Supplementary Information for:

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1 Supplementary Information for: In-situ measurement of electric-field screening in hysteresis-free PTAA/ FA.83 Cs.7 Pb(I.83 Br.7 ) 3 /C6 perovskite solar cells gives an ion mobility of ~3 x -7 cm /Vs; to 4 orders of magnitude faster than reported in metal-oxide-contacted perovskite cells with hysteresis. Luca Bertoluzzi, Rebecca A. Belisle, Kevin A. Bush, Rongrong Cheacharoen, Michael D. McGehee, Brian C. O'Regan * Photo S. Scanning electron micrograph of the fractured edge of a ITO/PTAA/ FA.83 Cs.7 Pb(I.83 Br.7 ) 3 /C6/BCP/Ag cell. S

2 a 5 b Photocurrent, ma/cm Current, ma/cm 5.7 Sun Forward.7 Sun Reverse Dark Voltage, V Voltage, V.8.. c d Current, ma/cm 5.7 Sun Forward.7 Sun Return Dark Current, ma/cm 5 Forward Reverse Forward Reverse..4.8 Voltage, V Voltage, V Figure SI_ a) JVs for 5 different cells with the composition ITO/PTAA/FA.83 Cs.7 Pb(I.83 Br.7 ) 3 /C6/ BCP/Ag and one cell where Cs + is replaced by MA + (dashed line). Illumination: simulated AM.5. The JV's were scanned from. volt to -. V. The ITO/PTAA/FA.83 Cs.7 Pb(I.83 Br.7 ) 3 /C6/BCP/Ag cells come from 3 different batches made 3 months apart. b-d) Cyclic JV scans under ~.7 sun white LED light. Scan rate V/s. The cells were equilibrated for ~ min at short circuit and then scanned to forward and immediately reverse. b,c) Cell composition ITO/PTAA/ FA.83 Cs.7 Pb(I.83 Br.7 ) 3 /C6/BCP/Ag. d) Two similar cells with MA + replacing Cs +. One has no hysteresis, the other has a small amount of "inverse" hysteresis wherein the Jsc is lower on the return scan. The transients for both MA + cells were essentially identical to the Cs + cells, implying that the inverse hysteresis is probably not directly mediated by the ion movement..8.. S

3 Photocurrent, µa/cm Ions at dark SC position Probe a Voltage Photocurrent, µa/cm Ions Moved by 5 ms at.8 V Probe b Voltage.75 V.85 V.95V. V.5 V. V. V Time, µs Time, µs 4 6 c V.3 V.4 V.7 V x -6 - x Fig SI_ a,b. a) Transient data from figure a without vertical offsets. The voltage step to the probe voltage occurs at -5 µs. b) Transient data from figure b without vertical offsets. c) Transients with lower pulse intensity (~. mw/cm relative.7 mw/cm for a and b. In c, the transients at intermediate voltages have a lower slope during the pulse, consistent with the slope being related to charge accumulation. We have generally used ~.7 mw/cm because of the low signal to noise in the data with the lower intensity. S3

4 3 a 4 b Jtr-6µs, ma/cm Jtr-6µs, µa/cm - -4 ~ mw Pulse µs 3 µs.5 ms ~. mw Pulse J x 4.7 µs 3 µs.5 ms..4.8 Probe Voltage, V...4 Probe Voltage, V.8 Potential Change Across RII ( V RII ), V Time, ms Avg -4 µs Avg 4-8 µs Avg -4 µs 4 5 c Potential Change Across RII ( V RII ), V d Cell with Cs + Cell with MA Time, ms Figure SI_3. a) Repeats of the SDSP experiment with no dwell time at.8 V before the step to the probe voltage. Repeats done at the beginning middle, and end of the experiment in figure 3a. There is no apparent drift in the cell characteristics. b) Jtr-6µs vs V pr from SDSP experiments with different pulse intensities. Solid lines are results from a ~ mw/cm pulse, and dashed lines from ~. mw/cm. The data have been normalized to match in the low voltage plateau area. The important point is that the x-axis intercept and the shift of the intercept with time are the same for both data sets. c) ΔV RII (t d ) curves generated from the same SDSP transient data used for figure 3a, but using different time segments of the transient to quantify the transient magnitude. The analysis uses the transient magnitude average over -4, 4-8, and -4 µs to construct plots like figure 3a, and from that the ΔV RII (t d ) vs t d plot as in figure 4. Despite the fact that the photocurrent transients are not "square", the three choices of time segment give the same lifetime for the charge screening process. d) Comparison of the rate of screening equilibration of the internal potential after a step to.8 V for a cell with Cs + and one with MA + S4

