Plasmonic Organic Photovoltaics: Unraveling Plasmonic

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Plasmonic Organic Photovoltaics: Unraveling Plasmonic Enhancement for Realistic Cell Geometries Ioannis Vangelidis, Anna Theodosi, Michail J Beliatis, Keyur Gandhi, Argiris Laskarakis, Panos Patsalas, Stergios Logothetidis, S. Ravi P. P Silva, and Elefterios Lidorikis ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01390 • Publication Date (Web): 23 Jan 2018 Downloaded from http://pubs.acs.org on January 23, 2018

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Plasmonic Organic Photovoltaics: Unraveling Plasmonic Enhancement for Realistic Cell Geometries Ioannis Vangelidis1, Anna Theodosi1, Michail J. Beliatis2, Keyur K. Gandhi2, Argiris Laskarakis1,3, Panos Patsalas1,3, Stergios Logothetidis3, S. Ravi P. Silva2, Elefterios Lidorikis1,* 1 2

Department of Materials Science and Engineering, University of Ioannina, 45110 Ioannina, Greece

Advanced Technology Institute, Department of Electrical and Electronic Engineering, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom

3

Laboratory for Thin Films-Nanobiomaterials, Nanosystems and Nanometrology (LTFN), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece *

[email protected]

ABSTRACT Incorporating plasmonic nanoparticles in Organic Photovoltaic (OPV) devices can increase the optical thickness of the organic absorber layer while keeping its physical thickness small. However, trade-offs between various structure parameters have caused contradictions regarding the effectiveness of plasmonics in the literature, that have somewhat stunted the progressing of a unified theoretical understanding for practical applications. We examine the optical enhancement mechanisms of practical PCDTBT:PC70BM OPV cells incorporating metal nanoparticles. The plasmonic near- and far-field contributions are differentiated, with spectrum- and space-wide current enhancements found in the plasmon scattering regime and spectrum- and space-specific current enhancements in the near-field regime. A remarkable system complexity is revealed, where the plasmonic enhancement trends change and even reverse by simple changes in the device geometry. This accounts for many of the contradictory results published in the literature on plasmonic effects in OPVs. By exploring the full structural parameter phase-space we are able to now propose a unified representation that intuitively explains literature findings and trends. Our results show that an already optimized PCDTBT:PC70BM cell can be further optically enhanced by plasmonic effects by at least 20% with the incorporation of Ag nanoparticles.

KEYWORDS: organic photovoltaics, surface plasmon resonance, metal nanoparticles

An environmentally friendly, large area compatible, low maintenance, easily deployable and cost efficient alternative to silicon photovoltaics for sustainable solar energy are solution-processed organic photovoltaics (OPV)1-4, augmented further with their compatibility to low temperature printing by roll-

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to-roll production methods5,6. The OPV photoactive layer typically consists of electron donor and acceptor semiconducting polymers1,7 intermixed to form bulk heterojunctions (BHJ)8-13 in order to increase their interfacial area and thus improve the exciton dissociation efficiency14,15. However, the low bulk carrier mobility16,17 and fast free charge carrier recombination rates place limitations on the optimum active layer thickness sustainable within a typical device structure. But due to the photon absorption length being greater than the carrier transport length, a reduction in the photoactive layer thickness to compensate for carrier recombination will also result in poor photon absorption and thus less charge generation, giving rise to low power output. Typically, optimized OPV architectures have a photoactive layer thickness ~100 nm exhibiting minimal charge carrier recombination but also limited light absorption, generally holding the power conversion efficiency (PCE) below 10%18. This absorption-extraction trade-off raises the need for careful engineering of the absorbing media19-22 and of the device architectures (e.g. for conventional cells9,23-30 or inverted cells31-35) so that the absorption can be maximized while keeping the photoactive layer thickness reasonable. To overcome the limitations associated with finite absorption volumes of bulk materials, techniques for better photon management and light trapping inside the BHJ have been considered36-39,40. One such approach is the introduction of plasmonic metallic nanoparticles (NP)41-46,47-50 to enhance the light-matter interaction in the nanoscale between the plasmonic metal and the semiconductor active layers51 NPs are particularly interesting because they are compatible with the solution processing techniques used for organic materials. For metallic NPs with dimensions below the wavelength of the incident light, the extinction and scattering cross sections are given by = { } and = | | /6

respectively, where

= 3( / − 1)/( / + 2) is the NP polarizability in the quasi-static limit52, V the NP volume and εm, εh the dielectric functions of the NP and of the host material. For the frequency where ≈ −2 , light scattering and absorption cross sections are maximized to what is known as localized surface plasmon resonance (LSPR)53. These are collective coherent oscillations of the NP’s free electrons excited by the incident electromagnetic radiation, resulting in a strong enhancement of both near field around the NP and far field scattered waves. The LSPR spectral region is determined by the shape, size and type of the NPs as well as their dispersion and their host environment. Noble metal NP LSPR is mostly excited in the visible or near infrared and are thus most suitable for application in plasmonic organic photovoltaic applications54-58. Extended research has been conducted for NPs placed in the front or back buffer layers of the OPV architecture59-70. Various short-circuit current enhancement values of up to 25% have been typically reported for large NPs (diameter of 40-70nm)59,61,62,65-68,71,72, reaching more than 30% for


