Performance Evaluation of Semi-Transparent Perovskite Solar Cells for Application in Four- Terminal Tandem Cells. Supporting information

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1 Performance Evaluation of Semi-Transparent Perovskite Solar Cells for Application in Four- Terminal Tandem Cells Thomas Kirchartz 1,2, Sophie Korgitzsch 1, Jürgen Hüpkes 1*, César O. R. Quiroz 3, Christoph J. Brabec 3,4 1 IEK5-Photovoltaics, Forschungszentrum Jülich, 5 Jülich, Germany 2 Faculty of Engineering and CENIDE, University of Duisburg-Essen, Carl-Benz-Str. 9, Duisburg, Germany 3 i-meet, Friedrich-Alexander University Erlangen-Nürnberg, Martensstrasse 7, Erlangen, Germany 4 Bavarian Center for Applied Energy Research (ZAE Bayern), Immerwahrstraße 2, Erlangen, Germany Supporting information In the first section we discuss the meaning of slope and y-intersect and the difference in linear regression and the variation of the product. In addition we provide some discussion on further aspects and the limitation regarding applicability of the FOMs towards 2-terminal tandem cells, figure of merit data using CIGS solar cells as bottom partner or varying the bandgap of the top cell. In the second part we explain the assumption on the negligible influence of the filtered spectrum on the fill factor. Finally, we provide two Matlab /Octave scripts, which 1. calculate the figures of merit, tandem cell efficiency and the slope of the linear relationship between tandem cell and the single junction bottom cell efficiency and 2. create the graphs of the main paper for user-specified top cell data. The input files include data of various top and bottom cells taken from literature as described in the main paper. The documentation of the scripts is provided in the script files. 1

2 Meaning of slope and y-intersect The linear fit through the data of Figure 2 in the main paper results in a real linear equation ( )= +. (S1) The slope / and y-intersect are determined for each top cell for two cases. Figure S1 shows the slopes from linear regression and product variation versus each other and the corresponding y-intersects as function of the top cell efficiency. The data sets roughly follow = (dashed line). However, slight deviations occur in all cases. The slopes correspond to the effective transmittance of the top cells, which was highest for the product variation due to the high IR response of the record silicon cell. However, due to the tendency of lower for less efficient bottom cells, the resulting slope of the linear regression gets larger than the highest transmittance for any specific bottom cell. For the linear regression the y-intercept differs from the top cell efficiency due to the scattering of the tandem cell efficiency values in Figure 2a. For the idealized case the explanation of the deviation is more complicated. Fitted exp. slope dη tan /dη si (a) y-intercept η top (%) ~ (b) VocFF variation linear regression Idealized slope dη tan /dη si Top cell efficiency η top (%) Figure S1: a) Slopes from linear regression to experimental data vs. slope from product variation. b) y-intercepts of the linear regression and product variation as function of the top cell efficiency. The labels link to the references in the main paper. 2

3 After Eq. 4 the efficiency η tan is calculated as = + = 1+ ln( ) + (S2) with the voltage loss factor being a function of and, which is related to. When varying the product the resulting linear relation changes. We can rewrite the Eq. S2 as ( )= + ln( ) +. (S3) = + Here it is obvious, if is constant and is varied to result in a different, the second term becomes constant and contributes to the y-intersect. At the same time, the slope equals the effective transmittance. If we vary the fill factor and is constant, the second term contributes to the slope and the y-intersect equals. In reality we used the experimental sets of and in case of the silicon bottom cells and varied both values from a virtual maximum to 0.8 of these values in case of CIGS bottom cells ( =85%,, =800 ), so the real cases in Figure 2b and S2 represent an intermediate state between the two simple cases. 3

4 Cu(In,Ga)Se 2 solar cells as bottom partner efficiency (a) ShenEnEnvSci JacksonPSSRRL (b) ShenEnEnvSci JacksonPSSRRL15 Efficiency η tan (%) 26 Slope dη tan /dη si transparency Efficiency η si (%) Efficiency η tan (η si =%) (%) Figure S2: a) Four-terminal tandem solar cell efficiency as a function of the CIGS single junction cell efficiencies 4-5 using the variation model and the top cell of Quiroz et al. 6 b) Slope dη tan /dη si vs. tandem cell efficiency for a range of perovskite top cells from literature and using two reference CIGS cells. The slope dη tan /dη CIGS is a measure for the weighted transparency of the top cell. There are much more top cells in the shaded region (η tan > %), which are capable of a net improvement in efficiency, than for the silicon scenario with % efficiency (Fig 3a). Figure S2 shows data according to Fig 2 and 3a in the main manuscript using CIGS solar cells as bottom cells

5 Influence of filtered spectrum on the fill factor Fill factor FF Open circuit voltage V oc [V] Figure S3: The fill factor was calculated according to Eqn. S4 and is plotted as function of the open circuit voltage V oc. The fill factor of solar cells with negligible effect of series and shunt resistances can be calculated easily by the following equation 7 (.) ; = (S4) using the elementary charge q, the Boltzmann s constant k, and the absolute temperature T. The ideality factor was set to unity. The fill factor hardly changes with. Considering the drop in by =0.97 due to the filtered sun spectrum in the bottom cell, the calculated loss in would be around 0.5% relative. Thus we neglected the change in for our calculations. 5

