Disentangling Thermal from Electronic Contributions in the Spectral Response of Photoexcited Perovskite Materials

Disentangling electronic and thermal effects in photoexcited perovskite materials is crucial for photovoltaic and optoelectronic applications but remains a challenge due to their intertwined nature in both the time and energy domains. In this study, we employed temperature-dependent variable-angle spectroscopic ellipsometry, density functional theory calculations, and broadband transient absorption spectroscopy spanning the visible to mid-to-deep-ultraviolet (UV) ranges on MAPbBr3 thin films. The use of deep-UV detection opens a new spectral window that enables the exploration of high-energy excitations at various symmetry points within the Brillouin zone, facilitating an understanding of the ultrafast responses of the UV bands and the underlying mechanisms governing them. Our investigation reveals that the photoinduced spectral features remarkably resemble those generated by pure lattice heating, and we disentangle the relative thermal and electronic contributions and their evolutions at different delay times using combinations of decay-associated spectra and temperature-induced differential absorption. The results demonstrate that the photoinduced transients possess a significant thermal origin and cannot be attributed solely to electronic effects. Following photoexcitation, as carriers (electrons and holes) transfer their energy to the lattice, the thermal contribution increases from ∼15% at 1 ps to ∼55% at 500 ps and subsequently decreases to ∼35–50% at 1 ns. These findings elucidate the intricate energy exchange between charge carriers and the lattice in photoexcited perovskite materials and provide insights into the limited utilization efficiency of photogenerated charge carriers.


Experimental Methods
Sample preparation and characterization.For MAPbBr 3 films used for TA experiments, prior to the deposition, the quartz substrates underwent a sequential cleaning process.Firstly, the substrates were subjected to ultrasonic treatment in detergent, de-ionized water, acetone, and isopropyl alcohol.After drying, the cleaned substrates were further treated with UV-ozone (Model: 42, Jelight, USA) for 25 minutes.The MAPbBr 3 precursor solution was prepared by combining 0.015 g of MABr (Dyesol) with 0.0481 g of PbBr 2 (Sigma-Aldrich, 99.999%) in an anhydrous dimethyl sulfoxide (DMSO, Sigma-Aldrich) solution (1070 μl) at 60°C.The solution was stirred for 12 hours.To fabricate the MAPbBr 3 perovskite thin film, a consecutive two-step spin-coating process was employed.The solution was spin-coated onto the quartz substrates at 500 rpm for 7 seconds, followed by a spin-coating at 4000 rpm for 70 seconds.Additionally, at 43 seconds during the spin coating, 250 μl of chloroform solvent was dropped onto the surface of the precursor film.Subsequently, the MAPbBr 3 perovskite film was annealed on a hotplate at 70°C for 10 minutes.It is noteworthy that all the procedures for preparing the MAPbBr 3 precursor solution and films were conducted inside a nitrogen-filled glove box with oxygen and moisture levels maintained below 1 ppm.
For MAPbBr 3 single crystals used for ellipsometric experiments, the precursor MABr (0.748 g) was dissolved in anhydrous dimethylformamide (4 mL) in a 20 mL glass vial to form a clear solution.Then, PbBr 2 (2.452 g) was added into the glass vial with stirring to obtain a nearly saturated clear MAPbBr 3 solution.The glass vial was then placed onto a hotplate at 50 °C without disturbance for slow evaporation.Bulk MAPbBr 3 single crystals with dimensions in the centimeter range can be obtained from the solution after 12 h.These procedures were all performed inside a fume hood.

