www.sciencemag.org/content/360/6384/67/suppl/DC1

Supplementary Materials for Light-induced lattice expansion leads to high-efficiency perovskite solar

cells

Hsinhan Tsai, Reza Asadpour, Jean-Christophe Blancon, Constantinos C. Stoumpos, Olivier Durand, Joseph W. Strzalka, Bo Chen, Rafael Verduzco, Pulickel M. Ajayan,

Sergei Tretiak, Jacky Even, Muhammad Ashraf Alam, Mercouri G. Kanatzidis, Wanyi Nie,* Aditya D. Mohite*

*Corresponding author. Email: wanyi@lanl.gov (W.N.); amohite@lanl.gov (A.D.M.)

Published 6 April 2018, Science 360, 67 (2018)

DOI: 10.1126/science.aap8671

This PDF file includes:

Materials and Methods Supplementary Text Figs. S1 to S21 Tables S1 to S9 References

2

Materials and Methods

Materials

Lead iodide (PbI2), methylammonium iodide (MAI), formamidinium iodide (FAI),

Cesium iodide (CsI), Nickel (II) acetate tetrahydrate, monoethanolamine(MEA), fullerene

(C60), absolute ethanol (200 proof) and dimethyl sulfoxide (DMSO) were all purchase from

Sigma-Aldrich and no further purification was required.

Precursor preparation

LiNiO precursor solution was prepared according to literature (42) by dissolving

0.1M Nickel (II) acetate tetrahydrate in absolute ethanol with MEA. The molar ratio of

Ni2+ and MEA is kept to be 1:1. After the solution was stirred at 60 ºC for 1 hour, a clear

and deep green solution was formed. 5% molar lithium nitrate was then added in the

precursor as Li+ source to improve the conductivity of the NiO film (LiNiO).

Perovskites solution was mix of PbI2, FAI, MAI and CsI (molar ratio

=1:0.7:0.25:0.05) with desired molar ration and dissolved in anhydrous DMSO with molar

concentration of 0.43M. The prepared solution was stirred for at least 24 hours at 70 ºC

before using(43).

Device fabrication

The patterned fluorine doped Tin Oxide (FTO, Thin Film Device Inc) substrates

were first cleaned in ultra-sonication bath in water, acetone and isopropyl alcohol for 15

min respectively. The substrates were then dried under nitrogen air flow followed by

baking on hot-plate in air for 30 min. The dried substrates were treated by oxygen plasma

3

for 3 min before coating. The LiNiO precursor solution at 3000 rpm for 40 Sec to serve as

hole transporting layer (HTL)(44). The substrates were dried at 150 ºC for 20 min in the

air. Then the LiNiO/FTO substrates were then taken into a tube furnace for 400 ºC sintering

in ambient condition. The coated substrates were then transferred into an argon filled

glovebox for perovskite and top contact deposition. The FA0.7MA0.25Cs0.05PbI3 and

MAPbI3 layers were produced by hot casting method(10, 27), where the LiNiO coated FTO

substrates were first heated at 165 ºC and then quickly transferred to the spin coater chunk

with spinning process started immediately after dropping the precursor on the substrates at

5000 rpm without ramping for 20 Sec. The film color changed from transparent to dark

brown almost simultaneously after solvent escaped. The obtained FA0.7MA0.25Cs0.05PbI3 or

MAPbI3 on LiNiO/FTO substrates then loaded into a vacuum chamber for electron

transporting layer (fullerene) and aluminum deposition with shadowed mask (working area

varying between 0.3~0.5 cm2).

Grazing incidence wide angle X-ray scattering (GIWAXS) analysis

For synchrotron GIWAXS measurements, all the samples were prepared with

perovskites solutions on LiNiO/FTO substrates as described in device fabrication. The

samples were placed on a programmable temperature control stage (temperature set at 25

ºC) inside a vacuum chamber pumped down to 10-5 Torr. To conduct in-situ GIWAXS

measurements under light, we install AM 1.5G solar simulator on top of the vacuum

chamber, the light will come through the glass window above the sample for continuous

light soaking while collecting the data. The two-dimensional GIWAXS maps were

obtained with incident angle of 0.25º and 10s exposures for every 10 minutes interval.

4

GIWAXS data were processing with GIXSGUI package (45) for Matlab (Mathworks) with

correction for detector sensitivity, X-ray polarization and geometrical solid-angle. The

line-cut analysis of GIWAXS maps for perovskite thin-films were compared and indexed

with peaks from regular GIXRD spectra with well-resolved peaks.

Crystal structure analysis: Integral Breadths (IB) analysis with pseudo-

Voigt fits of the GIXRD pattern

In powder diffraction, line profile analysis of the Bragg-Brentano diffraction peaks

is a well-known method to obtain a measure of the coherent-correlation lengths and to

characterize the micro-strains distribution. Among these techniques, the integral-breadth

(IB) method, using the simulation of the diffraction line-profile, mostly using Voigt

functions or pseudo-Voigt functions, provides a rapid and convenient measure of both these

parameters. The line broadening is characterized to the correlation length L and to the

micro-strain parameter ε. It is therefore possible to obtain both a measure of these

parameters by merely using, respectively, the relations of Scherrer (46, 47) or of Stockes

and Wilson (48):

(S1)

(S2)

Where q is the Bragg peak position βL(2θ) is the integral breadth of the diffraction peak

due to a loss of diffraction coherence and βε(2θ) is the integral breadth of the diffraction

peak due to a broadening from the micro-strains, into scale of the variable 2θ variable. K

BL

KLqqb

lcos)2(

=

Banqqbe e cot)2(41

=

5

is the Scherrer constant fixed at 0.9 in the following. These integral breadths have been

turned into scale of the variable by the well-known following relationship:

(S3)

The separation of both strain and correlation effects in the IB measurements can be

done. In the past, approximate methods have usually involved the assumption that the

constituent profiles are either Cauchy or Gaussian (Williamson–Hall plots). Schoening

(49) and Halder and Wagner (50) have shown that the correlation contribution is

approximatively described by a Cauchy (Lorentzian) function and the strain profile is

represented by a Gaussian function. Therefore, a better representation of the experimental

profile is given either by a convolution of these functions (51, 52) (Voigt functions) or by

a linear combination of these functions (pseudo-Voigt functions) (53). Halder and Wagner

(50) have developed the approximate equation to separate both the effects:

(S4)

with β(S) the measured IB. This gives, using Eqs. (S1) and (S2), the correlation length and

the micro-strain parameter. Eq. (S4) can be written as follows, using Eqs. (S1) (S2) and

(S3):

(S5)

lqsin2

=S

lqqbb cos)2()( =S

)()().()( 22 SsSs GaussCauchy bbbb +=

222 )(9.04))((

Ss

LSs beb

+=

6

Therefore, the slope of as a function of yields the Cauchy

component due to the small crystallite size L (54) and the origin of the curve e. This plot

is called “Halder–Wagner plot” (a kind of modified “Williamson–Hall” plot).

