Light-activated photocurrent degradation and self-healing in perovskite solar cells

Solution-processed organometallic perovskite solar cells have emerged as one of the most promising thin-film photovoltaic technology. However, a key challenge is their lack of stability over prolonged solar irradiation. Few studies have investigated the effect of light soaking on hybrid perovskites and have attributed the degradation in the optoelectronic properties to photochemical or field-assisted ion migration. Here we show that the slow photocurrent degradation in thin-film photovoltaic devices is due to the formation of light-activated meta-stable deep-level trap states. However, the devices can self-heal completely by resting them in the dark for <1 min or the degradation can be completely prevented by operating the devices at 0 °C. We investigate several physical mechanisms to explain the microscopic origin for the formation of these trap states, among which the creation of small polaronic states involving localized cooperative lattice strain and molecular orientations emerges as a credible microscopic mechanism requiring further detailed studies.

with recovery in dark (by resting the sample in the dark between each data point). The dark curve serves as reference and corresponds to the signal response of the perovskite thin film freshly prepared and is measured under very low excitation photon power density (0.9 μJ/cm 2 ) to prevent the formation of the light-activated meta-stable trap states. After a power density increase/decrease cycle, the thin film response is measured again at low excitation power density. The 'high photon fluence' corresponds to an excitation power density of 125 μJ/cm 2 .

Supplementary Note 1. Statistics of photo-degradation over several devices
To further validate our measurements, we have performed for 2 additional devices the same measurements of photo-degradation as in the main text (Supplementary Figure 2). Identical to what is reported in the main text, the V OC do not change over time once it reaches the steady state value, the only degradation parameter is the J SC and thus leads to PCE change.
Moreover, we investigated the photocurrent photo-degradation in four additional devices  Based on these, we suspect that the observed change in XRD at 12° is possibly due to the testing condition of XRD, which was performed, in this particular case, in ambient air.

Photoluminescence spectroscopy
Second, structural and chemical photo-stability were also verified by time-resolved

Photocurrent spectrum
Finally, the device photocurrent spectrum was tested in AC mode (from monochromatic light chopping at 100 Hz) at short circuit while it is biased with constant DC AM1.5 1-sun illumination as a function of time (Supplementary Figure 4). Over time we observed photocurrent reduction in magnitude that is consistent with J SC measurement with light J-V characteristics. However, the photocurrent spectra remain identical when normalized as plotted in Supplementary Figure 4. Therefore, the degradation observed by J SC over time does not alter the spectral shape of the photocurrent, and this is additional evidence that long time illumination does not degrade the crystal structure.
In summary, in this section we have demonstrated that we do not detect any light-activated structural phase transition, as verified by X-Ray diffraction (XRD), photoluminescence spectroscopy, and spectrally-resolved photocurrent

Supplementary Note 3. Exclusion of other possibility at the origin of photocurrent degradation
In order to validate our hypothesis on the origin of photo-stability in large-grain-based organometallic perovskite solar cells, we did control experiment in dark to excluded a) heating effect and b) bias effect over device stability.

Excluding the heating effect in dark
We

Photocurrent degradation for different perovskite recipes
We also verified that the photocurrent J SC degradation is independent of crystal structures in

Supplementary Note 4. Photocurrent degradation/recovery in solar cells
In this section, we present results complementary to those reported in Figures 1 and 2 of the main manuscript that we feel important for the readers and the understanding of our work.

Fill factor degradation under constant illumination
As complementary of the figures of merit reported in Fig. 1c-e, we derived the corresponding fill factor during the first cycle of space charge accumulation (Supplementary Figure 1).

Photocurrent degradation for devices stressed at different load points
Although this report focuses on the degradation of performances in solar cells devices

Power dependence of photocurrent degradation and temperature dependence of photocurrent recovery
We also measured the percentage of degradation in the J SC of the solar cell as a function of light excitation power (or number of suns) (Supplementary Figure 9). The solar cell performances degrade almost four times faster under a constant illumination intensity of seven sun as compared to the standard one sun photo-excitation (J SC degrades by 2.12% at 1 sun up to 7.6% at 6.6 suns) indicating that the density of light-activated trap states is directly proportional to the light excitation power density as observed in the photoluminescence data.

