Communicating Two States in Perovskite Revealed by Time-Resolved Photoluminescence Spectroscopy

Organic-inorganic perovskite as a promising candidate for solar energy harvesting has attracted immense interest for its low-cost preparation and extremely high quantum efficiency. However, the fundamental understanding of the photophysics in perovskite remains elusive. In this work, we have revealed two distinct states in MAPbI3 thin films at low temperature through time-resolved photoluminescence spectroscopy (TRPL). In particular, we observed a photo-induced carrier injection from the high energy (HE) state to the low energy (LE) state which has a longer lifetime. The strong interaction between the two states, evidenced by the injection kinetics, can be sensitively controlled through the excitation power. Understanding of the interacting two-states not only sheds light on the long PL lifetime in perovskite but also helps to understand the different behavior of perovskite in response to different excitation power. Further efforts in modifying the low energy state could significantly improve the quantum efficiency and lead to novel application in optoelectronics based on perovskite.

. Photoluminescence (PL) measurement of MAPbI 3 thin film. (a) PL spectra at room temperature (red) and 77 K (blue) with the CW laser excitation centered at 2.33 eV (λ = 532 nm). The excitation power is 1 µW, with a beam spot size of ~2 µm. (b) Normalized time-resolved PL (TRPL) at RT and 77 K with a pulsed (~120 fs pulse width) laser excitation centered at 2.61 eV (λ = 475 nm). The excitation fluence is 4.0 µJ/cm 2 . (c) Power dependence of PL spectra at 77 K. The LE peak amplitude is higher than that of the HE peak at low excitation power, while the HE peak becomes the dominant one with increasing power. on the time scale of hundreds of picoseconds. A similar behavior had been previously shown in MAPbBr 3 single crystals 30 .
To explore the rising delay of peak B in TRPL, we varied the excitation fluence (Fig. 2). The normalized signal over time of peaks A and B as a function of fluence are shown in a color contour plot in Fig. 2c and d, respectively. It is evident that peak A rises instantaneously after excitation, followed by an exponential decay. The peak position in time as indicated by the dashed line does not vary with increasing fluence as typical for a delocalized band state. However, peak B behaves distinctly different (Fig. 2d). With increasing excitation fluence its rise time delay decreases and the delay disappears entirely for the highest fleunces applied 31,32 . The difference can also be seen in the typical TPRL spectra at specific excitation fluence as shown in Fig. 2a and b, which corresponds to the specific line cuts in color plot Fig. 2c and d, respectively. At the excitation fluence of 0.12 µJ/cm 2 , the maximum of the TRPL signal from peak B occurs at 300 ps. This maximum TRPL position shifts close to time zero as the excitation fluence increases, and remains at the same position as the excitation fluence exceeds 60 µJ/cm 2 . For example, the TRPL of peak B at excitation fluence of 100 µJ/cm 2 exhibits the typical TPRL behavior with a sharp rise at time zero followed by an exponential decay (Fig. 2b).

