Photovoltaic devices that convert solar energy into electrical energy have the potential to provide a virtually unlimited source of energy that is renewable and environmentally benign. However, to be competitive with fossil-fuel technologies, the cost of current photovoltaic technologies needs to decrease substantially. At present, the solar cell market is mainly based on crystalline and polycrystalline silicon with a thickness of approximately several hundred microns, resulting in high cost for materials and processing. Therefore, there is great interest in thin-film solar cells [1], with film thicknesses of a few hundred nanometers, which can be deposited on different substrates like glass and plastics. To date, thin-film solar cells have been fabricated using various active materials, including amorphous silicon [2], GaAs [3], CuIn_xGa_1-xSe₂ and CdTe [4,5], as well as organic semiconductors [6–9]. Compared with their inorganic counterparts, organic photovoltaics (OPVs) based on conjugated polymer and fullerene composites can be fabricated over large areas by means of low-cost ink-jet printing and coating technologies. The simultaneous patterning of the active materials on lightweight flexible substrates raises the prospect of organic photovoltaics potentially as inexpensive as paint [10–12]. However, the low charge-carrier mobility and small exciton diffusion length of most molecular and polymeric materials [13,14] limit the thickness of the active layers (30-150 nm) [15–19] in OPVs, and lead to poor solar light absorption. This in turn results in insufficient carrier generation and low power conversion efficiency.

To overcome this thickness limitation, light trapping strategies may be explored in the design of OPVs to achieve high optical absorption. The traditional light trapping strategy in bulk solar cells typically employs random surface textures at the micrometer level [20–22], which are larger than the active layer of OPVs and no longer suitable for thin film photovoltaics. Consequently, researchers proposed novel plasmonic nanostructures to achieve effective light trapping for thin-film solar cells [23]. Surface plasmon polaritons (SPPs) are collective oscillations of free electrons at the boundary of a metal and a nonconducting dielectric or semiconductor material [24–26]. By properly engineering novel plasmonic nanostructures, light can be concentrated into the thin active layer, thereby increasing its absorption. For device optimization, a broad absorption enhancement is desirable to improve the performance of photovoltaic devices. In recent years, researchers employed various nanoplasmonic structures to improve the performance of solar cells, including nanoparticles [27–35], and periodic nanostructures [36–40], which have been described in a recent review [23]. In the present work, we propose a novel architecture based on an ultra-thin nanopatterned metallic structure to improve the performance of very thin-film organic solar cells. Because of the excitation of short-range SPP modes inside the absorption layer, a broad absorption enhancement is achieved. The design principles and physical mechanisms were analyzed numerically and analytically. The improved device performance was evaluated systematically through calculations of the short circuit current density based on the enhanced absorption in the active layer. To date, the best reported power conversion efficiency for polymer-based OPVs is approximately 7% [9,15,16]. We believe that introducing a metal electrode patterned with a plasmonic nanostructure is a promising approach to surpass this experimentally achieved record on the power conversion efficiency.

Figure 1 shows a schematic diagram of the proposed organic solar cell. The structure consists of a glass substrate, on which is deposited a 20nm thick indium tin oxide (ITO) layer that serves as a transparent anode, a 10nm thick highly conductive hole transport layer, poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS), and a 30nm thick active layer. The active layer used in our design is an organic bulk heterojunction system consisting of the electron-donor material regioregular poly(3-hexylthiophene) (P3HT) and the electron-acceptor fullerene derivative [6,6]-phenyl-C₇₁ butyric acid methyl ester (PC₇₀BM). This is followed by a 20nm nanopatterned silver structure with a periodic subwavelength hole array that is placed immediately above the active layer. Figure 1 shows the subwavelength holes with numerically tunable diameters (D) and periods (P), which are square-symmetrically etched on the Ag layer and assumed to be air-filled.

 

Fig. 1 A schematic diagram of the proposed plasmonic organic solar cell.

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In order to investigate optical absorption enhancement in this solar cell system, we perform full-field electromagnetic simulation using the three dimensional (3D) finite-difference time domain (FDTD) method. First, to demonstrate the reliability of our modeling, we performed a 3D simulation of the optical absorbance of this OPV structure. Our calculation of the optical absorbance of a P3HT:PC₇₀BM bulk heterojunction composite film agrees well with previously reported experimental results for an identical structure [9,41], (see Fig. 6 in Appendix A), validating the predictive capability of our simulation for reproducing experimental results.

