Optical role of the thin metal layer in a TiO_x/Ag/TiO_x transparent and conductive electrode for organic solar cells

Abstract

One possible alternative to ITO, the most commonly used transparent and conductive electrode (TCE) for Organic Solar Cells (OSCs) and other optoelectronic components, is to use an oxide|metal|oxide multilayer. Glass|cathode|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) inverted OSC structures are realized, where the cathode can be a TiO_x|Ag|TiO_x or ITO reference TCE. The sizing of the TiO_x|Ag|TiO_x (TAT) TCE structure is numerically realized by optimization of the normalized squared electric field inside the active P3HT:PCBM layer. The optimized TAT design in the whole design is different from the one involving optimization of transparency at the output of the trilayer structure in air. A photovoltaic efficiency of 2.7% is obtained for OSC with the TiO_x (22 nm)|Ag (15 nm)|TiO_x (19 nm) structure and can be compared to the 3.14% of efficiency obtained with the ITO reference. The short-circuit current density is identified as the crucial photoelectrical parameter. The morphology of the silver layer in TAT can give rise to an exaltation of the electromagnetic field, leading to an enhanced and undesirable absorption inside the metal layer. This exaltation is dependent of the thickness of the metal layer and induces changes in current density proportional to the normalized squared electric field inside this layer. The lost in short-circuit current density is estimated between 0.3 and 0.6 mA cm⁻², and is comparable to a thickness variation of 20 nm for both TiO_x layers or 2.5 nm of the silver layer. We define an exaltation coefficient of the bare electrode, which can be considered as a factor of merit to qualify the quality of the optical role of the silver layer and thereby of the trilayer electrode.

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1. Introduction

Indium Tin Oxide (ITO) presents excellent optoelectrical parameters and is intensively used as a Transparent and Conductive Electrode (TCE). Nevertheless, the Indium used in ITO layers could become rare and expensive. The ceramic structure of ITO also restricts its application in flexible devices. Consequently, the search for indium-free TCEs is a substantial scientific investigation field for the international community.¹

One alternative to ITO consists of using a thin metal layer integrated between two other layers (oxides or dielectrics) which is typically called an oxide|metal|oxide or OMO electrode. This idea comes originally from a work published by Gillham et al. in 1955,² which presented a Bi₂O₃|Au|Bi₂O₃ transparent and conductive trilayer for cockpit plane defrosting. A maximum transparency, higher than 80%, and a low sheet resistance, less than 5 Ω □⁻¹, were already reached. This trilayer structure was further studied as heat or IR reflector for windows application.^3–9 Later, the concept of trilayer was considered as TCE in OSC. The first objective was to reduce the thickness of the ITO single layer, and many publications described ITO|metal|ITO^10–14 multilayers. Then, a large range of materials has been used to replace ITO in trilayer such as: PEDOT:PSS,¹⁵ ZnO,^16–20 SnO₂,^21–24 ZnS,^25–29 MoO₃,^26,29–34 V₂O₅,³⁵ WO₃,^36–38 GZO,³⁹ AZO,^39,40 TiInZnO,⁴¹ Nb₂O₅,⁴² ZrON⁴³… Several metals have also been studied such as Ag,^27,36 Cu,^44,45 Au,¹¹ Mo,^40,46 and Al.^30,47,48

Some publications of J. C. C. Fan et al.^49,50 around 1975 based on several patents^51,52 are earliest works about trilayers using TiO₂ as oxide. Other more recent studies on TiO₂|metal|TiO₂ (ref. 53–62) employing mainly Ag as metal have been lead.

The optimization of trilayer electrodes is often experimentally done by maximizing their figures of merit which take into account their transmittance T and their sheet resistance R_S. The figure of merit Φ_T, proposed by G. Haacke ⁶³ for transparent conductors, is given by:

However, the optical behavior of such structures through its only transparency is a too simplistic view. Indeed, the optimization of the transparency of a thin film multilayer ETC can be done through the management of the normalized squared electromagnetic field |E|² in air via interferences. But if such ETC is integrated inside a photovoltaic (PV) device, the repartition of |E|² is completely different inside the PV active layer, and also inside the metal layer of the trilayer, where a detrimental higher absorption than expected can occur. Finally, the particular non-homogeneous morphology of silver can also induce Localized Surface Plasmon Resonance (LSPR) which can greatly enhance the electromagnetic field.⁶⁴

2. Experimental details

TiO_x/Ag/TiO_x (TAT) electrodes are produced with an Oerlikon Leybold Vacuum Univex 300 E-beam evaporator at normal incidence and with a distance of 20 cm from the liner containing the material to be deposited. The substrates consist in cleaned plain glass slides with a 1 mm thickness. The Ag thin film is deposited from 99.99% pure Ag into a 4cc Graphite liner at an average rate of 2 nm s⁻¹ under a pressure around 5 × 10⁻⁵ mbar. This high deposition rate has been found to be crucial to get percolated Ag layers at the lowest thickness. The TiO_x layer is deposited from 99.99% pure TiO₂ into a 4cc Mo liner at an average rate of 0.05 nm s⁻¹ under a pressure around 3 × 10⁻⁵ mbar. All depositions are done without intentional heating or gas supply. The oxide deposition process leads to an increase of the temperature inside the chamber that is not monitored. A waiting time is systematically enforced between the underlying titanium oxide and silver depositions to avoid unintentionally heated substrate.

The thicknesses are controlled by a quartz crystal oscillator monitor placed near the substrate during deposition, then checked by a mechanical profilometer. Optical constants and further validation of thickness values are measured from a SE-2000 spectroscopic ellipsometer of SEMILAB© using a fit model provided by SEA software (Fig. S1–S3†). Samples are optically characterized by a LAMBDA 950 UV/Vis/NIR PerkinElmer Spectrophotometer with light entering the device via the glass substrate. Electrical measurements are performed at (0.1; 1; 10) × π/ln(2) mA with a CPS Resistivity Test Fixture from CASCADE© combined with a C4S 4-Point Probe Head, which owns osmium probes with radii of 125 μm and space between them of 1.55 mm.

