Transparent metal grid combining with plasmonic absorption enhancement is a promising replacement to indium tin oxide thin films. We numerically demonstrate metal grids in one or two dimension lead to plasmonic absorption enhancements in ultrathin organic solar cells. In this paper, we study optical design of metal grids for plasmonic light trapping and identify different plasmonic modes of the surface plasmon polaritons excited at the interfaces of glass/metal grids, metal grids/active layers, and the localized surface plasmon resonance of the metal grids using numerical calculations. One dimension metal grids with the optimal design of a width and a period lead to the absorption enhancement in the ultrathin active layers of 20 nm thickness by a factor of 2.6 under transverse electric polarized light compared to the case without the metal grids. Similarly, two dimensional metal grids provide the absorption enhancement by a factor of 1.8 under randomly polarized light.
©2013 Optical Society of America
Organic solar cells have shown a great promise for one of alternative technologies to conventional ones such as c-Si solar cells due to their cost-effective cell processing and low cost source materials. However, power conversion efficiency of organic solar cells is much lower than that their inorganic counter partner although they have been showing a steady growth and exceeded 10% recently [1, 2]. Numerous efforts have been made to further improve power conversion efficiency of organic solar cells and reduce cell cost.
One of limiting factors to the power conversion efficiency of organic solar cells is low carrier mobility in organic semiconductors, which hinders efficient charge collection in thick active layers . This issue has been tackled by using light trapping approaches, and a plasmonic approach is one of promising and viable options [4, 5]. Using a plasmonic scheme, optical absorption is boosted up by placing metal nanostructures in the proximity or inside of active layers by amplification of light fields via excitation of surface plasmons at the interfaces of metal and dielectric [6, 7]. This approach enables thinner active layers to absorb more photons, leading to more efficient charge collection and in turn high power conversion efficiency.
Transparent conducting electrode is one of essential components for organic solar cells, and indium tin oxide (ITO) is most widely used, but its high cost stemming from rarity of indium needs to be addressed for practical use of organic solar cells. A plethora of research has been devoted to demonstrate that metal grids or wires made of Ag or Au in one or two dimension can have high optical transparency and electrical conductivity for transparent electrode of thin film solar cells [8–11]. A replacement of expensive ITO films in organic solar cells by thin metals would lead to substantially lower cell cost.
If metal grids are designed in nano scale to have surface plasmon resonance in wavelengths where optical absorption in active layers of organic solar cells is weak, they can serve as optical absorption booster as well as transparent electrode. The enhanced optical absorption by the metal grids allows for thinner active layers, and the metal grids can be a replacement to expensive ITO films . In multi-layered solar cell structures, elaborate design of metal grids is required for spectrally broad absorption enhancements.
In this study, we identified multiple surface plasmon modes by numerical calculations and provide design guide of metal grids to maximize optical absorption enhancements in ultrathin active layers of organic solar cells based on conducting polymer.
First, one dimension (1D) metal grid was considered as design of plasmonic transparent electrode for organic solar cells. Schematic device structure to perform numerical calculations for optical absorption in organic solar cells is shown in Fig. 1. The 1D metal grid of Ag is embedded in a buffer layer of poly(3,4-ethylenedioxythiophene) (PEDOT): poly(styrenesulfonate) (PSS) in polymer solar cells based on poly-3-hexythiphene (P3HT): phenyl-C61-butyric acid methyl ester (PCBM) with Ag cathode, which also act as back reflector. Finite-difference-time-domain (FDTD) calculations were made on this device structure using a commercial software package (Lumerical FDTD 8.0). Periodic boundary conditions were put on the x-direction, and perfectly matched layers on the upper and the lower boundaries. Solar radiation in transverse magnetic (TM) or transverse electric (TE) polarization was incident from glass substrate of a refractive index 1.5. Randomly polarized light was introduced by averaging TM and TE polarized light. The refractive indices of Ag were determined using sputtered thin films by spectroscopic ellipsometry. As for a buffer and an active layer, the refractive indices were extracted from literature .
