Performance Evaluation of Semitransparent Perovskite Solar Cells for

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Letter

Performance Evaluation of Semi-Transparent Perovskite Solar Cells for Application in Four-Terminal Tandem Cells Thomas Kirchartz, Sophie Korgitzsch, Juergen Huepkes, César Omar Ramírez Quiroz, and Christoph J. Brabec ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.8b00598 • Publication Date (Web): 11 Jul 2018 Downloaded from http://pubs.acs.org on July 11, 2018

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ACS Energy Letters

Performance Evaluation of Semi-Transparent Perovskite Solar Cells for Application in FourTerminal Tandem Cells Thomas Kirchartz1,2, Sophie Korgitzsch1, Jürgen Hüpkes1*, César O. R. Quiroz3, Christoph J. Brabec3,4 1

IEK5-Photovoltaics, Forschungszentrum Jülich, 52425 Jülich, Germany Faculty of Engineering and CENIDE, University of Duisburg-Essen, Carl-Benz-Str. 199, 47057 Duisburg, Germany 3 i-MEET, Friedrich-Alexander University Erlangen-Nürnberg, Martensstrasse 7, 91058 Erlangen, Germany 2

4

Bavarian Center for Applied Energy Research (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, Germany

[email protected] [email protected] *Corresponding Author [email protected], tel: +49 2461 61-2594, ORCID®: 0000-0001-8927-8778 [email protected] [email protected]

1

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Abstract The efficiency of perovskite-based tandem solar cells and the respective efficiency gain over the single junction operation of the bottom cell strongly depends 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 literature. We focus on 4-terminal configurations but also estimate and discuss the differences between 4- and 2terminal 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 future.

TOC GRAPHICS

gain

ηtop(%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

loss ηsilicon(%)

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While crystalline silicon solar cells1 are approaching their fundamental efficiency limits,2 substantial further efficiency improvements require the combination of silicon with a high bandgap solar cell in a tandem configuration.3-4 Metal-halide perovskite based solar cells are currently the only non-III-V material with sufficiently high efficiencies for application as the high bandgap partner for crystalline Si in two or four-terminal tandem solar cells.3, 5-6 While two-terminal tandem cells have the advantage of reducing the number of transparent contacts and therefore the amount of parasitic absorption, four-terminal (4T) tandem solar cells bear several advantages: The bandgap restrictions for the top cell imposed by the choice of bottom cell targeting energy yield are more relaxed,4-5,

7

higher energy yield was predicted by

simulations for various top cell bandgaps 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 four-terminal 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 just consist of a gap of air or transparent glue as optical coupler.10-11 The gap by itself 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 towards 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 four-terminal tandems, the development of semi-transparent perovskite top cells meets several challenges: At first, the overall electrical device performance must outperform the bottom cell in terms of a higher 3 ACS Paragon Plus Environment

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product in order to profit from the tandem device concept. Secondly, the reduction of parasitic absorption in the electron and hole transport layers and the transparent conductive anode and cathode layers must be extended towards 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 lead 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, which is independent of the experimentally available bottom cell. Though, a precise determination of the 4T tandem cell performance requires the measurement of the two optically coupled sub cells, 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 an 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 an 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 4 ACS Paragon Plus Environment

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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 the top cell. Second, the electrical properties of the bottom cell are well approximated by a single diode model and variations of fill factor with light intensity are negligible. In order to calculate the efficiency of a given four-terminal 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 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 external quantum efficiency of the bottom cell in single junction operation, the top cell transmittance, and the solar spectrum . Using

=

≡

= ,

(1)

we obtain a corrected short circuit current density for the bottom cell. We also introduced a weighted transmittance , which is a scalar value derived from with the spectral photocurrent density of the bottom solar cell as weighting factor. For monolithic tandem cells should ideally have a value 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 open-circuit voltage Voc. The new can be written as

= +

! " #

'*+,

ln & '()( ()

(2)

where is the open-circuit voltage of the bottom cell operated as a single junction device

under one sun conditions. However, depends logarithmically on the short circuit current 5 ACS Paragon Plus Environment

ACS Energy Letters

density, therefore a typical reduction of is on the order of . /0 ln 2 ≈ 20 mV and thus is quite small. While any change in would also affect the fill factor , a change of around . /0 in leads to even smaller relative changes in . In addition, including changes of as a function of light intensity would require assumptions on the limitations of the in these devices (i.e. series resistance effects relative to losses due to the ideality factor being > 1). Therefore, we neglected changes in for this study, but we present a brief estimate of the magnitude of the effect in the supporting information.

