Perovskite Tandem Solar Cells

Sep 19, 2017 - Australian Centre for Advanced Photovoltaics (ACAP), School of Photovoltaic and Renewable Energy Engineering, University of New South W...
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Monolithic Wide Band Gap Perovskite/ Perovskite Tandem Solar Cells with Organic Recombination Layers Rui Sheng, Maximilian T. Hoerantner, Zhiping Wang, Yajie Jiang, Wei Zhang, Amedeo Agosti, Shujuan Huang, Xiaojing Hao, Anita W. Y. Ho-Baillie, Martin A. Green, and Henry J. Snaith J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05517 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 19, 2017

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This document is confidential and is proprietary to the American Chemical Society and its authors. Do not copy or disclose without written permission. If you have received this item in error, notify the sender and delete all copies.

Monolithic Wide Band Gap Perovskite/ Perovskite Tandem Solar Cells with Organic Recombination Layers

Journal: Manuscript ID Manuscript Type: Date Submitted by the Author: Complete List of Authors:

The Journal of Physical Chemistry jp-2017-05517n.R2 Article 19-Sep-2017 Sheng, Rui; University of New South Wales, Australia, School of Photovoltaic and Renewable Energy Engineering Hoerantner, Maximilian; University of Oxford, Condensed Matter Physics Wang, Zhiping; University of Oxford, Department of Physics Jiang, Yajie; University of New South Wales, School of Photovoltaics and Renewable energy Engineering Zhang, Wei; University of Surrey Agosti, Amedeo; Eidgenossische Technische Hochschule Zurich Huang, Shujuan; University of New South Wales, Australia, School of Photovoltaic and Renewable Energy Engineering Hao, Xiaojing; University of New South Wales, School of Photovoltaic and Renewable Energy Engineering Centre of Excellence for Advanced Silicon Photovoltaics and Photonics Ho-Baillie, Anita; University of New South Wales, Australia, School of Photovoltaic and Renewable Energy Engineering Green, Martin; University of New South Wales, ARC Photovoltaics Centre of Excellence Snaith, Henry; University of Oxford, Physics

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Monolithic Wide Band Gap Perovskite/ Perovskite Tandem Solar Cells with Organic Recombination Layers Rui Shenga†, Maximilian T. Hörantnerb†, Zhiping Wangb, Yajie Jianga, Wei Zhang,c, Amedeo Agostid, Shujuan Huanga, Xiaojing Haoa, Anita Ho-Bailliea*, Martin Greena, Henry J. Snaithb*

a

Australian Centre for Advanced Photovoltaics (ACAP), School of Photovoltaic and

Renewable Energy Engineering, University of New South Wales, Sydney 2052, Australia

b

Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, United

Kingdom

c

Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK

d

Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland

† These authors contribute equally to this work

*Corresponding author: [email protected], [email protected]

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Abstract We demonstrate a monolithic tandem solar cell by sequentially depositing a higher-bandgap (2.3 eV) CH3NH3PbBr3 sub-cell and a lower-bandgap (1.55 eV) CH3NH3PbI3 sub-cell bandgap perovskite cells, in conjugation with a solution-processed organic charge carrier recombination layer, which serves to protect the underlying sub-cell and allows for voltage addition of the two sub-cells. Owing to the lowloss series connection, we achieve a large open-circuit voltage of 1.96 V. Through optical and electronic modelling, we estimate the feasible efficiency of this device architecture to be 25.9 %, achievable with integrating a best-in-class CH3NH3PbI3 sub cell and a 2.05 eV wide bandgap perovskite cell with an optimised optical structure. Compared to previous reported all-perovskite tandem cells, we solely employ Pb-based perovskites, which although have wider band gap than Sn based perovskites, are not at risk of instability due to the unstable charge state of the Sn2+ ion. Additionally, the bandgap combination we use in this study could be an advantage for triple junction cells on top of silicon. Our findings indicate that wide band gap all-perovskite tandems could be a feasible device structure for higher efficiency perovskite thin-film solar cells.

