Hot Biexciton Effect on Optical Gain in CsPbI3 Perovskite Nanocrystals

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials 3

Hot Biexciton Effect on Optical Gain in CsPbI Perovskite Nanocrystals Go Yumoto, Hirokazu Tahara, Tokuhisa Kawawaki, Masaki Saruyama, Ryota Sato, Toshiharu Teranishi, and Yoshihiko Kanemitsu J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01029 • Publication Date (Web): 12 Apr 2018 Downloaded from http://pubs.acs.org on April 12, 2018

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The Journal of Physical Chemistry Letters

Hot Biexciton Effect on Optical Gain in CsPbI3 Perovskite Nanocrystals Go Yumoto, Hirokazu Tahara, Tokuhisa Kawawaki, Masaki Saruyama, Ryota Sato, Toshiharu Teranishi, and Yoshihiko Kanemitsu* Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].

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ABSTRACT Combining the superior optical properties of their bulk counterparts with quantum confinement effects, lead halide perovskite nanocrystals are unique laser materials with low-threshold optical gain. In such nonlinear optical regime, multiple excitons are generated in the nanocrystals and strongly affect the optical gain through many-body interactions. Here, we investigate the excitonexciton interactions in CsPbI3 nanocrystals by femtosecond transient absorption spectroscopy. From the analysis of the induced absorption signal observed immediately after the pump excitation, we estimated the binding energy for the hot biexcitons that are composed of an exciton at the band edge and a hot exciton generated by the pump pulse. We found that the exciton-exciton interaction becomes stronger for hot excitons with larger excess energies and that the optical gain can be controlled by changing the excess energy of the hot excitons.

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The solution-processed lead halide perovskites enable high solar cell conversion efficiencies of over 22%,1 and are receiving much attention as materials for flexible high-performance optoelectronics. This versatility and the good efficiencies have their origin in the superior optoelectronic properties of the lead halide perovskites such as a sharp absorption edge, strong absorption, low defect density, long carrier diffusion length, and a room temperature behavior that is governed by free carriers.2-8 The high solar cell conversion efficiencies indicate that the lead halide perovskites are also suited materials for photonic devices; for example, light-emitting diodes (LEDs) with relatively high conversion efficiencies have been reported.9-11 Furthermore, the large absorption coefficients and low defect densities of the lead halide perovskites enable unique photoluminescence (PL) properties, which may be useful in applications that exploit optical gain. Actually, amplified spontaneous emission and lasing have been already observed from organic-inorganic lead halide perovskite thin films.12,13 By employing quantum dots, quantum wells or other nanostructures, low-threshold lasing can be achieved by quantum confinement effects such as the enhancement of the PL efficiency and an improved density of states at the band edge. In addition to their bulk counterparts, high-quality lead halide perovskite nanocrystals (NCs) have recently been prepared successfully. PL quantum yields as high as 90% have been reported for the all-inorganic CsPbX3 (X=I, Br, Cl) NCs, as well as the possibility to cover the whole visible spectrum by controlling the bandgap via halide exchange.14 Due to the high PL quantum yield and wavelength tunability, the CsPbX3 NCs have been attracting much attention for application in photonic devices such as LEDs.15,16 The low-threshold optical amplification in the whole visible regime has been observed from CsPbX3 NCs, which indicates the importance of this materials system for optical gain applications.17,18 In such a nonlinear optical regime,


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multiple excitons are formed in the NCs,19-22 and the optical gain is strongly influenced by the dynamics of multiple excitons in NCs.23-27 It is important to note that extremely large biexciton binding energies have been reported in both CsPbBr3 NCs and CsPbI3 NCs.28 The multiple excitons have so far been studied mainly in CsPbBr3 NCs because these NCs are more stable than the CsPbI3 NCs. However, CsPbI3 NCs have a longer biexciton Auger lifetime compared to CsPbBr3 NCs with the same absorption cross section,28 which indicates that CsPbI3 NCs are preferable for optical gain applications. Besides, the structural stability of CsPbI3 NCs has been rapidly improving, supported by efforts in recent studies.29-31 Therefore, the thorough understanding of the exciton-exciton interactions in CsPbI3 NCs is important for material design of perovskite lasers. In this work, we employed femtosecond transient absorption spectroscopy to clarify the effects of the biexcitons on the optical responses of CsPbI3 NCs. From the excitation energy dependence of the transient absorption spectra, we estimated the binding energy of the hot biexcitons that are composed of an exciton at the band edge and a hot exciton generated by the pump pulse. We observed that the biexciton binding energy becomes larger for hot excitons with larger excess energies, but approaches a constant level. Furthermore, we found that the optical gain can be controlled via the hot biexciton state.


