Supporting Information. The Potential of Multi-Junction Perovskite Solar Cells

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1 Supporting Information The Potential of Multi-Junction Perovskite Solar Cells Maximilian T. Hörantner 1,4 *, Tomas Leijtens 2, Mark E. Ziffer 3, Giles E. Eperon 3,5, M. Greyson Christoforo 4, Michael D. McGehee 2, Henry J. Snaith 4* 1 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, USA 2 Department of Materials Science, Stanford University, 476 Lomita Mall, Stanford CA 94305, United States 3 Department of Chemistry, University of Washington, Seattle, Washington WA 9195, USA 4 Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, OX1 3PU, Oxford, United Kingdom 5 Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK These authors contributed equally to the work. *Corresponding authors: maxhoer@mit.edu, henry.snaith@physics.ox.ac.uk Methods: Spectroscopic ellipsometry was measured on films of MA0.4FA0.6Sn0.6Pb0.4I3 on both glass substrates and Si substrates (300 nm thermal oxide) using a J.A. Woollam M2000 ellipsometer. For samples on glass, measurements of the polarization state of reflected light (ψ and ) were taken with Scotch tape adhered to the back side of the glass substrates to scatter any backside reflections at glass/sample chuck interface. Transmittance of the glass samples was also

2 measured on the Woollam M2000 and was used as an additional data set to help constrain the fits for modelling the optical constants and thicknesses using the CompleteEASE software package. Figures S2 a and b show the fits to the ψ and data along with the transmittance data for the glass/ma0.4fa0.6sn0.6pb0.4i3 sample. The n and κ values for the glass substrate were determined independently on a blank glass substrate. To model n and κ for the MA0.4FA0.6Sn0.6Pb0.4I3, the data was first fit in the transparent region of the sample only ( nm) using a Cauchy dispersion model, with the thickness of the MA0.4FA0.6Sn0.6Pb0.4I3 layer constrained close to the thickness measured using a Bruker Dektak profilometer ( nm). The Cauchy model in the transparent region was then re-parameterized using a Kramers-Kronig consistent B-spline model. 1 The K-K consistent B-spline model was then extrapolated into the absorbing region (~ nm) by simultaneously fitting the ψ and data along with the transmittance data. Throughout the fits the thickness was constrained to be close to 145 nm. The final fits gave a thickness of nm for the MA0.4FA0.6Sn0.6Pb0.4I3 layer including a surface roughness layer of 6.2 nm. The optical constants modelled for MA0.4FA0.6Sn0.6Pb0.4I3 from the glass/ MA0.4FA0.6Sn0.6Pb0.4I3 sample were then used to fit the (ψ and ) data measured on the Si/ MA0.4FA0.6Sn0.6Pb0.4I3 sample. A model for the Si substrate was determined by measuring a blank reference Si substrate. The fits to the ψ and data measured for the Si/ MA0.4FA0.6Sn0.6Pb0.4I3 sample are shown in Figure S2c. The fitted thickness for the MA0.4FA0.6Sn0.6Pb0.4I3 layer was nm with a surface roughness of 5.23 nm. The thickness was close to that measured on a profilometer ( nm). Based the agreement between the fits for the data on the glass/ MA0.4FA0.6Sn0.6Pb0.4I3 and Si/ MA0.4FA0.6Sn0.6Pb0.4I3 samples using a common n and κ model, along with the agreement in the fitted thicknesses with the experimentally measured values we determined the n and κ model for MA0.4FA0.6Sn0.6Pb0.4I3 to be correct.

3 All subsequent optical and device modelling was carried out with the exact same methodology described by Hoerantner and Snaith 2. In short, optical constants and thicknesses were used to calculate the absorption spectra of all active layers via a transfer matrix model. With the assumption of IQE = 1, these were taken as the device EQEs, which could then be combined with the detailed balance limit formulation and a one-diode equivalent circuit model to derive the combined JV curves of the devices. A differential evolution algorithm was used to optimize the thicknesses for maximum PCE. For energy yield simulations, the hourly changing incidence angles and power of the direct and diffuse spectra were combined with the TMM and device model and then summed up to yield an annual energy output. Shockley Queisser limits of multi-junction devices: From a purely theoretical perspective, the efficiency potential of multi-junction solar cells can be evaluated by calculating the detailed balance limit for varying bandgap combinations. This thermodynamic approach assumes that every photon with an energy within the band gap of the absorbing material will be absorbed and will excite an electron. We carried out such calculations for three different multijunction architectures. For double junction solar cell devices, we varied the bottom layer and top layer bandgaps in the range from ev and calculated the expected PCE of the combined device assuming that all photons with energy greater than the top cell bandgap are absorbed in the top cell and all photons with energy between the top cell bandgap and bottom cell bandgap are absorbed in the bottom cell. We show the results on a contour plot in Figure S1a. For the triple junction architectures, we modelled a stack with a bottom absorber of fixed bandgap and then varied the overlying middle and top absorber bandgaps in a similar manner. To estimate the maximum efficiency of allperovskite triple-junction solar cells we assumed a base absorber with 1.22 ev, which is

