1. Introduction

Multi-crystalline solar cell modules have high material and processing costs, and complex production processes [1]. These limitations have spurred the research for easy-to-process low cost devices, giving rise to thin-film photovoltaics (PV) based on organic semiconducting materials. In the initial research work on organic solar cells (OSCs), very low power conversion efficiencies (PCEs) (of ∼1% to 2%) were reported [2]. Recently, PCEs of low bandgap polymer-based OSCs have been reported to be 10.5%, even without any plasmonic nanostructures being present in the OSC [3]. Tandem OSCs with PCEs of over 13% [4–7] have also been reported. Even with these developments, still higher efficiency is necessary before OSCs are considered viable in the PV industry.

Organic semiconductors do not generate free carriers directly on photo excitation, instead generating a bound electron-hole pair. This electron-hole pair, or exciton, is separated to form free carriers at the electron-donor (n-type) and electron-acceptor (p-type) interface of the PV device. The effective generation of free carriers upon photoexcitation is therefore dependent on the retention of the exciton as it successfully creates free carriers. This is determined by the lifetime and diffusion length of the exciton. Free charges are easily created from the excitons generated close to the p-n interface. Increasing the interface area boosts charge generation, and is achieved by mixing the p- and n-type materials into a bulk heterojunction (BHJ). The BHJ is designed with appropriate phase separation of the p- and n-domains to sustain efficient charge transport. Low yield limitations of organic semiconductors are overcome by the ultrafast electron transfer mechanisms of buckminster fullerenes [8]. In an active blend of a semiconducting polymer and a soluble C60 derivative, upon excitation, the excitons easily dissociate at the interpenetrated interface. The polymer serves as an electron donor to provide a conductive pathway for the holes, while the C60 derivative acts as the strong electron acceptor for the transport of electrons.

Low carrier mobility also constraints the quantum efficiency of the OSCs [9]. A thicker active layer will absorb more photons, but at the same time will also lead to higher losses due to recombination. Current loss due to carrier recombination in active layer thicknesses greater than carrier diffusion length degrades the PCE. The tradeoff between minimizing recombination and increasing absorption is a significant factor in designing OSCs. High absorption coefficients, of the order of 10⁵cm⁻¹, enable active layer thicknesses of 100s of nanometers [10]. The thin active layer consequently lowers the chances for charge recombination while increasing the carrier drift velocity due to a higher electric field. A thin layer also reduces the electrical resistance of the device.

Large bandgap in organic materials leads to a narrow spectrum absorption of incident solar radiation. A 1.1eV (1100 nm) bandgap material can harvest about 77% of solar light [10]. Most semiconducting polymers have bandgaps of the order of 2eV (620 nm) which absorb only around 30% of the incident solar spectrum. To increase efficiency, materials with low bandgap and thus, a broad absorption spectra, have been explored [11]. At the same time, multiple donor materials with non-overlapping absorption spectra have been stacked in multiple junctions to achieve broad spectrum absorption of solar radiation [12]. These cells with multi-junctions are connected either in series or parallel to provide improvements in the open circuit voltage V_OC and the short circuit current density J_SC, respectively [13,14]. Typical tandem cells have a top subcell with a high-bandgap material over a bottom subcell with a low-bandgap material. The effective series connection of the cells results in a higher V_OC than either of the subcells. The top subcell has the higher V_OC due to its higher bandgap. Various materials have been matched over broad bandwidths, adjusting the current of the subcells to optimize the V_OC and the J_SC and therefore, increase the PCE.

Enhancement of photon harvesting has also been explored by increasing the travel path length of the incident light in the active medium. This has been done by introducing scattering effects and plasmonic resonances in the active layer [15–17], in the buffer layers [18,19] or both [20,21]. Surface electrons oscillate coherently with the incident light to enhance and localize optical fields to sub-wavelength regions close to the surface [22]. This is unlike photonic scattering, where light couples to slow Bloch modes to increase the light-material interaction time leading to higher absorption [23]. Localized surface plasmon resonance (LSPR) augmented light absorption has been achieved by adding metallic nanoparticles (NPs) in the form of nanospheres [24,25], nanorods [26,27], nanodisks [28,29], metal grids [30], lumpy nanoparticles [31], and nanoshell structures [32,33]. Plasmonic nanostructures with sharp tips have higher field enhancements and superior scattering effects [34]. FDTD simulations of OSCs with plasmonic nanoparticles have been reported [35–37]. In previous studies, double junction tandem solar cells containing plasmonic nanoparticles have been primarily demonstrated with inorganic active materials. Moreover, studies with nanoparticles in both the top and the bottom subcells have had the same particle geometry in both subcells [38].

This paper details the investigation of a double junction tandem OSC containing silver (Ag) nanospheres and silver (Ag) nanostars present over the top and in the bottom subcells, respectively using FDTD. PTB7:PC₇₀BM and PDPPSDTPS:PC₆₀BM were taken as the active layer materials in the top subcell and the bottom subcell, respectively. Different geometries of the plasmonic nanoparticles (nanospheres and nanostars) were used in the top subcell and the bottom subcell, respectively, so that the absorption in the different spectral regimes — corresponding to the bandgaps of the active layers in the two subcells (PTB7:PC₇₀BM in the top subcell and LBG:PC₆₀BM in the bottom subcell) — could be enhanced. The effect of the two nano-particle geometries were thoroughly investigated, with varying surface coverage, selectively placed over the top surface and within the bottom subcell active layer. The thickness of the bottom subcell active layer as well as the geometries of the plasmonic nanoparticles were optimized such that the short circuit current densities in the two subcells could be matched in the tandem OSC. The focus of the work is in the use of active layer materials to encompass a wide solar spectrum and the introduction of different plasmonic nanoparticles for further J_SC enhancement. An overall enhancement of 26% in the short circuit current density was achieved in a tandem OSC containing the optimized Ag nanospheres over the top surface and Ag nanostars inside the bottom subcell active layer. The presence of plasmonic nanoparticles along with the wide spectrum absorption band of the active materials in the tandem OSC leads to a typical power conversion efficiency of 15.43%, which is higher than that of a reference tandem organic solar cell (12.25%) that does not contain any nanoparticles.

2. Solar cell structure and simulation parameters

Figure 1 shows the schematic diagrams for the different tandem OSCs structures that were simulated; both without and with the plasmonic nanoparticles integrated over the top surface and within the bottom subcell. For the reference tandem OSC (without any nanoparticles) shown in Fig. 1(a), a 50 nm layer of indium tin oxide was taken as the cathode and a 50 nm layer of TiO₂ as the hole transport layer. The high bandgap active layer was a blend of electron donor PTB7 and acceptor PC₇₀BM. Intermediate electron and hole transport layers were taken to be MoO₃ and TiO₂, respectively and having a thickness of 50 nm. The low bandgap active layer was taken to be a blend of PDPPSDTPS (henceforth, referred to as LBG) and PC₆₀BM. The anode buffer layer was taken to be 50 nm of MoO₃. Silver was taken as the final reflecting anode layer with a thickness of 100 nm. The active layer materials were adopted to cover the wide spectrum from 300 nm to 1150 nm with high absorption efficiency. The data of the comparative simulations of the different materials explored for the active layers in the top and bottom subcells are presented in Appendix A. While optical properties of the above active layer materials were taken from literature [39,40] (see plot in Fig. 1(f)), the complex refractive index of silver was obtained from Palik. The complex dielectric constants of ITO, TiO₂, and MoO₃ were taken from literature [41].