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periodic Ag nanodot arrays73. Composite core/shell NPs (e.g. Au/Ag nanocubes)74,75 have also been studied with the aim to broaden and/or tune the plasmonic response spectrum. The main mechanism reported is forward or backward scattering, but in many cases the NP diameter is larger than the buffer thickness and thus the NPs extend into the photoactive layer offering enhanced near-fields as well. Also reported is an enhancement in exciton dissociation efficiency and carrier lifetime59,67,68 or morphology changes of the buffer/active interface64. On the other hand, small NPs completely embedded inside the front buffer layer (e.g. PEDOT:PSS) generally offered only a benefit in the electrical characteristics and no direct optical enhancement due to enhanced NP parasitic absorption and shadowing losses60,63. Mixing the NPs inside the photoactive layer offers the advantage of plasmonic near field effects fully utilized to enhance the absorption within the active layer74,76-83. Also, scattering from NPs results in increased optical paths inside the photoactive layer and light trapping by total internal reflection at the glass/air interface. Again, various enhancement values of up to 25% are found for large Ag76,79,80 and Au80,81 NPs, as well as Au/Ag core/shell nanocubes74 However, when placed inside the photoactive layer, the metal NPs can also act as free carrier recombination centers, limiting the overall performance74,78,83. This effect is stronger for the smaller NPs78,83 due to the larger surface-to-volume ratio. Using a suitable thin dielectric insulating shell around the NPs suppresses recombination74,84-87 but can also limit the absorption enhancement if it is too thick87-88. It is thus well established that there is significant potential to further enhance the efficiency of solution-based OPV devices by the incorporation of plasmonic NPs in their structure. Nevertheless, we still lack a universal quantitative understanding of the effect of plasmonic NPs on the optoelectronic properties of OPVs, whereas many works are reporting different, in cases contradictory, performance enhancement values55. Aside from the electrical effects contributing to these contradictions, there are still several important reasons stemming out from just the optical regime. NPs will enhance the absorption in a specific spectral region provided that in this region the organic material absorbs poorly, otherwise they can cause a reduction in the photoactive layer absorption due to their own parasitic absorption. In this sense, different active materials could require different NP distributions for optimal performance. The vertical architecture of the device will also have a strong impact on the NP performance due to the standing wave patterns created inside the photoactive layer: reporting on unoptimized devices will unavoidably result in different, in some cases exaggerated, enhancement values. The exact positioning of the NPs inside the device will also have a specific effect on the device functionality. Therefore, it is important to understand the optical mechanisms and enhancement limits in a realistic optimized plasmonic OPV device before embarking with (the otherwise necessary) fully coupled optical-electrical optimizations81,89-91. To this end, a systematic evaluation of all structural


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parameters involved in plasmonic OPVs becomes important in order to enable their optimum optical design with both near-field and far-field scattering maximized and constructively contributing to the total absorption enhancement and/or to tailoring the absorption distribution within the active layer. In this work we perform a comprehensive optical simulation study on the effects of incorporating plasmonic spherical NPs in a OPV cell, assuming a representative photoactive layer consisting of a PCDTBT:PC70BM BHJ blend. The optical simulations were performed with the finite-difference timedomain (FDTD) method92-94. We explore the full phase-space of Ag and Au NP sizes and distributions and manage for the first time to clearly separate the synergetic effects of LSPR near-field focusing and far-field scattering in the optical absorption enhancement. Most interestingly, we find that the plasmonic enhancement is sensitive to the precise device geometry: depending on the NP configuration a different OPV vertical layout becomes optimal. This effect is strong enough to even reverse certain trends regarding optimizing the NP configuration and explains the distribution of reported enhancement values in the literature. Our systematic modeling unravels all the enhancement mechanisms in play and the true physical limits of plasmonic optical enhancement by spherical NPs in PCDTBT:PC70BM:AgNP fully optimized OPVs to be around 20%. We apply our methods to other polymer blends (P3HT:PC60BM and PTB7:PC70BM) in both direct and inverted devices and establish the generality of our main conclusions. The formalism described in this work is generic and applicable to any OPV architecture with any kind of polymer system as the photoactive layer.

RESULTS AND DISCUSSION

We explore the absorption enhancement for an optimized OPV architecture (Figure 1a) with a PCDTBT:PC70BM BHJ structure as the photoactive layer (Figure 1b) after the incorporation of silver (Ag) or gold (Au) NPs of different sizes, placement and distribution. The measured PCDTBT:PC70BM absorption coefficient is shown in Figure 1c, along with the solar spectrum. Indium-tin oxide (ITO) is the transparent anode (thickness of 120 nm), PEDOT:PSS (thickness of 40 nm) the hole transport layer (HTL), TiO2 (thickness of 10 nm) the electron transport layer (ETL) and aluminum the metallic cathode. Plasmonic effects emerge as a combination of near-field enhancement and scattering, both depending on NP size, shape and distribution inside the host material. On top of that, vertical interference (including ‘optical spacer effects’) determines the standing wave configuration and thus the magnitude of the plasmonic excitations. To facilitate our discussion we only consider spherical NPs periodically dispersed on a particular plane inside the PCDTBT:BC70BM BHJ layer in a square lattice arrangement. Particle size and periodicity are the geometry’s two independent parameters and to


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distinguish between near- and far-field phenomena requires that we exhaust all the geometrical phasespace provided by them. Assuming for simplicity a square array arrangement, a simple parametrization considers the nominal thickness tNP of a hypothetical uniform film (denoted hereafter as “equivalent film”) occupying the same volume as the NP array according to !"# = $% /(6& ), where d is the NP diameter and L the array periodicity. The equivalent film thickness !"# is then directly linked to the NP concentration, for example assuming the NPs distributed within an active layer of thickness H, the NP volume concentration is simply !"# /'. We thus perform our simulations for nominal metal thickness tNP=1-10 nm and array periodicity L=20-400 nm. For each simulated plasmonic OPV geometry, we extract the exciton generation rate G(r,ω) and integrate it over the photoactive layer volume and over frequency to get the ideal short circuit current density Jsc (rate of charge generation) assuming no exciton quenching and no free carrier recombination, in order to isolate and study the optical effects alone. More details on the computational processes and assumptions are presented in the Methods section.

NPs in the active area. * * Figure 2 shows the calculated enhancement of the ideal short-circuit current (() − () )/() × 100 as a

function of the NP array period and equivalent metal film thickness of the Ag (Figure 2a) and Au NPs (Figure 2b) dispersed inside the photoactive layer on the back ETL buffer, as shown in the insets of Figure 2. We assume a fixed blend volume so that the total active thickness after the NP incorporation * is tact=tBHJ+tNP, where tBHJ= 80 nm. () is the ideal short-circuit current value of the same OPV device

without any NPs in its structure. The white (dashed) contour lines indicate the Jsc enhancement, whereas the brown (dotted) contour lines indicate the NP diameter d. The NP phase-space is bounded by the d = 80 nm contour line, which is the active layer thickness without the NPs. In the case of Ag NPs, we observe in Figure 2a an enhancement on the calculated Jsc in two specific regions. The first one is the near-field area, involving small Ag NPs at small periodicities, clearly visible at L~40 nm and tNP> 8 nm for NPs of around d = 30 nm, offering ~15% enhancement. These are NPs forming a dense array, with the peak enhancement following approximately the line L~ 1.6×d, i.e. arrays where the inter-particle gap remains fixed at ~60% of the diameter providing for strong near-fields in-between them. This array is below the diffraction limit so off-normal scattering is by definition prohibited. The second area of Jsc enhancement in Figure 2a is the scattering area, involving large Ag NPs at large periodicities, yielding a maximum enhancement of >20% for d = 80 nm NPs at tNP ~ 4 nm and L ~ 280 nm periodicity. In this region the NPs are sparsely spaced above the diffraction


