Cations substitution tuning phase stability in hybrid perovskite single crystals by strain relaxation

Methylammonium (MA) and formamidinium (FA) are two typical A site cations in lead halide perovskites. Instability of synthesised crystals will degrade the properties of the photoelectrical device constructed by such perovskites. MAPbI3 and FAPbI3 in cubic crystal structure have been demonstrated to be the most stable at room temperature. Herein we synthesised MA(EA)PbI3 and FA(MA)PbI3 single crystals using an inverse-temperature crystallization strategy by partially substituting the methylammonium (MA) with ethylammonium (EA) and the formamidinium (FA) with methylammonium (MA) respectively. The XRD results show that both crystal structures are cubic, which means organic incorporation can stabilize the crystal structure of lead halide perovskites. The lattice distortion decrease and strain relaxation in single crystals were considered to be the reason leading to higher stability. The single crystals of MA(EA)PbI3 and FA(MA)PbI3 with low trap state density exhibit excellent light-absorbing properties, indicating their potential applications in photoelectric devices.


Introduction
Organic-lead trihalide hybrid perovskites have been widely investigated for solar cells, 1 photodetectors, 2 lasing, 3 lightemitting diodes, 4 and hydrogen production, 5 owing to their superior characteristics including direct bandgap, highly balanced hole and electron mobility, strong absorption coefficient and long carrier lifetime etc. 6 As is well known, the perovskite structure of ABX 3 (where A is an organic cation, B is a metal cation, and X is a halide anion) consists of a threedimensional array of [BX 6 ] octahedra with a cation occupying the 12-coordinated cubo-octahedral cavities of the 3D network. In the ABX 3 perovskite structure, the size of precursor ions needs to follow one principal, which can be expressed as where R A , R B and R X are the ionic radii of the corresponding ions. When the tolerance factor t of the perovskite is between 0.8 to 1, a stable three-dimensional (3D) crystal structure can be obtained. While maintaining a highsymmetry cubic structure, the value of t should be close to 1. 7 Currently, the most-studied lead halide perovskites usually have formamidinium (FA) or methylammonium (MA) at the A site.
In fact, there are three types of MAPbI 3 crystals, orthorhombic, tetragonal and cubic structures. 8 Two phase transitions occur at 162.2 K and 327.4 K for orthorhombic-tetragonal and tetragonal-cubic transitions, respectively. 9 The phase transition of MAPbI 3 from cubic to tetragonal phases at 327.4 K may cause undesired lattice distortion and strain which is harmful to photoelectric devices. 10 Compared with MAPbI 3 , FAPbI 3 perovskite demonstrates better thermal stability and even better photoelectric property. However, FAPbI 3 suffers from the well-known spontaneous phase transition from the desired cubic phase (a phase) black perovskite to d-phase yellow non-perovskite at room temperature. 11 This phase transition is the main obstacle for high efficiency and long-term stability of FAPbI 3 -based optelectric devices. Therefore, an urgent assignment is engineering and synthesizing of cubic MAPbI 3 and FAPbI 3 crystals which can stability exist at room temperature.
Zhu et al. 12 reported the incorporation of cations with smaller effective radius can adjust the tolerance factor and relax the crystal strain of FA-based perovskites. Peng et al. 13 studied the incorporation of cations with bigger effective radius to obtain cubic phase perovskite. M. T. Weller and O. J. Weber's research group have investigated the routes and kinetics of degradation of thin lms of methylammonium (MA)/ formamidinium (FA) lead iodide perovskites (FA x MA 1Àx PbI 3 ). 14 Meantime, they focused on growth of MA/FA system perovskite crystals and exploration of the phase transition mechanism. 15 Herein, we synthesised cubic phase MA(EA)PbI 3 and FA(MA) PbI 3 single crystals by an inverse-temperature crystallization strategy, and investigated their thermodynamic and electronic property.

Growth of the mixed-perovskite crystals
Perovskite crystals were grown by a reported method of inverse temperature crystallization. 16 Briey, 1 M PbI 2 and 1 M CH 3 NH 3 I (MAI) were dissolved in 2 ml g-GBL at 40 C, and stirred until the solution becomes clear. The solution was then kept at 90 C for about 12 h to allow for pure MAPbI 3 crystal growth. For the FA + cation mixed with MAPbI 3 , 0.922 g PbI 2 , 0.159 g MAI, and 0.172 g HC(NH 2 ) 2 I(FAI) were dissolved in 2 ml GBL solution under the same conditions outlined above, to facilitate mixed MAPbI 3 crystal growth. This same method has been used for the incorporation of EA cations.
Characterization of the mixed-perovskite crystals X-ray diffraction (XRD) data from single crystals were collected by a Bruker D8-Advance, using Cu Ka radiation. Thermogravimetric analysis (TGA) was performed on a TGA analyzer (PYRTS 1). Differential scanning calorimetry (DSC) analysis was carried out by using Q2000 to test phase transition. Photoluminescence (PL) measurements of bulk crystals were performed with a Renishaw inVia Raman Microscope using a 532 nm laser as excitation source. The 1 H Nuclear Magnetic Resonance (NMR) spectra were recorded in dimethyl sulfoxide (DMSO) using a Bruker Advance 300 spectrometer. UV-vis diffuse reectance spectroscopy was measured using a UV-vis spectrophotometer (U-3900). V-I characteristics were tested using a Keithley 2400 instrument.