 

Fig. 1. Schematics of the simulated double junction tandem OSCs: (a) OSC without nanoparticles — reference tandem OSC, (b) OSC with nanospheres over the top surface only, (c) OSC with nanospheres in the bottom subcell only, (d) OSC with nanostars in the bottom subcell only, (e) OSC with nanospheres over the top surface and nanostars inside the bottom subcell, and (f) Real (n) and complex (k) refractive indices of the active layer materials PTB7:PC₇₀BM and LBG:PC₆₀BM (Inset: Ag nanosphere with radius R_T/B and Ag nanostar with core radius r_B and prong length L_B, where subscripts T and B are for the top surface of the OSC and the bottom subcell, respectively). The low bandgap (LBG) material taken is PDPPSDTPS. The top and the bottom subcells of the tandem OSCs are also marked in (c).

Download Full Size | PDF

Three-dimensional (3-D) Finite-Difference Time Domain (FDTD) simulations were carried out using a commercially available FDTD software - Lumerical FDTD Solutions to model the different parameters of the tandem OSC. The shape, size, and periodicity of the nanoparticles were optimized to maximize the absorption of the solar spectrum. The OSC was studied under periodic boundary conditions in the FDTD domain to simulate periodic arrays of the plasmonic nanoparticles. The top and bottom boundaries were perfectly matched layers (PML). A mesh size of 2×2×2 nm³ was used across the entire simulation region. A broadband plane wave source (with wavelength ranging from 300 to 1150 nm) was used to mimic the light incident on the OSCs from a distance of 500 nm away from the top surface. We did not consider TM and TE polarization dependence due to the symmetry of the nanoparticles along the axes. Appropriate frequency-domain field power monitors were placed within the active regions to calculate the absorption in the respective layers. The monitor in the bottom subcell was modelled to exclude the absorption of light by the inserted nanoparticles.

The short circuit current density was evaluated, by integrating the absorption with the AM1.5G solar spectrum, assuming all generated electron-hole pairs contribute to the current

The open circuit voltage of a cell based on a blend of donor and acceptor is given by:

In active layer materials – $E_{HOMO}^{PTB7} = 5.2\;eV$, $E_{LUMO}^{P{C_{70}}BM} = 4.0\;eV$, $E_{HOMO}^{LBG} = 5.17\;eV$, $E_{LUMO}^{P{C_{60}}BM} = 4.16\;eV$ [39,40]. For the top subcell, a V_OC1 of 0.9 V is obtained while for the bottom subcell V_OC2 is 0.71 V. The open circuit voltage of the tandem OSC was evaluated to be 1.61 V, as the sum of the open circuit voltage of each subcell.

Finally, the PCE was calculated for the cells by using the formula,

3. Results and discussion

3.1 Tandem OSCs without nanoparticles – reference tandem OSCs

In order to match the short circuit current density (J_SC) of the top and the bottom subcells of the double junction tandem OSC not containing any nanoparticles, the appropriate thicknesses of the active layers of the two subcells were determined. Figure 2(a) shows the variation of the short circuit current densities for the top subcell (with PTB7:PC₇₀BM as the active layer) and the bottom subcell (with LBG:PC₆₀BM as the active layer) as the thickness of the active layer of the bottom subcell (t_bottom) was varied, keeping the top subcell active layer thickness to be constant at 170 nm. As t_bottom is increased from 50 nm to 150 nm, the J_SC in the bottom subcell increases from 8.76 mA/cm² to 16.43 mA/cm², as shown in Fig. 2(a). On the other hand it can be observed from Fig. 2(a) that the J_SC of the top subcell decreases from 15.23 mA/cm² to 14.86 mA/cm² as t_bottom is increased from 50 nm to 150 nm. The increase in the value of the J_SC of the bottom subcell results from greater absorption of solar energy by the bottom subcell active layer as its thickness is increased. This consequently reduces the energy conversion of the top subcell, thereby leading to a reduction in the J_SC as t_bottom is increased. The two curves intersect for a bottom subcell active layer thickness of 110 nm, with an overall matched J_SC of 15.06 mA/cm² (see Fig. 2(a)). The addition of nanoparticles to the different layers of the tandem OSC is expected to lead to an increase in the absorption (and therefore in the J_SC) in both the active layers of the top and the bottom subcells (see sections 3.2 and 3.3 below). This increase shifts both the curves up and the point of intersection moves left, to a lower thickness of the bottom subcell active layer. Taking this into account, and to validate that the metallic nanoparticles are responsible for the enhancement, the nanoparticles were optimized for a tandem OSC taking the top subcell active layer thickness to be 170 nm and the bottom subcell active layer thickness to be 80 nm. In Fig. 2(b), the absorption spectra for this reference tandem OSC is shown. The absorption was measured in the active layer of the subcells, since photons absorbed in the other layers do not contribute to device performance. The top subcell with the high bandgap material, has high absorption in the lower wavelength range of 300 nm to 700 nm, while the bottom subcell with the low bandgap material has absorption peaks for higher wavelengths beyond 700 nm, up to 1100 nm. The top subcell J_SC of 15.12 mA/cm² and the bottom subcell J_SC of 12.68 mA/cm² as well as the absorption spectra were taken as the baseline for further comparisons. The overall absorption spectrum of the reference tandem OSC (shown by the dashed maroon curve in Fig. 2(b)) is the sum of the spectra for the absorptions in the top subcell and bottom subcell active layers.

 

Fig. 2. (a) Short circuit current density (J_SC) generated in the top and bottom subcells of a tandem OSC as a function of the bottom subcell thickness (t_bottom) with a fixed top subcell active layer thickness of 170 nm, when no nanoparticles are not present in the tandem OSC (referred to as the reference tandem OSC), (b) Results of FDTD simulations showing absorption spectra as a function of wavelength for a reference tandem OSC, where the absorption in the top subcell is shown by the solid black line and in the bottom subcell by a dashed black line. PTB7:PC₇₀BM (170 nm thickness) and PDPPSDTPS:PC₆₀BM (80 nm thickness) are the active layer materials in the top and the bottom subcells, respectively. The overall absorption spectrum of the reference tandem OSC (shown by a dashed maroon line) is the sum of the spectra for the absorptions in the top subcell and bottom subcell active layers. The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm.

Download Full Size | PDF

3.2 Tandem OSCs with Ag nanospheres over the top surface

Ag nanospheres of different radii and surface coverage were placed over the top surface of the tandem OSC, as shown in Fig. 1(b). The surface coverage of the nanoparticles was varied by changing the size and periodicity of the nanospheres, surface coverage being the ratio of the shadow area of nanoparticles to the total simulation area of the solar cell. The radii (R_T) of the nanospheres placed over the top surface were varied from 70 nm to 100 nm (in steps of 10 nm). Nanospheres of different sizes lying between 70 nm and 100 nm can controllably be prepared using chemical synthesis [43]. The nanospheres were placed with periods (P_T) ranging from 300 nm to 500 nm, in steps of 50 nm. Ag nanospheres were considered from both performance and cost points of view. The surface plasmon resonances of these Ag nanoparticles in air lie in the visible spectral region, thereby leading to plasmonic enhancement in these spectral regions that coincide with the peak solar intensity. For solar cells, gold is less desirable due to its high absorption losses in the 500–600 nm spectral region [44]. Moreover, considering widespread application, the higher cost of gold is a deterrent. Figure 3 shows the variation of short circuit current density (J_SC) as a function of radii (of the Ag nanospheres placed on the top surface of the tandem OSC) for different periodicities of the Ag nanospheres. The highest enhancement in the short circuit current density of the top subcell was calculated to be 16.02 mA/cm² — which is 6% higher than that for the reference tandem OSC — when the nanosphere radius ‘R_T’ and periodicity ‘P_T’ were taken to be 90 nm and 500 nm, respectively. The corresponding bottom subcell J_SC was calculated to be 14.32 mA/cm² — an enhancement of 13% over that for the reference tandem OSC. For R_T being 90 nm and P_T being 450 nm, the J_SC was marginally higher (14.36 mA/cm²) for the bottom subcell and lower (15.92 mA/cm²) for the top subcell as compared to the case when R_T and P_T were taken to be 90 nm and 500 nm, respectively.

