Organic-inorganic halide perovskite materials have attracted great interest due to outstanding optoelectronic properties, such as high carrier mobility [1], as well as tunable photoluminescence (PL) properties [2]. At present, perovskite materials have already achieved great success in the field of photovoltaics. For example, the efficiency of perovskite solar cells can be up to 25.2% [3], which is comparable to that of polycrystalline silicon solar cells [4]. Meanwhile, perovskite materials have been widely used for light-emitting diodes [5,6]. Recently, the excellent nonlinear optical (NLO) properties of organic-inorganic halide perovskite materials have increasingly attracted attention [7]. It is well known that the original molecular polarization of materials resulting from charge transfer between the molecular portion A and BX3 in perovskite exhibits the electron cloud distortion under intensive light, which leads to NLO properties [8]. Compared with all-inorganic perovskite materials, the organic-inorganic hybrid perovskite with a softer framework allows for the change of A-cation orientation, which may enhance the optical nonlinearity. For instance, a comparative study on the NLO properties of colloidal MAPbBr3(MA=CH3NH3) and CsPbBr3 quantum dots (QDs) was conducted by Lu et al., proving that the nonlinear absorption characteristics of organic-inorganic hybrid perovskite QDs are much more pronounced than those of all-inorganic perovskite QDs because of the photoinduced orientation effects [9]. Suárez et al. studied the NLO properties of MAPbX3 poly-crystalline thin films [10]. It was found that both the nonlinear absorption coefficient (β) and the nonlinear refraction index (n) of organic-inorganic halide perovskite thin films are three to four orders of magnitude larger than that of all-inorganic perovskite CsPbX3, which shows more potential in the field of NLO application. Additionally, it has been proved that the perovskite MAPbX3 (X=Cl, Br, I) thin film possesses a strong nonlinear absorption coefficient, comparable with the highest reported [11]. Kalanoor et al. investigated the NLO properties of the MAPbI3 thin film, which were dominated by bound carriers at lower pump intensities, but they were dominated by free carriers and two-photon absorption (TPA) at higher pump intensities [12].

Although a great progress has been made in the research of the NLO properties of organic-inorganic halide perovskite materials, there are still many unanswered questions. For example, the influences of constituents on the NLO properties in organic-inorganic halide perovskite materials still need further investigation. More importantly, the physical mechanism of coexistence of multiple NLO behaviors in such materials has not yet been well addressed.

In this work, comparative studies on the NLO properties of perovskite [MA1−xFAxPbI3, FA=CH(NH2)2, x=0, 0.2, 0.4, 0.6, and 0.8] were carried out by doping the A-site cations of organic-inorganic hybrid perovskite. The conversion process from TPA to saturable absorption (SA) in the MA1−xFAxPbI3 thin films has been observed at different excitation intensities, whose physical mechanism is then revealed through the measurements of nonlinear transmittance and femtosecond-transient absorption (fs-TA) spectrum.

High-purity (99.99%) PbI2 was purchased from Alfa Chemical Group. Methylammonium iodide (MAI) and formamidinium iodide (FAI) with a purity greater than 99.5% were purchased from Luminescence Technology Corp. To prepare MA1−xFAxPbI3 (x=0, 0.2, 0.4, 0.6, and 0.8) solutions with a concentration of 1 mol/L, MAI and FAI powders with the corresponding molar ratios, together with PbI₂, were added to dimethylformamide (DMF) and dimethylsulfoxide (DMSO), which had a volume ratio of 7:3. The solutions were stirred at the rate of 300 r/min and heated at 60°C for 2 h. Prior to spin coating on quartz substrates, the solution was filtered with 0.22 μm polytetrafluoroethylene filters. Finally, thin films of about ∼100nm, evaluated by scanning electron microscopy (SEM) via the intramolecular exchange method, were prepared. To avoid the sample degradation, another quartz substrate was used to capsulate the thin film. Pure FAPbI3 has not been synthesized successfully using this method because black α-FAPbI3 is not stable and easily collapses into yellow β-FAPbI3 structures at room temperature. However, the stable structure can be obtained when the proportion of FA is greater than 20%. Thin films fabricated by the above-mentioned method are dense and uniform.

