Efficient Charge Transfer in MAPbI3 QDs/TiO2 Heterojunctions for High-Performance Solar Cells

Methylammonium lead iodide (MAPbI3) perovskite quantum dots (QDs) have become one of the most promising materials for optoelectronics. Understanding the dynamics of the charge transfer from MAPbI3 QDs to the charge transport layer (CTL) is critical for improving the performance of MAPbI3 QD photoelectronic devices. However, there is currently less consensus on this. In this study, we used an ultrafast transient absorption (TA) technique to investigate the dynamics of charge transfer from MAPbI3 QDs to CTL titanium dioxide (TiO2), elucidating the dependence of these kinetics on QD size with an injection rate from 1.6 × 1010 to 4.3 × 1010 s−1. A QD solar cell based on MAPbI3/TiO2 junctions with a high-power conversion efficiency (PCE) of 11.03% was fabricated, indicating its great potential for application in high-performance solar cells.


Introduction
Metal halide perovskite semiconductor materials have been extensively investigated for potential applications in photovoltaics (PVs) [1,2], light-emitting diodes (LEDs) [3,4], detectors [5][6][7], and lasers [8,9]. To date, the power conversion efficiency (PCE) of bulk perovskite solar cells (PSCs) has been rapidly improved to 25.7%, which is comparable to that of large-scale commercial crystalline silicon solar cells [10]. Nevertheless, although progress has been achieved over the past few years, some challenges remain unsolved, such as instability resulting from moisture/thermal sensitivity, which hinders commercial applications [11]. The low-dimensional perovskite quantum dots (PQDs) possess new attractive features compared with their bulk counterparts, such as improved defect tolerance [12], enhanced stability [13], high photoluminescence quantum yield (PLQY) [14], and tunable bandgaps over the whole spectrum region [15,16]. More importantly, wide bandgap tunability makes PQDs particularly suitable when acting as a top cell in tandem solar cells [17]. The PQDs with precise size control and high PLQY have been successfully synthesized to date [14,18,19]. Apart from formamidinium lead triiodide (FAPbI 3 ) and Cesium lead triiodide (CsPbI 3 QDs), methylammonium lead triiodide (MAPbI 3 ) QDs, as one of the most promising materials has also been used in solar cells due to an appropriate Goldschmidt tolerance factor (τ is approximately 0.91) and low-temperature processing preparation [20,21].
To fully comprehend the fundamental photophysical process and take advantages of the unique properties of these QDs in photovoltaic devices, it is generally designed as heterojunction that QDs selectively contact other metal oxides (MOs) such as NiO x , TiO 2 or ZnO, where the MOs work as the charge transport layer (CTL) [19,22,23]. These QD/MO heterojunctions are an integral part of the QD solar cells, in which the main photogenerated charge carriers transfer from QDs to the QD/CTL interface, are extracted by the CTL, and must finally be collected by the electrodes [24]. The dynamic competition between charge transfer and charge recombination is a critical determinant of photovoltaic device performance. Therefore, a deep understanding of the electronic interactions of QDs with the CTL is crucial to enhancing the performance of MAPbI 3 QD-based optoelectronics. The electron injection rate from bulk MAPbI 3 to TiO 2 has been explored in several works [25,26]. However, little is known concerning the photoexcited carrier transfer kinetics at the MAPbI 3 QDs/TiO 2 heterojunction. Powerful ultrafast transient absorption (TA) spectroscopy enables us to study charge transfer dynamics [22,27,28]. In this study, we investigated the charge injection dynamics from MAPbI 3 QDs to TiO 2 for the first time, and the charge transfer rate of various sizes of QDs was determined and found to increase from 1.6 × 10 10 to 4.3 × 10 10 s −1 with the average QD size decreasing from 13.3 to 9.4 nm. Finally, A solar cell based on MAPbI 3 /TiO 2 junctions with a PCE of 11.03% was fabricated, indicating an efficient charge transfer through these junctions.