Device characterization

(1) Statistics on solar cell Figure-of-merit

The solar cells were characterized by taking current-voltage curves under solar

simulator with light intensity equivalent to 1-Sun (100 mW/cm2) with air mass 1.5 G filter.

The devices data were collected for over 30 devices from different batches and masked to

ensure that contributions from edge effects is negligible.

(2) External quantum efficiencies (EQE) of solar cells

The external quantum efficiencies were collected by illuminating the device under

monochromatic light using a tungsten source (chopped at 150 Hz) while collecting the

photocurrent by lock-in amplifier in AC mode. The light source spectrum response was

corrected by calibrated silicon diode (FDS1010, Thorlab).

(3) EL quantum efficiency

The electroluminescence spectra and brightness of RPLEDs were collected by

ocean optics spectrometer collecting at same integration time. The radiance/voltage curves

are collected by applying voltage with Keithley 2400 unit and collecting radiance value by

the calibrated silicon diode (FDS100-Cal, Thor Labs) with known spectral response. The

2))((Ssb

2)(

Ssb

7

Si diode was kept with a distance with the testing device and the solid angle can be thus

calculated from the area of the cell, distance and the area of the diode. The external

quantum efficiency was thus estimated by integrating the number of photon measured

assuming an Lambertian emission profile and divided by injected number of electrons.

(4) Electro-absorption spectroscopy

Electro-absorption spectrum is done in reflection mode by taking the 1st and 2nd

harmonic signal of the AC field applied across the photovoltaic device to measure the flat

band voltage and spectrum respectively. The light source comes from a monochromatic

light in DC mode, indecent at 45 º onto the device electrode, the reflected light is captured

with silicon diode. The diode is connected with current preamplifier then connected to

lock-in amplifier to collect the photocurrent. The photovoltaic device is biased under AC

field at frequency of 2 kH and amplitude of 0.25 mV (RMS) for DC bias dependent

measurements and 2 V (RMS) for spectrum collection. After the measurement, the DC

absorption spectrum is taken under the same setup in DC mode through digital multi-meter

as reference.

Once obtained the EA spectrum (fig. S17), the light source is fixed at band edge

absorption peak (in this case 794 nm) and a various DC voltage (+1 V to -3 V) is supper

imposed on top of the AC field across the device electrodes to measure the EA amplitude

as a function of DC bias in 1st harmonic mode.

Photoluminescence (PL) and PL quantum yield (PLQY)

8

PL measurements were performed with an in-lab-built confocal microscopy system

focusing a CW or monochromatic 6-ps-pulsed laser (repetition rate 40 MHz, tunable in the

visible spectral range) with a 4X objective (NA=0.13). PL spectral responses were obtained

through a spectrograph (Spectra-Pro 2300i) and a CCD camera (EMCCD 1024B) yielding

a maximum error of 2 nm. For all excitation wavelength used for PL measurements the

excitation intensity was typically maintained around 200 mW/cm2 to be close to solar

excitation conditions; sample degradation was verified to be absent. Samples were

measured under vacuum (10-5-10-6 Torr) under ambient conditions of temperature.

PLQY (in fig. S9) of the thin films were measured by means of an integrating sphere

with CW laser diode at various excitation wavelengths, following previous report (55),

under ambient conditions. Measurements were acquired directly after taking the samples

out of vacuum to minimize effects of air exposure which were found to be negligible for

few hours, and some of the samples were encapsulated for cross-check of the data.

To PL change with illumination under identical measurement condition as it was

done for GIWAXS and solar cell characterizations in the manuscript, we measured the PL

intensity under intermediate vacuum condition (10-5 Torr), as a function of illuminating

time using AM1.5G 1-Sun solar simulator source (fig. S10). To be more accurate, we have

also monitored the absorption change before and after illumination and found the

absorption amplitude of the sample does not change after light soaking, except for the small

red-shift of the band-edge reported (~ 8 meV). This suggests that the PL intensity should

scale with PLQY.

Device simulation (1) Optical Modeling

9

Optical absorption in different layers of the PV cell is calculated by the full-wave

solution of Maxwell’s equations with the input of AM 1.5 illumination. The materials in

different layers of the cell are characterized by absorption coefficient and refractive indices

that are obtained from literature (56-58) or measured data by the authors. Transfer matrix

method (TMM) (59) calculations are used for the optical studies of the planar cell structure.

In this approach, the entire solar cell stack, including the contact layers, is modeled using

a series of interface and phase matrices. The central quantity which is calculated in this

approach is the point-wise optical absorbance [A(λ,r)] inside various layers of the cell. The

wavelength range of 300–1500 nm has been used for our calculations. The spatially

resolved absorption profile is integrated over the wavelength range to create the generation

profile for the electron and holes for self-consistent carrier transport simulation, as

described below.

(2) Self-consistent transport simulation

The transport of charged carriers (electrons and holes) is modeled by generalized

drift-diffusion formalism (60). Photo-generation is calculated from the optical absorption

profile (integrated over the wavelengths) discussed previously. The electron and hole

transport inside the cell is simulated by a self-consistent solution of Poisson and continuity

equations by a commercial grade device simulator MEIDCITM (61). The generation term

in the e–h continuity equations is calculated from the solution of photo-generated profile.