(a)

Si single cell [12] 250

Power density P (W m-2 eV-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(η = 26.6 %)

(η = 20.3 %)

Tandem

200

(b)

Si single cell [14]

Tandem

(η = 27.1 %)

(η = 24.4 %)

150

Top cell [13]

Top cell [13]

(η = 16.4 %)

100

(η = 16.4 %)

50

Si bottom cell

Si bottom cell 0

1.5

2.0

2.5

3.0

1.5

Energy E (eV)

2.0

2.5

3.0

Energy E (eV)

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 four-terminal tandem solar cells. Panel (a) shows a high efficiency Si solar cell12 with the perovskite top cell by Quiroz et al.13 Panel (b) shows the 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 area, respectively.

Based on Eqs. (1) and (2), we calculate the efficiency of a four-terminal 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 nm to 1200 nm) as well as the efficiency 5 , 6 ACS Paragon Plus Environment

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, and 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 Fig. S2 in supporting information) as long as the reflectance of the bottom cell to air and effects are sufficiently low to be neglected. With these assumptions and using the of the top cell, Figure 1 illustrates the potential efficiency gain due to the increased (and increased 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 performance7, 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 performance 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 wafer14 (as shown in Figure 1b), the improvement is much more impressive (4.1 %) while the total tandem cell efficiency is lower than the tandem cell from Figure 1a. Note, that the values provided here are based on 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 7 ACS Paragon Plus Environment


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by a substantial increase of the product of the top cell relative to the one of the bottom cell. In order to develop some general figures of merit to quantify the quality of a given top cell, we have taken data of semitransparent perovskite solar cells13,

15-25

combined them with a range of silicon solar cells1, 12, 14,

from the literature. Upon

25, 28-40

or modules26-27 and

thorough literature inspection, we only selected references, where top cell transmittance and silicon cell were provided over the relevant range. The efficiency and short circuit current densities of the silicon cells were recalculated by using their 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, short circuit current density and open circuit voltage from forward and backward sweep or otherwise as given in the papers. In the first two cases the fill factors were calculated according to the averaged values. Though we observed deviations in short circuit current densities between 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 yintersect of the linear relation. Based on Eqs. 1 and 2 and using the measured efficiencies of the component cells and short circuit current density and open circuit voltage of the bottom cell operated as single junction cell we calculated the tandem cell efficiency: 56 = =

*+, 7 *+, '() +) ( '()

( 7+)

5 + 5

@

# 8A " ,+9 : :;: ( : : ?: ( '()

&1 +

! " ( # 7+)

ln - 5 + 5 .

(3)

Figure 2a shows the tandem cell efficiencies calculated from four selected top cells combined with 24 silicon bottom cells as function of the silicon cell efficiency 5 . 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 single 8 ACS Paragon Plus Environment

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junction operation (56 = 5 ). 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.

Efficiency ηtan (%)

28

ng Duo

(a)

17

(b)

7 ng1 Duo

7 Fu1

Fu17

24 20

Efficiency difference ηtan-ηsi (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

8 4 0

16 Chen 5 1 z Kran

16 Chen 5 1 z Kran

ηsi

(c) Che

ηSi

(d) Duon g17 Fu1 7

n16

Kran z

15

Che n16

Kran z1

Duo ng17 Fu 1 7

5

-4 16

18

20

22

24

Efficiency ηsi (%)

26

16

18

20

22

24

26

Efficiency ηsi (%)

Figure 2: Four-terminal tandem solar cell efficiency as a function of the Si single junction cell efficiency. Panel (a) shows the case where several perovskite top cells18-19, 21-22 are combined with various Si solar cells taken from literature and the lines are linear fits to the data. Panel (b) shows equivalent data but this time keeping the quantum efficiency for all silicon solar cells the same and just changing their CD 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. Panels (c) and (d) show the efficiency difference of the tandem cell relative to the Si cell (i.e. the distance to the dashed line in panels (a) and (b)). Figure 2b therefore shows an even simpler model, where the of the Si solar cell was kept constant (using the one from ref. 12) but the 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

spectrum. Figure 2c and d show the corresponding absolute efficiency difference relative to 9 ACS Paragon Plus Environment