 

Fig. 3. Short circuit current density (J_SC) of the top subcell containing PTB7:PC₇₀BM as the active layer and the bottom subcell containing PDPPSDTPS:PC₆₀BM as the active layer of the double junction tandem OSC containing Ag nanospheres over the top surface as a function of nanosphere radius (R_T) and nanosphere periodicity (P_T). The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm.

Download Full Size | PDF

It can be observed from Fig. 3 that smaller values of the Ag nanosphere periodicity (P_T) — which implies a greater surface coverage — leads to a marked reduction in the J_SC, primarily due to greater light absorption by the metallic nanospheres and greater blocking or shadowing of light. On the other hand, very large periodicities are also not desirable as fewer nanospheres over the top surface of the OSC are ineffective in sufficient scattering of incident light into the active layers [38].

In one of the absorption spectral curves (in red color) shown in Fig. 4, we observe a more broadened absorption peak in the spectral region lying between 500 nm and 700 nm (where the solar radiation has strong intensity) as compared with the absorption (in black color) in a tandem OSC without any nanoparticles. The Ag nanospheres present over the top surface of the tandem OSC scatter the incident solar radiation forward into the substrate [38] leading to the enhancement in the absorption in the top subcell in the spectral region lying between 500 nm and 700 nm. A reduced absorption by the top subcell is also seen for the lower wavelengths but the higher enhancement spectral region lying between 500 nm and 700 nm more than makes up for this reduction, giving a net improvement over the reference tandem OSC. The nanospheres cause destructive interference between the scattered and incident light for wavelengths below the resonance, a phenomenon called Fano resonance, thereby causing the lower absorbance [44,45]. The absorption enhancement in the bottom subcell is due to the stronger light coupling capability of the nanospheres in the longer wavelength region [38]. The influence of the localized near-field effect of the Ag nanospheres (placed over the tandem OSC top surface) is substantially reduced within the intermediate layers between the nanospheres and the top subcell active layer.

 

Fig. 4. (a) Comparison of absorption in each subcell (in the top subcell and in the bottom subcell) of double junction tandem OSCs without (black) and with Ag nanospheres (red) over the top surface. Schematics of the tandem OSCs: (b) without Ag nanospheres (OSC A) and (c) with Ag nanospheres over the top surface (OSC B) of the OSC. The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. The dimensions of the top Ag nanospheres were taken to be: R_T = 90 nm and P_T = 500 nm.

Download Full Size | PDF

3.3 Tandem OSCs with Ag nanoparticles in the bottom subcell

Ag nanoparticles of varying sizes and surface coverages were introduced within the active layer of the bottom subcell, as shown in Figs. 1(c) and 1(d). The nanoparticles were added to the active layer, to harvest the impact of their localized near-field effects as well as of their capability of scattering light into the active layers of the OSC. The Ag nanospheres in the bottom subcell had radii (R_B) of either 20 nm, 25 nm, or 30 nm placed at periods P_B ranging from 100 nm to 300 nm. The nanostars, shown in Fig. 1 (inset), had core radii (r_B) of either 20 nm, 25 nm, or 30 nm and a prong length (L_B) = 20 nm. Such nanostars can be chemically synthesized with controlled size and prong length [46]. The prong length was not varied to prevent the introduction of an additional parameter and thus, simplify the computational complexity. Silver was used here as well, because the response of gold in the surrounding active layer material pushes the nanoparticle plasmonic resonances to wavelengths in the IR region [47], which is beyond the spectrum of our study.

The plots showing the optimizations of the short circuit current density (J_SC) for different dimensional parameters are shown in Fig. 5. It was observed that for larger sizes of the nanoparticles in the bottom subcell, there is an increase in the J_SC of the bottom subcell. A high value of enhancement in the J_SC (over that of the reference tandem OSC) was observed for sphere radius (R_B) of 30 nm and periodicity (P_B) of 100 nm, with the value of the bottom subcell J_SC being 15.21 mA/cm² (Fig. 5(b)). The respective top subcell J_SC is 15.08 mA/cm². This enhancement in J_SC is due to the localized near-field enhancement and the enhanced in-plane scattering by the Ag nanospheres. It was also found that for larger sizes of the nanoparticles in the bottom subcell, there is a reduction in the performance of the top subcell (as shown in Fig. 5(a)). The large in-plane scattering in the bottom subcell due to the presence of the larger sized nanospheres leads to less light scattering back to the top subcell, which then effectively reduces the J_SC of the top subcell.

 

Fig. 5. Short circuit current density (J_SC) of each subcell (the top subcell and the bottom subcell) of a double junction tandem OSCs for OSCs containing Ag nanospheres – (a) and (b) and Ag nanostars – (c) and (d) within the bottom subcell, as a function of nanosphere radius (R_B) and nanostar core radius (r_B), respectively for varying periodicity (P_B). The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm.

Download Full Size | PDF

Plasmonic nanostars were introduced in the bottom sucbell active layer to further increase the absorption in the bottom subcell and to obtain a value of the J_SC which is closer to that generated in the top subcell. In the presence of the Ag nanostars, the bottom subcell J_SC increased to 15.51 mA/cm², for core radius (r_B) of 30 nm and period (P_B) of 250 nm (Fig. 5(d)). The anomalous behavior of the nanostars with period, P_B = 100 nm is due to the large absorption by the particle themselves as the density of the nanostars is very high for this periodicity. With an increase in the periodicity of the nanostars, in-plane scattering and near-field enhancement leads to an increase in the J_SC of the bottom subcell, with a corresponding decrease in the J_SC of the top subcell. The respective J_SC of the top subcell was lower at 14.12 mA/cm². The performance of the top subcell was poorer than that of the reference tandem OSC, for all dimensions of the plasmonic nanostars.

