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Unraveling the degradation process of 2D passivated and Cs stabilized FAPbI3 by optical pump THz probe spectroscopy

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Abstract

The carrier dynamics and time-dependent photo-physical properties in the degradation period of hybrid organic-inorganic lead halide perovskites (HOIPs) are still unclear. Here a non-contact optical pump THz probe measurement was performed to observe the long-term degradation process of 2D passivated and cesium stabilized formamidinium lead iodide perovskite (FAPbI3) films. We find that photoconductivity and carrier mobility of the FA0.9Cs0.1PbI3 film decay steadily, while these of the 2D phenylethylammonium lead iodide (PEA2PbI4) passivated FAPbI3 film show an accelerated decay rate. Moreover, it’s also revealed that the localization of charge carriers increases with the transformation process from the fitted results by the Drude-Smith model. These results indicate that the stabilized effect of Cs incorporation is continuous, while the passivated effect of PEA2PbI4 can be weakened by the newly emerged phase boundaries. This report proposes a new perspective and sheds light on the degradation process of HOIPs.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Benefited from the outstanding optoelectronic properties and easy fabrication techniques, hybrid organic-inorganic lead halide perovskites (HOIPs) have been widely studied in photovoltaic and nanophotonic applications [14], with the power conversion efficiency (PCE) of perovskite solar cells reaching a phenomenal advancement [57]. The general formula of HOIPs is ABX3, where A is a monovalent cation, usually including methylammonium (MA+, CH3NH3+), formamidinium (FA+, CH(NH2)2+) or cesium (Cs+). The B-site cation usually is Pb2+ or Sn2+, and the final component is an anion (Cl, Br, I). Despite the achievement of impressive PCE, one primary problem which hinders the commercialization of HOIPs is their environmental instability. For example, it has been reported that pure FAPbI3 (FAPI) perovskite exhibited poor stability after exposure to humidity, and the black trigonal perovskite $\mathrm{\alpha }$ phase readily turned into undesirable yellow hexagonal non-perovskite $\mathrm{\delta }$ phase [812]. It’s demonstrated that the δ phase shows a poor absorbance in visible spectra range compared to $\mathrm{\alpha }$ phase [13]. This unpleasant transformation severely affects its photoelectric performance and hinders its further applications. In order to improve the stability of HOIPs, additive and compositional engineering have been actively explored [14]. Additive engineering usually introduces a controlled amount of organics into the precursor. The added component can contribute to the reduction of trap-state density [15] and improvement of morphology [16]. And sometimes the hydrophobic additives are prone to distribute along grain boundaries and surfaces, which can protect the perovskite from moisture [17]. By contrast, compositional engineering incorporates different ions into the structure and thus provides more freedom to improve the intrinsic properties of perovskite materials [6]. Hence great efforts utilizing the compositional engineering have been widely made in recent years [1820].

To reveal the effect of additive and compositional engineering on the performance of HOIPs, various methods have been employed [3,5,6,19,2125]. The maximum power point tracking method is frequently adopted to demonstrate the degradation process of solar cells based on HOIPs [14]. However, when a perovskite film is incorporated in a layered solar cell, it has been shown that the adjacent layers [21] and their interfaces [26] also have an effect on the perovskite stability. It’s unfriendly for us to observe the degradation process clearly. Therefore, it’s important to identify directly the properties changes of the photoactive layer in the transformation period. The anelastic and dielectric measurements were performed to study the transformation of cubic FAPbI3, showing that loose α-FAPbI3 powder could remain stable in normally humid air at room temperature (RT) for at last 100 days [27]. Some other optical techniques are also developed to investigate the performance of HOIPs. For example, the effect of doping on the phase stability and on the photo-physical properties of CsPbI2Br perovskites was explored using photoluminescence and absorbance spectra [28]. Moreover, the ultrafast transient absorption spectrum (TAS) and optical pump THz probe (OPTP) spectroscopy were performed to provide information on carrier dynamics of HOIPs [2933]. For instance, Liu et al. demonstrated that the internal charge transfer can efficiently separate electrons and holes to the upper and bottom surfaces of 2D perovskite film by TAS [30]. Milot et al. found that monomolecular carrier recombination rate firstly decreased, and then increased significantly with increasing PEA fraction by OPTP spectroscopy [34]. However, among these researches, more attention is focused on the optimization of optoelectronic performance by additive and compositional engineering. Little understanding has been established on the charge carrier dynamics and photo-physical changes in the natural degradation period.

In this report, we employed the time-resolved spectroscopy, that is, optical pump THz probe spectroscopy, to observe the long-term degradation process of 2D passivated and cesium stabilized FAPbI3 films. It’s found that although both the incorporation of PEA and Cs have a positive effect on the stability of $\alpha $-FAPI perovskite phase, photoconductivity of the FAPI and FAPEAPI films exhibits an accelerated decay rate, while that of FACsPI film decreases slowly at a relatively steady rate in the degradation process. To further enhance the understanding of the degradation process, Drude-Smith model was adopted to fit the complex photoconductivity of different samples, obtaining the evolution of carrier mobility. It’s found that the evolution of mobility shows a similar rule as the photoconductivity, and it’s also inferred that the localization of carrier increases with the degradation. These results indicate Cs incorporation can provide sustainable stabilized effect, while the passivated effect of PEA2PbI4 can be weakened by the newly emerged phase boundaries. This report helps understand the influence about additive and composition engineering on the freedom in the sample preparation or examination procedure. It’s thus expected that further advancement would be inspired through these findings.

2. Experimental methods

The samples were prepared as follows. A 0.5 mm-thick quartz substrate was cleaned with deionized water, ethanol and acetone, then treated with UV-ozone cleaning for 20 minutes. The FAPI perovskite solution was prepared by dissolving 172 mg formamidinium iodide (FAI) and 461 mg lead iodide (PbI2) in a 1 ml mixture of N,N-dimethylformamide (DMF) /dimethyl sulfoxide (DMSO) (9:1 volume ratio). The FACsPI perovskite solution was prepared by dissolving 155 mg FAI, 26 mg cesium iodide (CsI) and 461 mg PbI2 in a 1 ml mixture of DMF/ DMSO, while the FAPEAPI solution was prepared by dissolving 4.1 mg phenethylannonium iodide (PEAI), 169 mg FAI and 461 mg PbI2 in the DMF/DMSO mixture. Thin films were fabricated on the quartz substrate by one-step spin-coating method. All films were coated at 1000 rpm for 10 s at the beginning, then 3000 rpm for 30 s with 30 $\mu$l toluene as the anti-solvent dripped in the last 15 s. The FACsPI film was annealed at 110${^\circ{\textrm C}}$ for 15 minutes while the FAPI and FAPEAPI films were annealed at 150${^\circ{\textrm C}}$ for 30 minutes. all the steps were performed in a N2 filled glove box. The samples were kept in the dark under normal laboratory air conditions during the degradation period.

The crystal structure of all samples was obtained by X-ray diffraction (XRD, Rigaku) with Cu K$\mathrm{\alpha }$ radiation. To observe the surface morphology of the perovskite films on the quartz substrate, surface scanning electron microscope (SEM, JSM-6700F) was characterized. A homebuilt OPTP setup was utilized, in which the femtosecond pulses were provided by a Ti:sapphire regenerative amplifier (Spitfire Ace-35F, Spectra-physics) with a center wavelength of 800 nm and pulse duration of 35 fs. The generation and detection of THz radiation was performed by two pieces of 0.5 mm thick (110)-oriented zinc telluride crystals. The THz peak electric field $E(\tau )$ and the photo-induced change $\Delta E(\tau )$ of samples as a function of pump-probe time delay $\tau $ was measured by controlling the delay line, with measurement performed in a box filled with dry air (RH 3% - RH 5%).