Light-activated space charge accumulation in solar cells verified by C-V measurements
The charge density profiles reported in Fig. 2a of the main text are obtained from the C-V characteristics in Supplementary Figure 10. From the C-V measurements the charge density where x is the depletion width determined by ε r is relative dielectric constant calculated from the capacitance of the device at zero bias (~20), and A is the device active area (0.035 cm 2 ), and ε 0 is the vacuum permittivity.

Transient photocurrent at room temperature
The photocurrent transient measurements also support the hypothesis of the formation and (ii) 'Recovered system in dark', the sample is illuminated only during the measurement time and we waited for the system to recover in dark in between each data point of the power density cycle.

Recombination kinetics
The dynamics of carriers in crystal grain perovskite at room temperature were described by 1 st order rate equations, after initial fast relaxation (~few ps) of free carriers to the bandedge unresolved in our measurements. In this picture, variations of the photo-generated excess carrier density u(t) at the band-edge are well described by: 25,54,55 The three terms on the right-hand side of (Supplementary equation 5) correspond to, respectively, the initial photo-excitation generation rate density of carrier (where the density of electrons is equivalent to the density of holes, calculated from the absorbance and the absorption coefficient α), the bimolecular radiation recombination (or spontaneous emission of light by the recombination of a free electron and hole at the band-edge), and the non-radiative trap-assisted recombination of free carriers. The measured photoluminescence intensity can be expressed as: where N D corresponds to the total doping density of the material ( = electron + hole ).
Detailed analysis of the carrier recombination dynamics is beyond the scope of this paper and should be reported in future works. We emphasise that the relevant information in this paper is the comparison of the carrier effective lifetime 56 and PL integrated intensity between experiments (i) and (ii).

Decay lifetime and photo-emission vs. excitation power density
Following the modelling of the recombination kinetics described above of the data reported in Supplementary Figure 14

Photo-bleaching effect and recovery mechanism
As mentioned in the previous sub-sections and the main text, the PL can be partially photobleached using high excitation power density. To better understand and correlate the mechanism of PL photo-bleaching to the photocurrent degradation observed in solar cells, we investigated the change of the power density threshold at which the photo-bleaching occurs for two temperatures (Supplementary Figure 16). We underline here that for this experiment we constantly illuminate the perovskite thin film at different power density (light soaking) and monitor the PL response at regular time intervals by temporarily lowering the power density to its lowest (where no degradation was observed). In this way, we were able to follow the evolution of the photoluminescence under the same conditions for all experiments, corresponding also to the PL monitoring conditions used for studying the recovery mechanism (Fig. 3b) in which case the sample is rested in the dark and the PL is probed at low power density at regular time intervals. At room temperature (25 °C), the power density photo-bleaching threshold is observed when illuminating the thin film with 20-30 μJ/cm 2 corresponding to a clear quenching of the PL amplitude monitored at low power density. By heating the sample to 47 °C (which could better reflect the temperature of solar cells under standard operating conditions), the photo-bleaching threshold is lowered to few μJ/cm 2 . Therefore, considering the broadband excitation provided by 1-Sun light and the internal temperature increase of solar cells, we believe that PL spectroscopy (monochromatic light at 640 nm) is able to probe the same degradation mechanism. The strong temperature dependence observed here is in good agreement with the recovery dynamics and the model proposed in the main text.

No observable XRD and PL changes
As illustrated in Supplementary Figure 3, we do not observe any structural change in XRD before and after illumination (i.e. no additional peak nor significant change in peak amplitudes). As suggested by previous reports 13,17 , monitoring the photoemission of the

Field dependence
According to recent reports, ion migration is significantly affected by applied external field 17,18,20,21 . Therefore, we examine our photocurrent degradation process under external field. Specifically we applied a forward bias to the photovoltaic device in the dark and monitor the photocurrent and open circuit voltage change as shown in Fig. 3c (main text).
The results indicate that photocurrent does not degrade over time by biasing the device in the dark. On the contrary, the open circuit voltage increases slightly (± 0.05 mV) when a forward bias is applied in the dark. The voltage returns to its original value after removing the bias. This might be a consequence of ion migration. However, the miniscule change in V OC of ± 0.05 mV again suggests that ion migration is negligible and is not the dominant mechanism that causes photocurrent degradation.