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limit, so both near-field and scattering effects are activated. Any other combination of Ag NP size and separation is inferior to these two NP geometries, as clearly observed in Figure 2a. These are rather strict limitations, with only two configurations over the entire phase-space giving rise to notable plasmonic enhancements to the OPV device short circuit current. In the Au NP map in Figure 2b the Jsc enhancement terrain is much simpler: only the far-field scattering regime contributes to the enhancement (albeit with smaller magnitude at slightly larger periodicities compared to Ag NPs), while for dense arrays of small Au NPs we get quenching. The latter should be expected given that Au NPs suffer from stronger self-absorption losses than the Ag NPs. Thus, any benefit in active layer absorption is overwhelmed by the parasitic absorption inside the Au NPs. While both Ag and Au can be used as large NP scatterers, the use of Ag NPs offers both near- and far-field contributions and thus are of interest in examining the interplay between the two types of enhancement. Therefore, in the following we continue with the study of Ag NPs. Interesting features arise in the performance map of Figure 2a. For low metal coverage (e.g. tNP = 4 nm) we observe a mostly monotonic increase of the Jsc enhancement with periodicity: this is expected as increasing the periodicity at fixed tNP involves larger more sparsely spaced NPs and the eventual activation of scattering. For a given wavelength λ, the first diffraction order appears at L =

λ/nBHJ, where nBHJ is the refractive index of the host material (here the BHJ). Assuming for simplicity an average index nBHJ ~ 2 and a minimum wavelength λ = 300 nm, we get the critical periodicity Lc = 150 nm, which is exactly where we see the enhancement increasing in Figure 2a. At very small thickness of the equivalent metal layer, the Jsc enhancement quickly diminishes because of the shrinking NP size. On the other hand, for higher values of the equivalent metal layer thickness, the trend with periodicity is non-monotonic. NPs are generally larger here and a peak for NPs close to each other (at around L = 40 nm) with large inter-particle near fields is clear, with the enhancement dropping for larger periodicities where the NPs get separated. The enhancement starts increasing again for L> 150 nm where scattering gets enabled. Figure 3 shows the calculated spatially-integrated spectral absorption in the BHJ film in the case of two characteristic NP geometries; one involving small Ag NPs (d = 30 nm at L = 40 nm) and one involving large Ag NPs (d=70 nm at L = 280 nm). Large gains in absorption are found in both cases, with the one for large NPs being significantly more uniform over the entire spectrum pointing towards the scattering mechanism. Resonance and interference effects, on the other hand, seem to be active in the small NPs case, including the NP self absorption which causes the absorption dip within the 300 350 nm wavelength range.


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Vertical interference due to the standing wave formation that arises from the back mirror reflection was noted in the beginning of this section. In a bare BHJ configuration this interference leads to an optimized BHJ thickness of ~80 nm. However, the introduction of NPs inside the photoactive layer does not guarantee that the same standing wave patterns will emerge and thus that the optimal BHJ thickness will remain ~80 nm. This is a very important point that is generally overlooked in the literature. In Figure 3b we plot the spectrally integrated ideal current as a function of position in the BHJ where it is generated (zero is on the top face where light impinges and distance increases towards the back) for the two characteristic cases shown in Figure 3a. We observe a remarkable change in the configuration of current generation for the small NPs, while for the large NPs it remains similar to that of the bare BHJ case, albeit almost uniformly enhanced. Specifically, for the large NP case we get a uniform enhancement in the top half of the BHJ and an increasingly larger enhancement as we approach the back mirror. In this region near-fields and NPmirror cavity effects yield the extra boost in current generation. In overall however, the standing wave pattern is not disrupted, with the maximum ideal current still being at the BHJ center. For the small NPs, in contrast, the standing wave pattern has been completely transformed, with a large peak emerging on the back side due to the NP plasmonic near fields. These findings point to the great difference between the two NP assemblies: for the large NPs the separation distance is enough for the incoming light to mostly sample the empty space in-between them and thus sense an unaltered BHJ optical thickness. The small NPs, on the other hand, create an extra optically dense layer at the bottom, which changes the overall optical thickness and thus the standing wave pattern. The uptake from the above is that there is still room for improvement in the small NP case by tuning the layer thicknesses and adjusting the standing wave configuration. In Figure 4 we plot the generated ideal current for the two cases as a function of the BHJ+TiO2 thickness (tTiO2 = 10 nm). For comparison we also plot the bare cell case as well as two other large NP cases. The result is a striking verification of our earlier conclusion: all large NP cases (at L = 280 nm) show the exact same trend as the bare case, following the standing wave resonances created by the mirror reflection. Optimal condition is when one, two or more resonances are symmetrically positioned inside the photoactive layer, which yields the bare case maxima of tBHJ+tTiO2= 80 nm and 220 nm shown in Figure 4 (the second resonance is of course overestimated here because we ignore free carrier recombination). Only differences between bare and large NP cases is a vertical shift of the latter to larger currents due to light scattering. In contrast, the small NP case shows a markedly different trend, with the peak performance at tBHJ+tTiO2= 130 nm, exactly where the bare and large NP cases get their lowest performance. This subtle point can be (and has been) a source of tremendous confusion and contradiction, as simulations with slightly different layer thicknesses can yield vastly different trends regarding the benefit of introducing ACS Paragon Plus Environment

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NPs in the device. This is the reason we quote in Figure 4 the total back thickness tBHJ+tTiO2: the standing wave formation depends on the total thickness, not just tBHJ. From the above it becomes obvious that one should not draw a global conclusion after studying only one device architecture, particularly if this is far from the optimal configuration. Different layer materials, different photoactive polymers and different device concepts may (and will) in general yield different optimal configurations and different conclusions regarding the benefit of plasmonic NP introduction, not only quantitatively but sometimes also qualitatively. A different picture emerges when the NPs are placed in the top side of the photoactive layer, as shown in the global performance map of Figure 5. While the large NPs region where scattering prevails still yields high enhancements (albeit slightly lower quantitatively), the small NP near-field region has been completely transformed into a strongly quenched regime. This is due to strong absorption in the smaller NPs as well as to additional reflection losses due to the lack of off-normal scattering in the subwavelength NP array: as a result, much less light makes it past the NP array and into the photoactive region. For the large NPs on the other hand, diffraction is allowed resulting in light scattered in the forward direction into the photoactive layer at large angles and thus with greater possibility to get absorbed. The spectral absorption and current generation distribution are plotted for the two characteristic NP cases plotted in Figure 6. The large NP case appears to be unaffected by the change in NP vertical placement, offering a wide spectral and spatial enhancement due to scattering. In the small NP case, however, the change is dramatic: only at the very long wavelengths there is some small absorption enhancement in an otherwise uniform spectral quenching. Spatially, the signature of the plasmonic near field enhancement is clear in the top of the active layer with the peak positioned exactly at the NP center (15 nm), but below the NPs there is a strong shadowing effect. The standing wave configuration is still visible, albeit strongly diminished. The effect of active layer thickness onto the standing wave configuration and thus onto performance is plotted in Figure 7. The large NP case is very similar to the bare case, confirming that its performance is similar irrespective of NP placement in the photoactive region. The small NP case indeed showcases strong quenching effects. Interestingly, the trend with thickness now also follows the bare case. This however should be expected, since the extra optically dense layer offered by the NPs is now at the top of the overall active region and thus the standing wave configuration is less affected as compared to the previous case where this layer was just above the mirror. A clear quantitative picture of the LSPR and its interplay with the vertical cavity created by the mirror has not been offered up to now. To get this we plot in Figure 8 the relative absorption enhancement (ANP-Abare)/Abare as a function of wavelength and BHJ thickness. Strong plasmonic ACS Paragon Plus Environment

