Performance Evaluation of Semi-Transparent Perovskite Solar Cells

Performance Evaluation of Semitransparent Perovskite Solar Cells for Application in FourTerminal Tandem Cells ACS Energy Lett. 2018.3:1861-1867. Downloaded from pubs.acs.org by UNIV PIERRE ET MARIE CURIE on 08/27/18. For personal use only.

Thomas Kirchartz,†,‡ Sophie Korgitzsch,† Jürgen Hüpkes,*,† César O. R. Quiroz,§ and Christoph J. Brabec§,∥ †

IEK5-Photovoltaics, Forschungszentrum Jülich, 52425 Jülich, Germany Faculty of Engineering and CENIDE, University of Duisburg-Essen, Carl-Benz-Straße 199, 47057 Duisburg, Germany § i-MEET, Friedrich-Alexander University Erlangen-Nürnberg, Martensstrasse 7, 91058 Erlangen, Germany ∥ Bavarian Center for Applied Energy Research (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, Germany ‡

S Supporting Information *

ABSTRACT: The efficiency of perovskite-based tandem solar cells and the respective efficiency gain over the single-junction operation of the bottom cell strongly depend on the performance of the component cells. Thus, a fair comparison of reported top cells is difficult. We therefore compute the tandem cell efficiency for the combination of several semitransparent perovskite top solar cells and crystalline silicon or chalcopyrite bottom cells from the literature. We focus on four-terminal configurations but also estimate and discuss the differences between four- and two-terminal configurations. For each top cell, we thereby determine the tandem cell performance as a function of the bottom cell efficiency, which results in a linear relationship. From these data, we extract two parameters to quantify the suitability of the top cell: (i) the slope of the tandem vs. bottom cell efficiency, which is the effective transparency of the top cell, and (ii) the tandem cell efficiency for a targeted bottom cell. These two figures of merit were calculated for a representative set of bottom cells and may serve for comparison of semitransparent perovskite top cells in the future. hile crystalline silicon solar cells1 are approaching their fundamental efficiency limits,2 substantial further efficiency improvements require the combination of silicon with a high-band-gap solar cell in a tandem configuration.3,4 Metal halide perovskite-based solar cells are currently the only non-III−V materials with sufficiently high efficiencies for application as the high-band-gap partner for crystalline Si in two- (2T) or four-terminal (4T) tandem solar cells.3,5,6 While 2T tandem cells have the advantage of reducing the number of transparent contacts and therefore the amount of parasitic absorption, 4T tandem solar cells bear several advantages: The band gap restrictions for the top cell imposed by the choice of the bottom cell targeting the energy yield are more relaxed,4,5,7 the higher energy yield was predicted by simulations for various top cell band gaps and locations,8 the component cells can be fabricated using optimized processes without any additional processing restrictions,3,9 and finally the module design is very flexible and may serve as add-on for commercial solar modules.9 In a 4T tandem device, the component cells are electrically independent while being optically coupled. In practice, the two cells would be stacked mechanically on top of each other and the optical coupling would typically consist of just a gap of air or transparent glue as an optical coupler.10,11 The gap by itself

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© 2018 American Chemical Society

would serve as an intermediate reflector, reflecting part of the light back into the perovskite top cell. The light then has to couple from either air or the optical coupling medium into the bottom cell. Because of the use of antireflective coatings and surface textures, the reflectivity of state-of-the-art Si solar cells is typically below 5% over a broad spectral range.1 Thus, harvesting of light that is reflected from the front of the bottom solar cell toward the perovskite solar cells is a small contribution to the total photocurrent in the perovskite solar cell.11 While the bottom cell is technologically mature and requires little adaptation if used in 4T tandems, the development of semitransparent perovskite top cells meets several challenges: At first, the overall electrical device performance must outperform the bottom cell in terms of a higher Voc·FF product in order to profit from the tandem device concept (Voc: open-circuit voltage; FF: fill factor). Second, the reduction of parasitic absorption in the electron and hole transport layers and the transparent conductive anode Received: April 13, 2018 Accepted: July 11, 2018 Published: July 11, 2018 1861