Colloidal Synthesis of MAPbI 3 Quantum Dots (QDs)
At first, a 50 mL three-neck flask was charged with 1 g of MA-acetate and 20 mL of OA, and the mixture was dried for 1 min at room temperature (RT) and then heated to 80 • C under nitrogen until all the MA-acetate had reacted with OA, and the MAOA precursor was obtained (it must be preheated to 60 • C before injection). Subsequently, 0.344 g of PbI 2 and 20 mL of ODE were loaded into a 50 mL three-neck flask and degassed under a vacuum for 1 h at 120 • C. A total of 6 mL of OA and 3 mL of OAm were injected at 120 • C under nitrogen atmosphere. After the complete solubilization of PbI 2 , the mixture was cooled down to 60, 80 or 100 • C, and a 4, 5, or 6 mL MAOA precursor solution was swiftly injected (the volume ratio of MAOA precursor and the injection temperature were regulated to control the QDs size). About 10 s later, the reaction mixture was quenched with an icewater bath. The crude QD solution was divided into two tubes, and the mixture of 1 mL Toluene together with 5 mL MeOAc was added to each tube, followed by centrifugation at 9300 rpm for 4 min 20 s. The supernatant was discarded, and the precipitate was dried with nitrogen and then dispersed in hexane (the precipitate was dispersed in octane to prepare the MAPbI 3 QD solar cells). The obtained QD solution was kept in a refrigerator until use.

Fabrication of the QDs/MOs Heterojunction
Mesoporous TiO 2 and Al 2 O 3 films were prepared according to our previous reports [19,23]. Briefly, the purchased 30NR-D titania paste was diluted by ethanol and was deposited on a glass substrate via the doctor blade method using mending tape as a spacer before it was then dried at 180 • C for 10 min. Finally, the dried films were calcined in the air at 500 • C for 30 min. The preparation method of the Al 2 O 3 film was similar to that of TiO 2 . The QDs/MOs heterojunction was obtained by directly adsorbing the QDs on MOs; that is, the mesoporous TiO 2 or Al 2 O 3 films were immersed in a MAPbI 3 QD colloidal solution Nanomaterials 2023, 13, 1292 3 of 12 in hexane for 8 h, subsequently, the adsorbed QD films were rinsed in hexane and dried with nitrogen.

Fabrication of the MAPbI 3 QD Planar Heterojunction Solar Cells
The FTO glass substrates were cleaned with successive sonication in ethanol, acetone, and 2-propanol for 20 min, respectively, and then treated in an ultraviolet-ozone chamber for 10 min before use. The compact TiO 2 layer with approximately 50 nm was deposited on FTO substrates and annealed at 450 • C for 30 min [29]. The MAPbI 3 colloidal QD solution in octane with a concentration of 100 mg/mL was spin-cast on TiO 2 at 2000 rpm for 20 s in a nitrogen glovebox; the resulting film was dipped into a Pb (NO 3 ) 2 in MeOAc saturated solution for 5 s, rinsed with neat MeOAc 3 times, and dried at 2000 rpm for 20 s. The above QD deposition process was repeated four times to achieve the desired film thickness. After that, the films were soaked in FAI in EtOAc saturated solution for 10 s, and dried at 2000 rpm for 20 s. The spiro-OMeTAD (0.09 g of spiro-OMeTAD, 1 mL of chlorobenzene, 22 µL of Li-TFSI (520 mg/mL) and 36 µL of 4-TBP) was then spin-cast on the QD absorber layers at 5000 rpm 30 s. Finally, the Au electrode with a thickness of 80 nm was deposited using thermal evaporation. The active surface area of the solar cells was 0.16 cm 2 .

