is the speed of light in free space. It is worth mentioning that the absorption of various concentrators (involving single metallic cavity, single nanosphere, or plasmonic hybrid system) should be precluded in the volume integral above. A spectral enhancement factor (SEF) is the absorption spectrum of the OSC incorporating concentrators over that excluding concentrators. Integrating with a standard solar irradiance spectrum (air mass 1.5 global), one can get the total absorption of OSCs
TA=400nm800nmSA(λ)Γ(λ)dλ
(15)
where Γ is the solar irradiance spectrum. Likewise, a total enhancement factor (TEF) is the total absorption of the OSC incorporating concentrators over that excluding concentrators. To understand the mode hybridization for plasmon coupling, the polarization charge distribution on the surface of metallic nanostructure is given as follows
ρp=(ɛ0E)=P
(16)
where P = (ɛɛ 0) E is the polarization density. Based on the divergence-free condition, the polarization charge is definitely zero except on the heterogeneous boundaries. From the VIE solution, one can obtain the polarization current J and the total electric field E. After a postprocessing procedure with Eqs. (14) and (15), the SEF and TEF can be easily accessible. In addition, both the two layered OSC structure and embedded concentrators are meshed by the volumetric cuboid cells with a uniform grid size of 1 nm.

3. Results and Discussions

Figure 1 shows the schematic pattern of a heterojunction OSC. A hybrid plasmonic system, which comprises a plasmonic cavity coupled with a dielectric core-metal shell nanosphere, is employed for improving the optical absorption of the active polymer material. A transparent spacer is inserted to avoid local shunt and extract carriers. The incident light is propagated from the spacer to the active layer at the vertical incident angle with an E-field polarized along the x direction. Figure 2(a) shows the real and imaginary parts of the refractive index of the active material measured from ellipsometry [25

25. W. C. H. Choy and H. H. Fong, “Comprehensive investigation of absolute optical properties of organic materials,” J. Phys. D: Appl. Phys. 41, 155109 (2008). [CrossRef]

]. The complex refractive index of metal silver can be expressed by the Brendel-Bormann model [26

26. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]

]. The SiO2 as a dielectric layer is adopted for the core-shell sphere and its refractive index can be found in the literature [27

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

].

Fig. 1 (Color online) The schematic pattern of a heterojunction OSC. A hybrid plasmonic system, which comprises a plasmonic cavity coupled with a dielectric core-metal shell nanosphere, is employed for improving the optical absorption of the active polymer material. A transparent spacer is inserted to avoid local shunt and extract carriers. The structural parameters are t 1 = 20 nm, t 2 = 60 nm, w 1 = 30 nm, w 2 = 90 nm, and d = 21 nm. The radius of the core layer (denoted by the yellow arrow) and that of the shell layer (denoted by the blue arrow) are set to r 1 = 7.5 nm and r 2 = 15 nm, respectively. For a bonding coupling mode in the hybrid system, the polarity of its polarization charge is also marked.
Fig. 2 (Color online) (a) The real and imaginary parts of the refractive index of the active material; (b) The spectral enhancement factors for various nanospheres. D denotes the dielectric sphere (n=4, k=0), M denotes the metal silver sphere, MC-DS denotes the metal core-dielectric shell sphere, and DC-MS denotes the dielectric core-metal shell sphere. The SiO2 and Ag as a dielectric and metal layers are adopted for the core-shell spheres; (c) The scattering cross section (SCS) normalized to the geometrical cross section of each nanosphere; (d) The SCS of the DC-MS sphere as a function of the core radius (nm).