3. Results and discussion

Figure 1(a)–1(c) shows the XRD results of our samples. It’s clear that no $\delta $ and PbI2 diffraction peaks can be found in the XRD patterns, which demonstrates the high quality of our samples. Besides, the central thickness of the FAPI, FAPEAPI, FACsPI films is about 476 nm, 453 nm and 440 nm, respectively. With similar thickness of thin film, it can be seen that the${\; }\alpha $ perovskite phase diffraction peaks in the FAPEAPI and FACsPI XRD patterns are higher than the one of FAPI, which suggests that the addition of PEAI and CsI into the precursor solution effectively improves the crystallinity of $\alpha $ perovskite phase. As shown in Fig. 1(d)–1(f), obvious cracks are observed in the FAPI, FAPEAPI surface and cracks in the FAPI film are larger. Meanwhile, no obvious cracks are found in the FACsPI film and it has a more uniform grain size. Cracks and boundaries are related to the crystallization kinetics of different material compositions [20]. On the other hand, cracks are also possibly attributed to the thermal coefficient mismatch between the perovskite films and the quartz substrate [35], which perhaps cause an obvious difference in corresponding photoelectric performance. So it may be effective to suppress the formation of cracks by choosing different substrates [36].

 figure: Fig. 1.

Fig. 1. XRD patterns of (a) FAPI, (b) FAPEAPI, (c) FACsPI films. SEM images of (d) FAPI, (e) FAPEAPI, (f) FACsPI films.

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It’s widely acknowledged that the FAPI perovskite phase tends to transform from $\alpha $ phase to photo-inactive $\delta $ phase at RT, resulting in a serious degradation of photovoltaic performance [37]. In this report, OPTP measurement was performed to observe the degradation process. The schematic structure of the samples is presented in Fig. 2(a). Simple double-layer structure makes sure that the degradation is mostly caused by the storage environment. All the three kinds of films were illuminated with 800 nm femtosecond pump pulse (540µJ cm−2) to ensure an obvious signal changes in the degradation period. Figure 2(b)–2(d) shows the transient THz transmission changes of the three films in a degradation period. It’s found that the FACsPI film shows the best phase stability, and the maximal change of THz transmission electric amplitude (-$\Delta E/E$) retains about 8% from 19% after 43 days (Fig. 2(d)). Meanwhile, the FAPI film decreases to 9% from 15.5% (Fig. 2(b)) only after 5 days. The addition of PEAI also enhances the phase stability, the FAPEAPI film retains 9.5% from 17% after 10 days (Fig. 2(c)). The enhancement of maximal -$\Delta $E/E of the FAPEAPI and FACsPI films is caused by the improved crystallinity, which can be demonstrated in the XRD patterns.

 figure: Fig. 2.

Fig. 2. The time-dependent THz characterization of the perovskite films. (a) Graphical representation of the sample structure with the pump-probe laser beams. The transient THz transmission change of (b) FAPI, (c) FAPEAPI, (d) FACsPI films.

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The free carrier excitation and relaxation dynamics of FAPI, FAPEAPI and FACsPI perovskite films are included in the transient transmission amplitude evolution when the femtosecond pump pulse strikes the perovskite films. Therefore, to analyze the ultrafast free carrier dynamics of the three samples, a bi-exponential function given as

$$- \frac{{\Delta E}}{E} = {A_F}exp\left( { - \frac{t}{{{\tau_F}}}} \right) + {A_S}exp\left( { - \frac{t}{{{\tau_S}}}} \right)$$
was adopted to describe the observed temporal response of the THz electric field, where ${\tau _F}$ and ${\tau _S}$ represent the time constant for the fast and slow process, respectively. The fitted bi-exponential curves are shown with the traces in Fig. 2(b)–2(d). The changes of ${\tau _F}$ and ${\tau _S}$ in a degradation period is depicted in Fig. 3. It’s seen that the fast time constant ${\tau _F}$ is several ps and decreases gradually with the degradation reaction for all the three samples. The slow time constant ${\tau _S}$ is around 180 ps and fluctuates slightly during the whole degradation period. Comparable values have been reported on similar materials [38,39]. Since the fluence (540µJ cm−2) is much higher than the amplified spontaneous emission (ASE) threshold of most perovskites [40], The ${\tau _F}$ may be related with the ASE process and the observed decreasing trend can be explained by the degradation of the gain properties of the perovskite films [38]. As for the reason why ${\tau _S}$ does not change obviously with the degradation process, it may be caused by the phonon bottleneck effect, which induces the carrier cooling [41]. Besides, although we tried to concentrate the THz spot on the center area of the 10 mm × 10 mm samples by our eyes, it’s difficult to ensure the completely same spot because the diameter of the spot where THz wave passing through is 2 mm. Additionally, an uneven color change happened during the degradation process which can be found in Fig. 4(a). so we attribute the fluctuations in the curves of ${\tau _F}$ and ${\tau _S}$ to the difference in the measured area at different measured time.

 figure: Fig. 3.

Fig. 3. The time-dependent ${\tau _F}$, ${\tau _S}$ of the perovskite films. FAPI (a) and (d), FAPEAPI (b) and (e), FACsPI (c) and (f). The error bars are the standard error of the fitting analysis.

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 figure: Fig. 4.

Fig. 4. Improved stability of the FAPEAPI, FACsPI films. (a) Photographs of the Perovskite films in a degradation period. Schematics of the (b) FAPEAPI and (c) FACsPI films. Evolution of photoconductivity of (d) FAPI, (e) FAPEAPI, (f) FACsPI film.

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It’s clearly observed that the FACsPI film kept black after 43 days while the FAPI and FAPEAPI films turned bleached during 6 and 12 days, respectively (Fig. 4(a)). The photo-induced THz conductivity is used to display the decay process. The peak photoconductivity is estimated by [42,43]

$$\Delta \sigma (t )\approx{-} {\varepsilon _o}\frac{c}{d}({1 + {n_{sub}}} )\frac{{\Delta E(t )}}{{E(t )}}$$
where the $c,\,d,\,{\varepsilon _o},\,{\; }{n_{sub}}{\; }$are the speed of light in vacuum, sample thickness, the free space permittivity and the refractive index of the quartz substrate, respectively. Figure 4(d)–4(f) shows the photoconductivity variation of the three samples. We can see that the FAPI and FAPEAPI films show a critical time point of 2nd and 7th day, beyond which the photoconductivity decreases rapidly. While the FACsPI film shows a comparatively steady decay rate. It has been observed that the degradation in FAPI film initiates with the water condensation at grain boundaries [11,44], and the decay reaction seems autocatalytic through the degradation products [12,27]. Water condensation was reported to occur preferentially at cracks and grain boundaries [6,34]. Moreover, grain boundaries often have a higher density of defects, which help both the adsorption and reaction of water molecules [27]. In the beginning of degradation process, only few $\alpha \to \delta $ transformations happened and this would not result in a rapid decrease of photoconductivity. However, with the continuous phase transformation, more $\delta $ phase appears with more phase boundaries. These newly born boundaries can act as new centers for water condensation. Meanwhile, the $\delta $ phase shows a higher hygroscopicity [12], which speeds up the water absorption. This presumably is why the reaction sequence shows an accelerated transformation rate. As for the FAPEAPI film shown in Fig. 4(e), the critical time point beyond which the photoconductivity decreases rapidly is elongated. It has been pointed out that at small to moderate concentrations, complete 2D layered perovskite can’t be formatted and the 2D perovskite just spontaneously forms at grain boundaries and surfaces to passivate the ingression pathway of moisture and suppress ion migration [25,45]. A schematic in Fig. 4(b) shows the formatted 2D perovskite at the grain boundaries of the 3D FAPI. As the PEA fraction in the precursor solution of FAPEAPI film is just 1.67 mol%, we attribute the delay of the critical time point and enhanced stability to the passivated effect of 2D PEA2PbI4 perovskite at the grain boundaries. However, with the reaction of phase transition, more boundaries emerge, but the amount of the 2D perovskite is not changed. So the effect of protection is weakened with the emerging phase boundaries and the degradation rate jumps. As for the FACsPI film, the crystal structure schematic is shown in Fig. 4(c). It seems that more grain boundaries are formatted because of the smaller grain size (Fig. 2(f)), increasing possibility of water absorption. However, the incorporation of Cs also optimizes the Goldschmidt tolerance factor [20], which favors the formation of $\alpha $ perovskite phase thermodynamically [22] and suppresses the cracks effectively. What’s more, it’s energetically unfavorable for the unpleasant transformation reaction for the FACsPI film [22]. In other words, the introduction of Cs can reduce the sensitivity to moisture effectively, that is why the FACsPI film shows a steady decay rate even with more grain boundaries, as well as the best performance on stability in normal ambient conditions.

