Metal nanogratings as one of the promising architectures for effective light trapping in organic photovoltaics (OPVs) have been actively studied over the past decade. Here we designed a novel metal nanowall grating with ultra-small period and ultra-high aspect-ratio as the back electrode of the OPV device. Such grating results in the strong hot spot effect in-between the neighboring nanowalls and the localized surface plasmon effect at the corners of nanowalls. These combined effects make the integrated absorption efficiency of light over the wavelength range from 400 to 650 nm in the active layer for the proposed structure, with respect to the equivalent planar structure, increases by 102% at TM polarization and by 36.5% at the TM/TE hybrid polarization, respectively. Moreover, it is noted that the hot spot effect in the proposed structure is more effective for ultra-thin active layers, which is very favorable for the exciton dissociation and charge collection. Therefore such a nanowall grating is expected to improve the overall performance of OPV devices.
© 2014 Optical Society of America
Organic photovoltaics (OPVs) have great potential as a renewable energy source due to their relatively low-cost, ease of fabrication as well as their compatibility with large area flexible substrates [1, 2]. But their energy conversion efficiencies are significantly low at present compared with their inorganic counterparts. In OPV devices, the thin active layers are necessary due to the intrinsic properties of organic materials, such as the low carrier mobility and short exciton diffusion length. However, very thin active layers could not efficiently absorb the incident photons. This incompatibility is one of the main reasons for the low energy conversion efficiency of OPV devices. To compensate for the poor absorption in the thin active layers, various light trapping strategies have been proposed [3–5]. The metallic nanostructures inducing surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs), are considered to be highly promising candidate for effective absorption enhancement without increasing the thickness of active layers [6–8]. Among them, the periodic metal gratings are one main type frequently used in OPVs for enhanced optical absorption, meanwhile as the electrode, like the back reflecting cathode, top transparent anode or both [9–22]. To match the excitation of SPPs or LSPs with the absorption band of active materials, typical periods of one-dimensional (1D) metal gratings are hundreds of nanometers [9, 13, 15, 19, 20] while those with small periods (especially less than 100 nm) have been rarely explored for OPV applications. Recently, the high aspect-ratio metal grating held by polyurethaner matrix had been proposed as a potential alternative to ITO electrodes [23, 24]. Such grating is also named as a 1D metal nanowall grating due to its high aspect ratio (height of metal strip over its width). It is mentioned that in Refs . and , the periods of the metal gratings are much larger than 100 nm as well.
In this work, we theoretically propose a novel 1D metal nanowall grating with ultra-small period (of 20 nm) as well as ultra-high aspect-ratio (of 30:7). Our systematical numerical analysis indicates that when this nanowall grating on top of a continuous metal reflective film is incorporated into an OPV device based on P3HT:PCBM [1:1 ratio mixture of poly-3-hexylthiophene (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM)] as the back cathode, we achieve an increased optical absorption in the active layer which is broadband and angular insensitive. Moreover, this increased absorption can allow for the use of ultra-thin active layers, resulting in decreased charge carrier transport losses to the device electrodes in practice. Particularly, this grating is deeply penetrated into the organic active layer so that the electrons could be directly collected to the metallic grating cathode with a short transport path.
In such a unique structure, of which the metal nanowalls are quite close to each other (with a separation of 13 nm), a novel physical mechanism, named as the hot spot effect [25–28], is excited with the electric field of enhanced magnitude distributed in-between neighboring metal nanowalls at transverse magnetic (TM) polarization (the magnetic component is parallel to the grating). In the last period, the hot spot effect has been mainly reported in the area of single molecule detections via surface-enhanced Raman scattering (SERS) [27, 28]. When two particles are placed with a separation of a few nanometers or many particles are manipulated to form a high density aggregate, the electric field induced between the particles can be amplified by several orders of magnitude. But these hot spots are hardly ever mentioned in OPV applications to date. Beside of the hot spot effect, LSP resonances at the top and bottom corners of metall nanowalls are also simultaneously triggered in our design. As a result, such nanowall grating greatly enhances the TM-polarized light absorption integrated over the wavelength range from 400 to 650 nm in the P3HT:PCBM layer by a factor of 102% with respect to the equivalent planar structure which has the same volume of P3HT:PCBM. For the transverse electric (TE) polarized illumination with the electric component parallel to the grating, the metal nanowalls result in suppression in optical absorption of the active layer. That is ascribed to the damped interference intensity influenced by the changed position of the reflective plane, which is a common phenomenon for 1D metal nanogratings [6, 10, 11]. However, as the absorption enhancement at TM polarization is stronger than the suppression at TE polarization, the optical absorption of the active layer at TM/TE hybrid polarization is enhanced by 36.5% for our designed OPV device compared with that of the equivalent planar structure.