Result and discussion
MA(EA)PbI 3 precursors solutions were prepared using MAI and EAI with a molar ratio of 1 : 3 while FA(MA)PbI 3 precursors solutions were prepared using MAI and FAI with a molar ratio of 1 : 1. Aer growing for about 12 h, the single crystal sizes of 4 mm Â 3 mm Â 1 mm and 2 mm Â 2 mm Â 1 mm are nally obtained for MA(EA)PbI 3 and FA(MA)PbI 3 respectively, as shown in Fig. 1. XRD patterns of the perovskite crystals are shown in Fig. 2. It shows that the main peaks for MA(EA)PbI 3 is at 2q ¼ 14.1 , 28.3 and 31.7 . The diffraction pattern of the tetragonal MAPbI 3 crystal is also shown in Fig. 2a for comparing. The reported calculated and experimental data of MAPbI 3 show that the X-ray peaks (211) and (213) were used to differentiate tetragonal and cubic phase. 17 No (211) reection at 2q ¼ 23.5 was observed, which proves that MA(EA)PbI 3 has a cubic structure. Previously report the sizes of the MA + (2.03 A) and EA + (2.42 A) were calculated. 18 We speculate mixed of different size organic cations in perovskite caused lattice dilation, altered Pb-I-Pb bond angle and nally increased the crystal symmetry. When the A site is occupied by big size organic cation such as EA + , the lead halide perovskite will become a two-dimensional (2D) layer structure. This is due to the large ionic radius of EA + resulting in a tolerance factor out of the empirical range for a stable 3D perovskite structure. We propose that MA(EA)PbI 3 could show a stable 3D PbI 6 octahedral framework owing to two lattice-distortion factors: (1) the small radius of MA + causes lattice contraction; (2) the large radius of EA + causes lattice dilation. This cell dilation adjusts the tolerance factor toward 1, favourable to stabilize the cubic perovskite. The diffraction pattern of FA(MA)PbI 3 in a good agreement with the recently reported cubic phase FAPbI 3 which were shown in Fig. 2b.  Strain in the (111) plane of the cubic phase FAPbI 3 is a driving force for its easy phase transition into the d-phase, where the (111) plane acts as the nucleation site for the (0001) d-phase. 19 When small organic cation MA + incorporated, the strain in (111) was relaxed. As shown in the inset of Fig. 2b, the diffraction peak positions shi to higher angles when MA + cation incorporates, indicating the decrease of the lattice plane space. The FWHM for cubic phase FAPbI 3 is 0.187 while for FA(MA)PbI 3 is 0.177 . The sharpening of the peak indicates the relaxation of strain. 20 Fig. 3 shows the time-dependent XRD measurements of FAPbI 3 and FA(MA)PbI 3 crystals. In the air at room temperature, FAPbI 3 exhibits a phase transition while FA(MA)PbI 3 does not. Spontaneous phase transition of FAPbI 3 from cubic phase to non-perovskite phase was prevented when MA + incorporated. The result is consistent with the reported literature. 15 Schematic representation of the incorporation of organic cations was shown in Fig. 4. Cell parameters of MA(EA)PbI 3 and FA(MA)PbI 3 crystals were shown in Table 1.
Unfortunately, the organic components show much lower diffraction intensity and intense rotating motion, we could not resolve their distributions. 18 To further conrm the composition, we used solution-phase 1 H NMR spectroscopy. The species corresponding to the 1H peaks are listed. Compared with tetragonal MAPbI 3 sample, we can identify B, C 1H species in MA(EA)PbI 3 and D 1H species in FA(MA)PbI 3 . It means that EA and MA had incorporated in MAPbI 3 and FAPbI 3 , respectively. From 1 H NMR spectroscopy of MA(EA)PbI 3 , integration of B and C peaks shows a B/C ratio of 1.00 : 0.66 which is consistent with   the proton population ratio -CH 3 /-CH 2in EA + . The B/A ratio is 1 : 6 which indicates an EA/MA ratio of 1 : 6. While from 1 H NMR spectroscopy of FA(MA)PbI 3 , A/D ratio indicates a FA/MA ratio of 1 : 1 (Fig. 5).
To examine the thermal properties of perovskite MA(EA)PbI 3 and FA(MA)PbI 3 thermogravimetric analysis (TGA) was measured from room temperature to 500 C under nitrogen ow. As shown in Fig. 6a, the decomposition temperature of MA(EA) PbI 3 is about 255 C, which is slightly higher than that of MAPbI 3 single crystal (240 C). While FA(MA)PbI 3 decomposed at 275 C, which is smaller than FAPbI 3 (300 C). It should be noted that this decomposition, by sequential loss of HI followed by organic part, only occurs when the organic species are incorporated into the perovskite structure. 14 The identical thermal behavior was also observed from differential scanning calorimetry (DSC) in Fig. 6b. The thermal stability is related to the probability of HI formation, which is directly related to the acidity of the organic cation. 