Supporting Information for Modulating the Electron - Hole Interaction in a Hybrid Lead Halide Perovskite with an Electric Field Tomas Leijtens 1,2, Ajay Ram Srimath Kandada 1, Giles E. Eperon 2, Giulia Grancini 1, Valerio D Innocenzo 1,3, James M. Ball 1, Samuel D. Stranks 2, Henry J. Snaith 2, and Annamaria Petrozza 1 1 Center for Nano Science and Technology @Polimi, Istituto Italiano di Tecnologia, via Giovanni Pascoli 70/3, 20133, Milan, Italy 2 University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom 3 Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milano, Italy. Note 1. The effective electric field dropped across the perovskite semiconductor was approximated by considering the thicknesses of all the layers (total Al 2 O 3 150-200 nm, perovskite 300 nm) and their static dielectric constants (Al 2 O 3 : 9, perovskite: 70). To approximate the bias per unit cell, we took the length of the average axis perpendicular to the substrate to be 1 nm, which is between the values of the a and c axes (0.9 and 1.2 nm respectively). Note 2. The PL quenching at RT and 3 V applied under continuous wave excitation at 630 nm (different from that in Fig. 1b), is weakened as the excitation density is increased as shown in Figure 2a. This implies that the electric field is screened by the presence of many free carriers that have drifted towards the electrodes, screening the applied bias. Comparing the data in Figure 2a to that in 1b, we roughly extrapolate that the high excitation intensity PL quenching of only 1-2 % will only be achieved at applied biases around 1 V, so that the total field screened by the photo generated carriers will be less than 0.4 V (considering the relative contributions from both Al 2 O 3 and perovskite). To screen 0.4 V across a 300 nm film of pervskite, the accumulated charge densities should reach 10 12 cm -2 at the contacts. To enable this, the total photogenerated charge density should then be on the order of 10 16 cm -3. This can be easily reached at an excitation fluence of 500 mw cm -2, which corresponds to 10 18 cm -2 s -1 absorbed photons. With our measured lifetimes of 200-300 ns this yields a steady state charge density of 10 16 cm -3 which should be able to provide the observed screening, especially when the added density of mobile charged defects expected to be on the order of 10 16 cm -3 is considered 1. S1
Figure S1. Absorption and photoluminescence spectra of the complete devices described in Figure 1. There is a clear red shift of the band edge and PL peak at 190K, along with an enhanced excitonic feature. The offsets in absorption are due to absorption and reflection at the semitransparent gold electrode. Figure S2. Steady state absorption and PL spectra before and during application of a 10 V bias at both RT and 190K. These spectra demonstrate that the change in PL cannot be explained by a change in absorption coefficient at the excitation wavelength of 510 nm. The PL enhancement at 190K is most pronounced on the lower energy side, but since we are detecting the PL at an S2
emission wavelength of 790 nm with approximately 5 nm bandwidth, this will not affect our measured PL decays. Figure S3. Steady state dpl/pl for several more temperatures not included in Figure 1b of the main text. These demonstrate that while the electric field effect at high temperatures is primarily a PL quenching and that at low temperature is primarily an enhancement, the two are in competition at non extreme temperatures such as 270 and 215K. The magnitude of the effect is slightly different here than in Fig 1b because a different excitation was used (cw 630 nm at 50 mw cm -2 ). Figure S4. Photoluminescence decay at various applied biases at room temperature and a high excitation density of 10 17 cm -3. The inset quantifies the decrease in initial amplitude of the signal. S3
Figure S5. The PL is further quenched after removal of the electric field. This effect is remains for over 100 s. Figure S6. The PL decays of a sample with a fast monomolecular decay rate, measured at various applied fields and low excitation intensity (10 15 cm -3 ). The decays for such a sample at a low fluence are purely monomolecular, and this is evident from the fact that the data appears perfectly straight on the log linear scale across 3 orders of magnitude of intensity 1,2. As in the main text, as the electric field is increased, the initial amplitude is quenched by the lifetime massively enhanced. Since the decay is purely monomolecular, any changes to the bimolecular radiative decay due to carrier drift will not be observed. The results then strongly suggest a large reduction in trapping rates upon application of the electric field 1, while the reduction in amplitude shows that free carriers are still drifting apart. As explained in the main text, we interpret these results as being the result of a slow drift of charged defects out of the bulk of the material, effectively reducing nonradiative decay rates. S4