Transient spectroscopic measurements.
The experiments were performed using two different setups: one for broadband visible probe and the other for broadband deep-UV probe.
(a) For the broadband visible probe setup, a 1 kHz regenerative amplifier provides 30 fs pulses at 800 nm with an energy of approximately 720 μJ per pulse.A noncollinear optical parametric amplifier (NOPA) was utilized to generate tunable visible pump pulses with ∼15 nm bandwidth and energy ranging from 2-4 μJ per pulse.The probe beam was focused onto a CaF 2 plane to generate white light in the range of 450-750 nm (1.65-2.75eV).
(b) For the broadband deep-UV probe setup 1,2 , a 20 kHz Ti:sapphire regenerative amplifier (KMLabs, Wyvern500), providing 50 fs pulses at 800 nm with an energy of 0.6 mJ.These pulses were used to pumps a NOPA, generating sub-90 fs visible pulses at 13 μJ per pulse in the range of 510-740 nm (1.68-2.43eV).About 40% of the NOPA output was used to generate broadband UV probe pulses with a bandwidth of ∼100 nm through an achromatic doubling scheme 3 .The probe pulses were further compressed using chirp mirrors to achieve <20 fs pulse duration.The relative polarization between the pump and probe beams was set at the magic angle (54.74°) using a halfwave plate to avoid photo-selection effects.After passing through the sample, the transmitted broadband probe beam was focused into a 5 m multi-mode optical fiber, which was coupled to the entrance slit of a 0.25 m imaging spectrograph (Chromex 250is).The beam was dispersed by a 150 gr/mm holographic grating and imaged onto a multichannel detector consisting of a 512-pixel CMOS linear sensor (Hamamatsu S11105) with a pixel size of 12.5×250 µm.The pixel readout rate could reach up to 50 MHz.The typical spot sizes of the pump and probe beams were approximately 120 μm and 50 μm full widths at half-maximum, respectively.In all measurements, the pump fluence at 400 nm (3.1 eV) was approximately 50 μJ/cm 2 with ~10% uncertainty due to laser power measurement and laser beam spot size.The pump power was recorded on a shot-to-shot basis using a calibrated photodiode for each pump wavelength, enabling the normalization of the data for the pump power.The thin film perovskite samples were mounted in a film sample holder with a nitrogen gas flow to protect the sample surface.The probe signal was measured after transmission through the sample, and its detection was synchronized with the laser repetition rate.
Temperature-dependent in-situ spectroscopic ellipsometry.Temperature-dependent in-situ spectroscopic ellipsometry was performed using an M-2000 DI device (J. A. Woollam, USA), which operated in the 193-1690 nm wavelength range, coupled with an INSTEC heating stage, which allowed thermal scanning from room temperature up to 560 °C under an N 2 gas flow.The sample was measured at a minimum of three angles of incidences (65°, 70°, and 75°), at temperatures ranging from 298 to 418 K, which are below the phase transition temperature of ~530 K 4 .The VASE data was fitted using an isotropic "B-spline" mode 5 , allowing for the determination of the absorption coefficients and refractive indexes at each measured temperature, and the data analysis was performed using the Complete EASE 6.51 software package.The raw and fitted data are shown in Fig. S8.
DFT calculations.We performed the DFT calculations using the projector-augmented wave method implemented in the Vienna Ab Initio Simulation Package code 6,7 .The GGA and PBE exchange-correlation functional were used, and van der Waals interactions were also included in the calculations using the zero-damping DFT-D3 method of Grimme.A uniform grid of 6 × 6 × 6 k-mesh in the Brillouin zone was employed to optimize the crystal structure of cubic-phase MAPbBr 3 .The energy cutoffs of the wave functions were set to 500 eV for bulk MAPbBr 3 .The atomic positions of all the structures were fully relaxed until the Hellman-Feynman forces on each atom were less than 0.01 eV/Å.To assess the influence of the hot-lattice effect on the electronic structure, we systematically vary the lattice parameters by increments of 0.5%, 1.0%, 1.5%, and 2.0%, thereby emulating the crystal structures at different temperatures.approximately 3.4 eV, 3.8 eV, and 4.45 eV, accompanied by a positive signal around 4.15 eV.The energies of these bleaching (negative) signals are consistent with the ellipsometric measurements conducted within the same spectral range.Following a similar methodology used for the assignment of interband transitions in MAPbI 3 , 8,9 we determined the energy distances at each symmetry point in the Brillouin zone (BZ).Accordingly, the ~3.4 eV peak is assigned to the transition from VB3 to CB1 at the R point, while the ~3.8 eV and ~4.45 eV peaks are assigned to transitions between VB1 and CB1 at the M and X points, respectively (Figure S2).
When excited below the energy gap at the M and X points, direct population at these highsymmetry points is not involved.Consequently, the transient signal at ~3.4 eV (R point) exhibits a different sensitivity compared to the bleaches at ~3.8 eV (M point) and ~4.45 eV (X point).This distinction is evident from the early time traces shown in Fig. S6, where the transient signals at ~3.8 eV and ~4.45 eV experience a prompt rise, while the signal at ~3.4 eV rises more gradually, due to the cooling of electrons towards the bottom of CB at the M point.Furthermore, the significant red-shifted peak energy at ~3.8 eV observed at longer delay times indicates that this bleach could be primarily attributed to Coulomb screening rather than band filling (See normalized spectral traces in Figure S23).Conversely, the transient signal at ~4.45 eV shows minimal peak shift, which can be attributed to the relatively flat VB at the Γ-to-X valleys in the BZ.

