Inverted Ultrathin Organic Solar Cells with a Quasi-Grating Structure for Efficient Carrier Collection and Dip-less Visible Optical Absorption

We propose a metallic-particle-based two-dimensional quasi-grating structure for application to an organic solar cell. With the use of oblate spheroidal nanoparticles in contact with an anode of inverted, ultrathin organic solar cells (OSCs), the quasi-grating structure offers strong hybridization between localized surface plasmons and plasmonic gap modes leading to broadband (300~800 nm) and uniform (average ~90%) optical absorption spectra. Both strong optical enhancement in extreme confinement within the active layer (90 nm) and improved hole collection are thus realized. A coupled optical-electrical multi-physics optimization shows a large (~33%) enhancement in the optical absorption (corresponding to an absorption efficiency of ~47%, AM1.5G weighted, visible) when compared to a control OSC without the quasi-grating structure. That translates into a significant electrical performance gain of ~22% in short circuit current and ~15% in the power conversion efficiency (PCE), leading to an energy conversion efficiency (~6%) which is comparable to that of optically-thick inverted OSCs (3–7%). Detailed analysis on the influences of mode hybridization to optical field distributions, exciton generation rate, charge carrier collection efficiency and electrical conversion efficiency is provided, to offer an integrated understanding on the coupled optical-electrical optimization of ultrathin OSCs.

Specifically, with the use of an oblate nanoparticle (ONP) array in electrical contact with the anode, we achieve short-distance, efficient hole collection due to the increased ONP-anode surface, in addition to dip-less wideband optical absorption from the strong hybridization between the LSP and plasmonic gap modes. Rigorous optical-electrical coupled numerical analysis shows that the large mode overlap between the LSP and gap modes, derived from the tight confinement of the light around the ONP-anode interface in the ultra-thin (90 nm) active layer, plays a crucial role in obtaining broadband (300~800 nm) and uniform (average ~90%) optical absorption spectra. With the introduction of the ONP array optimized in terms of both optical absorption and electrical collection, a large improvement of ∼ 33% in the optical absorption (corresponding to an absorption efficiency of ~47%, AM1.5G, visible) and significant electrical performance gains of ~22% in short circuit current and ~15% in PCE are demonstrated, when compared to control OSCs.