21 The stronger the acidic character of the cation, the higher the chance that the organic cation can be deprotonated to yield HI. Since the FA cation is less acidic than MA and EA organic species, it is natural that the thermal decomposition is difficult in FA-incorporated perovskites. The pure FAPbI 3 exhibits a peak at 156 C, indicating a phase transition of FAPbI 3 from the yellow d phase to the perovskite structure at this temperature. MAPbI 3 shows a peak at 57 C which indicates a phase transition of tetragonal-cubic transition. Neither of the mixed perovskites shows any peaks, indicating that these mixed perovskites are stable over the investigated temperature range. UV-vis diffuse reectance of perovskites were characterized by an UV-vis diffuse reectance spectrometer to conrm the band gap energy of single crystals. Reectance spectra for the single crystals as a function of wavelength in the range of 740-860 nm are presented in Fig. 6c. A further analysis of optical spectra can be performed to calculate band gap energy. The Kubelka-Munk equation at any wavelength is where S and K are scattering absorption and coefficients, respectively. F(R N ) is called the Kubelka-Munk function. The band gap E g and the absorption coefficient a of a direct band gap semiconductor are related through the well-known equation 22,23 ahn where a is linear absorption coefficient of the material, hn is the photon energy, and C 1 is a proportionality constant. When the material scatters in a perfectly diffuse manner, the Kubelka-Munk absorption coefficient S is constant with respect to wavelength, and using the remission function in eqn (2), we obtain the expression: 24 Therefore, obtaining F(R N ) from eqn (1) and plotting [F(R N ) hn] 2 against hn, the band gap energy, E g , can be obtained easily, and are shown in Fig. 6d. The optical bandgap of MA(EA)PbI 3 is determined to be about 1.49 eV which is similar to MAPbI 3 . While the value of FA(MA)PbI 3 is about 1.43 eV, that is smaller than MAPbI 3 . Fig. 6c also shows the photoluminescence (PL) spectra of the perovskite. MA(EA)PbI 3 and FA(MA)PbI 3 exhibit narrow PL peaks at 709 nm and 800 nm, respectively. PL measurement shows the light emission peak position of the single crystal is very close to the absorption onset, indicating low trap state density. From the UV-vis spectra and PL spectra, both MA(EA) PbI 3 and FA(MA)PbI 3 have superior light-absorbing capability which holds potential to be a suitable photoelectric material.
The trap density (n trap ) in cubic phase single crystals was investigated by using dark I-V technique to characterize fabricated hole-only device. When the applied voltage is lower than the kink-point voltage, the current I increase linearly with applied voltage V, demonstrating an ohmic response between the electrode and the perovskite for the hole-only device. As the applied voltage exceeds the kink-point voltage the current I exhibit a quick non-linear increase, indicating that the trap states are fully lled by the injected carriers. The applied voltage at the kink point is dened as the trap-lled limit voltage (V TFL ), which is determined by the trap state density: 19 where L is the thickness of the perovskite single crystals, 3 is the relative dielectric constant and 3 0 is the vacuum permittivity. Hence the trap n trap can be calculated using eqn (1). Based on Fig. 7a and b, the corresponding hole trap density is 8.49 Â 10 10 cm À3 for MA(EA)PbI 3 and 6.29 Â 10 9 cm À3 for FA(MA)PbI 3 . The values are declined by most one order magnitude of these found in MAPbI 3 , 25 demonstrating the high quality of these new materials.

Conclusions
In summary, we report a route to synthesis cubic phase crystal MA(EA)PbI 3 and FA(MA)PbI 3 by using inverse temperature reactive crystallization process. Big size organic cation EA + incorporated into MAPbI 3 and small size MA + mixed with FA(MA)PbI 3 could obtain stable cubic single crystal via altering the PbI 6 octahedral cage and relaxed strain. The large radius of EA + causes lattice dilation and adjusts the tolerance factor toward 1, favourable to stabilize the cubic perovskite. MA + cation incorporated has reduced the lattice volume and relaxed the strain in lattice and thereby prevent the phase transition from the cubic phase to d-phase. Both MA(EA)PbI 3 and FA(MA) PbI 3 single crystals show remarkable thermal stability with no endothermic peak at range 50-170 C. Direct dark I-V measurement of cubic phase crystals indicates low trap state density. Both MA(EA)PbI 3 and FA(MA)PbI 3 have superior lightabsorbing capability which holds potential to be a suitable photoelectric material.

Conflicts of interest
There are no conicts to declare.