The absorption spectrum for the bottom subcell of a tandem OSC (OSC C shown in Fig. 6(c)) containing Ag nanospheres in the bottom subcell (having a radius of 30 nm and a periodicity of 100 nm) shows an increased absorption for wavelengths greater than 850 nm as compared to the reference tandem OSC (as shown in Fig. 6). There is also a considerable shift in the peaks of the top subcell as compared to the reference tandem OSC. Light for most short wavelengths does not penetrate through to the bottom subcell and is absorbed within the top subcell. For certain wavelengths, there is either destructive or constructive interference between incident light and the light scattered back from the Ag reflector. This causes selective regions of high and low absorbance. In the bottom subcell, the nanospheres also scatter the longer wavelengths of light at high oblique angles along the active layer. This increases the optical path length within the active layer, resulting in an enhanced absorption (absorption enhancement of ∼20%) over the reference tandem OSC. We can see from Fig. 6 that there is a greater absorption in the bottom subcell of a tandem OSC (OSC D in Fig. 6(d)) when the bottom subcell contains Ag nanostars for wavelengths greater than 600 nm (except for a small spectral region between 775 nm and 850 nm) as compared to the reference tandem OSC. The prongs present in the plasmonic nanostars studied in this paper have a greater scattering cross-section leading to a greater in-plane scattering of the light at certain wavelengths, and the pointed tips promote high electric field concentration. The combination of these two factors leads to greater in-plane scattering of the incident light as compared to the nanospheres, with a J_SC enhancement of 22% over the reference tandem OSC. There is very low absorption in the bottom subcell below a wavelength of 600 nm, as light for shorter wavelengths does not penetrate through to the bottom subcell and is absorbed within the top subcell. The absorption in the top subcell of OSC D follows the spectral profile of the reference tandem OSC till 550 nm after which it decreases due to Fano resonance, as shown in the absorption spectrum in Fig. 6(a).

 

Fig. 6. (a) Comparison of absorption in each subcell (in the top subcell and in the bottom subcell) of tandem OSCs without any nanoparticles in the bottom subcell (in black color), with Ag nanospheres in the bottom subcell (in green color), and with Ag nanostars in the bottom subcell (in red color). Schematics of the tandem OSCs (b) without Ag nanospheres (OSC A), (c) with Ag nanospheres inside the bottom subcell (OSC C), and (d) with Ag nanostars inside the bottom subcell (OSC D). The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. Bottom Ag nanosphere dimensions were taken to be: R_B = 30 nm, and P_B = 100 nm. Bottom Ag nanostar dimensions were taken to be: r_B = 30 nm, L_B = 20 nm, and P_B = 250 nm.

Download Full Size | PDF

The enhancement in absorption and J_SC in the bottom subcell due to the presence of either Ag nanospheres or Ag nanostars in the bottom subcell active layer is not large enough for the bottom subcell J_SC to match that of the top subcell (16.02 mA/cm²) having Ag nanospheres over the top surface. At the same time, the introduction of Ag nanospheres over the top surface of the tandem OSCs enhances the performance of the bottom subcell by about 13%. So, in order to further improve the J_SC of the bottom subcell, Ag nanospheres were incorporated over the top surface of the OSC containing Ag nanostars or Ag nanospheres in the bottom subcell.

3.4 Tandem OSCs with Ag nanoparticles integrated over the top surface and in the bottom subcell

The schematic of a tandem OSC with Ag nanoparticles integrated over the top surface and within the bottom active layer is shown in Fig. 1(e). There are two such tandem OSCs under investigation in this section — the first OSC containing Ag nanospheres (having a radius of 90 nm and periodicity of 500 nm) over the top surface of the OSC and Ag nanospheres (having a radius of 30 nm and periodicity of 100 nm) inside the bottom subcell of the OSC. This OSC will henceforth be referred to as OSC E in this paper. This OSC was implemented with 25 nanospheres in the bottom subcell for every nanosphere over the top surface in given area, as shown in Fig. 7(a). The second OSC consists of Ag nanospheres (having a radius of 90 nm and periodicity of 500 nm) over the top surface of the OSC as well as Ag nanostars (having a core radius of 30 nm, eight prongs of length 20 nm, and a periodicity of 250 nm) inside the bottom subcell of the OSC. This OSC will henceforth be referred to as OSC F in this paper. This OSC was executed with 4 nanostars in the bottom subcell for every nanosphere over the top surface, as shown in Fig. 7(b). The dimensions of the nanoparticles taken in OSC E and OSC F — radii and periodicities for OSC E and OSC F and prong lengths for OSC F — are the optimized dimensions determined in sections 3.2 and 3.3 so as to obtain the highest value of J_SC.

 

Fig. 7. The arrangement of (a) Ag nanospheres in the bottom subcell with respect to Ag nanospheres over the top surface of the OSCs, and (b) Ag nanostars in the bottom subcell with respect to Ag nanospheres over the top surface of the OSCs. The FDTD simulation region is periodic over 500 nm, in X and Y directions. The scales along the X and the Y directions are different for both (a) and (b).

Download Full Size | PDF

The absorption curves from the subcells of OSC E are compared with those of OSC F and with those of the reference tandem OSC (OSC A), as shown in Fig. 8. We can observe from Fig. 8(a) that the spectra for absorption in the top subcell of OSC E is very similar to the top subcell absorption spectra for the tandem OSC with only Ag nanospheres over the top surface of the OSC (i.e. OSC B shown in Fig. 4(c)). It is to be noted that the value of J_SC generated in the top subcell of OSC E (15.47 mA/cm²) is less than that generated in the top subcell of OSC B. Similarly, the spectra for absorption in the bottom subcell of OSC E is comparable to the spectra for absorption in the bottom subcell of OSC C (shown in Fig. 6(c)) which has Ag nanospheres only in the bottom subcell active layer. OSC E, which has a combination of Ag nanospheres over the OSC top surface and Ag nanospheres inside the bottom subcell active layer, has a marginally higher bottom subcell J_SC of 15.35 mA/cm² as compared to the J_SC of the bottom subcell of OSC C (which has Ag nanospheres only inside the bottom subcell active layer).

 

Fig. 8. (a) Comparison of absorption in each subcell (in the top subcell and in the bottom subcell) of tandem OSCs without any nanoparticles in the bottom subcell (in black color), with Ag nanospheres over the OSC top surface and Ag nanospheres in the bottom subcell (in green color), and with Ag nanospheres over the OSC top surface and Ag nanostars in the bottom subcell (in red color). Schematics of the tandem OSCs (b) without Ag nanospheres (OSC A), (c) with Ag nanospheres over the top surface and Ag nanospheres in the bottom subcell (OSC E), and (d) with Ag nanospheres over the top surface and Ag nanostars in the bottom subcell (OSC F). The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. Top Ag nanosphere dimensions were taken to be: R_T = 90 nm, and P_T = 500 nm. Bottom Ag nanosphere dimensions were taken to be: R_B = 30 nm, and P_B = 100 nm. Bottom Ag nanostar dimensions were taken to be: r_B = 30 nm, L_B = 20 nm, and P_B = 250 nm.

Download Full Size | PDF

The integration of both Ag nanospheres on the top surface and Ag nanostars inside the bottom subcell of the tandem OSC (in OSC F in Fig. 8(d)) leads to slightly broader and flatter peaks in the absorption spectra (shown in red color in Fig. 8(a)) — for absorption in both the top subcell and the bottom subcell — as compared to those for OSC E. The absorption in the top subcell (as shown by the solid red line in Fig. 8(a)) of OSC F is higher than that for OSC E for wavelengths up to 500 nm. It reduces slightly beyond 500 nm (up to 650 nm), after which it increases again. The J_SC generated in the top subcell of the OSC F was calculated to be 15.97 mA/cm² which is a 5.6% enhancement over the top subcell J_SC (15.12 mA/cm²) of the reference tandem OSC (OSC A). The effect of the position of the Ag nanospheres and of the Ag nanostars in this tandem OSC (OSC F) — on the absorption spectra and on the Jsc — was also studied and is described in Appendix B.

