1. Introduction

Transparent electrodes (TEs) are materials that show a high transmittance while simultaneously providing a high conductivity. TEs are key components in modern optoelectronic applications, e.g. flat panel displays, photovoltaics or flexible electronics [1]. The most common materials for TEs are transparent conductive oxides (TCOs) like tin-doped indium oxide (ITO), aluminium-doped zinc oxide (AZO) or fluorine-doped tin oxide (FTO). Especially ITO is widely employed due to its high optical transmittance and low resistivity [2]. The main drawback of ITO is the scarcity of the rare earth element indium, and its resulting high costs. There has been a growing research interest in alternative materials such as carbon nanotubes, graphene, conductive polymer films, metal nanowires, metal meshes and ultrathin metal (UTM) films being reported as the most promising candidates [3–7]. TEs that are applicable to modern and flexible optoelectronic devices (like thin film photovoltaic foils) must fulfil a number of challenging requirements, such as low deposition temperatures and a high stability against mechanical stress. Thus, the brittle and barely flexible TCOs, which usually require high process temperatures, are not well suited for this kind of applications [6].

Composite transparent electrodes based on ultrathin metals (UTMs) consist of ultrathin Ag, Au, Cu or Al embedded between two dielectric materials and have been studied for low emissivity coatings in the last decades [8,9]. They exhibit promising features, such as widely adjustable optical and electrical properties through film thickness and material variations, ambient-temperature deposition, mechanical stability on flexible substrates due to metal ductility [3,6,10], low roughness [11] and temperature stability [12]. The electrical conductivity of these trilayer electrodes is mainly dependent on the thickness of the metal layer, which must be below 10-12 nm in order to avoid significant optical losses. The optical transmittance can be further controlled by the choice and thickness of the dielectric materials. It is possible to adjust the transmittance range of the TE according to the characteristics of the optoelectronic device, e.g. the luminosity function for flat screen displays. This adjustment is often performed by trial-and-error like variation of the dielectric layer thicknesses, although various simulation methods [6,13–15] allow the careful design of the layer structure and thicknesses beforehand. A challenging task in the deposition of ultrathin metal films is to avoid nanometer-sized, island-like patterns instead of continuous films. Thus, the percolation threshold must be surpassed to reach high transparency and small sheet resistance values [6].

In this paper, we present a comprehensive study of dielectric/Cu/dielectric electrodes, as Cu is a low-cost alternative to the more commonly used Ag or Au. A great variety of dielectric materials, covering a broad range of refractive indices (n_{λ = 550} from 1.5 to 2.6), have been considered in transfer matrix method (TMM) simulations, so as to maximise the electrode transmittance. TMM allows transmittance optimization for selected wavelength ranges, depending on the application requirements. Based on the simulation results, an optimum trilayer structure of TiO_x/Cu/AZO has been identified, which contains only low-cost materials. The experimental optimization of this trilayer on glass yielded superior figure of merit as compared to Cu-based TEs in the literature. It was further seen that the sputter power for Cu deposition greatly influences the TE performance for ultrathin metallic films and to similar extent improves the agreement between the simulated and experimental optical spectra. The paper also investigates the coating of this electrode on flexible polyethylene terephthalate (PET) substrate and compares its performance to the one on glass, revealing strong differences between the two cases. Finally, the Cu-based TE performance was simulated and evaluated in a complete hybrid-perovskite solar cell with inverted architecture, demonstrating the importance of in-device electrode simulation and optimization as opposed to simulations with air as ambient medium.

2. Methods

2.1 Simulation method

Optical simulations based on the transfer matrix method (TMM) [16,17] were performed to calculate direct transmittance and specular reflectance of coherent thin film multilayer stacks on a substrate (glass and PET). The substrate was considered incoherently by adding following expression for a non-absorbing substrate to the simulations [18]:

2.2 Thin film deposition

The films were deposited by DC magnetron sputtering (Leybold Univex 450C) on soda-lime glass substrates (Menzel Gläser) and PET (Dupont-Teijin Melinex ST506). The substrates were cleaned in ultrapure water and isopropanol ultrasonication baths and blown-dry using nitrogen. TiO_X was deposited by reactive sputtering from a 4-in Ti target in Ar/O₂ (80/20 mixture) atmosphere at 120 W sputter power, yielding a sputter rate of 0.015 nm/s. Cu was deposited from a 3-in Cu target in pure Ar atmosphere at sputter powers of 20, 40, 80 and 100 W, corresponding to rates of 0.23, 0.45, 0.90 and 1.09 nm/s. Al-doped ZnO (AZO) was sputtered from a 4-in ZnO target with 2 wt.% Al₂O₃ in pure Ar atmosphere at 80 W, resulting in a deposition rate of 0.43 nm/s. All materials were deposited at a gas pressure of 0.1 Pa. The target-substrate distance was 10 cm. When the Ti target is reactively sputtered, this relatively large target-substrate distance increases the probability of oxidation of metallic species in the Ar/O2 plasma, yielding more stoichiometric oxide films, but at the expense of lowering the sputtering rate. This configuration is also dictated by the construction characteristics of the sputter tool. The substrates were water-cooled at 25°C during the deposition process to allow for controlled conditions and further avoid heat induced deterioration of the flexible substrates during deposition. The sputter chambers have been evacuated to base pressures of 1.9 – 7.0 × 10⁻⁶ Pa. A profilometer (KLA-Tencor-Alpha-Step IQ) was used to determine the layer thicknesses by step-height analysis. Annealing was performed on a hot plate in air. The samples were put on the plate prior to the ramp-up process (5-20 min depending on the final temperature) and remained at a constant temperature for 60 min before being removed immediately. In the following, the thickness of a specific layer is denoted with a subscript. For example, Cu_7.5 stands for a Cu layer of 7.5 nm thickness.

2.3 Characterization

The samples were optically characterized using a Bruker Vertex 70 Fourier transform infrared spectrometer (FTIR), additionally equipped with a visible light source. Direct transmittance was measured for normal incident light and referenced to the sample holder without the sample (air). Total transmittance (direct plus diffuse transmittance) was measured with a teflon (PTFE) integration sphere accessory for the Vertex 70. Reflectance was measured with the A513QA accessory of the spectrometer, at 13 deg angle of incidence and unpolarized light. The measured signal was referenced to a calibrated mirror (Ocean Optics, STAN-SSH-NIST) in the range from 330 nm to 1150 nm. A GaP and Si detector were used to record spectra in the range of 330-550 nm and 550-1150 nm, respectively. The sheet resistance of the samples was determined by four-point, in-line probe technique (Süss MicroTec probes connected to an Agilent 4156C semiconductor parameter analyzer). The surface morphology of the Cu films was studied by scanning electron microscopy (SEM) (Zeiss, SUPRA 40) with 5 kV acceleration voltage and in-lens detector. Atomic force microscopy (AFM) (Molecular Imaging, PicoPlus) measurements of PET electrodes were performed in tapping mode.

3. Results and discussion

3.1 Simulation-based optimization

The general structure of the investigated Cu trilayer TE is shown in Fig. 1(a). The Cu is embedded between two dielectric layers to reduce reflection losses and prevent the ultrathin metal (UTM) from oxidation. In the following, a systematic investigation will be presented, suggesting which dielectric materials would lead to highest transmittance in a certain wavelength range. Based on comprehensive reviews on transparent electrodes [3,5,6], the following dielectric materials were considered for the simulation (sorted by increasing refractive index at λ = 550 nm, n_{λ = 550}): AZO [11], ITO [20], ZnO [21], NiO [22], MoO₃ [23], TeO₂ [24], Nb₂O₅ [25], ZnS [26] and TiO_X [13]. Furthermore, SiO₂ [27] and MgO [28] were added to cover a broad range of refractive indices (n_{λ = 550} from 1.48 to 2.53). The real and imaginary (where available) parts of the refractive index (n and k, respectively) were retrieved from the literature. The optical properties of Cu were taken from literature [29].

 

Fig. 1 (a) Sketch of transparent electrode layer design. (b) Simulated average transmittance in the range from λ = 400 nm to 900 nm for various material combinations with optimized dielectric layer thicknesses. The materials are ordered with increasing refractive index value at λ = 550 nm.