By recording the transmitted THz signals through the sample Esam, and through the quartz substrate Esub, we can abstract the complex transmission function and then the complex refractive index. Finally, the complex photoconductivity $\Delta \sigma (w )= \Delta {\sigma _1}(w )+ i\Delta {\sigma _2}(w )$ is obtained through the complex refractive index [43,46]. As the real photoconductivity ($\Delta {\sigma _1}(w )$) increases with the frequency and the imaginary part ($\Delta {\sigma _2}(w )$) is negative, Drude-Smith (DS) model is adopted to extract the carrier density and mobility. In the DS model, the complex photoconductivity is given by [46,47]

$$\Delta \tilde{\sigma } = \frac{{N{e^2}}}{{{m^{\ast }}\gamma }}{\; }\frac{1}{{1 - iw/\gamma }}\left[ {1 + \frac{{{c_1}}}{{1 - iw/\gamma }}} \right]$$

Where N is the carrier density, $\gamma $ is the scattering rate between free carrier and ions, ${m^{\ast }} = 0.2m$ is the effective carrier mass [23,42,48], w is the angular frequency, and e is the elementary charge. The parameter ${c_1}$, which is defined as the fraction of initial velocity of carrier after a collision, is presumably decided by the grain boundaries or defects of the perovskite films [49]. The fitted data are displayed in Fig. 5(a) and 5(b). It’s calculated that initial ${c_1}$ for the FAPI, FAPEAPI and FACsPI films is -0.98, -0.89, -0.91, respectively. The smaller${\; }|{{c_1}} |$ values of FAPEAPI and FACsPI imply that the addition of PEAI and CsI can both improve the crystallinity, as shown in the XRD patterns. It’s also found that the absolute value of ${c_1}$ increases with the phase transformation reaction, meaning the localization of carrier is increasing [42]. The ${c_1}$ of FAPI film reaches -1 in two days, suggesting most of the carriers were localized [50]. So we don’t display its time-dependent effective carrier mobility in the graph. The fitted carrier concentrations for the FAPI, FAPEAPI and FACsPI films are 1.42${\times} $1021 cm−3, 1.56${\times} $1021 cm−3 and 1.55${\times} $1021 cm−3, respectively, which are attributed to the higher optical pump intensity (540µJ cm−2) [31]. The carrier mobility can be extracted by the formula $\mu = \frac{e}{{\gamma {m^{\ast }}}}$. Considering the influence of disorder, Fig. 5(c) and 5(d) shows the time dependence of $({1 + {c_1}} )\mu $. It’s clear that the time-dependent carrier mobility also shows a critical time point in the FAPEAPI film while that of the FACsPI film shows a steady decreasing rate. Meanwhile, the initial mobility of FAPEAPI is almost twice as that of FACsPI film, it’s possibly caused by the smaller grain size of FACsPI film (Fig. 1(f)). In the end, we estimated the diffusion length ${L_D}$via ${L_D} = \sqrt {D/{R_{total}}} $, where the total recombination rate is ${R_{total}} ={-} \frac{1}{{N(\tau )}}\frac{{dN(\tau )}}{{d\tau }}$, and $N(\tau )$ is the carrier concentration at different delay time. The diffusion constant D is calculated by the carrier mobility and the temperature T via $D = \frac{{\mu {k_b}T}}{e}$, where${\; }{k_b}$ is the Boltzmann’s constant. It’s reported that the quantum efficiency of HOIPs is between 0.03 and 0.065 [48,51,52], and we chose 0.05 as a possible value. As a result, the diffusion length of the FAPI, FAPEAPI and FACsPI films is 0.49 µm, 0.57 µm, 1.20 µm, respectively. This relative result is possibly caused by cracks which are shown in the SEM images (Fig. 1(d)–1(f)), and demonstrates that the addition of PEAI and CsI can both improve the optoelectronic properties.

 figure: Fig. 5.

Fig. 5. The complex photoconductivity and time-dependent carrier mobility of different samples. (a) Real and (b) imaginary conductivity of the perovskite films. Experimentally extracted data and the fitted data are displayed by points and solid lines, respectively. The effective carrier mobility evolution of the (c) FAPEAPI and (d) FACsPI films.

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4. Conclusions

In conclusion, the charge-carrier dynamics of the 2D passivated and Cs stabilized FAPI perovskite films has been determined by the optical pump THz probe technique. We observed the critical time point beyond which the optoelectronic performance decreased rapidly in the FAPI and FAPEAPI films while the FACsPI film showed a steady decay rate. It’s inevitable to format grain boundaries in the crystallization process, and water condensation tends to happen at the boundaries and accelerates the degradation reaction. So the photoconductivity of the FAPI film showed an accelerated decay rate. When the 2D PEA2PbI4 forms at the grain boundaries of FAPI, it can effective suppress the water condensation and enhance the stability performance. However, the effect of protection will be weakened with the emerging phase boundaries. As for the FACsPI film, the incorporation of Cs effectively reduced its sensitivity to water and no obvious cracks formatted in the annealing process, so the FACsPI film showed the best stability and no critical point found in the degradation process. Moreover, Drude-Smith model was applied to fit the complex conductivity. Similar rules are also found in the evolution of carrier mobility. It’s also revealed that the localization of carrier increased with the degradation process, and the time of complete localization is consistent with the observed stability performances. This report offers a new perspective on the degradation process of the HOIPs, and it can promote our understanding on the degradation process. Furthermore, subsequent works can be investigated to obtain more information and improve the environmental instability of HOIPs, by varying amounts of PEA or Cs in the HOIPs, employing heterogeneous (multi-layered) preparation with PEA, and utilizing different substrates to avoid cracks, and so on.

Funding

National Natural Science Foundation of China (11704373, 51627901); National Key Research and Development Program of China (2020YFA0710100); Anhui Initiative in Quantum Initiative in Quantum Information Technologies (AHY100000); Fundamental Research Funds for the Central Universities (WK2340000071).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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24. W. Rehman, D. P. McMeekin, J. B. Patel, R. L. Milot, M. B. Johnston, H. J. Snaith, and L. M. Herz, “Photovoltaic mixed-cation lead mixed-halide perovskites: links between crystallinity, photo-stability and electronic properties,” Energy Environ. Sci. 10(1), 361–369 (2017). [CrossRef]  

25. N. Li, Z. Zhu, C.-C. Chueh, H. Liu, B. Peng, A. Petrone, X. Li, L. Wang, and A. K. Y. Jen, “Mixed cation FAxPEA1-xPbI3with enhanced phase and ambient stability toward high-performance perovskite solar cells,” Adv. Energy Mater. 7(1), 1601307 (2017). [CrossRef]  

26. P. Schulz, “Interface design for metal halide perovskite solar cells,” ACS Energy Lett. 3(6), 1287–1293 (2018). [CrossRef]  