Inverted organic solar cells based on TAT electrodes has been realized according to the following structure: glass/TAT/ZnO (20 nm)/P3HT:PCBM (250 nm)/PEDOT:PSS (50 nm)/Ag (150 nm). A thin layer of ZnO nanoparticles (Genes'ink, 5 nm-diameters) is coated onto TAT multilayer using a speed of 4000 rpm for 50 s. An annealing of 130 °C for 10 min under ambient conditions is done in order to remove the solvent. The active layer consists in a blend of 60 mg of poly(3-hexylthiophene (P3HT, RiekeMetals) and 48 mg of 1-(3-methoxycarbonyl)-propyl-1-phenyl (6,6)C₆₁(PCBM, American Dye Source) in 2 ml of 1,2-dichlorobenzene, which is prepared 24 h before being used. The P3HT:PCBM is spin-coated directly over the ZnO NPs layer at 1100 rpm for 35 s in a glove box under nitrogen atmosphere. Then, a solvent-annealing is performed keeping the samples inside a covered glass jar for 120 min. Next, the PEDOT:PSS (Clevios F010) layer is coated at 5000 rpm for 50 s. Finally, the Ag cathodes are deposited by thermal evaporation process at a pressure of 2 × 10⁻⁶ torr using a shadow mask (0.18 cm²). Photocurrent density–voltage (J–V) curves are measured using a Keithley 2400 source measurement unit and photovoltaic performances are measured under an illumination intensity of 100 mW cm⁻² generated using a Newport Solar simulator at AM1.5 G conditions. Solar irradiance is calibrated using a reference silicon solar cell and a miss-match factor calculated using the IPCE. This IPCE is measured under an illumination from a TS-428 Acton 250 W tungsten halogen lamp supplied by a JQE 25–10 M Kepco voltage unit and monochromated using an CORNERSTONE 130. The photocurrent is detected by a Keithley 2400 source measurement unit and compared to the signal obtained under the same illumination conditions by an OSD 15 photodiode whose spectral response is given by the manufacturer.

3. Results & discussion

3.1 TAT integration in organic solar cells

3.1.1 Architecture of the inverted organic solar cell. TiO_x|Ag|TiO_x electrodes^65,66 have been experimented as alternative to ITO cathodes as a cathode inside bulk heterojunction based inverted organic solar cells with the glass|cathode|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) design. The structure is shown in Fig. 1.

Fig. 1 3D view of the manufactured inverted organic solar cell with the glass|TAT|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) design.

By calculating the intrinsic absorption efficiency for wavelength between [350–660] nm inside the sole active layer η_A,active versus the thicknesses t_ox1 and t_ox2 from both titanium dioxide layers with our previously described Transfer Matrix Method,^67,68 we obtained the cartography of Fig. 2. This gives an optimum intrinsic absorption efficiency of 69.5% for the glass|TiO_x (30 nm)|Ag (12 nm)|TiO_x (45 nm)|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) architecture.

Fig. 2 Map of the calculated intrinsic absorption efficiency inside P3HT:PCBM for glass|TiO_x (t_ox1 nm)|Ag (12 nm)|TiO_x (t_ox2 nm)|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) structures versus titanium dioxide thicknesses.

The t_ox1 and t_ox2 thicknesses can vary of roughly 10 nm around the respectively optimized 30 and 45 nm values, without any noteworthy loss for the intrinsic absorption efficiency. The same work was done for other thickness values of silver resulting in similar titanium dioxide thicknesses to optimize η_A,active. The optimal silver thickness is calculated to be below 10 nm, but TAT electrodes with such silver thickness have been previously shown to absorb much more than the numerical prediction.⁶⁵

3.1.2 Photovoltaic characteristics of the inversed organic solar cells. Different TAT electrodes were manufactured with titanium dioxide thicknesses around their numerically optimized values and varying Ag thicknesses. These electrodes were the integrated within organic solar cells during two experimental batches including each a reference cell with an ITO cathode whose structure is glass|ITO (200 nm)|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm). Table 1 summarizes the photovoltaic characteristics measured on the organic solar cells, which are annotated according to the formulation (TAT_{(tox1-tAg-tox2)}) where t_ox1, t_Ag and t_ox2 are respectively the thickness of the TiO_x,glass-side, Ag and TiO_x,cell-side layers.

Table 1 Photovoltaic parameters of the produced organic solar cells

Samples	Batch no.	R□ (Ω □^−1)	VOC (V)	JSC (mA cm^−2)	FF	Rseries (Ω)	Rshunt (Ω)	η (%)
(TAT(30-12.5-40))	s1	5.4	0.56	7.87	0.57	85	4996	2.48
(TAT(26-16-27))	s1	3.4	0.53	7.63	0.61	46	2703	2.48
(TAT(30-14.5-38))	s1	4.3	0.39	8.26	0.36	118	384	1.14
(TAT(30-13.5-23))	s1	5.1	0.49	7.85	0.55	183	1895	2.06
(TAT(30-12.5-23))	s1	5.3	0.52	7	0.48	103	2260	1.72
ITO reference	s1	6.6	0.55	9.56	0.60	53	2391	3.12
(TAT(30-11.5-38))	s2	6.3	0.53	6.87	0.55	62	2267	2
(TAT(22-15-19))	s2	4.1	0.52	8.37	0.62	51	2941	2.7
(TAT(22-14.5-19))	s2	5.2	0.53	7.82	0.59	60	2135	2.46
(TAT(27-16-28))	s2	3.9	0.52	6.62	0.60	68	2321	2.04
ITO reference	s2	6.6	0.53	9.17	0.63	45	4010	3.14

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The best measured efficiency of 2.7% for a solar cell with a TAT electrode can be compared to the 3.14% efficiency for the reference cell with ITO cathode (only 10% less). This shows the ability of an indium-free TAT electrode as to replace ITO in an organic solar cell. Efficiencies around 2.5% are obtained for several cells comprising different electrode's structures.

