Embedding metal electrodes in thick active layers for ITO-free plasmonic organic solar cells with improved performance

Abstract: We propose and numerically investigate the optical performance of a novel plasmonic organic solar cell with metallic nanowire electrodes embedded within the active layer. A significant improvement (~15%) in optical absorption over both a conventional ITO organic solar cell and a conventional plasmonic organic solar cell with top-loaded metallic grating is predicted in the proposed structure. Optimal positioning of the embedded metal electrodes (EME) is shown to preserve the condition for their strong plasmonic coupling with the metallic back-plane, meanwhile halving the hole path length to the anode which allows for a thicker active layer that increases the optical path length of propagating modes. With a smaller sheet resistance than a typical 100 nm thick ITO film transparent electrode, and an increased optical absorption and hole collection efficiency, our EME scheme could be an excellent alternative to ITO organic solar cells.


Introduction
High optical transparency and large electrical conductivity of top-loaded electrodes in solar cells ensures efficient transmission of light into the active layer and efficient transport of collected charge carriers.While indium tin oxide (ITO) has been widely adopted as an excellent transparent electrode for organic solar cells [1,2], its high fabrication cost, mechanical brittleness, limited supply, and problematic contamination of organics [2][3][4] has prompted a search for ITO-free electrode schemes.Previously considered ITO alternatives include an un-patterned (flat) thin metal film [5,6], randomly [7,8] or periodically [9][10][11][12][13] patterned metal layers, conducting polymers [14], carbon nanotubes [15], and graphene [16].Among these, nano-patterned metal electrodes which further serve as the functional element in plasmonic solar cells [17][18][19][20][21][22] have offered improved or comparable performance to their ITO-counterparts owing to their strong plasmonic enhancement of optical absorption (i.e., electron-hole pair production) in the active layer [9][10][11][12][13].For example, the organic solar cell with top-loaded nanowire electrode has demonstrated exceptional performance due to strong plasmonic coupling between the electrodes and metallic back-plane [9][10][11][12]22].But an inherent drawback of this scheme is that its performance is strongly dependent on the active layer thickness (i.e., the distance between electrodes and back-plane) which determines the plasmonic coupling strength, placing an upper limit on the active layer thickness, beyond which performance becomes worse than its ITO-counterpart [9][10][11].The potential performance benefits associated with increased active layer thickness, such as increased optical path length of propagating modes in the active layer, thus become inaccessible.
In this paper, we propose and theoretically investigate the optical and electrical performance of a novel implementation scheme of metal nanowire electrodes designed to overcome the performance limitations of a conventional plasmonic organic solar cells with top-loaded metallic gratings (denoted 'conventional metal electrode' (CME, Fig. 1(a)) [9][10][11][12][13]).Our proposed structure, consisting of a periodic Ag nanowire anode (rectangular element size wAg x dAg) embedded with an index matching SiO 2 element (wAg x dSiO 2 ) is denoted 'embedded metal electrode' (EME, Fig. 1(b)).As a reference, both CME and EME are compared to a typical ITO-based structure with top-loaded 100 nm thick ITO film (Fig. 1(c)).Our results show that, contrary to the CME and ITO reference, the EME exhibits an optical absorption that increases monotonically with the active layer thickness owing to its preservation of optimal plasmonic coupling between the electrode array and metallic backplane, at the same time as the optical path length is increased in the thicker active layer.Furthermore, embedding of the electrodes in our EME scheme preserves the hole path length (to the anode) of the optimal CME despite a two-fold increase in active layer thickness.On top of its improved optical performance, our calculations of the EME sheet resistance suggest it as a suitable replacement of ITO as a transparent electrode in organic solar cells.