27. F. Cordero, F. Craciun, F. Trequattrini, A. Generosi, B. Paci, A. M. Paoletti, and G. Pennesi, “Stability of cubic FAPbI3 from x-ray diffraction, anelastic, and dielectric measurements,” J. Phys. Chem. Lett. 10(10), 2463–2469 (2019). [CrossRef]  

28. L. Atourki, M. Bernabé, M. Makha, K. Bouabid, M. Regragui, A. Ihlal, M. Abd-lefdil, and M. Mollar, “Effect of doping on the phase stability and photophysical properties of CsPbI2Br perovskite thin films,” RSC Adv. 11(3), 1440–1449 (2021). [CrossRef]  

29. C. Wehrenfennig, G. E. Eperon, M. B. Johnston, H. J. Snaith, and L. M. Herz, “High charge carrier mobilities and lifetimes in organolead trihalide perovskites,” Adv. Mater. 26(10), 1584–1589 (2014). [CrossRef]  

30. J. Liu, J. Leng, K. Wu, J. Zhang, and S. Jin, “Observation of internal photoinduced electron and hole separation in hybrid two-dimentional perovskite films,” J. Am. Chem. Soc. 139(4), 1432–1435 (2017). [CrossRef]  

31. A. Chanana, X. Liu, C. Zhang, Z. V. Vardeny, and A. Nahata, “Ultrafast frequency-agile terahertz devices using methylammonium lead halide perovskites,” Sci. Adv. 4(5), eaar7353 (2018). [CrossRef]  

32. W. Rehman, R. L. Milot, G. E. Eperon, C. Wehrenfennig, J. L. Boland, H. J. Snaith, M. B. Johnston, and L. M. Herz, “Charge-Carrier Dynamics and Mobilities in formamidinium lead mixed-halide perovskites,” Adv. Mater. 27(48), 7938–7944 (2015). [CrossRef]  

33. C. C. S. Chan, K. Fan, H. Wang, Z. Huang, D. Novko, K. Yan, J. Xu, W. C. H. Choy, I. Lončarić, and K. S. Wong, “Uncovering the electron-phonon interplay and dynamical energy-dissipation mechanisms of hot carriers in hybrid lead halide perovskites,” Adv. Energy Mater. 11(9), 2003071 (2021). [CrossRef]  

34. R. L. Milot, R. J. Sutton, G. E. Eperon, A. A. Haghighirad, J. Martinez Hardigree, L. Miranda, H. J. Snaith, M. B. Johnston, and L. M. Herz, “Charge-carrier dynamics in 2D hybrid metal-halide perovskites,” Nano Lett. 16(11), 7001–7007 (2016). [CrossRef]  

35. A. Thote, I. Jeon, J.-W. Lee, S. Seo, H.-S. Lin, Y. Yang, H. Daiguji, S. Maruyama, and Y. Matsuo, “Stable and reproducible 2D/3D formamidinium–lead–iodide perovskite solar cells,” ACS Appl. Energy Mater. 2(4), 2486–2493 (2019). [CrossRef]  

36. J. A. Schwenzer, T. Hellmann, B. A. Nejand, H. Hu, T. Abzieher, F. Schackmar, I. M. Hossain, P. Fassl, T. Mayer, W. Jaegermann, U. Lemmer, and U. W. Paetzold, “Thermal stability and cation composition of hybrid organic-inorganic perovskites,” ACS Appl. Mater. Interfaces 13(13), 15292–15304 (2021). [CrossRef]  

37. G. E. Eperon, S. D. Stranks, C. Menelaou, M. B. Johnston, L. M. Herz, and H. J. Snaith, “Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells,” Energy Environ. Sci. 7(3), 982 (2014). [CrossRef]  

38. H. Okochi, H. Katsuki, M. Tsubouchi, R. Itakura, and H. Yanagi, “Photon energy-dependent ultrafast photoinduced terahertz response in a microcrystalline film of CH3NH3PbBr3,” J. Phys. Chem. Lett. 11(15), 6068–6076 (2020). [CrossRef]  

39. H. Zhu, Y. Fu, F. Meng, X. Wu, Z. Gong, Q. Ding, M. V. Gustafsson, M. T. Trinh, S. Jin, and X. Y. Zhu, “Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors,” Nat. Mater. 14(6), 636–642 (2015). [CrossRef]  

40. P. Brenner, O. Bar-On, M. Jakoby, I. Allegro, B. S. Richards, U. W. Paetzold, I. A. Howard, J. Scheuer, and U. Lemmer, “Continuous wave amplified spontaneous emission in phase-stable lead halide perovskites,” Nat. Commun. 10(1), 988 (2019). [CrossRef]  

41. V. V. Klimov, P. Haring Bolivar, and H. Kurz, “Hot-phonon effects in femtosecond luminescence spectra of electron-hole plasmas in CdS,” Phys. Rev. B 52(7), 4728–4731 (1995). [CrossRef]  

42. G. R. Yettapu, D. Talukdar, S. Sarkar, A. Swarnkar, A. Nag, P. Ghosh, and P. Mandal, “Terahertz conductivity within colloidal CsPbBr3 perovskite nanocrystals: remarkably high carrier mobilities and large diffusion lengths,” Nano Lett. 16(8), 4838–4848 (2016). [CrossRef]  

43. H.-K. Nienhuys and V. Sundström, “Intrinsic complications in the analysis of optical-pump, terahertz probe experiments,” Phys. Rev. B 71(23), 235110 (2005). [CrossRef]  

44. J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016). [CrossRef]  

45. I. C. Smith, E. T. Hoke, D. Solis-Ibarra, M. D. McGehee, and H. I. Karunadasa, “A layered hybrid perovskite solar-cell absorber with enhanced moisture stability,” Angew. Chem., Int. Ed. 53(42), 11232–11235 (2014). [CrossRef]  

46. D. Zhao and E. E. M. Chia, “Free carrier, exciton, and phonon dynamics in lead-halide perovskites studied with ultrafast terahertz spectroscopy,” Adv. Opt. Mater. 8(3), 1900783 (2020). [CrossRef]  

47. T. L. Cocker, D. Baillie, M. Buruma, L. V. Titova, R. D. Sydora, F. Marsiglio, and F. A. Hegmann, “Microscopic origin of the Drude-Smith model,” Phys. Rev. B 96(20), 205439 (2017). [CrossRef]  

48. O. V. C. La, T. Salim, J. Kadro, M. T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M. E. Michel-Beyerle, and E. E. Chia, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 6(1), 7903 (2015). [CrossRef]  

49. N. Smith, “Classical generalization of the Drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001). [CrossRef]  

50. R. Lovrinčić and A. Pucci, “Infrared optical properties of chromium nanoscale films with a phase transition,” Phys. Rev. B 80(20), 205404 (2009). [CrossRef]  

51. A. Solanki, P. Yadav, S.-H. Turren-Cruz, S. S. Lim, M. Saliba, and T. C. Sum, “Cation influence on carrier dynamics in perovskite solar cells,” Nano Energy 58, 604–611 (2019). [CrossRef]  

52. H. Zhang, M. Kramarenko, G. Martinez-Denegri, J. Osmond, J. Toudert, and J. Martorell, “Formamidinium incorporation into compact lead iodide for low band gap perovskite solar cells with open-circuit voltage approaching the radiative limit,” ACS Appl. Mater. Interfaces 11(9), 9083–9092 (2019). [CrossRef]  

