Influence of Photon Pump Fluence on Charge Carriers in FAPbI3 and Manganite Perovskites

FAPbI ₃ and FA(Mn:Pb)I ₃ perovskite films were prepared and evaluated through steady and transient absorption spectroscopy. According to the analysis using Elliot’s model, there were no considerable differences except for the absorption intensity between FAPbI₃ and FA(Mn:Pb)I₃ perovskite films: the value of the optical gap (E_g) and the position of exciton resonance (E₀) were the same. The femtosecond transient absorption showed biexponential relaxation properties of the charge carriers, suggesting that biexcitons are more easily generated in FA(Mn:Pb)I₃ than FAPbI₃ perovskite. The generation of biexcitons in FA(Mn:Pb)I₃ was also confirmed by the photon pump fluence dependence. Moreover, we were able to estimate the average number of absorbed photons <N> directly from the photon pump power dependence without needing any further experimental measurements such as photoluminescence. Our findings may offer a new way of understanding photoinduced carrier dynamics in perovskite manganites.

• FAPbI3
• Perovskite Manganites
• Transient Absorption

1. Introduction

Formamidinium lead iodide (FAPbI₃) has attracted substantial attention [1] - [12]. The band gap of FAPbI₃ allows for broader absorption of the solar spectrum relative to MAPbI₃. A composite of FAPbI₃ and MAPbBr₃ layer obtained a power conversion efficiency exceeding 20% [6]. To date, perovskite solar cells (PSCs) with photo conversion efficiencies (PCEs) of >25% mainly use FAPbI₃-dominated perovskite as a light absorber due to their superior opto-electrical properties, narrower band gap, longer charge-diffusion length, and better photostability and thermostability [12]. Meanwhile, perovskite manganites may provide a useful material platform for new magnetic materials [13]. MA(Mn:Pb)I₃ has been studied by Nafradi et al., and they found that photo-excited electrons melt the local magnetic order in the ferromagnetic photovoltaic MA(Mn:Pb)I₃ [14]. Technologically relevant materials may emerge when magnetic interactions of spins are present and competing to determine the ground state [15]. This may provide potential for realizing magnetic bits, information storage, and increased manipulation speed [14] [16] [17]. A deeper understanding of charge generation, exciton dissociation, trapping and recombination in photovoltaic manganite perovskites is needed to unravel the operating mechanism.

In this work, we report on studies examining FAPbI₃ and manganite FA(Mn:Pb)I₃ perovskite films using static and transient absorption spectroscopy to explore charge carrier generation, relaxation, and photon fluence dependence. We used femtosecond transient absorption (TA) spectroscopy to investigate the dynamics of the carriers [18]. The measurements were carried out under various pump fluences, and Poisson statistics were used to interpret the data. We found no considerable differences in the optical gap (E_g) or the position of exciton resonance (E₀) between FA(Mn:Pb)I₃ and FAPbI₃. Biexcitons were considered to be more easily generated in FA(Mn:Pb)I₃ than FAPbI₃. There was a difference in photon pump power dependence between the biexcitons and single excitons generated in FA(Mn:Pb)I₃ and FAPbI₃, respectively. Meanwhile, we were able to estimate the value of the average number of absorbed photons directly from the pump power-dependence without needing further optical measurements such as photoluminescence (PL) [18] [19] [20].

2. Samples and Measurements

The fabrication of the FAPbI₃ and FA(Mn:Pb)I₃ thin films with thickness of about 400 nm has been carried out through two-step sequential deposition and solvent engineering representative of wet processes that can yield perovskite films for high-performance perovskite solar cells. FAPbI₃ films were synthesized as described in previous publications [6] [10]. For the mixed halide perovskite FA(Mn:Pb)I₃ films, details are referred from a reference [14]. Femtosecond transient absorption measurements were carried out with the Femtosecond Multidimensional Laser Spectroscopic System (FMLS) at the Korea Basic Science Institute.

3. Results and Discussion

The absorption spectrum in direct semiconductors near the bandgap can be described using the Elliott formula [21] - [26], where the contributions of discrete exciton transitions are added to the continuum transitions [22] [23] [25] [26]. Figure 1(a) shows the absorption spectrum of a FAPbI₃ film near the optical gap

at room temperature. We have analyzed the absorption spectra in this study using Elliot’s formula:

A ( ω ) = A 0 ⋅ θ ( ℏ ω − E g ) ⋅ ( π e π x sinh ( π x ) )     + A 0 ⋅ R e x ∑ n e x = 1 ∞ 4 π n e x 3 ⋅ δ ( ℏ ω − E g + R e x / n e x 2 ) (1)

where A₀ is a constant related to the transition matrix element; ω is the frequency of light, θ is the step function; E_g is the bandgap; x is defined as R e x 1 / 2 / ( ℏ ω − E g ) 1 / 2 , where R_ex is the exciton binding energy; n_ex is the principal quantum number; and δ denotes a delta function. To account for inhomogeneous broadening, the continuum and excitonic part of Equation (1) are convolved with Gaussian functions with standard deviations. The standard deviation of the exitonic part Gaussian function was found to be 23.9 meV. A model based on Elliott’s formula reproduced the spectra very well. In Figure 1(a), an excitonic absorption peak appears just below the bandgap energy, while on the high-energy side of the exciton peak, the absorbance shows a plateau with a slight slope, which is attributed to the continuum contribution described by the first term of the right-hand side of Equation (1). From the best fitting of the model, we extracted that the exciton resonance (E₀) is centered at 1.589 eV. The exciton resonance of 1.589 eV is smaller than that (1.631 eV) in MaPbI₃ [26] ). The bandgap (E_g) of continuum transitions was found at 1.60 eV, which is consistent with recently reported values (1.48 - 2.43 eV) for FAPbI₃ [3] [12]. The bandgap (E_g) at 1.60 eV yields an exciton binding energy ( R e x = E g − E 0 ) of 11 meV (which is the same as that (11 meV) in MAPbI₃ [26]. Figure 1(b) shows the absorbance spectra of FA(Mn:Pb)I₃ films compared with the measurement of FAPbI₃. The spectra of the MA(Mn:Pb)I₃ films show no distinguishable difference between them except the reduced intensities with increased Mn concentrations. Elucidating the role of excitons and free carriers in these materials would provide a deeper understanding of the mechanisms that give rise to the exceptional performance of hybrid perovskite-based devices [27]. Although the absorption coefficient was smaller, the other parameters were the same. We used the same exciton binding energy (R_ex = 11 meV) and bandgap (E_g = 1.60 eV) used for the FAPbI₃ to fit the data [9]. Increased Mn content may have caused changes in absorption intensity [28] - [34].

Figure 2 shows the relaxation of transient absorption (ΔT/T), which was measured at the power of 0.16 µW for FAPbI₃ and FA(Mn:Pb)I₃ films, normalized at the initial maximum points. The decay essentially reflects the temporal evolution of the charge carrier density while assuming that the carrier mobilities are unchanged [35]. The different relaxation pattern suggests that there are both fast (with τ₁) and slow (with τ₂) components. Thus, the relaxation of the transmission signals can be fitted to a biexponential decay. Therefore, we used the

equation, y ( t ) = A 1 e − t τ 1 + A 2 e − t τ 2 + C to analyze the relaxation data [18] [36].

For the FA(Mn:Pb)I₃ sample, we obtained

y FA ( Mn : Pb ) I 3 ( t ) = 0.108 e − t 362   ps + 0.281 e − t 843   ps + 0.62 for the best fit. For the FAPbI₃ sample, we obtained y FAPbI 3 ( t ) = 0.054 e − t 132   ps + 0.254 e − t 961   ps + 0.7 .

In semiconductor nanoparticles, one can generate states in which several excitons occupy a volume comparable to or smaller than that of a bulk exciton [16]. The fast relaxation is known to be originated from the biexcitons, while the slow relaxation is attributed to single excitons [18] [19] [20] [37]. The experimental detection of strongly confined multiexcitons is usually associated with their very short (picoseconds to hundreds of picoseconds) lifetimes, which are limited by nonradiative Auger recombination [16]. We aimed to determine the possible existence of trions by assigning triple exponential decays [18], but we did not find any success. So, we simplified it to biexponential decay, as opposed to triple exponential decay which includes trions. Therefore, we regarded simply that the intensity of the fast component (A₁) can be mainly attributed to the biexcitons. Our result suggests that biexcitons are more easily generated in FA(Mn:Pb)I₃ than in FAPbI₃ (since A_1M = 0.108 >A_1F = 0.054) [16] [18].

To further clarify the origins of the major charge carriers immediately after photoexcitation, we investigated the photon pump fluence dependence of ΔT/T before the relaxation of the photoinduced charges was initiated. Figure 3(a) shows the photoinduced transient absorption (ΔT/T) at different pump powers

[18] [36] for early short times (<3 ps) for (a) FA(Mn:Pb)I₃ and (b) FAPbI₃. The TA signals rise instantaneously after photoexcitation in about ~0.5 ps (which is the proper instrument response time), then reach their peak, at which they are saturated and stable. We only measured for the first 5 ps time scale before the appearance of fast relaxation. For long delays, only single excitons would be left. In Figure 3(b), the values of ΔT/T are plotted as a function of the excitation laser power, and a fit is presented as a visual guide. It is expected that biexcitons are more easily generated with increasing power in FA(Mn:Pb)I₃, while excitons are mainly generated in FAPbI₃. This is comparable to the behavior of perovskite films with well-defined band edges [37].