First, various nanosphere concentrators (excluding the plasmonic cavity) are systematically and comparatively observed. These nanospheres include a dielectric sphere, a metal sphere, a metal core-dielectric shell (MC-DS) sphere, and a dielectric core-metal shell (DC-MS) sphere [28

28. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [CrossRef] [PubMed]

]. The scattering cross section (SCS) of the nanospheres can be obtained from the generalized reflection coefficients of the spherically layered media [29

29. W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley-IEEE Press, 1999). [CrossRef]

, 30

30. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000). [CrossRef]

]
σs=2πK32m=1(2m+1)(|R˜3,2TM(m)|2+|R˜3,2TE(m)|2)
(17)
where 1, 2, and 3 denote the core, shell, and active layers as shown in Fig. 1, respectively, m is the order of the modified spherical Bessel (Hankel) functions, and R˜3,2TM and R˜3,2TE are the generalized reflection coefficients of the TM and TE spherical waves in the layer 3 reflected by the layer 2. For small spherical particles, the leading term (m = 1) of R˜3,2TM determines the value of the SCS. The generalized reflection coefficient can be written as a recursive equation
R˜i,i1TM=Ri,i1TM+Ti1,iTMR˜i1,i2TMTi,i1TM1Ri1,iTMR˜i1,i2TM
(18)
and
Ri,i+1TM=ɛi+1μiH^m(1)(Ki+1ri)H^m(1)(Kiri)ɛiμi+1H^m(1)(Ki+1ri)H^m(1)(Kiri)ɛiμi+1J^m(Kiri)H^m(1)(Ki+1ri)ɛi+1μiH^m(1)(Ki+1ri)J^m(Kiri)
(19)
Ti,i+1TM=i0ɛi+1μi+1/ɛiɛiμi+1J^m(Kiri)H^m(1)(Ki+1ri)ɛi+1μiH^m(1)(Ki+1ri)J^m(Kiri)
(20)
Ri,i1TM=ɛiμi1J^m(Kiri1)J^m(Ki1ri1)ɛi1μiJ^m(Kiri1)J^m(Ki1ri1)ɛi1μiJ^m(Ki1ri1)H^m(1)(Kiri1)ɛiμi1H^m(1)(Kiri1)J^m(Ki1ri1)
(21)
Ti,i1TM=i0ɛi1μi1/ɛiɛi1μiJ^m(Ki1ri1)H^m(1)(Kiri1)ɛiμi1H^m(1)(Kiri1)J^m(Ki1ri1)
(22)
where ri, ɛi, μi, and Ki are the radius, permittivity, permeability, and wave number of the ith spherical layer, respectively. Figure 2(b) and 2(c) show the SEFs and the SCS of the nanospheres, respectively. As seen in Figs. 2(b) and 2(c), the peaks of the SEFs agree with those of the SCS well. The small dielectric nanosphere, although has no loss and large refractive index (n=4), is not a good concentrator for OSCs. The dielectric nanosphere with positive refractive index cannot produce a strong dipole resonance compared to the metal nanosphere. Moreover, in contrast to the DC-MS sphere that has a metal layer adjacent to different materials (SiO2 and polymer), the resonance of the MC-DS sphere is blue-shifted because only one material SiO2 with lower refractive index is adjacent to the metal layer. The near field of the MC-DS sphere confines to the shell layer and cannot sufficiently scatter to the active layer. As a result, the optical enhancement by the MC-DS sphere is very weak. Figure 2(d) shows a tunable plasmon resonance by engineering the geometry of the DC-MS sphere. The resonance is red-shifted and becomes damped as the core radius increases.

Fig. 3 (Color online) (a) The spectral enhancement factor (SEF) for the plasmonic cavity (Cav) and for that coupled with the dielectric (D) or the metal-core dielectric-shell (MC-DS) sphere; (b) The dispersion relations of surface plasmon polariton (SPP), and a symmetric (Sym) and asymmetric (Asym) surface wave modes. The surface plasmon polariton propagates at the interface between semi-infinite polymer and Ag half-spaces. The symmetric and asymmetric modes propagate in the active polymer layer bounded between the two metal claddings with finite thicknesses; (c) The decay lengths penetrated into the active material; (d) The SEFs for the plasmonic cavity and for that coupled with the metal (M) or the dielectric-core metal-shell (DC-MS) sphere.
Fig. 4 (Color online) The near-field distributions in the active polymer layer at the wavelengths denoted with the arrows of Fig. 3(a). (a) 500 nm; (b) 580 nm; (c) 800 nm.