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In this study, the transparent electrode was optimized for maximum average transmittance T_400-900 in the wavelength range of 400-900 nm. The average transmittance in this range was calculated for each material combination using the TMM algorithm. The thicknesses of the dielectrics were varied between 0 nm and 100 nm to find the optimal layer thickness, while the Cu thickness was initially fixed to 7.5 nm. The highest transmittance values with optimized layer thicknesses are depicted in Fig. 1(b). In general, the best transmittance values are achieved for a bottom layer with high refractive index (n_{λ = 550} = 2.3–2.4) and a top coating of medium refractive index (n_{λ = 550} = 1.7 –2.0). The highest average transmittance is 0.845 for TeO_2;40/Cu_7.5/MgO₇₀. Being an insulator, MgO is not suited as the top layer that connects the electrode with the functional materials of the device (e.g. the absorption layer in solar cells). There are many possibilities to select the optimal material combination, as the transmittance is higher than 0.82 if n_{Mat 1, 550} > 2.0 and 1.7 < n_{Mat 2, 550} < 2.1.

The ideal thicknesses of the dielectric layers were in the range of 25 nm to 75 nm (if SiO₂ is excluded). Figure 2 presents the differences of the layer thicknesses Δd = d_{Mat 1} – d_{Mat 2}. For symmetric electrodes, employing the same material in both layers, the optimal thicknesses are for both layers identical. For asymmetric electrodes, the material with higher reflective index must be thinner than the lower refractive index material. The thickness difference increases with the difference of the refractive indices.

 

Fig. 2 Layer thickness difference Δd = d_{Mat 1} – d_{Mat 2} of various material combinations for maximum average transmittance in the spectral range from 400 nm to 900 nm.

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Based on the screening of dielectric materials and the respective applicability to optoelectronic devices, a designed trilayer structure, consisting of TiO_X as the bottom layer and AZO as the top layer, was investigated in more detail. A schematic view of the electrode is presented in Fig. 3(a). Three different Cu mass-equivalent thicknesses d_Cu, namely 5, 7.5 and 10 nm, were further investigated. These are typical values for UTM electrodes to keep the absorption losses in the UTM low [3]. For each d_Cu, the thicknesses d_TiOx and d_AZO of the TiO_x and AZO layer, respectively, were determined by applying the TMM algorithm. d_TiOx and d_AZO were varied from 0 nm to 100 nm and for each thickness combination, the average transmittance T_400-900 was calculated. The results are shown in Fig. 3(b) for the Cu_7.5 case, yielding a maximum transmittance of almost 0.83. The obtained optimal trilayers are TiO_x;30/Cu₅/AZO₆₅, TiO_x;31/Cu_7.5/AZO₆₀ and TiO_x;32/Cu₁₀/AZO₅₈.

 

Fig. 3 (a) Sketch of transparent electrode layer design used in this study. (b) Simulated average transmittance of a Cu_7.5 electrode for different thicknesses of the TiO_X and AZO layers in the wavelength range of 400-900 nm.

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3.2 Experimental optimization on glass substrate

The experimental and simulated transmittance and reflectance spectra of the designed transparent electrodes are presented in Fig. 4 for three different Cu thicknesses. Otherwise identical samples were prepared with two different sputter power values of 40 W and 100 W for the Cu deposition. The simulated transmittance of the Cu₅ electrode is above 0.80 in a broad wavelength range from 450 to 900 nm. The transmittance around 700 nm rises slightly with increasing Cu thickness, but at the same time the transmittance drop around 530 nm becomes more significant for larger Cu thicknesses. This wavelength corresponds to an energy of 2.33 eV, where light absorption is expected from d-band electron transitions [30]. For the Cu₁₀ trilayer, the shape of the experimental transmittance curve agrees well with the simulated one, although the measured transmittance is lower by about 0.03. The same applies for the Cu₅ and Cu_7.5 electrodes at wavelengths below 600 nm. Above 600 nm, the transmittance of the samples deposited at 40 W drops significantly in comparison to the simulation, which predicts high transmittance (>0.85) in this range for both electrode designs. Increasing the Cu sputter power to 100 W improves the overall transmittance for all electrodes, most remarkably for thinner Cu films. The influence of the sputter power on the electrode performance will be discussed in more detail later.