Hysteresis test for devices before and after photo-degradation
The device hysteresis effect is tested for device reaches a steady state and after degraded by 1 sun illumination for 2 hours. According to literature report 18,19 , the ionic migration contributes to the hysteresis effect by fast J-V scans which will lead to a "S-shape" curve at -1 V reverse bias. We therefore tested our hysteresis free device (Supplementary Figure 18, upper panel) for 2 hours constant illumination till the photocurrent degrades to 80% of its original value, and resulted hysteresis test are illustrated in Supplementary Figure 18 (lower panels), we do not observe hysteresis curves for different scan direction and scan rates.
Therefore, we can conclude the constant illumination does not trigger ion migration induced J-V hysteresis and thus rule out any major contribution from ion migration.

Dielectric constant change measured by capacitance
The relative dielectric constant change in Fig. 2d

Supplementary Note 7. Theoretical modeling of spatial localization of charge carrier wave function
Our study attributes the photo-degradation phenomena in perovskite solar cell devices to the light-activated meta-stable trap states of atomistic origin (polarons). Namely, we assume that there are two distinct types of charge states: free charges and polarons. The former have delocalized wave functions, low effective mass and are very mobile with diffusion length exceeding micron in the high quality crystalline perovskites. The second type of charge carrier is a heavy polaron being a spatially localized electron or hole with a large effective mass and, therefore, very short diffusion length as illustrated on Supplementary   Figure 23a,b. These carriers correspond to dressed quasiparticules, the dressing stemming in the non-polar case from the volumetric strain and interactions with neighboring MA (CH 3 NH 3 + ) cations that rotate so as to adiabatically follow the charge moving through the medium.

Symmetry analysis
To unravel the nature of light induced meta-stable trap states, symmetry consideration yields primary information about possible coupling between charge carriers and vibrational/rotational degrees of freedom. Starting with the parent cubic lattice, we analyze collective vibrations (phonons) and molecular reorientations (pseudo-spins) separately.
Both of the most common notations for irreducible representations (IR) will be indicated: first that of Altmann 67 whereas that of Millers and Love 68 will be given in parenthesis.
Lattice phonons involve atoms from the inorganic octahedra and the center of mass of the molecular cation. Therefore, molecular vibrations can be decomposed into two parts: translation of the center of mass and reorientation of the C-N axis when the cation is Electron-phonon coupling occurs if the IR of a given phonon is contained in the product of IR of electronic states. For electronic states at the R-point of the Brillouin zone (BZ), the IR are A1g (R1 + ) for the valence band (VB) and a triply degenerated T1u (R4 -) for the conduction band (CB). Taking into account spin-orbit coupling (SOC) 69 , the IR become E1/2g for the VB, E1/2u for the bottom of the CB and F3/2u for the other states arising from spin-orbit split-off. 70 The product of these IR leads to: A1g (Γ1 + ) for the VB and Model B: A1g+Eg+T2g+T1u+T2u (Γ1 + +Γ3 + +Γ5 + +Γ4 -+Γ5 -) ; Model C: A1g+T2g+A2u+T1u (Γ1 + +Γ5 + +Γ2 -+Γ4 -).
This clearly shows that at the Γ-point of the BZ, the totally symmetric IR A1g is contained in all three decompositions. Therefore the electronic states can couple to any of the molecular arrangements out of the three models defining possible tumbling of the organic cations. Noteworthy, the totally symmetric Γ1 + IR corresponds to equal occupation probabilities for each orientation.
In summary, this symmetry analysis shows that free carriers can only undergo non-polar coupling through deformation potentials with acoustic phonons related to short-range interactions, local volumetric strain and to specific symmetric configurations of the molecular cations. The influence of local lattice deformations will be tested in the next part using DFT computations. Finally, let's discuss the polar coupling mechanisms. The fact that low-frequency polar coupling to acoustic phonons, namely piezoelectric like mechanism 71 , is symmetry forbidden in the Pm-3m cubic lattice, in addition to the scarcity of the deformation potential mechanisms in relation with SOC 69 , is most probably at the origin of good carrier transport and very large diffusion lengths 73 in these hybrid perovskites. The polar coupling to optical phonons, namely Fröhlich mechanism, is usually related to longrange interactions, the splitting between longitudinal and transverse phonon modes (LO-TO splitting) due a triply and polar degenerate IR (like Γ4for hybrid perovskites) as well as increments in the dielectric constant. This interaction is expected to occur in the hybrid perovskites at much higher frequencies (optical phonons energies in hybrid perovskites are on the order of 12meV i.e. 100cm -1 ) than the interaction with low frequency acoustic phonons (which undergo energy dispersion down to 0 meV) or molecular pseudospins (typical relaxation times at 300 K amount to 5 ps i.e. 0.12 meV. 74 A polar coupling mechanism to pseudospins, connected to the triply degenerate and polar IR Γ4in the decompositions of the pseudo-spins IR, is thus expected to appear also at low frequency and yield additional contributions for the formation of polarons.

