Plasmonic nanostructures for effective light trapping in a variety of photovoltaics have been actively studied. Metallic nanograting structures are one of promising architectures. In this study, we investigated numerically absorption enhancement mechanisms in inverted polymer photovoltaics with one dimensional Ag nanograting in backcontact. An optical spacer layer of TiO2, which also may act as an electron transport layer, was introduced between nanograting pillars. Using a finite-difference-time domain method and performing a modal analysis, we explored correlations between absorption enhancements and dimensional parameters of nanograting such as period as well as height and width. The optimal design of nanograting for effective light trapping especially near optical band gap of an active layer was discussed, and 23% of absorption enhancement in a random polarization was demonstrated numerically with the optimally designed nanograting. In addition, the beneficial role of the optical spacer in plasmonic light trapping was also discussed.
©2012 Optical Society of America
A power conversion efficiency of organic solar cells has been growing rapidly over the last few years and recently reached 8.4% in a single junction and even higher in a double junction [1, 2]. The active layers of most organic solar cells, however, are not thicker than 200 nm, which is not thick enough to harvest all the solar radiation below their optical band gap. This limitation in a thickness of the active layers is mostly due to short charge carrier diffusion lengths stemming from their poor charge carrier mobility. In this regard, a large number of light trapping technologies have been explored in efforts to boost the optical absorption enhancement in active layers of organic solar cells, especially near optical band gap, and a plasmonic approach, which can exceed the thermodynamic limit of 4n2, is one of the most promising schemes [3–7]. Plasmonic light trapping in organic solar cells has been realized by incorporating metal nanoparticles in buffer layers or active layers [8, 9]. It was theoretically demonstrated that embedding metal nanoparticles in active layers leads to much greater absorption enhancements compared to the case with metal nanoparticles in buffer layers . In this case, metal nanoparticles act as a local field enhancer or a light scattering center depending on the size of metal nanoparticles . Larger metal nanoparticles tend to scatter light more dominantly than smaller ones. Embedding metallic nanograting on frontcontact or backcontact of solar cells is another promising approach; in this case, incident light scattered by nano-grating is coupled into waveguide modes or surface plasmon polariton (SPP) resulting in the absorption enhancement [12–15]. In this architecture, nanograting provides momentum in the in-plane direction for scattered light to be coupled into propagation modes; thus, geometrical parameters of nanograting such as period, height and width must be carefully designed to achieve the maximized absorption enhancement. The absorption enhancement by plasmonic metallic nanograting structures in a thin film Si solar cell has been well studied by correlating propagation modes and design of nanograting [16, 17]. Also, metallic nanograting on backcontact for polymer solar cells was numerically demonstrated to enhance absorption in active layers by excitation of surface plasmon polariton (SPP) or localization of surface plasmon resonance (LSPR) [18–20]. However, there has been rare study on exploiting waveguide mode coupling for light trapping in polymer solar cells with active layers thinner than 200 nm.
In this study, we show by numerical calculations that incorporation of optimally designed plasmonic one dimensional (1D) nanograting on backcontact leads to the absorption enhancement by 23% in 150 nm thick blended polymer, P3HT:PCBM(poly-3-hexythiphene and phenyl-C61-butyric acid methyl ester), which is one of the most widely used materials for polymer solar cells. An inverted polymer solar cell structure, which has cathode contact on substrate, was studied since there have been growing interests in this type of solar cell over conventional ones owing to its advantages such as better vertical phase separation and environmental stability over conventional ones [21–23]. Furthermore, plasmonic backcontact in inverted architecture can be more easily implemented. In addition, we introduced an optical spacer layer, TiO2 between an active layer and cathode, which also acts as an electron transport layer. This spacer layer increases an optical thickness and in turn optical modes in a waveguide. In order to optimize metallic nanograting design, we performed a modal analysis in multilayered solar cell structures using an Eigen mode solver and identified waveguide and SPP modes depending on polarizations. Optical absorption, electromagnetic field distributions as a function of nanograting design were numerically calculated by a finite-difference-time-domain (FDTD) method using a commercial software package (Lumerical 7.5).