Characterization
The morphologies of MAPbI 3 QDs and MAPbI 3 QDs/TiO 2 nanoparticles were obtained using high-resolution transmission electron microscopy (HRTEM, JEM-2100F, Akishima, Japan). The UV-vis absorption spectra for all samples were measured by a spectrophotometer (HITACHI, U-3900H, Tokyo, Japan). The phase identification was performed on a powder X-ray diffraction (XRD, TTR-III, Rigaku Corporation, Tokyo, Japan). The photoluminescence quantum yield (PLQY) of the QD solution was obtained with an integrating sphere of an Absolute PL Quantum Yield Spectrometer system (C11347, Hamamatsu Photonics, Hamamatsu, Japan), and the excitation power was 0.1 mW. The photoelectron yield spectra (PYS) were recorded by an ionization energy measurement system (Model BIP-KV205, Bunkoukeiki Co., Ltd., Tokyo, Japan). Time-resolved PL (TRPL) spectra were characterized by a NIR PL lifetime spectrometer (C12132, Hamamatsu Photonics, Hamamatsu, Japan). The J-V curves measurement of MAPbI 3 quantum dot solar cell was performed on a Keithley 2400 digital source meter (Tektronix, Tokyo, Japan) under AM 1.5 irradiation at a scan step of 0.05 V, and the device area of 0.16 cm 2 was defined using a black metal aperture. The external quantum efficiency (EQE) measurements were carried out using monochromatic illumination (300 W xenon arc lamp through Nikon G250 monochromator, Tokyo, Japan). Transient absorption (TA) measurements were carried out using a femtosecond (fs) TA setup. The pump and probe pulses were delivered by a titanium/sapphire laser (CPA-2010, Clark-MXR Inc., Dexter, MI, USA) with a pulse width of 150 fs, a wavelength of 775 nm, and a repetition rate of 1000 HZ. The laser light was split into two parts; one part was incident on a sapphire plate to produce white light for the probe beam. The other part was used as a pump pulse (wavelength can be tuned from 290 nm to 3 µm) converted from an optical parametric amplifier (a TOAPS from Quantronix, Hamden, CT, USA). The pump light was used to excite the sample. A silicon photodiode was exploited to collect the probe light passed through the sample. In this work, a pump light with a wavelength of 470 nm was used to excite all the samples. The intensity of pump light varied from 119 µJ/cm 2 to 1.5 µJ/cm 2 .

Results and Discussion
Various sizes of MAPbI 3 QDs were synthesized by a modified hot-injection approach (details can be found in Section 2), as illustrated in Figure 1 [30]. (~5.6 nm) [31]; thus these QDs are in the weaker confinement regime. A high-resolution transmission electron microscopy (HRTEM) pattern of L-MAPbI 3 QDs (Figure 2d) shows a lattice plane spacing of 0.31 nm corresponding to the (200) plane of the cubic MAPbI 3 QDs [32]. The clear lattice fringes indicate the high crystallinity of the MAPbI 3 QDs.

Results and Discussion
Various sizes of MAPbI3 QDs were synthesized by a modified hot-injection approac (details can be found in Section 2), as illustrated in Figure 1 [30]. Figure 2a-c shows th representative transmission electron microscopy (TEM) images and their correspondin size distribution histogram of MAPbI3 QDs of three sizes: all QDs are nearly cubic shape The average size of small (S), medium (M) and large (L) MAPbI3 QDs are 9.4 ± 1.3, 11.3 1.7 and 13.3 ± 1.5 nm, respectively, which are bigger than the exciton Bohr diameter MAPbI3 (~5.6 nm) [31]; thus these QDs are in the weaker confinement regime. A hig resolution transmission electron microscopy (HRTEM) pattern of L-MAPbI3 QDs (Figu 2d) shows a lattice plane spacing of 0.31 nm corresponding to the (200) plane of the cub MAPbI3 QDs [32]. The clear lattice fringes indicate the high crystallinity of the MAPb QDs.  X-ray diffraction (XRD) measurement was performed to further identify the crysta linity of obtained MAPbI3 QDs, as presented in Figure 3a, and all three sizes of MAPb QDs showed a pure cubic phase [33,34]. The typical diffraction peaks at 2θ with 14.10 28.51°, 31.75°, 40.68° and 43.16° corresponded to (100), (200), (210), (220) and (300), respe tively. Furthermore, both the normalized absorption and steady-state photoluminescenc (PL) spectra of MAPbI3 QDs in hexane with different sizes exhibited continuous tunabilit as can be seen in Figure 3b. To determine the optical band gap energy of various sizes MAPbI3 QDs, the dependency of (αhv) 2 upon the incident photons energy hv was plotte