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(a)

50 nm

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tpp (ps)

6 4 2 0 -2

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2500 2000 1500 1000 500

-∆αd (x10 )

2 0

IA

AB

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tpp = 0.4 ps 0.7 ps 1.0 ps 2.1 ps 500 ps

8 -3

-∆αd (x10 )

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6 4 2 0 -2 1.7

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Figure 1. (a) Absorption spectrum (red curve on the left axis) and the second derivative of the absorption spectrum (gray curve on the right axis) of the CsPbI3 NCs. The second derivative spectrum is offset for clarity. Inset: TEM image of the NCs. (b) Two-dimensional contour plot of the differential absorption spectra –∆αd obtained for a pump energy of 2.38 eV (Eex = 0.47 eV) and an excitation power of = 0.1. IA and AB denote induced absorption and absorption bleaching, respectively. (c) Several differential absorption spectra obtained at different pumpprobe delay times tpp.


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We investigated CsPbI3 NCs synthesized by the hot injection method (see details in the Experimental Methods). From the TEM image shown in the inset of Figure 1a we confirmed the formation of cubic NCs and an average edge length of 7.0±0.8 nm. We performed the femtosecond transient absorption measurements on the CsPbI3 NCs at room temperature. The CsPbI3 NCs were dispersed in octane within a 1-mm thick quartz cell, and to avoid the photocharging of the NCs during the measurements the solution was stirred with a magnetic stirrer (see further experimental details in the Experimental Methods). Figure 1a shows the steady-state absorption spectrum (red curve) and its second derivative (gray curve). The second derivative was used to obtain accurate fitting results for the energy levels,32,33 and is shown in arbitrary units with an offset for clarity. In this figure, α0 is the absorption coefficient without pump excitation, and d represents the thickness of the sample. It can be seen that there is an absorption structure at ~ 2.0 eV, in addition to the resonant excitation at the band edge at ~ 1.9 eV. We fitted the second derivative of the steady-state absorption spectrum under assumption of a Gaussian absorption structure, and the band-edge transition energy of 1.91 eV and an energy of 2.01 eV for the transition at the high energy side were estimated. The optical transition at 2.01 eV is considered to be a transition between discrete levels that are formed from the bulk band-edge states due to the quantum confinement effect (See details in Supporting Information). Figure 1b shows a two-dimensional plot of the differential absorption spectra –∆αd that were obtained under an excitation with 2.38 eV, corresponding to an excess energy of Eex = 0.47 eV, and an excitation power which corresponds to 0.1 excitons per NC on average, i.e., = 0.1. The average number of electron-hole pairs can be estimated from a fitting of the exciton amplitude with Poisson distributions. The amplitude is derived by global fitting of the excitation


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power dependence of the differential absorption dynamics at the band edge to three exponential functions (See details in Supporting Information).33-35 We estimated the absorption cross-section at 2.92 eV to be σ = 2.7×10-14 cm2, which is comparable to the previously reported value at 3.10 eV.33 Positive values –∆αd > 0 indicate absorption bleaching (AB), and negative values –∆αd < 0 indicate induced absorption (IA). Figure 1c plots the differential absorption spectra for different pump-probe delay times tpp. For tpp > 2.5 ns, a long-lasting absorption bleaching signal is observed near the band edge. In addition, immediately after the excitation we observe an induced absorption signal in the energy region below the band edge. The induced absorption signal around 1.84 eV appears only in the time range for tpp < 2 ps, and it can be seen that the differential absorption spectrum exhibits a derivative-like feature. The bleaching signal around 2.01 eV also appears only immediately after excitation. It is considered that this fast response is a state filling effect due to the transient occupation of the high energy state which is related to the optical transition observed in Figure 1a at 2.01 eV.36 A similar transient bleaching signal, which arises from the quantum confinement effect, has been reported in small size CsPbBr3 NCs.37


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(a)

(b)

(c)

(d)

