## 3 Results and Discussion
We may postulate at this stage that a significant number of photoexcited carriers in the PQDs are quickly transferred to the charge transport layer, which leads to a strong internal electric field, resulting in a large Stark effect to modify the bandgap of the PQDs and therefore the structure of transient absorption spectra [40; 41]. Another possibility is that the strong electronic coupling between the PbI\({}_{2}\) and the TiO\({}_{2}\), favoring a fast electron transfer process, leads to a broadened exciton band in the TA spectra [34]. The quick electron transfer may result in an imbalance of the electron and hole numbers in the PQDs. This imbalance may affect the time dependences of the PA signals probed at various wavelengths in a different way. Actually, we can see from Figure 2d some small differences of the normalized time dependences of the PA signals in 500-700 nm. We also note significant PB and PA signals remained at long delay time of 800 ps in Figure 2b, pointing to the existence of long-lived holes residing in the PQDs as a result of the quick electron transfer. Assured evidences of quick electron transfer will be given later. Figure 1: (**a**) The structure of FAPbI\({}_{3}\) PQDs layer grown with PTAA HTL and TiO\({}_{2}\) ETL; (**b**) energy levels of TiO\({}_{2}\), FAPbI\({}_{3}\) PQDs, and PTAA used in this work; (**c**) transmission electron microscope (TEM) image of pure FAPbI\({}_{3}\) PQDs film; (**d**) normalized UV\(-\)vis absorption spectra and PL spectra of FAPbI\({}_{3}\) PQDs solutions. Because the average size of FAPbI\({}_{3}\) PQDs is about 15 nm, much larger than its exciton Bohr radius (\(\sim\)8 nm), the photoexcited excitons in the FAPbI\({}_{3}\) PQDs quickly dissociate to become free carriers [44, 45]. The free carriers then decay via bimolecular recombination [37, 46]. However, the Auger recombination may emerge for large carrier density when the PQDs are excited with high pump fluences [41, 46]. The Auger recombination is normally much faster than the bimolecular recombination, and thus the decay of \(\Delta T/T\) signals may display two stages with different time scales [41, 46]. With increasing pump fluences, an even faster decaying process at the time scale of several picoseconds owing to the quick biexciton recombination may occur as previously discovered in some PQDs [41, 46, 47, 48, 49, 50]. This was also observed in our FAPbI\({}_{3}\) PQDs, as shown in the supplemental Figures S1 and S2 and Table S1 (Supplementary Materials). To avoid the very quick biexciton recombination and reduce the effect of the fast Auger recombination on the charge transfer processes, we have measured the temporal evolution of the \(\Delta T/T\) signals for both pure FAPbI\({}_{3}\) PQDs and PTAA/FAPbI\({}_{3}\)/TiO\({}_{2}\) at a low pump fluence of 3.5 \(\upmu\)J/cm\({}^{2}\). The measured time dependences of the PA signals at 570 nm and the PB signals at 770 nm are shown in Figure 3a,b. We then used a formula with the sum of two exponential decaying terms, \(\Delta T/T=A_{1}\mathrm{e}^{-t/\tau_{1}}+A_{2}\mathrm{e}^{-t/\tau_{2}}\), to fit the temporal evolution of the PA and PB decay signals (see solid curves as fitting results in the Figures). Both PA and PB in pure FAPbI\({}_{3}\) PQDs show a fast component with \(\tau_{1}\approx 120\) ps and a slow component with \(\tau_{2}\approx 1600\) ps (see Table 1), attributed to the Auger and bimolecular recombination, respectively. The slow component has much larger amplitude, indicating that the bimolecular recombination is the dominant decay mechanism. Figure 2: Differential transmission spectra of (**a**) pure FAPbI\({}_{3}\) PQDs film excited at 400 nm with pump fluence of \(\approx\)70 \(\upmu\)J/cm\({}^{2}\) and (**b**) PTAA HTL/FAPbI\({}_{3}\) PQDs/TiO\({}_{2}\) ETL excited at 400 nm with pump fluence of \(\approx\)21 \(\upmu\)J/cm\({}^{2}\). The numbers marked in the upper right corner indicate the delay times between the pump and probe pulses.