Results and Discussion
Various sizes of MAPbI3 QDs were synthesized by a modified hot-injection approach (details can be found in Section 2), as illustrated in Figure 1 [30]. Figure 2a-c shows the representative transmission electron microscopy (TEM) images and their corresponding size distribution histogram of MAPbI3 QDs of three sizes: all QDs are nearly cubic shapes. The average size of small (S), medium (M) and large (L) MAPbI3 QDs are 9.4 ± 1.3, 11.3 ± 1.7 and 13.3 ± 1.5 nm, respectively, which are bigger than the exciton Bohr diameter of MAPbI3 (~5.6 nm) [31]; thus these QDs are in the weaker confinement regime. A highresolution transmission electron microscopy (HRTEM) pattern of L-MAPbI3 QDs ( Figure  2d) shows a lattice plane spacing of 0.31 nm corresponding to the (200) plane of the cubic MAPbI3 QDs [32]. The clear lattice fringes indicate the high crystallinity of the MAPbI3 QDs.  X-ray diffraction (XRD) measurement was performed to further identify the crystallinity of obtained MAPbI3 QDs, as presented in Figure 3a, and all three sizes of MAPbI3 QDs showed a pure cubic phase [33,34]. The typical diffraction peaks at 2θ with 14.10°, 28.51°, 31.75°, 40.68° and 43.16° corresponded to (100), (200), (210), (220) and (300), respectively. Furthermore, both the normalized absorption and steady-state photoluminescence (PL) spectra of MAPbI3 QDs in hexane with different sizes exhibited continuous tunability, as can be seen in Figure 3b. To determine the optical band gap energy of various sizes of MAPbI3 QDs, the dependency of (αhv) 2 upon the incident photons energy hv was plotted, X-ray diffraction (XRD) measurement was performed to further identify the crystallinity of obtained MAPbI 3 QDs, as presented in Figure 3a, and all three sizes of MAPbI 3 QDs showed a pure cubic phase [33,34]. The typical diffraction peaks at 2θ with 14.10 • , 28.51 • , 31.75 • , 40.68 • and 43.16 • corresponded to (100), (200), (210), (220) and (300), respectively. Furthermore, both the normalized absorption and steady-state photoluminescence (PL) spectra of MAPbI 3 QDs in hexane with different sizes exhibited continuous tunability, as can be seen in Figure 3b. To determine the optical band gap energy of various sizes of MAPbI 3 QDs, the dependency of (αhv) 2 upon the incident photons energy hv was plotted, as depicted in Figure 3c, and the band gap (E g ) was estimated by extrapolating the linear part of (αhv) 2 versus (hv) [35]. As shown in Table 1, the E g of small, medium, and large MAPbI 3 QDs was 1.75 eV, 1.71 eV, and 1.67 eV, correspondingly. Analogously, the PL peak positions of various sizes of QDs were tuned from 722 to 758 nm. As-prepared MAPbI 3 QDs display a high PLQY of 97.8 ± 1.9%, 95.7 ± 3.5% and 96.6 ± 2.9% for large, medium, and small QDs (Table 1), respectively; after being saved in ambient conditions for 12 months, they still exhibited 84.2 ± 1.7%, 81.1 ± 1.5%, and 86.0 ± 1.8% (Figure 3d), correspondingly, suggesting the high quality of these QDs. The adsorption of QDs on the Al 2 O 3 or TiO 2 substrate was carried out by immersing the films in a hexane colloidal solution of MAPbI 3 QDs for 8 h before rinsed using hexane and drying with nitrogen (details are provided in Section 2.3) [19,23]. The HRTEM in Figure 2e also confirmed that MAPbI 3 QDs had been successfully and chemically adsorbed on TiO 2 (lattice plane spacing of 0.31 and 0.35 nm is associated with the (200) and (101) plane of cubic MAPbI 3 QDs and TiO 2 , respectively).