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resonances are found for the small NPs particularly in the longer wavelengths. Here the BHJ absorption is low and the absorption enhancement offered by the NPs can be substantial, at times exceeding ×100. However, being at the very tail of the absorption spectrum their contribution to the overall current remains small. Interestingly, their interaction with the vertical cavity is strong, with the LSPR following the Fabry-Perot lines and even causing a week anti-crossing behavior when they are placed on the back (Figure 8a). Enhancement and quenching regimes alternate as we scan the BHJ thickness in Figure 8a, showing how critical it is to get the thickness right when one uses dense arrays of small NPs. When placed in the top of the cell structure (Figure 8b) the quenching extends throughout the spectrum with the detrimental effect we observed in Figure 7. The large NP array on the other hand shows a fairly fixed LSPR peak at ~680 nm (Figure 8c) and a very week modulation between enhancement and quenching. This corroborates our previous finding of a generally good performance without shadowing or other detrimental effects.

Generallity of results with other active polymers and device architectures We have shown the importance of standing wave formation inside the OPV active region and how to maximize the total exciton generation rate (ideal current). In particular, the emerging simulation guideline calls for a systematic active layer thickness optimization of both the bare cell and every different NP configuration. It is understood, however, that the final OPV power conversion efficiency will be optimized only after a combined electrical and optical treatment89-90: depending on the different electron and hole mobilities, the actual spatial distribution of the exciton generation rate is important in addition to the total generation rate. The information shown in Figure 3b and Figure 6b thus becomes pivotal and offers an intuitive understanding of the NPs effects on the exciton generation distribution. In that sense, the NP distribution can (and should) be used to tailor the exciton generation distribution in the active89-90. The above considerations peg the question of how generic our findings are. We address this by studying two additional popular active blends, P3HT:PC60BM and PTB7:PC70BM, in the same device architecture

as

above

(direct)

as

well

as

in

the

inverted

architecture

ITO(120nm)/ZnO(20nm)/active(80nm)/PEDOT:PSS(30nm)/Al(100nm), under the incorporation of Ag NPs. Given that each active polymer yields different exciton generation in the bare (no NPs) case, we plot in Figure 9 the normalized ideal current distribution ("# (-)/(* (-) for the three polymers in the two device architectures, for the same small-NPs in the top and bottom (Figures 9a,b) and large-NPs in the top and bottom (Figures 9c,d) cases as before. In the small NP case the trends are strikingly similar for all polymers and both device architectures, with marked localized near-field peaks and modified


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standing wave patterns, including the strong shadowing for the NPs in the upper position. For the large NPs, on the other hand, the space-wide enhancement is reproduced for all three polymers, but a different trend is found between the two device architectures. A study on the details of these differences is beyond the scope of this work. We should also keep in mind these devices are not the fully optimized ones (particularly true for the inverted device) and thus some of these trends may change upon active layer thickness optimization. The take-away message is that metal NPs in the active layer lead to markedly different standing wave patterns and thus to different exciton generation distributions, following the general trends shown here. These trends will be very useful as design rules when optimizing devices with the electrical effects (e.g. carrier mobilities) also taken into account. We close this section by plotting the performance comparison of the three polymers in the two device architectures in Figure 10. A systematic trend is found, where the large NPs yield consistently up to 20% total current enhancement, irrespective of the initial (bare) value of ideal current. For the small NPs in the back, a small enhancement is found for the inverded device and a smaller one for the direct device. A similar slightly higher enhancement for the inverted is also seen for the large NPs. These can be expected since the inverted devices as further from optimal and thus get a larger benefit from the plasmonic enhancement. Finally, the small NPs in the front yield consistently a smaller current, with the quenching being morer significant for PTB7:PC70BM, i.e. the polymer with the heighest initial ideal current.

NP passivation coating. A point that has purposely been overlooked so far is free carrier recombination. As noted earlier, the reason for not considering free carrier recombination in the bulk of the heterojunction is to isolate the discussion on the optical mechanisms that govern the inclusion of plasmonic NPs in the BHJ layer. One should however expect increased free carrier recombination on the NP surface. Such a case could cause a devastating current quenching and invalidate the previous conclusions. If the NP is uncoated, several key factors affect the surface recombination rate, such as the NP’s surface-to-volume ratio, the existence of surface trap states and/or the metal work function relative to the donor and acceptor HOMO and LUMO levels. In any case, however, a thin insulating layer on the NP surface can eliminate this problem altogether74,85-87 and validate the simulation results for bare NP, provided of course the coating itself does not alter the optical performance. In recent work, we have analytically demonstrated in a simplified cell model that the coating's index of refraction is critical towards preserving the plasmonic enhancement88: when the coating index is smaller than the average surrounding index a strong


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plasmonic quenching occurs, whereas for a high index even a further performance enhancement may be possible. To test the analytical finding in the realistic cell case studied here, we perform calculations assuming different coating index and thickness. The resulting performance map is shown in Figure 11 for NPs with diameter d = 70 nm at periodicity L = 200 nm. The 18% enhancement (compared to a bare cell without NPs) obtained in the zero coating thickness (see also Figure 2) gets reduced as we increase the coating thickness. This reduction is different however depending on coating index: for small index even a small coating thickness yields a reduction that is strong enough to eliminate the plasmonic effect. An optimal coating index of ~2.6 (corresponding to e.g. TiO2) emerges, for which an e.g. 6 nm coating only results in the enhancement getting reduced from 18% down to 14%.The TiO2 choice is a particular interesting proposition for our cell employing a TiO2 ETL because it can in addition provide a direct path for electrons towards the cathode. We hereafter assume that such a coating can be applied to protect the NP surface from carrier recombination, without altering the overall performance, and thus continue our exploration of the optical phenomena and mechanisms with the simpler case of uncoated NPs.