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  37. G. E. Eperon, S. D. Stranks, C. Menelaou, M. B. Johnston, L. M. Herz, and H. J. Snaith, “Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells,” Energy Environ. Sci. 7(3), 982 (2014).
    [Crossref]
  38. H. Okochi, H. Katsuki, M. Tsubouchi, R. Itakura, and H. Yanagi, “Photon energy-dependent ultrafast photoinduced terahertz response in a microcrystalline film of CH3NH3PbBr3,” J. Phys. Chem. Lett. 11(15), 6068–6076 (2020).
    [Crossref]
  39. H. Zhu, Y. Fu, F. Meng, X. Wu, Z. Gong, Q. Ding, M. V. Gustafsson, M. T. Trinh, S. Jin, and X. Y. Zhu, “Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors,” Nat. Mater. 14(6), 636–642 (2015).
    [Crossref]
  40. P. Brenner, O. Bar-On, M. Jakoby, I. Allegro, B. S. Richards, U. W. Paetzold, I. A. Howard, J. Scheuer, and U. Lemmer, “Continuous wave amplified spontaneous emission in phase-stable lead halide perovskites,” Nat. Commun. 10(1), 988 (2019).
    [Crossref]
  41. V. V. Klimov, P. Haring Bolivar, and H. Kurz, “Hot-phonon effects in femtosecond luminescence spectra of electron-hole plasmas in CdS,” Phys. Rev. B 52(7), 4728–4731 (1995).
    [Crossref]
  42. G. R. Yettapu, D. Talukdar, S. Sarkar, A. Swarnkar, A. Nag, P. Ghosh, and P. Mandal, “Terahertz conductivity within colloidal CsPbBr3 perovskite nanocrystals: remarkably high carrier mobilities and large diffusion lengths,” Nano Lett. 16(8), 4838–4848 (2016).
    [Crossref]
  43. H.-K. Nienhuys and V. Sundström, “Intrinsic complications in the analysis of optical-pump, terahertz probe experiments,” Phys. Rev. B 71(23), 235110 (2005).
    [Crossref]
  44. J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016).
    [Crossref]
  45. I. C. Smith, E. T. Hoke, D. Solis-Ibarra, M. D. McGehee, and H. I. Karunadasa, “A layered hybrid perovskite solar-cell absorber with enhanced moisture stability,” Angew. Chem., Int. Ed. 53(42), 11232–11235 (2014).
    [Crossref]
  46. D. Zhao and E. E. M. Chia, “Free carrier, exciton, and phonon dynamics in lead-halide perovskites studied with ultrafast terahertz spectroscopy,” Adv. Opt. Mater. 8(3), 1900783 (2020).
    [Crossref]
  47. T. L. Cocker, D. Baillie, M. Buruma, L. V. Titova, R. D. Sydora, F. Marsiglio, and F. A. Hegmann, “Microscopic origin of the Drude-Smith model,” Phys. Rev. B 96(20), 205439 (2017).
    [Crossref]
  48. O. V. C. La, T. Salim, J. Kadro, M. T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M. E. Michel-Beyerle, and E. E. Chia, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 6(1), 7903 (2015).
    [Crossref]
  49. N. Smith, “Classical generalization of the Drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001).
    [Crossref]
  50. R. Lovrinčić and A. Pucci, “Infrared optical properties of chromium nanoscale films with a phase transition,” Phys. Rev. B 80(20), 205404 (2009).
    [Crossref]
  51. A. Solanki, P. Yadav, S.-H. Turren-Cruz, S. S. Lim, M. Saliba, and T. C. Sum, “Cation influence on carrier dynamics in perovskite solar cells,” Nano Energy 58, 604–611 (2019).
    [Crossref]
  52. H. Zhang, M. Kramarenko, G. Martinez-Denegri, J. Osmond, J. Toudert, and J. Martorell, “Formamidinium incorporation into compact lead iodide for low band gap perovskite solar cells with open-circuit voltage approaching the radiative limit,” ACS Appl. Mater. Interfaces 11(9), 9083–9092 (2019).
    [Crossref]

2021 (4)

H. Kim, J. W. Lee, G. R. Han, S. K. Kim, and J. H. Oh, “Synergistic effects of cation and anion in an ionic imidazolium tetrafluoroborate additive for improving the efficiency and stability of half-mixed Pb-Sn perovskite solar cells,” Adv. Funct. Mater. 30, 2008801 (2021).
[Crossref]

L. Atourki, M. Bernabé, M. Makha, K. Bouabid, M. Regragui, A. Ihlal, M. Abd-lefdil, and M. Mollar, “Effect of doping on the phase stability and photophysical properties of CsPbI2Br perovskite thin films,” RSC Adv. 11(3), 1440–1449 (2021).
[Crossref]

C. C. S. Chan, K. Fan, H. Wang, Z. Huang, D. Novko, K. Yan, J. Xu, W. C. H. Choy, I. Lončarić, and K. S. Wong, “Uncovering the electron-phonon interplay and dynamical energy-dissipation mechanisms of hot carriers in hybrid lead halide perovskites,” Adv. Energy Mater. 11(9), 2003071 (2021).
[Crossref]

J. A. Schwenzer, T. Hellmann, B. A. Nejand, H. Hu, T. Abzieher, F. Schackmar, I. M. Hossain, P. Fassl, T. Mayer, W. Jaegermann, U. Lemmer, and U. W. Paetzold, “Thermal stability and cation composition of hybrid organic-inorganic perovskites,” ACS Appl. Mater. Interfaces 13(13), 15292–15304 (2021).
[Crossref]

2020 (3)

H. Okochi, H. Katsuki, M. Tsubouchi, R. Itakura, and H. Yanagi, “Photon energy-dependent ultrafast photoinduced terahertz response in a microcrystalline film of CH3NH3PbBr3,” J. Phys. Chem. Lett. 11(15), 6068–6076 (2020).
[Crossref]

D. Zhao and E. E. M. Chia, “Free carrier, exciton, and phonon dynamics in lead-halide perovskites studied with ultrafast terahertz spectroscopy,” Adv. Opt. Mater. 8(3), 1900783 (2020).
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A. Kumar, A. Solanki, M. Manjappa, S. Ramesh, Y. K. Srivastava, P. Agarwal, T. C. Sum, and R. Singh, “Excitons in 2D perovskites for ultrafast terahertz photonic devices,” Sci. Adv. 6(8), eaax8821 (2020).
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2019 (8)

X. Ren, Z. S. Wang, and W. C. H. Choy, “Device physics of the carrier transporting layer in planar perovskite solar cells,” Adv. Opt. Mater. 7(20), 1900407 (2019).
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Y. M. Lee, J.-H. Yun, A. Matsuyama, S. Kobori, I. Maeng, M. Lyu, S. Wang, L. Wang, M.-C. Jung, and M. Nakamura, “Significant THz-wave absorption property in mixed δ- and α-FAPbI3 hybrid perovskite flexible thin film formed by sequential vacuum evaporation,” Appl. Phys. Express 12(5), 051003 (2019).
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Z. Zhao, F. Gu, H. Rao, S. Ye, Z. Liu, Z. Bian, and C. Huang, “Metal halide perovskite materials for solar cells with long-term stability,” Adv. Enengy. Mater. 9(3), 1802671 (2019).
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F. Cordero, F. Craciun, F. Trequattrini, A. Generosi, B. Paci, A. M. Paoletti, and G. Pennesi, “Stability of cubic FAPbI3 from x-ray diffraction, anelastic, and dielectric measurements,” J. Phys. Chem. Lett. 10(10), 2463–2469 (2019).
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A. Thote, I. Jeon, J.-W. Lee, S. Seo, H.-S. Lin, Y. Yang, H. Daiguji, S. Maruyama, and Y. Matsuo, “Stable and reproducible 2D/3D formamidinium–lead–iodide perovskite solar cells,” ACS Appl. Energy Mater. 2(4), 2486–2493 (2019).
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P. Brenner, O. Bar-On, M. Jakoby, I. Allegro, B. S. Richards, U. W. Paetzold, I. A. Howard, J. Scheuer, and U. Lemmer, “Continuous wave amplified spontaneous emission in phase-stable lead halide perovskites,” Nat. Commun. 10(1), 988 (2019).
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A. Solanki, P. Yadav, S.-H. Turren-Cruz, S. S. Lim, M. Saliba, and T. C. Sum, “Cation influence on carrier dynamics in perovskite solar cells,” Nano Energy 58, 604–611 (2019).
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H. Zhang, M. Kramarenko, G. Martinez-Denegri, J. Osmond, J. Toudert, and J. Martorell, “Formamidinium incorporation into compact lead iodide for low band gap perovskite solar cells with open-circuit voltage approaching the radiative limit,” ACS Appl. Mater. Interfaces 11(9), 9083–9092 (2019).
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2018 (8)