DOI: 10.1021/acsenergylett.8b00598 ACS Energy Lett. 2018, 3, 1861−1867

Letter

Cite This: ACS Energy Lett. 2018, 3, 1861−1867

Letter

ACS Energy Letters

Figure 1. Spectral power density as a function of photon energy for a specific top and two silicon bottom solar cells as well as their combination to 4T tandem solar cells. (a) High-efficiency Si solar cell12 with the perovskite top cell by R. Quiroz et al.13 (b) Same perovskite solar cell combined with a less-efficient Si solar cell from a pilot production with a 100 μm thin wafer.14 The area under the curves is proportional to the cell efficiency. The efficiency loss and gain relative to the silicon single-junction solar cell are represented by the red and green areas, respectively.

and cathode layers must be extended toward the near-infrared spectral range.9 Scientists working on these challenges typically face the problem that they want to judge the performance of their semitransparent perovskite solar cell for tandem applications. While the efficiency of the top cell will be easy to compare, most likely a comparison of the transparency and evaluation of 4T tandem cell performance or performance enhancement is difficult due to the free choice of the applied bottom cells. Typically, higher efficiency of bottom cells leads to higher efficiency in tandem devices. However, in these highly performing tandem devices, the efficiency improvement due to the top cell with respect to the single-junction operation of the bottom cell will be less pronounced (see Figure 1). Therefore, the purpose of this Letter is to propose a fair performance rating of semitransparent perovskite top cells that is independent of the experimentally available bottom cell. Although a precise determination of the 4T tandem cell performance requires measurement of the two optically coupled subcells, a good approximation of the tandem cell performance is achieved by independent measurements combined with calculations of the expected performance. The advantage of the latter approach is that it could be done for a range of different Si solar cells, which would allow an estimate of the 4T tandem cell efficiency as a function of the efficiency of the bottom cell. This represents objective judgment of the potential efficiency improvement to any bottom cell by adding a specific top cell. In addition, the method is independent of the availability of appropriate bottom cell technology to perovskite researchers. Two main assumptions are required to perform these simple calculations: At first, we assume simple optical coupling with the top cell being a filter for the bottom cell. Specifically, we assume that all light transmitted through the top cell is available to be harvested by the bottom cell and any reflection from the bottom cell is lost. As such, the calculated tandem solar cell performance represents a mild underestimation. In practice, this effect might be considered during top cell

characterization by using a slightly reflecting chuck or a bottom cell underneath of the top cell. Second, the electrical properties of the bottom cell are well approximated by a single diode model and variations of FF with light intensity are negligible. In order to calculate the efficiency of a given 4T tandem solar cell based on individual measurements of the component cells, we have to modify the efficiency of the bottom cell using the spectral transmittance Ttop(E) of the semitransparent top cell. First we correct the short-circuit current density of the bottom cell for the transmittance of the top cell. For this, we integrate the product of the external quantum efficiency EQEsi of the bottom cell in single-junction operation, the top cell transmittance, and the solar spectrum ϕsun. Using Jscbot = q

∫0

≡ Teff q

∞

T top(E)EQEsi(E)ϕsun(E) dE

∫0

∞

EQEsi(E)ϕsun(E) dE

= Teff Jscsi

(1)

we obtain a corrected short-circuit current density for the bottom cell. We also introduced a weighted transmittance Teff, which is a scalar value derived from Ttop(E) with the spectral photocurrent density of the bottom solar cell as a weighting factor. For monolithic tandem cells, Teff should ideally have a value of around 0.5, while in practice, we obtain values of 0.3− 0.5, as shown later. In addition, a reduced photocurrent due to the reduction in light intensity reaching the bottom cell will limit its Voc. The new Vbot oc can be written as si + Vocbot = V oc

bot nidkT ijjj Jsc yzzz lnjj si zz j J z q k sc {

(2)

Vsioc

where is the open-circuit voltage of the bottom cell operated as a single-junction device under 1 sun conditions. However, Voc depends logarithmically on the short-circuit current density; therefore, a typical reduction of Voc is on the 1862