A thickness of Ag metal grids was fixed at 20 nm for all the calculations. A thickness of the active layers was set for 20 nm unless stated otherwise. Optical absorptions in the active layers and the metal grids were calculated by integrating energy dissipation with varying widths from 20 nm to 100 nm and periods of the metallic grids from 100 nm to 400 nm. In order to identify surface plasmon modes, dispersion curves of surface plasmon polariton (SPP) modes generated on the interfaces of Ag/glass and Ag/active layer were calculated using an Eigen mode solver for a planar device structure of glass/Ag 20 nm/active layer 20 nm/Ag [14, 15]. Optical absorption spectra in the active layers and the metal grids were determined in the wavelength range of 400 nm to 800 nm. Absorption enhancements with inclusion of the metal grids were calculated by normalizing the number of absorbed photons in the active layers with the metal grids to the case without the metal grids. The number of absorbed photons was determined by integrating absorbed photons in a given layer under solar radiation of AM 1.5G at a light intensity of 100 mW/cm2. A thickness of the active layers was varied from 5 nm to 50 nm to investigate the influence of Ag back reflector on plasmonic absorption enhancements and also interaction between the metal grids and the back reflector. For the purpose of comparative study, optical absorption spectra of organic solar cells with two dimensional metal grids were calculated and compared.
3. Results and discussions
The contour plots of the optical absorption in the active layers of 20 nm thickness and the metal grids of 100 nm width under TM polarized illumination are shown as a function of the grid period in Figs. 2(a) and 2(b), respectively. The spectral absorptions in the active layers are broadened with increasing the width of the metal grids and exhibit the maximum at the period of 200 nm. In order to identify the surface plasmon modes, dispersion curves were calculated for a device structure of glass/Ag 20 nm/active layer 20 nm/Ag by solving electromagnetic wave equations using the Eigen mode solver and plotted in the same figures . Two surface plasmon modes were found in the given wavelength range. The strong optical absorption in the metal grids is shown following the dispersion curve denoted by a solid line, whereas no strong absorption is observed following the other one. This will be further discussed in this article. The optical field (H-field) profiles calculated using the Eigen mode solver in the y-direction reveals that one plasmonic mode is excited at the interface of glass/Ag, and another at the interface of Ag/active layer as illustrated in the inset figures in Fig. 2(b). As shown in inset (1) of Fig. 2(b), the optical filed is strongly amplified at the interface of Ag/glass and also penetrated into active layers . This plays a main role in absorption enhancements in the active layers with incorporation of the metal grids in the buffer layers. The optical field profile of another plasmonic mode shown in inset (2) of Fig. 2(b) indicates the SPP at the interfaces of thin Ag film/active layer is coupled to that at the interfaces of active layer/bulk Ag and is the typical symmetric mode in a metal/insulator/metal structure . However, this mode is not observed in the contour plots. The weak absorption in the metal grids at the longer wavelengths than 700 nm is caused by the LSPR of the metal grids of which resonance frequency mainly depends on size and shape of metal nanostructures but not period [17, 18]. The absorption peaks by this LSPR mode appear to lie in above the wavelength of 800 nm due to the high aspect ratio of the metal grids. This LSPR mode might be in interference or overlap with the SPP mode of Ag/active layer because they exhibit in the close wavelength range. This would be a reason the SPP mode at Ag/active layer is not distinctly observed in the 1D metal grids.