SEM (ZEISS GeminiSEM 300) was used to characterize the morphological properties of MA1−xFAxPbI3 thin films. X-ray diffraction (XRD) measurements were recorded on a Bruker D8 Discover X-ray diffraction system. The linear absorption spectra were recorded on an ultraviolet–visible–near-infrared spectrophotometer (Lambda 950, PerkinElmer, Inc.) at room temperature.

During the open-aperture (OA) Z-scan measurements, femtosecond pulses (100 fs, 1000 Hz) at 800 nm were focused on the samples by a spherical lens with a 500 mm focal length, and the transmitted light was then measured by a silicon detector. For the measurements of power-dependent transmittance, the fs pulses first passed through an electric ultrafast broadband variable attenuator (Newport VA-BB–4–CONEX) and were then focused onto the samples. The transmitted light was again collected by the silicon detector. The ultrafast dynamics of perovskite materials was investigated using a standard fs-TA spectroscopy excited at 1300 nm pulses (100 fs, 1000 Hz). The excited light spot area was ∼0.002cm2, while the spot area of probe light was ∼0.0005cm2.

Figure 1(a) presents the XRD patterns of the MA1−xFAxPbI3 (x=0, 0.2, 0.4, 0.6, and 0.8) thin films on quartz substrates. Structural changes are observed for the peaks at 14.10°, 19.95°, 24.41°, 28.50°, and 31.90°, respectively. Due to the larger size of FA cation, the crystal lattice will expand when MA is replaced by FA cation. Therefore, all peaks will shift slightly to smaller diffraction angles with the increase of FA content. This gradual blue shift of the diffraction angle (rather than the appearance of two separate peaks with variable intensities) is a strong indication that a mixed phase of MA1−xFAxPbI3 is formed, where the two cations both exist in the same lattice frame. It is worth noting that for MAPbI3, there is a peak at 23.45°, which is one of the characteristics of the tetragonal phase [13]. However, no such peaks for the other four samples can be detected, which suggests the cubic phase of MAPbI3. As shown in Fig. 1(b), the MA1−xFAxPbI3 thin films exhibit two absorption bands at ∼480 and ∼775nm, which implies that they possess a three-level band structure composed by a dual valence band (VB) and a single conduction band (CB) [14]. Furthermore, a continuous shift of the absorption bands to a longer wavelength with the increase of FA content is observed, which further proves the successful fabrication of mixed organic cation perovskites. The inset of Fig. 1(b) shows the SEM image of MA0.2FA0.8PbI3, and it can be clearly seen that the thickness of the thin film is about 100 nm.

It is noted that there are no NLO signals recorded for the quartz substrates under different excitation powers, which ensures the observed NLO behavior mainly originates from the perovskite materials. Typical OA Z-scan measurements for MA1−xFAxPbI3 (x=0, 0.2, 0.4, 0.6, and 0.8) at an excitation intensity of 0.8GW/cm2 were carried out, in which strong nonlinear absorption was observed for all the samples [Fig. 2(a)]. To be specific, a valley–hump–valley structured curve was only observed in the MAPbI3 thin film, while the other four samples exhibited simple-valley-structured curves. However, under the excitation of a higher power intensity (I0=1.2GW/cm2), the samples exhibit valley–hump–valley structured curves, indicating the coexistence of multiple nonlinear absorption effects. With a further increase in excitation intensity, the SA will dominate in the NLO process. To clearly express the NLO conversion process, as an example, the relevant power-dependent Z-scan data for the MA0.2FA0.8PbI3 thin film are presented in Fig. 2(b). The similar phenomenon has been reported in previous literature [15–17]. It is well known that the reverse saturable absorption (RSA) behavior is mainly contributed by TPA. Therefore, the TPA mechanism may also hold true for the nonlinear behavior of our MA1−xFAxPbI3 thin films at low excitation intensity.