The absorption in the bottom subcell of OSC F containing optimized nanospheres and nanostars (shown by the dotted red line in Fig. 8(a)) is much higher than that for OSC E (shown by the dotted green line in Fig. 8(a)) for wavelengths from 650 nm to 1100 nm. The J_SC generated in the bottom subcell of OSC F is 16.08 mA/cm², which is the highest value of J_SC obtained in either the top or the bottom subcell of any of the tandem OSCs studied in this work. This higher value of J_SC generated in the bottom subcell of OSC F as compared to that for OSC E results from higher in-plane scattering by the Ag nanostars due to a greater scattering cross-section of the Ag nanostars (present inside the bottom subcell of OSC F) as compared to that of the Ag nanospheres (present inside the bottom subcell of OSC E). Moreover, it results from a higher localized near-field enhancement in the vicinity of the Ag nanostars due to the presence of sharper prongs in the Ag nanostars. The overall J_SC of the tandem OSC with optimized nanospheres and nanostars is 15.97 mA/cm²; an enhancement of 25.9% over the overall J_SC (12.68 mA/cm²) of the reference tandem OSC with a 170 nm thick top active layer and an 80 nm thick bottom active layer. This is even higher than that of the matched tandem OSC (15.06 mA/cm²) without any nanoparticles and having a top active layer thickness of 170 nm and a bottom active layer thickness of 110 nm. Through the engineering of nanoparticles, the performance of the tandem OSC has been boosted, even with a 37% reduction in the bottom active layer thickness. The individual absorption responses from the subcells were added to obtain the total absorption of the tandem OSC with optimized nanospheres and nanostars (OSC F). The absorption enhancement from the profiles of Fig. 9(a) was obtained as the ratio of the absorption in the OSC containing the optimized nanospheres and nanostars to the absorption in the reference tandem OSC, and plotted in Fig. 9(b). Enhancement peaks were observed at 520 nm, 730 nm, and 920 nm. Further peaks, beyond 1000 nm, are a consequence of the falling tail of the peak in the spectrum, and are thus, not considered.

 

Fig. 9. (a) Total absorption – sum of absorption in top and bottom subcells – of the tandem OSC containing optimized nanospheres and nanostars (OSC F) (red), and the reference tandem OSC (OSC A) (black); (b) Absorption enhancement of the tandem OSC containing optimized nanospheres and nanostars (OSC F) over that of the reference tandem OSC (OSC A). The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer– 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. Top Ag nanosphere dimensions were taken to be: R_T = 90 nm, and P_T = 500 nm. Bottom Ag nanostar dimensions were taken to be: r_B = 30 nm, L_B = 20 nm, and P_B = 250 nm.

Download Full Size | PDF

To further explore the mechanism of enhancement in the tandem OSCs with optimized nanospheres and nanostars (OSC F), the normalized electric field distributions in OSC F were calculated for different wavelengths of the incident optical radiation: 520 nm, 730 nm and 920 nm (Fig. 10). These field distributions were compared with the respective field distributions of tandem OSCs containing either only Ag nanospheres on top or only Ag nanostars in the bottom subcell. In the spatial distributions for the reference tandem OSC (as shown in Figs. 10(a), 10(d) and 10(g)), weak interference fringes are observed due to the interaction between incident light and reflected light from the back electrode. Ag nanospheres over the top surface (Figs. 10(b), and 10(e)) increase the optical path length in the active layers of the OSCs (due to enhanced light scattering at plasmon resonant wavelengths) which then leads to coupling of the scattered light into the waveguide modes within the layers.

 

Fig. 10. Normalized spatial distribution of the electric field enhancement inside the double junction tandem OSCs. For a wavelength of 520 nm - (a) Reference tandem OSC; (b) OSC with Ag nanospheres over the top surface; (c) OSC having Ag nanospheres over the top surface and Ag nanostars in the bottom subcell. For a wavelength of 730 nm - (d) Reference tandem OSC; (e) OSC with Ag nanospheres over the top surface; (f) OSC having Ag nanospheres over the top surface and Ag nanostars in the bottom subcell. For a wavelength of 920 nm - (g) Reference tandem OSC; (h) OSC with Ag nanostars in the bottom subcell; (i) OSC having Ag nanosphere over the top surface and Ag nanostars in the bottom subcell. The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer– 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. Top Ag nanosphere dimensions were taken to be: R_T = 90 nm, and P_T = 500 nm. Bottom Ag nanostar dimensions were taken to be: r_B = 30 nm, L_B = 20 nm, and P_B = 250 nm.

Download Full Size | PDF

The localized near-field effect of the Ag nanostars in the bottom active layer (Fig. 10(h)) contributes to higher field confinement (due to the presence of sharp prongs in the Ag nanostars) and thus, more absorption in the bottom subcell of the OSC. They also have larger scattering of light to create higher field enhancements in both the subcells. When the optimized nanospheres and nanostars were integrated over and within the top and bottom subcells, respectively, a stronger electric field distribution is achieved, which is spread out along a larger volume of both active layers, as shown in Figs. 10(c), 10(f) and 10(i). This localized electric field enhancement leads to higher absorption in the bottom subcells. The effect of the Ag nanospheres over the top surface dominates in the lower wavelength region of the high bandgap top subcell as the resonance wavelength of Ag nanoparticles are in that wavelength regime. In the longer wavelengths, the low bandgap bottom active layer absorbs more light due to the Ag nanostars and reflection from the back electrode. In the 600–800 nm region, there is a combination of forward scattering by the Ag nanospheres on top, the in-plane scattering by the Ag nanostars and back reflection from the Ag electrode, creating hybrid modes which generate broad absorption profiles [38].

3.5 Power conversion efficiency of the tandem OSCs

In this paper, while the J-V characteristics of tandem OSCs were calculated by assuming ideal operating conditions, the calculation of power conversion efficiency was carried out using a realistic (non-ideal) fill factor. Ideal operating conditions have been employed previously to determine the J-V characteristics of OSCs using the diode equation [48]. For the ideal operating conditions of a zero series resistance and an infinite shunt resistance, the J-V curves of all the tandem OSCs under consideration in this paper were obtained using the diode equation [49] –

The open circuit condition, V = V_OC and J = 0, of the reference tandem OSC was used to evaluate the saturation dark current density, J₀, from Eq. 4. With V_OC = V_OC1 (top subcell) + V_OC2 (bottom subcell)= 0.9 V + 0.71 V = 1.61 V and J_SC = 12.68 mA/cm², we evaluated J₀ = 1.24 × 10⁻²⁵ A/m² for the reference tandem OSC. This value of J₀ was then taken as a constant for plotting the J-V curves of the tandem OSCs containing the nanoparticles, as shown in Fig. 11. J_SC value of 12.68 mA/cm² taken in this calculation is the effective J_SC of the reference tandem OSC, and is determined by taking the lower J_SC between the top and bottom subcell short circuit current densities. The lower value of J_SC was obtained for the bottom subcell of this reference OSC.

 

Fig. 11. J-V characteristics of double junction tandem OSCs containing Ag nanoparticles in the different regions of the OSCs, in comparison with the reference tandem OSC. The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. Top Ag nanosphere dimensions were taken to be: R_T = 90 nm, and P_T = 500 nm. Bottom Ag nanosphere dimensions were taken to be: R_B = 30 nm, and P_B = 100 nm. Bottom Ag nanostar dimensions were taken to be: r_B = 30 nm, L_B = 20 nm, and P_B = 250 nm.