Figure 2. (a) Schematics of the biexciton effect on the transient absorption spectra at different delay times tpp. The black (blue) shaded curve represents the absorption bleaching (induced absorption) spectrum centered at Eg (Eg+∆xx). The red shaded curve is the sum of the two spectra. (b) Pump-induced dynamics of –∆α/α0 probed at 1.84 eV (solid circles) and 1.91 eV (open circles) under an excitation power of = 0.1 for different pump excess energies of Eex = 0.11,


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0.19 and 0.47 eV. Solid curves are fitting results. (c) Pump excess energy dependence of the rise time of the bleaching signal obtained from the fitting of the data probed at 1.91 eV in (b). Error bars are determined by the standard deviation of the fitting parameter. Error bars smaller than the size of the data points are not shown. (d) Pump excess energy dependence of the amplitude of the induced absorption component estimated from the fitting of the data probed at 1.84 eV in (b).

The origin of the derivative-like feature in the differential absorption spectra obtained immediately after excitation can be assigned to an energy shift due to a biexciton effect.33,38,39 Figure 2a shows the schematics of this idea. The biexciton effect concerns the Coulomb interaction between the hot exciton that was generated by the pump pulse and the exciton that was generated by the probe pulse at the band edge. Due to this exciton-exciton interaction, the energy of the lowest optical transition is shifted compared to the transition energy under absence of the hot exciton, Eg, by the biexciton binding energy ∆xx, and becomes Eg+∆xx. Because ∆xx has a negative value (see the discussion below), the lowest optical transition exhibits a redshift. The induced absorption below the band edge and bleaching at around the band edge are observed until the hot exciton has relaxed to the band edge. After the relaxation of the hot exciton, a strong bleaching signal appears at around the band edge due to the state filling effect, and the induced absorption vanishes. Figure 2b shows the dynamics of the normalized differential absorption spectra –∆α/α0 that were obtained for the two different probe energies 1.84 eV (in the energy region below the band edge, shown with the closed circles) and 1.91 eV (near the band edge, shown with the open circles) under excess energies of Eex = 0.11, 0.19 and 0.47 eV, and an excitation power corresponding to = 0.1. The excitation powers for each excess energy are estimated by


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the same procedure as described in Figure S2 in Supporting Information. It can be seen that the initial rise of the bleaching signal at 1.91 eV becomes faster for smaller Eex. This initial rise can be well fitted by an exponential function with lifetime τrise that is convoluted with a Gaussian function (see Figure S3 in Supporting Information). We fixed the full width at half maximum of the Gaussian function to 120 fs, as estimated from the width of the cross-correlation between the probe pulse and the reference pulse at 1.91 eV. By using this function, the Eex dependence of the initial rise time could be clarified and the fitting results are shown in Figure 2c. The initial rise time reflects the intraband relaxation time,36 and therefore this fitting result shows that the carrier relaxation depends on the excitation energy and occurs on the sub-picosecond time scale. On the other hand, the absorption dynamics at 1.84 eV can be reproduced with the sum of a bleaching signal that rises with τrise and an induced absorption signal that decays exponentially with τdecay = τrise. By performing this fitting procedure, we clarified that the induced absorption signal increases for larger Eex as shown in Figure 2d. The Eex dependence of the induced absorption signal at a fixed probe energy suggests that the biexciton binding energy ∆xx changes and the biexciton absorption band shifts to lower energy side with larger excess energy of the pump pulse as it is discussed below.


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(a)

(b)

Figure 3. (a) Early-time differential absorption spectra –∆αd for different pump excess energies. The spectrum for Eex = 0.05 eV was measured at tpp = 0.16 ps and the other spectra were measured at tpp = 0.3 ps. The spectra are offset for clarity. The fitting results are shown with the black curves. (b) Estimated excess energy dependence of the biexciton binding energy (red dots). Error bars are determined by the standard deviation of the fitting parameter. Error bars smaller than the size of the data points are not shown. The steady-state absorption spectrum (black curve) and its second derivative (gray curve) are shown for reference.


