Supporting information

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1 Supporting information Origin of Open-Circuit Voltage Loss in Polymer Solar Cells and Perovskite Solar Cells Hyung Do Kim, Nayu Yanagawa, Ai Shimazaki, Masaru Endo, Atsushi Wakamiya, Hideo Ohkita, *, Hiroaki enten, and Shinzaburo Ito Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo, Kyoto , Japan. Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 6-00, Japan. address: S-

2 . Estimation of HOMO and LUMO Levels We measured HOMO of donor by photoelectron yield spectroscopy (PYS) and LUMO of acceptor by square wave voltammetry (SWV). The resultant values are summarized in Table S. In the measurement of PYS, the analysis of the HOMO level of P3HT can be divided into two classes as shown in Figure S. This means that P3HT forms a large number of crystalline domains interconnected with amorphous regions. The shallow and deep HOMO levels of P3HT are attributed to the high crystalline regions and the amorphous regions, respectively. The deep LUMO level of amorphous P3HT was employed to evaluate the E DA in P3HT/PCM and P3HT/PFTT systems because the recombination sites are attributed mainly to P3HT/acceptor mixed region in which P3HT is amorphous rather than crystalline. On the other hand, in the measurement of SWV, the LUMO levels were calculated from the average potential of oxidation reduction peaks on the assumption that the energy level of the ferrocene/ferrocenium redox couple is 4.8 ev below the vacuum level. S S-

3 Figure S. a) Absorption (solid lines) and photoluminescence spectra (broken lines) of donor polymers: P3HT (red), PCDTT (blue), and PDTTT-EF-T (green). b) Photoelectron yield spectroscopy of the donor polymers employed in this study: PCDTT (open circles), PTQ (open triangles), and P3HT (open squares). c) Square wave voltammetry of the acceptor material films in acetonitrile/o-dichlorobenzene solutions containing 0. M of tetrabutylammonium perchlorate. The scan rate is set to be in the range of 0 50 mv s : PFTT (open circles) and PCM (open triangles). S-3

4 Table S. The HOMO level of donor and LUMO level of acceptor. Samples HOMO level (ev) LUMO level (ev) P3HT 4.95 PTQ 5. PCDTT 5.39 PDTTT-EF-T 5.0 PCM 3.85 PFTT 3.3 N S-4

5 Table S. Photovoltaic parameters of organic solar cells and perovskite solar cells under AM.5G simulated solar illumination with 00 mw cm. Device a) P3HT/PCM PTQ/PCM PCDTT/PCM P3HT/PFTT PTQ/N00 PDTTT-EF-T/N00 MAPbI 3 (mp-tio ) MAPbI 3 (d-tio ) J SC (ma cm ) 6.38 (6. ± 0.07) 8.34 (8.06 ± 0.9) 8.79 (8.53 ± 0.3) 3.3 (3.03 ± 0.0) 8. (7.94 ± 0.5) 0. (9.66 ± 0.9) 0.6 (0.4 ± 0.3) 3.5 (3.3 ± 0.36) V OC (V) FF PCE (%) (0.593 ± 0.00) (0.599 ± 0.03) (.7 ± 0.) (0.853 ± 0.0) (0.475 ± 0.03) (3.8 ± 0.0) (0.897 ± 0.0) (0.433 ± 0.0) (3.3 ± 0.08) (.4 ± 0.0) (0.470 ± 0.0) (.77 ± 0.09) (0.75 ± 0.0) (0.388 ± 0.0) (.3 ± 0.4) (0.763 ± 0.0) (0.479 ± 0.03) (3.5 ± 0.0) (.0 ± 0.0) (0.67 ± 0.0) (4. ± 0.3) (.06 ± 0.00) (0.704 ± 0.0) (7.4 ± 0.63) a) The photovoltaic parameters in parentheses are averaged for at least 6 devices. The photovoltaic parameters of perovskite solar cells were measured from. to 0.50 V (reverse scan) with a delay time of s. S-5

6 . Hysteresis of Perovskite Solar Cells Figure S. J V characteristics of the perovskite solar cells measured from 0.50 to. V (forward scan), from. to 0.50 V (reverse scan) with a delay time of s: a) mp- TiO based perovskite solar cells and b) d-tio based perovskite solar cells. All the devices were measured in a vacuum with a metal mask to give an active area of 0.09 cm. S-6

7 3. Temperature Dependence of qv OC for Polymer Solar Cells qv OC / ev.5 qv OC / ev PTQ/PCM 0.5 PTQ/N00 qv OC / ev.5 qv OC / ev.5 PCDTT/PCM Temperature / K PDTTT-EF-T/N Temperature / K Figure S3. Temperature dependence of qv OC for polymer solar cells. The solid lines are extracted by a fit to experimental data with Equation () in the text. The correlation coefficients (r) between the data and the fitting line are more than 0.99: PTQ/PCM (r = ), PCDTT/PCM (r = ), PTQ/N00 (r = ), and PDTTT-EF-T/N00 (r = ). The broken and dotted lines represent bandgap energy (E g ) and state energy (E DA ), respectively. The dashed dotted lines indicate the effective bandgap energy (E eff g ). S-7