A. Chanana, X. Liu, C. Zhang, Z. V. Vardeny, and A. Nahata, “Ultrafast frequency-agile terahertz devices using methylammonium lead halide perovskites,” Sci. Adv. 4(5), eaar7353 (2018).
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J. S. Yun, J. Kim, T. Young, R. J. Patterson, D. Kim, J. Seidel, S. Lim, M. A. Green, S. Huang, and A. Ho-Baillie, “Humidity-induced degradation via grain boundaries of HC(NH2)2PbI3 planar perovskite solar cells,” Adv. Funct. Mater. 28(11), 1705363 (2018).
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J. Chen and N.-G. Park, “Inorganic hole transporting materials for stable and high efficiency perovskite solar cells,” J. Phys. Chem. C 122(25), 14039–14063 (2018).
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P. Schulz, “Interface design for metal halide perovskite solar cells,” ACS Energy Lett. 3(6), 1287–1293 (2018).
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T. Niu, J. Lu, R. Munir, J. Li, D. Barrit, X. Zhang, H. Hu, Z. Yang, A. Amassian, K. Zhao, and S. F. Liu, “stable high-performance perovskite solar cells via grain boundary passivation,” Adv. Mater. 30(16), 1706576 (2018).
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D. Luo, W. Yang, Z. Wang, A. Sadhanala, Q. Hu, R. Su, R. Shivanna, G. F. Trindade, J. F. Watts, Z. Xu, T. Liu, K. Chen, F. Ye, P. Wu, L. Zhao, J. Wu, Y. Tu, Y. Zhang, X. Yang, W. Zhang, R. H. Friend, Q. Gong, H. J. Snaith, and R. Zhu, “Enhanced photovoltage for inverted planar heterojunction perovskite solar cells,” Science 360(6396), 1442–1446 (2018).
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J. Duan, Y. Zhao, B. He, and Q. Tang, “High-purity inorganic perovskite films for solar cells with 9.72% efficiency,” Angew. Chem., Int. Ed. 57(14), 3787–3791 (2018).
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J. W. Lee, Z. Dai, T. H. Han, C. Choi, S. Y. Chang, S. J. Lee, N. De Marco, H. Zhao, P. Sun, Y. Huang, and Y. Yang, “2D perovskite stabilized phase-pure formamidinium perovskite solar cells,” Nat. Commun. 9(1), 3021 (2018).
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2017 (6)

X. Ren, Z. Wang, W. E. I. Sha, and W. C. H. Choy, “Exploring the way to approach the efficiency limit of perovskite solar cells by drift-diffusion model,” ACS Photonics 4(4), 934–942 (2017).
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W. Rehman, D. P. McMeekin, J. B. Patel, R. L. Milot, M. B. Johnston, H. J. Snaith, and L. M. Herz, “Photovoltaic mixed-cation lead mixed-halide perovskites: links between crystallinity, photo-stability and electronic properties,” Energy Environ. Sci. 10(1), 361–369 (2017).
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N. Li, Z. Zhu, C.-C. Chueh, H. Liu, B. Peng, A. Petrone, X. Li, L. Wang, and A. K. Y. Jen, “Mixed cation FAxPEA1-xPbI3with enhanced phase and ambient stability toward high-performance perovskite solar cells,” Adv. Energy Mater. 7(1), 1601307 (2017).
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S. Pont, D. Bryant, C.-T. Lin, N. Aristidou, S. Wheeler, X. Ma, R. Godin, S. A. Haque, and J. R. Durrant, “Tuning CH3NH3Pb(I1−xBrx)3 perovskite oxygen stability in thin films and solar cells,” J. Mater. Chem. A 5(20), 9553–9560 (2017).
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J. Liu, J. Leng, K. Wu, J. Zhang, and S. Jin, “Observation of internal photoinduced electron and hole separation in hybrid two-dimentional perovskite films,” J. Am. Chem. Soc. 139(4), 1432–1435 (2017).
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T. L. Cocker, D. Baillie, M. Buruma, L. V. Titova, R. D. Sydora, F. Marsiglio, and F. A. Hegmann, “Microscopic origin of the Drude-Smith model,” Phys. Rev. B 96(20), 205439 (2017).
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2016 (8)

J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016).
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G. R. Yettapu, D. Talukdar, S. Sarkar, A. Swarnkar, A. Nag, P. Ghosh, and P. Mandal, “Terahertz conductivity within colloidal CsPbBr3 perovskite nanocrystals: remarkably high carrier mobilities and large diffusion lengths,” Nano Lett. 16(8), 4838–4848 (2016).
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R. L. Milot, R. J. Sutton, G. E. Eperon, A. A. Haghighirad, J. Martinez Hardigree, L. Miranda, H. J. Snaith, M. B. Johnston, and L. M. Herz, “Charge-carrier dynamics in 2D hybrid metal-halide perovskites,” Nano Lett. 16(11), 7001–7007 (2016).
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C. Yi, J. Luo, S. Meloni, A. Boziki, N. Ashari-Astani, C. Grätzel, S. M. Zakeeruddin, U. Röthlisberger, and M. Grätzel, “Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells,” Energy Environ. Sci. 9(2), 656–662 (2016).
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K. Galkowski, A. Mitioglu, A. Miyata, P. Plochocka, O. Portugall, G. E. Eperon, J. T.-W. Wang, T. Stergiopoulos, S. D. Stranks, H. J. Snaith, and R. J. Nicholas, “Determination of the exciton binding energy and effective masses for methylammonium and formamidinium lead tri-halide perovskite semiconductors,” Energy Environ. Sci. 9(3), 962–970 (2016).
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D. P. McMeekin, G. Sadoughi, W. Rehman, G. E. Eperon, M. Saliba, M. T. Horantner, A. Haghighirad, N. Sakai, L. Korte, B. Rech, M. B. Johnston, L. M. Herz, and H. J. Snaith, “A mixed-cation lead mixed-halide perovskite absorber for tandem solar cells,” Science 351(6269), 151–155 (2016).
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T. M. Koh, V. Shanmugam, J. Schlipf, L. Oesinghaus, P. Muller-Buschbaum, N. Ramakrishnan, V. Swamy, N. Mathews, P. P. Boix, and S. G. Mhaisalkar, “Nanostructuring Mixed-Dimensional Perovskites: A Route Toward Tunable, Efficient Photovoltaics,” Adv. Mater. 28(19), 3653–3661 (2016).
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Z. Li, M. Yang, J.-S. Park, S.-H. Wei, J. J. Berry, and K. Zhu, “Stabilizing perovskite structures by tuning tolerance factor: formation of formamidinium and cesium lead iodide solid-state alloys,” Chem. Mater. 28(1), 284–292 (2016).
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2015 (4)