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To further investigate the excess energy dependence of the biexciton binding energy, we estimated the biexciton binding energy ∆xx from the differential absorption spectra that were obtained with different excess energies immediately after excitation at tpp = 0.16 ps for Eex = 0.05 eV and tpp = 0.3 ps for the other excess energies. Figure 3a shows the data of the differential absorption spectra, which were offset for clarity. We fitted the data in Figure 3a assuming that the differential absorption spectra –∆αd can be expressed with the sum of two Gaussian functions representing the induced absorption at Eg+∆xx and the absorption bleaching at Eg: –∆αd(E) = -A0exp(-[(E-Eg-∆xx)/w0]2) +A1exp(-[(E-Eg)/w0]2). Here, A0 and A1 express the magnitudes of the induced absorption and absorption bleaching, respectively. Further, w0 represents the line width of the band-edge transition, and we used the results Eg = 1.91 eV and w0 = 44 meV that were obtained from the fitting of the second derivative of the steady-state absorption spectrum. For Eex = 0.05 eV, a sharp increase is observed in the differential absorption spectrum –∆αd at the energy region that corresponds to the pump energy. Therefore, we performed the fitting in a range where the influence of the pump energy peak can be neglected. The fitting results are shown with the black curves in Figure 3a, and it can be confirmed that the experimental results are well reproduced. The Eex dependence of ∆xx that was obtained from the fitting is shown in Figure 3b. The steady-state absorption spectrum and its second derivative are shown for reference with the black and gray curves, respectively. The obtained ∆xx exhibits negative values, which implies that the exciton-exciton interaction is attractive.39 With increasing Eex, |∆xx| increases monotonically up to Eex ~ 0.3 eV and reaches ~ 60 meV, which is 1.6 times larger than that for Eex = 0.05 eV. Afterwards a nearly constant behavior is observed. This result reflects the electronic structure of


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hot biexcitons that are composed of a band-edge exciton and a hot exciton. We note that it has been reported that the inhomogeneous broadening has a minor contribution to the ensemble spectral line width of CsPbX3 NCs.40 Furthermore, our previous report on CsPbBr3 NCs revealed that the absorption cross sections and exciton dynamics estimated from the NC ensemble match those of the single NCs well, which indicates that the effects of energy transfer and inhomogeneity are negligible under our experimental conditions.34 Therefore, the effects of energy transfer and the NC size variation, which leads to the inhomogeneous line broadening, should have almost no influence on our results. The Eex dependence of |∆xx| observed in Figure 3b can be explained as follows. The biexciton binding energy is determined by the imbalance of the attractive and repulsive Coulomb forces between the two electrons and two holes that form the biexciton, and thus |∆xx| reflects their wave functions. As the distribution of the wave function amplitudes of the four charge carriers becomes more asymmetric, the imbalance between the forces becomes larger and |∆xx| increases.41 Because the hot exciton wave function for smaller Eex more closely resembles that of the band-edge exciton, whose wave function distribution is concentrated in the center of the NC, |∆xx| is smaller for lower Eex. With increasing Eex, the amplitude of the wave function of the hot exciton becomes more distributed over the NC. For even larger Eex, it is considered that the second valence band starts to contribute to the formation of the hot exciton (see Supporting Information). Therefore, the asymmetry between the hot and the band-edge exciton wave function distributions increases for larger Eex, which leads to the enhancement of |∆xx|. However, the observed |∆xx| shows a saturation behavior, which indicates that the asymmetry at Eex ~ 0.3 eV reached a level where any further change of the hot exciton state has little influence on the imbalance between the attractive and repulsive Coulomb forces.


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(a)

(b)

(c)

Figure 4. (a) Absorption spectra at tpp = 0.3 ps obtained under a strong excitation power of = 1 for three different pump excess energies Eex = 0.05, 0.11 and 0.26 eV. The steady-state absorption spectrum is shown with the gray broken curve. (b) Pump-induced dynamics of –∆α/α0 probed at 1.80 eV under the same excitation power and excess energies as those in (a). Solid curves are fitting results. Inset: Induced absorption (blue curve) and bleaching (red curve)


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components derived from the fit of the pump-induced dynamics with Eex = 0.26 eV. (c) The dependence of –∆α/α0 on the excitation power for a probe energy of 1.80 eV and excess energies Eex = 0.05, 0.11 and 0.26 eV at tpp = 0.3 ps (left panel) and 3 ps (right panel).