NPs in the PEDOT:PSS layer.

Several reports from the literature have focused on the incorporation of metallic NPs inside the HTL PEDOT:PSS layer or the PEDOT:PSS/BHJ interface59-62,65,65,73-75. Processing-wise this is easier and helps reduce the free carrier recombination if NPs are fully capped by the HTL. However, there have been contradictory reports with this setup. When the NPs are larger than the HTL thickness, even if capped they extend towards the photoactive layer and contribute with their plasmonic fields and thus to the optical enhancement59,61,62,65. But when they are small and fully embed inside the HTL, their plasmonic near fields do not penetrate into the photoactive layer and thus do not offer any optical enhancement, whereas they contribute only in the electrical characteristics of the OPV device60. We utilize the two NP setups studied in the previous section and explore the performance variation as the NPs are moved from the bottom of the BHJ layer up into the HTL. Results are shown in Figure 12a, where the x-axis shows the distance of the NP center from the top of the TiO2 ETL. Simulation points are shown up until the NP top surface touches to the top HTL interface with ITO. A monotonic drop is found for all cases, much stronger for the small NPs. In the large NP case the response remains positive except in the very last point. This is consistent to literature works with large NPs in the HTL59,61,62,65. Overall, however, it gets clear that NP incorporation in the HTL is problematic regarding the optical performance because of NP absorption and shadowing effects. In Figure 12b we


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plot the local relative current enhancement ( J ( z ) − J 0 ( z )) / J 0 ( z ) for the two NP arrays as they are moved from the bottom of the BHJ to the top of the HTL. The strong shadowing effect for the small NPs is apparent. Finally, we assume an array with fixed Ag NP size (d = 70 nm) in the middle of 90 nm PEDOT:PSS HTL. Contrary to the previous calculations, the NP array is now fully enclosed inside the HTL and thus it does not significantly contribute with plasmonic near fields. With increasing NP separation the performance increases from negative enhancement values towards zero, as shown in Figure 13. In essence, the optimal case is not having NPs in the HTL at all. In addition to the simulation results shown here, we have performed an exhausting study of NP sizes and periodicities for various values of the HTL thickness and could not identify a case with an important improvement in performance. Therefore, our study confirms that there are no forward scattering effects (i.e. strong enough to overcome NP internal absorption and reflection) by the metallic NPs when they are fully enclosed into a thick HTL and any enhancement would therefore be due to improved HTL electrical characteristics. 2D modeling and disorder We conclude our study with a cumulative 2D study, i.e. where the NPs are cylindrical nanorods (NR). The purpose of this is to complement our rigorous 3D study in two fronts: (a) to have a side-byside comparison of 3D/2D modeling as a general validation of the 2D modeling approach, and (b) to allow us to perform large cell disordered NP configurations as well as to study a typically overlooked mechanism, namely, back-reflections coming from the top glass surface. We start with a full parameter phase-space map similarly to Figure 2a and Figure 5, adjusted in the 2D geometry assuming infinite Ag NRs as the scattering elements. Since plasmonic effects are expected only for light polarized perpendicular to the NRs, we just study this polarization. Results for two positions of the NRs in the active are shown in Figure 14. Note here that for simplicity and for ease of comparison with the 3D case, the metal thickness quoted in the ordinate is the equivalent t NP for 3D; the actual metal thickness yielding the NR diameters quoted in the contour lines of Figure 14 is 2 t NR = (9πLt NP / 16)1/ 3 . Also note that because t NR can become quite large in the 2D system, in these

simulations we chose to keep the total active thickness fixed irrespective of metal thickness in order to avoid extra interference effects that would shadow the NR effects (as observed previously). A very similar, qualitatively, performance map is obtained for NRs (Figure 14a) and NPs (Figure 2a) on the backside of the active with clearly identifiable near-field and scattering phase-space


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regions. The quantitative agreement for the performance enhancement is of course not as good, but close enough to qualitatively validate the 2D approximation. For the NRs positioned on the top (Figure 14b) the agreement with NPs on the top (Figure 5) is less perfect. This is a result of a much stronger shadowing effect in 2D. Having validated the 2D approach, we turn into disorder studies having the NRs in the photoactive layer on the back surface (see inset of Figure 14a). We focus on two sizes: 20 nm NRs, which for a suitable spacing correspond to the near-field region (see the 20 nm contour line in Figure 14a), and 40 nm NRs, which for a suitable spacing correspond to the scattering region (see the 40 nm contour line in Figure 14a). To facilitate our study we adopt a 2 µm wide simulation system, and change the number of NRs that fit into it. For the dense cases we simulate the small NRs while for the sparse cases we simulate the large NRs. This is in effect as if starting from the top left of Figure 14a along the 20 nm contour line probing the near-fields and switching at some point to the 40 nm contour line probing the scattering. Simulation results are shown in Figure 15. We study both periodic (solid lines) and disordered arrays (dashed lines). Multiple runs were repeated in the latter case in order to have a good statistical sampling resulting in the error bars shown in the figure. Here we also look at the effect of backscattering from the top glass surface70. Specifically, we compare results from two cell types with: (a) semi-infinite glass, where the incident radiation is coming from within the glass and outgoing waves are free to exit the simulation cell and (b) finite glass, where the incident radiation is coming from the air. More details are in Methods. Interesting features are observed in the periodic cases, where the performance is higher for the small NRs (20 nm) at their most dense configuration with the near-fields being the prime mechanism for these sub-diffraction arrays. As the NR density decreases the performance degrades quickly. The finiteglass case shows a consistently better performance due to the top glass back-reflection70 which becomes more obvious for decreasing density. The performance degradation is much slower, on the other hand, for the disordered cases: the near-fields diminish at smaller NR densities but scattering becomes increasingly allowed and retains a good performance. Of course the overall slope is negative in both cases because we are removing plasmonic material as we decrease the NR density. The relative contribution of each mechanism can be extracted from Figure 15 as a function of NR density (in a qualitative manner, we note, being a 2D calculation). For the more dense arrays we switch to the large NRs (40 nm). The lines are almost continuous but the trend now changes remarkably: the periodic arrays become much stronger than the disordered ones, which remain very similar to the ones for the small NRs. This is because the large NR array is