2. Simulation model and methods
A three dimensional (3D) schematic and a two dimensional (2D) cross-section image of an inverted plasmonic polymer solar cell in this study are illustrated in Fig. 1 . Silver nanograting is placed on top of substrate, and the troughs of nanograting are filled with TiO2. Sequentially, P3HT:PCBM and poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT:PSS) are stacked. The media surrounding the cell is air. Conductive PEDOT:PSS serves as anode, and highly conductive metal grid may be deposited on top of anode to reduce series resistance of the solar cell. This ITO-free inverted solar cell is highly promising as low-cost applications, and numerous researches are on-going [24, 25].
For a modal analysis, dispersion relations of waveguide modes in multilayered solar cells without nanograting were calculated by solving one dimensional wave equation using an Eigen mode solver (MODEIG98) [26–28]. FDTD simulations to calculate optical absorption and light field distributions were performed using a 2D model. In order to implement the periodic nanograting in the calculations, periodic boundary conditions in x-direction were imposed, and perfectly matched layer conditions were used on the boundary of top and bottom. The incident light with a TM (transverse magnetic) or TE (transverse electric) polarization is plane wave of which wavelengths range from 350 nm to 800 nm. Thicknesses of the PEDOT:PSS buffer layer and the Ag back reflector are set for 50 nm and 300 nm, respectively for all the calculations. For comparative study, FDTD calculations for solar cells without nanograting were also performed. The refractive indices of TiO2, PEDOT:PSS and P3HT:PCBM used in calculations were extracted from literature [29, 30]. The refractive index of Ag was determined by the ellipsometry analysis of an Ag thin film prepared by sputtering. In this paper, all the optical absorptions in the active layers were calculated by normalizing the optical absorbed power to the incident light power. The optical absorbed power, P in active layers was calculated using the following equation:
3. Simulation results and discussion
The use of an optical spacer is one of the widely used approaches to achieve enhanced absorption in polymer solar cells . In this respect, we investigated the effect of the optical spacer thickness on absorption in active layers with varying the active layer thickness using the FDTD method. The number of absorbed photons in the active layers was calculated by integrating optical absorption over a solar radiation of AM (air mass) 1.5G at a light intensity of 100 mW/cm2. The number of absorbed photons as a function of the active layer thickness with varying the spacer thickness is shown in Fig. 2(a) . Slight oscillations in the optical absorption with varying the active layer thickness are attributed to the optical interference effect. The significant reductions in the optical absorption are observed especially for the active layers thinner than 100 nm. In contrast, the absorption enhancements are observed for some thicknesses over 100 nm, but they do not exceed 5% as seen in Fig. 2(b). Thus, the sole use of an optical spacer cannot be an effective way to enhance the optical absorption in our device structures.
For further calculations, we chose 150 nm for a thickness of the active layer. The optical band gap of P3HT is known to be around 1.9 eV, which corresponds to absorption edge of ~653 nm . Although P3HT is a strong absorber, it has weak absorption near its optical band gap; hence, we focus on boosting optical absorption at the spectral range of 600 ~700 nm. Using the Eigen mode solver, we performed a modal analysis in the wavelength range of 600 nm ~800 nm for two different planar device structures of Ag/TiO2 50 nm/P3HT:PCBM 150 nm/PEDOT:PSS 50 nm and Ag/P3HT:PCBM 150 nm/PEDOT:PSS 50 nm without Ag nanograting, and the dispersion curves are plotted in Fig. 3(a) . It has been well reported that the dispersion curves of waveguide and SPP modes are disturbed and split by the optical modulation of metallic grating depending on the grating shape. Thus, the dispersion curves in Fig. 3(a) would not be exact but provide a guide to identify absorption enhancement mechanism by Ag nanograting [33, 34]. On the other hand, two configurations of standing waves arise due to the interference of forward traveling and backward traveling waves at the Bragg refection conditions by nanograting. The optical fields of the standing waves are concentrated on the peaks of grating in one configuration and concentrated on the troughs of grating in the other configuration. The dispersion curves determined for the cases with and without TiO2 by the modal analysis would approximate the dispersion curves for the standing waves with concentrated fields on the troughs and the peaks for nanograting, respectively. The simulated optical field distributions in the devices with nanograting using a FDTD method would support this, which will be described later in this article.