 

Fig. 6 Comparison between the simulated and measured absorbance [see the red dots, reproduced from Fig. 2(b) in Ref. [9]. of a 150nm thick P3HT:PC₇₀BM layer.

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Now we employ the modeling to investigate optical absorption enhancement in the proposed nanostructured OPV. The device is illuminated through the transparent anode, as shown in Fig. 1. The spectrally dispersive dielectric properties of the ITO, PEDOT:PSS [42], P3HT:PC₇₀BM (1:0.8 in weight) [40], Ag and glass (SiO₂) [43] are used in the calculation. Periodic boundary conditions are employed and polarized incident light (electric component parallel to X-axis) is assumed. First, the optical absorption of the active layer is determined by calculating the difference between the optical power incident on and transmitted through the layer. The absorption spectrum [A(λ)] is obtained by calculating the optical absorption at each single wavelength across a broad spectral range from 400nm to 900nm [9,41]. Figure 2(a) shows the absorption spectra of devices with a flat metallic structure above the active layer (dotted line), and a subwavelength metallic nanohole array (D = 150nm and P = 300nm, see the solid line). Figure 2(a) also shows the absorption enhancement spectrum (dashed line), which is given by the ratio of the absorption spectra using a nanopatterned and a flat metal film. The results show a large absorption enhancement, with a factor of 6 observed at a wavelength of 725nm. This enhancement is consistent with previous observations on nanopatterned ultra-thin metal films [44] that less light is transmitted through an ultra-thin nanopatterned metal film than through a simple thin metal film. This absorption enhancement was attributed to the excitation of short-range SPP modes, although no field distribution analysis was provided to support this prediction.

 

Fig. 2 Calculations on the device with the nanopatterned metallic structure of diameter D = 150nm, and period P = 300nm. (a) Solid line - the absorption spectrum with a nanopatterned metallic structure; dotted line - the absorption spectrum with a flat metallic structure; and dashed line - the absorption enhancement spectrum. (b) and (c) are time averaged magnetic intensity (|H_y|²) distributions at the SPP resonance wavelength. (b) is the intensity distribution in the x-y plane, and (c) is the intensity distribution in x-z plane. The spatial mode profile is plotted in the right panel of (c).

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To investigate the physics of the absorption enhancement at the peak wavelength of 725nm, the time-averaged magnetic field intensity (|H_y|²) distribution at the P3HT:PC₇₀BM/Ag interface was calculated and is plotted in Fig. 2(b) and 2(c). Figure 2(b) shows the intensity distribution in the X-Y plane, which demonstrates that the SPP mode is mainly confined in the space between holes. In the X-Z plane shown in Fig. 2(c), the SPP mode is confined in the active layer adjacent to organic/Ag interface. To visualize the mode distribution more clearly, the spatial mode profile is plotted in the right panel in Fig. 2(c). However, based on the intensity distribution shown in Fig. 2(b) and 2(c), it is still not clear whether the SPP modes are short range SPPs, as previously predicted [44].

It is well known that for an optically opaque metal film, there is only one type of SPP mode, the single-interface surface plasmon polariton [24]. For thinner metal films (usually less than 100 nm), the two single-interface SPPs interact with each other and lead to two coupled SPPs, the long-range and short-range surface plasmon polariton [45]. The long-range mode has an asymmetric charge distribution between the top and bottom surfaces with the electric field predominantly normal to the surface inside the metal. Conversely, the short-range surface plasmon polariton (SRSPP) has a charge distribution which is symmetric between the top and bottom surfaces with the electric field essentially parallel to the surface [46]. Consequently, we can determine the physical origin of the SPP modes by calculating their surface charge distributions. Figure 3(a) and 3(b) show the electric field distributions for the device discussed in Fig. 2 (t = 20nm, D = 150nm and P = 300nm). The time-averaged electric field strength is shown in Fig. 3(a) with the instantaneous E_XZ vector and surface charge distributions in the X-Z plane. One can see that the spatial variation of the surface charge distribution on the top surface is clearly in phase with that on the bottom surface (symmetric distribution). The E_Z vector distributions at the top (P3HT:PC₇₀BM/Ag) and bottom (Ag/Air) interfaces are displayed in Fig. 3(b). The observed antisymmetric E_Z field pattern also corresponds to a symmetric surface charge distribution, thus demonstrating that the SPP modes excited in the device shown in Fig. 2 are SRSPP modes.

