Supporting Information Kinetics of Ion Transport in Perovskite Active Layers and its Implications for Active Layer Stability Monojit Bag, Lawrence A. Renna, Ramesh Adhikari, Supravat Karak, Feng Liu, Paul M. Lahti, Thomas P. Russell, Mark T. Tuominen, and D. Venkataraman * Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003-9303, United States. Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9303, United States. Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-1730, United States. Department of Polymer Science & Engineering, University of Massachusetts, Amherst, Massachusetts 01003-9303, United States. These authors contributed equally * Correspondence should be addressed to DV (dv@umass.edu). S1
Figure S1. (a) J-V characteristics of MAPbI 3, FAPbI 3 and MA x FA 1-x PbI 3 samples (best device efficiency). Statistical distribution on the reproducibility of (b) MAPbI 3 (c) MA x FA 1-x PbI 3 perovskite solar cells. AFM height image of (d) MAPbI 3 (e) MA x FA 1-x PbI 3 (f) FAPbI 3 perovskite solar cell. Scale bar is 2 µm. Inset: magnified image of perovskite nano-crystal. S2
Figure S2. Photo-stability of MAPbI 3 and MA x FA 1-x PbI 3 perovskite solar cells under AM1.5G solar simulator 100 mwcm -2 light intensity and under white-led (20 mwcm -2 ). Devices were continuously kept under light at 0 applied bias. 3% Error bar represents measurement variability (multiple measurement) due to hysteresis. Device efficiency was normalized with respect to the initial (at t = 0 h) efficiency of the device. S3
Figure S3. MAPbI 3 Device performance parameters after prolonged exposure to light. (a) Power conversion efficiency (PCE), (b) short circuit current density (J SC ), (c) open circuit voltage (V OC ), (d) fill factor (FF), (e) series resistance (R S ) and (f) shunt resistance (R SH ). Device was exposed to AM1.5G solar simulator at 100 mw cm -2 light intensity for 70 hours with 15-minute intervals in dark for each dark impedance measurement. Filled symbol represents device parameters just before impedance measurement and open symbols represents parameters just after impedance measurement (dark interval). R S and R SH were extracted from the light J-V curve. S4
Figure S4. Device stability of three types of solar cells in dark under N 2 atmosphere inside glove box. Error bar represents 5% tolerance level accounted for the measurement error on each day. However devices were exposed to AM1.5G solar simulator at 100 mw.cm -2 optical power during J-V measurement under applied bias which could also promote the photo-degradation of MAPbI 3. S5
Figure S5. Typical device J-V characteristics under AM1.5G solar simulator at 100 mwcm -2 optical power with forward and reverse voltage-scan direction at a scan rate of 250 mv.s -1 showing hysteresis in measurement. (a) MAPbI 3 samples (b) MA x FA 1-x PbI 3 samples. Average device efficiency was 10% 11%. S6
Figure S6. Light intensity dependent impedance measurements. (a) Nyquist plot of MAPbI 3 perovskite sample under different light intensity at 0 V bias. (b) Carrier lifetime (τ e ) calculated from the high frequency component of the Nyquist plot as a function of light intensity. S7
Figure S7. (a) Nyquist plot of perovskite solar cells under dark at different bias voltages. (b) Nyquist plot of perovskite solar cells under AM1.5G solar simulator at different bias voltages. (c) Nyquist plot of P3HT:PCBM bulk heterojunction (BHJ) solar cells under dark. (d) Nyquist plot of BHJ solar cells under AM1.5G solar simulator. S8
Figure S8. Temperature dependent impedance of perovskite solar cells. Impedance plot of perovskite sample under 100 mw.cm -2 light intensity and at different temperature at 0 V applied bias for (a) MAPbI 3 (b) FAPbI 3 (c) MA x FA 1-x PbI 3. (d) Temperature dependent dark impedance plot of MA x FA 1-x PbI 3 at 800 mv bias. Inset: Dark impedance at 0 V DC bias. S9