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optimal for both scattering and plasmonic near fields. By inserting disorder, the scattering not only is decreased in these over-diffraction optimized arrays, but in fact it could be partially suppressed if the NR density in the disordered array becomes locally large and/or small. Also, for the disordered arrays the average distribution of near fields around the NRs may not be at its maximum. In all cases, the finite glass case yields a consistent benefit over the semi-infinite case, showing the important effect of backscattering from the top air/glass interface. Incorporating periodic NP arrays in OPVs requires advanced techniques such as laser interference lithography73 and has indeed been shown to yield significantly enhanced plasmonic OPVs73. The case of solution processed NPs, however, unavoidably results in disordered arrays. Our disordered 2D study shows that when the plasmonic NPs are placed in the optimal position, namely in the back surface of the photoactive layer, their sizes and distribution have a smaller effect on the optoelectronic performance of the device. In essence, our simulations show that while the interplay between the different plasmonic enhancement mechanisms can be very rich when considering fixed periodic arrays, it becomes of less consequence when the arrays are disordered. As long as the NPs are inserted in the right positions and the layer thicknesses are appropriately optimized, the plasmonic benefit will be present. Overall, and by contrasting the 3D periodic results with the 2D periodic and disordered results, we find that the maximum possible plasmonic enhancement for the PCDTBT:PC70BM case can be up to 20% when using spherical Ag NPs embedded inside the photoactive layer. CONCLUSIONS

We performed a systematic simulation and optimization study of Ag nanoparticles in a realistic optimized PCDTBT:PC70BM OPV cell. By exploring all the possible NP distribution phase-space (size and periodicity) we were able to identify the region where plasmonic near field effects dominate the performance enhancement and the region where scattering dominates, with maximum enhancement in current generation reaching up to 20%. The traits of the two mechanisms are quite distinct: dense arrays of small NPs in the photoactive layer rely on the near field effect, exhibiting enhanced current generation only in specific spectral (LSPR) and spatial (at the NP position) regions. Sparse arrays of large NPs, on the other hand, rely on the scattering effect and exhibit enhanced current generation throughout the spectrum and throughout the volume of the photoactive layer. Importantly, the vertical interference resonances in the active layer are disturbed in the former case, but not in the latter. This means that a different optimal active thickness emerges for dense arrays of small NPs. We show that this small detail can easily lead to conflicting reports between different numerical studies depending on the


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initial active layer thickness used. It cannot be overstressed, thus, the importance of performing studies on fully optimized OPV cells. By studying in addition other polymer blends and device architectures we found that our main conclusions are in fact generic. We also explored different positions for the NP arrays in the OPV cell, namely on the top of the active and inside the PEDOT:PSS HTL. In the former case we find enhancement only for sparse arrays of large NPs exhibiting strong scattering, while severe degradation is found for the dense arrays of small NPs because of the increased absorption in the NPs. When the Ag NPs were fully placed inside a thick HTL we could not find a case of enhancement: only due to improved electric characteristics can this configuration lead to improved performance. Finally, we studied a thin passivation coating on the Ag NPs and concluded that this does not degrade the performance provided that the coating refractive index is larger than that of the surrounding. Specifically, an optimal refractive index of around 2.6 is found, pointing towards TiO2 as a particularly suitable and optimal choice for our cell which employs a TiO2 ETL. This justifies our initial proposition that we can study the effect of NPs in the photoactive layer without conserns about free carrier recombination effects, assuming that a suitable passivation coating can be applied. Finally, we expanded our calculations to 2D cells in order to include disordered NP arrays and the effects of a finite glass substrate. The global phase-space study of periodic 2D arrays (of Ag nanorods) shows a similar qualitative picture as that of 3D arrays of spherical Ag NPs. We found that the disorder generally increases the scattering and thus promotes the far field effects as the dominant enhancement mechanism. However, this resulted into similar performance irrespective of NP size and distribution. We also found a small but consistent contribution into the performance enhancement coming form back-reflections at the top air/glass interface. With a precaution regarding the quantitative validity of the 2D calculations, we can conclude that while there is an intricate interplay between different modes and mechanisms in periodic arrays, the scattering caused by disordered NP arrays tends to dominate the overall plasmonic enhancement effects. The general rule emerging calls for NP arrays embedded in the photoactive region close to its back surface, with the photoactive layer thickness reoptimized depending on the NP size and density. However, the maximum enhancement was still obtained for the periodic sparse arrays of large NPs. Overall, and by contrasting the 3D periodic results with the 2D periodic and disordered results, we find that the maximum possible plasmonic enhancement for the PCDTBT:PC70BM case can be up to 20% when using spherical Ag NPs embedded inside the photoactive layer.

METHODS


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Optical modeling and simulations. Optical calculations were performed by a full-vector 3D finite-difference time domain (FDTD) method92-94. Normal incidence plane wave excitation was employed in all cases. The refractive index of each dispersive material was fitted into a Drude-Lorentz model (see Figure 16) and inserted in the FDTD scheme through suitable polarization equations coupled with Maxwell's equations93,94. We used periodic boundary conditions along the lateral and perfectly matched layer (PML) boundary conditions along the normal direction. In the 3D calculations we assumed a semi-infinite glass substrate with the light incident from within it but with its intensity reduced by the corresponding top air/glass interface reflection. Outgoing waves reflected by the OPV inner layers were free to exit the simulation cell. For the 2D calculations we assumed, in addition to the semi-infinite glass case, a finite glass of ~1µm thickness and performed several calculations with different glass thickness to average-out the artifact Fabry-Perot resonances (due to computational limitations we could not simulate a realistic glass thickness of several hundred microns or millimeters). A statistical sampling was performed for the disordered simulations as well. Fourier transforms at every point in the photoactive layer yielded the spectral absorption distribution. The exciton generation rate G(r)

was

found

by

spectral

integration

of

the

absorption

A(r,λ)

according

to

G (r ) = (e / hc) ∫ λA(r, λ ) S (λ ) dλ , where S (λ ) is the solar irradiance spectrum AM1.5. By integration within the photoactive layer volume we get the sort circuit current density J sc = ∫ η iqe (r)G(r)dr , where V′

η iqe (r ) is the internal quantum efficiency and V' the active volume excluding the NPs. The vertical current distribution was obtained by integration over a plane J ( z ) = ∫ ηiqe (ρ)G(ρ)dρ , where S' is the S′

corresponding active area at z excluding the NPs. In to isolate the optical effects, in our calculations we ignored exciton quenching and free carrier recombination and set η iqe (r ) =1 to quote the ideal current generated.