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Introduction

Methylammonium lead halide perovskite solar cells have attracted enormous research interest since the seminal work of CH3NH3PbX3 (X=Br, I) perovskite-sensitized solar cells reported by Kojima et al. in 2009, and the demonstration of highly efficient solid-state perovskite solar cells in 20121,2. Tremendous power conversion efficiency enhancements have been achieved since then3-8,

42

. The improved photovoltaic performance has been

attributed to excellent optical properties9, long carrier diffusion lengths

10-13

, and high light

emission yields14. Apart from improving the properties of the perovskite solar cell, overall efficiency gains can be achieved by moving towards multiple junctions, where a series of solar cells that absorb in different regions of the solar spectrum are stacked on top of each other. By this means, more energy is extracted from the sun light, which raises the sealing on the ultimate efficiency achievable once fully optimised. Much work thus far has focused on developing “hybrid” tandem cells by combining perovskite with established photovoltaics like silicon. However, compared with the tandem cell structure with a high efficiency silicon bottom cell and a perovskite top cell15-19, the combination of two large band gap perovskite cells is capable of providing much higher voltage, which could be very interesting for not just solar photovoltaic electricity generation, but also enabling direct power conversion from solar energy to chemical energy such as solar fuels20,21. There are many aspects requiring optimisation, in order to enable a multi-junction solar cell to operate efficiently. One of which is the recombination layer between the junctions, which serves both as charge recombination centre and as a protection layer for the underlying cell during the deposition of second junction. Many materials have been proposed as the recombination layer for the perovskite/silicon tandem architecture15,19 and for perovskite/perovskite tandem structures. 20 Recently, Eperon et al. demonstrated that efficient 2-terminal all-perovskite tandem solar cells could be fabricated by including a dense sputter-coated indium oxide tin oxide (ITO)

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layer as the intermediate recombination electrode, which also served to protect the underlying cell from subsequent processing steps22. However, sputter coating, which is a relatively aggressive deposition technique, upon the sensitive perovskite cells requires the introduction of multiple additional “buffer” layers in order to protect the underlying perovskite cells from sputter damage, and prevent the potential effect of sputter induced unintentional heating. In addition, the thick ITO layer, with a lower refractive index to the perovskite layers, is likely to introduce optical interference loses which are non-ideal for maximising the efficiency of a tandem solar cell. It would be desirable if a printable recombination layer could be developed which obviated the requirement for the sputter coated ITO. Additionally, we use two complementary Pb based absorbers which do not suffer from the same oxygen sensitivities of the lower band gap Sn based perovskite absorbers. In this study, we introduce a bi-layer of C60 and PEDOT:PSS as the recombination junction, and

demonstrate a device structure of FTO/ compact TiO2/ mesoporous TiO2/

CH3NH3PbBr3/ Spiro-OMeTAD/ PEDOT: PSS/ C60/ CH3NH3PbI3/ Spiro-OMeTAD/ Au, and achieved a high open circuit voltage of up to 1.96 V. We subsequently perform combined optical and electronic modelling to reveal where the present major optical loses exist, and identify a precise device stack which could lead to tandem open-circuit voltages of up to 2.69 V, and solar cell efficiencies of up to 25.9 %, with realistic device characteristics for the top and bottom cells. Results and discussion Figure 1(a) shows the energy band diagram of the proposed tandem cells. Both top cell and bottom cell have the regular n-i-p structure with Spiro-OMeTAD as the hole transport material (HTM). Here we define the cell first receiving the light as the top cell, and the bottom cell is the second cell to be processed, which is subsequently capped with a metallic

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Au electrode. The primary criteria for a recombination layer is for it to have an appropriate work function to contact the p-type side of one cell and the n-type side of the other cell. In our current device structure the holes generated from CH3NH3PbBr3 cell and electrons from CH3NH3PbI3 cell must recombine in the recombination layer. Therefore either a highly doped “metallic” recombination layer is required, or a layer consisting of a highly doped p- and ntype tunnel-junction. Another requirement for the recombination layer for all-perovskite tandem cells is that we do not subject it to excessive thermal treatment, otherwise accelerated degradation of the underlying bromide cell could occur. As a solution processed recombination layer, orthogonal solvents are also required for each adjacent layer. We employ Spiro-OMeTAD as the first p-type layer to transport holes from the bromide top cell, and C60 as the n-type electron transporter extracting electrons from the iodine bottom cell. For the recombination layer we simply employ a thin and pinhole-free layer of PEDOT:PSS.