In the following we discuss the optical responses under a higher excitation power of = 1. Figure 4a shows the nonlinear absorption spectra αNLd = α0d+∆αd that were obtained immediately after the excitation at tpp = 0.3 ps for different Eex. For Eex = 0.05 eV, we find αNLd < 0 in the energy region below ~ 1.80 eV, which means that optical gain occurs in this region. By increasing the excess energy, the region of the optical gain exhibits a redshift. For Eex = 0.26 eV no optical gain appears and the absorption is stronger than the steady-state absorption spectrum α0d (Figure 4a; gray broken curve). The suppression of the optical gain is a result of the peak energy shift of the biexciton absorption band, Eg+∆xx, which is about 20 meV towards the lower energy side when Eex is increased from 0.05 to 0.26 eV. Next, in order to investigate the optical gain dynamics, the selected pump-probe delay dependence of the normalized differential absorption spectrum –∆α/α0 for 1.80 eV is plotted in Figure 4b (see Figure S4 in Supporting Information for full comparison). The optical gain is achieved in the region of –∆α/α0 > 1. This data reveals that for larger excess energies Eex, the time until the optical gain regime is reached, τgain, becomes longer. For Eex = 0.26 eV it takes about 1 ps to reach the optical gain regime. By performing the same fitting procedure as done for Figure 2d, the contributions of absorption bleaching and induced absorption for the signal obtained under Eex = 0.26 eV were estimated and are shown in the inset of Figure 4b. It can be seen that immediately after the excitation, the induced absorption signal governs the dynamics of the normalized differential absorption spectrum –∆α/α0, and at later times the absorption


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bleaching signal becomes dominant and the optical gain regime is reached. This implies that the induced absorption due to the biexciton effect suppresses the optical gain and prolongs τgain. It is considered that the observed Eex dependence of the optical gain spectra and their dynamics is a result of a larger redshift of the induced absorption arising from hot biexcitons including a hot exciton with larger excess energies (Figure 3b). In addition, we consider that the dependence also reflects that the hot exciton with larger Eex requires a longer time for relaxation to the band edge. We note that the carrier trapping effect due to defects or surface trap states plays a minor role in the observed Eex dependence of the optical gain. We found that the temporal evolution of –∆α/α0 under weak excitation powers (Figure S5 in Supporting Information) can be described with a single decay component. The absence of faster decay components indicates that the carrier trapping effects due to defects or surface traps are negligible in our sample. Figure 4c shows the dependence of –∆α/α0 on the excitation power at tpp = 0.3 and 3 ps. At tpp = 0.3 ps the threshold of the optical gain changes with Eex, and for Eex = 0.26 eV we find -∆α/α0 < 1 for all excitation powers. This indicates a strong absorption due to the hot biexciton absorption band. However, the dependence on Eex vanishes completely at tpp = 3 ps. It can be considered that at tpp = 3 ps, hot excitons generated by the pump pulse have already relaxed to the band edge for all Eex used in this experiment. The observed dynamics of the optical gain suggests that the optical gain build-up can be controlled on the femto- to pico-second time scale by changing the excitation energy. Therefore, femtosecond pulse generation and a variable optical gain switching via control of the excitation energy can be expected. In conclusion, we performed femtosecond transient absorption spectroscopy on CsPbI3 NCs with an average size of 7.0±0.8 nm, and observed ultrafast spectral changes that are related to the exciton-exciton interactions. From these changes in the spectra, we estimated the biexciton


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binding energy and revealed the electronic structure of the hot biexcitons. We found that the interaction between the hot exciton and the band-edge excitons becomes stronger when the excess energy of the hot exciton increases, but approaches a constant level above the threshold excess energy Eex ~ 0.3 eV, where |∆xx | is 1.6 times larger than that for Eex = 0.05 eV. This reflects that the asymmetry between the wave functions of the hot exciton and the band-edge exciton depends on the excess energy of the hot exciton. Furthermore, under strong excitation conditions we observed optical gain spectra and we analyzed their dynamics. We found that a hot biexciton including a hot exciton with larger excess energies leads to a stronger suppression of the optical gain on the femto- to pico-second time scale due to an enhanced biexciton absorption band. The observed ultrafast gain and loss dynamics controlled by hot biexciton states in CsPbI3 NCs would pave the way for novel halide perovskite-based all-optical ultrafast switching devices and femtosecond pulse generation.