Results
Structure of inverted ultrathin OSCs with the proposed quasi-grating anode. Figure 1 illustrates the proposed quasi-grating structure embedded in the inverted ultrathin OSCs. A control device assumes the same material compositions except for ONP array. The control OSC is composed of a 90 nm thick PCDTBT:PC70BM active layer, sandwiched between a 20 nm thick sol-gel processed ZnO electron-transport top layer and a 2 nm thick MoO3 hole-transport layer 16,17 which sits atop a bulk Ag substrate (anode). The energy levels of these relevant functional layers are also shown in Fig. 1b. This alignment of the material compositions 15,[18][19][20][21][22] facilitates efficient electron transport between the electron transport layer (ETL) and the active layer, and allows extraction of holes without excessive interface recombination between the hole transport layer (HTL) and active layer. The use of molybdenum oxides as a HTL increases the work function of the anode, for better alignment to the energy level of active materials 15,18 . The periodic two-dimensional Ag nanowire network on the device surface serves as an electrical contact (cathode). Networks of Ag nanowire are made with a height of 20 nm, width of 60 nm and pitch of 860 nm, for sufficient light transmission (average transmission of 91.7%) and also to guarantee low sheet resistance (19.1 Ω /sq). Within the visible wavelength range of our interest, the designed transparent electrode provides comparable sheet resistance and higher optical transmittance, when compared to the conventional ITO electrodes (80~150 nm thickness) 23,24 . Optimization procedures for the transparent electrode are detailed in the Supporting Information ( Figure S1). Within these frameworks, we load the ONP array in contact with the Ag substrate to form a quasi-grating anode structure, which is covered with an ONP-conforming MoO3 layer and a thin active layer, completing the flat top surface (Fig. 1c). It is noted that the choice of oblate nanoparticles in an ultrathin active layer yields optically superior properties when compared to the use of a spherical nanoparticle 7 , such as; enhanced in-plane scattering ( Figure S2a), bigger modal volume and stronger light confinement ( Figure S2b,c) all from the 'oblate geometry' , and a larger surface area leading to greater scattering cross-section ( Figure S2d). As noted earlier, with the increased anode surface area from the presence of oblate spheroid metallic particles dispersed within the active layer, in contact with the anode, enhancement in hole collection and reduced hole traveling lengths also become possible. Considering the interplay between optical-absorption and electrical carrier collection, an optical-electrical multidisciplinary numerical optimization of the overall performance of the OSC has been carried out. First, the radius and aspect ratio of the ONP and the period of the ONP array have been optimized using finite element method (FEM) calculations, to obtain a structure that provides the largest optical absorption enhancement (weighted by AM1.5G). Then, considering the electrical performance contribution from the electrical carrier collection efficiency, the short circuit current and final ultimate performance factor (the PEC of the OSC) were calculated to find the optical-electrical optimum point (r x,y = 70 nm, r z = 30 nm and P 1 = 200 nm), which involved scanning over a number of different quasi-grating parameter sets near the optically-obtained optimum structure (r x,y = 90 nm, r z = 30 nm and P 1 = 200 nm).
Optical characteristics: Dip-less broadband, wide angle absorption from strong mode hybridization. Figure 2a shows the percentage optical absorption (i.e., the ratio of number of photons absorbed to number of incident photons at a given wavelength) in the active layer (solid lines) and total structure (dotted lines), calculated for the optimized OSC structure when illuminated by normal incident light (AM1.5G solar spectrum). The enhancement ratio of optical absorption relative to that of the control OSCs is also plotted in Fig. 2a.
With the introduction of the ONP quasi-grating, the absorption in the active layer is considerably enhanced when compared to the control OSC, especially in the region of 430 ~ 740 nm, achieving dip-less total absorption (average ~90%) over the entire spectra. The cumulative improvements in optical absorption are found to be ~114% (total) and ~33% (active layer), respectively, from the definition of FOM (in supporting information). In Fig. 2b,c, we also show the distributions of the electric field magnitude, for the reference and quasi-grating OSCs at the absorption peaks of the active layer (λ = 570 nm). With the presence of the quasi-grating structure, a significant increase in the near-field modal volume is evident, together with the enhancement of the electric field with extreme confinement in ultrathin active layer. The field distributions at the absorption peak of the total structure (λ = 670 nm) can be found in Figure S3a-b, exhibiting similar behavior.
Together with the induced surface charge distributions (see Fig. 3) calculated as a function of the grating period, the physical origins of the observed absorption enhancement can be better understood. Strong spatial-overlap between the LSP modes residing on the surface of the ONP and the plasmonic gap modes formed in the ONP-anode gap, provides robust mode-hybridization with negligible dependence on the grating period. It is worth noting that this strong mode hybridization around the ONP is physically different from the conventional  simple combination of metal grating and metal nanoparticles located in different spatial regions (e.g., active layer and transport layer), which results in negligible mode-hybridization of spectrally-separated resonances [11][12][13] . As a result of strong mode hybridization in our case, dip-less wideband strong optical absorption becomes possible, tightly confined near the ONP-anode embedded in the ultra-thin active layer. Furthermore, this strong optical absorption limited to the near proximity of the ONP-anode region also yields the additional benefit of negligible device performance dependency on the period of the grating (Supplement Figure S3a,b), allowing large tolerances (190 nm ≤ P 1 ≤ 400 nm) in the control of the ONP-ONP distance.
To test the device's performance for all-day usage, the optical absorption under oblique incidence in the − 70° < θ < 70° range also has been characterized. As a result of strong mode confinement near the ONP-anode substrate region, excellent optical absorption with an almost flat response across the incident angle variation of − 60° < θ < 60° has been obtained ( Figure S5a), irrespective of the incident angle ( Figure S5b,c).
Electrical characteristics: enhancement in hole collection from the quasi-grating anode. Having demonstrated the excellent light absorption properties of the proposed ONP quasi-grating OSCs, we now determine the actual device performance by calculating its electrical characteristics. First of all, to elucidate the impact of the dip-less wideband optical absorption on the electrical performance, we calculated the spectral response of incident photon to electron conversion efficiency (IPCE) and IPCE enhancement. The spectrum shown in Fig. 4a (blue line for the control device and red line for the quasi-grating OSCs) shows a clear enhancement in IPCE, with the introduction of the proposed ONP quasi-grating anode. Noting the spectral similarity between the calculated IPCE and optical absorption, these results indicate that there is a negligible penalty from the carrier recombination, with the reduced hole traveling lengths and the increased area of the hole-collection interface.
The details of the overall performance of the OSCs are summarized in Fig. 4b and Table 1. The performance factors of the control device are in good agreement with previous experimental reports 15,18,19,21 : with a power conversion efficiency (PCE) of 5.21%, an open-circuit voltage of 0.882 V, a short circuit current 9.32 mA/cm 2 , and a fill factor (FF; J max V max /J sc V oc ) of 63.5%. To compare, for the proposed OSC, large improvements in J sc and PCE were observed, approaching ∼ 22% and ∼ 15% respectively, with a PCE of 6.01% and an open-circuit voltage of 0.881 V, a short circuit current of 11.37 mA/cm 2 , and a FF of 60.0%. It is worthy of note that these performance factors that were achieved for the optical-electrical optimum design (at optical absorption efficiency of ~47%, with r x,y = 70 nm, r z = 30 nm ONPs of 200-nm period) are higher than those obtained from the optical-absorption optimum design (at optical absorption efficiency of ~49%, with r x,y = 90 nm, r z = 30 nm ONPs of 200-nm period), as summarized in Table 1. These observed performance differences are well explained by comparing the carrier transport, for the electrical-optical optimum (Fig. 5) and the optical-optimum design ( Figure S6). Even though the increased eccentricity of the optically-optimal structure derives stronger mode hybridization for better optical properties, it is also observed that the same increased eccentricity of strong spatial mode localization induces non-uniform photo-carrier generation, perturbing the flow of carriers and thus reducing the power conversion efficiency and FF (see Table 1), in agreement with the prior art 7,20,25,26 .