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the single junction operation of the Si solar cell. The difference decreases strongly for higher values of the Si cell efficiency. Based on Figure 2, there is a range of tandem efficiency values that could describe the quality of a top cell. Obviously, both approaches (Figure 2a or b) can be summed up by a linear relation between 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 and the loss in of the bottom cell with the filtered irradiation as compared to the single junction operation. The efficiency 56 5 =

*+, 7+) ( 7+)

5 + 5 = &1 +

! " ( # 7+)

ln - 5 + 5

≡ E 5 + 5 ,

(4)

can be described mathematically by the y-axis intercept 5 and the slope of the linear relation. Note, that the intercept 5F of the lines slightly differs from the top cell efficiency 5 (see also Figure S1 in supporting information). The parameter E describes the loss in with light intensity and it is typically very close to unity. Assuming = 0.4 we obtain E = 0.97 assuming a realistic for a high efficiency silicon solar cell of 720 mV and an ideality factor of KL = 1. Thus, the slope in Figure 2

?M,N> ?M(

is mostly given by just the

weighted transmittance , 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, top cell efficiency 5 and effective transmittance . However, top cells of different efficiency might result in similar tandem efficiencies due to compensation by . In order to compare the various top cells for realistic scenarios we provide 56 rather than the top cell efficiency only, and chose a relevant silicon bottom cell technology with 5 = 25% as basis. 10 ACS Paragon Plus Environment

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linear regression VocFF variation

(a) 0.48

19

0.44

25

24 22 26 27 16 22

0.40

15 26 27 16 17 15 17

0.36 0.32 0.28

21 13

20 2324 20

21

transparency

19 13

23

18

22

24

(b)

26

19

13

26 24 21 23

24 20

18

22 22 1615 26 2717

20

18

18

20

Efficiency ηtan(ηsi=25%) (%)

efficiency

Slope dηtan/dηsi

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

25

28

10

12

14

16

Top cell efficiency ηtop (%)

Efficiency ηtan(ηsi=25%) (%)

Figure 3: a) Slope dηtan/dηsi (according to Figure 2a (spheres) and b (open squares)) vs. tandem cell efficiency for a range of perovskite top cells from 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) Four-terminal 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 two FOMs, tandem cell efficiency 56 5 = 25% and the slope given by Eq. (4) are calculated for a variety of semi-transparent perovskite solar cells. The spheres and open squares in Figure 3a correspond to the fits to experimental data and the results using the simplified 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 5 = 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 wafer based solar cells typically exhibit quite similar spectral 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,


ACS Energy Letters

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 single junction 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 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 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 Refs13, 19 and18 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 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 Fig. S2 in supporting information).

(a)

4-terminal tandem cells

25 VOC of top cell limited to 1250 meV

20 top cells 15

10

2-terminal tandem cells 1.4

1.6

1.8

2.0

Photovoltaic bandgap Egap

PV

0.6

(b)

2.1 2.0 1.9

0.5

VOC = VOC,0 + ∆EgapPV VOC, max = 1250 meV top cell of Quiroz et al.

1.60

0.4 1.5 0.3

1.4 EgapPV = 1.3 eV

0.2 20

(eV)

1.8

transparency

30

Transmittance x voltage loss Teff γ

4-terminal tandem cell efficiency

Efficiency ηtop , ηtan (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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22

24

26

28

Efficiency η4T-tan(ηsi=25%) (%)

Figure 4: a) Efficiencies of top and tandem cells calculated after shifting the photovoltaic YZ bandgap X6 of the top cell. b) Effective transmittance times voltage loss factor γ versus tandem cell efficiency for the variation of the photovoltaic bandgap. The red asterisk indicates 12 ACS Paragon Plus Environment