The recombination term in continuity consists of direct and SRH recombination with

lifetime found from literature. We do not account for hot electron effects. The excitons –

if any – are presumed to dissociate into free electron and hole pairs immediately after

10

generation. See Table S1 for model equations and see Table S2 to S4 for simulation

parameters. The parameters with references are taken from the literature; the rest are

assumed to match the data for mixed cation perovskite layer.

Device stability tests

We test the long-term stability under constant 1-Sun (or 10-Sun) illumination from

standard solar simulator source with air mass 1.5 global filter. The devices are encapsulated

with microscope cover glass sealed with UV-curable epoxy. The devices are sitting under

light connected with a resistor to reach the maximum power output point. A small desktop

fan is used to dissipate the heat generated by illumination. The devices are taken off from

the stability test stage and moved to 1-Sun standard source for J-V measurements at certain

time interval for PCE and JSC evaluation.

Supplementary Text

Crystal structure analysis for mixed cation thin film obtained by hot-

casting method

We investigated the structural formation by systematically recording the GIWAXS

maps with progressive change of the cations loadings, results are summarized in Fig. S1-

S2. Fig.S1A-C show the grazing incidence wide-angle X-ray scattering (GIWAXS) maps

for three different systems: pure MAPbI3 with tetragonal phase (Fig.S1A),

FA0.7MA0.25Cs0.05PbI3 alloy with cubic phase (Fig.S1B) and FA0.95Cs0.05PbI3 alloy with

delta phase (Fig.S1C). All the GIWAXS maps show the classic Debye-Scherrer ring

11

features, however, some spot feathers are observed in FA0.7MA0.25Cs0.05PbI3 system, which

implies that the crystallinity of FA0.7MA0.25Cs0.05PbI3 is superior to that off MAPbI3 and

FA0.95Cs0.05PbI3. Fig.S1D-E is the line-cut obtained from the GIWAXS maps for various

mix-cation FA/MA/Cs molar ratio. By comparing the peak positions of XRD spectra in

Fig. S1D with the reported FAPbI3 single crystal diffraction pattern (62, 63), we found that

the (211) peak in the MAPbI3 spectrum (black line) is suppressed when 50% FA is

incorporated (blue line). With further increasing the FA loading to up to 70% (red line),

the (200) and (202) signature diffraction peaks in tetragonal phase shift to the formation of

the cubic phase with characteristic (110), (111) peaks identified in the

FA0.7MA0.25Cs0.05PbI3 triple-cation pure-iodide thin-film. However, the FA/Cs alloy by

itself (green line) does not form a stable cubic phase, instead it forms a mixture of the

characteristic perovskite black phase (or a-phase) and the insulating yellow phase (d-

phase) identified by indexing the peaks in Fig. S1D. Fig. S1E shows the zoomed in region

around the (001) peak (from Fig. S1D), which systematically shifts towards lower angle

indicating an increase in lattice constant, which is consistent with the incorporation of the

larger FA cation into the crystal structure.

Furthermore, in order to elucidate the role of Cs we further compare the FA0.7MA0.3-

xCsxPbI3 alloy pattern with and without Cs as illustrated in Fig.S2. The FA0.7MA0.3PbI3

thin-film (black line) without Cs exhibits asymmetric peaks in (001), (110), (111) and (002)

with multiple shoulders as compared to the FA0.7MA0.25Cs0.05PbI3 alloy film (red line). We

observe that the asymmetric (001) peak with multiple shoulders of the alloy (Fig. S2B)

with 0% Cs is well fitted by the (110) peak of MAPbI3 (red dotted lines) and (001) peak of

FAPbI3 (red dotted lines), suggesting the thin-film without Cs shows phase segregation into

12

FA and MA domains. In conclusion, we successfully show that triple cation pure iodide

perovskite alloy can be kinetically stabilized into a cubic phase without the need of

bromide, thus mitigating the possibility of phase segregation due to halide migration under

extreme conditions(64, 65) . In addition, the existence of MA is to stabilize the a phase of

the alloy and the incorporation of Cs is essential to stabilize the MA/FA alloy, preventing

the two phases gets segregated.

Proposed microscopic mechanism based on bond change

Our experimentally observed lattice expansion and strain relaxation could arise

from a recently proposed theoretical and experimental work (19, 66) describe the

weakening of the hydrogen bonding between MA+ and I- under illumination, which creates

a higher degree of rotational freedom for MA cations and also results in relaxation of the

locally distorted Pb-I-Pb bonds. In our study, we maintain the light exposure for a few

hours, which allows us to observe the lattice expansion and relaxation. This effect reflects

the effective Pb-I-Pb bond-angle change caused by the synergetic effect of the

hydrodynamic rotation of MA and relaxation of the Pb-I-Pb bonds and angles and this is

supported experimentally by recent studies (refer to Ref-23,24 in main text). Although

recent studies have suggested the photo-induced effect preserves the Pb-I bond lengths and

enlarges the angles, we performed a crystallography study on MAPbI3 single crystal and

obtained precise atomic coordinates under dark and under continuous illumination (Tables

S5-S9). In MAPbI3 single crystal, we observe that the Pb-I-Pb angles appear to be

preserved and the Pb-I bonds are elongated. We therefore conclude that the exact

observation on the optical property changes associated with bond angle change (red shift

13

in PL) or elongation of Pb-I bond (blue shift) will largely depend on the sample preparation

conditions, such as thin film with interfacial materials or standing single crystal, or even

complicated mixed-cation system.

X-ray photo-electron spectroscopy analysis

We conducted X-ray photo-electron spectroscopy with depth profiling for the

FA0.7MA0.25Cs0.05PbI3 mixed cation thin films studied in the MS to examine the

composition as a function of film thickness before and after illumination. The results are

illustrated in Fig. S7. From the spectra in Fig. S7 (a), the peaks can be identified by Pb (4f7)

with a binding energy of 618 eV and 630 eV, and the I (3d5) with binding energy of 137

eV and 142 eV respectively (62). The depth profiling is done by taking the XPS spectra

progressively as we etch through the FA0.7MA0.25Cs0.05PbI3 film of thickness 400 nm

similar to the one used for structural and solar cell measurements presented in the

manuscript. Each etching cycle represents a certain depth in the film. The 15th cycle (Fig.