The E-field intensity distributions normalized to that of incident light are shown in Fig. 2(c) at the wavelength of 412 nm and the period of 200 nm. As expected from the dispersion curve, the E-fields are strongly amplified at the interface of Ag/glass, indicating the SPP mode is excited. The amplified E-fields penetrate into the active layers, leading to absorption enhancements. With varying the periods of the metal grids, the absorption enhancements were calculated under TM and TE polarized illumination and plotted in Fig. 2(d). In a TM polarization, the absorption is enhanced by approximately a factor of 2.0 at the period of 200 nm owing to the SPP excitation. In a TE polarization, however, there is no boost in the optical absorption by the metal grids because any surface plasmon modes cannot be excited, and the metal grids just block the incident light resulting in reduced optical absorption in comparison with the case including the metal grids. Thus, as the period becomes larger, the absorption enhancement approaches a unity. In randomly polarized illumination, the maximum absorption enhancement is 1.25 at the period of 200 nm. Although there are substantial absorption enhancements with introduction of the SPP mode, the absorption in the metal grids is not avoidable as seen in Fig. 2(b). In this regard, it might be more beneficial to keep the SPP peak absorption wavelength as low as 400 nm or even lower. We may introduce another plasmonic mode of the LSPR by changing the aspect ratio of the metal grids. We kept the period for 150 nm to have the SPP mode excited at the wavelengths of ~400 nm and varied the width of the metal grids from 20 nm to 100 nm in order to tune the LSPR wavelengths. The contour plots of absorption spectra in the active layers and the metal grids are shown in Figs. 3(a) and 3(b), respectively. With increasing the width of the metal grids from 20 nm, the spectral absorptions are distinctly broadened especially near the absorption wavelength edge of 650 nm and show the maximum broadening with the metal grid width of 40 nm. The contour plot of the absorption in the metal grids show two plasmonic modes. One plasmonic mode is the SPP located around the wavelength of 400 nm, and another in the range of 630 nm to 800 nm depending on the aspect ratio of the metal grids. The similar multiple plasmonic modes by a 1D Ag array were reported to lead to significant absorption enhancements in small molecular weight organic solar cells . The E-field intensity distributions at the wavelength of 640 nm for the metal grid width of 40 nm show the optical fields are concentrated at the corners of the metal grid. Interestingly, the E-fields are much more intensified at the corners facing the active layer and the Ag back reflector. The reasons for this are two folds: (1) the refractive index of active layer is higher than glass and (2) the strong interaction of the LSPR with reflected light on the Ag back reflector [19, 20]. The amplified E-fields between the metal grids and the Ag back reflector lead to the significant absorption enhancements. In a TM polarization, the maximum absorption enhancement by a factor of 2.6 is observed for the metal grids of a 40 nm width as shown in Fig. 3(c). In a TE polarization, the narrower metal grids result in the higher absorption enhancements for the same reason as stated above. Under randomly polarized illumination, the maximum absorption enhancement is 1.7 with the metal grids of a 40 nm width.
The strong interaction of the metal grids with the Ag reflector can be understood by an image dipole induced at the reflector . If the metal grid induces an anti-paralleled image dipole in the Ag reflector, the LSPR wavelength would shift toward longer wavelengths. As the distance between the metal grid and the reflector is closer, the interaction would be stronger resulting in the more shifts of the LSPR wavelengths. This is confirmed by calculation the optical absorption in the metal grids of 40 nm width and of 150 nm period with varying the thickness of the active layers as shown in Fig. 4(a). The peak absorption wavelengths change from 800 nm to 640 nm with varying the active layer from 5 nm to 20 nm. As for the case with thicker active layers than 20 nm, the shifts of the peak absorption wavelengths is negligible indicating the interaction is greatly weakened . Under TM, TE polarized and randomly polarized illumination, photocurrents for the cells of 40 nm gird width and 150 nm period were calculated by assuming internal quantum efficiency is 100% and compared with the cases without the metal grids in Fig. 4(b). As the active layer thickness increases up to 20 nm, the photocurrent of the cells with the metal grids increases dramatically under TM polarized illumination. The photocurrent exhibits the maximum at the thickness of 30 nm, followed by decreases at the thicknesses of 40 and 50 nm. This is because the optical absorption in the metal grids, which is not desirable, compromises the absorption enhancements in the thick active layers. In contrast, under TE polarized illumination the photocurrent with the metal grids consistently increases with thickness similarly to the cases without the metal grids under randomly polarized illumination. Thus, the plasmonic metal grids are only beneficial in the active layers thinner than 40 nm.