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the original top cell of Quiroz et al.13 Note the deviation between integrated power density and efficiency data from literature (Figures 2, 3). The open symbols represent a shift of top cell with the bandgap, while solid symbols represent the constrained model. The effective transmittance and open circuit voltage of the top cell should vary with its bandgap. However, we could not observe any significant trend in the dependence of or on the perovskite bandgap. This means, that the transparency and Voc in most of the cells are not governed by the actual perovskite bandgap, 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 modified top cell bandgap. As a point of reference, we used the inflection point of the external quantum efficiency, which we YZ 42 denote as photovoltaic bandgap X6 . In order to modify the bandgap we have stretched and

compressed the energy axis above and below the photovoltaic bandgap and used the resulting transmittance and quantum efficiency data for the efficiency calculations. We used two YZ YZ models for the open-circuit voltage. The first model assumes \] ^ X6 _ = \], + ` X6 , YZ where ` X6 is the difference in bandgap relative to the bandgap 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 2-terminal 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 4-terminal tandem cells exhibit their maximum of 28.5% at top cell bandgaps well beyond the maximum for single junction perovskite cells. In case of constrained \] , the highest tandem cell efficiency is slightly reduced to 28.1%. At the 13 ACS Paragon Plus Environment


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bandgap of 1.65 eV the 2-terminal tandem cells exhibit their maximum of 27.5%, which is 1% lower than the best 4-terminal configuration. The lower efficiency and discrepancy of the maxima of 2- and 4-terminal tandem cells would be reduced for top cells approaching the Shockley-Queisser limit. The tendencies roughly agree to previously reported data,4,

8

however, the exact numbers derived from our calculations for 2-terminal 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 curves. Figure 4b shows the figure of merits calculated for the bandgap variation. The data of Figure 3a relate to the values E averaged over the ensemble of silicon bottom cells, while the data for bandgap variation represent the actual effective transmittance and voltage loss parameter calculated for the record silicon cell by Yoshikawa et al.12 The given effective transmittance increases in the evaluated range of bandgaps from 23% to 63%. In conclusion, we have presented a simple method to estimate the performance of semitransparent perovskite solar cells for applications in four-terminal tandem cells. The general requirements of top cells for highest tandem cell performance are high and low parasitic absorption in the relevant wavelength range. Note that transparency and are functions of the perovskite bandgap with opposing trends and perovskite bandgap 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 fourterminal tandem cells as a function of bottom cell efficiency in analogy to Figure 2. The advantages of this method are the two scalar values and the simplicity to derive 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 to evaluate 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 free parameter and recalculate the figures of merit for 14 ACS Paragon Plus Environment

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the cells from 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.

Supporting Information Available: More insights on the calculations, applicability towards 2-terminal tandem cells, application to Cu(In,Ga)Se2 solar cells as bottom partner, fill factor dependence on light intensity, MATLAB®/Octave script and literature data to calculate the FOMs for user-defined top cells.

Acknowledgements 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 ErlangenNürnberg. TK acknowledges support from the DFG (Grant KI-1571/2-1). CJB acknowledges funding from the Bavarian SolTech Initaitve "Solar goes Hybrid".

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Yoshikawa, K.; Kawasaki, H.; Yoshida, W.; Irie, T.; Konishi, K.; Nakano, K.; Uto, T.; Adachi, D.; Kanematsu, M.; Uzu, H. et al. Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%. Nat. Energy 2017, 2 (5), 17032/1-8. Richter, A.; Hermle, M.; Glunz, S. W. Reassessment of the limiting efficiency for crystalline silicon solar cells. IEEE J. Photovoltaics 2013, 3 (4), 1184-1191. Werner, J.; Niesen, B.; Ballif, C. Perovskite/silicon tandem solar cells: marriage of convenience or true love story? – An overview. Adv. Mater. Interfaces 2017, 1700731,1-19. 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. Eperon, G. E.; Hörantner, M. T.; Snaith, H. J. Metal halide perovskite tandem and multiple-junction photovoltaics. Nat. Rev. Chem. 2017, 1, 0095/1-18. 15 ACS Paragon Plus Environment


(6)

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TOC Figure 299x199mm (300 x 300 DPI)



Figure 1 279x180mm (300 x 300 DPI)


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Figure 2 289x187mm (300 x 300 DPI)



Figure 3 400x199mm (300 x 300 DPI)


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Figure 4 400x199mm (300 x 300 DPI)


Performance Evaluation of Semitransparent Perovskite Solar Cells for

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