EXPERIMENTAL METHODS Sample synthesis. CsPbI3 NCs were synthesized by the anion exchange of CsPbBr3 NCs reported by Nedelcu et al.42 with some modifications. We first synthesized CsPbBr3 NCs dispersed in toluene according to the previously reported procedures.34 Next, a mixture of dried 1-octadecene (3 mL, Aldrich), oleic acid (1.0 mL, Tokyo Chemical Industry Co., 85%), oleylamine (1.0 mL, Acros Organics, 80%–90%), and PbI2 (0.56 mmol, Kanto Chemical Co., Inc., 98%) was added into a 50-mL flask, degassed in vacuum for 1 h at 120 °C, and then heated to 150 °C under N2 atmosphere until PbI2 was completely dissolved. Then the flask was cooled down to 50 °C and the toluene solution including the CsPbBr3 NCs was injected into the PbI2


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mixture. After a reaction time of 10 min, the CsPbI3 NCs solution was centrifuged at 8900 rpm for 30 min, and the precipitate was redispersed in dried octane (3 mL, Aldrich). Femtosecond transient absorption spectroscopy. For femtosecond transient absorption spectroscopy, we used a Yb:KGW-based femtosecond laser system (Pharos, Light Conversion). The output laser pulse of the regenerative amplifier with center wavelength 1028 nm, repetition rate 50 kHz, and pulse width of 300 fs was split into two paths, which were used for the generation of the pump and probe pulses. For the generation of the quasi-monochromatic pump pulse we used an optical parametric amplifier (Orpheus, Light Conversion), and the white-light probe pulse was generated with a 5-mm thick sapphire crystal. The arrival time between the white-light probe pulse and the quasi-monochromatic pump pulse was adjusted with a delay stage and we scanned the pump-probe delay time. The chirp of the probe pulse was calibrated by measuring the cross-correlation between the probe pulse and a reference pulse.


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ACKNOWLEDGMENT The authors acknowledge funding support from JST-CREST (Grant No. JPMJCR16N3). ASSOCIATED CONTENT Supporting Information NC-size dependent absorption spectra, analysis of the electronic structure of NCs, estimation of and the absorption cross-section, fittings to the absorption bleaching signals, pump excess energy dependence of the optical gain dynamics and excitation power dependence of the pump-induced dynamics. AUTHOR INFORMATION Notes The authors declare no competing financial interest.


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REFERENCES (1) Yang, W. S.; Park, B.-W.; Jung, E. H.; Jeon, N. J.; Kim, Y. C.; Lee, D. U.; Shin, S. S.; Seo, J.; Kim, E. K.; Noh, J. H., et al. Iodide Management in Formamidinium-Lead-Halide-Based Perovskite Layers for Efficient Solar Cells. Science 2017, 356, 1376-1379. (2) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J. P.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, 341-344. (3) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic CH3NH3PbI3. Science 2013, 342, 344-347. (4) De Wolf, S.; Holovsky, J.; Moon, S.-J.; Löper, P.; Niesen, B.; Ledinsky, M.; Haug, F.-J.; Yum, J.-H.; Ballif, C. Organometallic Halide Perovskites: Sharp Optical Absorption Edge and Its Relation to Photovoltaic Performance. J. Phys. Chem. Lett. 2014, 5, 1035-1039. (5) Yamada, Y.; Nakamura, T.; Endo, M.; Wakamiya, A.; Kanemitsu, Y. Near-Band-Edge Optical Responses of Solution-Processed Organic–Inorganic Hybrid Perovskite CH3NH3PbI3 on Mesoporous TiO2 Electrodes. Appl. Phys. Express 2014, 7, 032302. (6) Yamada, Y.; Nakamura, T.; Endo, M.; Wakamiya, A.; Kanemitsu, Y. Photocarrier Recombination Dynamics in Perovskite CH3NH3PbI3 for Solar Cell Applications. J. Am. Chem. Soc. 2014, 136, 11610-11613. (7) Yamada, Y.; Yamada, T.; Phuong, L. Q.; Maruyama, N.; Nishimura, H.; Wakamiya, A.; Murata, Y.; Kanemitsu, Y. Dynamic Optical Properties of CH3NH3PbI3 Single Crystals As


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Hot Biexciton Effect on Optical Gain in CsPbI3 Perovskite Nanocrystals

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