Third, we study the hybrid plasmonic system, which comprises a plasmonic cavity coupled with a nanosphere. The optical enhancement shows little improvements when the cavity is coupled with the dielectric or MC-DS sphere as illustrated in Fig. 3(a). However, a significant enhancement can be achieved if the cavity is coupled with metal or DC-MS sphere as shown in Fig. 3(d). By evaluating the TEF with the aid of Eq. (15), the optical absorption of the active polymer material has a four-fold increase when the cavity is coupled with the DC-MS sphere. We calculate the algebraic summation of the SEF by the uncoupled single cavity and that by the uncoupled single DC-MS sphere. As shown in Fig. 5, the summation is observably smaller than the SEF by the cavity coupled with the DC-MS sphere at long wavelengths ranging from 620 nm to 800 nm. The coherent interplay between the cavity and the DC-MS sphere is undoubtedly confirmed by the result. Then, we analyze the metal dissipation ratio defined as the metal loss of the coupled concentrator over that of the uncoupled one. The inset of Fig. 5 shows that the metal dissipation ratio of the DC-MS sphere is substantially larger than that of the cavity. The evanescent SPPs from the inner surface of metallic cavity sufficiently penetrate the DC-MS sphere inducing stronger local plasmon resonance as well as larger metallic loss. Thus the DC-MS sphere becomes more effective concentrator when it is coupled with the cavity. Finally, we discuss the coupling modes in the hybrid plasmonic system. Figure 6 depicts a polarization charge distribution on the surface of the cavity by using Eq. (16), indicating a bonding and antibonding coupling modes in the hybrid system. The bonding modes at 620 nm and 750 nm have a denser charge distribution if the distance between the cavity and the shell surfaces becomes closer. However, the antibonding mode at 650 nm reverses the polarity of the polarization charge when the face-to-face distance approaches the minimum. The near fields of the bonding modes show more concentrated field at the gap between the DC-MS sphere and the cavity, which can be seen in the inset of Fig. 5. For the bonding mode, the polarity of its polarization charge is marked in Fig. 1. Due to the in-phase plasmon oscillation and hybridization, the bonding mode is superradiant or strongly radiative, and provides a great help for the optical enhancement.

Fig. 5 (Color online) The spectral enhancement factor (SEF) comparisons. The SEF by the cavity (Cav) coupled with the dielectric core-metal shell (DC-MS) sphere is drawn with red straight line. The algebraic summation of the SEF by the uncoupled single cavity and that by the uncoupled single DC-MS sphere is plotted with black dash line. The near-field distributions at the wavelengths denoted with the green arrows are shown in the inset on a logarithmic scale. The metal dissipation ratio of the cavity is defined as the metal loss of the coupled cavity over that of the uncoupled one. Likewise, the metal dissipation ratio of the DC-MS sphere is defined as the metal loss of the coupled DC-MS sphere over that of the uncoupled one.
Fig. 6 (Color online) The polarization charge distributions on the surface of the cavity at the wavelengths denoted with the arrows of Fig. 5.

4. Conclusion

The hybrid plasmonic system, which comprises the plasmonic cavity coupled with the DC-MS nanosphere, can increase the optical absorption of the OSC by four fold. The significant enhancement mainly results from the coupling of symmetric surface wave modes supported by the cavity resonator and strongly depends on the decay length of surface plasmon waves penetrated into the active layer. Furthermore, the coherent interplay between the cavity and the DC-MS nanosphere is strongly demonstrated by our theoretical model. The bonding coupling mode in the hybrid plasmonic system enhances the optical absorption further. The work provides detailed physical explanations for the hybrid plasmonic cavity device structure to enhance the optical absorption of organic photovoltaics.

Acknowledgments

The authors acknowledge the support of the Research Grant Council of the Hong Kong Special Administrative Region, China (grants No. 712108, No. 711508, and No. 711609). This project is also supported in part by a Hong Kong UGC Special Equipment Grant ( SEG HKU09).