To ascertain whether the generated charges in FA(Mn:Pb)I₃ and FAPbI₃ films (Figure 3) are mostly biexciton dominant or exciton dominant, we have used Poisson statistics to analyze the results. According to the Poisson distribution, the probability of exciton (biexciton) generation [18] [19], P • ( P • • ) in nanocrystals, is described as follows:

P • ( j e x ) = 1 − e − σ j e x (2)

P • • ( j e x ) = 1 − e − σ j e x − σ j e x e − σ j e x (3)

where j_ex is the excitation photon fluence and σ is the absorption cross-section of the material. The excitation photon fluence j_ex is determined by the pump power. We presumed that j_ex is proportional to photon pump power. The value of ΔT/T is related to the photon bleaching (PB) intensity. The PB intensity of excitons (biexcitons) is proportional to the number of excitons (biexcitons) generated in the material. Thus, we can plot ΔT/T related to the generation probability [18] [37] of the biexciton in FA(Mn:Pb)I₃ and the exciton in the FAPbI₃ sample, respectively. We therefore presumed that the amplitudes of TA can be expressed using the following equations.

Δ T / T i n F A ( X ) ∝ P • ( j e x ) = A F A ( 1 − e − S ⋅ X ) (4)

Δ T / T i n M M ( X ) ∝ P • • ( j e x ) = A M M ( 1 − e − S ⋅ X − S ⋅ X e − S ⋅ X ) , (5)

where X denotes the “pump power” and X ≡ j e x / k , where k is an unknown factor. We set S ≡ k σ . Thus, S ⋅ X = σ j e x = 〈 N 〉 , the average number of absorbed photons. The subscripts _FA and _MM respectively refer to FAPbI₃ and FA(Mn:Pb)I₃ film. A_FA and A_MM are unique proportional factors in the FAPbI₃ and FA(Mn:Pb)I₃ samples, respectively.

Thus, in Figure 4(a) and Figure 4(b), the amplitudes of TA are plotted as a function of the pump power for different values of S. As shown in the log-log plot, only the slope matters in comparing the two different types of charges: biexciton or exciton. We obtained A_MM = 0.335 (Figure 4(a)) and A_FA = 0.003 (Figure 4(b)), and S = 4.5 was obtained to give the best fit for both. In Figure 4(a), the generated charges in FA(Mn:Pb)I₃ exhibit an increase similar to that of the biexciton amplitude, while the charges in the FAPbI₃ sample show an increase following that of single exciton amplitude ( P • ) in Figure 4(b). This is

consistent with the implication showing that the biexciton is more dominant in FA(Mn:Pb)I₃, which is not the case in FAPbI₃ (as shown in Figure 2) at low pump power.

Finally, in Figure 5, the normalized ΔT/T was depicted as a function of 〈 N 〉 . To obtain the value of 〈 N 〉 here, we simply calculated S ⋅ X = σ j e x = 〈 N 〉 without the need for any further measurements such as the photon pump fluence dependence of transient photoluminescence [18] [20] [37]. Our estimation of 〈 N 〉 is comparable to the previously reported experimental values of 〈 N 〉 which were obtained using similar transient absorption and PL methods [18] [19] [20].

4. Conclusion

In conclusion, FAPbI₃ and FA(Mn:Pb)I₃ perovskite films were prepared and evaluated through steady and transient absorption spectroscopy. There was no considerable variation in the absorption spectrum between the FAPbI₃ and FA(Mn:Pb)I₃ perovskite films, except for the absorption intensity in the steady absorption spectrum. The femtosecond transient absorption showed biexponential relaxation properties of the charge carriers, which suggested that biexcitons are more easily generated in FA(Mn:Pb)I₃ than FAPbI₃ perovskite; the generation of biexcitons was also confirmed by the photon pump fluence dependence. We estimated the average number of absorbed photons 〈 N 〉 directly from the photon pump power dependence without relying on any further experimental measurements such as PL. Our findings may offer a new way of understanding photoinduced carrier dynamics in perovskite manganites.

Acknowledgements

This research was supported by a grant from the Korea Research Institute of Chemical Technology (KRICT) (SS2122-20), and by the National Research Council of Science & Technology (NST) grant by the Korea government (MSIT) (No. CAP18054-200). This research was partly supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03028062). Femtosecond transient absorption measurements were carried out with the Femtosecond Multidimensional Laser Spectroscopic System (FMLS) at the Korea Basic Science Institute.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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