Conflict of interest. The authors declare no competing financial interest. Acknowlwdgment. This work has been financially supported by the European Union Seventh Framework (FP7/2007-2013) Program through the project SMARTONICS, Grant Agreement No. 310229. SRPS wishes to thank the EPSRC Strategic Equipment Account EP/L02263X/1 for support to conduct this work.

REFERENCES


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[67] Wu, J.-L.; Chen, F.-C.; Hsiao, Y. S.; Chien, F.-C.; Chen, P.; Kuo, C. H.; Huang, M. H.; Hsu, C. S. Surface plasmonic effects of metallic nanoparticles on the performance of polymer bulk heterojunction solar cells. ACS Nano 2011, 5, 959. [68] Chen, F.-C.; Wu, J.-L.; Lee, C.-L.; Hong, Y.; Kuo, C.-H.; Huang, M. H.; Plasmonic-enhanced polymer photovoltaic devices incorporating solution-processable metal nanoparticles. Appl. Phys. Lett. 2009, 95, 013305. [69] Cheng, P.-P.; Ma, G.-F.; Li, J.; Xiao, Y.; Xu, Z.-Q.; Fan, G.-Q.; Li, Y.-Q.; Lee, S.-T.; Tang, J.-X. Plasmonic backscattering enhancement for inverted polymer solar cells. J. Mater. Chem. 2012 , 22, 22781. [70] Kakavelakis, G.; Vangelidis, I.; Heuer-Jungemann, A.; Kanaras, A. G.; Lidorikis, E.; Stratakis, E.; Kymakis, E. Plasmonic Backscattering Effect in High-Efficient Organic Photovoltaic Devices. Adv. Energy Mater. 2016, 6, 1501640. [71] Beliatis, M.J.; Henley, S.J.; Han, S.; Gandhi, K.; Adikaari, A.; Stratakis, E.; et al. Organic solar cells with plasmonic layers formed by laser nanofabrication. Phys. Chem. Chem. Phys. 2013, 15, 8237. [72] Gandhi, K.K.; Nejim, A.; Beliatis, M.J.; Mills, C.A.; Henley, S.J.; Silva, S.R.P.; Simultaneous optical and electrical modeling of plasmonic light trapping in thin-film amorphous silicon photovoltaic devices. J. Photonics for Energy 2015, 5, 057007. [73] Oh, Y.; Lim, J. W.; Kim, J. G.; Wang, H.; Kang, B.-H.; Park, Y. W.; Kim, H.; Jang, Y. J.; Kim, J.; Kim, D. H.; Ju, B.-K. Plasmonic periodic nanodot arrays via laser interference lithography for organic photovoltaic cells with >10% efficiency. ACS Nano 2016, 10, 10143-10151. [74] Liu, S.; Jiang, R.; You, P.; Zhu, X.; Wang, J.; Yan, F. Au/Ag core-shell cell nanocuboids for highefficiency organic solar cells with broadband plasmonic enhancement. Energy Environ. Sci. 2016, 9, 898-905. [75] Baek, S.-W.; Park, G.; Noh, J.; Cho, C.; Lee, C.-H.; Seo, M.-K.; Song, H.; Lee, J.-Y. Au@Ag coreshell nanocubes for efficient plasmonic light scattering effect in low bandgap organic solar cells. ACS Nano, 2014, 8, 3302-3312. [76] Wang, D. H.; Park, K. H.; Seo, J. H.; Seifter, J.; Jeon, J. H.; Kim, J. K.; Park, J. H.; Park, O. O.; Heeger, A. J. Enhanced Power Conversion Efficiency in PCDTBT/PC70BM Bulk Heterojunction Photovoltaic Devices with Embedded Silver Nanoparticle Clusters. Adv. Energy Mater. 2011, 1, 766. [77] Li, X.; Choy, W. C. H.; Lu, H.; Sha, W. E. I.; Ho, A. H. P. Efficiency Enhancement of Organic Solar Cells by Using Shape‐Dependent Broadband Plasmonic Absorption in Metallic Nanoparticles. Adv. Funct. Mater. 2013, 23, 2728.


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[78] Xue, M.; Li, L.; de Villers, B. J. T.; Shen, H.; Zhu, J.; Yu, Z.; Stieg, A. Z.; Pei, Q.; Schwartz, B. J.; Wang, K. L. Charge-carrier dynamics in hybrid plasmonic organic solar cells with Ag nanoparticles. Appl. Phys. Lett. 2011, 98, 253302. [79] Wang, D. H.; Kim, J. K.; Lim, G.-H.; Park, K. H.; Park, O. O.; Lim, B.; Park, J. H. Enhanced light harvesting in bulk heterojunction photovoltaic devices with shape-controlled Ag nanomaterials: Ag nanoparticles versus Ag nanoplates. RSC Adv. 2012, 2, 7268. [80] Chen, H.-C.; Chou, S.-W.; Tseng, W.-H.; Chen, I. W. P.; Liu, C.-C.; Liu, C.; Liu, C.-L.; Chen, C.-I. Wu C.-H.; Chou, P.-T. Large AuAg Alloy Nanoparticles Synthesized in Organic Media Using a One‐Pot Reaction: Their Applications for High‐Performance Bulk Heterojunction Solar Cells. Adv. Funct. Mater. 2012, 22, 3975. [81] Wang, C. C. D.; Choy, W. C. H.; Duan, C.; Fung, D. D. S.; Sha, W. E. I.; Xie, F.-X.; Huang, F.; Cao, Y. Optical and electrical effects of gold nanoparticles in the active layer of polymer solar cells. J. Mater. Chem. 2012, 22, 1206. [82] Spyropoulos, G. D.; Stylianakis, M. M.; Stratakis, E.; Kymakis, E. Organic bulk heterojunction photovoltaic devices with surfactant-free Au nanoparticles embedded in the active layer. Appl. Phys. Lett. 2012, 100, 213904. [83] Kim, W.; Cha, B. G.; Kim, J. K.; Kang, W.; Kim, E.; Ahn, T. K.; Wang, D. H.; Du, Q. G.; Cho, J. H.; Kim, J.; Park, J. H. Tailoring Dispersion and Aggregation of Au Nanoparticles in the BHJ Layer of Polymer Solar Cells: Plasmon Effects versus Electrical Effects. ChemSusChem 2014, 7, 3452. [84] Wang, J.; Lee, Y.-J.; Chadha, A. S.; Yi, J.; Jespersen, M. L.; Kelley, J. J.; Nguyen, H. M.; Nimmo, M.; Malko, A. V.; Vaia, R. A.; et al. Effect of Plasmonic Au Nanoparticles on Inverted Organic Solar Cell Performance. J. Phys. Chem. C 2013 117, 85. [85] Du,P.; Jing, P.; Li, D.; Cao, Y.; Liu, Z.; Sun, Z. Plasmonic Ag@oxide nanoprisms for enhanced performance of organic solar cells. Small 2015, 11, 2454. [86] Kymakis, E.; Spyropoulos, G.D.; Fernandes, R.; Kakavelakis, G.; Kanaras, A.G.; Stratakis, E. Plasmonic bulk heterojunction solar cells: the role of nanoparticle ligand coating. ACS Photonics 2015, 2, 714. [87] Xu, X.; Kyaw, A. K. K.; Peng, B.; Zhao, D.; Wong, T. K. S.; Xiong, Q.; Sun X. W.; Heeger, A. J. A plasmonically enhanced polymer solar cell with gold–silica core–shell nanorods. Org. Electron. 2013, 14, 2360. [88] Lidorikis, E. Modeling of Enhanced Absorption and Raman Scattering Caused by Plasmonic Nanoparticle Near Fields . J. Quant. Spectr. Rad. Transf. 2012, 113, 2573.