This monolayer adsorption can ensure that the charge transfer dynamics at the interface of QDs and CTL can be studied without other complicated processes. months, they still exhibited 84.2 ± 1.7%, 81.1 ± 1.5%, and 86.0 ± 1.8% (Figure 3d), correspondingly, suggesting the high quality of these QDs. The adsorption of QDs on the Al2O3 or TiO2 substrate was carried out by immersing the films in a hexane colloidal solution of MAPbI3 QDs for 8 h before rinsed using hexane and drying with nitrogen (details are provided in Section 2.3) [19,23]. The HRTEM in Figure 2e also confirmed that MAPbI3 QDs had been successfully and chemically adsorbed on TiO2 (lattice plane spacing of 0.31 and 0.35 nm is associated with the (200) and (101) plane of cubic MAPbI3 QDs and TiO2, respectively). This monolayer adsorption can ensure that the charge transfer dynamics at the interface of QDs and CTL can be studied without other complicated processes.  To confirm the thermodynamical feasibility of charge transfer from all MAPbI3 QDs to TiO2, firstly, the photoelectron yield spectra (PYS) of all QDs were measured, and the valence band energy level of each QD sample was obtained from the extrapolation of the linear portion of each spectrum, as shown in Figure 4a. The band gap of all QDs was determined from the Tauc plots, as discussed above. For the TiO2, similarly, the band gap and position of the valence band maximum (VBM) were determined by the Tauc plot  To confirm the thermodynamical feasibility of charge transfer from all MAPbI 3 QDs to TiO 2 , firstly, the photoelectron yield spectra (PYS) of all QDs were measured, and the valence band energy level of each QD sample was obtained from the extrapolation of the linear portion of each spectrum, as shown in Figure 4a. The band gap of all QDs was determined from the Tauc plots, as discussed above. For the TiO 2 , similarly, the band gap and position of the valence band maximum (VBM) were determined by the Tauc plot ( Figure 4b) and PYS spectra (Figure 4c), respectively. All sizes of MAPbI 3 QDs showed a shallow conduction band (CB) energy level (−3.87, −3.81, −3.75 eV for large, medium and small QDs, respectively) compared to that of TiO 2 (−4.19 eV), which were in favor of the charge transfer, while the Al 2 O 3 acted as a charge-transfer barrier for its high CB edge (electron injection is not thermodynamically feasible) [19,36,37]. Figure 4d-e schematically exhibits the available charge transfer pathway in MAPbI 3 QDs. Therefore, a comparison of the charge transfer dynamics of the QD solution, adsorbed on Al 2 O 3 as well as TiO 2 films, allows us to estimate the transfer rate of the carrier from QDs to TiO 2 .
In particular, as shown in Figure 5a-c, an obvious PL quenching of MAPbI 3 QDs adsorbed on insulating Al 2 O 3 films was observed. Considering that there was no charge transfer between QDs and Al 2 O 3 , this quenched PL may result from the absence of surface ligands of QDs attached to Al 2 O 3 films, which can lead to the introduction of nonradiative recombination sites. As expected, the MAPbI 3 QDs adsorbed on TiO 2 shows great PL quenching compared to the QD solution and that attached on Al 2 O 3 films (Figure 5a-c), suggesting that the effective charge transfer occurred in QDs/TiO 2 heterojunctions [19,23]. als 2023, 13, x FOR PEER REVIEW 6 of 13 transfer, while the Al2O3 acted as a charge-transfer barrier for its high CB edge (electron injection is not thermodynamically feasible) [19,36,37]. Figure 4d-e schematically exhibits the available charge transfer pathway in MAPbI3 QDs. Therefore, a comparison of the charge transfer dynamics of the QD solution, adsorbed on Al2O3 as well as TiO2 films, allows us to estimate the transfer rate of the carrier from QDs to TiO2. In particular, as shown in Figure 5a-c, an obvious PL quenching of MAPbI3 QDs adsorbed on insulating Al2O3 films was observed. Considering that there was no charge transfer between QDs and Al2O3, this quenched PL may result from the absence of surface ligands of QDs attached to Al2O3 films, which can lead to the introduction of nonradiative recombination sites. As expected, the MAPbI3 QDs adsorbed on TiO2 shows great PL quenching compared to the QD solution and that attached on Al2O3 films (Figure 5a-c), suggesting that the effective charge transfer occurred in QDs/TiO2 heterojunctions [19,23]. charge transfer dynamics of the QD solution, adsorbed on Al2O3 as well as TiO2 films, allows us to estimate the transfer rate of the carrier from QDs to TiO2. In particular, as shown in Figure 5a-c, an obvious PL quenching of MAPbI3 QDs adsorbed on insulating Al2O3 films was observed. Considering that there was no charge transfer