Figure 1. (a) Schematic energy band diagram and (b) device architecture of perovskite/ perovskite tandem structure. We show the complete tandem device architecture in Figure 1b, and a schematic of the energy levels of the materials we employ in Figure 1a. For cell fabrication we spin-coated a compact layer of TiO2 on patterned fluorine doped tin oxide (FTO) substrates, followed by a thin layer of mesoporous TiO2. Subsequently, we fabricated the CH3NH3PbBr3 film by the vapour-assisted solution-processing method within the mesoporous structure12,23: We first

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spin-coated a PbBr2 solution in DMF on top of mesoporous TiO2. We then exposed the annealed PbBr2 film to a CH3NH3Br vapour (crucible temperature 175 ⁰C) for 10 min in dry air. After the bromide cell perovskite deposition we spin-coated Spiro-OMeTAD. For the conductive charge recombination layer we diluted the PEDOT:PSS (PH1000, Heraeus) in isopropanol (IPA) and spin-coated the film, followed by a 120 ᵒC anneal for ten minutes in air. We subsequently deposited the C60 in dichlorobenzene by spin-coating. To increase the wettability, and also the conductivity of C60, we added 10 mg/ml 4-(1,3-dimethyl-2,3dihydro-1H-benzimidazol-2-yl)-N,N-diphenylaniline (N-DPBI) (in dichlorobenzene) to the C60 solution as an n-dopant, with a concentration of 10 µl/ml24. Encouragingly, we observed no evidence of the Spiro-OMeTAD being dissolved by the subsequent C60 deposition process, This implies that the PEDOT:PSS layer is suitably dense and pin-hole free so as to protect the underlying cell. We also note that this structure is not compatible with solution processing of the CH3NH3PbI3 film that involves the use of solvent Dimethylformamide (DMF), which we found dissolves the underlying perovskite structure, indicating that DMF can permeate through this multi-layer device stack. To overcome this issue we employed a sequential vapour-solution processing method whereby we deposited a CH3NH3PbI3 film by thermal evaporation of the PbI2 and then converted to perovskite via inter-diffusion of MAI from an isopropanol solution25. Although perovskite films can be fabricated via this method, due to the limited penetration of CH3NH3I, thick PbI2 films results in unreacted residual PbI2. Therefore we found that the optimized PbI2 thickness for maximizing the single junction device performance was only 115 nm, leading to ~200 nm thick final perovskite film. Following this second perovskite layer deposition, we spin-coated the final Spiro-OMeTAD film and capped the devices with a gold electrode. We show a scanning electron microscope (SEM) cross-sectional image in Figure 2a of CH3NH3PbBr3/CH3NH3PbI3 tandem solar cell, with a complete layered structure (with layer

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thickness’ in brackets) of FTO (300nm) compact TiO2 (40nm), mesoporous TiO2 (350nm), CH3NH3PbBr3 (350nm), Spiro-OMeTAD (185nm), PEDOT: PSS (80nm), C60 (30nm), CH3NH3PbI3 (200nm), Spiro-OMeTAD (250nm) and gold (100nm). Notably, we observe a rather rough but fully covered C60 film. This may be due to the poor wettability of C60 solution on the PEDOT: PSS film.

Figure 2. (a) Cross-sectional SEM image of tandem cell and (b) JV curves for individual cell and monolithic tandem. (c) Stabilized efficiency and current output of tandem cell. We show the J-V curves and photovoltaic performance parameters of the fabricated individual cells and tandem cells in Figure 2b and in Table 1. The structure for single junction iodine cell is glass/ FTO/ compact TiO2/ CH3NH3PbI3/ Spiro/ Au. For high band gap single junction cell is glass/ FTO/ compact TiO2/ mesoporous TiO2/ CH3NH3PbBr3/ Spiro/ Au. We measure an open-circuit voltage of over 1.4 V for the single junction bromide cell, which as others have observed can be attributed to the large bandgap of CH3NH3PbBr3. We observe a significantly boosted open-circuit voltage for the tandem solar cell, up to 1.96 V. However, this tandem cell open-circuit voltage is not the linear sum of both sub cells, which should be up to 2.44 V, indicating that we have introduced some additional voltage losses in the tandem cell construction or in the recombination layer. In addition, the J-V curve of tandem device shows a low fill factor, also indicative of resistive losses in the recombination. In Figure 2c, we show the power output measured over time for the tandem cell. We observe

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that the efficiency of the tandem cell take up to 500 s before it reaches its stabilized value of 5.9%. We did not observe this severe light soaking in either of the single junction iodine and bromide cells. This indicates that some “light healing” effect is occurring26. Previous study suggested that the C60 layer would be partially washed away after perovskite deposition, which would result in inhomogeneous/discontinuous morphology38. We therefore postulate that we have some regions of direct contact of the perovskite to the PEDOT:PSS recombination layer through pin-holes in the C60. These regions will induce rapid surface recombination in the CH3NH3PbI3 layer being detrimental to open-circuit voltage. Upon light soaking, defects at this interface, through which the surface recombination occurs, may become temporarily passivated through ion migration. Table 1. Photovoltaic performance of single junction and tandem cell.