The width and the period of metal grids were varied, and their dependence on the absorption enhancements were investigated and shown in Fig. 5. Under TM polarized illumination, the SPP excited at the interface of glass/Ag and the LSPR of the metal grid play a main role in the absorption enhancements. The period of 150 nm and the width of 40 nm for the metal grids provide the maximum enhancement. In case of TE polarized illumination, the thinner width and the larger period of the metal grids lead to less optical loss by the metal grating and approach a unity of the absorption enhancement. On average of TE and TM polarizations, a maximum absorption enhancement was found at the same width of 40 nm and the period of 150 nm as the TM polarization case
ITO thin films in optoelectronic applications have high optical transparency of 80% ~90% in the visible range. For comparative study, optical transparency of the 1D metal grids on glass substrate was calculated under TM, TE and randomly polarized light and plotted in Fig. 6. The width and the period of the metal grids are 40 nm and 150 nm for the calculations, respectively. A large dip in the transmission at the wavelength of 407 nm under TM polarized light results from the LSPR mode of the Ag grids. Although the transmission decreases with increasing the wavelength of the TE polarized light, high optical transparency above 80% under the randomly polarized light, which is comparable to most ITO thin films, was exhibited in the visible range except shorter wavelengths than 440 nm.
Lastly, the metal grids of cross shape having four-fold symmetry were embedded in the buffer layer as shown in Fig. 7(a). This two dimensional (2D) metal grid has advantages over one dimensional (1D) grid because it does not have electrical and optical anisotropy as transparent electrode and plasmonic absorption enhancer. As seen in Fig. 7(b), the absorption spectrum of the cell with the 2D metal grids resembles that with the 1D metal grids under randomly polarization except the stronger absorption enhancement by the LSPR at the wavelength of ~640 nm and another absorption peak (denoted by an arrow in the figure) at the wavelength of ~695 nm. The E-field intensity distributions reveal the origin of the absorption peak at ~695 nm in Fig. 7(c). Under polarized light in the x-direction, the E-field is strongly concentrated along the interfaces of metal bar/active layer extended in the same direction as the polarization as seen in the figure. This is the SPP mode generated at the interface of Ag/active layer, which was expected from the dispersion curves in Fig. 2. As stated above, this SPP mode is coupled to that excited at the interface of active layer/Ag back reflector, resulting in strong amplification of optical fields in the active layers as seen in Fig. 2 . The LSPR mode in the 2D metal grids is strongly concentrated along the metal bars extended in the z-direction under polarized light in the x-direction. On the other hand, the SPP mode, however, is excited in the metal bars extended in the x-direction by scattered light from the metal grids as seen in Fig. 7(c). So the interference between the SPP mode and the LSPR mode would be greatly weakened owing to this spatial separation of two plasmonic modes, leading to a strong absorption enhancement by the SPP mode unlike the 1D metal grids. As a result, the cell with the 2D metal grids shows higher photocurrent by 8% than that with the 1D grids under randomly polarized light. Lower bandgap polymer than P3HT would exploit this surface plasmon resonance mode more effectively.
Using FDTD calculations, we numerically demonstrated that 1D metal grids lead to optical absorption enhancements in ultrathin active layers of 20 nm thickness by a factor of 2.6 in TM polarized illumination, when compared with the cases without the metal grids. We also identified the plasmon modes in the ultrathin organic solar cells; the absorption enhancements in the cells with inclusion of the metal grids were attributed to two surface plasmon modes: (1) the SPP mode excited at the interface of glass/Ag, (2) the LSPR mode of the metal grids. Another SPR mode of the SPP concentrated at the interface of metal grids/active layers was found at the wavelength of ~695 nm with incorporation of 2D metal grids. The 2D metal grids are a promising replacement to expensive ITO films in that they can serve as optical absorption enhancers while keeping good electrical conductivity. Although we showed this approach is useful for especially ultrathin organic solar cells, the optical absorptions would be enhanced for other types of thin film solar cells by carefully tuning resonance wavelengths for the different SPR modes.
The authors acknowledge the financial support from Korea Institute of Science and Technology (KIST) (Grant No. 2E24012).
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