5 a) V d =.8 V, ms J disp C6/ I II BCP Mobile Ions III ITO/ PTAA V d =.8 V, 5 ms b) J disp C6/ BCP I II Mobile Ions III ITO/ PTAA V app.8 V V app.8 V Fixed Ions Fixed Ions c) C6/ BCP I V d =.8 V, 5 ms; V pr =.8 V J tr II Photogenerated Carriers III ITO/ PTAA d) C6/ BCP I V d =.8 V, 5 ms; V pr =. V J tr II III ITO/ PTAA V app.8 V hν V app.5 V hν J-drift J-diffu J-diffu Scheme SI_. a) Band edge potential profiles just after the application of.8 V forward bias to the cell. Mobile ions are shown drifting across region II under the influence of the applied electric field. b) Suggested band edge potential profiles after 5 ms at.8 V when most of the applied field has been screened to the space charge layers (RI and RIII). c) Effect of a light pulse at.8 V, after the cell has been held at.8 V for 5 ms. The band edge profile in RII is nearly flat so diffusion dominates the movement of photogenerated carriers. The "correct" charges are collected by the band bending in RI and RIII giving a positive photocurrent transient. d) Effect of a light pulse just after a step to. V, after the cell has been held at.8 V for 5 ms. There is now an inverted potential gradient across RII so that diffusive current dominates. As the photoexcited free carriers diffuse toward the band valleys at the edges of RII, they create a displacement current in the external circuit. From figure b we can see that a probe voltage of. V gives a slightly negative photocurrent transient, as depicted in panel d. Note that as the cell equilibrates to forward bias, the thickness of the depletion zone (RI) decreases. Thus the width of RII increases. The larger fraction of the absorber occupied by RII will S5

6 allow a smaller inverted slope across RII to create a balance between the positive and negative photocurrents created in RI II and III. This is a partial explanation for the fact that when the ions are equilibrated at SC, it takes an applied voltage of.4 V to create a balanced photocurrent (Jtr-6µs = ). However, when the ions are equilibrated to.8 V, it takes only an additional.5 V to create a Jtr-6µs =. Photocurrent, µa/cm 3 - a Probe Voltage, V Photocurrent, µa/cm - b Probe Voltage, V Time, µs 3 4 Time, µs 4 Unscreened Potential Drop (V) Dwell Time at.8 V Cell 5 ms ms Cell ms ms Cell 3 ms ms 3 4 Time, ms 5 6 Potential Change Across RII, V Dwell Time Re-equil. at.8 V Lifetime.5 ms,.3 ms ms.38 ms ms.4 ms Time, seconds Figure SI_4 a) Photocurrent transients at V pr after ms at.8 V and no re-equilibration time. b) Photocurrent transients at V pr after ms at.8 V and ms re-equilibration at SC. c) Examples for three different cells of the time scale for re-equilibration at SC after different dwell times at.8 V. Data normalized slightly (<=%) for comparison. For two of the cells, there is no dependence of the decay time on the dwell time. For the third, the difference is ~% of the decay half time. Cell has MA +, the other two cells have Cs +. d) Expanded view of one of the cells for shorter dwell times at.8 V. Solid lines are exponential fits to the data. Graph9_, TR_May_7 Mar 8 ACCUM file CdTe a S6

7 . a 3 b Current, ma/cm Charge nc/cm Time, ms Time, ms 8 Figure SI_5 a) Dark current transient after a step to SC following ms of equilibration to.8 V. b) Integration of the current in panel a, along with two other cells. Calculation of mobile ion concentration To calculate the concentration of mobile ions, we start with the measured ion charge moved between equilibration at.8 V and equilibration at V (figure SI_5b). We assume a depletion zone in RI and a ion accumulation layer in RIII (Scheme SI). For a depletion zone alone, the ion concentration could be calculated from the voltage change across the depletion zone and the measured ion charge moved, using formula S, S) N d =ΔQ dz /{e o eq((v bi -V a ).5 - (V bi -V b ).5 ) }, where N d is the bulk mobile ion concentration, ΔQ dz is the charge moved in stepping between two applied voltages, V a and V b, e o is the uum permittivity, e is the relative dielectric constant, q is the electron charge, and V bi is the built in voltage. S is derived from the standard expressions for a depletion zone, S and S3. S) Q dz = qx dz N d S3) X dz =(e o e(v bi -V)/(qN d )).5 Note (V bi - V) is the total potential drop across the absorber at applied voltage V. However, in the cell, some of the potential across the absorber drops across the ion accumulation layer in RIII, so only a fraction of the (V bi - V) drops across the depletion zone. Not only that, the fraction of the total potential that drops across the depletion zone is not the same for different applied potentials. Thus we have to modify S to S4 S4) N d =ΔQ dz /{e o eq((v bi -V a -V aca ).5 - (V bi -V b -V acb ).5 ) } S7