 

Fig. 4 Simulated (Sim.) and experimental (Exp.) transmittance T (solid) and reflectance R (dashed) spectra for two different sputter powers (P) and different Cu thicknesses for (a) TiO_X;30/Cu₅/AZO₆₅, (b) TiO_X;31/Cu_7.5 /AZO₆₀ and (c) TiO_X;32/Cu₁₀/AZO₅₈.

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The measured reflectance spectra fit well to the simulation results. The reflectance is less than 0.15 over the whole spectral range of the simulation and reaches minimum values of 0.04, proving that the layer thicknesses obtained by the TMM suppress reflection losses effectively. Total transmittance (direct plus scattered transmittance) was additionally measured for samples with 40 W and 100 W (data not shown here), showing good agreement (within 0.01) with direct transmittance measurements and therefore indicating that no scattering is present. The difference between simulation and experiment, especially for samples prepared at 40 W, must be therefore solely due to increased absorption losses in the ultrathin Cu layer.

The optical and electrical properties compared to commercial available ITO (703192-Sigma Aldrich, with app. thickness 120-160 nm) are summarized in Fig. 5. The average transmittance in the range of 400-900 nm is presented in Fig. 5(a) for the simulated and fabricated electrodes. The simulated average transmittance decreases with increasing Cu thickness. The average transmittance of the 100 W electrodes shows the same behaviour and reaches 0.82 for both Cu₅ and Cu_7.5 electrodes. The results for the 40 W electrodes differ significantly from the simulation due to the low transmittance above 600 nm, especially at low Cu thicknesses.

 

Fig. 5 (a) Average transmittance T_400-900, (b) sheet resistance R_S and (c) Haake’s figure of merit for T_400-900 as a function of Cu thickness for 40 W (green) and 100 W (orange) Cu sputter power. The measured values of commercial ITO are also depicted.

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The sheet resistance R_S (as shown in Fig. 5(b)) of the TiO_x;30/Cu₅/AZO₆₅ electrode drops significantly from 89 Ω/sq (ohms per square) to 21 Ω/sq when the sputter power is increased from 40 W to 100 W. A moderate decrease is observed for the TiO_x;31/Cu_7.5/AZO₆₀ sample where the R_s decreases to 11 Ω/sq. For the TiO_x;32/Cu₁₀/AZO₅₈ electrode the sheet resistance is not influenced by the Cu sputter power and remains at 6.5 Ω/sq.

To quantify the performance of the transparent electrode, the figure of merit (FoM) for transparent electrodes $\varphi =T^{10}/R_S$, where T is the transmittance and R_S is the sheet resistance [31], was evaluated. Figure 5(c) presents the FoM for the 40 W and 100 W electrodes taking into account the average transmittance, T_400-900, from 400 nm to 900 nm. The TE with Cu thickness 10 nm yields the best FoM_400-900 with 1.45 × 10⁻² Ω⁻¹. Compared to other Cu-based trilayer electrodes, this is one of the best reported FoM values for average transmittance. Song et al. [32] reported a FoM_avg. of 1.94 × 10⁻² Ω⁻¹ for AZO₄₀/Cu₈/AZO₄₀, and Wu et al. [33] recently reported FoM_400-800 of 1.46 × 10⁻² Ω⁻¹ for a BaSnO_3;50/Cu₉/BaSnO_3;50 electrode. However, both groups referenced the transmittance to the glass substrate transmittance, T_glass, which naturally yields higher FoM values. The FoM when referenced to glass can be given by the relation: ${\varphi }_{glass-ref}={(T/T_{glass})}^{10}/R_S$, which is related to the FoM used in this work by: $\varphi =T_{glass}^{10}{\varphi }_{glass-ref}$. Assuming a transmittance value of T_glass≈0.92 over a broad wavelength range, a correction factor of $T_{glass}^{10}=0.43$ can be deduced. Considering this, the Cu_7.5 and Cu₁₀ electrodes presented in this paper perform superior to the Cu-based electrodes aforementioned. The commercial ITO sample has an average transmittance T_400-900 of 0.86 and a sheet resistance of 11 Ω/sq resulting in a FoM_400-900 of 1.95 × 10⁻² Ω⁻¹. Cu-based trilayer electrodes were measured right after deposition and after being stored for several months in ambient conditions. No changes in the optical and electrical performance have been observed. It is therefore concluded that the dielectric top layer efficiently protects the Cu layer from oxidation, as has been also pointed out for Cu- and Ag-based transparent electrodes in literature [12,34–36].