 

Fig. 3 (a) and (b) are electric field distributions at the SRSPP resonance wavelength at 725nm. (a) Time-averaged (color-scale) and instantaneous (arrows) electric field strengths and surface charge distribution in x-z plane, and (b) Instantaneous E_Z vector distribution at the top and bottom surfaces of the Ag nanostructure. (c) Map of the absorption enhancement versus wavelength and metallic nanostructure thickness. The solid arrow corresponds to the resonance wavelength of the single-interface SPP Bloch mode. The dashed line corresponds to the analytical solutions of the SRSPP Bloch modes.

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The next issue that arises after confining the mode in the absorption layer is to study the coupling mechanism. It is known that the momentum mismatch between SPPs and free-space light can be bridged by Bragg vectors inherent in the periodic nanostructures [24,47]. The nanopatterned metallic structure in the proposed OPV structure enables incident light to couple to SPP Bloch modes. The Bragg grating vectors can be expressed as G_ij = i G_x + j G_y, where i and j are integers. |G_x| = |G_y| = 2π/P are the reciprocal lattice vectors of the square array. For normal incidence, the in-plane wave-vector is zero. Consequently, the in-plane wave-vector can be expressed by:

Here S₁, S₂, and S₃ are defined as S₁² = k_SPP²-ε_d1k₀², S₂² = k_SPP²-ε_mk₀², S₃² = k_SPP²-ε_d2k₀², k₀ = ω/c, and t is the thickness of the metal film. In our design ε_d1, ε_d2, and ε_m are the dielectric constants of P3HT:PC₇₀BM, air (ε_d2 = 1), and Ag, respectively. Under the Bragg coupling condition, the dispersion relation of the SRSPP Bloch mode can be obtained by combining Eqs. (1) and (3). The numerical map of the absorption enhancement versus wavelength and the metallic nanostructure thickness is plotted in Fig. 3(c). The analytical solutions for the SPP modes excited by the lowest order Bragg vectors {(i,j) = (1,0),(−1,0),(0,1),(0,-1)} are also plotted in this figure to verify the generation of the SPP Bloch modes. The black dashed line represents the SRSPP Bloch mode excited under the Bragg coupling condition as a function of metal film thickness (t). The excitation frequency of the single-interface SPP Bloch mode is calculated by combining Eqs. (1) and (2) (indicated by the red solid arrow). As shown in Fig. 3(c), these analytical predictions agree well with the numerical simulation of the absorption enhancement obtained by the FDTD modeling. When the thickness decreases from 100nm to 10nm, one can see that the SPP Bloch mode transits from single-interface SPP to SRSPP gradually, with an obvious red-shift of the resonant wavelength. More importantly, the bandwidth of the absorption enhancement becomes wider when the mode enters the SRSPP region. This is because the complex wave-vectors obtained from Eq. (3) have larger imaginary parts than that from Eq. (2). As shown in Fig. 3(c), the width of the enhancement spectrum at the thickness of 20nm is approximately twice that at 100nm. Consequently, these SRSPP Bloch modes on a thinner metallic structure can provide broader band absorption.

Tuning the SRSPP resonant wavelength may be accomplished by tailoring the nanopatterned metallic structure. The absorption enhancement band should be tuned spectrally in order to achieve more effective utilization of the solar energy (see Fig. 7 in Appendix B). According to Eqs. (1) and (3), the SRSPP resonant wavelength is strongly related to the period (P) of the hole array. For simplicity, here we set the metallic nanostructure thickness to 20nm, and tune the period with a constant period/diameter ratio of 2. The map of the absorption enhancement versus wavelength and period for nanostructured P3HT:PC₇₀BM cells is plotted in Fig. 4(a) . The analytical solution of the SRSPP Bloch mode is also plotted in this figure (see the black dashed line), correlating well with the absorption peak position, and verifying that the absorption enhancement results from SRSPPs. One can see that the SRSPP resonant peak exhibits a red-shift as the period is increased. Importantly, this nanopatterned ultra-thin metallic structure design is quite general and can be employed for different organic active layers. Figure 4(b) shows similar results for another polymer, a composite blend of poly[2,6-(4,4-bis-(2-ethylhexyl)-4H- cyclopenta [2,1-b;3,4-b’]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) and [6,6]-phenyl-C₆₁ butyric acid methyl ester (PCBM). The calculation for this solar cell was performed by simply replacing the P3HT:PC₇₀BM layer with a PCPDTBT:PCBM layer (1:3 in weight) [9,40]. Figure 4(b) shows the map of the absorption enhancement versus wavelength and period for the nanostructured PCPDTBT:PCBM cell. The analytical solution of the SRSPP Bloch mode is also plotted in this figure (see the black dashed line), showing good agreement with the absorption peak position. Based on the results shown in Fig. 4, one can see that the enhancement spectra originating from the SRSPP Bloch modes may be tuned over a very broad range of wavelengths, which is highly desirable for enhancing OPV performance.