Figure S9. Temperature dependent conductivity of MAPbI 3 sample at 0 V applied bias under AM1.5G solar simulator at 100 mw cm -2 light intensity. Ion conductivity: Activation energy barrier, E a, is also related to the ionic conductivity (σ ion ) through equation, exp where n is the number of ions and e is the ionic charge. The temperature dependent ionic conductivity (σ ion ) is independently obtained from the Warburg impedance (A W ). A plot of ln(σ ion ) vs. 1/T is linear as seen in Figure S9, the plot shows decreasing conductivity with increasing temperature for MAPbI 3. However from the diffusion coefficient measurement, we have observed E a ~56 kj.mol -1. This may be due to the trapping of ions at interfaces or loss of ions through chemical degradation. From the conductivity measurements, we estimate the ratio of charge carriers present at 306 K and at 318 K to be (n 306 :n 318 ) ~4:1. S10
Figure S10. White-LED, solar simulator, and AM1.5G solar spectrum. Solar simulator and AM1.5G spectra data were adopted from the Newport and NREL website. S11
Figure S11. (a) Device stability under commercial white-led array of 20 mwcm -2 light intensity and under AM1.5G solar simulator at 79 mwcm -2 light intensity. (b) EIS plot of MAPbI 3 perovskite solar cells under white-led (red circle) and under AM1.5G solar simulator (black square). Symbols represent impedance at 0 mv applied. S12
Figure S12. 2D diffractogram pattern for GIWAXS scattering data of (a) MAPbI 3, (b) FAPbI 3 and (c) MA x FA 1-x PbI 3 perovskite samples. (d) Circular average of GIWAXS pattern. S13
Figure S13. (a) PXRD of MAPbI3 sample at room temperature (~25 C) and after 15 min in AM1.5G solar simulator. Substrate temperature is ~45 C. (b) d-spacing shift of 3 different perovskite samples measured at room temperature as well at ~45 C. S14
Figure S14. XRD of MAPbI 3 sample at room temperature (~25 C) and after heating (~45 C substrate temperature measured by a thermocouple). Perovskite peak at 2θ = 23.48 is marked with the asterisk (*) and indicates a tetragonal phase. S15
Figure S15. (a) Cubic (Pm3m) perovskite structure showing disorder in the MA counterion. (b) Tetragonal (I4cm) perovskite structure. (c) Trigonal (P3m1) perovskite structure showing disorder in FA. (d-f) PXRD of 3 perovskite samples fabricated from sequential deposition of MAI, FAI and mixture of MAI and FAI (1:1 by wt.) on PbI 2 film. FAI sample was annealed at 160 C for 10 min and other two samples were annealed at 85 C for 30 min. Some of the perovskite peaks are highlighted with the asterisk (*) symbol to distinguish from PbI 2 peaks. (g) Crystallographic data for perovskite samples from Reitveld refinement of PXRD spectra to known structures. S16
ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY MODEL Device impedance was measured under dark conditions and under illumination at 100 mwcm -2 light intensity with variable DC bias voltages. AC amplitude was kept constant at 20 mv and the frequency (ω) was swept from 100 Hz to 1 MHz. Device temperature was monitored by a thermoelectric heater/cooler at a constant current mode. The device temperature was measured under operating condition by a thermocouple attached to the heating/cooling stage. EIS measurement of a MAPbI 3 under dark is shown in main Figure 2a. At low DC bias (< 400 mv) we observed a charge transport regime. 1 When the DC bias was increased we observed a recombination semicircle indicating only one charge transport process. Nyquist plot of MAPbI 3 at 0 V bias under light is shown in Supporting Figure S16 and main Figure 2b. Two distinct features were observed under light, a high frequency semicircle and a low frequency semicircle. Each semicircle can be modelled with simple RC component as shown in Model_1. However the low-frequency component requires a constant phase element (CPE) 2 with exponent (α ~ 0.58) much lower than unity to fit the experimental result (Model_2). The observed large photocapacitance value has been attributed to either charge accumulation at the interface 3 or the phase transition under light. 4 Ionic movement has been speculated in perovskite solar cells, 5-11 and we have observed a gradual degradation of MAPbI 3 to PbI 2 under illumination indicating that the counterions (MA + ) may diffuse towards the electrode. Hence they can form electric double layer capacitance at the electrode interface. Estimating large capacitance from the Q parameter of a CPE is thus erroneous. 2 We therefore argue that the origin of low frequency component is predominantly from the ion diffusion. Similar behavior is also observed in EIS measurement of mixed electronic and ionic conductors. 12,13 Therefore, it is intuitive to replace low frequency component with Warburg diffusion 14 as shown in Model_3. The impedance then can be written in as: S17