between QDs and Al2O3, this quenched PL may result from the absence of surface ligands of QDs attached to Al2O3 films, which can lead to the introduction of nonradiative recombination sites. As expected, the MAPbI3 QDs adsorbed on TiO2 shows great PL quenching compared to the QD solution and that attached on Al2O3 films (Figure 5a-c), suggesting that the effective charge transfer occurred in QDs/TiO2 heterojunctions [19,23]. In addition, time-resolved photoluminescence (TRPL) measurements were employed to examine the carrier kinetics of various sizes of MAPbI 3 QDs and QDs/MOs heterojunction, as shown in Figure 6a-c. All the decay curves of various sizes of QDs as well as QDs/Al 2 O 3 were well fitted by a biexponential model (y = A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 ), where A 1 and A 2 are constant, τ 1 and τ 2 represent lifetime, and t is time), and the obtained parameters were listed in Table 2. Since there was nearly a 100% PLQY of all sizes of MAPbI 3 QDs mentioned above, the nonradiative recombination process of the carrier could be neglected; thus, the fast process (τ 1 , approximately 50 ns) with dominant contribution (>90%) of all three sized QDs could be ascribed to the radiative recombination of excitons (electron-hole pairs), while the slower process may have resulted from the quasi-free carrier radiative recombination, due to the weaker quantum confinement effect of these QDs. (The photoexcited excitons of QDs can rapidly dissociate to become quasi-free carriers, which then decay through bimolecular recombination) [19,38]. The average lifetimes were calcu-Nanomaterials 2023, 13, 1292 7 of 12 lated by τ ave = , and those of all QD solution were similar (68~80 ns). In particular, it was found that the QDs attached to Al 2 O 3 showed a shorter average lifetime (18~23 ns) than those of the QD solution, which was caused by the introduced defects. In addition, the decay curves of QDs/TiO 2 heterojunctions were fitted using a mono-exponential equation ( Table 2). As can be seen from Figure 6a-c, the QDs attached on TiO 2 films present a much shorter PL lifetime (<2.8 ns) than those adsorbed on Al 2 O 3 as well as the QD solution, which gives important evidence that the effective charge transfer occurred in this heterojunction and indicates that the charge transfer process was the dominant route of the photoexcited carrier in QDs/TiO 2 . of all three sized QDs could be ascribed to the radiative recombination of excitons (electron-hole pairs), while the slower process may have resulted from the quasi-free carrier radiative recombination, due to the weaker quantum confinement effect of these QDs. (The photoexcited excitons of QDs can rapidly dissociate to become quasi-free carriers, which then decay through bimolecular recombination) [19,38]. The average lifetimes were calculated by ∑ ∑ , and those of all QD solution were similar (68~80 ns). In particular, it was found that the QDs attached to Al2O3 showed a shorter average lifetime (18~23 ns) than those of the QD solution, which was caused by the introduced defects. In addition, the decay curves of QDs/TiO2 heterojunctions were fitted using a mono-exponential equation ( Table 2). As can be seen from Figure 6a-c, the QDs attached on TiO2 films present a much shorter PL lifetime (<2.8 ns) than those adsorbed on Al2O3 as well as the QD solution, which gives important evidence that the effective charge transfer occurred in this heterojunction and indicates that the charge transfer process was the dominant route of the photoexcited carrier in QDs/TiO2.  Nevertheless, the nanosecond timescale is difficult when revealing charge transfer dynamics in the QDs/TiO2 heterojunction. Thus, femtosecond transient absorption (TA) measurements were carried out at an excitation wavelength of 470 nm. The three-body Auger recombination process may appear at a higher excitation intensity, and this process generally is much faster than the bimolecular recombination, thus, can possibly overlap with the charge transfer process, which makes the discussion complicated [39]. First, the  The decay curves were fitted by a biexponential (y = A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 )) and single-exponential model (y = A 1 exp (−t/τ 1 )), where A 1 and A 2 are constant, τ 1 and τ 2 represent lifetime, t is time. τ ave is average lifetime calculated by τ ave = ∑ A i τ 2 i ∑ A i τ i . Nevertheless, the nanosecond timescale is difficult when revealing charge transfer dynamics in the QDs/TiO 2 heterojunction. Thus, femtosecond transient absorption (TA) measurements were carried out at an excitation wavelength of 470 nm. The three-body Auger recombination