 

Fig. 7 The photon flux density of the solar spectrum.

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Fig. 4 Maps of the absorption enhancement versus wavelength and period for two organic solar cells, i.e. a P3HT:PC₇₀BM cell (a), and a PCPDTBT:PCBM cell (b). The dashed lines correspond to the analytical solutions of the SRSPP Bloch modes.

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Next, we investigate the plasmon-assisted absorption enhancement and the resulting performance improvement of these two OPV devices under solar irradiance for the standard air mass (AM1.5). For unpolarized incident sunlight, the square-symmetrically distributed nanostructures exhibit polarization-independence. Incident light with electric field components parallel to X-axis or Y-axis will excite the same SRSPP Bloch modes. According to previous reports [44], the resonant frequency shifts only slightly when the electric field is polarized along the diagonal of the square-symmetric array. For this polarization-independent solar cell design, the optical absorption is described by the expression $A={\displaystyle {\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}A(\lambda )S(\lambda )}d\lambda$, where S(λ) is the solar irradiance spectrum for the standard air mass (AM1.5). The absorption enhancement (relative to a reference structure with a flat metallic layer) is given by (A/A_ref −1). It is also useful to define the absorbed photon flux Ф^abs(λ) (number of photons absorbed per unit time and unit area) at a single wavelength as Ф^abs(λ) = A(λ)S(λ)/E_photon(λ), where E_photon(λ) = hc/λ denotes the energy of a single photon, and h is Planck’s constant. In the following calculations, we assume for convenience that every absorbed photon generates one exciton, which dissociates into holes and electrons at the donor/acceptor interface, and that all photo-induced charge carriers are collected by the electrodes [37,40]. Under these ideal conditions, the short circuit current density J_SC of the prototype device can be calculated using $J_{SC}=e\cdot {\displaystyle {\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}{\Phi }^{abs}(\lambda )}d\lambda$, where e is the charge of an electron. As a point of reference, the J_SC for the P3HT:PC₇₀BM device with a flat metallic layer is calculated to be J_SC-ref = 6.07 (mA/cm²). In this case, the enhancement of J_SC is given by (J_SC/J_SC-ref −1). To demonstrate the achievable enhancement, the short circuit current density of the P3HT:PC₇₀BM cell is calculated as a function of the period, P, of the nanopatterned metallic structure [shown in Fig. 5(a) ]. The peak value of J_SC is found to be 8.9 (mA/cm²) at an optimal period P of 260nm. The resulting enhancement in J_SC is approximately 47% (corresponding to a 39% enhancement in optical absorption). Large J_SC enhancements (over 40%) can be achieved over a broad range of periods (200nm to 400nm in this simulation), indicating a good fabrication tolerance for practical devices that can be readily realized using current nanofabrication procedures. The inset of Fig. 5(a) shows the absorbed photon spectra with a nanopatterned metallic nanostructure (solid line, P = 260nm) and a flat Ag metallic structure (dotted line). The photon absorption at wavelengths near 680nm is increased greatly relative to the reference with a flat metallic layer. With this metallic nanopatterned design, light at shorter wavelengths is effectively absorbed by the cell, while the weakly absorbed red and infrared light is trapped at the back surface leading to increased absorption. This provides greater enhancement than the front surface design, which can suppress absorption at short wavelengths because of destructive interference [23,34].

 

Fig. 5 (a) The short-circuit current density (J_SC) and its corresponding enhancement versus period of the nanopatterned metallic structure for the P3HT:PC₇₀BM cell. The inset shows the absorbed photons spectra of the device with a nanopatterned metallic structure (solid line, P = 260nm) and a flat metallic surface (dotted line). (b) J_SC and its corresponding enhancement versus period of the nanopatterned structure for the PCPDTBT:PCBM cell. The inset shows the absorbed photons spectra of the device with nanopatterned metallic structure (solid line, P = 320nm) and flat metallic surface (dotted line).