2. Structures and methods
The proposed OPV device with periodic silver nanowalls is shown in Fig. 1(a).In detail, the transparent indium-tin-oxide (ITO) of 100 nm thickness is used as the top anode, PEDOT:PSS of 50 nm thickness as the hole transport layer and P3HT:PCBM with thickness of t = 35 nm as the active layer. The silver nanowalls with period p, width w and height h placed on top of a continuous silver film of 200 nm thick are deeply inserted into the active layer as the back reflecting cathode as well as the light trapping elements. In our simulations, the experimentally measured complex refractive indices of P3HT: PCBM (1:1), PEDOT: PSS and ITO are used directly without approximation treatment [as shown in Fig. 1(b)] while complex refractive indices of Ag with wavelength dependence are obtained from Ref .
Here, all of the OPV structures are simulated by the Rigorous Coupled-wave Analysis (RCWA) method  which has been verified by repeating the work in Ref . The calculations are conducted within one unit cell [see the dotted box in Fig. 1(a)] with periodic boundary conditions applied along the x-axis and perfectly matched layer (PML) boundaries along the y-axis. Light is incident from the top into the device and the investigated wave wavelength range (λ) is from 400 to 800 nm to match the P3HT:PCBM absorption band as well as the solar irradiance spectrum. The problems are first investigated at TM and TE polarizations, respectively. Then, the efficiencies at the TM/TE hybrid polarization are obtained by taking the average of the corresponding values at TM and TE polarizations. Unless otherwise noted, the device with geometrical parameters of p = 20 nm, w = 7 nm, h = 30 nm and t = 35 nm is considered. The planar device without any grating profiles is also investigated as the reference as shown in the inset of Fig. 2(a), of which the thickness of the active layer is denoted by teff. For fair comparison, we ensure that the volumes of the active material in our designed structure and the planar reference are the same. Except in the study on the angular performance of the device, we consider the normal incidence situation. Unless stated otherwise, the integrated absorption efficiency of light in the active layer (denoted by ATotal) is calculated within the wavelength range from 400 to 650 nm without considering the weight of AM 1.5 solar spectrum.
3. Results and discussions
First, we demonstrate the absorption performance of the planar device. Figure 2(a) shows the integrated absorption efficiency of light in the active layer as a function of the thickness of the active layer. It is found that the Fabry-Pérot maxima produced according to the interference theory are located at teff = 60 and 205 nm (denoted by R2 and R3) with ATotal equal to 75.4% and 78.9%, respectively. The inset of Fig. 2(a) shows their absorption spectra as well as that of an ultrathin OPV device (denoted by R1 with teff = 24.5 nm). It reflects that at the Fabry-Pérot maxima, a very large amount of the incident light is absorbed by the active material. But in reality, such thick active layers are not favorable to the exciton dissociation and charge collection due to the intrinsic deficiencies of organic materials. However, when the thickness of the organic layer allows for good electric performance (e.g., the device R1), the light absorption by the active layer would be quite poor as shown by the dashed line in the inset of Fig. 2(a), which corresponds to an integrated absorption efficiency ATotal equal to 35.1%, less than half of that at teff = 60 nm. Therefore, it is very difficult, for the planar device, to achieve a good trade-off between the optical absorption efficiency and the exciton dissociation and charge collection efficiency. However, by resorting to a metal nanowall grating with ultra-small period and ultra-high aspect-ratio, the performance of the ultrathin OPV device can be greatly improved, approaching that of the thick planar device at TM polarization.