S7 (a) inset) shows the substrates peak (fluorine doped tin oxide) indicating the film is fully

etched. The spectra in Fig. S1 (a) shows several spectra with different etching cycles before

illumination, we found that the I/Pb ratio through the film thickness distributed uniformly

in our sample. The absolute ratio of I/Pb is measured to be identical to that of a MAPbI3

single crystal measured under the same condition as a function of depth, suggesting a

uniform perovskite composition formed using the hot-casting method without any

secondary phase formation. The profiling was done on 5 samples and different spots across

the samples to establish the statistical validity of results. The spectra remained similar with

the peak position variation < 1% from sample to sample.

14

Next, we performed the same measurements, but after illumination under

intermediate vacuum (10-5 Torr), identical to the measurement conditions carried out for

the in-situ GIWAXS measurements described in the manuscript. The obtained spectra after

illumination are plotted along with that before illumination in Fig. S7 (b). We found that

the spectra are nearly identical with small variation in peak intensity due to perhaps

changes in the relative morphology.

To specifically examine the change in the iodine concentration with illumination,

we zoom-in to the region in the XPS spectra that shows the iodine peaks and is illustrated

in Fig. S8 (a)-(b). From the spectra in Fig. S8 (a), we found the iodine peaks are identical

for different etching cycles, suggesting a uniform iodine distribution in the sample. After

illumination, the iodine peaks for samples does not change appreciably in their position nor

intensity.

The I/Pb ratio is extracted as a function of etching depth for thin films before (blue)

and after (red) illumination and plotted in Fig. S8(c). The data are averaged from 5 different

samples, which are plotted with the error bars. From the result, we conclude that the I/Pb

ratio does not vary with illumination, indicating the absence of iodine redistribution and as

a result directly proving that ion migration in the mixed cation film (FA0.7MA0.25Cs0.05PbI3)

does not occur. This is in sharp contrast with the observed iodine change across the film

thickness as observed in the study of Ref [22].

Control experiments with applied bias under dark environment

1. Detailed experimental setup and protocols

We fabricated mixed cation planar solar cell in the same processing condition and

device architecture described in the manuscript. To test the device in exactly the manner

15

suggested by the reviewer, we first performed a current-voltage scan in dark as well as in

1-Sun illumination to find the voltage set point for the bias experiment. The light and dark

J-V curves are shown in Fig. S18(A). We chose 3 points on the dark curve (labeled by

yellow stars): low voltage (0.2 V), medium voltage (0.5 V) and high voltage (0.76 V) just

above the diode turn-on. The dark current is monitored first as shown in Fig. S18(B). It can

be clearly observed that the current density does not change significantly for both low and

medium voltage and for high voltage, the current density decreases slightly from 3.49

mA/cm2 to 3.22 mA/cm2 and then remains stable at that value. Here we denote the dark

current corresponding to the diode turn-on voltage as JON.

2. Dark and Light J-V characteristics under bias in dark

Based on the dark current monitoring experiments, we choose the high voltage

point at 0.76 V for the dark control experiment in constant current mode. Specifically, we

sat the device in dark while applying a constant current (JON, 3.49 mA/cm2) and measured

the device J-V characteristics (dark and light) periodically. The light curve was measured

in less than 1-min to avoid light exposure induced effects that may otherwise compromise

the experiment. The device was measured for a total biasing time up to 180 min,

comparable to the maximum light soaking time reported in the manuscript. The results are

summarized in Fig. S19. Fig. S19(A) shows the JV curves for a typical device before

illumination. We reproduced both of the signatures reported with “before illumination”

case for pristine device in MS, which are the slope near open circuit (low VOC and F.F.)

and the crossover of the dark and light J-V at low fields. We further overlay the light J-V

curves in Fig. R19(B) to visualize the change of J-V curves under bias in dark. The variation

of the J-V characteristics is negligible in contrast to the case after light soaking (Fig. 2 in

16

MS). The values of VOC and F.F. are plotted in Fig. S182 (C)-(D). As a comparison, we

also plot the VOC and F.F. as a function of illumination time taken from the manuscript. In

sharp contrast to the device performance change with light soaking, under forward bias

condition in dark (constant current mode), the average VOC and F.F. remain invariant, at

low values of (0.77±0.04) V and (65.3±3.01) % respectively. Moreover, we measured the

devices at other bias voltages labeled in Fig. S18 (A), as illustrated in Fig. S19(E) and

obtained a similar trend.

3. Confirming the device performance and excluding degradation

To further confirm that after 3-hour, the devices do not undergo degradation, we

take the “after-biased” device and keep the device under illumination for 2 hours and

examine the final stabilized power conversion efficiency output as shown in Fig. S20(A).

The efficiency improved from ~12% % to 19.3 %, largely due to increase in VOC and F.F.

after illumination. This value is comparable to the average device performance reported in

the manuscript and hence one can exclude any device degradation. In addition, we also

performed in-situ grazing incidence wide angle X-Ray scattering (GIWAXS) as a control

experiment for the device under a bias of 1V in the dark. The GIWAXS line-cuts for the

device before (black dotted line) and after (red solid line) 1V bias are plotted in Fig. S20

(B). The GIWAXS spectra remains unchanged after dark biasing the device indicating an

absence of degradation with forward bias. Thus, from both of the data we confirm that no

degradation was observed with forward bias and further validate our control experiments

illustrated in Fig. S19.

17

In summary, from the above experiments, we unambiguously prove that the

increase in the device performance is indeed caused by light-induced lattice expansion,

which lowers the interface barrier and not due to ionic migration.

Device stability tests under various stressing conditions

We evaluated the device stability under various operation conditions in the presence

of light-induced lattice expansion in photovoltaic cells (Fig. S21). The long-term stabilities

under continuous light are discussed in Fig. 4 in the main text. Here we measured the EQE

spectrum measured after 5 and 10 days of continuous illumination (Fig. S21A), it remains

unchanged implying no evidence of phase segregation, consistent with our observation of

GIWAX studies.