CH3NH3PbI3 CH3NH3PbBr3 Monolithic tandem

Scan sirection Reverse Forward Reverse Forward Reverse Forward

Voc (V) 1.04 1.04 1.41 1.35 1.96 1.87

Jsc (mA/cm2) 17.30 17.66 6.16 5.81 6.40 6.00

FF (%) 71 61 64 55 41 40

PCE (%) 12.7 11.1 5.2 4.4 5.1 4.6

We have constructed working all-perovskite tandem solar cells, however, their operation is non-optimum and significant improvement is required in order to make them competitive and eventually superior to the best single junction perovskite cells. However, it is valuable to understand where the current losses are, and how efficient these wide-band-gap all-perovskite tandem cells could become, once fully optimized. For this purpose, we firstly estimate the optical losses in our tandem device stack, via performing an optical transfer matrix model. We account for the roughness of each layer by employing an effective medium approximation between the adjacent layers.

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We extract the optical constants, refractive index n and extinction coefficient k, of each individual layer by fitting ellipsometry data as well as transmission spectra over the wavelength range of interest. We show the measured and modelled transmittance (T) of the top bromide cell and recombination layer in Figure S2, which show good agreement between the experimental and modelled data with the discrepancy attributable to the non-uniformity of the mesoporous layer and the roughness of C60 layer, see Figure 2a for cross-sectional SEM image, which propagates throughout the whole structure. This fitting also validates the optical model36, 37. We used the determined optical constants and thickness of each layer to calculate the total reflection and absorption occurring within each layer of the device27. Under the assumption that 100% IQE (Internal Quantum Efficiency) across the measured spectrum could be achieved28,29, we determined the External Quantum Efficiency (EQE) by assuming all light absorbed within each perovskite layer leads to photocurrent generation. In order to estimate the current-voltage characteristic of each sub cell we employed the detailed balance limit theory, taking into account parasitic power consuming parameters from an equivalent one-diode circuit model, such as series resistance, shunt resistance and ideality factor30,31. Specifically for determining these device parameters, we extracted the shunt and series resistances, and ideality factor by fitting published experimental data from the best in class 1.55 eV band gap perovskite cells32. We show the extracted diode parameters in the SI. We calculated the reverse saturation dark current via integrating our calculated EQE spectrum over the black body spectrum at 300K, following methods reported in the literature33. In Figure 3a we present our modeled external quantum efficiency spectrum of the device stack we used experimentally, which we calculate assuming 100% internal quantum

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efficiency for light absorbed in each perovskite junction. It is quite apparent that there are many optical losses in the region of the spectrum. Because PEDOT:PSS does absorb a fraction of the solar spectrum itself. As a final optimisation, we reduced the PEDOT:PSS thickness to zero, and allowed all layer thickness to vary. Although this seems unrealistic, it is equivalent to swapping PEDOT:PSS for a more transparent highly doped organic semiconductor, which for instance Bolink et al 47. have shown to work very well in allevaporated perovskite multi-junction cells. We fix the band gap of the rear cell to that of MAPbI3, shift the band gap of the top cell in 0.1eV steps and allow each structure to optimise. For calculating the efficiency of the MAPbBr3 cell, we now apply the diode characteristics of the best-in-class lower gap perovskite cell, to estimate the ultimate efficiency feasible once these wider gap cells can be optimised to work comparably to the best lower gap cells. From our calculations, the band gap of the top cell which delivers the overall highest tandem efficiency is 2.05 eV. We note that the band gap of the MAPbBr3 and FAPbBr3 films are 2.3 eV 12 and 2.25 eV 44. Therefore, there is a requirement to drop this band gap 2.05eV in order to optimise a top-cell for a wide band gap all-perovskite tandem, employing only Pb based perovskites. We show the EQE of the device stack with optimum layer thickness in Figure 3c, thickness FTO (200 nm), compact TiO2 (33 nm), CH3NH3PbBr3 (1280 nm), Spiro-OMeTAD (140 nm), C60 (44 nm), CH3NH3PbI3 (1488 nm), SpiroOMeTAD (141 nm) and gold (100 nm). In Figure 3b and Table 2, we show the simulated cell performance parameters for the top, bottom and tandem junctions for all the calculated devices. It is apparent that in optimized stack, the maximum short-circuit current density (Jsc) we could obtain from the front cell is 11.6 mA/cm2, and the maximum Jsc from the rear cell is 12.2 mA/cm2. For the tandem cell, the maximum VOC achievable is 2.69 V, with a corresponding power conversion efficiency of 25.9 %. Our simulated results reveal that, by