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[89] Sha, W. E. I.; Li, X.; Choy, W. C. H. Breaking the Space Charge Limit in Organic Solar Cells by a Novel Plasmonic-Electrical Concept. Sci. Rep. 2014, 4, 6236. [90] Sha, W. E. I.; Zhu, H. L.; Chen, L.; Chew, W. C.; Choy, W. C. H. A General Design Rule to Manipulate Photocarrier Transport Path in Solar Cells and Its Realization by the Plasmonic-Electrical Effect. Sci. Rep. 2015, 5, 8525. [91] Chan, K.; Wright, M.; Elumalai, N.; Uddin A.; Pillai, S. Plasmonics in Organic and Perovskite Solar Cells: Optical and Electrical Effects. Adv. Optical Mater. 2017, 5, 1600698. [92] Taflove, A.; Hagness, S. C. Computational Electrodynamics: the FDTD Method , 3rd ed., Artech House , Norword, MA, USA 2005 . [93] Lidorikis, E.; Egusa , S.; Joannopoulos , J. D.; Effective medium properties and photonic crystal superstructures of metallic nanoparticle arrays. J. Appl. Phys. 2007, 101, 054304. [94] Lagos, N.; Sigalas , M. M.; Lidorikis , E. Theory of plasmonic near-field enhanced absorption in solar cells. Appl. Phys. Lett. 2011, 99, 063304. [95] Hoppe H.; et al. Optical constants of conjugated polymer/fullerene based bulk-heterojunction organic solar cells. Mol. Cryst. Liq. Cryst. 2002, 385, 113. [96] Palik, E.D. Handbook of Optical Constants of Solids; Academic; San Diego, 1998). [97] Shiles, E.; et al. Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: Applications to aluminium. Phys. Rev. B 1980, 22, 1612. [98] Stelling C.; et al. Plasmonic nanomeshes: their ambivalent role as transparent electrodes in organic solar cells. Sci. Rep. 2017, 7, 42530.


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Figure 1: (a) Schematic of the OPV cell studied. (b) The active molecules considered in the study. (c) The measured absorption spectrum of PCDTBT:PC70BM along with the solar spectrum.


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Figure 2: Ideal short-circuit current enhancement for (a) Ag and (b) Au NPs placed in the BHJ on the back surface (as shown in the inset schematics) as a function of NP periodicity L and metal nominal thickness tNP. Color-coded with red/violet is the highest/lowest enhancement. The contour lines mark corresponding NP diameter (brown) and the current enhancement (white). Only NPs up to diameter 80 nm were considered.


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Figure 4: Ideal short-circuit current Jsc as a function of total BHJ+ETL thickness for the three cells of Figure 3. For the large NP case two additional diameters were studied.


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Figure 5: Ideal short-circuit current enhancement for Ag NPs placed in the BHJ on the front surface (as shown in the inset schematic) as a function of NP periodicity and metal nominal thickness. Contour lines mark corresponding NP diameter (brown) and the current enhancement (white). Only NPs up to diameter 80 nm were considered.


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Figure 9: Current generation distribution in the active layer for three different polymer blends (P3HT:PC60BM, PCDTBT:PC70BM and PTB7:PC70BM) in two device architectures (solid lines for direct and dashed lines for inverted) when Ag NPs are included: (a) amall NPs in the front, (b) small NPs on the back, (c) large NPs in the front and (d) large NPs on the back. The small and large NP configurations are the same as in all previous figures.


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Figure 14: 2D calculations of the ideal sort-circuit current enhancement for Ag NRs placed in the BHJ on the (a) back and (b) front surface (as shown in the inset schematics) as a function of NR periodicity and metal nominal (equivalent 3D) thickness. Contour lines mark corresponding NR diameter (brown) and the current enhancement (white). Only NRs up to diameter 80 nm were considered.


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Figure 15: 2D calculations of ideal sort-circuit current enhancement employing periodic and disordered arrays of NRs embedded in the active layer on the back surface as a function of NR density. A supercell of 2 µm is used in all cases. Two different NR diameters (d = 20, 40 nm) are used and a statistical sampling is performed for the disordered cases. Also two different cell terminations are considered: one with a semi-infinite glass and one with a finite glass (see insets).


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For Table of Contents Use Only

Plasmonic Organic Photovoltaics: Unraveling Plasmonic Enhancement for Realistic Cell Geometries

Ioannis Vangelidis, Anna Theodosi, Michail J. Beliatis, Keyur K. Gandhi, Argiris Laskarakis, Panos Patsalas, Stergios Logothetidis, S. Ravi P. Silva, Elefterios Lidorikis

A comprehensive computational study of realistic plasmonic organic photovoltaic cells unravels the plasmonic near-field and far-field effects. In a full geometrical parameter scan (nanoparticle array period and nominal metal thickness) the corresponding performance enhancement map (color-coded on the left figure, quantified by the white contour lines) identifies two distinct regions of high enhancement corresponding to different nanoparticle setups: dense arrays of small NPs and sparce arrays of large NPs. Their features are spectrum/space-specific and spectrum/space-wide current enhancements respectively (right figure). A rich complexity on device geometry is revealed that explains many of the contradictory results published in the literature and offers a protocol towards plasmonic OPV optimization.

41 ACS Paragon Plus Environment

Plasmonic Organic Photovoltaics: Unraveling Plasmonic

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