Probing buried recombination pathways in perovskite structures using 3D photoluminescence tomography

Perovskite solar cells and light-emission devices are yet to achieve their full potential owing in part to spatially heterogeneous non-radiative loss pathways that are both on, and buried beneath, the surfaces of films and crystals.

(Dyesol) and Pb(Ac)2·3H2O (Sigma-Aldrich) were dissolved in anhydrous N,Ndimethylformamide (DMF) at a 3:1 molar ratio with final concentration of 37 wt % and HPA added to an HPA:Pb molar ratio of ∼11%. The precursor solution was spin coated at 2,000 rpm for 45 s in a nitrogen-filled glove box, and the substrates were then dried at room temperature for 10 min before annealing at 100°C for 5 min. All samples were then stored in a nitrogen-filled glove box until used.  The light-soaking measurements were performed by photo-exciting perovskite films on coverslips enclosed in a custom-built flow chamber capable of flowing ultra-high purity gases in a controllably humidified form (40%-50% relative humidity). The samples were photoexcited with a 532-nm CW laser at intensities approximately equivalent to the photon fluxes of 2 sun irradiation (150 mW/cm 2 ) for 30 minutes. They were then sealed and shipped for measurement the following day.
Triple Cation Samples and Devices: The organic cations were purchased from Dyesol; the lead compounds from TCI; CsI from  Figure S1 for X-Ray diffraction (XRD) and scanning electron microscope (SEM) images).
Finally, the substrates were extracted from the solutions and annealed on a hot plate at 110°C for 5 mins. All procedures were performed at ambient conditions with ~55-57% relative humidity. The Scanning Electron Microscope (SEM) image of the MAPbBr3 micro-crystal film was taken on FEI Quanta 600. XRD was measured using Bruker AXS D8 Advance powder diffractometer with Cu-Kα radiation.
Scanning electron microscopy: The surface morphology of the films was examined using a field-emission scanning electron microscope (Merlin). An electron beam accelerated to 3 kV was used with an in-lens detector.

Solar-cell characterization:
Current-voltage characteristics were recorded by applying an external potential bias to the cell while recording the generated photocurrent with a digital source meter (Keithley Model 2400 1100 nm which in-turn is optically coupled to the input of the microscope through a 950 nm short-pass dichroic. We used a pulse-picker to bring the repetition rate of our laser down to 5 MHz and 1.25 MHz for TRPL measurements. Photoluminescence was filtered with a 945 nm short-pass filter, collected through a 100 μm pinhole and into detection optics. For spectral collection we used an Acton 2300i spectrometer with 150 groves/mm grating and an Andor iXon electron-multiplied CCD. For time-resolved collection we first spectrally-filtered the PL using a linear variable long-pass filter and then collected with a single-photon avalanche diode (Micro Photon Devices PDM series). A PicoQuant PicoHarp 300 time-correlated single-photon counting (TCSPC) system was used to record the timing data.
At 23-27 μW with a repetition rate of 1.25MHz, a laser pulse energy of ~20 pJ/pulse was used to excite (with 2P) the untreated and treated perovskite films in Figure 2 and Figure S8. Because of the high absorption coefficient of methylammonium lead halide perovskites, photons with energy above the band-gap are absorbed near the surface. In order for onephoton measurements to be as surface sensitive as possible, we used an excitation wavelength 6 of 510 nm for which we estimate a penetration depth 5 of the order of 100 nm. Single photons with wavelengths longer than the absorption edge do not carry enough energy to promote electrons to the conduction band and travel therefore deep into the material. Measurements in the bulk were performed with a 1100 nm excitation beam tightly focused by the confocal system described above.
The lateral resolution of the excitation is diffraction limited, with a full width at half maximum (FWHM) of 626 nm ( Figure S3). Vertically, we exploit the fact that the transition probability for the 2P absorption process depends on the square of the intensity of the light beam used for the excitation, if the two photons have the same energy 6 . We estimate the depth resolution around the focal point to be about 1 μm. In order to mitigate the effect of reabsorption and photon-recycling, we use a linearly variable long-pass filter in the detection path to select the red-most tail of the PL emission spectrum for time-resolved measurements.  The proportionality factor β between the two-photon absorption coefficient α and the light intensity was recently measured for MAPbBr3 and found to be about 20 cm per GW at 800 nm 7 . At an average power of a few dozens of microwatts, the absorption coefficient at the focal point at 800 nm would be of the order of 10 3 cm -1 , two orders of magnitude smaller than for one-photon absorption. We expect β to be significantly lower at 1100 nm. To obtain the same order of magnitude of photoluminescence intensity, we used a few nanowatts of 1P excitation and an average power between 23 μW and 27 μW (peak power between 125 W and 145 W) for 2P. This suggests that the absorption coefficient is 3-4 orders of magnitude lower with 2P than with 1P at 1100 nm, hence somewhere around 100 cm -1 . By looking at the parameter space in Figure S2, β could be around 5 cm·GW -1 , which is consistent with the fact that it should be less than 20 cm·GW -1 , smaller at 1100 nm than its reported 7 value at 800 nm. Figure S3. Beam profile of the laser used for 2P measurements.
Data analysis: All maps were recorded as multidimensional matrices, and analysed using a Python code. 3D visualisation was achieved through the Mayavi module. Lifetimes were extracted from the 8 TRPL measurements as the time at which (1-1/e) of the photons had been detected. 3D images were reconstructed from stacks of 2D TRPL maps, from which the pixels outside of the crystals were removed.