Note that the open-circuit voltages V_OC of the TAT-cells are ranging between 0.45 and 0.56 V, similarly to the reference ITO-cells presenting V_OC values between 0.53 and 0.55 V. The values of the series resistances R_series for TAT-cells do not exceed three times the value of the ones with ITO; the lowest R_series is obtained for the TAT_(26-16-27) electrode. Similarly, the TAT-cell fill factors FF are slightly below the ones of ITO-cells, excepted for two of them which are better in the batch s1.

As shown by the J(V) (Fig. 3) and EQE (Fig. 4) curves, the main parameter causing difference between both types of cells is the short-circuit current density J_SC, which is found to be lower for TAT-cells than ITO-cells. This can be attributed to one of the two following processes (or a combination of both): the TAT electrode can lead to a lower power dissipation in the P3HT:PCBM active layer^69,70 than that of ITO or the contact between the TAT and the cell could induce more charge losses than with ITO.

Fig. 3 Measured J(V) curves for (TAT_(30-12.5-40)), (TAT_(22-15-19)) and ITO organic solar cells.

Fig. 4 Measured External Quantum Efficiency (EQE) curves for (TAT_(30-12.5-40)) and ITO organic solar cells.

3.1.3 Discussions about the short-circuit current density. From the intrinsic absorption calculated for the active layer, we obtained⁷¹ the simulated short-circuit current density J_SC,sim for the reference cell glass|ITO|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm), a value of 14.2 mA cm⁻² is obtained with the assumption of 100% internal quantum efficiency (IQE). If we compare the values of J_SC (10 mA cm⁻²) and EQE measured for ITO-cells, we can deduce the IQE as a function of the wavelength. By assuming this same IQE curve for TAT-cells, Fig. 5 presents the cartography of the calculated J_SC,sim versus t_ox1 and t_ox2, respectively the thicknesses of the glass-side and the cell-side TiO_x, of the TAT-cells with glass|TiO_x (t_ox1 nm)|Ag (12 nm)|TiO_x (t_ox2 nm)|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) structures.

Fig. 5 Map of the calculated short-circuit current density values for glass|TiO_x (t_ox1 nm)|Ag (12 nm)|TiO_x (t_ox2 nm)|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) structures versus titanium dioxide thicknesses (by considering the IQE values corrected from the ITO-cells).

The experimental and simulated short-circuit current densities, respectively J_SC,exp and J_SC,sim, of the manufactured cells are presented on Table 2. Generally, a slight dispersion of the J_SC,exp can be expected relative to the repeatability of the manufacturing process linked to the thicknesses of the layers really deposited. But the high J_SC,exp value for the (TAT_(22-15-19)) cell is not theoretically predicted. However, obtaining a higher experimental J_SC value than the theoretical one could be possible if a slight variation of the active layer thickness leads to a change in the optimal t_ox2 thickness of the TiO_x. It means that a TAT structure which appears theatrically less suitable than another could experimentally become more favorable. We will demonstrate in the next sections of this paper that valuable reasons can be proposed to justify this phenomenon.

Table 2 Experimental and simulated short-circuit current densities and ratio between both values for the manufactured organic solar cells

Samples	JSC,exp (mA cm^−2) measured	JSC,sim (mA cm^−2) simulated	JSC,exp/JSC,sim	η (%) (reported from Table 1)
(TAT(30-12.5-40))	7.87	8.71	0.90	2.48
(TAT(26-16-27))	7.63	7.63	1.00	2.48
(TAT(30-14.5-38))	8.26	8.28	1.00	1.14
(TAT(30-13.5-23))	7.85	8.05	0.98	2.06
(TAT(30-12.5-23))	7	8.27	0.85	1.72
(TAT(30-11.5-38))	6.87	8.87	0.77	2
(TAT(22-15-19))	8.37	7.46	1.12	2.7
(TAT(22-14.5-19))	7.82	7.56	1.03	2.46

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Nevertheless, the simulated values of J_SC are generally close – around five percent – to the measured ones. A substantial difference (ratios of 0.77, 0.85 and 0.90) appears for the (TAT_(30-11.5-38)), (TAT_(30-12.5-23)) and (TAT_(30-12.5-40)) samples even if there is just one nanometer of silver separating them. A high overvaluation of the J_SC prediction for the (TAT_(30-11.5-38)) cells is noticed. The low thickness of the silver layer – 11.5 nm – is a plausible reason. We will discuss the behavior of bare electrodes to understand and to include these differences in our calculation.

3.2 Bare electrodes

The objective of the following part is to investigate the correlation between numerical and experimental optical properties of a TiO_x|Ag|TiO_x electrode in the air and to determine the parameters that are relevant for a better prediction of the optical performance of this same electrode inside an organic solar cell.

