## 3 Results and Discussion
### The Laser Power Effect on the PL Lifetime  
Figure 9a,b shows the PL lifetime of the perovskites (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) and (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\). PL lifetime of the perovskite (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) decreases from 0.75 ns to 0.50 ns when laser power increases from 10 mW to 100 mW. In contrast, PL lifetime of the perovskite (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\) decreases from 0.67 ns to 0.46 ns when laser power increases from 10 mW to 100 mW. Figure 9c shows the laser power dependence of the PL intensity of the perovskites (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) (red curve) and (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\) (blue curve). It can be observed that the PL lifetime decreases with increasing laser power. PL lifetime of the perovskite (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) is larger than that of the perovskite (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\) at the same laser power. The internal quantum efficiency [6] is calculated as:  
\[\mathrm{Q}=\tau_{\mathrm{nr}}/(\tau_{\mathrm{r}}+\tau_{\mathrm{nr}}) \tag{6}\]  
Figure 8: Laser power dependence of the photoluminescence (PL) intensity of the perovskites (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) (red curve) and (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\) (blue curve).  
Figure 7: The bright field and dark field optical microscope images of the perovskites (**a**) (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\); (**b**) (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\); the two-photon PL spectrum of the perovskites (**c**) (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\); (**d**) (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\).  
where \(\tau_{\rm r}\) and \(\tau_{\rm nr}\) are the radiative and nonradiative decay lifetime respectively. According to Equation (6), the internal quantum efficiency of the perovskite (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) varies from 81.48% to 90.91%, and the internal quantum efficiency of the perovskite (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\) varies from 83.55% to 91.28%.  
The fluence-dependence of PL intensity and lifetime with laser power can be explained with the energy level diagram [24; 25; 26], which is shown in Figure 10. The perovskite molecules will absorb two  
Figure 9: The PL lifetime of the perovskites (**a**) (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\); (**b**) (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\); (**c**) laser power dependence of the PL lifetime of the perovskites (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbBr\({}_{4}\) (red curve) and (C\({}_{6}\)H\({}_{5}\)CH\({}_{2}\)NH\({}_{3}\))\({}_{2}\)PbI\({}_{4}\) (blue curve).  
photons after the 800 nm laser excitation, promoting the electron transfer from VB to CB. Some electrons in CB will return to VB and produce exciton emission. Meanwhile, some electrons in CB will move to ESS by relaxation. The relaxation to ESS, or ESS recombination, can possess certain non-geminate recombination characteristics. This emission is a kind of non-geminate recombination, which is the intensity-dependent two-photon absorption cross-section [27]. When laser power increases, more electrons transfer from VB to CB, and move to ESS by relaxation after absorbing two photons. As a consequence, the carrier density increases and the emission is dominated by non-geminate recombination, which results in the increase of PL intensity and decrease of lifetime.