8 4. Saturation Current (J 0 ) As reported previously, S J 0 can be given by the Arrhenius equation. eff E = g J 0 J 00 exp n k T (S) id where J 00 is the pre-exponential factor, n id is the ideality factor, and E g eff is the effective bandgap energy of the semiconductors. an idealiity factor can be set to unity. y considering radiative recombination alone, Substituting Equation (S) with n id = into J 0 of Equation (5), Equation (S) under the assumption J SC /J 0 > can be expressed by eff J 00 qv = OC Eg k T ln (S) J SC For the real PV devices, J 0 is typically not restricted to the radiative recombination current but includes an additional current via non-radiative recombination, and thus is given by J 0 = J 0,rad + J 0,non. As a result, Equation (S) can be rewritten as Equation (7) in the main text. ased on J 0,rad = qn(t), J 0,rad can be derived by the integraion of N(E,T) with the step funtion of η(e) on the Equation (4) in the text. As a result, J 0,rad is given by S3 qk T E Eulk E J 0, rad = η γ + ( η0 η ) γ ulk exp exp 3 4π h c kt kt (S3) Here, γ and γ ulk are given by γ γ ulk = ( E = ( E + k T ) ulk + k T ) + k T + k T = E = E + k TE ulk + k TE + k T ulk + k T (S4) Equation (S3) has the same structure of Equation (S) in which an ideality factor of n id S-8

9 = and E g eff is identified with E, and hence J 00 is given by qk T E J 00 = η γ + ( η0 η ) γ ulk exp 3 4π h c E k T ulk (S5) As a result, the voltage loss in PV devices can be quantitatively split into two types of recombination processes based on Equation (6) in the main text taking into account J 0 that both radiative and non-radiative recombination contribute to the device current. S-9

10 5. Simulation of Voltage Loss in Polymer Solar Cells qv OC / V. qv OC / V PTQ/PCM P3HT/PFTT.4.4 qv OC / V. qv OC / V. 0.8 PCDTT/PCM Temperature / K 0.8 PTQ/N Temperature / K Figure S4. Temperature dependence of qv OC split into two types of loss processes based on the modified SQ theory in polymer solar cells. The dashed dotted lines represent the effective bandgap energy (E eff g ). The black broken lines are the calculated values on the basis of Equation (6) taking into account J 0 that both the radiative and non-radiative recombinations contribute to device current. This is in good agreement with the grey solid lines, which were extracted by a fit to experimental data with Equation in the text. The correlation coefficients (r) between the data and the fitting line are more than 0.99: PTQ/PCM (r = ), PCDTT/PCM (r = ), P3HT/PFTT (r = 0.996), and PTQ/N00 (r = ). The blue dashed two-dotted lines represent thermodynamically inevitable loss in qv OC as a function of temperature. In this simulation, β = J 0,non /J 0,rad was employed as a fitting parameter, which is independent of temperature. Each experimental J SC measured was used to fit the temperature dependent V OC. η A was fixed at for all the polymer solar cells. S-0

11 S-

12 6. Fitting Parameters on the Simulation of Voltage Loss Table S3. The fitting parameters on simulation of voltage loss in polymer solar cells and perovskite solar cells. Devices J SC exp (ma cm ) a) η A β E eff g (ev) P3HT/PCM PTQ/PCM PCDTT/PCM P3HT/PFTT PTQ/N PDTTT-EF-T/N MAPbI 3 (mp-tio ) MAPbI 3 (d-tio ) a) J exp SC is the experimental photocurrent measured under AM.5G simulated solar illumination with 00 mw cm. S-

13 References [S] Pommerehne, J.; Vestweber, H.; Guss, W.; Mahrt, R. F.; ässler, H.; Porsch, M.; Daub, J. Efficient Two Layer LEDs on a Polymer lend asis. Adv. Mater. 995, 7, [S] Sze, S. M. Physics of Semiconductor Devices, nd ed; John Wiley & Sons: New York, 98. [S3] Hörmann, U.; Lorch, C.; Hinderhofer, A.; Gerlach, A.; Gruber, M.; Kraus, J.; Sykora,.; Grob, S.; Linderl, T.; Wilke, A.; Opitz, A.; Hansson, R.; Anselmo, A. S.; Ozawa, Y.; Nakayama, Y.; Ishii, H.; Koch, N.; Moons, E.; Schreiber, F.; rütting, W. V OC from a Morphology Point of View: The Influence of Molecular Orientation on the Open Circuit Voltage of Organic Planar Heterojunction Solar Cells. J. Phys. Chem. C 04, 8, S-3