The blue and the red solid lines were calculated using a following analytical equation for the semi-infinite bilayer structures of Ag/P3HT:PCBM and Ag/TiO2, respectively .
The dispersion curve of the SPP mode for the case of the device structure without TiO2 lies very close to the blue line, while that with TiO2 moves toward a longer wavelength region and lies between the blue and the red line. Likewise, inclusion of the spacer layer, TiO2 leads to shift of dispersion curves toward longer wavelengths for the modes of TM0 and TE0. In the normal incidence of solar radiation, the in-plane momentum is provided only by nanograting, and thus, the propagation wavevector is determined by a period of nanograting by the equation:17]. Using Eq. (3), the dispersion curves are re-drawn as a function of the period of nano-grating in Fig. 3(b) for the first diffraction order (n = 1). This would be a guide map for the design of nanograting for maximization of absorption enhancements.
The waveguide modes and the SPP modes shown by their dispersion curves are confirmed by investigating their optical field profiles. Normalized field profiles in y-direction for the case without and with TiO2 were determined also using the Eigen mode solver and are shown in Fig. 3(c) and 3(d) for the wavelength of 650 nm. In all the modes, the optical fields are well confined within the multi-layers of the cell. The optical fields for the SPP modes are strongly amplified at the Ag interface and permeate into the active layer. However, they decay fast along the depth, and thus, if a thick TiO2 layer is inserted, only a weak tail of the SPP evanescent fields would be exploited for absorption enhancements, which limits a thickness of a spacer layer as seen in Fig. 3(d). The optical fields for the TE0 modes show a typical fundamental wave guide mode, where one maximum intensity peak is located in a wave guide . On the other hand, the TM0 modes for both cases are seemed to be coupled with a SPP mode in that the field distribution near the Ag interface is similar to that of the SPP mode. Interestingly, the presence of TiO2 enhances the optical field for the SPP mode at the Ag interface as well as that for the TM0 mode at the active layer of P3HT:PCBM. This is because the optical fields of SPP modes in lossless media (TiO2) is greatly enhanced over those in lossy media (P3HT:PCBM) . Therefore, the presence of an optical spacer with the optimal thickness would be beneficial for absorption enhancements. The excitation wavelengths of above TE0, TM0 and SPP modes rely on the periods of nanograting. Absorption spectra of a 150 nm thick P3HT:PCBM active layer vs. a period of nanograting in a TE polarization are shown in Fig. 4 .
For the present, a thickness of a spacer layer is set for 50 nm, and a height and a width of nanograting are 50 nm and 150 nm, respectively. As a period of nanograting increases, spectral broadening of absorption in a long wavelength region above 630 nm is observed. The dispersion curves of the TE0 modes for the cases with and without a 50 nm thick TiO2 layer, which were determined by modal analysis, are drawn in the white lines. The dashed line is the dispersion curve of the TE0 mode for the case with TiO2, and the dash-dotted line is that for the case without TiO2. The E-field distributions at the wavelength of 650 nm and 678 nm with a period of 400 nm, which correspond to 1 and 2 respectively in Fig. 4(a), show TE0 waveguide modes clearly as seen in Fig. 4(b) and 4(c). As expected from the modal analysis, the E-field excited at position 1 is confined above one dimensional Ag pillar in Fig. 4(b), and that at position 2 is confined above the trough of Ag nanograting where a thin TiO2 layer exists in Fig. 4(c). Therefore, the spectral split of a TE0 mode originates from difference in optical thicknesses induced by nanograting and the optical spacer. This spectral split may be further tuned by changing a material of an optical spacer or its thickness. Note the TE0 waveguide mode excited on the peaks of nanograting becomes weakened and moves toward the top surface at position 2.
