We present investigation and optimization of a newly proposed plasmonic organic solar cell geometry based on the incorporation of nanovoids into conventional rectangular backplane gratings. Hybridization of strongly localized plasmonic modes of the nanovoids with Fabry-Perot cavity modes originating from surface plasmon reflection at the grating elements is shown to significantly boost performance in the long wavelength regime. This constitutes improved broadband operation while maintaining absorption enhancements at short wavelengths derived from conventional rectangular grating. Our calculations predict a figure of merit enhancement of up to 41% compared to when the nanovoid indented grating is absent. This is a significant improvement over the previously considered rectangular grating structures, which is further shown to be maintained over the entire angular range.
©2013 Optical Society of America
Organic solar cells are drawing increased attention owing to reduced material and processing costs. Thin active layers are preferred to ensure efficient charge collection, but at the cost of lower energy conversion efficiency due to a reduced optical path length [1–4]. Among various techniques for improving photon absorption, plasmon-enhanced solar cells incorporating metallic nanostructures are considered as a strong candidate. There are at least two main mechanisms for increasing the light-trapping efficiency of plasmonic solar cells. Firstly, periodic metallic gratings could be used to couple incident light into surface plasmon polaritons (SPP) propagating along the metal-dielectric interfaces of the active layer, thus increasing the optical path length [5–8]. Secondly, the excitation of localized surface plasmons (LSP) yields spatially localized field enhancement and increased absorption near the surface of subwavelength metallic nanostructures [9–12].
While many reports have investigated individually the light-harvesting effects of metallic gratings [7, 8], subwavelength nanoparticles [9–12], or nanovoid arrays [13, 14] on different types of solar cell, studies of combining these various elements are rare. Use of multiple grating structures  has been theoretically studied by Shen, and Li et. al. [16, 17] were the first to experimentally demonstrate nanoparticle combination with grating (or nanoprism) for broadband light absorption. While the broadband performance improvements were attributed to the hybridization / combination of various photonic / plasmonic modes [16–18], yet a detailed description of the hybridization process itself (per the structural transformation) and its performance impact were not clearly elucidated.
In this paper, we propose a geometry that incorporates nanovoid indents into conventional metallic gratings elements as an alternative strategy to the controlled hybridization of SPP and LSP modes in a single structure. In particular, full quantitative details regarding the transition of decoupled modes through to strong hybridization (under gradual variation of geometric parameters) are presented and discussed (including geometric optimization). From finite element analysis , we demonstrate that the proposed geometry leads to significant broadband and wide-angle absorption enhancement over a conventional metallic grating .
2. Device architecture and simulation details
The proposed hybrid structure, in the form of a one-dimensional periodic grating (rectangular element size wGrat x dGrat) with nanovoid indents wNV x dNV is shown in Fig. 1(a) . This type of structure could be fabricated using a multi-step lithography process such as in , and depositing P3HT:PCBM and PEDOT:PSS films subsequently. While similar structures (T-shaped arrays) have been previously considered for applications to narrowband thermal emitters, biosensors, and plasmonic filters in the infrared (IR) region [21, 22], these were focused only on the properties of isolated LSP modes in the gaps (nanovoids). The 100nm thick active layer (P3HT:PCBM(1:1)) is sandwiched between a 50nm thick PEDOT:PSS layer and an Ag metallic grating-substrate. The material properties (Fig. 1(b)) were taken from the experimentally measured complex and dispersive optical constants (P3HT:PCBM , PEDOT:PSS , and Ag ).
Under TM / TE incident plane wave (magnetic / electric field parallel to the z-axis), 2-D FEM calculations are conducted on a single unit cell uniform in the z-direction; with periodic boundary conditions along the x-axis, and perfectly matched layers at the top and bottom of the cell (Fig. 1(a)). Absorption properties of the solar cells are investigated in the wavelength range of 300nm to 800nm, using the relative illumination intensity obtained from the standard AM1.5G solar radiation spectrum. To quantify the absorption performance over the entire considered spectral range, we also defined a figure of merit (FOM) based on the ratio of number of photons absorbed in the active layer to the total number of incident photons ,6]:Eq. (2)) during post-processing in COMSOL ; λ and E are the free space wavelength and magnitude of electric field vector, and ε2 is the imaginary part of the dielectric constant.
3. Optimization of the conventional rectangular grating
To later make a comparison with the proposed grating structure, we begin with optimization of a solar cell based on a conventional rectangular grating. Figure 2(a) shows the FOM enhancement (with respect to flat solar cell without grating) as a function of the period and fill factor ( = wGrat/Period x 100) under normally incident TM polarization, at the optimal grating height of dGrat = 50nm (optimization over dGrat not shown). It can be seen that for a Period = 300nm and wGrat = 75nm (Fill factor = 25%), the FOM enhancement has a maximum value 1.33. As shown in Fig. 2(b), the absorption efficiency for the optimized case (blue dash curve) is larger than that of the flat case (black dash) over the entire wavelength range, except below 340nm where Ag loses its metallic property. It is well known that this spectrally broad enhancement is due to the grating induced coupling of incident light into plasmonic / photonic modes [6–8]. One can also see that the absorption enhancement (with respect to flat solar cell without grating) has a shoulder at λ = 590nm, and a peak value at λ = 640nm. From Fig. 2(c) it can be seen that λ = 590nm corresponds to enhancement and localization of the magnetic field mainly near the top of the rectangular elements. This non-retarded LSP resonance originates from the incident electric field driven near-surface current to form an electric dipole. On the other hand, Fig. 2(d) for λ = 640nm shows field enhancement also near the bottom corners of and in between neighboring grating elements. This is attributed to a Fabry-Perot (FP) SPP mode which corresponds to planar surface plasmons (of the Ag/dielectric interface) reflecting back and forth between two neighboring grating elements.