Supplementary Note S2: The difference between the transient absorption and reflection
In TA measurements, the ΔA signal mainly depends on the ratio of the intensity of transmitted probe light with and without pump excitation, assuming that the loss of transmitted probe light is solely resulting from the sample absorption (assuming that the TA signal is proportional to the change in absorption, ΔT/T∝ΔA 10 ).light with (or without) the excitation of pump light.
In transient reflection (TR) measurements, which share the same experimental setup, the TR signal (ΔR/R) can be determined by the ratio of the intensity of reflected probe light with and without pump excitation.However, unlike TA measurements that primarily probe the bulk property of the samples, the TR signal mainly detects variations in photo-induced reflection due to the changes in the refractive index at the sample surface 11,12 .
Where n and k represent the real and imaginary parts, respectively, of the complex refractive index ñ=n+ik.Carrier-induced optical effects cause small changes in reflection coefficient R. Therefore, the change in reflectance, ∆R, can be described in terms of the complex index of refraction.Since ∆R is very small, it can be approximately expressed in a linear form by considering and as: The relation between and the is essential for interpreting the signal of the differential ∆ ∆ reflectivity.Assuming that the magnitude of n is significantly larger than k, the photo-induced ∆R is dominated by , rather than .This is in contrast to photo-induced ΔA, which is ∆ ∆ predominantly influenced by ∆k.Therefore, the TR spectral characteristics and kinetics can differ significantly different from those of TA, even examining the same sample.
Where, is the heat absorbed by the material, is the mass of the heating absorbing subject,     is the specific capacity and is the change in temperature.We assume half of the absorbed ∆ photon energy are converted in to heat ( 50%).In MAPbBr 3 , Cp = 8.2 J/(mol•K), ρ = 3.83  ≈ g/cm 3 , and , the laser penetration depth we roughly take the film thickness of ~80  =  •  •  2  nm 16 , is the pump laser spot radius of ~60 μm, however, as only the most intense center mostly  cause the heating and here we approximately take half of it ( ).
, where, P is the  ≈ 30μm Q =   •  pump laser power, r is the repetition rate and is the absorption coefficient at the used pump  wavelength (400 nm, ~0.4).Thus, it can be written as: Therefore, for the TDA spectrum, we select the temperature roughly at 373 K (≈273+96=369 K), although all of the TDA spectra exhibit similar profiles.
increasing over time until it reaches the grain boundary, where heat diffusion becomes notably less efficient (Figure S24).As a preliminary estimate, considering i) d = 40 nm, the timescale for thermal transport is ~250 ps; ii) d = 50 nm, the timescale for thermal transport is ~400 ps; iii) d = 60 nm, the timescale for thermal transport is ~550 ps.These estimates align reasonably well with the observations made in our experiments.The TA data for the photo-excited cases were chosen starting from 1 ps, while the thermally excited cases span a temperature range of 313 to 418 K.

Figure S1 .
Figure S1.Schematic diagram of photon-and thermally excited differential absorption.a, Conventional pump-probe scheme, where the generated ΔOD is determined by the pump photons.b, Thermal excitation of the perovskite crystal, where the ΔOD is obtained by subtracting the absorption measured at high temperature with that at room temperature.

Figure S2 .
Figure S2.Absorption spectrum of a MAPbBr 3 single crystal, highlighting the labeled absorption peaks corresponding to the respective band transitions at various energy levels.The spectrum were obtained by fitting the data measured with spectroscopic ellipsometry.

Figure S3 .
Figure S3.Calculated energy band diagram (the details are described in the method section).The 3.1 eV excitation is indicated by the blue arrow, while the probed bleached signals that can be detected by the employed broadband visible and mid-to-deep-UV probes are represented by the yellow and red arrows, respectively.The number 1, 2 and 3 are labeled in the order of the CB and VB at each symmetry point.

Figure S5 .
Figure S5.Time traces probed at 2.35 and 4.45 eV, respectively.The traces are cut and normalized at 100 ps to illustrate the long-term decay behaviors.The inset displays a comparison of the normalized full twotime traces.

Figure S6 .
Figure S6.Fitting residuals of the time-energy TA map probed in the visible spectral region.The scale bar is consistent with the experimental and fitted TA maps shown in Fig. 1a and c.

Figure S7 .
Figure S7.Time traces of the rising TA signals probed at 4.15 eV (positive) and 3.8 eV (negative), respectively.The traces are zoomed in to the first 8 ps and the signals are normalized at their maximum amplitudes.The TA signal at 3.8 eV is flipped to positive for comparison purposes.