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Figure 2. 4T tandem solar cell efficiency as a function of the Si single-junction cell efficiency. (a) Case where several perovskite top cells18,19,21,22 are combined with various Si solar cells taken from the literature and the lines are linear fits to the data. (b) Equivalent data but this time keeping the quantum efficiency for all silicon solar cells the same and just changing their Voc·FF product. The dashed lines highlight ηtan = ηsi, i.e., only results above this line will lead to any efficiency improvement of the tandem solar cell relative to the Si solar cell. (c,d) Efficiency difference of the tandem cell relative to the Si cell (i.e., the distance to the dashed line in panels (a) and (b)).

order of kTq−1 ln(2) ≈ 20 mV and thus is quite small. While any change in Voc would also affect the FF, a change of around kTq−1 in Voc leads to even smaller relative changes in the FF. In addition, including changes of the FF as a function of light intensity would require assumptions on the limitations of the FF in these devices (i.e., series resistance effects relative to losses due to the ideality factor being > 1). Therefore, we neglected changes in the FF for this study, but we present a brief estimate of the magnitude of the effect in the Supporting Information. On the basis of eqs 1 and 2, we calculate the efficiency of a 4T tandem solar cell using the efficiency of the semitransparent top cell, its transmittance curve over the spectral region relevant for the silicon bottom cell (350−1200 nm), as well as the efficiency ηsi, Vsioc, FF, and EQE of the bottom cell. While we focus on silicon solar cells as bottom cell technology, the same procedure can also be performed for bottom cells made from other materials such as Cu(In,Ga)Se2 (see Figure S2 in the Supporting Information) as long as the reflectance of the bottom cell to air and FF effects are sufficiently low to be neglected. With these assumptions and using the EQE of the top cell, Figure 1 illustrates the potential efficiency gain due to the increased Voc (and increased Voc·FF product) of the perovskite top cell relative to the bottom cell and the losses mainly due to parasitic absorption in the top cell. While a spectral efficiency might be useful to evaluate the top cell performance,7 the spectral power density is easily calculated for both component cells and allows a direct comparison of single-junction and tandem device performance. Figure 1a shows the spectral power densities for the record silicon solar cell at the time of writing (26.6%, black dotted line)12 combined with a semitransparent perovskite solar cell published by Quiroz et al. (blue area under dashed line).13 The corresponding curve for the tandem solar cell is given in green, with the filtered silicon bottom cell in purple. By comparing the single-junction and tandem solar cell performances in Figure 1a, the efficiency improvement is fairly modest (0.5%). However, the total efficiency of 27.1% would

be higher (0.4% absolute) than what has been published so far for perovskite silicon tandem solar cells with efficiencies up to 26.7%.13 In contrast, if the same top cell is combined with a less-efficient silicon solar cell from a pilot production with a 100 μm thin wafer 14 (as shown in Figure 1b), the improvement is much more impressive (4.1%), while the total tandem cell efficiency is lower than that of the tandem cell from Figure 1a. Note that the values provided here are based on EQE measurements and differ from those in the next sections, which are based on top cell efficiency data in the respective publications. The difference in spectral power density between the tandem cell and the single-junction operation of the silicon cell alone shows that the key for a successful tandem solar cell is a low loss by parasitic absorption of the top cell (red shaded area), which has to be compensated by a substantial increase of the Voc·FF product of the top cell relative to the one of the bottom cell. In order to develop some general figures of merit (FOMs) to quantify the quality of a given top cell, we have taken data of semitransparent perovskite solar cells13,15−25 or modules26,27 and combined them with a range of silicon solar cells1,12,14,25,28−40 from the literature. Upon thorough literature inspection, we only selected references where the top cell transmittance and silicon cell EQE were provided over the relevant range. The efficiency and short-circuit current densities of the silicon cells were recalculated using their EQE data. In contrast, the top cell parameters completely rely on efficiency data from the literature. The data were extracted with priority to stabilized efficiency, averaged efficiency, shortcircuit current density, and open-circuit voltage from forward and backward sweep or otherwise as given in the papers. In the first two cases, the FFs were calculated according to the averaged values. Though we observed deviations in shortcircuit current densities between JV measurements and EQE integration, we rely on the numbers provided in the publications. Any uncertainty in top cell efficiency directly translates into the tandem cell efficiency as the y-intersect of the linear relation. On the basis of eqs 1 and 2 and using the 1863