Moreover, we performed aggressive stability tests under much higher solar intensities and

current injection regimes (EL) as illustrated in Fig. S21 B-C. We first evaluate the charge

collection efficiency by measuring JSC as a function of illumination power from 0.1-Sun to

20-Sun as shown in Fig. 4D. The JSC for the FA0.7MA0.25Cs0.05PbI3 device, can be described

using a linear fit across the entire power range indicative of near perfect charge collection

while the MAPbI3 device tends to deviate at higher power likely due to degradation. Fig.

S21C plots the EL and PL spectrums under forward injection current ranges from 10

mA/cm2 to 1000 mA/cm2 and excitation power ranges from 76 mW/cm2 to 760 mW/cm2

with 415 nm laser. In both of the cases, the emission spectrums remain unchanged

fortifying the robustness of the mixed-cation pure-halide perovskites.

18

Supplementary Figure

Thin-film structure characterization

Fig. S1 Effect of FA loading in the alloy thin film. GIWAXS maps for (A) MAPbI3, (B) FA0.7MA0.25Cs0.05PbI3 and (C) FA0.95Cs0.05PbI3 perovskites. (D) Line-cut of GIWAXS maps with different cation ratio and zoon-in for (100) plane for peak shifting analysis (E).

Fig. S2. Role of Cs in mix-cation pure iodide perovskites system. (A) Line-cut of GIWAXS maps for alloy system with and without Cs incorporated. (B) Zoom-in for (100) plane with comparison of MAPbI3 and FAPbI3 peaks.

MAPbI3 FA70MA25Cs5PbI3A B C FA95Cs5PbI3

3.02.52.01.51.0q (Å-1)

*

δδ

(110) (220)95% FA 0% MA

70% FA 25% MA

50% FA 45% MA

0% FA 95% MA

α α αα

δ δ δ δ

D

1.21.11.00.90.8q (Å-1)

(110)

E

(100)(100) (200)

1.151.101.051.000.950.90q (Å-1)

(100) 0% Cs FAPbI3 MAPbI3

MAPbCl3

3.02.52.01.51.0q (Å-1)

FA/MA Alloy with 0% Cs 5% Cs

(100

)

(110

)

(111

)

*

*

(200

)

(210

)

(211

)

(220

)

(221

)

A B

19

Fig. S3. Optical properties of mixed cation perovskites. (A) Solar cell external quantum efficiency spectrum near the band edge normalized by peak value for mixed cation perovskite absorber with various FA loadings. (B) electroluminescence (EL) spectrum for mixed cation (FA0.7MA0.25Cs0.05PbI3) and MAPbI3 device using solar cell device structure.

GIWAXS for device

Fig. S4 In-Situ GIWAXS diffraction pattern under constant illumination for device configuration (A) Line-cut from GIWAXS map for FA0.7MA0.25Cs0.05PbI3 device under constant illumination in structure illustrated in (B). (C) correlated change in q space with the change in VOC measured at the same time.

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

m. E

L (a

.u.)

900800700600Wavelength (nm)

FA0.7MA0.25Cs0.05PbI3 MAPbI3

A B1.0

0.8

0.6

0.4

0.2

0.0

Nor

m. E

QE

(a.u

.)

900850800750700Wavelength (nm)

MAPbI3 FA0.25MA0.45Cs0.05 FA0.5MA0.45Cs0.05 FA0.7MA0.25Cs0.05

Inte

nsity

3.02.52.01.51.0q (Å-1)

108642

x103

3.02.92.82.72.6

Open CIrcuit Condition

FTO/Glass

NiOPerovskitePCBM

Au Au

B2

1

0

|∆q/

q| (1

0-3)

6040200Illumination Time (min)

600

550

500

450

VO

C (mV)

0.15

0.10

0.05

∆V/V0

C

A

20

Lattice expansion for MAPbI3

Fig. S5 Lattice expansion measurements for MAPbI3 thin film with in-Situ GIWAXS measurement under 1-Sun illumination. (A) Line-cut from in-situ GIWAXS maps for MAPbI3 thin film under 1-Sun illuminations. (B)-(C) extracted change in q value as a function of illumination time for (110) and (220) planes for MAPbI3 (blue) as compared to mixed cation thin film (red).

Effect of heating

10

8

6

4

2

0

Δq/

q (x

10-3

Å-1

)

16012080400Illumination Time (Min)

(100) peak

MAPbI3

FA0.7MA0.25Cs0.05PbI3

10

8

6

4

2

0

Δq/

q (x

10-3

Å-1

)16012080400

Illumination Time (Min)

MAPbI3

FA0.7MA0.25Cs0.05PbI3

(200) peak

654321I (

103 c

ount

s)3.02.52.01.51.0

q (Å-1

)

MAPbI3 0 min 20 min 30 min 60 min 90 min 120 min

A

B C

10

8

6

4

2

0

Inte

nsity

(103 c

ount

s)

3.02.52.01.51.00.5q (Å

-1)

25 ºC 35 ºC 60 ºC 80 ºC 90 ºC

10

5

0

Inte

nsity

(103 c

ount

s)

1.041.000.96q (Å

-1)

(100)

2.042.001.96q (Å-1)

(200)

25 ºC 40 ºC 50 ºC

A

C40

35

30

25Tem

pera

ture

(ºC

)

6040200Time (Min)

B

21

Fig. S6 Effect of heating in dark (A) GIWAXS pattern for mixed cation perovskite thin film at various heating temperatures, the spectrums were taken after temperature stabilizes. (B) Temperature raise under 1-Sun illumination with cooling stage as a function of time. (C) zoomed-in region of the main diffraction peaks for temperature range from 25 ºC to 50 ºC, much larger range than the experimental temperature raises in (B).

X-ray photo-electron spectroscopy (XPS) with depth profiling

Fig. S7 XPS spectra for mixed cation thin film without and with illumination. (a) the XPS spectra on the mixed cation thin film before illumination with various etching cycles representing the composition from the surface to the bulk of the thin film. The spectrum is dominated by the substrate peak beyond 10th cycle (inset) indicating the film was etched all the way through. (b) the XPS spectra for the 5th cycle probing the middle of the film for mixed cation thin film before (black) and after (red) illumination with AM1.5G 1-Sun illumination for 3-hour. The samples were kept under intermediate vacuum (10-5 Torr) during illumination.

(a)

(b)

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

m. I

nten

sity

(a.u

.)

