## 3 Results and Discussion  
Figure 1a shows the structure of PTAA/FAPbI\({}_{3}\)/TiO\({}_{2}\) sample, where the thickness of the ETL TiO\({}_{2}\), the light harvester layer FAPbI\({}_{3}\) PQDs, and the HTL PTAA doped by tris(pentafluorophenyl)borane is \(\sim\)50 nm, \(\sim\)160 nm, and \(\sim\)40 nm, respectively. As shown in Figure 1b, FAPbI\({}_{3}\) PQDs exhibit deep valence band (VB) energy level of \(-\)5.46 eV, whereas the PTAA exhibits shallower highest occupied molecular orbital (HOMO) energy level of \(-\)5.20 eV [24; 25], and the conduction band (CB) energy level values of FAPbI\({}_{3}\) PQDs and TiO\({}_{2}\) are \(-\)3.94 eV and \(-\)4.15 eV [25; 33; 34], respectively, which are in favor of the charge transfer. From the TEM image of the pure FAPbI\({}_{3}\) PQDs (Figure 1c), we found the PQDs have an average size of about 15 nm. The UV\(-\)vis absorption spectra show a broad absorption with the first absorption peak at \(\sim\)770 nm as a result of optical transition from the ground state to the first excitonic state (Figure 1d). A narrow PL peak centered at \(\sim\)770 nm can also be identified in the PL spectra. Based on this structure, the PCE of our FAPbI\({}_{3}\) PQDs solar cells has reached 11.6% [25]. Using PTAA as the hole transport material (HTM) instead of the conventional 2,2,7,7-tetrakis-(\(N\),\(N\)-di-p-methoxyphenylamine)-9,9-bifluorene (Spiro-OMeTAD) can reduce manufacturing costs and avoid device instability caused by complex doping and oxidation processes [15; 35; 36]. We then performed the ultrafast TA measurements in the pure FAPbI\({}_{3}\) PQDs and PTAA/FAPbI\({}_{3}\)/TiO\({}_{2}\). Figure 2a,b show their transmission modulation (\(\Delta T\)/\(T\)) spectra under excitation of 400-nm pump laser pulses. The spectra of pure FAPbI\({}_{3}\) display positive photoinduced bleaching (PB) signals in the range of 650-1000 nm. These PB signals are pronouncedly enhanced around 750 nm, which coincides with the wavelength of the first absorption peak, shown in Figure 1d, resulting from the transition from the ground state to the first excitonic state. We can thus ascribe the strong PB signals to the ground state bleaching (GSB). Actually, previous works have demonstrated that in the FAPbI\({}_{3}\) PQDs the strong PB signals was mainly contributed by the holes in the valence band after laser excitation [37; 38; 39]. We note a slight red shift of the PB peak with increasing time delay. This shift may be attributed to the bandgap renormalization (BGR) as a result of the Coulomb interaction of photoexcited free carriers near the band edge [40; 41]. In the range of 500-650 nm, the \(\Delta T\)/\(T\) spectra show negative photoinduced absorption (PA) signals. The time dependences of the PA signals at different wavelengths are nearly identical, as shown in Figure 2c. This indicates that the PA signals are mainly originated from one component of the photoexcited species, since different components typically have distinct dynamics and spectra weight. In principle, both transient absorption of conduction band electron and BGR may contribute to the PA signals [42; 43]. However, both contributions in the pure FAPbI\({}_{3}\) PQDs are proportional to the number of electrons or holes which exist as pairs, therefore, their dynamics are expected to behave in the same way. Compared to the pure FAPbI\({}_{3}\) PQDs, the \(\Delta T/T\) spectra in PTAA/FAPbI\({}_{3}\)/TiO\({}_{2}\) also display the apparent PB and PA features. However, the PA wavelength range in the latter is broadened to above 700 nm and the PA peak is shifted to the longer wavelength of \(\sim\)650 nm. Consequently the strong PB signals only appear in a much narrower wavelength range, and the PB peaks show negligible red shift over a long time delay.