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Figure 3. (a) Slope dηtan/dηsi (according to Figure 2a (spheres) and b (open squares)) vs. the tandem cell efficiency for a range of perovskite top cells from the literature. The slope dηtan/dηsi is a measure for the weighted transparency of the top cell. Only the top cells in the shaded region (ηtan > 25%) are capable of a net improvement in efficiency. (b) 4T tandem solar cell efficiency as a function of the top cell efficiency. In both graphs, the bottom cell is represented by the virtual silicon cell with 25% efficiency and the labels correspond to the respective references.

the filtered irradiation as compared to the single-junction operation. The tandem cell efficiency

measured efficiencies of the component cells and short-circuit current density and open-circuit voltage of the bottom cell operated as a single-junction cell, we calculated the tandem cell efficiency ηtan =

=

Jscbot Vocbot si Jscsi V oc

q∫

∞

0

ij y Vocbot jj1 + nidkT ln(T )zzzη + η j eff z si ηsi + ηtop = Teff j si top z si V oc qV oc k { ≡ Teff γηsi + ηtop

ηtan(ηsi ) = Teff

ηsi + ηtop

T top(E)EQEsi(E)ϕsun(E) dE ij y jj1 + nidkT ln(T )zzzη + η jj eff z si si top z si Jsc qV oc { k

(4)

can be described mathematically by the y-axis intercept ηtop and the slope of the linear relation. Note that the intercept η̃top of the fit lines slightly differs from the top cell efficiency ηtop (see also Figure S1 in the Supporting Information). The parameter γ describes the loss in Voc with light intensity, and it is typically very close to unity. Assuming Teff = 0.4, we obtain γ = 0.97 assuming a realistic Vsioc for a high-efficiency silicon solar cell of 720 mV and an ideality factor of nid = 1. Thus, the slope in Figure 2 dηtan /dηsi is mostly given by just the weighted transmittance Teff, which was defined in eq 1 and is now an average value for the ensemble of selected bottom cells. Thus, the top cell is well-described by the two parameters, the top cell efficiency ηtop and effective transmittance Teff. However, top cells of different efficiency might result in similar tandem efficiencies due to compensation by Teff. In order to compare the various top cells for realistic scenarios, we provide ηtan rather than the top cell efficiency only and choose a relevant silicon bottom cell technology with ηsi = 25% as the basis. The two FOMs, the tandem cell efficiency ηtan(ηsi = 25%), and the slope given by eq 4 are calculated for a variety of semitransparent perovskite solar cells. The spheres and open squares in Figure 3a correspond to the fits to experimental data and the results using the simplified Voc·FF product variation, respectively. The y-axis ranks the perovskite top solar cells mainly in terms of their effective transmittance (slope), while the x-axis is calculated according to eq 4 with ηsi = 25%. The top cell rating for a specific bottom cell is given by the x-axis only. However, the slope is an important factor to judge the quality for tandem cells using a silicon bottom cell of different efficiency level. The actual slope slightly depends on the spectral sensitivity of the bottom cell. However, silicon waferbased solar cells typically exhibit quite similar spectral

(3)

Figure 2a shows the tandem cell efficiencies calculated from 4 selected top cells combined with 24 silicon bottom cells as a function of the silicon cell efficiency ηsi. The solid lines are linear fits to the data for each top cell, and the dashed lines highlight the point of zero gain, where the tandem cell exhibits the same efficiency as the respective silicon cell in singlejunction operation (ηtan = ηsi). In fact, this line separates the area of net gain and loss. There is some scatter on every line because each silicon solar cell exhibits slightly different quantum efficiency, thus weighting the top cell transparency in a different way. Figure 2b therefore shows an even simpler model, where the EQE of the Si solar cell was kept constant (using the one from ref 12) but the Voc·FF product of the silicon single-junction cell was varied. This approach automatically yields a straight line for each perovskite top cell and emulates a variation of bottom cell efficiency based on just one expemplary EQE spectrum. Figure 2c,d show the corresponding absolute efficiency difference relative to the single-junction operation of the Si solar cell. The difference decreases strongly for higher values of the Si cell efficiency. On the basis of Figure 2, there is a range of tandem efficiency values that could describe the quality of a top cell. Obviously, both approaches (Figure 2a,b) can be summed up by a linear relation between the tandem cell efficiency (or efficiency difference) and the single-junction bottom solar cell efficiency. As discussed earlier (see eqs 1 and 2), for the tandem cell efficiency, we consider the effective top cell transmittance Teff and the loss in Voc of the bottom cell with 1864