Figure 2(b) displays the absorption spectra of the active layer for the proposed structure with p = 20 nm, w = 7 nm, h = 30 nm and t = 35 nm at TM (thick solid), TE (thin solid) and the hybrid polarization (triangular symbol), respectively. It is observed that at TM polarization, the absorption efficiencies within the whole wavelength range from 400 to 600 nm are outstanding, exceeding 70%. By comparing the thick solid line in Fig. 2(b) with the circular symbol line in the inset of Fig. 2(a), we observe that the proposed ultrathin OPV device (t = 35 nm) with metal nanowall grating is not much inferior to the planar optimized device with a much thicker active layer (teff = 60 nm) in absorbing TM-polarized light. The integrated absorption efficiency of the active layer (ATotal) for the proposed structure reaches 71.2% at TM polarization, approaching the absorption level (75.4%) for the planar thick device with teff = 60 nm. If the weight of the AM 1.5 spectrum of the sun is considered, the integrated absorption efficiency is 71.4%, indicating that the enhancement of absorption in the active layer matches with the solar spectrum. For fair, we also make a comparison between our proposed device and the equivalent planar reference device (i.e., R1 with teff = 24.5 nm) [dashed, Fig. 2(b)]. It is observed that for our proposed device at TM polarization, the broadband absorption enhancement is observed over the wavelength range from 400 to 650 nm. Especially, the enhancement factor at the wavelength around 583 nm is pretty large, about five times. Finally, the broadband absorption enhancement yields ATotal enhanced by 102% in comparison with that for the equivalent planar device. However, at TE polarization, the absorption efficiency decreases within the whole wavelength range with respect to the equivalent planar device. Even so, the enhancement at TM polarization still overwhelms the decrement at TE polarization. As a result, the broadband absorption enhancement is still achieved at the TM/TE hybrid polarization [triangular symbol, Fig. 2 (b)]. By calculation, we know that ATotal of our propose device at the hybrid polarization is 47.9%, increases by 36.5% compared with that of the equivalent planar device. Figure 2(c) displays the ratio of the integrated absorption efficiency of light in the active layer (Aratio) for the proposed structure over that of the planar reference device as a function of the active layer thickness (t). All of the planar devices in comparison have the equivalent thickness teff so that the volume of the active material in planar device is always identical to that of the proposed structure. It is found that when the thickness of the active layer increases, Aratio for TM-polarized light decreases gradually while that for TE-polarized light increases gradually. By taking the average of those them, we find that the variation tendency of Aratio at the hybrid polarization is first reduced and then increased minorly. Overall, under TE/TM hybrid polarization, our metal nanowall grating works positively on enhancing the light absorption in active layer for OPV devices with the active layer thinner than 50 nm.
Next, we will focus on investigating the device performance at TM polarization. Figure 2(d) shows the absorption spectra of other function layers of Ag and PEDOT:PSS as well as the whole device, with that of P3HT:PCBM redraw for clear illustration. It can be seen that within the wavelength range from 400 to 600 nm, the absorption efficiency of the whole device is close to unity, reflecting that this device has very good anti-reflection property. The contribution from different function layers indicates that the absorption of light by the PEDOT: PSS layer is quite weak and negligible, a small part of light is consumed by the Ag layer, while most of the light absorption originates from the P3HT:PCBM layer. From the absorption spectra of the Ag layer, we observe several absorption peaks (one close to 400 nm, the other two near 600 nm) produced by plasmonic resonances. It would be these plasmonic resonances helps greatly trapping the incident light into the propose structure, particularly the active layer.
In order to better understand the mechanism of light absorption enhancement, the distributions of electromagnetic field of the proposed structure are studied. There are three wavelengths labeled on the absorption spectra of the active layer for our proposed device at TM polarization in Fig. 2(b), two of which corresponding to the peaks and one the valley. In detail, they are λ1 = 460 nm, λ2 = 528 nm and λ3 = 583 nm. Figure 3(a) and (b) shows the distributions of the electric field |E| and magnetic field |H| at λ1, λ2 and λ3, respectively, under TM-polarized illumination. Here, the incident amplitude of |E| is set to 1 V/m. It can be seen from Fig. 3(a) that the electric field distributed in-between neighboring metallic nanowalls are greatly strengthened at all the three peaks. However, the distribution of the magnetic field [see Fig. 3(b)] does not display any apparent difference from the plane wave. This feature is distinct from that of the traditional plasmonic waveguide resonance with the magnetic field amplitude being amplified in the gap between two separated metal/dielectric interfaces (also named as the MIM structure) . But it is very similar to the hot spot effect widely applied in SERS applications [25, 26]. The hot spot effect exists when two particles are placed with a separation of a few nanometers or when many particles are manipulated to form a high density aggregate. Besides, the excitation of the hot spot effect depends greatly on the direction of the electric field of the incident light. If only the incident light includes the electric field component parallel to the axis connecting the neighboring metal nanoparticles, the hot spot effect is possible to be produced. In addition, the distance between neighboring metal nanoparticles has very strict requirement, and the typical length is around 10 nm. If the above-mentioned conditions are fulfilled, the electric field induced between the neighboring metal nanoparticles could be amplified greatly.