The conversion mechanism from TPA to SA can be revealed by using fs-TA spectroscopy. Considering that the absorption band edges of the samples are at around 775 nm, the excitation wavelength at 1300 nm was selected, to exclude the influences of direct transition from the valance band to conduction band. By tracking the corresponding bleaching recovery process, the photogenerated carrier dynamics in MA1−xFAxPbI3 thin films can be investigated. Taking the MA0.2FA0.8PbI3 thin film as an example, the fs-TA spectrum in Fig. 3(a) shows the recovery dynamics of its photoinduced bleaching, in which the two bleaching bands at 486 and 775 nm correspond to the absorption bands in Fig. 1(b), respectively, which proves the existence of dual VBs in MA1−xFAxPbI3. The bleaching band at 486 nm appears in a short time of ∼0.36ps, and its intensity gradually decreases as time increases. However, the bleaching band at 775 nm does not show any signal until 0.51 ps, and its intensity subsequently increases with the increase of time. This implies that the photoinduced carriers in MA0.2FA0.8PbI3 have undergone two different transition processes. When the laser pulses arrive, electrons in the two valence bands will be excited simultaneously, which will induce the first transition from VB1 to VB2. In principle, the two bleaching peaks (486 and 775 nm) should appear at the same time. However, it is noted that the transition time of electrons from VB1 to VB2 is around 0.3 ps [18], and the time for VB1 to fully bleach is 0.36 ps [as shown in Fig. 3(a)]. Therefore, at this moment, the vacancies in VB2 are occupied by the excited electrons from VB1. For this reason, no bleaching signal appears. After VB1 is completely bleached, that is, after 0.36 ps, the bleaching signal of VB2 will appear. The normalized kinetic profile of the band-edge transitions at 775 nm is shown in Fig. 3(b). As shown in the schematic diagram of the band structure illustrated in the inset of Fig. 3(b), considering the band gap between VB1 and VB2 [13], the electrons transition rules and the nonlinear absorption signals in Z-scan measurements, at the excitation wavelength of 1300 nm (0.95 eV), electrons in VB2 (486 nm) first are excited to VB1 (775 nm) through single-photon absorption, which are then excited to CB through the TPA process. This explanation is consistent with the nonlinear behavior observed in the Z-scan measurement. Under low power excitation at 800 nm (1.55 eV), the TPA in Z-scan measurement should be due to the transition from VB1 to CB (1.6 eV). With the increase of excitation intensity, the electron population in the CB gradually becomes saturated, and the excessive photons that cannot be absorbed will pass through thin films directly, resulting in the occurrence of SA. It should be noted that there is no nonlinear signal in the Z-scan measurement excited at a very low intensity (0<I0<0.5GW/cm2), which is consistent with the fact that the TPA occurs at a relatively higher excitation intensity.

The conversion of nonlinear absorption processes can be explained by defining a nonlinear absorption coefficient α(I), which is a sum of independent positive (due to SA) and negative (due to RSA) transmission coefficients. The total absorption coefficient for the perovskite materials can be described by [19] where α0 denotes the linear absorption coefficient, I represents the total input intensity, Isat stands for the saturation intensity, and β is the TPA coefficient. As for the OA Z-scan measurement, the normalized transmittance can be expressed as [20] where Leff=(1−e−α0L)/α0, z is the longitudinal displacement of the sample from the focus (z=0), I0 is the on-axis peak intensity at the focus, Leff is the effective interaction length, L is the sample length, and z0 is the Rayleigh diffraction length. Theoretical fit of the experimental data could be conducted by the substitution of Eq. (1) into Eq. (2).