As shown before, the conductivity and transmittance are lower for Cu deposition power of 40 W than for 100 W. To investigate the reason for this, bilayers of TiO_x;30/Cu₅ were deposited at different Cu sputter powers of 20 W, 40 W, 80 W and 100 W. The morphology of the Cu layer was studied with SEM and the images are presented in Fig. 6.

 

Fig. 6 SEM images of TiO_x;30/Cu₅ bilayer samples at different Cu sputter powers and their respective sheet resistance.

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At 20 W the Cu film is separated into small islands. With increasing sputter power the small islands merge into bigger clusters. The meander-like trenches at 80 W between the Cu islands reduce significantly with increasing power and transform to elongated voids at 100 W. In addition, the sheet resistance of the bilayer electrode decreases strongly. The film sputtered at 20 W is non-conductive. The sheet resistance drops to 3.8 kΩ/sq at 40 W, further to 137 Ω/sq at 80 W, down to 53 Ω/sq at 100 W. Bilayer films of TiO_x;30/Cu_7.5 (SEM data not shown) also show meander-like trenches for low sputter powers, which gradually disappear to form a continuous, defect-free film at 100 W. For the TiO_x;30/Cu₁₀ samples, a practically continuous Cu film is obtained even at 40 W power, with minor differences to the case of 100 W deposition. These observations regarding the Cu morphology are reflected by the differences in the corresponding optical spectra in Fig. 4. The importance of the choice of sputter power on film growth is pointed out in literature and is associated with strong crystallinity, faster growth, faster nucleation and improved electrical properties compared to Cu films, which were deposited at lower sputter powers [37]. Let us note that the presented sheet resistance values of the bilayers are influenced by oxidation of the unprotected Cu layer. When the AZO layer is deposited atop, the carrier transport will be eased by the filling of the voids in the Cu film, giving rise to the observed lower sheet resistance of the trilayer structures.

The performance of the TEs can be further increased by post-deposition annealing. Figure 7 presents the effects of thermal annealing for 1 h on the average transmittance and the sheet resistance of the TiO_x;31/Cu_7.5/AZO₆₀ electrode. The average transmittance (400-900 nm) rises by ~0.02 when the electrodes are annealed between 150° C and 250° C. The sheet resistance, on the other hand, varies within ~1 Ω/sq. Annealing at 300° C reduced the performance to the as-deposited state. The electrode annealed at 250° C yielded a FoM_400-900 of 1.5 × 10⁻² Ω⁻¹.

 

Fig. 7 Average transmittance from 400 nm to 900 nm (black circles) and sheet resistance (red squares) as a function of annealing temperature for TiO_x;31/Cu_7.5/AZO₆₀.

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The significance of the TiOx bottom layer goes beyond optical properties, as it offers an excellent adhesion of Cu to the substrate, as verified by adhesive-tape tests, and can be sputtered with low roughness on glass. The root-mean-square roughness of TiOx is 0.75 nm, as measured by AFM. It should be noted that for certain applications of these electrodes, e.g. in low emissivity coatings, high processing temperature steps are required, which dictate the use of additional layers to avoid agglomeration and diffusion of Cu into adjacent layers [8,9].

3.3 Experimental implementation of trilayer structure on flexible substrate

The trilayer structure was further applied to a flexible PET substrate. Simulations indicate, that even though PET has a slightly higher refractive index than glass (n_PET≈1.65, n_glass≈1.5), the optimal layer thicknesses of the dielectrics, as well as the transmittance spectra stays virtually unchanged. Figure 8(b) shows the direct and total (direct plus scatter) transmittance and specular reflectance spectra of the electrodes on glass and PET. The transmittance decreases significantly on PET and is in average about 0.2 lower than on glass. The reflectance is increased throughout the investigated wavelength range. Total transmittance measurements with an integration sphere showed that in the high wavelength regime about 0.07 of the direct transmittance loss is caused by light scattering, while at 600 nm no light scattering occurs. Taking into account scattering and reflection of the trilayer on PET and glass in the range 550-1150 nm shows that more than 0.15 of the transmittance loss is caused by increased absorption in the Cu layer. Furthermore, R_S increased from 11 Ω/sq on glass to an average of 340 Ω/sq on PET and showed high variations over the electrodes surface (σ_Rs = 170 Ω/sq).