800 700 600 500 400 300 200 100Binding Energy (eV)

800 600 400 200Binding Energy (eV)

Cycle 15 FTO Cycle 2 Cycle 5 Cycle 10

800 600 400 200Binding Energy (eV)

80

60

40

20

Cou

nts

(103 )

before light after light

I 3d5

Pb 4f7

22

Fig. S8 Iodine distribution remain unchanged with illumination revealed by XPS depth profiling. (a)-(b) iodine peaks for the surface of the film (1st cycle) and middle of the film (10th cycle) for before and after illumination respectively. (c) I/Pb ratio corrected by the MAPbI3 single crystal XPS profiling as a function of etching depth (cycles) for before (blue) and after (red) 3-hour illumination. The value is averaged from 5 scans on different samples and different spots.

Photoluminescence (PL) characterizations on thin film

Fig. S9 photoluminescence quantum yield (PLQY) value as a function of excitation power for FA0.7MA0.25Cs0.05PbI3 thin film studied in the manuscript.

Nor

m. I

nten

sity

(a.u

)

650 640 630 620 610 600Binding Energy (eV)

1st cycle

10th cycle I (3d5)

Nor

m. I

nten

sity

(a.u

)

650 640 630 620 610 600Binding Energy (eV)

1st cycle

10th cycle I (3d5)

(a) (b)

4.0

3.5

3.0

2.5

2.0

corr

ecte

d I/P

b ra

tio

108642Etching cycles (counts)

Before Light After Light

(c)

10-3

10-2

10-1

100

101

PLQ

Y (%

)

2 410

1 2 410

2 2 410

3

Excitation power (mW/cm2)

FA0.7MA0.25Cs0.05PbI3

23

Fig. S10 PL characterization on the thin film as a function of light soaking time. (a) normalized PL intensity change (by the initial time point) as a function of laser excitation time. (b) the PL red shift amplitude (red) and PL intensity increase (Red) as a function of excitation wavelength.

Fig. S11 High resolution photoluminescence intensity map for mixed cation thin-film (a) before and (b) after 1-Sun solar simulator white light soaking for 3-hours in intermediate vacuum. The scale bar is 10 µm. (c) PL peak position shift as a function of light soaking time.

-5-4-3

-2-10

Pea

k sh

ift (m

eV)

600550500450Excitation wavelength (nm)

2.0

1.5

1.0

0.5

PLQ

Y change (rel. units)

2.0

1.5

1.0

0.5

0.0PLQ

Y c

hang

e (r

el. u

nits

)

150100500Light soaking (min.)

Excitation at 425 nm

(a) (b)

-10

-8

-6

-4

-2

0

PL

peak

shi

ft (m

eV)

403020100Light soaking (min.)

intensity

(a) (b) (c)

24

Statistic data on solar cell figure of merit on the optimized processing

conditions

Fig. S12. Device statistics with figure-of-merit for over 30 devices. Histograms of (A)open circuit voltage (VOC)(B) Current density (JSC)(C) Fill Factor (F.F) and (D) power conversion efficiency (PCE).

Hysteresis test for device

Fig. S13 Hysteresis test for mixed cation solar cell (A) light JV-curve with voltage scan from positive to negative (blue) and negative to positive (red). (B) JV-curves for different voltage delay time between 0.2 V step, from 10 mS to 300 mS. (C) short circuit current transient by turning the light on (yellow region) and off (grey region).

20

15

10

5

0

Cou

nts

1.151.101.051.000.95VOC (V)

12

10

8

6

4

2

0

Cou

nts

262524232221JSC (mA/cm

2)

12

10

8

6

4

2

0

Cou

nts

858075706560Fill Factor (%)

10

8

6

4

2

0

Cou

nts

22201816PCE (%)

A B C D

-30

-20

-10

0

10

J (m

A/c

m2 )

1.20.80.40.0-0.4Voltage (V)

-30

-20

-10

0

10

J (m

A/c

m2 )

0.80.40.0V (V)

10 mS 100 mS 300 mS

Voltage delay time (0.2 V step)

A B C

24

22

20

18

16

J SC (m

A/c

m2 )

800600400200Time (Sec)

25

Simulation for experimental observed JV-characteristics.

Fig. S14 JV-simulation by changing bulk recombination lifetime. Experimental (symbols) and simulated (solid line) JV curves by varying bulk recombination lifetime and mobility from (A) 10 nS, 1.0 cm2/V/S to (B) 1 nS 6.0 cm2/V/S while the interfacial recombination remain the same.

Fig. S15. JV-simulation by changing interface recombination lifetime. Experimental (symbols) and simulated (solid line) JV curves by varying interface recombination lifetime from (A) 0.004 nS to (B) 2 nS while the bulk properties remain the same.

!",$@'()*+,-.*/= 2 ∗ 1056/!789:;,< = 1 ∗ 105=/

>" = 1.0 .@A

B. />$ = 1.0 .@

A

B. /

!",$@'()*+,-.*/= 2 ∗ 1056/!789:;,< = 1 ∗ 1056/

>" = 6.0 .@A

B. />$ = 6.0 .@

A

B. /

A B

!",$@'()*+,-.*/= 4 ∗ 10567/!89:;<,= = 1 ∗ 105>/

?" = 6.0 .B7

C. /?$ = 6.0 .B

7

C. /

!",$@'()*+,-.*/= 2 ∗ 105E/!89:;<,= = 1 ∗ 105>/

?" = 6.0 .B7

C. /?$ = 6.0 .B

7

C. /

A B

Before light After light

26

Fig. S16 JV-simulation by changing interface recombination lifetime and adding interfacial energetic barriers. Experimental (symbols) and simulated (solid line) JV curves along with the recombination profile (middle panel) and charge density distribution (bottom panel) as a function of film position. Electro-absorption spectrum

Fig.S17 Electro-absorption spectrum for mixed cation device before and after illumination. The measurements are in reflection mode taken under 2nd harmonic frequency of the AC field frequency. The only signal in the full spectrum is found at the energy of band edge absorption of mixed cation perovskites (794 nm), indicating the EA modulation is along the band edge of the absorbing layer without the contribution from any other layer in the cell.