Here, the distance between our neighboring nanowalls is 13 nm, close to the typical particle distance for the excitation of the hot spots. And the incident electric filed at normal TM-polarized illumination is along x-axis, parallel to the direction connecting neighboring nanowalls. Moreover, we observe amplified amplitude of the electric field between neighboring nanowalls. Thus, it is natural to attribute the excited resonance to the hot spot effect. Beside of the hot spot effect, it is also noticed that there are accumulated electric field at the top and bottom corners of nanowalls, especially at λ3. This is a typical kind of LSP resonances. In order to distinguish the contribution of the LSP effect on the absorption enhancement in the active layer, we smooth all of the right angles of the metal nanowalls into arc-shaped angles. By this way, we eliminate the LSP effect (not shown here) and retain the hot spot effect. Calculation shows that the integrated absorption efficiency of the active layer (ATotal) suffers negligible changes (from 71.16% to 71.09%). This indicates the hot spots play dominant role in enhancing the light absorption of the active layer over the broadband spectrum at TM polarization.
Figure 3(c) and (d) present the distributions of electromagnetic fields of the proposed structure at λ1, λ2 and λ3 under TE-polarized illumination. One sees that there are no observable local resonances and the distributions basically retain the plane wave property. The reduction of the absorption of light in the active layer at TE polarization is produced mainly because the reflective plane of the back cathode moves up (i.e., along positive z-axis) influenced by the additional metal nanowalls. This leads to the active layer becomes much thinner than in the equivalent planar device. In other words, the proposed device has a wider deviation from the constructive Fabry-Pérot maximum (R2 planar device) than the equivalent planar device. As a result, it leads to the interference intensity much damped. Moreover, the Ag nanowalls should produce more absorption than the planar Ag film, which could be another reason of the absorption reduction.
Further study shows that the absorption performance of our proposed structure is angular insensitive. Figure 4(a-c) demonstrates the angular dependent absorption spectra under TM, TE and the hybrid polarizations, respectively, and Fig. 4(d) displays the corresponding integrated absorption efficiency of the active layer (ATotal) versus the incidence angle. As can be seen, the proposed device has high absorption efficiency (> 70%) within a wide angular range from 0 to 70 degree at TM polarization. But at TE polarization, the roll-off of the integrated absorption efficiency is observed with the increase of the incident angle, which is derived from the gradually blueshift absorption band [see Fig. 4(b)] influenced by the wavevector matching condition. Benefit from the high-efficiency, broad-band, and wide-angle absorption at TM polarization, the designed structure exhibits an invariable high integrated absorption efficiency of the active layer within a very wide range of angle [symbol line, Fig. 4(d)]. Such omnidirectional feature is very favorable for practical applications.
Finally, we investigate the dependence of the device performance on the geometrical parameters of the metal nanowalls when other parameters are set the same as those in Fig. 2(b). Figure 5(a-c) present the maps of the integrated absorption efficiency of the active layer versus the nanowall dimensions w and h at different polarizations. It can be seen from Fig. 5(a) that at TM polarization the absorption is strongly dependent on the dimensions w and h. The optimized TM-polarized light absorption is realized when w = 7 nm and h = 30 nm [labeled as case A, i.e., the device studied in Fig. 2(b)]. Figure 5(a) also reflects that the absorption enhancement produced by the hot spot effect takes place when the wall-to-wall distance is not much deviated from the optimized value. If the wall-to-wall distance is too large or too small, the hot spot effect is eliminated. Besides, the device performance is less sensitive to the wall height with respect to the wall width. It is apparent that the walls with too small height cannot excite the hot spot effect because it modifies the flat Ag plate negligibly. At TE polarization, it can be seen from Fig. 5(b) that the absorption is weakened with increasing w and h, which is mainly attributed to the reduced volume of active layer and the raised reflective plane of the back cathode. Figure 5(c) presents the map of the integrated absorption efficiency (ATotal) versus w and h at the hybrid polarization. By taking the average of TM and TE results, the maximum absorption at the hybrid polarization changes to the case with w = 7 nm and h = 8 nm (labeled as case C). For such an optimized device at the hybrid polarization, the integrated absorption efficiency of the active layer (ATotal) is 53.6%, 11.9% greater than that for case A. From Fig. 5(c), we also know that the performance of our proposed device at the hybrid polarization can retain very well with wide ranges of both w and h. The two dashed line in Fig. 5(c) represent the contour lines corresponding to the integrated efficiency of 95% and 90% of the maximum. Case B with w = 7 nm and h = 23 nm lies on the 95%*AT_Max contour line and case A is close to the 90% contour line. It is observed that the tolerance on w is smaller than on that on h if the optimized device of case C is to fabricate.