Figure S16. (a) Nyquist plot of MAPbI 3 sample fabricated by sequential deposition method at 0 V applied DC bias under 100 mwcm -2 light intensity. Symbol represents experimental data and line represents model fit. There are four different models used to fit the experimental data. (b) Zoomed view of the Nyquist plot shown in rectangular box. (c) Equivalent circuit of perovskite solar cells under working condition. Model_1 and Model_2 are the general circuit model used for organic photovoltaic devices. Model_3 and Model_4 are the proposed equivalent circuit for perovskite solar cells. S18
Z( jω)= A W ω ja W 1/2 ω 1/2 [1] Where A W is the Warburg impedance. j= 1 denotes complex number. Therefore, to justify the Warburg impedance model, imaginary ( Z ) and real ( Z ) component of Z(ω) vs. ω -1/2 is plotted as shown in main text Figure 2c. The slope of both the components are equal to A W. 15 This observation is unequivocal proof that the low frequency component arises from Warburg ion diffusion 15. Generalized Warburg diffusion W S is related to the equation: ( ) P ( ) P tanh jωt W S = A W W jωt W [2] Where T W is the Warburg time constant and the exponent P ~ 0.5 for finite-length Warburg diffusion (model valid for diffusion length equal to the thickness of the film). 16 The high frequency component in the Nyquist plot is represented by a combination of transport resistance (R tr ) and a geometrical or bulk capacitance (C g ). Sometimes this capacitance can be also represented as chemical capacitance C µ. Warburg diffusion is always associated with interfacial charge transfer resistance (R CT ) because of imperfect electrode and a Debye layer capacitance (C dl ) due to ion accumulation at the electrode interface. R S is the series resistance of the device. We have modified Model_3 by introducing another resistance (R electr ) in parallel to the bulk capacitance (C g ) to accommodate charge transport/recombination originating from the electronic component (free electrons and holes) but is not coupled to ion diffusion/accumulation at the interface as shown in Model_4. 17 Using ZView 3.4c (Scribner Associates Inc.) we fit the experimental data with the model using multiple iterations until the solution converges. All the circuit components and χ 2 (goodness-of-fit) values are given in Table 1. S19
Table 1. Methyl ammonium lead tri-iodide perovskite solar cells performance parameters Parameters Model_1 Model_2 Model_3 Model_4 R S (Ω) 88.67 79.96 85.85 85.66 R hf / R tr (Ω) 1300 1125 1136 1276 C hf / C g (nf) 2.70 2.87 2.58 2.58 R rec (Ω) 2206 11968 C bulk (µf), α 0.446, 1 10.2, 0.58 R CT (Ω) 57.17 207.8 C dl (F) 2.54E-8 3.43E-8 A W (Ω) 3732 13421 T W (s) / P 0.006, 0.51 0.018, 0.63 R electr (Ω) 11332 χ 2 (Error) 0.01395 0.005116 0.00437 0.00425 References 1. Fabregat-Santiago, F. et al. Characterization of nanostructured hybrid and organic solar cells by impedance spectroscopy. Phys. Chem. Chem. Phys 13, 9083-9118, (2011). 2. Zoltowski, P. On the electrical capacitance of interfaces exhibiting constant phase element behaviour. J. Electroanal. CHem. 443, 149-154, (1998). 3. Kim, H.-S. et al. Mechanism of carrier accumulation in perovskite thin-absorber solar cells. Nat. Commun. 4, (2013). 4. Juarez-Perez, E. J. et al. Photoinduced giant dielectric constant in lead halide perovskite solar cells. J. Phys. Chem. Lett. 5, 2390-2394, (2014). 5. Unger, E. L. et al. Hysteresis and transient behavior in current-voltage measurements of hybrid-perovskite absorber solar cells. Energ. Environ. Sci. 7, 3690-3698, (2014). 6. Xiao, Z. et al. Giant switchable photovoltaic effect in organometal trihalide perovskite devices. Nat. Mater. 14, 193-198, (2015). S20
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