Discussion
In conclusion, we proposed a quasi-grating structure composed of an oblate nanoparticle array in electrical contact with the anode, for application to inverted ultrathin OSCs. Short-distance and efficient hole collection, together with dip-less strong hybridization in tight mode confinement provide large improvements in both PCE and broadband optical absorption when compared to the reference structure: ~33% in optical absorption, ~22% in the short circuit current, and ~15% in the PCE enhancements were obtained using coupled optical-electrical multidisciplinary numerical analysis. By analyzing the optical-and electrical-field profiles, together with surface charge distributions, exciton generation rates, IPCE spectra, J-V characteristics and the hole-electron concentration, the key factors and underlying physics for the observed device performance improvement have been clarified. The results of optical and electrical combined optimization for the device geometry clearly reveals the need for multi-domain design considerations involving both optical absorption and electrical carrier collection. The proposed platform of a quasi-grating structure offering strong plasmonic hybridization and increased anode surface area, together with the combined electrical-optical device optimization approach should be applicable to the design of highly efficient OSCs employing different active materials and optical-electrical scale lengths. ). The electric field intensity |E(x,y,z)| 2 was obtained via the optical simulation using the Maxwell equation solver and was then used as the input to the electrical part of the calculation, which solves the coupled-Poisson, charge carrier drift-diffusion and continuity equations. The coupled Poisson, carrier drift-diffusion and continuity equations are given by:  where q is the elementary charge, k B is the Boltzmann constant, φ is the electrostatic potential, Q is the local dissociation probability, R is the local recombination rate, μ n and μ p are the electron and hole motilities, N d + and N a − are the concentrations of ionized donors and acceptors, p and n are the charge carrier densities, p eq and n eq are the equilibrium densities, and τ n , τ p are the lifetimes of electrons and holes, respectively.

Comprehensive
For the dissociation rate, we use the Onsager-Braun dissociation expressions (i.e., D = G opt ·Q(x,y,z)) which include local changes in the exciton density due to field-dependent exciton dissociation probability. The exciton generation rate (in the active layer) was obtained from G opt (λ) = ε"|E(x,y,z)| 2 /2ћ, where ε" is the imaginary part of dielectric permittivity, and ћ is the reduced Planck constant ( Figure S7). According to the Poole-Frenkel model the spatially-dependent electron or hole mobility is a function of the local electric field magnitude 36,37 : μ(E,T)=μ 0 exp(γ((E 1/2 )/(T))), where μ 0 is the zero-field mobility, γ is a material-related activation energy, and T is the temperature. J-V curves are then obtained by applying a potential difference between the top and bottom boundaries of the unit cell. From these J-V curves, we can calculate all standard solar cell performance parameters, such as J sc , V oc , FF, IPCE and PCE. We note that the band-to-band Langevin bimolecular recombination 38 , trap-assisted Shockley-Read-Hall (SRH) recombination 39 , surface recombination 40 and the Onsager-Braun dissociation 26,[41][42][43] expressions are included in the continuity equations (Eq. 2-3); deep trap states are not considered which is a common assumption in the modelling of organic solar cells. These states negligibly contribute to the space charge field 43,44 . Recently reported electrical effects, such as plasmonically induced hot carriers transfer and charge accumulation effects 15,45 for the performance improvement of OSCs are not included in current analysis. More specific simulation details of the electrical simulation part such as determination of pre-illumination electronic equilibrium parameters can be found in 7, 22 and 40.