Figure S8 .
Figure S8.Time traces of the rising TA signals probed at 3.4, 3.8 and 4.45 eV, respectively.The traces are zoomed in to the first 3 ps and normalized at their maximum amplitudes.

Figure S9 .
Figure S9.Fitting residuals of the time-energy TA map probed in the UV spectral region.The scale bar is consistent with the experimental and fitted TA maps shown in Fig. 1e and g.

Figure S10 .
Figure S10.The variable angle spectroscopic ellipsometry (VASE) data of MAPbBr 3 perovskite measured at temperatures ranging from room temperature to 418 K in 15 K intervals, with measurements taken at 65°, 70°, and 75°.The dots are the experimental data, and the solid lines are the fits.The absorption coefficients and refractive indexes are extracted based on these fits.

Figure S11 .
Figure S11.Calculated bandgaps of MAPbBr 3 perovskite as a function of lattice expansion, compared to the temperature dependent bandgaps.The experimental band gaps are approximately determined by identifying the points of intersection between the tangent lines to the first absorption peaks and the horizontal coordinate.

Figure S14 .
Figure S14.Reconstructed differential absorption map using various ratio of combinations (m and n).a, Visible spectral region.b, UV spectral region.On the left side, the signal amplitude is calculated based on DAS1 + m×DAS2 to simulate the complex spectral evolution immediately after photo-excitation.The value of m is varied from 1 to 5. On the right side, the signal amplitude is calculated based on 5×DAS2 + n×DAS3 to simulate the complex spectral evolution in the long-term component.We vary the value of n from 1 to 15.

Figure S17 .
Figure S17.Experimental visible-probed spectral traces and their fittings using different combinations of DAS spectra (a×DAS2 + b×DAS3).The fitting starting from 1 ps, where the band gap renormalization signals have completely vanished.The grey solid lines represent the experimental traces, while the magenta depict the fitted spectra.All figures share the same coordinate system.

Figure S18 .
Figure S18.Experimental UV-probed spectral traces and their fittings using different combinations of DAS spectra (a×DAS2 + b×DAS3).The fitting starting from 1 ps.The grey solid lines represent the experimental traces, while the magenta depict the fitted spectra.All figures share the same coordinate system.

Figure S19 .
Figure S19.Experimental visible-probed spectral traces and their fittings using combinations of a×DAS2 + b×TDA.The fitting starting from 1 ps, using the same method with Fig. S15.The grey solid lines represent the experimental traces, while the magenta depict the fitted spectra.All figures share the same coordinate system.

Figure S20 .
Figure S20.Experimental UV-probed spectral traces and their fittings using combinations of a×DAS2 + b×TDA.The fitting starting from 1 ps, using the same method with Fig. S16.The grey solid lines represent the experimental traces, while the magenta depict the fitted spectra.All figures share the same coordinate system.

Figure S21 .
Figure S21.Evolution of visible-probed TA spectral traces under different pump fluences.a, at 200 fs.b, at 1 ps.c, at 10 ps.The blue curves represent the spectral traces used in the main text with a pump fluence of 50 μJ/cm 2 , while the red curves represent the spectral traces at the same delay times but with an increased fluence of 75 μJ/cm 2 (1.5 times higher).The two spectral traces are normalized at their signal minimum.Increasing the pump fluence results in immediate broadening of the overall bleaching signal after photoexcitation, particularly on the high-energy side.At a later time delay (1 ps), a ~3.6 meV blue shift in the spectra indicates a larger band gap due to increased lattice heating, consistent with experimental and theoretical results on changes in optical properties induced by temperature.In the long-term component (10 ps), the spectral response under high fluence shows no visible shift, only broadening.

Figure S22 .
Figure S22.Reconstructed differential absorption map using various ratio of combinations of DAS2 and TDA.a, Visible spectral region.b, UV spectral region.The signal amplitude is calculated based on 5×DAS2 + n×TDA to simulate the complex spectral evolution in the mid-to-long-term component, i.e., >1ps.The value of n is varied from 1 to 6, and 6 to 4. It is important to note that, while the relative electronic contribution to the overall TA signal increases at longer delay times, both the electronic and thermal effects are in fact diminishing as a function of delay time.

Figure S24 .
Figure S24.Schematic representation illustrating the thermal decay of a laser-induced hot spot within MAPbBr 3 films, depicting heat transfer from the center of the spot in both horizontal and vertical directions.