The fitting results of the nonlinear absorption coefficient β and saturation intensity Isat for MA1−xFAxPbI3 are displayed in Fig. 4(a). Both β and Isat show a strong dependence on the doping concentration (x) of FA. As the value of x increases from 0 to 0.8, β reduces from 18.7 to 13.2 cm/MW, while Isat increases from 125.8 to 156.7GW/cm2. Figure 4(b) shows the excitation-intensity-dependent normalized transmittance for MA1−xFAxPbI3 at 1300 nm, which first decreases slightly and then increases sharply, as a result of the TPA saturation followed by the SA process. In addition, even under very low excitation power, the normalized transmittance of MA1−xFAxPbI3 still decreases, indicating the presence of absorption. Considering the intensity range of excitation-intensity transmittance includes that of Z-scan, and there is no signal in the Z-scan curve under the same intensity, it could be concluded that the absorption-induced transmittance decrease at low excitation intensity in the MA1−xFAxPbI3 thin films should be caused by the single-photon transition from VB2 to VB1, instead of TPA from VB to CB.

Previous literature mainly focused on the effects of A-site cations in MA1−xFAxPbI3 (0≤x≤1) on their NLO properties. In addition, previous results have demonstrated the influence of the expansion in the unit cell [21] and the increase in the number of hydrogen bonding [22,23] on the properties of MA1−xFAxPbI3, which is caused by the introduction of FA cation. The structures of MA, FA, MAPbI3, and FAPbI3 are given in Fig. 5. When FA is coordinated with [PbI6]4− octahedron to form a perovskite structure, due to its larger size, the unit cell will expand, resulting in a more significant octahedral distortion. This degree of distortion will change with different ratios of MA and FA, which directly leads to the increase of the Pb–I bond length and the Pb–I–Pb bond angle [21], weakening the traction of I− to Pb2+ and reducing Pb2+ electron cloud distortion. Apart from this, hydrogen bonds also play an important role in material properties. It has been found that hydrogen atoms allow the iodides to move closer together so that they can bridge two iodide sites in organic-inorganic hybrid perovskite [24] (analogous behavior has been discussed in oxide perovskites [25]), reducing the interaction between I− and Pb2+. Although the hydrogen bonds formed by MA may be slightly stronger than by FA, the number of hydrogen bonds (NH–I) is determined by the hydrogen atoms carried by N atoms. Therefore, FA cations have a higher propensity to form hydrogen bonds [22,23]. The formation of more hydrogen bonds caused by the incorporation of FA will further weaken the Pb–I bond, leading to the weaker distortion of the Pb2+ electron cloud. It is well known that the NLO properties originate from the electron cloud distortion. In addition, it has been confirmed that the NLO properties of MA1−xFAxPbI3 (x=0, 0.2, 0.4, 0.6, and 0.8) materials were determined by their CBs, which are contributed by the p orbit of Pb2+ [33]. As a result, the reduced distortion of the electron cloud of Pb2+ leads to the decrease of the nonlinear absorption coefficient.

For comparisons, the nonlinear absorption coefficient β and saturated absorption intensity Isat of different materials are summarized in Table 1, including the perovskite single crystal, nanocrystals, III–V semiconductor, metal nanoparticle, etc. Among all of them, the nonlinear absorption coefficients β of MA1−xFAxPbI3 (x=0, 0.2, 0.4, 0.6, and 0.8) are overall several orders of magnitude larger than those of other materials. It is worth noting that the nonlinear absorption coefficient is closely related to the crystal structure and quality, sample thickness [34], and nonradiative energy transfer [7]. The larger nonlinear absorption coefficient of our perovskite thin films implies the huge development prospects in nonlinear optical applications.

In summary, the NLO properties of perovskite MA1−xFAxPbI3 (x=0, 0.2, 0.4, 0.6, and 0.8) have been investigated. They exhibit strong doping concentration-dependent NLO properties, and a giant nonlinear absorption coefficient up to 18.7 cm/MW was achieved with a doping concentration of x=0. With the x increase, as a result of the cell volume expansion and the formation of more hydrogen bonds, the TPA coefficient of MA1−xFAxPbI3 gradually decreases, while the saturation intensity gradually increases. Our study provides a strategy to enhance the NLO properties of organic-inorganic hybrid perovskites via doping A-cation, which is vital for the application in the field of nonlinear optical devices.