Figure 5(d) presents the dependence of the integrated absorption efficiency (ATotal) on the grating period p for case A at TM, TE, and the hybrid polarizations, respectively. It can be seen that the integrated absorption is sensitive to the grating period for both TM and TE polarization. As p increases to be larger than the optimized value (20 nm), the integrated absorption is weakened at TM polarization because the enlarged separation between neighboring nanowalls weakens and finally eliminates the hot spot effect. While at TE polarization, the partition coefficient of the metal nanowall decreases with increasing p makes the device closer to the planar device, and thus increases the absorption. In other words, when the period is large, the propose device is close to a planar device with teff = 35 nm. After averaging the TM/TE results, we obtain that the total absorption increases gradually as the period increases and it becomes stable when the period is greater than 40 nm. Similar studies have also been carried out for case B and case C as shown in Fig. 5(e). And it is found that for case C, the integrated efficiency first increases and then decreases, and reaches its maximum value at p = 18 nm.
The P3HT: PCBM based OPV device with an Ag nanowall grating with ultra-small period as well as ultra-high aspect-ratio as the back electrode is designed. The light trapping behavior is explored numerically for enhancing the optical absorption of ultra-thin active layers. The results indicate that the introduction of the Ag nanowall grating results in broadband optical absorption enhancement for TM-polarized light. For the proposed structure, the integrated absorption efficiency of the active layer at normal TM-polarized illumination is 71.2%, enhanced by 102% relative to the planar device with equivalent active layer thickness. This is mainly attributed to the excitation of the hot spot effect. Despite that the absorption performance at TE polarization is degraded, the integrated absorption efficiency of the active layer at the TM/TE hybrid polarization is still enhanced by 36.5%. Besides, our study shows that this structure exhibits a wide angular optical absorption of the active layer at both TM and the hybrid polarizations. We emphasize that this work provide a route to design ultra-thin photovoltaic devices, which is beneficial for decreasing charge carrier transport losses. The propose Ag nanowall grating as the back electrode is expected to improving the overall performance of OPV devices.
This research work was financially supported by National Natural Scientific Foundation of China (61274056, 11204205, 61205179, 21101111, 21071108, 11204202, 91233208), Key Laboratory Foundation of Advanced Display and System Applications of Ministry of Education in Shanghai University, International Science & Technology Cooperation Program of China (2012DFR50460), and Shanxi Natural Scientific Foundation (2010021023-2, 2011021022-2, 2012011020-4). Cui is thankful to Prof. Furong Zhu from Hong Kong Baptist University for his kindly help on this work and acknowledges the New Teachers' Fund for Doctor Stations (20121402120017), Hong Kong Scholar Plan (XJ2013002), and the Top Young Academic Leaders of Higher Learning Institutions of Shanxi.