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increasing the thickness of CH3NH3PbBr3 capping layer to 395 nm, and CH3NH3PbI3 layer to 313 nm, the tandem structure can reach the maximum output. A specific challenge with fine-tuning of the band gap for perovskite solar cells is that this relies on precise compositional control of mixed halides. The Br and I compositions can segregate in the perovskite layer, which can lead to reduction in the open-circuit voltage 45. Although this can be suppressed for cells with band gaps around 1.7eV, halide segregation is especially problematic for high Br contents in the I-Br mixed halide perovskites 46. Here, we therefor estimate the efficiency achievable in a Pb-perovskite-on-Pb-Perovskite tandem solar cell, if the band gap of the wide band gap cell has to remain at the band gap of the neat Br perovskite, FAPbBr3, which is 2.25eV. If we combine the 2.25 eV band gap with a 1.55 eV rear cell, we determine a maximum efficiency of 21.3%, with Jsc of 8.37 mA/cm2 and VOC of 2.9 V. If we allow the rear-cell band gap to widen, to satisfy current matching conditions, we combine the 2.25 eV cell with a 1.80 eV rear cell, and determine an efficiency of 22.23%, with a Jsc of 8.34 mA/cm2, VOC of 3.12 V, and a FF of 0.85. We present the simulated data in Figure S3, S4 and Table S1, S2. Notably, these latter efficiencies are not significantly higher than the best single junction perovskite solar cells reported to-date, which have band gaps between 1.55 and 1.63eV. Therefore, our calculations highlight that FAPbBr3 is not a suitable top cell material for Pb-perovskite-on-Pb-Perovskite tandem cells. Therefore, an essential challenge is to achieve good stable efficiency with an absorber material with a band gap closer to 2eV.

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Figure 3. (a) simulated EQE for experimental stack, and simulated (b) JV and (c) EQE of optimized cell architecture. Table 2. Photovoltaic performance of single junction and tandem cell for calculated devices.

CH3NH3PbI3 CH3NH3PbX3 Monolithic tandem

Voc (V) 1.07 1.61 2.69

Jsc (mA/cm2) 12.2 11.6 11.6

FF 0.84 0.83 0.83

PCE (%) 10.76 15.2 25.94

Conclusion

We have demonstrated operational all-perovskite tandem solar cells employing a solution processed interlayer. Through subsequent optical and electronic modeling we have identified that increasing the thickness of our rear lower band gap cell is required to further improve the tandem cells. Of equal importance, improvement to the recombination layer is required in order to overcome our present electrical losses. Once this has been achieved, our modeling has revealed that tandem solar cell efficiencies of 25.9 % are feasible with a 2.05 eV band gap top junction and a 1.55 eV band gap bottom junction, once the PV performance of each junction reaches that of the current highest efficiency single junction cells. This is in comparison to 22% efficiency, which is the current world-record for a single junction perovskite cell. Therefore, future research in this area should focus on developing lossless recombination junctions, and optimizing perovskite wide gap cells with close to 2.05 eV band gaps. As a final consideration, these wide band gap perovskite tandem cells are well matched to sit on top of silicon in a perovskite-perovskite-silicon triple junction cells. Investigating the prospect of such triple junction cells is the subject of ongoing work.