Complementary measurements:
The 1P and 2P PL maps recorded on the MAPbI3 thin film in Figure 1a and b (main text) were normalised to the mean of each distribution, respectively. Normalising to the total counts ( Figure S4) shows more clearly that emission is more localised below the surface, however it is more difficult to resolve the brightness contrast between grains. Normalising to the mean highlights this contrast better. Nonetheless, comparing the two figures (with different normalisations) helps to see that the emission is a lot more homogeneous at the surface than below: the 1P map is not affected by this change in normalisation whereas the 2P map changes significantly. Comparison of the count rate distributions again normalised to the total counts.

9
Spectral maps were also recorded on the MAPbI3 thin film alongside with the PL maps shown in Figure 1a and b (main text) and in Figure S5a and c. In the maps in Figure S5b and d, there does not appear to be any spectral shift below the surface.

Passivated Samples:
A different MAPbI3 film was used for comparative measurements with the treated film shown in Figure 2 of the main text. The histograms in Figure 3 of the main text were extracted from the PL count rate ( Figure S8a and d), lifetime ( Figure S8b and c) and spectral median ( Figure S8c and f) maps recorded on this sample. The contrast between 1P and 2P excitation was weaker on this film than on the one shown in Figure S4 and S5, which may be due to some ageing, small atmospheric exposure in transit or a very slightly higher excitation fluence (such that carrier diffusion may influence the maps). The lifetime and spectral median do not appear to change at or below the surface.  In order to compare the luminescence of the untreated and treated films at and below the surface, the PL maps of the treated film in Figure S9a and d are normalised to the maximum obtained with 1P and 2P on the untreated film in Figure S8(a,d), respectively. In order to assess potential correlations between the PL and lifetime for both films, untreated and treated, we show in Figure S10 scatter plots of the data contained in the maps (blue dots).
14 We binned the PL count rate data (into 15 bins) and computed the mean lifetime for each bin (orange dots). As a guide to the eye, we performed a linear fit on the binned data (red dotted lines). Bins containing fewer than 10 data points were discarded and excluded from the analysis. In the untreated sample, brighter areas appear to have a longer lifetime under both 1P ( Figure S10a) and 2P ( Figure S10c) excitation, whereas we observe the opposite trend in the treated sample, again with both 1P ( Figure S10b) and 2P ( Figure S10d) excitation. films, using one-photon (1P) and two-photon (2P) excitation. 15 We also considered correlations between the 1PPL and 2PPL maps, for both the untreated and treated samples ( Figure S11). Grains that appear bright at the surface seem to be bright as well in the bulk. The scatter plot for the untreated film ( Figure S11, left panel) contains fewer data points than for the treated film ( Figure S11, right panel), because only the data contained in the top half of the map was used for the correlations. The bottom half of this 1PPL map (shown in Figure S8a appears distorted (shrunk) when compared with the 2PPL map in Figure S8d), and we therefore did not use it to evaluate spatial correlations. Figure S11. Spatial correlations between 1PPL and 2PPL in untreated (left) and treated (right) films, using one-photon (1P) and two-photon (2P) excitation, respectively.

Bulk Crystal Films:
We also performed 3D time-resolved tomography on a micro-crystal film of MAPbI3 (XRD data shown in Figure S12). The chosen PL count-rate and lifetime isosurfaces are shown in Figure S13a, b and c, along with a 2P optical image of the luminescence of a single microcrystal in Figure S13d.   averaged across all such pixels at each depth. Bright pixels are defined as pixels where the PL count-rate is above 30% of the maximum PL count-rate on the whole 2D map (shown in Figure S15a), while dark grains have a PL count-rate below 25% of this maximum. Green arrows in the left-most panel indicate the dependence of the lifetime upon an increase in excitation power, highlighting different recombination regimes. All measurements are normalised to their maximum.