Effect of MA rotation and volumetric strain from DFT simulations
We start our DFT modeling using the bulk structure for the low temperature orthorhombic phase of MAPbI3. 75 In fact, it is well known that at room temperature (RT), the MA cations undergo dynamical disorder related to incompatible site symmetry with the RT space group  Figure 23 (g,h)). In both cases observed separation of charges is going to reduce radiative recombination between mobile and localized carriers.
Notably, there is a significant reduction of the band gap caused by orientation of the MA dipoles (Supplementary Figure 24). Regardless of whether or not SOC is included, the band gap in the system with rotated MA molecules is smaller by 0.1 to 0.2 eV compared to that of the unperturbed structure.
In order to model the effect of volumetric strain on the charge density, the experimental structure was first fully relaxed (forces < 0.025 eV/Å) allowing both atomic positions and the cell parameters to change. Then, considering a supercell of 192 atoms, a single Pb atom was replaced with either a Bi (+3 cation) or a Tl (+1 cation) atom and the new structure was optimized by just allowing the atomic positions to move. It is important to note that atoms surrounding the defect will move both because of the loss of charge balance as well as a change in atomic size. The changes in bond length, in pm, from the atoms immediately surrounding the defect atom are shown in Supplementary Table 1. In many ways these results are expected, as when the Bi atom is present, there is an additional positive charge that will cause the equatorial Iodine atoms to move closer, and the positively charge N atom to move farther way. It should be noted that the apical Iodine atoms actually move away from the Bi atom. This non-symmetric volumetric strain is likely a bias related to the use of an orthorhombic supercell. Tl, being only a +1 cation, will not attract the surrounding Iodine atoms as strongly and they will move farther way, while the MA atoms will want to be closer. The most probable reason for the much larger reorientation in the case of Bi substitution is the fact that Bi is much smaller than the similarly sized Tl and Pb.
Once the modified systems were optimized the charge densities were calculated.
Supplementary Figure 25a,b shows a schematic of what volumetric strain may look like.
Supplementary Figure 25c shows the localized charge density of the HOMO when Tl replaces a Pb atom. This is expected as Tl is a weaker cation than Pb. Supplementary Figure   25d shows the localized charge density of the LUMO when Bi replaces a Pb atom.
As further evidence of the change in charge density that volumetric strain can cause, the atomic coordinates that were obtained after optimization of the system containing a Bi atom were used to calculate the charge density of a system with all Pb atoms. The localized HOMO is shown in Supplementary Figure 26. Here charge balance has been restored by reintroducing the original Pb atom, and only relative atomic displacement is causing the observed localization.

Density functional theory computation details
All While in this case there were negligible changes in the band gaps and orbital charge densities, future investigations will focus on how dispersive forces play a role in the dynamics of the system.