6 Application to tandem cells in 2-terminal configuration Our calculations are based on simple assumption about the optical coupling between top and bottom cell and we have to mention the limitation of our assumptions if targeting 2-terminal tandem cells: The experimental data used for the silicon bottom cells are not representative for cells that could realistically be used in 2-terminal configuration. The light management in most silicon single junction cells relies on effective light coupling from air towards the silicon by rough surfaces and the anti-reflection effect of the front TCO or passivation layer. While the light scattering at the back surface could be retained in 2-terminal tandem cells, the front surface should be fairly smooth to allow simple solution processing of the perovskite top cells. 1 Recently, a monolithically stacked tandem cell has been realized using the textured surface of the silicon wafer with evaporatin processes for the perovskite cell. 8 In any case the light management cannot be covered by our simple approach using the top cell as filter for the sun spectrum and rigorous optical simulations are required. 2-3 However, we took the same assumptions and calculated 2-terminal solar cell performance using the parameters from the 4-terminal component cells. The curves were created by a single diode model without taking series or shunt resistance into account. The ideality factor was calculated by solving Eq. S4. According to Figs. 2 and 3 of the main paper, we created Figure S4 and S5. The linear relation remains valid for 2-terminal configuration. In general, the tandem cell performance of 2-terminal configuration is reduced as compared to the 4-terminal configuration due to limitation by matching of top and bottom cell current densities. Note, that the assumptions are very rough and some might be invalid for 2-terminal tandem cell application, so the values have to be considered with caution. 6

7 Efficiency η tan (%) Efficiency difference η tan -η si (%) (a) Kranz15 (b) (c) Chen16 Chen16 Kranz15 η si Duong17 Fu17 4-Terminal 2-terminal Duong17 Fu Efficiency η si (%) Figure S4: 2-terminal (open triangles) and 4-terminal (solid spheres) tandem solar cell efficiency as a function of the Si single junction cell efficiency. The lines are representative for the top cells. Thus, the slopes also differ and do not represent the transparency of the top cell as described for 4-terminal application, but it now includes an additional contribution from electrical interconnection. With our assumptions, the highest tandem cell performance was found for the 4-terninal configuration. 7

8 efficiency Slope dη tan /dη si terminal tandem 2-terminal tandem Efficiency η tan (η si =%) (%) transparency and current mismatch Figure S5: Slope dη tan /dη si (according to Figure S4) vs. tandem cell efficiency for a range of perovskite top cells from literature. The slope dη tan /dη si is a measure for the weighted transparency of the top cell and the power matching of the component cells in case of 2- terminal configuration. Only the top cells in the shaded region (η tan > %) are capable of a net improvement in efficiency, which is less pronounced for 2-terminal configuration. 1. Grant, D. T.; Catchpole, K. R.; Weber, K. J.; White, T. P., Design guidelines for perovskite/silicon 2-terminal tandem solar cells: an optical study. Opt. Express 16, (22), A1454-A Futscher, M. H.; Ehrler, B., Modeling the Performance Limitations and Prospects of Perovskite/Si Tandem Solar Cells under Realistic Operating Conditions. ACS Energy Lett. 17, 2 (9), Hörantner, M. T.; Snaith, H. J., Predicting and optimising the energy yield of perovskite-on-silicon tandem solar cells under real world conditions. Energy Environ. Sci. 17, 2, Jackson, P.; Hariskos, D.; Wuerz, R.; Kiowski, O.; Bauer, A.; Magorian Friedlmeier, T.; Powalla, M., Properties of Cu(In,Ga)Se 2 solar cells with new record efficiencies up to 21.7%. physica status solidi (RRL) Rapid Research Letters 15, 9 (1), Shen, H.; Duong, T.; Peng, J.; Jacobs, D.; Wu, N.; Gong, J.; Wu, Y.; Karuturi, S. K.; Fu, X.; Weber, K.; Xiao, X.; White, T. P.; Catchpole, K., Mechanically-stacked perovskite/cigs tandem solar cells with efficiency of.9% and reduced oxygen sensitivity. Energy Environ. Sci., 11 (2),

9 6. Quiroz, C. O. R.; Shen, Y.; Salvador, M.; Forberich, K.; Schrenker, N.; Spyropoulos, G. D.; Heumuller, T.; Wilkinson, B.; Kirchartz, T.; Spiecker, E.; Verlinden, P. J.; Zhang, X.; Green, M. A.; Ho-Baillie, A.; Brabec, C. J., Balancing electrical and optical losses for efficient 4-terminal Si-perovskite solar cells with solution processed percolation electrodes. J. Mater. Chem. A, 6, Green, M. A., Solar cell fill factors: General graph and empirical expressions. Solid- State Electronics 81, (8), Sahli, F.; Werner, J.; Kamino, B. A.; Bräuninger, M.; Monnard, R.; Paviet-Salomon, B.; Barraud, L.; Ding, L.; Diaz Leon, J. J.; Sacchetto, D. et al. Fully textured monolithic perovskite/silicon tandem solar cells with.2% power conversion efficiency. Nature Mater., in press, doi: /s