3.2.1 Origin of the optical differences between measurements and simulations. We previously described⁶⁸ the Transfer Matrix Method used to numerically determine the simulated transmittance, reflectance and absorptance of a stack composed of perfectly flat and homogenous layers, while a detailed studied was dedicated to the TAT electrodes. We observed a good agreement between the numerical and experimental optical properties for the majority of the tested structures. The main difference in transmittance came from the absorption part. We observed that for a fixed silver thickness, the difference ΔA_M–S between the measured and simulated absorption is dependent on the air-side oxide layer thickness (Fig. 6). We also demonstrated that for a silver layer under a thickness of around 12 nm, the measured absorption is much higher than the simulated one on a large wavelength scale ([300–1500] nm), but for a silver layer thicker than 12 nm, the measured absorption is quite similar to the simulated one, excepted for a spectral band generally centered around a 450–480 nm in wavelength. This behavior was attributed to the silver morphology which changes drastically around the “percolating thickness” and depends, with similar Ag deposition parameters, on the nature of the underlying layer and not of its roughness, which is otherwise low (Fig. S4 and S5†).⁶⁶ Less than 12 nm silver layer is not fully covering the TiO_x sublayer and presents a surface morphology with holes of a decreasing size when the silver thickness increases. After a threshold thickness, the sublayer is generally fully covered but could still presents nanograins of silver or nanoholes with sizes between few nanometers to a couple of a dozen nanometers. These different configurations lead to the presence of nanostructures (NSs) at the surface of the metal layer which can induce Localized Surface Plasmon Resonance (LSPR); LSPR is an optical phenomenon generated when an electromagnetic wave interacts with conductive NSs that are smaller than the incident wavelength. The electric field of the incident light can collectively excite the cloud of peripheral electrons of silver, resulting in coherent localized plasmon oscillations at a resonant frequency which strongly depends on the composition, size, geometry, dielectric environment and separation distance of the NSs. The electromagnetic field E is greatly enhanced by this LSPR,⁶⁴ while the normalized electric field squared modulus |E|² inside the material is directly proportional to its absorption. Hence, LSPR at the Ag|TiO_x interface of the glass|TiO_x|Ag|TiO_x stack could induce an increase of the electric field and then of the absorption inside and around the metal layer. This near-field phenomenon is not taken into account by the TMM model. It is necessary to understand that the trilayer optical behavior is predominantly linked to the control, by the oxide layers thicknesses and optical constants, of the electric field interferences inside and outside of the stack. Hence, the value of the electric field squared modulus inside the metal layer will be modulating by the oxide thicknesses, which mean that LSPR will have more or less impact on the ΔA_M–S if the |E|² is minimized or not inside this metal layer. This is also true when the trilayer electrode is embedded inside a thin film optoelectronic system such as an organic solar cell.

Fig. 6 Measured absorptance curves for (a) glass|TiO_x (20 nm)|Ag (15 nm)|TiO_x (t_ox2 nm) structures and (b) glass|TiO_x (t_ox1 nm)|Ag (13 nm)|TiO_x (28 nm) structures versus wavelength – inset: ΔA_M–S differences of absorption between simulated and measured values.⁶⁵

3.2.2 Experimental evidence of the presence of an exalted electric field inside the silver layer. The effect of a change in the intensity of the normalized electric field squared modulus |E|² on the absorption inside the trilayer can be experimentally observed by realizing several glass|TiO_x|Ag|TiO_x structures with fixed silver and glass-side TiO_x layers thicknesses while the air-side TiO_x thickness is varying.

Fig. 6(a) presents the measured absorption of three glass|TiO_x (20 nm)|Ag (15 nm)|TiO_x (t_ox2 nm) structures, with an increasing air-side TiO_x thickness of (9; 32; 37) nm.

We detect that the absorption decreases with the increase of the air-side TiO_x layer thickness. The difference ΔA_M–S between the measured and calculated absorptions is shown to decrease with the increase of the air-side TiO_x layer thickness (inset of Fig. 6(a)). To check that these changes are linked to variations of the electric field intensity inside the silver layer, Fig. 7(a) presents the calculation with our 1D-TMM model⁶⁸ of the |E|² intensity at the Ag|TiO_x,air-side interface, for the same structures as the manufactured ones and for wavelengths between [300–1500] nm. Note that for wavelengths between [300–650] nm, the |E|² intensity decreases drastically with the increase of the air-side TiO_x thickness. For wavelengths above 650 nm, |E|² is comparable for all structures. At the wavelength 460 nm which corresponds to the maximum of ΔA_M–S, the simulated |E|² intensity is plotted inside the multilayer electrodes (Fig. 8(a)) showing a progressive reduction of the field inside the silver layer when the outside oxide thickness increases.

Fig. 7 Calculated normalized electric field squared modulus curves at the Ag|TiO_x,air-side interface for (a) glass|TiO_x (20 nm)|Ag (15 nm)|TiO_x (t_ox2 nm) structures and (b) glass|TiO_x (t_ox1 nm)|Ag (13 nm)|TiO_x (28 nm) structures versus wavelength.

Fig. 8 Calculated normalized electric field squared modulus curves inside the trilayer electrodes at the 460 nm wavelength for (a) glass|TiO_x (20 nm)|Ag (15 nm)|TiO_x (t_ox2 nm) structures and (b) glass|TiO_x (t_ox1 nm)|Ag (13 nm)|TiO_x (28 nm) structures versus the distance from the glass|trilayer interface.

Then, we performed several glass|TiO_x|Ag|TiO_x structures with fixed silver and air-side TiO_x layers thicknesses while the glass-side TiO_x thickness is varying. Fig. 6(b) presents the absorption of three glass|TiO_x (t_ox1 nm)|Ag (13 nm)|TiO_x (28 nm) structures, with an increasing air-side TiO_x thickness (16; 28; 35) nm. The difference ΔA_M–S between the measured and calculated absorptions are ratter similar when the glass-side TiO_x layer thickness increases (inset of Fig. 6(b)). Fig. 7(b) shows no influence of the glass-side TiO_x thickness along the [300–1500] nm spectrum on the calculated value of the |E|² intensity at the Ag|TiO_x,air-side interface. At the 460 nm wavelength which corresponds to the maximum of ΔA_M–S, the simulated |E|² intensity is plotted inside the corresponding multilayer electrodes (Fig. 8(b)) and shows similar electric field intensity inside the whole stack, in particular inside the metal layer. This result is in agreement with the ΔA_M–S stability when the glass-side TiO_x thickness varies.