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Similarly, Fig. 5(b) shows the J_SC enhancement for a PCPDTBT:PCBM solar cell. The reference short circuit current density for the PCPDTBT:PCBM cell, J_SC-ref, is calculated to be 3.62 (mA/cm²). As shown in Fig. 5(b), the J_SC of the plasmonic-assisted device is dramatically improved to 8.36 (mA/cm²) with an impressive enhancement factor of ~130% in J_sc at the optimal period of 320nm (corresponding to an optical absorption enhancement of 112%). The large enhancement is achieved because the absorption coefficient of the PCPDTBT:PCBM polymer is relatively small over the entire solar spectrum [9,41] (with a small absorption peak at 750nm), resulting in a small value of J_SC-ref. If the SRSPP modes are excited around the intrinsic absorption peak at 750nm, the short circuit current density enhancement could therefore be improved significantly. The inset of Fig. 5(b) shows the absorbed photon spectra with a nanopatterned metallic structure (solid line, P = 320nm) and a flat Ag back surface (dotted line). One can see that the photon absorption increases significantly in the spectral region around 750nm, also the resonant wavelength of the SRSPP. The enhancement occurs over a very broad spectral range, resulting in the very large improvement in device performance. The results in Fig. 5 demonstrate that the maximum potential J_SC of 8.9 (mA/cm²) and 8.36 (mA/cm²) can be achieved for the two nanostructured OPVs with 30nm active layers, under the assumption of ideal charge collection (unity internal quantum efficiency). One can show from similar calculations that considerable SRSPP enhanced performance occurs for thicker OPV active layers as well (see Fig. 8 in Appendix C), although the trade-off between the actual collection efficiency of photo-generated charge carriers and the optical absorption needs to be accurately taken into account. Consequently, it is important to investigate the optimal thickness of the active layer to achieve the maximum conversion efficiency of the OPV at the device level [18]. Such a study would require detailed information of the intrinsic properties of the active materials, and an understanding of the relation between the internal quantum efficiency and the active layer thickness, and should be the subject of a future investigation, together with an experimental characterization of SPP enhanced organic OPVs.

 

Fig. 8 The relation between the J_SC and the active layer thickness of the P3HT:PC₇₀BM device. The red curve is the J_SC of the device with nanostructured back reflector; the black curve is the J_SC of the device with a 20nm flat back reflector. Inset: The relation between the J_SC enhancement factor (the ratio of the J_SC-nano and J_SC-ref) and the active layer thickness.

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It should be noted that an optically opaque flat metal film, rather than the ultra thin metal film considered here, is normally employed as the back reflector for conventional OPVs. Our modeling results (not shown here) revealed only a small change in the enhancement in absorbed photon density (< 10%) when the thickness of the flat back reflector increases from 20nm to 100nm. In addition, in terms of the practical device application, another issue should also be noted: for polymer OPVs, although 30-50nm thick active layers employed in our modeling were used in certain devices [7,19], the thickness is typically 100-150nm. In this case, optical waveguide modes could be introduced to play important roles in absorption enhancement. Previous studies [36] and [37] have explored the roles of these optical modes.

The SRSPP-assisted absorption enhancement results presented in this work for polymer based OPVs compare favorably (P3HT:PC₇₀BM) or in case of (PCPDTBT:PCBM) surpass those reported previously for OPVs based on molecular systems [39] where a theoretical enhancement of 50% in optical absorption was reported for one dimensional metallic gratings placed on 15nm thick organic heterojunction. For comparison, our modeling results for a 15nm thick P3HT:PC₇₀BM layer yields an 83% enhancement in optical absorption, which corresponds to an enhancement of 94% in J_sc (see Fig. 8 in Appendix C). Similarly, the absorption enhancement for a 15nm film of PCPDTBT:PCBM would be on the order of 200%. This indicates that a larger overlap between the enhanced absorption spectrum and the solar spectrum is achieved with the proposed ultra-thin nanopatterns.

In conclusion, an ultra-thin nanopatterned metallic structure placed next to the organic active layer is proposed for improved OPV devices. Due to the excitation of SRSPP Bloch modes, a large broadband absorption enhancement is achieved, and may be spectrally tuned by tailoring the geometric parameters of the plasmonic nanostructure. Using this nanostructure, calculations show that the short circuit current densities can be enhanced by 47% for an OPV based on P3HT:PC₇₀BM and by 130% for one based on PCPDTBT:PCBM. It is demonstrated that large enhancements can be achieved over a broad range of periods, providing very good fabrication tolerance for practical devices. The design principle of the nanopatterned metallic nanostructure proposed in this article is quite general and can be employed to systematically engineer and optimize the parameters for improved photovoltaic devices.