Download Full Size | PDF

The power conversion efficiency of the above tandem OSCs were calculated using a realistic condition with an OSC fill factor of 0.6 [39,40]. Using Eq. (3), P_in = 100 mW/cm² and V_OC = 1.61 V, PCE for the tandem OSCs reduces to:

Table 1. Photovoltaic characteristics of the tandem OSCs containing plasmonic nanospheres and nanostars

View Table | View all tables in this article

In the calculations shown in Table 1, the same typical fill factor (0.6) was used to determine the PCEs for all the OSCs. The introduction of nanospheres and nanostars may enhance the fill factor of the OSCs as described in literature [19,50]. Thus the fabrication of the proposed tandem OSC containing the nanoparticles may yield an even higher PCE than 15.43% (closer to the ideal value) due to a higher fill factor than what has been assumed in this paper.

4. Conclusion

In summary, we have proposed novel designs of plasmonic double junction tandem OSCs in which Ag nanospheres are present over the top surface of the OSC and Ag nanostars are present in the bottom subcell which substantially enhance the absorption, short circuit current density, and efficiency of the OSC as compared to the reference tandem OSCs that do not contain any nanoparticles. Different geometries of the plasmonic nanoparticles (nanospheres and nanostars) were used in the top subcell and the bottom subcell, respectively, so that the absorption in the different spectral regimes — corresponding to the bandgaps of the active layers in the two subcells (PTB7:PC₇₀BM in the top subcell and LBG:PC₆₀BM in the bottom subcell) — could be enhanced. The thickness of the bottom subcell active layer as well as the geometries of the plasmonic nanoparticles were optimized such that the short circuit current densities in the two subcells could be matched in the tandem OSC. It was also observed that a combination of plasmonic nanoparticles over the top surface and inside the bottom subcell of the tandem OSCs provided a higher enhancement in absorption and short circuit current density as compared to the cases when the plasmonic nanoparticles were present only inside the bottom subcell or only on the top surface of the OSCs. Moreover, the tandem OSC (OSC F) containing a combination of plasmonic nanospheres over the top surface and plasmonic nanostars inside the bottom subcell had a higher value of short circuit current density and efficiency as compared to a tandem OSC containing plasmonic nanospheres both on the top surface and inside the bottom subcell of the OSC (OSC E). Directing the scattering mechanisms by manipulation of the shape, size and surface coverage of the plasmonic nanoparticles present in the different regions of the tandem OSC, an enhancement of about 26% in the short circuit current density can be achieved in the plasmonic tandem OSC as compared to the tandem OSC without any nanoparticles, with a reduced bottom subcell active layer thickness of 80 nm. Under realistic conditions with an OSC fill factor of 0.6, the tandem OSC containing the optimized Ag nanospheres and nanostars has a calculated PCE of ∼15.43%, while the maximum PCE of the reference tandem OSC is 12.25%. This approach unfolds a viable route for high performance and cost-effective tandem organic solar cells.

Appendix A: Active layer materials for the tandem OSC

The choice of the subcell active layer materials was made to have an overall minimally overlapping absorption spectrum for the entire tandem OSC — i.e. the absorption bands of the active layer materials of the two subcells should cover different wavelength regions of the solar spectrum. The different combinations that were explored are:

• i. A blend of PTB7 and PC₇₀BM as the top subcell active layer material; and a blend of PDPPSDTPS (LBG) and PC₆₀BM as the bottom subcell active layer material, as shown in Fig. 12(a).
• ii. A blend of PTB7 and PC₇₀BM as the top subcell active layer material; and a blend of PMDPP3T:PC₇₀BM as the bottom subcell active layer material, as shown in Fig. 12(b).
• iii. A blend of P3HT:PC₇₀BM as the top subcell active layer material; and a blend of PDPPSDTPS (LBG) and PC₇₀BM as the bottom subcell active layer material, as shown in Fig. 12(c).

 

Fig. 12. Short circuit current density (J_SC) generated in the top and bottom subcells of a tandem OSC:(a) as a function of the bottom subcell thickness (t_bottom) with a fixed top subcell active layer thickness of 170 nm, (b) as a function of the top subcell thickness (t_top) with a fixed bottom subcell active layer thickness of 110 nm, and (c) as a function of the bottom subcell thickness (t_bottom) with a fixed top subcell active layer thickness of 170 nm.

Download Full Size | PDF

The respective subcell layer thickness optimizations for the tandem OSCs with the above mentioned active layer materials are shown in Fig. 12. The matched short circuit current density (J_SC) of the tandem OSC in Fig. 12(a) is 15.06 mA/cm². For the tandem OSC in Fig. 12(b) and in Fig. 12(c) the matched J_SC values are 13.29 mA/cm² and 12.14 mA/cm², respectively. Therefore, the tandem OSC shown in Fig. 12(a) – OSC A was chosen for further study.

Appendix B: Effect of the position of the Ag nanoparticles in the tandem OSC

As Ag nanospheres scatter light in the forward direction, placing them further inside the solar cell instead of on the surface leads to the coupling of light in the intermediate layers and away from the top subcell active layer. Adding the Ag nanospheres over the top surface effectively creates high electric field regions in the top subcell and bottom subcell active layers, as shown in Figs. 10(b) and 10(e).

As Ag nanostars are responsible for in-plane scattering, placing them in the intermediate layers (the TiO₂ and MoO₃ layers) of the bottom subcell leads to an increase in the optical path length of the incident light in the intermediate layers and not in the active layer, where the absorption actually takes place. Therefore, the Ag nanostars are best placed in the bottom subcell active layer.

The simulation data of OSCs containing Ag nanospheres and Ag nanostars in different positions in the solar cell is presented in Fig. 13. The J_SC of the OSCs presented in Fig. 13 are tabulated in Table 2.

 

Fig. 13. (a) Comparison of absorption in each subcell (in the top subcell and in the bottom subcell) of tandem OSCs – with Ag nanospheres over the OSC top surface and Ag nanostars in the bottom subcell (in black color), with Ag nanospheres over the OSC top surface and Ag nanostars in the intermediate layer (TiO₂) extending into the bottom subcell active layer (in green color), with Ag nanospheres in the top buffer layer (TiO₂) extending into the top subcell active layer and Ag nanostars in the intermediate layer (TiO₂) extending into the bottom subcell active layer (in red color), and with Ag nanospheres in the top buffer layer (TiO₂) extending into the top subcell active layer and Ag nanostars in the bottom subcell (in purple color). Schematics of the tandem OSCs (b) with Ag nanospheres over the OSC top surface and Ag nanostars in the bottom subcell (OSC F), (c) with Ag nanospheres over the OSC top surface and Ag nanostars in the intermediate layer (TiO₂) extending into the bottom subcell active layer (OSC H), (d) with Ag nanospheres in the top buffer layer (TiO₂) extending into the top subcell active layer and Ag nanostars in the intermediate layer (TiO₂) extending into the bottom subcell active layer (OSC I) and (e) with Ag nanospheres in the top buffer layer (TiO₂) extending into the top subcell active layer and Ag nanostars in the bottom subcell (OSC J). The thicknesses of the different layers of the OSC were taken to be: ITO layer – 50 nm, PTB7:PC₇₀BM layer – 170 nm, PDPPSDTPS:PC₆₀BM (i.e. LBG:PC₆₀BM) layer – 80 nm, TiO₂ layer – 50 nm, MoO₃ layer – 50 nm, and Ag back electrode – 100 nm. Top Ag nanosphere dimensions were taken to be: R_T = 90 nm, and P_T = 500 nm. Bottom Ag nanostar dimensions were taken to be: r_B = 30 nm, L_B = 20 nm, and P_B = 250 nm.