Before After

A B

40

20

0

-20

∆R (1

0-6)

850800750700650600Wavelength (nm)

before after

2nd Harmonic

27

Control Experiments with applied bias

Fig. S18 Applied bias for solar cell devices under dark. (A) dark and light current density-voltage (J-V) curves for device before any experimental stimulus. (B) dark forward current for this device at three different applied biases points labeled in (A) with yellow stars. The dark current for low bias condition did not increase while that under 0.76 V decreased slightly from 3.49 mA/cm2 to 3.22 mA/cm2. We therefore bias the device in the dark with constant current mode (3.49 mA/cm2) in the following experiments.

-20

-10

0

10J

(mA

/cm

2 )

0.80.60.40.20.0-0.2Voltage (V)

Dark Light Vapp

10-4

10-3

10-2

10-1

100

101

J (m

A/c

m2 )

150100500Time (Min)

(A) (B)

0.2 V

0.5 V

0.76 V

28

Fig. S19 Control experiments analysis. (A) dark (black lines) and light (colored lines) J-V curves for device under constant JON in the dark for various time period (from 5 min to 180 min). (B) The light J-V plots by overlaying the light J-V curves from (A). The extracted average (C) open circuit voltage (VOC) and (D) fill factor (F.F.) for devices under JON in dark are plotted as a function of time. The values are averaged among 6 different devices with error bars. As a comparison, we plotted device’s VOC and F.F. as a function of time under constant illumination taken from the manuscript, shown as dotted lines in (C) and (D). From the results, we did not observe significant increase in VOC nor F.F. when biasing in dark in all three testing conditions comparing to light soaking. It is therefore conclusive that under forward bias where ionic movement should be triggered by the generated electrical field in dark did not contribute to the observed change in device performance in the current system.

-20

-10

0

10

J (m

A/c

m2 )

0.80.60.40.20.0-0.2Voltage (V)

0.80.60.40.20.0-0.2Voltage (V)

0.80.60.40.20.0-0.2

Voltage (V)

0.80.60.40.20.0-0.2

Voltage (V)

5 min 20 min 60 min 180 min

-20

-10

0

10

J (m

A/c

m2 )

0.80.40.0Voltage (V)

0 min 5 min 20 min 60 min 180 min

(A)

(B) (C) (D)

8070605040

F.F.

(%)

150100500Time (min)

0.2 V

1.0

0.8

0.6VO

C (V

)

150100500Time (min)

0.2 V

8070605040

F.F.

(%)

150100500Time (min)

0.5 V

1.0

0.8

0.6VO

C (V

)

150100500Time (min)

0.5 V

(E)

1.0

0.8

0.6

VO

C (V

)

150100500Time (min)

Bias in dark

In light80

70

60

50

F.F.

(%)

150100500Time (min)

29

Fig. S20 Devices and structure characterization before and after illumination. (A) light J-V curves under 1-Sun illumination for device before light soaking (after 3-hour bias at 0.76 V described in Fig. S19) and after light soaking. (B) GIWAXS line-cut for device before and after forward bias in dark. The above two experiments suggest that the device did not undergo degradation after biasing, thus validating the conclusion obtained from the above experiments. Extended stability tests under various stressing conditions

Fig. S21 Stability tests under various stressing conditions (A), Device EQE spectrum by sitting under 1-Sun illumination for 5-Day and 10-Day without shift in spectrum. (B) short-circuit current density as a function of light intensity are plotted for devices with triple cation (red) and MAPbI3 as absorbers (blue); (C) Device EL and PL spectrums as a function of injection current (10~103 mA/cm2 range) and excitation power (76~7600 mW/cm2) without shift in energy.

-20

-10

0

10

J (m

A/c

m2 )

1.20.80.40.0Voltage (V)

Before Light After Light

(A) (B)20

15

10

5

0

Inte

nsity

(103 )

3.02.52.01.51.0q (Å-1)

1 V bias for: 10 min 180 min

80

60

40

20

EQE

(%)

800700600500400Wavelength (nm)

5-DAY 10-DAY

2

1

J SC (1

02 mA

/cm

2 )

1000800600400200Light Intensity (mW/cm2)

J~I0.96

J~I0.73

FA0.7MA0.25Cs0.05PbI3 MAPbI3 Fit Line

1.5

1.0

0.5

0.0

Nor

m. E

L/P

L in

tens

ity (a

.u.)

900800700

10

300

JInj (mA/cm2)

EL

900800700

76

7600

Laser Power (mW/cm

2)

PL

Wavelength (nm)

A B C

30

Supplementary Tables

Table S1. Equations for Carrier Transport

Poisson Equation: 𝜖"𝜖#∇%𝜓 = −𝑞(𝑛- − 𝑛.)

Continuity: ∇𝐽.,- = 2𝐺.,- − 𝑅.,-(𝑛., 𝑛-)5

Drift-Diffusion: 𝐽.,- = 𝜇.,-𝑛.,-(−∇𝜓) ± 𝐷.,-∇𝑛.,-

Recombination:

𝑅.,-(𝑛., 𝑛-) = 𝐵(𝑛.𝑛- − 𝑛:%) +𝑛.𝑛- − 𝑛:%

𝜏(𝑛. + 𝑛-)

Table S2. Absorber Parameters (Perovskite)

Symbol Description Parameter value 𝐿>?@A"?." Thickness of absorber layer 450 nm

𝜇. Electron mobility in absorber 20.0 (cm2/V.s) 𝜇- Hole mobility in absorber 10.0 (cm2/V.s) 𝜏. Electron lifetime in absorber 10 (ns) 𝜏- Hole lifetime in absorber 10 (ns) (67)

𝐿𝑈𝑀𝑂 Lowest Unoccupied Molecular Orbital 3.73 (eV) (68)

𝐸F Band gap of absorber 1.62 (eV) 𝜀" Relative dielectric constant 45 𝑁> Self-Doping concentration (P-type) 5.0 e16 (#/cm3)

Table S3. Electron Transport Material Parameters (ETM = C60/PCBM)