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Figure 4. (a) Efficiencies of top and tandem cells calculated after shifting the photovoltaic band gap EPV gap of the top cell. (b) Effective transmittance times the voltage loss factor Teffγ versus the tandem cell efficiency for variation of the photovoltaic band gap. The red asterisk indicates the original top cell of R. Quiroz et al.13 Note the deviation between integrated power density and efficiency data from the literature (Figures 2 and 3). The open symbols represent a shift of the top cell Voc with the band gap, while solid symbols represent the constrained Voc model.

circuit voltage. The first model assumes VOC(EPV gap) = VOC,0 + PV ΔEPV gap, where ΔEgap is the difference in band gap relative to the band gap of the reference cell (1.60 eV). The second model takes into account that increasing the band gap above about 1.75 eV has so far proven difficult due to I−Br segregation for high Br concentrations.43,44 Recent work suggests ways of overcoming the I−Br segregation problem.45 This motivates the more optimistic first model. For calculation of 2T devices (brown pentagrams), the optical model used was exactly the same. However, for the efficiency calculation, the two subcells were electrically connected in series, as described in more detail in the Supporting Information. For the unconstrained VOC model, the 4T tandem cells exhibit a maximum of 28.5% at top cell band gaps, well beyond the maximum for single-junction perovskite cells. In the case of constrained Voc, the highest tandem cell efficiency is slightly reduced to 28.1%. At a band gap of 1.65 eV, the 2T tandem cells exhibit a maximum of 27.5%, which is 1% lower than that of the best 4T configuration. The lower efficiency and discrepancy of the maxima of 2T and 4T tandem cells would be reduced for top cells approaching the Shockley−Queisser limit. The tendencies roughly agree with previously reported data;4,8 however, the exact numbers derived from our calculations for 2T devices are to be taken with caution due to the lack of a proper model taking into account realistic light incoupling in a monolithically stacked system and a better description of the JV curves. Figure 4b shows the FOMs calculated for the band gap variation. The data of Figure 3a relate to the values of Teffγ averaged over the ensemble of silicon bottom cells, while the data for band gap variation represent the actual effective transmittance and voltage loss parameters calculated for the record silicon cell by Yoshikawa et al.12 The given effective transmittance Teff increases in the evaluated range of band gaps from 23 to 63%. In conclusion, we have presented a simple method to estimate the performance of semitransparent perovskite solar cells for applications in 4T tandem cells. The general requirements of top cells for highest tandem cell performance are a high Voc·FF and low parasitic absorption in the relevant wavelength range. Note that the transparency and Voc·FF are

response, and the general trends of both data from fits to experimental data and the idealized cell with the highest IR response are quite similar. Thus, the FOMs are of general validity, and one must not recalculate them for each individual bottom cell. Figure 3a shows that for a 25% efficient silicon cell only few of the proposed perovskite top cells actually have the potential to lift the tandem cell efficiency significantly beyond the singlejunction efficiency (shaded green area). For all other semitransparent perovskite solar cells, the voltage loss in the bottom cell and parasitic absorption overcompensate the gain by the higher Voc·FF product of the top cell. Note that for lower or higher silicon cell efficiencies these criteria for net gain would be less or even more rigid, respectively. Figure 3b shows the tandem cell efficiency as a function of top cell efficiency. The tandem cell efficiency was calculated according to eq 4 with the silicon cell efficiency being 25%. Most data lie on a straight line. The outliers for the top cells from refs 13, 19 and 18 exhibit very high and low effective transmittance, respectively (see also Figure 3a). Similar calculations were performed for tandem cells using Cu(In,Ga)Se224,41 as the bottom partner. For the combination of perovskite solar cells with Cu(In,Ga)Se2 of 20% efficiency, tandem cells beyond 25% efficiency are feasible (see Figure S2 in the Supporting Information). The effective transmittance Teff and open-circuit voltage Voc of the top cell should vary with its band gap. However, we could not observe any significant trend in the dependence of Teff or Voc on the perovskite band gap. This means that the transparency and Voc in most of the cells are not governed by the actual perovskite band gap, but they are limited by parasitic absorption and voltage drop at interfaces, respectively. To have a deeper insight, Figure 4a shows calculated top cell and tandem cell efficiencies using the top and bottom cells of Figure 1a with a modified top cell band gap. As a point of reference, we used the inflection point of the EQE, which we 42 denote as the photovoltaic band gap EPV gap. In order to modify the band gap, we stretched and compressed the energy axis above and below the photovoltaic band gap and used the resulting transmittance and quantum efficiency data for the efficiency calculations. We used two models for the open1865