Download Full Size | PDF

Table 2. J_SC of the top and bottom subcell for different positions of nanoparticles

View Table | View all tables in this article

From all the variations above, the best results were obtained for the tandem OSC with top and bottom subcell active layer materials PTB7:PC₇₀BM and PDPPSDTPS:PC₆₀BM, respectively containing Ag nanospheres over the top surface and Ag nanostars in the bottom subcell active layer with an effective J_SC of 15.97 mA/cm².

Funding

Defence Research and Development Organisation (RPO3356); Department of Biotechnology , Ministry of Science and Technology (RPO2829, RPO3150); Science and Engineering Research Board (RP03055); Ministry of Human Resource Development (RP03246G: UAY program, RP03417G: IMPRINT program).

Acknowledgments

We would also like to thank the Digital India Corporation. This publication is an outcome of the R&D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation (formerly Media Lab Asia).

References

1. W. J. E. Beek, M. M. Wienk, M. Kemerink, X. Yang, and R. A. J. Janssen, “Hybrid zinc oxide conjugated polymer bulk heterojunction solar cells,” J. Phys. Chem. B 109(19), 9505–9516 (2005). [CrossRef]  

2. M. I. Alonso and M. Campoy-Quiles, “Organic solar cells,” Springer Ser. Opt. Sci. 212(3), 439–461 (2019). [CrossRef]  

3. C. Liu, C. Zhao, X. Zhang, W. Guo, K. Liu, and S. Ruan, “Unique Gold Nanorods Embedded Active Layer Enabling Strong Plasmonic Effect to Improve the Performance of Polymer Photovoltaic Devices,” J. Phys. Chem. C 120(11), 6198–6205 (2016). [CrossRef]  

4. Y. Cui, H. Yao, B. Gao, Y. Qin, S. Zhang, B. Yang, C. He, B. Xu, and J. Hou, “Fine-Tuned Photoactive and Interconnection Layers for Achieving over 13% Efficiency in a Fullerene-Free Tandem Organic Solar Cell,” J. Am. Chem. Soc. 139(21), 7302–7309 (2017). [CrossRef]  

5. M. Li, K. Gao, X. Wan, Q. Zhang, B. Kan, R. Xia, F. Liu, X. Yang, H. Feng, W. Ni, Y. Wang, J. Peng, H. Zhang, Z. Liang, H. L. Yip, X. Peng, Y. Cao, and Y. Chen, “Solution-processed organic tandem solar cells with power conversion efficiencies >12%,” Nat. Photonics 11(2), 85–90 (2017). [CrossRef]  

6. W. Zhao, S. Li, H. Yao, S. Zhang, Y. Zhang, B. Yang, and J. Hou, “Molecular Optimization Enables over 13% Efficiency in Organic Solar Cells,” J. Am. Chem. Soc. 139(21), 7148–7151 (2017). [CrossRef]  

7. X. Xu, T. Yu, Z. Bi, W. Ma, Y. Li, and Q. Peng, “Realizing Over 13% Efficiency in Green-Solvent-Processed Nonfullerene Organic Solar Cells Enabled by 1,3,4-Thiadiazole-Based Wide-Bandgap Copolymers,” Adv. Mater. 30(3), 1703973 (2018). [CrossRef]  

8. M. Glatthaar, M. Niggemann, B. Zimmermann, P. Lewer, M. Riede, A. Hinsch, and J. Luther, “Organic solar cells using inverted layer sequence,” Thin Solid Films 491(1–2), 298–300 (2005). [CrossRef]  

9. Y. Li and Y. Zou, “Conjugated polymer photovoltaic materials with broad absorption band and high charge carrier mobility,” Adv. Mater. 20(15), 2952–2958 (2008). [CrossRef]  

10. S. Günes, H. Neugebauer, and N. S. Sariciftci, “Conjugated polymer-based organic solar cells,” Chem. Rev. 107(4), 1324–1338 (2007). [CrossRef]  

11. S. Günes, H. Neugebauer, and N. S. Sariciftci, “Conjugated polymer-based organic solar cells,” Chem. Rev. 107(4), 1324–1338 (2007). [CrossRef]  

12. K. Q. Le, J. Bai, and P. Y. Chen, “Dielectric antireflection fiber arrays for absorption enhancement in thin-film organic tandem solar cells,” IEEE J. Sel. Top. Quantum Electron. 22(1), 1–6 (2016). [CrossRef]  

13. A. Hadipour, B. de Boer, and P. W. M. Blom, “Device operation of organic tandem solar cells,” Org. Electron. 9(5), 617–624 (2008). [CrossRef]  

14. L. Zuo, J. Yu, X. Shi, F. Lin, W. Tang, and A. K. Y. Jen, “High-Efficiency Nonfullerene Organic Solar Cells with a Parallel Tandem Configuration,” Adv. Mater. 29(34), 1702547 (2017). [CrossRef]  

15. T. Kawawaki, H. Wang, T. Kubo, K. Saito, J. Nakazaki, H. Segawa, and T. Tatsuma, “Efficiency enhancement of PbS quantum Dot/ZnO nanowire bulk-heterojunction solar cells by plasmonic silver nanocubes,” ACS Nano 9(4), 4165–4172 (2015). [CrossRef]  

16. I. Diukman, L. Tzabari, N. Berkovitch, N. Tessler, and M. Orenstein, “Controlling absorption enhancement in organic photovoltaic cells by patterning Au nano disks within the active layer,” Opt. Express 19(S1), A64–A71 (2011). [CrossRef]  

17. 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). [CrossRef]  

18. Z. Su, L. Wang, Y. Li, G. Zhang, H. Zhao, H. Yang, Y. Ma, B. Chu, and W. Li, “Surface plasmon enhanced organic solar cells with a MoO3 buffer layer,” ACS Appl. Mater. Interfaces 5(24), 12847–12853 (2013). [CrossRef]  

19. 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). [CrossRef]  

20. 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]  

21. D. Qu, F. Liu, Y. Huang, W. Xie, and Q. Xu, “Mechanism of optical absorption enhancement in thin film organic solar cells with plasmonic metal nanoparticles,” Opt. Express 19(24), 24795–24803 (2011). [CrossRef]  

22. L. O. Herrmann, V. K. Valev, C. Tserkezis, J. S. Barnard, S. Kasera, O. A. Scherman, J. Aizpurua, and J. J. Baumberg, “Threading plasmonic nanoparticle strings with light,” Nat. Commun. 5(1), 4568 (2014). [CrossRef]  

23. D. Duché, C. Masclaux, J. Le Rouzo, and C. Gourgon, “Photonic crystals for improving light absorption in organic solar cells,” J. Appl. Phys. 117(5), 053108 (2015). [CrossRef]  

24. F. Otieno, N. P. Shumbula, M. Airo, M. Mbuso, N. Moloto, R. M. Erasmus, A. Quandt, and D. Wamwangi, “Improved efficiency of organic solar cells using Au NPs incorporated into PEDOT:PSS buffer layer,” AIP Adv. 7(8), 085302 (2017). [CrossRef]  