Symbol Description Parameter value 𝐿IJK Thickness of ETM layer 60 nm 𝜇. Electron mobility in ETM 1e-2 (cm2/V.s) (69) 𝜇- Hole mobility in ETM 1e-2 (cm2/V.s) 𝜏. Electron lifetime in ETM 1000 (ns) 𝜏- Hole lifetime in ETM 1000 (ns)

𝐿𝑈𝑀𝑂 Lowest Unoccupied Molecular Orbital 4.17 (eV) (70)

𝐸F Band gap of ETM 2.0 (eV) (71) 𝜀" Relative dielectric constant 4 (72) 𝑁L Self-Doping concentration (N-type) 5.0 e17 (#/cm3) (69)

31

Table S4. Hole Transport Material Parameters (HTM = 𝐍𝐢𝐎𝐱)

Symbol Description Parameter value 𝐿QJK Thickness of HTM layer 40 nm 𝜇. Electron mobility in HTM 9e-2 (cm2/V.s) 𝜇- Hole mobility in HTM 9e-2 (cm2/V.s) (73) 𝜏. Electron lifetime in HTM 1000 (ns) 𝜏- Hole lifetime in HTM 1000 (ns)

𝐻𝑈𝑀𝑂 Highest Occupied Molecular Orbital 1.8 (eV) (74) 𝐸F Band gap of HTM 3.4 (eV) (75) 𝜀" Relative dielectric constant 15 𝑁> Self-Doping concentration (P-type) 3.0 e17 (#/cm3) (73)

Table S5. Crystal data and structure refinement for CH3NH3PbI3 at 293 K. Conditions Dark Light Formula weight 620 620 Temperature 293 K 293 K Wavelength 0.71073 Å 0.71073 Å Crystal system tetragonal tetragonal Space group I4cm I4cm

Unit cell dimensions a = 8.8675(2) Å c = 12.6438(7) Å

a = 8.8932(2) Å c = 12.6692(7) Å

Volume 994.21(6) Å3 1001.99(6) Å3 Z 4 4 Density (calculated) 4.1419 g/cm3 4.1097 g/cm3 Absorption coefficient 26.202 mm-1 25.998 mm-1 F(000) 1096 1040 θ range for data collection 3.22 to 33.32° 3.22 to 37.87°

Index ranges -13<=h<=13, -13<=k<=13, -19<=l<=19

-13<=h<=15, -15<=k<=14, -19<=l<=21

Reflections collected 10763 12435 Independent reflections 1040 [Rint = 0.0421] 1392 [Rint = 0.0451] Completeness to θ 100% 99% Data / restraints / parameters 1040 / 1 / 18 1392 / 1 / 18

Goodness-of-fit 3.33 3.21

Final R indices [I>2σ(I)] Robs = 0.0380, wRobs = 0.1309

Robs = 0.0381, wRobs = 0.1299

R indices [all data] Rall = 0.0425, wRall = 0.1318

Rall = 0.0471, wRall = 0.1307

Extinction coefficient 1830(110) 1840(90) Largest diff. peak and hole 1.86 and -2.11 e·Å-3 1.96 and -1.91 e·Å-3

32

Table S6. Atomic coordinates (x104) and equivalent isotropic displacement parameters (Å2x103) for CH3NH3PbI3 at 293 K with estimated standard deviations in parentheses. Light x y z Occupancy Ueq* Pb 0 0 33(1) 1 30(1) I(2) 2842(2) 2158(2) -14(4) 1 84(1) I(1) 0 0 2560(4) 1 83(1) C 5000 0 2350(30) 1 131(15) N 5000 0 3540(30) 1 131(15) H(1c) 4275.4 714.67 2099.38 0.25 157.6 H(2c) 5981.22 270.19 2099.38 0.25 157.6 H(3c) 4743.38 -984.86 2099.38 0.25 157.6 H(1n) 4110.77 -244.86 3764.79 0.25 157.6 H(2n) 5656.67 -647.67 3764.79 0.25 157.6 H(3n) 5232.56 892.53 3764.79 0.25 157.6 Dark x y z Occupancy Ueq* Pb 0 0 35(2) 1 30(1) I(2) 2844(2) 2156(2) -15(5) 1 83(1) I(1) 0 0 2559(5) 1 82(1) C 5000 0 2300(50) 1 190(40) N 5000 0 3480(50) 1 190(40) H(1c) 4278.26 721.74 2042.96 0.25 232.9 H(2c) 5985.91 264.17 2042.96 0.25 232.9 H(3c) 4735.83 -985.91 2042.96 0.25 232.9 H(1n) 4106.52 -239.41 3711.74 0.25 232.9 H(2n) 5654.07 -654.07 3711.74 0.25 232.9 H(3n) 5239.41 893.48 3711.74 0.25 232.9

33

Table S7. Anisotropic displacement parameters (Å2x103) for CH3NH3PbI3 at 293 K with estimated standard deviations in parentheses. Light U11 U22 U33 U12 U13 U23 Pb 30(1) 30(1) 30(1) 0 0 0 I(2) 70(1) 70(1) 112(2) -47(1) 26(2) -26(2) I(1) 115(1) 115(1) 20(1) 0 0 0 Dark U11 U22 U33 U12 U13 U23 Pb 30(1) 30(1) 30(1) 0 0 0 I(2) 70(1) 70(1) 110(2) -47(1) 25(2) -25(2) I(1) 113(2) 113(2) 20(1) 0 0 0

Table S8. Bond lengths [Å] for CH3NH3PbI3 at 293 K with estimated standard deviations in parentheses. Light Distances Pb-I(2) 3.1741(13) Pb-I(1) 3.201(5) Pb-I(1)’ 3.134(5) C-N 1.50(5) Dark Distances Pb-I(2) 3.1654(15) Pb-I(1) 3.191(6) Pb-I(1)’ 3.131(6) C-N 1.50 (9)

Table S9. Bond angles [°] for CH3NH3PbI3 at 293 K with estimated standard deviations in parentheses. Light Angles I(2)-Pb-I(2)’ 177.85(14) Pb-I(2)-Pb’ 164.26(5) Pb-I(1)-Pb’ 180.0(5) Dark Angles I(2)-Pb-I(2)’ 177.70(18) Pb-I(2)-Pb’ 164.14(6) Pb-I(1)-Pb’ 180.0(5)

34

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