Signatures of Polaron Dynamics in Photoexcited MAPbBr3 by Infrared Spectroscopy

Hybrid organic–inorganic perovskites (HOIPs) have attracted considerable attention in the past years as photoactive materials for low-cost, high-performance photovoltaics. Polaron formation through electron–phonon coupling has been recognized as the leading mechanism governing charge carrier transport and recombination in HOIPs. In this work, two types of MAPbBr3 film samples deposited on different substrates (transparent insulating SrTiO3 and a heterostructure mimicking a functioning photovoltaic cell) were photoexcited with above-bandgap radiation at 450 nm, and the effects of illumination on the sample were analyzed in the infrared region. The infrared absorbance detected at different powers of the photoexciting laser allowed us to obtain an estimate of the characteristic decay time of photoexcited polaron population of the order of 100–1000 ns. When focusing on the absorption features of the MA molecular cation in the region of the NH stretching modes, we observed the influence of hydrogen bonding and the effect of the polaron dynamics on the cation reorientation.


S2. UV-Vis absorption and Photoluminescence spectrum of Sample B and sample A
The UV-Vis spectrum was collected as already described in the main text, while the photoluminescence (PL) spectrum was collected on an optical table-mounted Raman setup.
Excitation of the sample was achieved with a wavelength-tunable Melles-Griot Argon ion laser emitting a 488 nm laser line.The power was kept below 10 mW.The photoluminescence signal was collected in backscattering geometry using an Olympus BX62 microscope equipped with an S5 objective of 10x magnification.The beam was then analyzed with a Triax 320 single pass Czerny-Turner spectrometer by Horiba-Jobin Yvon, employing an 1800 grooves/mm diffraction grating and a Peltier-cooled charge-coupled device (CCD) detector.As already described by M. Hirasawa et al. [2], and schematically reported in the energy level diagram of Figure S2b, the two features in the absorbance spectrum can be associated with two possible transitions at the R point of the Brillouin zone when accounting for spin-orbit (SO) coupling.
The observed absorption edge is in good agreement with the value reported in the literature [3,4] The PL spectrum, asymmetric in shape, was analyzed employing a two-peak convolution fit.
This analysis shows that the PL profile is composed of a main peak centered at 2.28 eV (544 nm), and a broader, secondary peak at lower energies 2.26 eV (549 nm), whose origin can be ascribed to the presence of intragap energy levels.(black).The dashed grey line is reported as a guide to the eyes to highlight the slope of the data.
Interference fringes are visible on the spectrum of the substrate alone, due to its heterostructured composition.

S3. Estimation of the number of polaron
The temporal evolution of polaron population can be described by the following equation: in which  is the photoinduced polaron formation rate, and is the characteristic decay  = 1/ time of the polaron population.
In the present experiment, in which each spectrum acquisition is about 20 sec long, we can reasonably assume that the number of detected polarons follows the asymptotic solution:

S4. Polaron absorption coefficient
A third sample, prepared with the same protocol of sample B but with a precursor concentration of 0.8 M in the initial solution, was synthesized for the estimation of the polaron absorption coefficient.The thickness of this film sample was measured at 101 nm.
The absorption coefficient in the IR was estimated using the relation , where A 2 and A 1 are the normalized polaronic absorbances of the two perovskite films deposited on STO of thicknesses 300 and 100 nm respectively, and the term d 2 -d 1 is the difference between the thicknesses of the two films.This calculation returns an absorption coefficient of  Pol in the range of 10-100 cm -1 , where the variability depends on the efficiency in polaron creation by the optical laser pumping.

S5. Estimate of the number of incident photons from laser power
The number of photons absorbed by the sample as a function of the laser output power was estimated as follows: being P is the optical output power of the laser diode (in Watt), S is the illuminated area (in cm 2 ) and d the film thickness.This quantity also accounts for MAPbBr 3 absorption coefficient α at 450 nm.

S6. Effects of temperature on the differential A spectrum
For the differential absorbance data interpretation, we here employ a two-level system model, in which the two levels are excited by IR and external laser irradiation.

S10
In this (semiclassical) model, only the ground state (G) and the first vibrational level (W) of a given molecular oscillator (e.g. the NH stretching mode at 3149 cm -1 ) are considered.In presence of IR radiation and laser excitation, the population for the W and G levels vary with rates and , respectively, in accordance with the kinetics equations: where:  is the rate of excitation of the vibrational state induced by indirect laser pumping; k 1 is the spontaneous emission coefficient for radiative decay; k 2 is the stimulated emission coefficient which includes the IR radiation density; k 3 is the stimulated absorption coefficient which includes the IR radiation density; In the limit of k 1 » k (being k = k 2 = k 3 ) and  = 0 the steady state populations under IR excitation reduce to

𝐺
Within the same approximation (=0) it is possible evaluate the percentage variation of the ground state population n G /n G 0 at different temperatures.This quantity is simply given by S11 and is proportional to the relative variation of absorption intensity.
If the influence of the laser is considered only as a thermal source rather than a promoter of the population of the W state, we can still use the approximation = 0 and evaluate the value of the relative population of the ground state due to the increase in temperature induced by the laser.An increase of temperature T upon light irradiation can be calculated by the expression ,  =

𝛼𝐷 𝜌𝑐
where  (cm -1 ) is the absorption coefficient at 450 nm, D the energy density (or fluence in J cm -2 ) of the laser at the spot of incidence with a given size,  the sample mass density (in g cm -3 ) and c the specific heat (in J K -1 g -1 ) [6].However, the use of this relation lead to unphysical results in our case, as the poorness of the model does not account for the complex heterostructure of our sample.Thus, we measured the temperature of the film with a thermocouple as close as possible to the laser spot.just after 60 s of illumination.This method suffers for poor thermal contacts of the thermocouple and returns underestimated values of the film surface temperature.Therefore, we arbitrarily consider the temperature of the sample as twice and three times the value that was detected.The measured temperatures corresponding to different laser powers are reported in Figure S4a.It is to be noted that the estimation of the sample local temperature here reported does S12 not exceed MAPbBr 3 melting temperature (>450 K) [7].As it can also be seen directly on the IR spectra, the features collected on the photoexcited films resembles the ones observed on the unperturbed one, meaning that the HOIP crystals did not undergo any substantial phase transition in the illumination conditions employed in this experiment.In Figure S4b, values of the relative ground state variation due to thermal effects and the experimental relative absorption detected upon laser irradiation are reported for a comparison.At the frequency of the NH bending mode, 1470 cm -1 , the observed decrease in absorption is compatible with the thermal effect alone, assuming that the local temperature reaches the values in Figure S4a.The result for the frequency of NH stretching (~3100 cm -1 ) is drastically different, since between the theoretical estimate and the experimental values there are several orders of magnitude in favor of the latter.This result advises for the crucial role of the electronic photoexcitation, which affects the constant rate  and the presence of which cannot be neglected in the case of high frequency molecular modes.

Figure S1 .
Figure S1.Top panel: Raman spectrum of Sample A acquired right after its synthesis (dark green)

Figure S2 .Figure S3 .
Figure S2.(a) Absorbance spectrum in the UV-Vis range of Sample B. The vertical blue arrows

Figure S4 .
Figure S4.(a) Temperatures measured on the MAPbBr 3 film at different laser power illuminations.

Figure S5 .
Figure S5.Differential absorbance A of Sample B in the NH stretching mode region, at different

Figure S6 .
Figure S6.Baseline spline subtraction on the spectra corresponding to an optical laser output power