4 currently the lowest achievable perovskite bandgap in efficient solar cells 3 (see Figure S1b). We used the same calculation with a base absorber bandgap of 1.1 ev (see Figure S1c) to judge the gain from two perovskite layers on top of a silicon solar cell. We find that the all-perovskite triple-junction can lead to efficiencies of 46.9 % when combining absorber layers with bandgaps of ~2.1 ev and ~1.6 ev on top of the 1.22 ev base absorber, which is only slightly higher than the Shockley-Queisser limit of double-junctions with an ideal bandgap combination, at 46.0%. However, the lower bandgap of silicon allows for an additional PCE gain to 49.4 %, when employing bandgaps of ~1.5 ev and ~2.0 ev for the middle and top junction. Figures and tables: Figure S1: a) Calculated Shockley-Queisser limits for double junction and of triple junction solar cells for base absorbing material with a band gap of (b) 1.22 ev (similar to low band gap perovskite) and (c) 1.1 ev (similar to silicon).

5 Figure S2: a.) and b.) ψ and data for three angles of incidence (55, 65, 75 ) along with c.) transmittance data measured on the glass/ MA 0.4FA 0.6Sn 0.6Pb 0.4I 3 sample. Fits to the data based on the model described above are shown by the black solid lines. d.) and e.) ψ and data for three angles of incidence (55, 65, 75 ) measured on the Si/ MA 0.4FA 0.6Sn 0.6Pb 0.4I 3 sample. Fits to the data using the optical constants derived for MA 0.4FA 0.6Sn 0.6Pb 0.4I 3 from the glass/ MA 0.4FA 0.6Sn 0.6Pb 0.4I 3 sample are shown by black solid lines.

6 Figure S3: Measured refractive index (n, green line) and extinction coefficient (k, blue line) of MA 0.4FA 0.6Sn 0.6Pb 0.4I 3 perovskite film (a). The data can be found in.csv format as additional Supporting Information. Modelled JV curve of single junction MA 0.4FA 0.6Sn 0.6Pb 0.4I 3 based device compared to experimentally obtained JV characteristic (b). Single-diode model parameters: n = 1.04, R S = 4x10-2 mω cm 2, R SH = 10 MΩ cm 2, EQE EL = 0.56 %. Figure S4: PCE of optimised 2PJ for varying maximum allowed bottom absorber thicknesses (a). Corresponding JV curves of devices with varying maximum bottom absorber thicknesses in nm (b).

7 Figure S5: EQEs comparing optimised 2PJ stack with currently feasible materials and thicknesses (as displayed in Figure 1a) with the same stack in which no glass is used (a); with a stack that replaces PEDOT:PSS with NiO (b); with a stack containing no ITO layers between recombination layers (c); with a stack that allows all charge transporting layers to be 5 nm thin (d), with a stack that is optimised for maximum absorption as depicted in Figure S6 (e). Corresponding JV curves of all comparing devices (f).

8 Figure S6: EQEs comparing optimised 3PJ stack with currently feasible materials and thicknesses (as displayed in Figure 1a) with the same stack in which no glass is used (a); with a stack that replaces PEDOT:PSS with NiO (b); with a stack containing no ITO layers between recombination layers (c); with a stack that allows all charge transporting layers to be 5 nm thin (d), with a stack that is optimised for maximum absorption as depicted in Figure S6 (e). Corresponding JV curves of all comparing devices (f).

9 Figure S7: a) Illustration of the 2PJ, 3PJ and 2PSJ architectures for optically ideal conditions. The thickness range used in the optical model for each layer is written upon the illustration and detailed in Table S1, S2, S3. b) All-perovskite double junction PCE for varied band-gap combinations of bottom and top absorber. c) All-perovskite triple junction solar cell PCE for varied band-gap combinations of bottom and top absorber on top of perovskite base absorber with fixed 1.22 ev band-gap. d) Perovskiteperovskite-silicon triple junction solar cell PCE for varied band-gap combinations of bottom and top perovskite absorber on top of fixed band-gap SHJ base absorber.

10 Figure S: EQEs and JV curves of optimised 2PSJ devices with 1.5 ev bandgap perovskite as bottom absorber for currently feasible materials and layer thicknesses (a,c), for optically ideal materials and layer thicknesses (b,d).