process may appear at a higher excitation intensity, and this process generally is much faster than the bimolecular recombination, thus, can possibly overlap with the charge transfer process, which makes the discussion complicated [39]. First, the excitation intensity was adjusted from 119 to 1.5 µJ/cm 2 to avoid the fast Auger recombination. As shown in Figure 7a, the fast decay component appeared in TA responses when the excitation intensity was larger than 3.0 µJ/cm 2 , and became more significant with the increase in intensity. When the excitation intensity was adjusted to 3.0 µJ/cm 2 , the fast decay process disappeared, and the normalized TA decay curves overlapped as well, which suggested that the Auger recombination was eliminated. The TA spectra of all sizes of QDs in hexane, QDs attached on the Al 2 O 3 and TiO 2 were collected 5 ps after band gap excitation under 1.5 µJ/cm 2 and are exhibited in Figure 7b-d. The wavelength of each bleaching maximum of TA spectra coincides with that of the lowest excitation state transition of absorption spectra (Table 1). All TA kinetic curves of QD solution and QDs/Al 2 O 3 monitored at each bleaching maximum can be well fitted by the singleexponential function (Figure 7e-g): y = A 0 exp (−t/τ) + y 0 . As shown in Table 3, the fitting lifetimes of the large, medium, and small MAPbI 3 QD colloidal solution are 123, 150 and 134 ps, respectively. Considering the absence of Auger recombination, these lifetimes can be assigned to the nonradiative combination (i.e., carrier trapping in defect states), although this process has been ignored in the nanoscale (the results in TRPL characterization). The constant component (lifetime >> 1 ns) can be attributed to radiative recombination. For the TA decay of QDs/Al 2 O 3 , the fitted lifetimes (278, 291, and 253 ps for large, medium, and small QDs/Al 2 O 3 , respectively) with an amplitude from 51% to 60% were considered to originate from the nonradiative recombination, whereas the constant part may mostly reflect the radiative recombination processes. In the case of QDs/TiO 2 , the TA kinetics of all sized QDs/TiO 2 were determined to be biexponential (y = A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 ) + y 0 ) (Figure 7e-g), as shown in Table 3, an additional faster decay of the signal traces with the lifetime of 62, 36, and 23 ps for large, medium, and small QDs, separately, was obtained. The fitting of the later slower parts of decay curves with a time constant of 215~331 ps was close to those of the QDs/Al 2 O 3 , which could be assigned to the nonradiative recombination. Thus, the fast parts of kinetics could be attributed to the charge transfer process from QDs to TiO 2 . The rate of charge transfer (k CT ) from QDs to TiO 2 could be calculated from: 1/τ 1 , those of large, medium, and small QDs were 1.6 × 10 10 , 2.8 × 10 10 and 4.3 × 10 10 s −1 , correspondingly. It is worth noting that the k CT of MAPbI 3 QDs depends on the QD size. This was perhaps caused by the different free energy forces (−∆G) of these QDs/TiO 2 systems. According to the Marcus theory, the k CT is a function of ∆G, which is the free energy change between the donor and acceptor and associated with the QDs size [40,41]. We calculated the ∆G through the following Equations:

MAPbI 3 QDs
where ∆E electron is the energy difference between the conduction band edge of the acceptor semiconductor TiO 2 and QDs, e is the elementary charge, R QD represents the radius of QDs, h is the distance between QDs and TiO 2 (the radius of QDs is very large compared to h; thus, it can be set to 0), and the ε acceptor and ε QD are the dielectric permittivity of TiO 2 and QDs (ε TiO2 = 80, ε QD = 26) [42,43]. We obtained the ∆G value using Equations (1) and (2), as shown in Figure 7h, and the value was −0.09, −0.11 and −0.13 eV for small, medium, and large QDs. Finally, we successfully fabricated the QD solar cell with the structure of glass/FTO/TiO 2 / QDs/spiro-OMeTAD/Au with the active area of 0.16 cm 2 (the details of the fabrication can be found in Section 2.4) using the medium size of QDs. The representative J-V curve is presented in Figure 8a, and the MAPbI 3 QDs/TiO 2 -based solar cell achieved a high PCE of 11.03%, with a J sc of 14.31 mA/cm 2 , V oc of 1.15 V, and fill factor (FF) of 67%, which demonstrated a significant enhancement over the same composition QD solar cells [21]. Figure 8b shows the external quantum efficiency (EQE) spectrum of this device, which is in good agreement with the J sc value obtained from the J-V curve. Additionally, the MAPbI 3 QD-based solar cell device exhibited high stability, which could maintain~81% of its initial PCE after 