N. J. Jeon, J. H. Noh, W. S. Yang, Y. C. Kim, S. Ryu, J. Seo, and S. I. Seok, “Compositional engineering of perovskite materials for high-performance solar cells,” Nature 517(7535), 476–480 (2015).
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W. Rehman, R. L. Milot, G. E. Eperon, C. Wehrenfennig, J. L. Boland, H. J. Snaith, M. B. Johnston, and L. M. Herz, “Charge-Carrier Dynamics and Mobilities in formamidinium lead mixed-halide perovskites,” Adv. Mater. 27(48), 7938–7944 (2015).
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H. Zhu, Y. Fu, F. Meng, X. Wu, Z. Gong, Q. Ding, M. V. Gustafsson, M. T. Trinh, S. Jin, and X. Y. Zhu, “Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors,” Nat. Mater. 14(6), 636–642 (2015).
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O. V. C. La, T. Salim, J. Kadro, M. T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M. E. Michel-Beyerle, and E. E. Chia, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 6(1), 7903 (2015).
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2014 (5)

I. C. Smith, E. T. Hoke, D. Solis-Ibarra, M. D. McGehee, and H. I. Karunadasa, “A layered hybrid perovskite solar-cell absorber with enhanced moisture stability,” Angew. Chem., Int. Ed. 53(42), 11232–11235 (2014).
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G. E. Eperon, S. D. Stranks, C. Menelaou, M. B. Johnston, L. M. Herz, and H. J. Snaith, “Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells,” Energy Environ. Sci. 7(3), 982 (2014).
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C. Wehrenfennig, G. E. Eperon, M. B. Johnston, H. J. Snaith, and L. M. Herz, “High charge carrier mobilities and lifetimes in organolead trihalide perovskites,” Adv. Mater. 26(10), 1584–1589 (2014).
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J. W. Lee, D. J. Seol, A. N. Cho, and N. G. Park, “High-efficiency perovskite solar cells based on the black polymorph of HC(NH2)2PbI3,” Adv. Mater. 26(29), 4991–4998 (2014).
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H. Zhou, Q. Chen, G. Li, S. Luo, T. B. Song, H. S. Duan, Z. Hong, J. You, Y. Liu, and Y. Yang, “Photovoltaics: interface engineering of highly efficient perovskite solar cells,” Science 345(6196), 542–546 (2014).
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2013 (1)

C. C. Stoumpos, C. D. Malliakas, and M. G. Kanatzidis, “Semiconducting tin and lead iodide perovskites with organic cations: phase transitions, high mobilities, and near-infrared photoluminescent properties,” Inorg. Chem. 52(15), 9019–9038 (2013).
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2009 (2)

A. Kojima, K. Teshima, Y. Shirai, and T. Miyasaka, “Organometal halide perovskites as visible-light sensitizers for photovoltaic cells,” J. Am. Chem. Soc. 131(17), 6050–6051 (2009).
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R. Lovrinčić and A. Pucci, “Infrared optical properties of chromium nanoscale films with a phase transition,” Phys. Rev. B 80(20), 205404 (2009).
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2005 (1)

H.-K. Nienhuys and V. Sundström, “Intrinsic complications in the analysis of optical-pump, terahertz probe experiments,” Phys. Rev. B 71(23), 235110 (2005).
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2001 (1)

N. Smith, “Classical generalization of the Drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001).
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1995 (1)

V. V. Klimov, P. Haring Bolivar, and H. Kurz, “Hot-phonon effects in femtosecond luminescence spectra of electron-hole plasmas in CdS,” Phys. Rev. B 52(7), 4728–4731 (1995).
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Abd-lefdil, M.

L. Atourki, M. Bernabé, M. Makha, K. Bouabid, M. Regragui, A. Ihlal, M. Abd-lefdil, and M. Mollar, “Effect of doping on the phase stability and photophysical properties of CsPbI2Br perovskite thin films,” RSC Adv. 11(3), 1440–1449 (2021).
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Abzieher, T.

J. A. Schwenzer, T. Hellmann, B. A. Nejand, H. Hu, T. Abzieher, F. Schackmar, I. M. Hossain, P. Fassl, T. Mayer, W. Jaegermann, U. Lemmer, and U. W. Paetzold, “Thermal stability and cation composition of hybrid organic-inorganic perovskites,” ACS Appl. Mater. Interfaces 13(13), 15292–15304 (2021).
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Agarwal, P.

A. Kumar, A. Solanki, M. Manjappa, S. Ramesh, Y. K. Srivastava, P. Agarwal, T. C. Sum, and R. Singh, “Excitons in 2D perovskites for ultrafast terahertz photonic devices,” Sci. Adv. 6(8), eaax8821 (2020).
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Aguiar, J. A.

J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016).
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Al-Jassim, M.

J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016).
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Allegro, I.

P. Brenner, O. Bar-On, M. Jakoby, I. Allegro, B. S. Richards, U. W. Paetzold, I. A. Howard, J. Scheuer, and U. Lemmer, “Continuous wave amplified spontaneous emission in phase-stable lead halide perovskites,” Nat. Commun. 10(1), 988 (2019).
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Amassian, A.

T. Niu, J. Lu, R. Munir, J. Li, D. Barrit, X. Zhang, H. Hu, Z. Yang, A. Amassian, K. Zhao, and S. F. Liu, “stable high-performance perovskite solar cells via grain boundary passivation,” Adv. Mater. 30(16), 1706576 (2018).
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Aoki, T.

J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016).
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Aristidou, N.

S. Pont, D. Bryant, C.-T. Lin, N. Aristidou, S. Wheeler, X. Ma, R. Godin, S. A. Haque, and J. R. Durrant, “Tuning CH3NH3Pb(I1−xBrx)3 perovskite oxygen stability in thin films and solar cells,” J. Mater. Chem. A 5(20), 9553–9560 (2017).
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Ashari-Astani, N.

C. Yi, J. Luo, S. Meloni, A. Boziki, N. Ashari-Astani, C. Grätzel, S. M. Zakeeruddin, U. Röthlisberger, and M. Grätzel, “Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells,” Energy Environ. Sci. 9(2), 656–662 (2016).
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Atourki, L.

L. Atourki, M. Bernabé, M. Makha, K. Bouabid, M. Regragui, A. Ihlal, M. Abd-lefdil, and M. Mollar, “Effect of doping on the phase stability and photophysical properties of CsPbI2Br perovskite thin films,” RSC Adv. 11(3), 1440–1449 (2021).
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Baillie, D.

T. L. Cocker, D. Baillie, M. Buruma, L. V. Titova, R. D. Sydora, F. Marsiglio, and F. A. Hegmann, “Microscopic origin of the Drude-Smith model,” Phys. Rev. B 96(20), 205439 (2017).
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Bar-On, O.

P. Brenner, O. Bar-On, M. Jakoby, I. Allegro, B. S. Richards, U. W. Paetzold, I. A. Howard, J. Scheuer, and U. Lemmer, “Continuous wave amplified spontaneous emission in phase-stable lead halide perovskites,” Nat. Commun. 10(1), 988 (2019).
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T. Niu, J. Lu, R. Munir, J. Li, D. Barrit, X. Zhang, H. Hu, Z. Yang, A. Amassian, K. Zhao, and S. F. Liu, “stable high-performance perovskite solar cells via grain boundary passivation,” Adv. Mater. 30(16), 1706576 (2018).
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Bernabé, M.

L. Atourki, M. Bernabé, M. Makha, K. Bouabid, M. Regragui, A. Ihlal, M. Abd-lefdil, and M. Mollar, “Effect of doping on the phase stability and photophysical properties of CsPbI2Br perovskite thin films,” RSC Adv. 11(3), 1440–1449 (2021).
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Berry, J. J.

Z. Li, M. Yang, J.-S. Park, S.-H. Wei, J. J. Berry, and K. Zhu, “Stabilizing perovskite structures by tuning tolerance factor: formation of formamidinium and cesium lead iodide solid-state alloys,” Chem. Mater. 28(1), 284–292 (2016).
[Crossref]

J. A. Aguiar, S. Wozny, T. G. Holesinger, T. Aoki, M. K. Patel, M. Yang, J. J. Berry, M. Al-Jassim, W. Zhou, and K. Zhu, “In situ investigation of the formation and metastability of formamidinium lead tri-iodide perovskite solar cells,” Energy Environ. Sci. 9(7), 2372–2382 (2016).
[Crossref]

Bian, Z.