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Experimental Section

CH3NH3Br and CH3NH3I were synthesized following a previously reported method34, by mixing methylamine (33% in methanol, Sigma-Aldrich) with hydrobromic acid (40% in methanol, Sigma-Aldrich) or hydriiodic acid (48% in water, Sigma-Aldrich) in a 1:1 molar ratio in a 250ml round bottom flask under continuous stirring at 0⁰C for 2h. The precipitates were recovered by rotary evaporation at 60⁰C. To increase the purity of products, the powder was then dissolved in ethanol, recrystallized from diethyl ether. The final product was collected after dehydration at 60⁰C and placed in a vacuum chamber for overnight. Solar cell devices were fabricated on fluorine-doped tin oxide (FTO) coated glass (Pilkington, 8 Ω/square). FTO was patterned with 2 M HCl and zinc powder. Substrates were then cleaned in 2% Hallmanex detergent, acetone and isopropanol in ultrasonic bath for 10min in each cleaning agent followed by oxygen plasma treatment for 10min. The compact TiO2 layer was deposited by spin-coating a mildly acidic solution of titanium isopropoxide in ethanol at 2500 rpm for 60 s followed by annealing at 500 ⁰C for 30 min. The mp-TiO2 layer composed of 20-nm-sized particles was deposited by spin-coating at 2000 rpm for 60s using a commercial TiO2 paste (Dyesol 18NRT, Dyesol) diluted in ethanol (2:7, weight ratio). After dried at 125 ⁰C, the TiO2 film was heated to 500 ⁰C, annealed at this temperature for 30 min and gradually cooled to room temperature. CH3NH3PbBr3 films were deposited using the vapour-assisted method. Firstly, PbBr2 solution in DMF with a concentration of 1 M was spin-coated on the mp-TiO2 at 2500 rpm for 60s. After annealing at 70 ⁰C for 30 min, the film was treated by CH3NH3Br vapour at 175 ⁰C for 10 min in a closed glass petri-dish with CH3NH3Br powder surrounded on a hotplate in glovebox, then rinsed in isopropanol at room temperature. HTM was then deposited by spin-coating at 2000 rpm for 60 s. The solution was prepared by dissolving 72.3

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mg

(2,2’,7,7’-tetrakis-(N,

N-di-p-methoxyphenyl-amine)-9,9’-spirobifluorene)

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(Spiro-

MeOTAD), 28.8 ml 4- tert-butylpyridine (4-TBP), anniqued 17.5 ml of a stock solution of 520 mg/ml lithium bis(trifluoromethane)sulfonimide (LiTFSI) in acetonitrile in 1 ml Chlorobenzene. The samples were left overnight in dry air before recombination layer deposition. PEDOT: PSS was diluted in IPA with volume ratio of 1:4, solution was spined on oxidized Spiro-OMeTAD films at 5000 rpm for 45 s, then was annealed at 120 ⁰C for 15 min. C60 was dissolved in Dichlorobenzene with concentration of 10 mg/ml, solution was kept at 100 ⁰C before spin-coating, which at 2000 rpm for 30 s. followed by annealing at 100 ⁰C for 10 min. CH3NH3PbI3 films were deposited by inter-diffusion method. 115 nm PbI2 was evaporated in a vacuum chamber; CH3NH3I solution in IPA with concentration of 20 mg/ml was then spin-coated at 6000 rpm for 30s. After annealing at 100 ⁰C for 60 min, Spiro-OMeTAD was deposited with identical recipe and spin-coating condition as described above. To complete the devices, 100nm gold contacts were thermally evaporated on the back through a shadow mask. The optical and electronic device simulation was carried out by initially applying a transfer matrix model43 with the input of published complex refractive indices for the layered materials. The modelled absorption spectrum was assumed to resemble the EQE, if 100% internal quantum efficiency is present. The EQE for each of the two absorbing layers was then used for the detailed balance theory39 to calculate JSC and J0 and plugged into the onediode equivalent circuit equation:

‫ܬ‬ሺܸ ሻ = ‫ܬ‬ௌ஼ − ‫ܬ‬଴ ൬݁

௤ሺ௏ା௃ሺ௏ሻோೄ ௠௞்

− 1൰ −

ܸ + ‫ܬ‬ሺܸሻܴௌ ܴௌு

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The loss parameters (RSH, RS) and ideality factor (m) were extracted from published currently best performing JV characteristics of the corresponding perovskite devices. The modelled JV characteristic curves were combined by limiting the combined JSC to the lower JSC delivering cell and adding the voltages of both devices for each current step40. The performance parameters, PCE, FF, VOC, JSC were then extracted from the resulting JV curve. In order to find the optimal thicknesses of the layers, a differential evolution optimisation algorithm41 was used to vary the thicknesses and maximise the resulting PCE.

Supporting Information

The supporting information is available free of charge on the ACS Publications website. Hysteresis of fabricated monolithic tandem solar cell, the measured and modelled transmittance of the top bromide cell and recombination layer, as well as the calculated JV for 2.25 eV top cell, and parameters used for simulation are presented in the supporting information.

Acknowledgement The Australian Centre for Advanced Photovoltaics (ACAP) encompasses the Australianbased activities of the Australia-US Institute for Advanced Photovoltaics (AUSIAPV) and is supported by the Australian Government through the Australian Renewable Energy Agency (ARENA). Responsibility for the views, information or advice expressed herein is not accepted by the Australian Government. This work is part funded by EPSRC, UK, through EP/M024881/1

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