Supporting Information. Quantum Wells

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1 Supporting Information Real-Time Observation of Exciton-Phonon Coupling Dynamics in Self-Assembled Hybrid Perovskite Quantum Wells Limeng Ni, Uyen Huynh, Alexandre Cheminal, Tudor H. Thomas, Ravichandran Shivanna, Ture F. Hinrichsen, Shahab Ahmad, Aditya Sadhanala, Akshay Rao * Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom Institute for Manufacturing - Department of Engineering, University of Cambridge, 17 Charles Babbage Road, Cambridge, CB3 0FS, United Kingdom AUTHOR INFORMATION * Corresponding Author: ar525@cam.ac.uk

2 Photothermal Deflection Spectroscopy Figure S1. PDS spectra of BA 2 PbI 4 and HA 2 PbI 4. a) Linear fit of the Urbach tails. b) Linear fit of the Urbach tail of BA 2 PbI 4 at two regions: close to band edge (grey) and close to excitonic peak (red). Two Urbach energies can be defined for BA 2 PbI 4 for the two absorbing features. However, they are similar values. One can compare the two Urbach energies of BA 2 PbI 4 with the energy of HA 2 PbI 4 for different purposes. For charge transport, the Urbach energy close to the band edge is more relevant, because charges/excitons tend to relax to and recombine at low

3 energy states. c) Below bandgap (<2 ev) states that are not due to the absorption of the substrate. HA 2 PbI 4 shows more below bandgap non-radiative states than BA 2 PbI 4, which might originate from different organic ligands/cations. Hexylammonium cation is longer than the butylammonium, therefore the probability of bending is higher than the butylammonium counterpart. The bending of the ligand can cause lattice distortion of the [PbI 4 ] 2- wells, which may give rise to non-radiative states. Photoluminescence Microscopy

4 Figure S2. PL microscopy on a polycrystalline BA 2 PbI 4 film. a) Optical microscope image of a spincoated BA 2 PbI 4 film with 20x objective magnification (red square is the µm 2 scanned area for PL mapping). b) Map of the total PL count in the scanned area. Collected with 100x objective. c) Map of the FWHM of the PL in the scanned area. d) PL spectra of different spots on a BA 2 PbI 4 film. The beam spot diameter is around 0.5 µm. Photoluminescence Measurement on Samples of Different Thickness Figure S3. a) Microscope image of BA 2 PbH 4 exfoliated thin sheets. b) PL spectra of BA 2 PbH 4 spin-coated film and exfoliated sheets with different thickness.

5 Temperature-dependent UV-Vis and Photoluminescence Measurement a) Temperature (K) Cooling Wavelength (nm) 300 b) Heating 290 Temperature (K) Wavelength (nm) Absorbance (a.u.) Figure S4. Temperature-dependent UV-Vis measurement of BA 2 PbI 4 obtained by two ways: a) cooling from room temperature. b) heating from 200 K. Figure S5. Separate contribution of the two phases of HA 2 PbI 4 over total integrated PL intensity versus temperature. Ratio over Total Integrated PL (a.u.) Phase transition point at 127 K Ratio of High-Energy Peak Ratio of Low-Energy Peak /T (1/K)

6 a) Low energy phase High energy phase Low energy phase High energy phase b) Absorbance (a.u.) Cooling 10 K 50 K 90 K 130 K 170 K 210 K Absorbance (a.u.) Heating 10 K 50 K 90 K 130 K 170 K 210 K Wavelength (nm) Wavelength (nm) Figure S6. Temperature-dependent UV-Vis spectra of HA 2 PbI 4 obtained by two methods: a) Cooling from room temperature, b) Heating from 10 K. Figure S7. Temperature-dependent PL and UV-Vis on a HA 2 PbI 4 film. a) PL peak position of HA 2 PbI 4 before phase transition point. The red dashed line is the linear regression fit of the peak shift rate. b) Temperature-dependent absorption spectra of HA 2 PbI 4 before phase transition point.

7 Femtosecond Transient Absorption Spectroscopy Figure S8. Transient absorption dynamics of a BA 2 PbI 4 film. a) TA kinetic of BA 2 PbI 4 at 820 nm (black) with a population fit using exponential function (red). The residual after subtracting the population (green) shows strong coherent artefact around t=0 fs. Afterwards small oscillations last for 2 ps. b) Spectrally resolved residual map after the population subtraction for all wavelengths. Only the vibrational datasets from 160 fs onwards were considered so that the contamination of coherent artefact is avoided. The bending of the residual is due to pump fluctuation, which adds noise to the FFT but does not affect the determined modes.

8 Figure S9. fs-ta on blank substrates. a) Transient absorption map of blank substrates pumped at 500 nm. No signal is observed from 560 to 880 nm. The data below 650 nm is noisy because of pump scatter. b) Wavelength-resolved Fourier-transform power map of blank substrates. Only noise is seen on the map. c) Fourier-transformed oscillation spectra of blank substrates averaged over nm. No vibrational mode can be seen apart from noise. Figure S10. fs-ta on non-crystallized PbI 2 precursor. a) Transient absorption map of PbI 2 precursor pumped at 500 nm. A weak PIA signal is observed from 560 to 880 nm. b) Wavelength-resolved Fourier-transform power map of PbI 2 precursor. c) Fourier-transformed oscillation spectra of PbI 2 precursor in comparison to blank substrates averaged over nm. A mode at 108 cm -1 is dominant.

9 Analysis of the PL Linewidth Figure S11. Fitting example of PL of HA 2 PbI 4 at 5 K with high-energy and low-energy phases.

10 Integrated PL Intensity (AU) I T Experimental data Fit curve using Arrhenius equation I0 = E 1+ Aexp( kt Temperature (K) b ) /T (1/K) Figure S12. Fitting of the integrated PL of the high-energy phase of HA 2 PbI 4 to calculate the binding energy of the impurities E b using Arrhenius equation.