In a TM polarization, the similar spectral broadenings in absorption are observed as shown in Fig. 5(a) . The dashed line is the dispersion curve for the SPP mode of the cell without TiO2, and the dash-dotted line is that for the TM0 mode of the cell with TiO2. The H-field intensity distributions at position 1 and 2 in Fig. 5(a) are shown in Fig. 5(b) and 5(c). The spectral broadenings in the long wavelength region ranging from 600 nm to 700 nm in a period between above 430 nm and below 320 nm are induced by the SPP mode and the TM0 mode. It is notable that the spectral broadenings in the same wavelength range are still observed in a period between 320 nm and 430 nm. The E-field distributions at position 3 in Fig. 5(a) reveal that both of the SPP mode and the TM0 mode exist in this period range.
The number of absorbed photons in the active layers under a solar radiation of AM1.5G at a light intensity of 100 mW/cm2 was calculated and is plotted in a period between 250 nm and 550 nm in Fig. 6 . For the periods shorter than 520 nm, more photons are absorbed in a TE polarization compared with a TM polarization. The maximum number of photons in a random polarization is absorbed in a period of 380 nm. As seen in Fig. 3(b), in this period range, the TE0 modes are excited near band gap of ~650 nm, and they make a main contribution to absorption enhancements in a random polarization. Likewise, in a TM polarization, in the same nanograting period the mixed mode of TM0 and SPP enhances absorption in the active layer near optical band gap of the active layer.
For further absorption enhancements, a height and a width of nanograting were varied independently, and absorption enhancements were calculated depending on polarizations (Fig. 7 ). The absorption enhancement was calculated by normalization of the number of absorbed photons for the case with nanograting to that for the case without nanograting. A thickness of the TiO2 spacer layer is kept at the same as that of the nanograting height. Depending on polarizations, the optimal width and height for the maximum absorption enhancement vary by the multiple reasons: the shift of dispersion curves by varying a nanograting height, and the change in area ratios of the regions with and without TiO2 by varying a nanograting width, and the volume change by varying either of a height or width of nanograting. In a TE polarization, the absorption enhancement is the maximum of 29% at a height of 70 nm and a width of 250 nm, while in a TM polarization the maximum absorption of 18% is shown at shorter and narrower nanograting of a 60 nm height and a 175 nm height. As a result, in a random polarization the maximum absorption enhancement is 23% at a height of 60 nm and a width of 200 nm. As the width of Ag nanograting becomes wider in a TM polarization, the regions with TiO2 become narrower resulting in weakening of the TM0 mode which is excited in the TiO2 regions and in turn lower absorption enhancement. This would be a reason in a TM polarization the maximum absorption enhancement is observed at narrower nanograting than in a TE polarization. The optimal height and width of nanograting must change accordingly if a thickness of the active layer varies.
The dispersion curves for thinner active layers (100 nm, 75 nm) shift toward shorter wavelengths as shown in Fig. 8 for both of polarizations. Similarly to the case with a 150 nm thick active layer, for both thicknesses of 100 nm and 75 nm two TE0 modes are observed in the range of wavelengths longer than 600 nm. However, a TM0 mode is not observed in a given period range above the wavelength of 600 nm. As a result, a spectral broadening of absorption is negligible in a TM polarization, while a significant absorption broadening is observed in a TE polarization. The optimal period for the maximum absorption shifts to the longer periods of 400 nm and 420 nm for a 100 nm thick and a 75 nm thick active layers, respectively.
Absorption spectra of the cell with a 150 nm thick active layer incorporating 380 nm period nanograting of a 50 nm height and a 200 nm width in TM and TE polarizations are compared with those of the cell without nanograting in Fig. 9(a) . Remarkable absorption enhancements are observed above the wavelength of ~600 nm for both of polarizations. These enhancements can be identified to be attributed from the waveguide modes of the TE0 mode and the TM0 and the SPP mixed mode in TE and TM polarizations, respectively. One small peak is observed at the wavelength of 709 nm in a TM polarization, which originates from the SPP mode at the interface of Ag/P3HT:PCBM. The absorption enhancements of the plasmonic cell with various thicknesses from 50 nm up to 250 nm and the number of absorbed photons in the active layers were calculated and shown in Fig. 9(b). The same nanograting parameters used in Fig. 9(a) were used for the calculations. Thin active layers of 50 nm and 75 nm thicknesses show dramatic absorption enhancements with plasmonic nanograting. The absorption enhancements for the active layers thinner than 100 nm are mainly attributed to the weakened absorptions of the reference cells without Ag nanograting due to the insertion of the TiO2 layer as shown in Fig. 2(a). The active layers of 100 nm to 200 nm thicknesses exhibit around 20% of absorption enhancements, and 6% of absorption enhancements are observed even in a 250 nm thick active layer.