Two-level System
Modelling. The abovementioned observation can be explained with a two-level system, as schematically in Fig. 3a. Here we are specifically interested in the quantification of the interaction and communication processes between the high energy (HE) and low energy (LE) states. The PL decay of peak A can be interpreted as the decay of the optically excited carriers in the high energy (HE) level, which is determined by the recombination rate k 1 (including both radiative and non-radiative channels) and the carrier injection rate k 12 . k 12 depicts the carrier injection from the high energy (HE) level to the low energy (LE) level. We separate the k 12 process from other non-radiative processes for its contribution to the increased PL of peak B. This carrier injection, however, is sensitive to the available states in the LE level. As the excitation fluence increases, the maximum number of states in the perovskite will be occupied and the carrier injection pathway from HE to LE will be blocked, which leads to the decrease of k 12 and the disappearance of the rising feature ( Fig. 2b and d). This interpretation also explains the fluence dependence of the PL spectra at 77 K ( Fig. 1c) under the CW laser excitation: as the excitation power increases, the PL from peak A becomes the dominant one since the carrier injection channel is blocked.
A quantitative description is given by the following rate equations: where n 1 and n 2 are optically excited carriers at the HE and LE state, respectively. k 1 is the decay rate for HE state, k 2 is the decay rate for the LE state, and k 12 is the injection rate of carriers from the HE to LE state. N 0 is the maximum number of states that can be occupied in the LE state. As shown in Fig. 3b, the TRPL data can be well fitted with this model. The obtained fitting parameters of k 1 , k 2 , and k 12 are plotted as a function of excitation fluence in Fig. 3c. It becomes apparent that the coupling rate k 12 is more than one order of magnitude larger than k 1 and k 2 , respectively, suggesting a strong coupling between the LE and HE states. It is this strong coupling that can explain the unusual decay of the TRPL spectra. In particular, by means of this strong coupling, Eq. (2) describes a delayed peaking at a time hundreds of picoseconds away from time zero, qualitatively different from the typical TPRL which is peaked at time zero (within the resolution dictated by the response time of the avalanche photodiode (APD). To quantitatively compare the communication between the two states with the lifetime extracted from the exponential fitting of the TRPL data, we re-organize the Eq. ). We choose Eq. (1) instead of (2) for the relative similarity, i.e., both Eq. (1) and exponential decay describe a dynamic event with the peak value locates at the time zero. We therefore obtain a time scale τ x, through 1/x, as a function of the excitation fluence, which is plotted along with the fluence dependence of τ 1 and τ 2 in Fig. 3d. It is clear that τ 2, the lifetime of the LE state, is longer than the lifetime of the HE state, τ 1 . The difference is most drastic at the low excitation fluence. At the excitation fluence of 0.12 µJ/cm 2 , τ 2 (~9.5 ns) is more than three times as large as the τ 1 (~3 ns). Considering the injection between the HE state and the LE state is particularly efficient under the low excitation fluence, the optically excited carrier can be transferred to the LE state with a longer lifetime.
Temperature Dependence. Previous studies have reported the observation of the two emission peaks in the low-temperature PL spectra of MAPbI 3 thin film [33][34][35][36][37][38][39][40] . While it is in general consensus that the HE energy state at 77 K is attributed to the free exciton with a binding energy in range of 20-60 meV 41,42 , the nature of the LE state is elusive, with the possibility of a bound exciton 43 , a exciton-receptor pair 37 , and possible tetragonal phase domain in the orthorhombic phase 31,44 . One recent study suggests that the LE state is possibly due to a MA-disordered phase among the otherwise ordered orthorhombic phase 34,45,46 . To investigate the nature of the LE state, we performed temperature dependent PL study in the range of 12 K to 85 K (Fig. 4a). Since the temperature remains below 150 K the MAPbI 3 thin film remains in the orthorhombic phase (see SI Section S4). From 12 K to 85 K the PL peak shows a blue shift, consistent with previous reports 33,34,36 . In parallel, the intensity ratio of HE peak and LE peak (I HE /I LE ) decreased from 2.34 to 1.38. The increased LE PL at higher temperature suggests a thermal activation of the carrier injection from the HE to the LE state. More detailed temperature-dependent PL spectra can be found in SI Section S4. Figure 4b shows the TRPL at 12 K and 85 K, and it is clear that the data at 85 K exhibits a slower rising, confirming the activation of the k 12 45,47 . The thermal activation behavior of the LE state is consistent with the MA-disordered domain picture. The kinetics extracted from TRPL, therefore, directly probe the interaction between the MA-ordered and MA-disordered domain. And such strong coupling may be achieved via electron-phonon interaction 23,38,48 , energy transfer caused by dipole-dipole interaction or defect assisted scattering. More insight into the interaction mechanism requires further investigations.

Conclusion
In summary, we have identified two communicating states in the MAPbI 3 thin film through the low-temperature PL spectroscopy measurement. TRPL spectroscopy reveals a sensitive power dependence of the optically excited carrier injection from the HE state to the LE state, and the injection is particularly efficient at low power excitation. The LE state shows a thermal activation behavior, which might be attributed to the MA-disordered domain in the orthorhombic phase. The low-temperature TRPL spectroscopy directly probes the kinetics of the two states in MAPbI 3 , which may enable the investigation of the modification effect on the LE state and help to improve our understanding of the optical properties of the perovskites.

Methods
Sample Preparation. The MAPbI 3 powder was synthesized and dissolved at a concentration of 1 mol/L in dimethyformamide (DMF). Microscope slides were washed sequentially with soap, de-ionized water, acetone, and isopropanol, before they were finally treated under oxygen plasma for 20 minutes to remove the organic residues. The MAPbI 3 solution was spin-coated at 3000 rpm for 60 seconds, and the substrates were subsequently heated at 100 °C on a hotplate in the glove box for 10 minutes to improve film quality.
Optical Spectroscopy. The steady-state photoluminescence (PL) and time-resolved photoluminescence (TRPL) spectroscopy measurements were performed with a home-built confocal microscope setup with either a CW or a femtosecond pulsed laser (repetition rate: 80 MHz). The excitation power of CW laser was typically maintained below 100 μW to prevent any sample degradation.
The TRPL measurement were performed by a Time-Correlated Single Photon Counting (TCSPC) module (PicoQuant TimeHarp-260) combined with an Avalanche Photo-Diode (MPD SPAD) through a spectrograph.