8 Where V aca and V acb are the potential drops across the accumulation layer for applied potentials V a and V b is the fraction of the total potential drop the drops across the depletion zone for the given applied potential. To link the accumulation layer and depletion zone, we note that the net charge in the depletion zone at any applied voltage must be the same as the net charge in the accumulation layer. With V aca, V acb and N d we can calculate the charge in the accumulation layer at V a and V b using the Gouy- Chapman model, S6 and S7.(ref bard) S6) Q GCa = (8kTee o (N d /)) / sinh(qv aca /(kt)) S7) Q GCb = (8kTee o (N d /)) / sinh(qv acb /(kt)) where Q GC is the the charge in the accumulation layer at with the given voltage drop. We have used N d / in S7 because in the derivation of the GC model, the density of charge species is twice the concentration whereas here it is not. In practice, we solve S4 - S7 iteratively starting from initial guesses for V aca and V acb. From S4 we get an initial value for N d. That N d inserted in equation S gives us a initial values for Q dza and Q dzb. The same N d inserted in S6 and S7 give use initial values for Q GCa and Q GCb. If Q dza Q GCa and/or Q dzb Q GCb then the initial guesses for V aca and V acb are adjusted. The values typically converge to within % in ~5 iterations. Note that in this calculation of N d, the only adjustable parameters are V bi and the dielectric constant. With a ΔQ = 3e-9, a dielectric constant of, and Vbi =., Nd= 7 x 7 /cm3 and the voltage drop on the accumulation layer is ~ mv when the cell is at SC, thus the voltage drop across the depletion zone is. V. We have experimented with adding a distance of closes approach of the mobile ions or ancies to the electrode, i.e. a Stern layer. Over a wide range of Stern layer thicknesses, the calculated N d is almost completely insensitive to the assumed Stern layer. This is because the Stern layer has a small percentage effect on the voltage term in equation S4. A Stern layer increases the total voltage drop on the accumulation layer side of the absorber. Thicker stern layers cause a larger change. We have tested Stern layers from. nm to 4 nm (~.3 to ~6 unit cells). With a Vbi of., a 4 nm stern layer adds 4 mv to the accumulation layer voltage at Va =, and 75 mv at Vb =.8. The change in the voltage term in S4 is only ~%. S8

9 .x -6.8 Mobility, cm /Vs.6.4. Cell Cell Potential Change Across RII, V Figure SI_6. a) Calculated ion mobility as a function of the remaining unscreened potential during the re-equilibration to SC for the cells in figure 4. Potential Change Across RII ( V RII ), V V.6 V.4 V Time, ms Figure SI_7 Screening of the potential drop across RII at applied biases of.8 V,.6 V, and.4 V. Measured by SDSP on a ITO/PTAA/FA.83 Cs.7 Pb(I.83 Br.7 ) 3 /C6/BCP/Ag cell. The equilibration rate at.8 V appears to be at factor ~ slower. S9

10 Drift-diffusion Model Details We aim at modeling the transient measurements of Figure a, where a probe voltage ( V pr) is applied to a device, initially at short circuit in the dark, followed by a 4µs light pulse applied 5µs after applying V pr. Thus, ions do not have time to migrate and equilibrate with the probe potential during the transient experiment. Hence their concentration profile is invariant and is equal to the one at short circuit in the dark, N (x). We developed our model based on the following hypotheses (boundary conditions): The total number of mobile ancies within the absorber is constant and equal to the number of ancies at equilibrium: L eq N (x)dx = N L () Electrons are selectively extracted (no hole current) at the electron selective contact (ETL) and are in thermal equilibrium with the ETL at the semiconductor/etl interface ( x = ). Under the Boltzmann statistics framework, this translates to: j p (x =, t) = () n(x =, t) & Φ n # = N exp $! (3) c % k BT " Holes are selectively extracted at the hole selective contact (HTL) and are in thermal equilibrium with the HTL at the semiconductor/htl interface ( x = L ): j n (x = L,t) = (4) p(x = L, t) & Φ p # = N exp $! (5) v % k BT " The reference for the electrostatic potential is chosen at x = : ϕ ( x =, t) = (6) The probe voltage, V pr, directly modulates the electrostatic field at the HTL: ϕ ( x = L, t) = V bi V pr (7)