3.2.3 Definition of the exaltation e. It is required to define the exaltation e of the |E|² in order to retrieve the ΔA_M–S obtained. The dissipated energy per second in layer j at position x of the stack at normal incidence is given by:⁷¹with c the light speed, ε₀ the permittivity of free space, n_j the refractive index of layer j and α_j the absorption coefficient calculated by:with λ the wavelength of the light and k_j the extinction coefficient of layer j.

The absorption during a defined time and inside a specific layer is then proportional to the |E|² normalized electric field squared modulus. If an exaltation e of the |E|² occurs due to a LSPR phenomenon, then the |E|_sim² simulated with the TMM will differ from the |E|_meas² measured (if possible), in particular near the Ag|TiO_x interface. Henceforth, |E|_meas² can be simply expressed by:

|E|_meas² = (e + 1)|E|_sim² (4)

with |E|_sim² and |E|_meas² the simulated and measured normalized electric field squared modulus.

Thus, the exaltation e which depends on wavelength can be defined by:

with A_sim and A_meas respectively the simulated and measured absorptances of the TAT electrode and ΔA_M–S the difference between both absorptions. The measured absorption can be approximated to the absorption of the silver layer if the oxide layers are transparent at the considered wavelengths, which is the case for our TiO_x thin films.

Finally the simulated absorption A^corr_sim of a given TAT sample corrected by the e exaltation coefficient values can be deduced from eqn (5):

A^corr_sim = (e + 1)A_sim ≈ A_meas (6)

3.2.4 Quantification of the exaltation e. By drawing the exaltation e versus wavelength (Fig. 9) for the same structures as those of Fig. 6, we represent the only influence of the supplementary absorption (mainly due to LSPR) regardless the change of absorption inside the TAT structure due to electric field interferences. We can observe a similar peak of exaltation for both groups of three electrodes (Fig. 9(a) and (b)). For the glass|TiO_x (20 nm)|Ag (15 nm)|TiO_x (9 nm) structure, the exaltation is unexpectedly low, maybe due to the morphology of the very thin TiO_x layer leading to reflectance changes. We neglect the reflective part variations in our corrected model to focus on the absorption part. This approximation seems valid for TiO_x layer thickness above 10 nm. For electrodes with a silver layer thickness of 13 nm, the e peaks are slightly higher than those of the electrodes with a silver layer thickness of 15 nm. Indeed, the morphology of the silver layer varies with its thickness.⁶⁶

Fig. 9 Calculated exaltation coefficient e for (a) glass|TiO_x (20 nm)|Ag (15 nm)|TiO_x (t_ox2 nm) and (b) glass|TiO_x (t_ox1 nm)|Ag (13 nm)|TiO_x (28 nm) structures versus wavelength of the incident light.

If we investigate the intensity of the calculated exaltation coefficient e as a function of the thickness of silver (Fig. 10) grown at the same deposition rate inside TAT electrodes, with both 30–35 nm TiO_x layers thicknesses, a large decreasing of the exaltation is shown when silver thickness increases from 9 to 13 nm. Above the thickness of 13 nm, the exaltation intensity is steady, but the width of the concerned spectral band can be reduced.

Fig. 10 Calculated exaltation coefficient e for glass|TiO_x (30–35 nm)|Ag (t_Ag nm)|TiO_x (30–35 nm) structures, with t_Ag varying from 9 to 24 nm, versus wavelength of the incident light.

At our knowledge, this is the first time that the role of silver is so probed inside such trilayer and that an exaltation coefficient is proposed to quantify its optical influence.

3.2.5 Utility of the exaltation e. The exaltation coefficient e can be used to qualify the quality of the silver layer in situ, i.e. inside the trilayer electrode regardless of the oxide nature and thicknesses, without any in situ morphology characterization (AFM or SEM). Otherwise it can serve as a factor of merit for trilayer electrode structures presenting identical metal nature layer but different oxide layers.

The exaltation e of a reference trilayer can be also useful to calculate the corrected simulated absorption A^corr_sim and consequently the corrected simulated transmittance T^corr_sim of other TAT electrodes with similar silver layer to the reference but with other TiO_x layer thicknesses, as in Fig. S6† of the additional information part.

Finally, we know that in the case of the TAT electrode in air, the exaltation of the electric field can only enhance the absorption in the single absorbing layer of the stack, i.e. the silver film. However, in the case of an organic solar cell integrating a TAT structure as transparent electrode, it could be possible to use the pre-determined exaltation of the bare electrode to deduce its impact on the final photovoltaic properties of the cell. This will be the subject of the last part of this paper.

3.3 Corrected numerical model applied to OSC

3.3.1 Observation of the exaltation coefficient impact on OSC. To quantify the losses of short-circuit current density due to the exaltation e of the normalized electric field squared modulus supposedly induced by the morphology of silver, we corrected our model by the calculation of the supplementary absorption inside the silver layer induced by the enhanced electric field. With the only TMM calculation, i.e. a perfectly flat silver layer, we obtained a difference ΔJ_M–S = J_SC,meas − J_SC,sim of 2 mA cm⁻² for the (TAT_(30-11.5-38)) cell and of 0.84 mA cm⁻² for the (TAT_(30-12.5-40)) cell. The overvaluation of the J_SC,sim is higher for the (TAT_(30-11.5-38)) cells than for the (TAT_(30-12.5-40)) ones (Table 2). By introducing the correction in our optical model via the exaltation coefficient, i.e. the representation of the real silver morphology, these ΔJ_M–S differences are reduced respectively to 1.52 mA cm⁻² (ΔJ_M–S,corr = 0.48 mA cm⁻²) and 0.47 mA cm⁻² (ΔJ_M–S,corr = 0.37 mA cm⁻²). The measurement of the optical properties of the bare electrodes prior to realization of the solar cells reveals a lower transparency of the (TAT_(30-11.5-38)) electrode than that of the (TAT_(30-12.5-40)) one; this difference being mainly due to a higher absorption in (TAT_(30-11.5-38)) electrode (Fig. 11) which can be the result of a broader exaltation of the electromagnetic field (Fig. 12). The remaining ΔJ_M–S difference can be attributed to the resistivity variation of the silver layer.