115 days of storage under an atmosphere with a humidity of <30% (Figure 8c-f). According to the previous experimental and theoretical studies, the efficiency of perovskite solar cells could be significantly improved through the application of metallic nanoparticles in the perovskite layer, or at the interface between the charge transfer layer and absorber layer due to the optical plasmon photovoltaic effect and intrinsic electric plasmonic effects [44,45]. Furthermore, the binding energy of the excitons could be reduced through the plasmons of metallic nanoparticles and the rapid dissociation of excitons that took place at the interface of the charge (electron or hole) transport layer and perovskite layer, which could significantly increase the photo-current of perovskite solar cells [45]. For PQD solar cells, low carrier mobility is the main reason for such lower J sc than that of bulk perovskite solar cells. Hence, the PQD solution dopped with metallic nanoparticles and the interface between the PQD layer and charge transport layer modified by metallic nanoparticles produced promising approaches for increasing the photocurrent of PQD solar cells and further optimizing the efficiency of PQD solar cell devices.    Table 3. The fitted parameters of TA kinetics for various size of MAPbI 3 QD colloidal solution, QDs/TiO 2 and QDs/Al 2 O 3 . The decay curves were fitted by single-exponential (y = y 0 + A 1 exp(−t/τ 1 )) or biexponential model (y = A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 ) + y 0 ), where y 0 , A 1 , A 2 are constant, τ 1 and τ 2 represent lifetime, t is time.  which demonstrated a significant enhancement over the same composition QD solar cells [21]. Figure 8b shows the external quantum efficiency (EQE) spectrum of this device, which is in good agreement with the Jsc value obtained from the J-V curve. Additionally, the MAPbI3 QD-based solar cell device exhibited high stability, which could maintain ~81% of its initial PCE after 115 days of storage under an atmosphere with a humidity of <30% (Figure 8c-f). According to the previous experimental and theoretical studies, the efficiency of perovskite solar cells could be significantly improved through the application of metallic nanoparticles in the perovskite layer, or at the interface between the charge transfer layer and absorber layer due to the optical plasmon photovoltaic effect and intrinsic electric plasmonic effects [44,45]. Furthermore, the binding energy of the excitons could be reduced through the plasmons of metallic nanoparticles and the rapid dissociation of excitons that took place at the interface of the charge (electron or hole) transport layer and perovskite layer, which could significantly increase the photo-current of perovskite solar cells [45]. For PQD solar cells, low carrier mobility is the main reason for such lower Jsc than that of bulk perovskite solar cells. Hence, the PQD solution dopped with metallic nanoparticles and the interface between the PQD layer and charge transport layer modified by metallic nanoparticles produced promising approaches for increasing the photocurrent of PQD solar cells and further optimizing the efficiency of PQD solar cell devices.

Conclusions
In summary, the charge transfer dynamics of MAPbI3 QD/MOs were comprehensively investigated using a TA characterization method. Effective charge injection in MAPbI3 QD/TiO2 heterojunctions was observed, and the size dependence of the rate of the charge transfer from QDs to TiO2 was further verified in our work. The rate of the charge transfer from large (13.3 ± 1.5 nm), medium (11.3 ± 1.7 nm), and small (9.4 ± 1.3 nm) QDs to TiO2 were determined to be 1.6 × 10 10 , 2.8 × 10 10 , and 4.3 × 10 10 s −1 , respectively. Furthermore, a high PCE of 11.03% based on QDs/TiO2 junctions was also achieved, demonstrating the great potential of using MAPbI3 QDs in high-performance photovoltaic devices.

Conclusions
In summary, the charge transfer dynamics of MAPbI 3 QD/MOs were comprehensively investigated using a TA characterization method. Effective charge injection in MAPbI 3 QD/TiO 2 heterojunctions was observed, and the size dependence of the rate of the charge transfer from QDs to TiO 2 was further verified in our work. The rate of the charge transfer from large (13.3 ± 1.5 nm), medium (11.3 ± 1.7 nm), and small (9.4 ± 1.3 nm) QDs to TiO 2 were determined to be 1.6 × 10 10 , 2.8 × 10 10 , and 4.3 × 10 10 s −1 , respectively. Furthermore, a high PCE of 11.03% based on QDs/TiO 2 junctions was also achieved, demonstrating the great potential of using MAPbI 3 QDs in high-performance photovoltaic devices.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.