 

Fig. 8 (a) Sketch of trilayer on different substrate configurations. (b) Direct transmittance (solid), total transmittance (circles) and specular reflectance (dashed) spectra of trilayer structure TiO_x;31/Cu_7.5/AZO₆₀ on glass, PET and PET/AZO₁₀ substrate.

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Former studies [10,12] of AZO/Au/AZO electrodes showed only minor property changes when the substrate was changed from glass to PET. Thus, the effects of an extra buffer layer of AZO between the PET and the trilayer structure was investigated. Simulations showed that an additional 10 nm AZO buffer layer had very little influence on the the transmittance of the electrode (< 0.02). The experimental results of a PET/AZO₁₀/TiO_x;31/Cu_7.5/AZO₆₀ electrode, and the respective spectra are shown in Fig. 8(b). The transmittance increased significantly, no light scattering was observed and the specular reflectance decreased. The total average transmittance of the TE remains still 0.08 lower than on glass substrate. With a sheet resistance of 17 Ω/sq and a FoM_400-900 of 3.1 × 10⁻³ Ω⁻¹ the electrode performed inferior on PET than on glass, but comparable to the PET/AZO₅₀/Au/AZO₅₀ electrodes [10]. The FoM is also similar to recently reported PET/ZnO₆₀/Cu₈/ZnO₆₀ and PET/ZnO₆₀/Cu(N)_6.5/ZnO₆₀ electrodes [34,38], but not reaching the best performing PET/ZnO₆₀/Cu(O = 5.0%)₈/ZnO₆₀ [38].

To elucidate the microscopic reason for the deterioration of the performance compared to glass, Fig. 9 presents AFM images (500 × 500 nm²) of PET coated with TiO_x and AZO/TiO_x. It has been shown, that the roughness of the transparent electrode can have a severe impact on the performance of the TE [13]. The roughness of the PET alone has a root mean square (RMS) value of 4.0 nm, while the roughness of TiO_x and AZO/TiO_x is significantly higher with 7.8 nm and 10.3 nm respectively. This is at first surprising as the layer structure PET/AZO₁₀/TiO_x;30 with higher RMS roughness value shows superior optical and electrical performance.

 

Fig. 9 AFM images of (a) PET, (b) PET/TiO_x;30 and (c) PET/AZO₁₀/TiO_x;30 including the RMS roughness, autocorrelation length (ACL) and kurtosis.

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Therefore, it is suggested that the RMS value as a quantity is not sufficient to explain the effect and additional quantities such as kurtosis and autocorrelation length (ACL) are needed. The kurtosis is a measure of the height distribution sharpness, with kurtosis > 3 caused by sharp peaks (spiky surface) and kurtosis < 3 by mild peaks (bumpy surface) [39]. The ACL is a measure of the average distance between surface irregularities. A higher ACL indicates a greater distance between grains in the profile. Even though the RMS roughness of the TiO_x directly on PET is lower compared to the case with the additional AZO buffer layer, the total height scale covers a bigger range. This is an indication for sharp features, such as spikes or steep valleys. This is confirmed by the kurtosis value of 4.0 and seen as deep and steep trenches in the surface. Further, the TiO_x directly on PET shows a smaller ACL, which indicates smaller grains compared to the case with the AZO buffer layer.

The TiO_x grown on PET/AZO₁₀ features a higher ACL and wider trenches, which are less steep and deep as indicated by the kurtosis value of 2.5. This promotes a smoother film growth of the Cu layer and explains the improved electrical and optical properties of the PET/AZO₁₀/TiO_x;31/Cu_7.5/AZO₆₀ electrodes compared to the case where no AZO buffer layer is present.