25. I. Vangelidis, A. Theodosi, M. J. Beliatis, K. K. Gandhi, A. Laskarakis, P. Patsalas, S. Logothetidis, S. R. P. Silva, and E. Lidorikis, “Plasmonic Organic Photovoltaics: Unraveling Plasmonic Enhancement for Realistic Cell Geometries,” ACS Photonics 5(4), 1440–1452 (2018). [CrossRef]  

26. V. Janković, Y. Yeng, J. You, L. Dou, Y. Liu, P. Cheung, J. P. Chang, and Y. Yang, “Active layer-incorporated, spectrally tuned Au/SiO2 core/shell nanorod-based light trapping for organic photovoltaics,” ACS Nano 7(5), 3815–3822 (2013). [CrossRef]  

27. S. Chang, Q. Li, X. Xiao, K. Y. Wong, and T. Chen, “Enhancement of low energy sunlight harvesting in dye-sensitized solar cells using plasmonic gold nanorods,” Energy Environ. Sci. 5(11), 9444–9448 (2012). [CrossRef]  

28. I. Kim, D. Seok Jeong, T. Seong Lee, W. Seong Lee, and K. S. Lee, “Plasmonic absorption enhancement in organic solar cells by nano disks in a buffer layer,” J. Appl. Phys. 111(10), 103121 (2012). [CrossRef]  

29. F.-J. Tsai, J.-Y. Wang, J.-J. Huang, Y.-W. Kiang, and C. C. Yang, “Absorption enhancement of an amorphous Si solar cell through surface plasmon-induced scattering with metal nanoparticles,” Opt. Express 18(S2), A207–A220 (2010). [CrossRef]  

30. I. Kim, T. S. Lee, D. S. Jeong, W. S. Lee, W. M. Kim, and K.-S. Lee, “Optical design of transparent metal grids for plasmonic absorption enhancement in ultrathin organic solar cells,” Opt. Express 21(S4), A669–A676 (2013). [CrossRef]  

31. B. Cai, Y. Peng, Y.-B. Cheng, and M. Gu, “4-Fold Photocurrent Enhancement in Ultrathin Nanoplasmonic Perovskite Solar Cells,” Opt. Express 23(24), A1700–A1706 (2015). [CrossRef]  

32. S. Liu, R. Jiang, P. You, X. Zhu, J. Wang, and F. Yan, “Au/Ag core-shell nanocuboids for high-efficiency organic solar cells with broadband plasmonic enhancement,” Energy Environ. Sci. 9(3), 898–905 (2016). [CrossRef]  

33. Q. Xu, F. Liu, W. Meng, and Y. Huang, “Plasmonic core-shell metal-organic nanoparticles enhanced dye-sensitized solar cells,” Opt. Express 20(S6), A898–A907 (2012). [CrossRef]  

34. M. Futamata, Y. Maruyama, and M. Ishikawa, “Local Electric Field and Scattering Cross Section of Ag Nanoparticles under Surface Plasmon Resonance by Finite Difference Time Domain Method,” J. Phys. Chem. B 107(31), 7607–7617 (2003). [CrossRef]  

35. Y. Taff, B. Apter, E. A. Katz, and U. Efron, “Modeling plasmonic efficiency enhancement in organic photovoltaics,” Appl. Opt. 54(26), 7957–7961 (2015). [CrossRef]  

36. R. S. Kim, J. Zhu, J. H. Park, L. Li, Z. Yu, H. Shen, M. Xue, K. L. Wang, G. Park, T. J. Anderson, and Q. Pei, “E-beam deposited Ag-nanoparticles plasmonic organic solar cell and its absorption enhancement analysis using FDTD-based cylindrical nano-particle optical model,” Opt. Express 20(12), 12649–12657 (2012). [CrossRef]  

37. C.-H. Poh, L. Rosa, S. Juodkazis, and P. Dastoor, “FDTD modeling to enhance the performance of an organic solar cell embedded with gold nanoparticles,” Opt. Mater. Express 1(7), 1326–1331 (2011). [CrossRef]  

38. B. Cai, X. Li, Y. Zhang, and B. Jia, “Significant light absorption enhancement in silicon thin film tandem solar cells with metallic nanoparticles,” Nanotechnology 27(19), 195401 (2016). [CrossRef]  

39. C. C. Chen, W. H. Chang, K. Yoshimura, K. Ohya, J. You, J. Gao, Z. Hong, and Y. Yang, “An efficient triple-junction polymer solar cell having a power conversion efficiency exceeding 11%,” Adv. Mater. 26(32), 5670–5677 (2014). [CrossRef]  

40. K. H. Hendriks, W. Li, M. M. Wienk, and R. A. J. Janssen, “Small-bandgap semiconducting polymers with high near-infrared photoresponse,” J. Am. Chem. Soc. 136(34), 12130–12136 (2014). [CrossRef]  

41. A. Hadipour, D. Cheyns, P. Heremans, and B. P. Rand, “Electrode considerations for the optical enhancement of organic bulk heterojunction solar cells,” Adv. Energy Mater. 1(5), 930–935 (2011). [CrossRef]  

42. M. C. Scharber, D. Mühlbacher, M. Koppe, P. Denk, C. Waldauf, A. J. Heeger, and C. J. Brabec, “Design rules for donors in bulk-heterojunction solar cells - Towards 10% energy-conversion efficiency,” Adv. Mater. 18(6), 789–794 (2006). [CrossRef]  

43. H. Liang, W. Wang, Y. Huang, S. Zhang, H. Wei, and H. Xu, “Controlled synthesis of uniform silver nanospheres,” J. Phys. Chem. C 114(16), 7427–7431 (2010). [CrossRef]  

44. Y. Zhang, Z. Ouyang, N. Stokes, B. Jia, Z. Shi, and M. Gu, “Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells,” Appl. Phys. Lett. 100(15), 151101 (2012). [CrossRef]  

45. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: Geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010). [CrossRef]  

46. A. Garcia-Leis, J. V. Garcia-Ramos, and S. Sanchez-Cortes, “Silver nanostars with high SERS performance,” J. Phys. Chem. C 117(15), 7791–7795 (2013). [CrossRef]  

47. Y. Hsiangkuo, G. K. Christopher, H. Hanjun, M. W. Christy, A. G. Gerald, and V.-D. Tuan, “Gold nanostars: surfactant-free synthesis, 3D modelling, and two-photon photoluminescence imaging,” Nanotechnology 23(7), 075102 (2012). [CrossRef]  

48. K. Kumar, U. K. Kumawat, R. Mital, and A. Dhawan, “Light trapping plasmonic butterfly-wing-shaped nanostructures for enhanced absorption and efficiency in organic solar cells,” J. Opt. Soc. Am. B 36(4), 978–990 (2019). [CrossRef]  

49. S. M. Sze and K. K. Ng, Physics of Semiconducting Devices (John Wiley and Sons, 2007).

50. Q. Luo, C. Zhang, X. Deng, H. Zhu, Z. Li, Z. Wang, X. Chen, and S. Huang, “Plasmonic Effects of Metallic Nanoparticles on Enhancing Performance of Perovskite Solar Cells,” ACS Appl. Mater. Interfaces 9(40), 34821–34832 (2017). [CrossRef]