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3.

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4.

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J. Jung, T. Sondergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83, 085419 (2011). [CrossRef]

19.

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]

20.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]

21.

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009). [CrossRef]

22.

A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980). [CrossRef]

23.

M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform,” IEEE Trans. Antennas Propag. 37, 528–537 (1989). [CrossRef]

24.

H. A. Vandervorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992). [CrossRef]

25.

W. C. H. Choy and H. H. Fong, “Comprehensive investigation of absolute optical properties of organic materials,” J. Phys. D: Appl. Phys. 41, 155109 (2008). [CrossRef]

26.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]

27.

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

28.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [CrossRef] [PubMed]

29.

W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley-IEEE Press, 1999). [CrossRef]

30.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000). [CrossRef]

31.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric-constant,” Phys. Rev. B 44, 13556–13572 (1991). [CrossRef]

32.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

33.

W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994). [CrossRef]

OCIS Codes
(040.5350) Detectors : Photovoltaic
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Solar Energy

History
Original Manuscript: June 7, 2011
Revised Manuscript: July 14, 2011
Manuscript Accepted: July 15, 2011
Published: August 4, 2011

Citation
Wei E. I. Sha, Wallace C. H. Choy, Yongpin P. Chen, and Weng Cho Chew, "Optical design of organic solar cell with hybrid plasmonic system," Opt. Express 19, 15908-15918 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15908


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References

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  11. M. G. Kang, T. Xu, H. J. Park, X. G. Luo, and L. J. Guo, “Efficiency enhancement of organic solar cells using transparent plasmonic Ag nanowire electrodes,” Adv. Mater. 22, 4378–4383 (2010). [CrossRef] [PubMed]
  12. C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, “Enhancement of optical absorption in thin-film organic solar cells through the excitation of plasmonic modes in metallic gratings,” Appl. Phys. Lett. 96, 133302 (2010). [CrossRef]
  13. W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “Angular response of thin-film organic solar cells with periodic metal back nanostrips,” Opt. Lett. 36, 478–480 (2011). [CrossRef] [PubMed]
  14. D. Duche, P. Torchio, L. Escoubas, F. Monestier, J. J. Simon, F. Flory, and G. Mathian, “Improving light absorption in organic solar cells by plasmonic contribution,” Sol. Energy Mater. Sol. Cells 93, 1377–1382 (2009). [CrossRef]
  15. J. Jung, T. G. Pedersen, T. Sondergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010). [CrossRef]
  16. S. J. Tsai, M. Ballarotto, D. B. Romero, W. N. Herman, H. C. Kan, and R. J. Phaneuf, “Effect of gold nanopillar arrays on the absorption spectrum of a bulk heterojunction organic solar cell,” Opt. Express 18, A528–A535 (2010). [CrossRef] [PubMed]
  17. I. Diukman, L. Tzabari, N. Berkovitch, N. Tessler, and M. Orenstein, “Controlling absorption enhancement in organic photovoltaic cells by patterning Au nano disks within the active layer,” Opt. Express 19, A64–A71 (2011). [CrossRef] [PubMed]
  18. J. Jung, T. Sondergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83, 085419 (2011). [CrossRef]
  19. 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]
  20. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
  21. A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009). [CrossRef]
  22. A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980). [CrossRef]
  23. M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform,” IEEE Trans. Antennas Propag. 37, 528–537 (1989). [CrossRef]
  24. H. A. Vandervorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992). [CrossRef]
  25. W. C. H. Choy and H. H. Fong, “Comprehensive investigation of absolute optical properties of organic materials,” J. Phys. D: Appl. Phys. 41, 155109 (2008). [CrossRef]
  26. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]
  27. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  28. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [CrossRef] [PubMed]
  29. W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley-IEEE Press, 1999). [CrossRef]
  30. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000). [CrossRef]
  31. B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric-constant,” Phys. Rev. B 44, 13556–13572 (1991). [CrossRef]
  32. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  33. W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994). [CrossRef]

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