Fig. 11 Measured (a) transmittance and (b) absorptance spectra of the (TAT_(30-11.5-38)) and (TAT_(30-12.5-40)) bare electrodes used to further realize the organic solar cells.

Fig. 12 Calculated exaltation coefficient spectra of the (TAT_(30-11.5-38)) and (TAT_(30-12.5-40)) bare electrodes used to further realize the organic solar cells.

Finally, the impact of the introduction of the exaltation correction inside the numerical model is significant. If we compare the ΔJ_M–S values to the variation of the J_SC,sim versus both titanium dioxide thicknesses (Fig. 5), it represents an equivalent variation of 20 nm around the optimal oxide thicknesses. It means that an electrode presenting non-optimal oxide thicknesses can give better photoelectrical performances than an optimal electrode if its silver morphology is smoother. This is typically true when the silver layer is thick. The next section will allow us to evaluate the optical influence of the silver thickness with or without the additional exaltation coefficient.

3.3.2 Evolution of the simulated short-circuit current density as a function of the silver thickness. On the Fig. 5, we are able to determine the oxide thicknesses to get optimal short-circuit current density for 12 nm-thick silver layer. The optimal short-circuit current densities are plotted for the same design of the OSC versus silver thickness between 7 and 20 nm on Fig. 13.

Fig. 13 Evolution of the predicted short-circuit current density versus silver thickness for organic solar cells integrating TAT electrode with optimal titanium dioxide thickness (the OSC design is given in the caption of the Fig. 5.

The short-circuit current density loss is around 0.5 mA cm⁻² every 2.5 nm step of increase of the silver thickness. This demonstrates the high importance of the silver layer thickness, as this 0.5 mA cm⁻² noticed loss corresponds also to a deviation of 20 nm for oxide thicknesses around the optimal value or of the integration of the exaltation coefficient correction linked to the morphology of the silver.

3.3.3 Measured and simulated short-circuit current density versus silver thickness. If we calculate the difference between the measured and simulated short-circuit current density ΔJ_M–S = J_SC,meas − J_SC,sim (Fig. 14, in grey) for all manufactured TAT-cells, we notice an increase of ΔJ_M–S with the increase of silver thickness. The ΔJ_M–S is negative on the [11.5–14] nm silver thickness range and positive above 14 nm. This can be correlated to the diminution of the sheet resistance versus silver layer (Fig. 14, in purple), as a result of the decrease of resistivity of the only metal layer. By taking an ITO layer of R_S = 6.3 Ω □⁻¹ as reference, our model should allow us to predict accurately the short-circuit current density of the TAT-cells having the same sheet resistance. Thereby, both R_S and ΔJ_M–S curves should intersect for R_S = 6.3 Ω □⁻¹ or ΔJ_M–S = 0 mA cm⁻² values. The intersection point is here around (t_Ag; R_S; ΔJ_M–S) = (13 nm; 5.4 Ω □⁻¹; −0.6 mA cm⁻²).

Fig. 14 Evolution of the difference ΔJ_M–S between measured and simulated short-circuit current density and of the difference ΔJ_M–S,corr between measured and corrected simulated short-circuit current density versus silver thickness for all manufactured organic solar cells integrating TAT electrodes (left y-axis). Evolution of the sheet resistance of the trilayer bare electrodes used for TAT-cells versus silver thickness (right y-axis).

If we calculate the difference between the measured and corrected simulated short-circuit current density ΔJ_M–S,corr = J_SC,meas − J_SC,sim,corr (Fig. 14, in green), taking into account the influence of the exaltation of the electromagnetic field for all TAT solar cells, the new intersection point between R_S and ΔJ_M–S,corr curves approaches the optimal intersection and is here around (t_Ag; R_S; ΔJ_M–S,corr) = (12.5 nm; 5.8 Ω □⁻¹; −0.35 mA cm⁻²). We previously showed that the exaltation of the electromagnetic field decreasing while its spectral band is narrowed when the silver layer thickness increases (Fig. 10), which can result in less supplementary absorption in the silver layer of the TAT electrode. So our exaltation correction model generates a non-linear correction from 0.6 mA cm⁻² for t_Ag = 11.5 nm to 0.3 mA cm⁻² for t_Ag = 15 nm, which induces a bend of the ΔJ_M–S,corr curve directly linked to the electrical quality of the silver layer itself.

In the end, the integration of the exaltation correction helps to predict more accurately the trilayer electrodes optical behavior likely to give better photovoltaic performances. The residual differences between simulated and measured short-circuit current densities should come from non-optical phenomena like thermal dissipation in the transparent conductive electrode or like energy level (work function) variation due to the different thicknesses of the oxide and silver layers depending on the TAT designs (Fig. S5†).

4. Conclusion

The possibility to achieve organic solar cells integrating TiO_x|Ag|TiO_x structure as transparent conductive electrode with photovoltaic performances approaching those obtained with indium tin oxide is confirmed. A maximum efficiency of 2.70% is reported for the glass|TiO_x (22 nm)|Ag (15 nm)|TiO_x (19 nm)|ZnO (20 nm)|P3HT:PCBM (250 nm)|PEDOT:PSS (50 nm)|Ag (150 nm) structure and is relatively close to the 3.14% obtained with the ITO reference. Parameters that can affect with comparable extent the short-circuit current density of the organic solar cells have been identified as: a variation of 20 nm of both titanium dioxide thicknesses over their optimum, a variation of 2.5 nm of the silver layer thickness and the integration in our model of the real silver morphology influence through an exaltation coefficient.