Device architecture and suggested fabrication method
The suggested EME based solar cell structure (Fig. 1(b)) could be easily fabricated, first by sequential deposition of SiO 2 and Ag on a glass substrate, followed by lithographic patterning to form the periodic structure.Sequential deposition of the hole transporting layer (MoO 3 ), active layer (P3HT:PC 61 BM(1:1)), and Cathode (Al reflector) completes the device.A 10nm thick conformal deposition was assumed for MoO 3 [23].Continuous deposition of the active layer is enabled by annealing under optimal conditions to ensure a flat surface at the Al/active layer interface.We note that the CME is a special case of EME where dSiO 2 = 0 [9][10][11][12][13].All material properties were taken from experimentally measured complex and dispersive optical constants (P3HT:PC 61 BM [1], Ag and Al [24], ITO [25]).The refractive indices of Glass and SiO 2 are fixed at n = 1.5.Note that our choice of SiO 2 as dielectric element (insulator) provides index matching with the glass substrate to simplify the analysis.

Optical absorption and electrical properties of EME solar cells
The sheet resistance R s of EME is calculated using Eq.(A3) in Appendix to determine the nanowire dimensions at which R s is comparable to an ITO transparent electrode (i.e., an ITO film) with the typical uniform thickness of 100 nm. Figure 2(a) shows R s as a function of wAg for Ag nanowires with dAg = 10, 20, and 30nm, and with the optimal Period of 300nm (see below); R s is inversely proportional to wAg.To ensure a better conductivity than the ITO film (i.e., R s <11Ω/sq -see gray shaded area on Fig. 2(a)) [6], it is evident that metal electrodes with wAg = 300nm (termed 'Flat', corresponding to the uniform Ag film) should be chosen when dAg = 10nm, wAg>~85nm when dAg = 20nm, and wAg>~45nm when dAg = 30nm.All considered EME structures satisfy these geometrical constraints.To serve as a useful comparison to our proposed EME scheme, we first geometrically optimize the CME with respect to the Figure of Merit (FOM).The FOM is defined as the ratio of the number of photons absorbed in the active layer to the total number of incident photons (see Appendix).We find the optimal parameters wAg = 120nm, dAct = 100nm, and Period = 300nm, when dAg = 20nm (see Appendix for details), and similarly wAg = 100nm, dAct = 100nm, and Period = 300nm, when dAg = 30nm.The EME nanowire dimensions (dAg, wAg, Period) were chosen to be the same as those of optimized CMEs at respective Ag thicknesses to ensure identical sheet resistance.Subsequently, the EME structure was optimized over dAct and dCav (see Fig. 2(b)).All of the EME structures with dAct>100nm exhibit a maximum in the FOM at dCav corresponding to that of the optimized CME (dCav = 80nm for dAg = 20nm, and dCav = 70nm for dAg = 30nm).This fact is due to preservation of strong plasmonic coupling between the electrodes and metallic backplane, as we discuss later.
Figure 2(c) shows FOMs as a function of dAct for optimized CMEs and EMEs with dAg = 20nm and 30nm, as well as flat metal electrode with dAg = 10nm (wAg = 300nm), and 100nm thick ITO reference structure.Sheet resistances of each of the considered EME are marked by circles in Fig. 2(a).A key aspect of Fig. 2 (c) is that a thicker active layer does not guarantee a larger FOM in CME when dAct>100nm.Indeed, in contrast with the ITO reference, we see that beyond the optimal thickness dAct~100nm, a further increase in dAct leads to serious reduction of the CME FOM, which is consistent with previous studies [9,10].This reduction of FOM is associated with a weakening of plasmonic coupling between the electrodes and metallic back-plane due to the increase in dCav (defined as cavity thickness between Cathode and Anode -Fig. 1 (a)) at longer wavelengths.Meanwhile, in the case of EME structures, we find that FOM linearly increases with dAct (see circular data points in Fig. 2 (c)).
Figures 2(e   In detail, the optimized CME exhibits strong absorption enhancement (compared to the ITO reference with dAct = 100nm -see black dashed line) at longer wavelengths (λ>570nm), and a distinct absorption peak at λ~600nm.The corresponding normalized electric field amplitude distributions at λ = 600nm are plotted in Fig. 3(c) for TM, and Fig. 3(d) for TE polarization.The characteristic coupled plasmonic mode between electrode and metallic back plane is evident for TM polarization [10,11], while a photonic mode (termed 'waveguide effect' in Ref [10]) is evident between neighboring electrodes for TE.Increasing dAct from 100nm to 200nm strikingly weakens the TM resonance, and transforms the TE resonance, as shown in Fig. 3(g) and 3(h).While the CME with dAct = 200nm is more highly absorbing in the shorter wavelength range for both polarizations (see blue curves in Fig. 2(e) and 2(f)), which is simply due to its larger active layer volume (compared to the optimized CME or EME structures) as shown in the field plots at λ = 400nm (Fig. 3(a), 3(e), and 3(i)), the severe degradation of the plasmonic coupled mode for TM polarization results in a poor FOM compared to the EME with same dAct.