References and links
1. G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6(3), 153–161 (2012). [CrossRef]
2. Z. He, C. Zhong, S. Su, M. Xu, H. Wu, and Y. Cao, “Enhanced power-conversion efficiency in polymer solar cells using an inverted device structure,” Nat. Photonics 6(9), 593–597 (2012). [CrossRef]
3. J. R. Tumbleston, D. H. Ko, E. T. Samulski, and R. Lopez, “Absorption and quasiguided mode analysis of organic solar cells with photonic crystal photoactive layers,” Opt. Express 17(9), 7670–7681 (2009). [CrossRef] [PubMed]
4. X. L. Zhang, J. F. Song, X. B. Li, J. Feng, and H. B. Sun, “Light trapping schemes in organic solar cells: A comparison between optical Tamm states and Fabry-Perot cavity modes,” Org. Electron. 14(6), 1577–1585 (2013). [CrossRef]
7. A. P. Kulkarni, K. M. Noone, K. Munechika, S. R. Guyer, and D. S. Ginger, “Plasmon-enhanced charge carrier generation in organic photovoltaic films using silver nanoprisms,” Nano Lett. 10(4), 1501–1505 (2010). [CrossRef] [PubMed]
8. D. H. Wang, Y. Kim, K. W. Choi, J. H. Seo, S. H. Im, J. H. Park, O. O. Park, and A. J. Heeger, “Enhancement of Donor-Acceptor polymer bulk heterojunction solar cell power conversion efficiencies by addition of Au nanoparticles,” Angew. Chem. Int. Ed. Engl. 50(24), 5519–5523 (2011). [CrossRef] [PubMed]
9. X. Li, W. C. H. Choy, L. Huo, F. Xie, W. E. I. Sha, B. Ding, X. Guo, Y. Li, J. Hou, J. You, and Y. Yang, “Dual plasmonic nanostructures for high performance inverted organic solar cells,” Adv. Mater. 24(22), 3046–3052 (2012). [CrossRef] [PubMed]
10. K. Tvingstedt, N. K. Persson, O. Inganas, A. Rahachou, and I. V. Zozoulenko, “Surface plasmon increase absorption in polymer photovoltaic cells,” Appl. Phys. Lett. 91(11), 113514 (2007). [CrossRef]
11. 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). [CrossRef]
12. 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. 22(39), 4378–4383 (2010). [CrossRef] [PubMed]
15. Z. Sun and X. Zuo, “Tunable absorption of light via localized plasmon resonances on a metal surface with interspaced ultra-thin metal gratings,” Plasmonics 6(1), 83–89 (2011). [CrossRef]
16. 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). [CrossRef] [PubMed]
17. M. A. Sefunc, A. K. Okyay, and H. V. Demir, “Volumetric plasmonic resonator architecture for thin-film solar cells,” Appl. Phys. Lett. 98(9), 093117 (2011). [CrossRef]
18. W. E. I. Sha, W. C. H. Choy, and W. Cho Chew, “The roles of metallic rectangular-grating and planar anodes in the photocarrier generation and transport of organic solar cells,” Appl. Phys. Lett. 101(22), 223302 (2012). [CrossRef]
19. Y. Liu and J. Kim, “Polarization-diverse broadband absorption enhancement in thin-film photovoltaic devices using long-pitch metallic gratings,” J. Opt. Soc. Am. B 28(8), 1934–1939 (2011). [CrossRef]
20. 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). [CrossRef]
21. 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). [CrossRef] [PubMed]
23. Z. Ye, S. Chaudhary, P. Kuang, and K.-M. Ho, “Broadband light absorption enhancement in polymer photovoltaics using metal nanowall gratings as transparent electrodes,” Opt. Express 20(11), 12213–12221 (2012). [CrossRef] [PubMed]
24. P. Kuang, J. M. Park, W. Leung, R. C. Mahadevapuram, K. S. Nalwa, T. G. Kim, S. Chaudhary, K. M. Ho, and K. Constant, “A New Architecture for Transparent Electrodes: Relieving the Trade-Off Between Electrical Conductivity and Optical Transmittance,” Adv. Mater. 23(21), 2469–2473 (2011). [CrossRef] [PubMed]
26. T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime,” Nano Lett. 4(9), 1627–1631 (2004). [CrossRef]
27. J. P. Camden, J. A. Dieringer, Y. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008). [CrossRef] [PubMed]
28. J. D. Caldwell, O. J. Glembocki, F. J. Bezares, M. I. Kariniemi, J. T. Niinistö, T. T. Hatanpää, R. W. Rendell, M. Ukaegbu, M. K. Ritala, S. M. Prokes, C. M. Hosten, M. A. Leskelä, and R. Kasica, “Large-area plasmonic hot-spot arrays: sub-2 nm interparticle separations with plasma-enhanced atomic layer deposition of Ag on periodic arrays of Si nanopillars,” Opt. Express 19(27), 26056–26064 (2011). [CrossRef] [PubMed]
29. E. D. Palik, Handbook of Optical Constants of Solids: Index (Access Online via Elsevier, 1998).
30. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3(11), 1780–1787 (1986). [CrossRef]