We demonstrate the crucial role of the thin metal layer morphology on the prediction of the optical properties of oxide/metal/oxide electrodes in air or integrated inside an organic solar cell. A factor of merit of the optical quality of the silver layer in oxide/silver/oxide structure was defined regardless the oxide's nature and thickness. This factor of merit has also proved its utility as a correction factor to predict more accurately the optical properties of bare multilayer electrodes or the photovoltaic performances of organic solar cells integrating such electrodes. This factor will allow researchers to compare different oxide/metal/oxide structures able to outdo the photovoltaic efficiency obtained with ITO.

Acknowledgements

The work presented in this paper was partially supported by the French Foundation of Technological Research (ANRT) under grant CIFRE-2012/0731.

References

1. K. Ellmer, Nat. Photonics, 2012, 6, 808–816.
2. E. J. Gillham, J. S. Preston and B. E. Williams, London, Edinburgh Dublin Philos. Mag. J. Sci., 1955, 46, 1051–1068.
3. C. G. Granqvist, Appl. Opt., 1981, 20, 2606–2615.
4. M. Koltun, S. Faiziev and U. Gaziev, Appl. Sol. Energy, 1974, 10, 42–48.
5. M. Koltun, S. Faiziev and U. Gaziev, Appl. Sol. Energy, 1976, 12, 33–35.
6. M. Koltun, S. Faiziev and U. Gaziev, Appl. Sol. Energy, 1977, 13, 27–28.
7. B. Bhargava, R. Bhattacharyya and V. V. Shah, Thin Solid Films, 1977, 40, L9–L11.
8. H. Köstlin and G. Frank, Thin Solid Films, 1982, 89, 287–293.
9. M. F. Al-Kuhaili, A. H. Al-Aswad, S. M. A. Durrani and I. A. Bakhtiari, Sol. Energy, 2012, 86, 3183–3189.
10. C. Guillén and J. Herrero, Sol. Energy Mater. Sol. Cells, 2008, 92, 938–941.
11. Y. S. Kim, J. H. Park, D. H. Choi, H. S. Jang, J. H. Lee, H. J. Park, J. I. Choi, D. H. Ju, J. Y. Lee and D. Kim, Appl. Surf. Sci., 2007, 254, 1524–1527.
12. M. Girtan, Sol. Energy Mater. Sol. Cells, 2012, 100, 153–161.
13. J.-A. Jeong and H.-K. Kim, Sol. Energy Mater. Sol. Cells, 2009, 93, 1801–1809.
14. J. H. Lee, K. Y. Woo, K. H. Kim, H.-D. Kim and T. G. Kim, Opt. Lett., 2013, 38, 5055.
15. H. Yang, B. Qu, S. Ma, Z. Chen, L. Xiao and Q. Gong, J. Phys. D: Appl. Phys., 2012, 45, 425102.
16. A. El Hajj, B. Lucas, M. Chakaroun, R. Antony, B. Ratier and M. Aldissi, Thin Solid Films, 2012, 520, 4666–4668.
17. D. R. Sahu and J.-L. Huang, Mater. Sci. Eng., B, 2006, 130, 295–299.
18. S. Vedraine, A. El Hajj, P. Torchio and B. Lucas, Org. Electron., 2013, 14, 1122–1129.
19. H. Han, N. D. Theodore and T. L. Alford, J. Appl. Phys., 2008, 103, 013708.
20. J. Ho Kim, J. Hwan Lee, S.-W. Kim, Y.-Z. Yoo and T.-Y. Seong, Ceram. Int., 2015, 41, 7146–7150.
21. S. J. Kim, E. A. Stach and C. A. Handwerker, Thin Solid Films, 2012, 520, 6189–6195.
22. S. H. Yu, C. H. Jia, H. W. Zheng, L. H. Ding and W. F. Zhang, Mater. Lett., 2012, 85, 68–70.
23. J.-D. Yang, S.-H. Cho, T.-W. Hong, D. I. Son, D.-H. Park, K.-H. Yoo and W.-K. Choi, Thin Solid Films, 2012, 520, 6215–6220.
24. S. Yu, W. Zhang, L. Li, D. Xu, H. Dong and Y. Jin, Thin Solid Films, 2014, 552, 150–154.
25. Y. Mouchaal, G. Louarn, A. Khelil, M. Morsli, N. Stephant, A. Bou, T. Abachi, L. Cattin, M. Makha, P. Torchio and J. C. Bernède, Vacuum, 2015, 111, 32–41.
26. H. Kermani, H. R. Fallah and M. Hajimahmoodzadeh, Phys. E, 2013, 47, 303–308.
27. H. Cho, C. Yun, J.-W. Park and S. Yoo, Org. Electron., 2009, 10, 1163–1169.
28. H. Kermani, H. R. Fallah, M. Hajimahmoodzadeh and N. Basri, Thin Solid Films, 2013, 539, 222–225.
29. Y. C. Han, M. S. Lim, J. H. Park and K. C. Choi, Org. Electron., 2013, 14, 3437–3443.
30. H.-W. Lu, C.-W. Huang, P.-C. Kao and S.-Y. Chu, Appl. Surf. Sci., 2015, 347, 116–121.
31. L. Cattin, M. Morsli, F. Dahou, S. Y. Abe, A. Khelil and J. C. Bernède, Thin Solid Films, 2010, 518, 4560–4563.
32. T. Abachi, L. Cattin, G. Louarn, Y. Lare, A. Bou, M. Makha, P. Torchio, M. Fleury, M. Morsli, M. Addou and J. C. Bernède, Thin Solid Films, 2013, 545, 438–444.