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(3) Werner, J.; Niesen, B.; Ballif, C. Perovskite/silicon tandem solar cells: marriage of convenience or true love story? − An overview. Adv. Mater. Interfaces 2018, 5, 1700731. (4) Futscher, M. H.; Ehrler, B. Modeling the performance limitations and prospects of perovskite/Si tandem solar cells under realistic operating conditions. ACS En. Lett. 2017, 2 (9), 2089−2095. (5) Eperon, G. E.; Hörantner, M. T.; Snaith, H. J. Metal halide perovskite tandem and multiple-junction photovoltaics. Nat. Rev. Chem. 2017, 1, 0095. (6) Shen, H.; Duong, T.; Wu, Y.; Peng, J.; Jacobs, D.; Wu, N.; Weber, K.; White, T.; Catchpole, K. Metal halide perovskite: a gamechanger for photovoltaics and solar devices via a tandem design. Sci. Technol. Adv. Mater. 2018, 19 (1), 53−75. (7) Yu, Z.; Leilaeioun, M.; Holman, Z. Selecting tandem partners for silicon solar cells. Nat. Energy 2016, 1, 16137. (8) Hörantner, M. T.; Snaith, H. J. Predicting and optimizing the energy yield of perovskite-on-silicon tandem solar cells under real world conditions. Energy Environ. Sci. 2017, 10, 1983. (9) Chen, B.; Zheng, X.; Bai, Y.; Padture, N. P.; Huang, J. Progress in tandem solar cells based on hybrid organic−inorganic perovskites. Adv. Energy Mater. 2017, 7 (14), 1602400. (10) Lin, Y.-T.; Chou, C.-H.; Chen, F.-C.; Chu, C.-W.; Hsu, C.-S. Reduced optical loss in mechanically stacked multi-junction organic solar cells exhibiting complementary absorptions. Opt. Express 2014, 22 (S2), A481−A490. (11) Kanda, H.; Uzum, A.; Nishino, H.; Umeyama, T.; Imahori, H.; Ishikawa, Y.; Uraoka, Y.; Ito, S. Interface optoelectronics engineering for mechanically stacked tandem solar cells based on perovskite and silicon. ACS Appl. Mater. Interfaces 2016, 8 (49), 33553−33561. (12) Yoshikawa, K.; Yoshida, W.; Irie, T.; Kawasaki, H.; Konishi, K.; Ishibashi, H.; Asatani, T.; Adachi, D.; Kanematsu, M.; Uzu, H.; et al. Exceeding conversion efficiency of 26% by heterojunction interdigitated back contact solar cell with thin film Si technology. Sol. Energy Mater. Sol. Cells 2017, 173, 37−42. (13) Ramirez Quiroz, C. O.; Shen, Y.; Salvador, M.; Forberich, K.; Schrenker, N.; Spyropoulos, G. D.; Heumuller, T.; Wilkinson, B.; Kirchartz, T.; Spiecker, E.; et al. Balancing electrical and optical losses for efficient 4-terminal Si-perovskite solar cells with solution processed percolation electrodes. J. Mater. Chem. A 2018, 6, 3583− 3592. (14) Terheiden, B.; Ballmann, T.; Horbelt, R.; Schiele, Y.; Seren, S.; Ebser, J.; Hahn, G.; Mertens, V.; Koentopp, M. B.; Scherff, M.; et al. Manufacturing 100-μm-thick silicon solar cells with efficiencies greater than 20% in a pilot production line. Phys. Status Solidi A 2015, 212 (1), 13−24. (15) Albrecht, S.; Saliba, M.; Correa Baena, J. P.; Lang, F.; Kegelmann, L.; Mews, M.; Steier, L.; Abate, A.; Rappich, J.; Korte, L.; et al. Monolithic perovskite/silicon-heterojunction tandem solar cells processed at low temperature. Energy Environ. Sci. 2016, 9 (1), 81−88. (16) Bailie, C. D.; Christoforo, M. G.; Mailoa, J. P.; Bowring, A. R.; Unger, E. L.; Nguyen, W. H.; Burschka, J.; Pellet, N.; Lee, J. Z.; Grätzel, M.; et al. Semi-transparent perovskite solar cells for tandems with silicon and CIGS. Energy Environ. Sci. 2015, 8 (3), 956−963. (17) Bush, K. A.; Bailie, C. D.; Chen, Y.; Bowring, A. R.; Wang, W.; Ma, W.; Leijtens, T.; Moghadam, F.; McGehee, M. D. Thermal and environmental stability of semi-transparent perovskite solar cells for tandems enabled by a solution-processed nanoparticle buffer layer and sputtered ITO electrode. Adv. Mater. 2016, 28 (20), 3937−3943. (18) Chen, B.; Bai, Y.; Yu, Z.; Li, T.; Zheng, X.; Dong, Q.; Shen, L.; Boccard, M.; Gruverman, A.; Holman, Z.; et al. Efficient semitransparent perovskite solar cells for 23.0%-efficiency perovskite/ silicon four-terminal tandem cells. Adv. Energy Mater. 2016, 6 (19), 1601128. (19) Duong, T.; Wu, Y.; Shen, H.; Peng, J.; Fu, X.; Jacobs, D.; Wang, E.-C.; Kho, T. C.; Fong, K. C.; Stocks, M.; et al. Rubidium multication perovskite with optimized Bandgap for perovskite-silicon tandem with over 26% efficiency. Adv. Energy Mater. 2017, 7 (14), 1700228.