Z. Zhao, F. Gu, H. Rao, S. Ye, Z. Liu, Z. Bian, and C. Huang, “Metal halide perovskite materials for solar cells with long-term stability,” Adv. Enengy. Mater. 9(3), 1802671 (2019).
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T. M. Koh, V. Shanmugam, J. Schlipf, L. Oesinghaus, P. Muller-Buschbaum, N. Ramakrishnan, V. Swamy, N. Mathews, P. P. Boix, and S. G. Mhaisalkar, “Nanostructuring Mixed-Dimensional Perovskites: A Route Toward Tunable, Efficient Photovoltaics,” Adv. Mater. 28(19), 3653–3661 (2016).
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Boland, J. L.

W. Rehman, R. L. Milot, G. E. Eperon, C. Wehrenfennig, J. L. Boland, H. J. Snaith, M. B. Johnston, and L. M. Herz, “Charge-Carrier Dynamics and Mobilities in formamidinium lead mixed-halide perovskites,” Adv. Mater. 27(48), 7938–7944 (2015).
[Crossref]

Bouabid, K.

L. Atourki, M. Bernabé, M. Makha, K. Bouabid, M. Regragui, A. Ihlal, M. Abd-lefdil, and M. Mollar, “Effect of doping on the phase stability and photophysical properties of CsPbI2Br perovskite thin films,” RSC Adv. 11(3), 1440–1449 (2021).
[Crossref]

Boziki, A.

C. Yi, J. Luo, S. Meloni, A. Boziki, N. Ashari-Astani, C. Grätzel, S. M. Zakeeruddin, U. Röthlisberger, and M. Grätzel, “Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells,” Energy Environ. Sci. 9(2), 656–662 (2016).
[Crossref]

Brenner, P.

P. Brenner, O. Bar-On, M. Jakoby, I. Allegro, B. S. Richards, U. W. Paetzold, I. A. Howard, J. Scheuer, and U. Lemmer, “Continuous wave amplified spontaneous emission in phase-stable lead halide perovskites,” Nat. Commun. 10(1), 988 (2019).
[Crossref]

Bryant, D.

S. Pont, D. Bryant, C.-T. Lin, N. Aristidou, S. Wheeler, X. Ma, R. Godin, S. A. Haque, and J. R. Durrant, “Tuning CH3NH3Pb(I1−xBrx)3 perovskite oxygen stability in thin films and solar cells,” J. Mater. Chem. A 5(20), 9553–9560 (2017).
[Crossref]

Buruma, M.

T. L. Cocker, D. Baillie, M. Buruma, L. V. Titova, R. D. Sydora, F. Marsiglio, and F. A. Hegmann, “Microscopic origin of the Drude-Smith model,” Phys. Rev. B 96(20), 205439 (2017).
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Chan, C. C. S.

C. C. S. Chan, K. Fan, H. Wang, Z. Huang, D. Novko, K. Yan, J. Xu, W. C. H. Choy, I. Lončarić, and K. S. Wong, “Uncovering the electron-phonon interplay and dynamical energy-dissipation mechanisms of hot carriers in hybrid lead halide perovskites,” Adv. Energy Mater. 11(9), 2003071 (2021).
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Chanana, A.

A. Chanana, X. Liu, C. Zhang, Z. V. Vardeny, and A. Nahata, “Ultrafast frequency-agile terahertz devices using methylammonium lead halide perovskites,” Sci. Adv. 4(5), eaar7353 (2018).
[Crossref]

Chang, S. Y.

J. W. Lee, Z. Dai, T. H. Han, C. Choi, S. Y. Chang, S. J. Lee, N. De Marco, H. Zhao, P. Sun, Y. Huang, and Y. Yang, “2D perovskite stabilized phase-pure formamidinium perovskite solar cells,” Nat. Commun. 9(1), 3021 (2018).
[Crossref]

Chen, J.

J. Chen and N.-G. Park, “Inorganic hole transporting materials for stable and high efficiency perovskite solar cells,” J. Phys. Chem. C 122(25), 14039–14063 (2018).
[Crossref]

Chen, K.

D. Luo, W. Yang, Z. Wang, A. Sadhanala, Q. Hu, R. Su, R. Shivanna, G. F. Trindade, J. F. Watts, Z. Xu, T. Liu, K. Chen, F. Ye, P. Wu, L. Zhao, J. Wu, Y. Tu, Y. Zhang, X. Yang, W. Zhang, R. H. Friend, Q. Gong, H. J. Snaith, and R. Zhu, “Enhanced photovoltage for inverted planar heterojunction perovskite solar cells,” Science 360(6396), 1442–1446 (2018).
[Crossref]

Chen, Q.

H. Zhou, Q. Chen, G. Li, S. Luo, T. B. Song, H. S. Duan, Z. Hong, J. You, Y. Liu, and Y. Yang, “Photovoltaics: interface engineering of highly efficient perovskite solar cells,” Science 345(6196), 542–546 (2014).
[Crossref]

Cheng, L.

O. V. C. La, T. Salim, J. Kadro, M. T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M. E. Michel-Beyerle, and E. E. Chia, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 6(1), 7903 (2015).
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Chia, E. E.

O. V. C. La, T. Salim, J. Kadro, M. T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M. E. Michel-Beyerle, and E. E. Chia, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 6(1), 7903 (2015).
[Crossref]

Chia, E. E. M.

D. Zhao and E. E. M. Chia, “Free carrier, exciton, and phonon dynamics in lead-halide perovskites studied with ultrafast terahertz spectroscopy,” Adv. Opt. Mater. 8(3), 1900783 (2020).
[Crossref]

Cho, A. N.

J. W. Lee, D. J. Seol, A. N. Cho, and N. G. Park, “High-efficiency perovskite solar cells based on the black polymorph of HC(NH2)2PbI3,” Adv. Mater. 26(29), 4991–4998 (2014).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. XRD patterns of (a) FAPI, (b) FAPEAPI, (c) FACsPI films. SEM images of (d) FAPI, (e) FAPEAPI, (f) FACsPI films.
Fig. 2.
Fig. 2. The time-dependent THz characterization of the perovskite films. (a) Graphical representation of the sample structure with the pump-probe laser beams. The transient THz transmission change of (b) FAPI, (c) FAPEAPI, (d) FACsPI films.
Fig. 3.
Fig. 3. The time-dependent ${\tau _F}$ , ${\tau _S}$ of the perovskite films. FAPI (a) and (d), FAPEAPI (b) and (e), FACsPI (c) and (f). The error bars are the standard error of the fitting analysis.
Fig. 4.
Fig. 4. Improved stability of the FAPEAPI, FACsPI films. (a) Photographs of the Perovskite films in a degradation period. Schematics of the (b) FAPEAPI and (c) FACsPI films. Evolution of photoconductivity of (d) FAPI, (e) FAPEAPI, (f) FACsPI film.
Fig. 5.
Fig. 5. The complex photoconductivity and time-dependent carrier mobility of different samples. (a) Real and (b) imaginary conductivity of the perovskite films. Experimentally extracted data and the fitted data are displayed by points and solid lines, respectively. The effective carrier mobility evolution of the (c) FAPEAPI and (d) FACsPI films.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Δ E E = A F e x p ( t τ F ) + A S e x p ( t τ S )
Δ σ ( t ) ε o c d ( 1 + n s u b ) Δ E ( t ) E ( t )
Δ σ ~ = N e 2 m γ 1 1 i w / γ [ 1 + c 1 1 i w / γ ]

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