33. I. P. Lopéz, L. Cattin, D.-T. Nguyen, M. Morsli and J. C. Bernède, Thin Solid Films, 2012, 520, 6419–6423.
34. L. Shen, S. Ruan, W. Guo, F. Meng and W. Chen, Sol. Energy Mater. Sol. Cells, 2012, 97, 59–63.
35. L. Shen, Y. Xu, F. Meng, F. Li, S. Ruan and W. Chen, Org. Electron., 2011, 12, 1223–1226.
36. M. Zadsar, H. R. Fallah, M. H. Mahmoodzadeh and S. V. Tabatabaei, J. Lumin., 2012, 132, 992–997.
37. F. Li, S. Ruan, Y. Xu, F. Meng, J. Wang, W. Chen and L. Shen, Sol. Energy Mater. Sol. Cells, 2011, 95, 877–880.
38. S. Kim, H. K. Yu, K. Hong, K. Kim, J. H. Son, I. Lee, K.-B. Kim, T.-Y. Kim and J.-L. Lee, Opt. Express, 2012, 20, 845.
39. H.-K. Park, J.-W. Kang, S.-I. Na, D.-Y. Kim and H.-K. Kim, Sol. Energy Mater. Sol. Cells, 2009, 93, 1994–2002.
40. H.-W. Wu and C.-H. Chu, Mater. Lett., 2013, 105, 65–67.
41. H.-H. Kim, E. Kim, K.-J. Lee, J. Park, Y. Lee, D.-C. Shin, T.-J. Hwang and G.-S. Heo, Jpn. J. Appl. Phys., 2014, 53, 032301.
42. A. Dhar and T. L. Alford, J. Appl. Phys., 2012, 112, 103113.
43. J. H. Song, J. W. Jeon, Y. H. Kim, J. H. Oh and T. Y. Seong, Superlattices Microstruct., 2013, 62, 119–127.
44. S. Shang, C. Zhu and W. Liu, Thin Solid Films, 2008, 516, 5127–5132.
45. D. R. Sahu and J.-L. Huang, Thin Solid Films, 2007, 516, 208–211.
46. J. A. Thornton, A. S. Penfold and J. L. Lamb, Thin Solid Films, 1980, 72, 101–110.
47. J. Meyer, S. Hamwi, M. Kröger, W. Kowalsky, T. Riedl and A. Kahn, Adv. Mater., 2012, 24, 5408–5427.
48. E. N. Cho, P. Moon, C. E. Kim and I. Yun, Expert Syst. Appl., 2012, 39, 8885–8889.
49. J. C. C. Fan and F. J. Bachner, Appl. Opt., 1976, 15, 1012–1017.
50. J. C. C. Fan, F. J. Bachner, G. H. Foley and P. M. Zavracky, Appl. Phys. Lett., 1974, 25, 693–695.
51. J. C. C. Fan and F. J. Bachner, Transparent heat-mirror, US Pat., 4337990 A, 1982.
52. J. C. C. Fan and F. J. Bachner, Transparent heat-mirror, US Pat., 4556277 A, 1985.
53. I. Dima, B. Popescu, F. Iova and G. Popescu, Thin Solid Films, 1991, 200, 11–18.
54. S. Ito, T. Takeuchi, T. Katayama, M. Sugiyama, M. Matsuda, T. Kitamura, Y. Wada and S. Yanagida, Chem. Mater., 2003, 15, 2824–2828.
55. S. M. A. Durrani, E. E. Khawaja, A. M. Al-Shukri and M. F. Al-Kuhaili, Energ. Build., 2004, 36, 891–898.
56. P. C. Lansåker, J. Backholm, G. A. Niklasson and C. G. Granqvist, Thin Solid Films, 2009, 518, 1225–1229.
57. A. Dhar and T. L. Alford, APL Mater., 2013, 1, 012102.
58. J. Kulczyk-Malecka, P. J. Kelly, G. West, G. C. B. Clarke, J. A. Ridealgh, K. P. Almtoft, A. L. Greer and Z. H. Barber, Acta Mater., 2014, 66, 396–404.
59. M. Ghasemi Varnamkhasti and E. Shahriari, Superlattices Microstruct., 2014, 69, 231–238.
60. M. Sendova-Vassileva, H. Dikov, G. Popkirov, E. Lazarova, V. Gancheva, G. Grancharov, D. Tsocheva, P. Mokreva and P. Vitanov, J. Phys.: Conf. Ser., 2014, 514, 012018.
61. J. H. Kim, H.-K. Lee, J.-Y. Na, S.-K. Kim, Y.-Z. Yoo and T.-Y. Seong, Ceram. Int., 2015, 41, 8059–8063.
62. J. H. Kim, D.-H. Kim and T.-Y. Seong, Ceram. Int., 2015, 41, 3064–3068.
63. G. Haacke, J. Appl. Phys., 1976, 47, 4086.
64. S. Vedraine, P. Torchio, A. Merlen, J. Bagierek, F. Flory, A. Sangar and L. Escoubas, Sol. Energy Mater. Sol. Cells, 2012, 102, 31–35.
65. A. Bou, P. Torchio, D. Barakel, P.-Y. Thoulon and M. Ricci, Thin Solid Films, 2015 DOI:10.1016/j.tsf.2015.12.041.
66. L. Peres, A. Bou, D. Barakel and P. Torchio, RSC Adv., 2016, 6, 61057–61063.
67. A. Bou, P. Torchio, D. Barakel, F. Thierry, A. Sangar, P.-Y. Thoulon and M. Ricci, J. Appl. Phys., 2014, 116, 023105.
68. A. Bou, P. Torchio, S. Vedraine, D. Barakel, B. Lucas, J.-C. Bernède, P.-Y. Thoulon and M. Ricci, Sol. Energy Mater. Sol. Cells, 2014, 125, 310–317.
69. P. Shen, L. Shen, Y. Long and G. Chen, IEEE Electron Device Lett., 2014, 35, 1109–1111.
70. Y. Chen, L. Shen, W. Yu, Y. Long, W. Guo, W. Chen and S. Ruan, Org. Electron., 2014, 15, 1545–1551.
71. L. A. A. Pettersson, L. S. Roman and O. Inganäs, J. Appl. Phys., 1999, 86, 487.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra22081a

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