Figure S7. Demonstration that the observed effect (reduction in intensity but longer lifetimes) at RT is the same at positive and negative biases, indicating that the devices are indeed symmetric. 20V 30V a) b) c) Figure S8. a) Steady state PL yield monitored over time as the bias is increased from 20 to 30 V. We use a high excitation density (1.2 W cm -2 ) in order to reduce the effect of PL quenching S5
induced by carrier drift as a consequence of field screening (see Figure 2a in main text). The high excitation fluence ensures that while the field is screened by a fraction of the carriers, most of the carriers stay in the bulk and do not drift substantially in response to the electric field. Of course a minority of the carriers do drift together with the ions. Since the majority of carriers are not drifting to screen the field, the effect on the bimolecular recombination is masked and there is no immediate drop in PL. Ions, of course, have drifted together with a minority of carriers, clearing the material of defects. The result is an early rise in PL over the course of approximately 10 seconds, which corresponds to the time scale expected for defect motion across films of this nature. 3 6 This is simply because the ion motion has reduced the trap density in the bulk and reduced the trapping rate, raising the fraction of carriers that recombine radiatively vs nonradiatively through traps. This is followed by a slower decay in PL, which may be associated with the recent observations of structural changes due to the presence of electric fields. 7 b) The steady state PL spectra as a function of time under bias, under low excitation conditions (30 mw cm -2 ) and high bias (40 V) to be able to observe the strongest effects. We find an instantaneous reduction in PL yield, consistent with carrier drift followed by a very slow continued quenching and blue shift of the PL spectrum over several minutes, which seems likely to be related to the structural changes described by Gottesman et. al. 7 c) When the field is removed, we observe an initial increase in PL over the first minutes, which may be ascribed to a redistribution of ions across the film (reducing the residual built in field and trapping described in Figure 2d of the main text) and then an extremely slow (hours) increase in PL, which we again tentatively assign to structural rearrangement. S6
a) b) Figure S9. a) The 1/e lifetimes are plotted for the decays at 190K shown in Figure 3a. In these regimes, the decays primarily reflect the bimolecular recombination of free carriers 1, as confirmed by the fits to stretch exponential functions with 0.5 stretch factor in Figures 3b-c. The radiative recombination rate is then significantly enhanced as the electric field is increased. b) The raw PL data for the high and low excitation densities are plotted together demonstrating that the effect is observed for both fluences and that the decay is significantly slower at lower fluences as compared to high fluences, confirming that we are probing behavior in the bimolecular regime. Figure S10. The steady state PL (at 190 K) is plotted as a function of time after the application of an electric field and also after its removal. All of the changes appear to be very slow. As the field is turned on, the initial response is an immediate quenching of the PL, consistent with field induced carrier separation and drift. However, this effect is slowly overcome by a slow change to the material, which is accelerated by a 10 X reduction in excitation fluence, ie an enhancement of effective electric field (since there will be fewer free carriers to screen the applied field). This S7
slow change is described in the text as originating from enhanced coulomb interactions between both geminate and free electrons and holes. We observe that as the electric field is removed, there is an initial fast rise in PL. This corresponds to a removal of the field induced quenching processes described in Figure 5: geminate carrier dissociation and carrier drift. The fact that this growth is not perfectly instantaneous is due to a relatively slow reorganization of any mobile charged defects, slowly weakening a residual defect induced built in field. The long living PL enhancement corresponds to the structural changes described by the Raman data in Figure 4 and the schematic in Figure 5. This enhanced the PL to values far greater than before the application of the field. Figure S11. The fitted peaks of the raman spectra are plotted, and their amplitude and width are tabulated. These peaks all correspond to previously identified modes, as determined via a combined experimental and theoretical study 8,9. Figure S12. The raman spectrum before, during, and several minutes after the application of the electric field demonstrates that the structural changes are only slowly reversible. S8
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