EME (TM) dAct=200nm
Both optimized CME and EME structures resemble each other in the shape of their absorption spectra, which shows that EME still maintains the cavity resonances of the optimized CME, while additional absorption is accrued due to an increased optical path length of propagating waves in the thicker active layer -compare Fig. 3(k) and 3(l) with Figs.3(c) and 3(d).Indeed, the electric field profiles show that the EME preserves conditions for optimal absorption enhancement associated with the plasmonic mode coupling -dCav, the main coupling parameter, taking the same value as in the optimized CME structure -while the increased active layer thickness provides additional absorption by increasing the path length of propagating waves in the active layer.Comparing field plots at λ = 500nm (Fig. 3(b), 3(f), and 3(j)) shows that the CME with dAct = 200nm exhibits poor plasmonic enhancement of absorption since the field of the localized plasmonic mode of the electrode is mostly confined to the Glass substrate.On the whole, for thicker electrodes of dAg = 30m, the superiority of EME is also preserved although the FOM decreases due to an increase in ohmic loss and light reflection.The effect of refractive index (nDie) of the dielectric element on the optical absorption for the optimized EMEs is shown in Fig. 2(d).The nDie range of 1.0~3.0 was chosen considering that MoO 3 , P3HT:PCBM, and Glass have indices within the range 1.5~2.2.Interestingly, it can be seen that the optimal case is nDie ≈1.5, which suggests that index matching of the dielectric element with the Glass substrate is preferable.
From Fig. 2 (c), we see that the optimized EME with dAg = 20nm has a maximum FOM of 0.5085 at dAct = 200nm, which constitutes a ~15% FOM improvement compared to the optimized CME (FOM = 0.4437).Even at large dAct, the EME structure maintains comparable optical performance to the ITO-counterpart with dAct = 200nm.However, it is important to note that the ITO reference with dAct = 200nm would exhibit very low charge collection efficiency, as does the CME, when dAct>100nm [1].In this regard, the EME makes the best use of a thick active layer without sacrificing the electrical performance.It is noteworthy that the hole mobility (3.0 x 10 −8 m 2 /V/s) is ten times smaller than the electron mobility (3.0 x 10 −7 m 2 /V/s) in active layer [1].Therefore, it is the hole mobility which limits the thickness of the active layer.But more generally, it is not the active layer thickness that is the limiting factor, but rather the distance between outlying electron-hole production sites and the metal electrodes (i.e., the anodes which function as hole collectors).A CME (or ITO reference) structure with dAct>100nm is not desirable in terms of electrical performance [9,10]; increased carrier recombination along the hole diffusion path would destroy the solar cell efficiency.Conversely, embedding of the electrodes into the active layer in the EME structure can preserve the same effective hole diffusion path length as the optimal CME while enabling a doubling of the active layer thickness.That is, the EME with dAct = 200nm preserves this distance at roughly 100nm since the electrodes are embedded roughly 100nm into the 200nm thick active layer, thus maintaining the same electrical performance as the CME with dAct = 100nm.

Conclusion
We proposed a new type of plasmonic organic solar cell based on a periodic array of metal nanowire electrodes embedded into an active layer.A large (~15%) enhancement of optical absorption in the EME structure over both conventional plasmonic solar cells with top-loaded metallic gratings and ITO based structures is demonstrated by effectively accessing the regime of large active layer thickness where its CME and ITO counterparts are known to suffer from poor plasmonic coupling and low hole collection efficiency.The performance improvements are shown to originate from the increased optical path length inherent to a thick active layer, while at the same time preserving the optimal conditions of plasmonic coupling between the metal nanowire and metallic back-plane.Our suggested EME scheme, providing improved optical performance, a similar charge collection efficiency to CME and ITO structures despite its twofold increase in the active layer thickness, and with a lower sheet resistance than a 100nm thick ITO transparent electrode, stands as an excellent candidate for ITO replacement in organic solar cells, and motivates further study of plasmonic organic solar cells with electrodes embedded into thick active layers.