11 The total current measured upon applying V pr is the sum of three contributions: the drift-diffusion currents of electrons ( j n (x,t)) and holes ( (x, t) ) and the displacement current ( j d (x, t) ) induced by fluctuation of the electric field, F (x, t), in time: Where, j (t) = j (x, t) + j (x, t) j (x, t) (8) tr n p + d & n(x, t) q # j (x, t) = qd $ + n(x, t)f(x, t)! (9) n n % x k BT " & p(x, t) q # j (x, t) = qd $ p(x, t)f(x, t)! () p p % x k BT " F(x, t) jd (x, t) = εε r () t ϕ(x, t) F(x, t) = () x The rate balance equations connect the drift diffusion currents and carrier concentration to the photogeneration G (x, t) and recombination processes (we assume a band to band recombination process for this model): j p n(x, t) t = q jn (x, t) + G(x, t) B n(x, t ( t)p(x, t) n ) i (3) p(x, t) jp (x, t) = + G(x, t) B n(x, t q t ( t)p(x, t) n ) The ancies are in steady state and their distribution is equal to their distribution at short circuit in the dark through the whole experiment. Therefore, N (x, t) N (x) and the net ionic drift diffusion current is zero: N (x) q = F (x)n x k BT (x) i = Where F (x) is the electric field distribution at short circuit in the dark. Finally, we solve Poisson equation to obtain the full distribution of electric field within the absorber: F(x, t) q = x ε ε r eq ( p(x, t) n(x, t) + N (x) N ) (4) (5) (6)

12 3 To calculate the transient photocurrent response (equation (8)), we solve equations (9) - (6) with the boundary conditions () - (7) for each step of the transient experiment: ) We calculate the initial steady state distribution of electrons ( n (x)), holes ( p (x)), ancies ( N (x) ) and electrostatic potential ( ϕ (x) ) at short circuit in dark (i.e. = j = j ). jn, p, d, = ) We calculate the time dependent electron and hole concentrations ( n (x,t) and p (x,t)) as well as the electrostatic potential distribution ( ϕ (x,t) ) and total transient current ( jtr, (t) ) right after applying V pr. The initial concentrations and electrostatic potential are the ones calculated at short circuit: n = (x, t = ) n (x) (7) p = (x, t = ) p (x) (8) ϕ x, t = ) = (x) (9) ( ϕ 3) After a time t ( t = 5µ s) at V pr, we turn on the light source (i.e. photogeneration at a rate G(x) = G exp( αx) ) and we calculate the time dependent electron and hole concentrations ( n (x, t) and (x,t)), the electrostatic potential distribution ( ϕ (x,t)) and the transient photocurrent ( (t) ) right after turning on the light. The initial conditions are: jtr, n (x,t) = n(x,t ) () p (x,t) = p(x,t ) () ϕ x,t ) = (x,t ) () ( ϕ 4) Finally, after a time t ( t = 4µ s), we turn off the light source ( G = ) and we calculate the time dependent electron and hole concentrations ( n 3 (x, t) and p 3 (x, t) ), the electrostatic potential distribution ( ϕ (x, 3 t) ) and the transient photocurrent ( j 3 (t)) right after turning the light off. The initial conditions are: tr, n 3 (x, t ) = n (x, t ) (3) p 3 (x, t ) = p (x, t ) (4) ϕ x, t ) = (x, t ) (5) 3( ϕ p

13 4 Model parameters Parameters Description Value q Electron charge 9.6 C k B T Thermal energy 6 mev ε Vacuum dielectric constant 8.85 Fcm ε r Relative permittivity L Device thickness 4 nm Φ Electron injection barrier. ev n Φ p Hole injection barrier. 5eV V bi Built-in potential. 9 V E g Band gap energy. 6eV N c Electron density at the bottom of the conduction band cm -3 N v Density of holes at the top of the valence band cm -3 eq 8 N Equilibrium density of ancies 4 cm -3 D Electron diffusion coefficient. 3cm s - n D p Hole diffusion coefficient. 3cm s - B Bimolecular recombination rate cm 3 s - α Absorption coefficient 5 cm - G Carrier photogeneration rate. cm -3 s - Table SI_. List of parameters used for the drift-diffusion simulations in figure 6 of main text.

14 Figure SI_8 a) Simulation of Jtr(V pr ) using identical parameters except for a change in the mobile ion concentration. b) Simulation of Jtr(V pr ) using identical parameters except for changes in the electron and hole drift mobilities. Potential Change Across RII, V At.8 V Forward Bias Re-equilbration at Short Circuit (x.5) Time, seconds Figure SI_9. Evolution of the field screening under.8 V forward bias (red) and during reequilibration to SC (blue) for an additional Cs + containing cell. Blue and red dashed lines and are single exponential fits; solid brown line is a double exponential fits. References. A.J Bard and L.R. Faulkner, Electrochemical Methods, Fundamentals and Applications, John Wiley and Sons, New York, 98, p5. S