Plasmonic Ag nanograting in backcontact of the inverted P3HT:PCBM solar cell with TiO2 as an optical spacer were proposed and design of nanograting for effective light trapping to enhance optical absorption in active layers were explored numerically. The modal analysis in the multilayered solar cells provided a design guide for the optimal period to boost optical absorption in the wavelengths above 600 nm. The FDTD calculations combined with the modal analysis allowed for the optimization of nanograting for maximization of optical absorption under a standard solar radiation, and the absorption enhancement of 23% in a random polarization with nanograting of a 60 nm height and a 200 nm width at the period of 380 nm was numerically demonstrated. The modal analysis and the FDTD calculations identified the absorption enhancement mechanisms and revealed excitation of the TE0 modes and the TM0 modes mixed with the SPP lead to the absorption enhancements in a TE polarization and a TM polarization, respectively. The influence of active layer thicknesses on the optimal period was also investigated, and it was shown that a thinner active layer shifts dispersion curves of waveguide modes toward shorter wavelengths resulting in the longer optimal periods.
The authors thank Korea Institute of Science and Technology (KIST) for the financial support of this research (Grant No. 2E22733).
References and links
1. Z. He, C. Zhong, X. Huang, W.-Y. Wong, H. Wu, L. Chen, S. Su, and Y. Cao, “Simultaneous Enhancement of Open-Circuit Voltage, Short-Circuit Current Density, and Fill Factor in Polymer Solar Cells,” Adv. Mater. (Deerfield Beach Fla.) 23(40), 4636–4643 (2011).
2. G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6(3), 153–161 (2012).
3. D.-H. Ko, J. R. Tumbleston, A. Gadisa, M. Aryal, Y. Liu, R. Lopez, and E. T. Samulski, “Light-trapping nano-structures in organic photovoltaic cells,” J. Mater. Chem. 21(41), 16293–16303 (2011).
4. M. A. Green, “Enhanced evanescent mode light trapping in organic solar cells and other low index optoelectronic devices,” Prog. Photovolt. Res. Appl. 19(4), 473–477 (2011).
5. 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).
6. 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(S4), A528–A535 (2010).
7. M.-G. Kang, T. Xu, H. J. Park, X. Luo, and L. J. Guo, “Efficiency Enhancement of Organic Solar Cells Using Transparent Plasmonic Ag Nanowire Electrodes,” Adv. Mater. (Deerfield Beach Fla.) 22(39), 4378–4383 (2010).
8. G. D. Spyropoulos, M. M. Stylianakis, E. Stratakis, and E. Kymakis, “Organic bulk heterojunction photovoltaic devices with surfactant-free Au nanoparticles embedded in the active layer,” Appl. Phys. Lett. 100(21), 213904 (2012).
9. J.-L. Wu, F.-C. Chen, Y.-S. Hsiao, F.-C. Chien, P. Chen, C.-H. Kuo, M. H. Huang, and C.-S. Hsu, “Surface Plasmonic Effects of Metallic Nanoparticles on the Performance of Polymer Bulk Heterojunction Solar Cells,” ACS Nano 5(2), 959–967 (2011).
10. W. E. I. Sha, W. C. H. Choy, Y. G. Liu, and W. C. Chew, “Near-field multiple scattering effects of plasmonic nanospheres embedded into thin-film organic solar cells,” Appl. Phys. Lett. 99(11), 113304 (2011).
11. J.-Y. Lee and P. Peumans, “The origin of enhanced optical absorption in solar cells with metal nanoparticles embedded in the active layer,” Opt. Express 18(10), 10078–10087 (2010).
12. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
13. M. A. Green and S. Pillai, “Harnessing plasmonics for solar cells,” Nat. Photonics 6(3), 130–132 (2012).
14. C. Min, J. Li, G. Veronis, J.-Y. Lee, S. 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(13), 133302 (2010).
15. 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(4), 478–480 (2011).
16. 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).
17. W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10(6), 2012–2018 (2010).
18. A. Abass, H. Shen, P. Bienstman, and B. Maes, “Angle insensitive enhancement of organic solar cells using metallic gratings,” J. Appl. Phys. 109(2), 023111 (2011).
19. M. A. Sefunc, A. K. Okyay, and H. V. Demir, “Plasmonic backcontact grating for P3HT:PCBM organic solar cells enabling strong optical absorption increased in all polarizations,” Opt. Express 19(15), 14200–14209 (2011).
20. A. Baba, N. Aoki, K. Shinbo, K. Kato, and F. Kaneko, “Grating-coupled surface plasmon enhanced short-circuit current in organic thin-film photovoltaic cells,” ACS Appl. Mater. Interfaces 3(6), 2080–2084 (2011).
21. L.-M. Chen, Z. Xu, Z. Hong, and Y. Yang, “Interface investigation and engineering - achieving high performance polymer photovoltaic devices,” J. Mater. Chem. 20(13), 2575–2598 (2010).
22. S. K. Hau, H.-L. Yip, N. S. Baek, J. Zou, K. O'Malley, and A. K. Y. Jen, “Air-stable inverted flexible polymer solar cells using zinc oxide nanoparticles as an electron selective layer,” Appl. Phys. Lett. 92(25), 253301 (2008).
23. F. Zhang, X. Xu, W. Tang, J. Zhang, Z. Zhuo, J. Wang, J. Wang, Z. Xu, and Y. Wang, “Recent development of the inverted configuration organic solar cells,” Sol. Energy Mater. Sol. Cells 95(7), 1785–1799 (2011).
24. J. Meiss, M. K. Riede, and K. Leo, “Towards efficient tin-doped indium oxide (ITO)-free inverted organic solar cells using metal cathodes,” Appl. Phys. Lett. 94(1), 013303 (2009).
25. M. Manceau, D. Angmo, M. Jørgensen, and F. C. Krebs, “ITO-free flexible polymer solar cells: From small model devices to roll-to-roll processed large modules,” Org. Electron. 12(4), 566–574 (2011).
26. J. M. Hammer, G. Ozgur, G. A. Evans, and J. K. Butler, “Integratable 40 dB optical waveguide isolators using a resonant-layer effect with mode coupling,” J. Appl. Phys. 100(10), 103103 (2006).
27. G. A. Evans, (Southern Methodist University, Dallas, 1998).
28. P. Yeh, Optical Waves in Layered Media (Wiley-Interscience, Singapore, 1988).
29. F. Monestier, J.-J. Simon, P. Torchio, L. Escoubas, F. Flory, S. Bailly, R. de Bettignies, S. Guillerez, and C. Defranoux, “Modeling the short-circuit current density of polymer solar cells based on P3HT:PCBM blend,” Sol. Energy Mater. Sol. Cells 91(5), 405–410 (2007).
30. D. R. Lide, CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 86th ed. (CRC Press, London: Taylor and Francis, 2004).
31. S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics 3(5), 297–302 (2009).
32. R. Kroon, M. Lenes, J. C. Hummelen, P. W. M. Blom, and B. de Boer, “Small Bandgap Polymers for Organic Solar Cells (Polymer Material Development in the Last 5 Years),” Pol. Rev. 48(3), 531–582 (2008).
33. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
34. X. H. Li, W. E. I. Sha, W. C. H. Choy, D. D. S. Fung, and F. X. Xie, “Efficient inverted polymer solar cells with directly patterned active layer and silver back grating,” J. Phys. Chem. C 116(12), 7200–7206 (2012).
35. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
36. R. Dynich, A. Ponyavina, and V. Filippov, “Local field enhancement near spherical nanoparticles in absorbing media,” J. Appl. Spectrosc. 76(5), 705–710 (2009).