functions of the perovskite band gap with opposing trends, and the perovskite band gap should be optimized with respect to tandem cell performance rather than single-junction cell efficiency only. Because both the tandem cell efficiency and the efficiency improvement are by design strong functions of the bottom cell efficiency, we propose to calculate the efficiency of 4T tandem cells as a function of the bottom cell efficiency, in analogy to Figure 2. The advantages of this method are the the simplicity of deriving tandem cell efficiencies for any bottom cell from a linear equation. We provide a MATLAB/Octave script including the required literature data, and we propose evaluating any future top cell for a fair comparison with previously published data. In addition, the user may define the efficiency level for the bottom cell as a free parameter and recalculate the FOMs for the cells from the literature. These scripts would allow easy comparison between different perovskite top cells, as presented in Figure 3a. We recommend this method of calculating the tandem cell efficiency as a function of bottom cell efficiency as an addition to experimental realization of tandem cells coupled optically during the measurement.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsenergylett.8b00598. More insights on the calculations, applicability toward two-terminal tandem cells, application to Cu(In,Ga)Se2 solar cells as the bottom partner, and fill factor dependence on light intensity (PDF) MATLAB/Octave scripts and literature data to calculate the FOMs for user-defined top cells (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49 2461 61-2594. ORCID

Thomas Kirchartz: 0000-0002-6954-8213 Jürgen Hüpkes: 0000-0001-8927-8778 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Bart Pieters (Jülich) for his programming support. The authors acknowledge financial support from the Bavarian Ministry of Economic Affairs and Media, Energy and Technology for the joint projects in the framework of the Helmholtz Institute Erlangen-Nürnberg. T.K. acknowledges support from the DFG (Grant KI-1571/2-1). C.J.B. acknowledges funding from the Bavarian SolTech Initaitve “Solar goes Hybrid”.

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REFERENCES

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