Appendix: Simulation details
Under TM / TE normally incident plane wave illumination (magnetic / electric field parallel to the z-axis) from Glass substrate, 2D FEM calculations are conducted on a single unit cell uniform in the z-direction, with periodic boundary conditions along the x-axis, and perfectly matched layers at the top and bottom of the unit cell.
Absorption properties of the solar cells are investigated in the wavelength range of 350nm to 750nm, using the relative illumination intensity obtained from the standard AM1.5G solar radiation spectrum.To quantify the absorption performance over the entire considered spectral range under averaged polarization of (TM+TE)/2, we also defined a figure of merit (FOM) based on the ratio of number of photons absorbed in the active layer to the total number of incident photons, where h, c, and I(λ) are the Plank constant, speed of light in free space, and solar irradiance spectrum (AM1.5G),respectively, and the optical absorption efficiency A(λ) is defined as the fraction of incident power absorbed in the active layer [26]: where Q av and P in are the time-averaged power loss per unit volume and the incident power.The integral is evaluated over the active layer, using the volume integration of Q av during post-processing in COMSOL [27]; λ and E are the free-space wavelength and electric field vector, and ε 2 is the imaginary part of the dielectric constant of the active layer.We determine the DC sheet resistance (R s ) of a periodic silver nanowire array by applying the 'FS:MS fitting model' to include quantum effects as follows [6,28]: where ρ FS , ρ MS , and ρ Bulk are the resistivities (in units of Ωm) of a thin metal film from the FS model, MS model, and bulk metal, respectively.The optimization of the CME structure is presented in Fig. 4, which shows color maps of FOMs for different Period, as a function of wAg/Period and dAct when dAg = 20nm.

Fig. 1 .
Fig. 1.Schematic diagrams of solar cells with (a) conventional metal electrodes (CME), (b) our proposed embedded metal electrode scheme (EME), and (c) 100nm thick ITO-based reference.Note that dashed arrows in the active region show examples of transport pathways of holes ( + ) and electrons (-).

#Fig. 2 .
Fig. 2. (a) Sheet resistance (R s ) as a function of wAg for silver nanowire electrodes with different thickness (dAg).(b) FOM as a function of dAct and dCav for EME with dAg = 20nm, wAg = 120nm.(c) FOM as a function of dAct for solar cells with indicated parameters.The black dashed lines in (a) and (c) correspond to the ITO reference structure.(d) FOM with varying index of the dielectric element for optimized EME (dAct = 200nm, dCav = 80nm for dAg = 20nm, wAg = 120nm).Absorption spectra for (e) TM and (f) TE polarizations in CMEs with dAct = 100nm (optimal) and 200nm, and optimized EME.The black dashed line corresponds to ITO structure with dAct = 100nm.

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210672 -$15.00USD Received 22 Apr 2014; revised 24 May 2014; accepted 27 May 2014; published 10 Jun 2014 (C) 2014 OSA ) and 2(f) show absorption efficiencies in the active layer (as defined in Appendix) as a function of wavelength in CMEs with dAct = 100nm (optimal) and 200nm, and optimized EME with dAct = 200nm, dCav = 80nm (for dAg = 20nm, wAg = 120nm), for TM and TE polarizations, respectively.It is noted that the absorption efficiencies for the optimized EME are systematically larger than the optimized CME over the entire wavelength range regardless of polarization.

Fig. 3 .
Fig. 3. Normalized electric field amplitudes: Upper, middle, and bottom rows are for optimized CME with dAct = 100nm, CME with dAct = 200nm, and optimized EME with dAct = 200nm respectively.First, second, and third columns are for TM polarization at λ = 400nm, 500nm, and 600nm, and fourth column is for TE polarization at λ = 600nm respectively.