3.4 Simulation of TE implementation in a perovskite solar cell

In the above, the optical properties of the TE were optimized with air as ambient medium. We need to consider though, that for implementation in a device, all subsequent layers need to be taken into account, due to partial reflection at multiple interfaces and therefore complex interference effects. This means concretely that the dielectric thicknesses that maximize the transmittance, when air is the ambient medium, will not generally be the same when all layers in the device are considered. This also underlines the importance of optical simulations in the optimization process for the device of interest. Recently, works have been carried out for the optimization of ultrathin metal based electrodes in organic solar cells [40–43].

In this section we consider the implementation of the TE in a solar cell with methylammonium lead tri-iodide (MAPbI₃) absorber and the so-called inverted architecture, shown in Fig. 10(a). The TiO_x/Cu_7.5/AZO electrode replaces the standardly-used ITO and resides on the glass substrate, followed by a PEDOT:PSS (poly(3,4-ethylenedioxythiophene):polystyrene sulfonic acid) hole transport layer. On top of this, the MAPbI₃ is deposited, followed by a double electron transport layer PCBM (phenyl-C61-butyric acid methyl ester)/ZnO. Finally, an Al cathode is considered. This solar cell architecture (with ITO as anode) has been experimentally investigated in the literature [44].

 

Fig. 10 (a) Sketch of the considered perovskite solar cell, (b) simulated absolute absorption in the perovskite layer of the cell in the wavelength range from 400 to 800 nm for a 7.5 nm Cu layer.

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Naturally, the absorption in the solar absorber is the important quantity and it is calculated with the TMM method as outlined in the methods section. Literature values were taken for the complex refractive indices of PEDOT:PSS [45], MAPbI₃ [46], PCBM [45], ZnO [47] and Al [48]. The absorption of the incident light in the wavelength range from 400 to 800 nm in the perovskite layer (excluding the absorption in the other layers), as a function of the TiO_x and AZO layer thicknesses is shown in Fig. 10(b). A maximum of 0.66 can be observed at d_TiOx = 25 nm and d_AZO = 62 nm for a Cu thickness of 7.5 nm. These thickness values are close to the optimized values obtained for air as ambient medium. This is the outcome of the considered device architecture. For instance, the simulations show that if the PEDOT:PSS is omitted, the AZO thickness for maximizing the absorption in the perovskite approaches zero.

The electric field intensity distribution within the active layer shows an exponential decay for wavelengths below 500 nm, where the extinction coefficient of the perovskite is highest. With increasing wavelength and consequently lower extinction coefficient, the intensity profile shows oscillations due to interference effects. Simulations showed that the field intensity distribution is similar compared to standard ITO electrodes with thickness 200 nm. Let us note that in an optimization process with the goal of maximizing absorption in the active layer, also variations in the thickness of the other layers, such as the PEDOT:PSS and the perovskite absorber, can be considered. This could modify the optimal dielectric thicknesses of the TE. However, the goal of the simulations presented here is to demonstrate that, for typically used device layer thicknesses, it is important to consider in-device simulations to optimize the electrode, as the results can be significantly different from the case when air is the ambient medium.

4. Summary

In conclusion, the introduced sputtered transparent electrode of TiO_x/Cu/AZO combines the advantage of being composed of low-cost materials, and having high average transmittance of 0.80 and a minimum sheet resistance of 6.5 Ω/sq (for a Cu thickness of 10 nm) when deposited on glass substrate. The electrode is therefore competitive to the standard ITO. It was shown that high sputter power was key to avoid island-like growth of the Cu film and obtain superior optical and electrical properties. The electrode deposited on PET is far from reaching its performance on glass, due to the roughness induced by the TiO_x deposition. The performance, though, can be partly restored by the introduction of an additional AZO buffer layer. The obtained electrode (for a Cu thickness of 7.5 nm) has an average transmittance of 0.74 and a sheet resistance of 17 Ω/sq. Finally, it was underlined that the optimization of the electrode design has to take into account the precise layer architecture of the device. For the particular case of an inverted hybrid perovskite absorber solar cell, it was shown that the electrode design optimized with air as ambient medium had to be adapted.