It is important to mention that the absorption spectra are evidently affected significantly if different parameters from those optimal are applied. For example, one can see that strong absorption enhancement at longer wavelengths can be obtained (e. g., point B in Fig. 2(a) and green curves in Fig. 2(b); strong enhancement is observed at λ = 700nm - see also Fig. 2(e)), but at the cost of lower absorption enhancement at shorter wavelengths. In the following section, we show that incorporation of nanovoids can lead to significant improvements at long wavelengths, yet without inhibiting absorption in the short wavelength regime.
4. Plasmon-enhanced absorption in the nanovoid indented grating structure
Optimization of the nanovoid indented grating is carried out using optimal parameters of the conventional rectangular structure (Period = 300nm, wGrat = 75nm and dGrat = 50nm). This allows us to see any performance improvements related directly to the introduction of nanovoids into the rectangular grating. Figure 3(a) presents the FOM enhancement as a function of nanovoid dimensions wNV and dNV, showing a maximum of 1.41 at the optimal condition wNV = 12.5nm and dNV = 20nm. This corresponds to an FOM enhancement of 41% over that of the flat solar cell, as compared to 33% for the conventional rectangular grating. Note that further improved performance could be achieved if the optimization is made over all five parameters of the nanovoid indented grating (i.e. including Period, wGrat, and dGrat). The absorption enhancement of both the optimized nanovoid indented and rectangular grating is almost identical at wavelengths less than ~640nm, as seen in Fig. 3(b). Strong similarities observed in the field profiles at λ = 640nm (Fig. 2(d) and Fig. 3(e)) indicate that the absorption enhancement may still be attributed to a FP-SPP resonance.
Meanwhile, Fig. 3(b) shows a new resonant mode at about λ = 700nm, at which a large absorption enhancement of 4.2 is observed. The corresponding field pattern (Fig. 3(f)) shows strong concentration of the magnetic field in both the nanovoid regions and P3HT:PCBM/Ag substrate interface, which indicates a hybridization of the nanovoid-LSP (NV-LSP) mode (i.e. electric dipole mode formed due to opposite charges collecting at the ceiling and floor of the void respectively) with the FP-SPP mode. It is important to note that this hybrid plasmonic mode is an additional mode directly introduced through the incorporation of nanovoids into the rectangular grating elements, and is responsible for the improved absorption performance in the long wavelength regime; thus improving broadband performance.
To better understand the origin of the hybrid plasmonic mode, the dNV (wNV) dependence of the absorption is separately investigated, while keeping wNV = 12.5nm (dNV = 20nm) fixed at the previously obtained optimal value. It can be seen in Fig. 3(c) that for dNV < ~10nm, the main absorption peak splits into two branches. The left branch of weaker enhancement remains at ~640 nm, and corresponds to the conventional grating-coupled FP modes as shown in Fig. 2(d), Fig. 3(e) and 3(g). The stronger right branch corresponds to an isolated NV-LSP mode (Fig. 3(h)), which exhibits a red-shift as dNV is reduced, in agreement with . As dNV increases above ~10nm, penetration of FP-SPPs into the nanovoids starts to provide hybridization between the NV-LSP and FP-SPP modes. The strong hybridization at dNV = 20nm shown in Fig. 3(f) corresponds to the optimal absorption enhancement. Tuning of the hybrid mode resonance is possible by control of wNV (Fig. 3(d)). Further increase of dNV > ~25nm leads to a weakening and annihilation of the NV-LSP modes, and a red-shift of the FP-SPP modes due to effective increase in the FP cavity length. To note, the incorporation of nanovoids was found to have negligible effects for the case of TE incident wave, as expected.
Finally, we also compared the angular dependence of FOM enhancement of both optimized nanovoid and rectangular grating structures. As can be seen from Fig. 4(a) , even at considerably large incident angles of θ = 45deg, hybridization of the NV-LSP mode with the FP-SPP mode persists, maintaining a resonance at 700nm, in contrast to the rectangular grating structure (Fig. 4(b)). As a result, nanovoid indented gratings are shown to provide larger FOM enhancement over the entire incident angular range (Fig. 4(c)).
In this paper, we proposed a new structure of organic (P3HT:PCBM) plasmonic solar cell based upon the incorporation of nanovoids into conventional rectangular gratings. Through the hybridization between the nanovoid LSP mode and the usual Fabry-Perot SPP mode existing between grating elements, it was possible to newly introduce a tunable resonance into the absorption spectra. While preserving performance improvements provided by conventional grating structures in the short wavelength regime, a further boost to the absorption efficiency and broadband operation was obtained in the long-wavelength regime through optimization of the nanovoid dimensions. Numerical analysis shows that incorporation of nanovoids into an optimized rectangular grating structure can lead to a further 8% enhancement (from 33% for rectangular, to 41% of nanovoid rectangular) of the flat-film normalized figure of merit (FOM). The mode hybridization is discussed and explained consistently through systematic investigation of its dependence on nanovoid geometry. Fully utilizing the usually hard-to-access long wavelength regime of organic solar cells, and providing a robust hybrid mode for wide reception angle, we expect our concept of nanovoid indented gratings will be useful for the design of efficient plasmonic solar cells.
This work was supported by the National Research Foundation; GRL, K20815000003, Global Frontier Program 2011-0031561, and Center for Subwavelength Optics, SRC 2012-0000606.
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