11 Table S1: Tabulated materials (and references for optical constants), thickness ranges for optimisations and resulting optimal thicknesses of 2PJ devices for currently feasible materials and layer thicknesses (left), for optically ideal materials and layer thicknesses (right) that have been used to calculate EQEs and JV curves in Figure 2a,d,g,j. Material Thickness range (nm) Optimal thickness (nm) 4 MgF Glass 1 mm 1 mm ITO NiO E g > 1.4 ev ev) 1.3 ev) C SnO ITO PEDOT:PSS Perov. (Fig S3) E g < 1.4 ev ev) (fixed E g: 1.22 ev) C Ag Material Thickness range (nm) Optimal thickness (nm) 4 MgF ITO NiO E g > 1.4 ev Perov. (Fig S3) E g < 1.4 ev ev) 1.0 ev) 1500 C NiO ev) (fixed E g: 1.22 ev) C Ag

12 Table S2: Tabulated materials (and references for optical constants), thickness ranges for optimisations and resulting optimal thicknesses of 3PJ devices for currently feasible materials and layer thicknesses (left), for optically ideal materials and layer thicknesses (right) that have been used to calculate EQEs and JV curves in Figure 2b,e,h,k. Material Thickness range (nm) Optimal thickness (nm) 4 MgF Glass 12 1 mm 1 mm ITO NiO E g > 1.4 ev ev) 2.04 ev) 1500 C SnO ITO NiO E g > 1.4 ev ev) 1.5 ev) 1500 C SnO ITO PEDOT:PSS Perov. (Fig S3) E g < 1.4 ev (fixed E g: 1.22 ev) (fixed E g: 1.22 ev) C Ag Material Thickness range (nm) Optimal thickness (nm) 4 MgF ITO NiO E g > 1.4 ev E g > 1.4 ev ev) 2.04 ev) 2. C NiO ev) Perov. (Fig S3) E g < 1.4 ev 1.5 ev) 1500 C NiO (fixed E g: 1.22 ev) (fixed E g: 1.22 ev) 1500 C Ag

13 Table S3: Tabulated materials (and references for optical constants), thickness ranges for optimisations and resulting optimal thicknesses of 2PSJ devices for currently feasible materials and layer thicknesses (left), for optically ideal materials and layer thicknesses (right) that have been used to calculate EQEs and JV curves in Figure 2c,f,i,l. Material Thickness range (nm) Optimal thickness (nm) 4 MgF Glass 12 1 mm 1 mm ITO Spiro E g > 1.4 ev ev) 1.95 ev) C Spiro E g > 1.4 ev ev) 1.44 ev) C ITO a-si (p) a-si (i) c-si mm 3.5 mm a-si (i) a-si (n) ITO Ag Material Thickness range (nm) Optimal thickness (nm) 4 MgF ITO NiO E g > 1.4 ev E g > 1.4 ev ev) 1.95 ev) C NiO ev) optimal E g: (1.44 ev) C ITO a-si (p) a-si (i) c-si mm 3.5 mm a-si (i) a-si (n) ITO Ag

14 Table S4: Tabulated materials (and references for optical constants), thickness ranges for optimisations and resulting optimal thicknesses of 2PSJ devices with 1.5 ev bandgap perovskite as bottom absorber for currently feasible materials and layer thicknesses (left), for optically ideal materials and layer thicknesses (right) that have been used to calculate EQEs and JV curves in Figure S. Material Thickness range (nm) Optimal thickness (nm) 4 MgF ITO Spiro E g > 1.4 ev ev) 2.0 ev) C Spiro E g > 1.4 ev (E g fixed: 1.5 ev) (fixed E g: 1.5 ev) C ITO a-si (p) a-si (i) c-si mm 3.5 mm a-si (i) a-si (n) ITO Ag Material Thickness range (nm) Optimal thickness (nm) 4 MgF ITO NiO E g > 1.4 ev E g > 1.4 ev ev) 2.0 ev) C NiO (E g fixed: 1.5 ev) (E g fixed: 1.5 ev) C ITO a-si (p) a-si (i) c-si mm 3.5 mm a-si (i) a-si (n) ITO Ag

15 Figure S9: All-perovskite double junction energy yield in Seattle for varied band-gap combinations of bottom and top absorber with currently feasible thickness constraints (a) and with optically idealised thickness constraints (d). All-perovskite triple junction solar cell energy yield in Seattle for varied bandgap combinations of bottom and top absorber on top of fixed perovskite base absorber (E g = 1.22 ev) with currently feasible thickness constraints (b) and with optically idealised thickness constraints (e). Perovskite-perovskite-silicon triple junction solar cell energy yield in Seattle for varied band-gap combinations of bottom and top perovskite absorber on top of fixed band-gap SHJ base absorber with currently feasible thickness constraints (c) and with optically idealised thickness constraints (f). References: (1) Johs, B.; Hale, J. S. Dielectric Function Representation by B-Splines. Phys. status solidi 200, 205, (2) 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. 2017, 10, (3) Eperon, G. E.; Leijtens, T.; Bush, K. A.; Prasanna, R.; Green, T.; Wang, J. T.-W.;

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