Insight into the Improved Phase Stability of CsPbI3 from First-Principles Calculations.

The effect of organic cation doping with aziridinium (Az+) on the material properties of CsPbI3 was investigated by applying first-principles calculations. The results showed that the phase stability is greatly improved by incorporating the organic cation Az+ at the A site of CsPbI3. However, the band gap of CsPbI3 is further enlarged from 1.76 to 2.27 eV when 12.5% of Az doping is used. The optical absorption coefficient of Cs0.875Az0.125PbI3 is also decreased in the visible light region. The reasons of the improved phase stability and the enlargement of band gap arising from the organic cation doping are revealed. Our calculated results can provide theoretical guidance for improving the phase stability of halide perovskites.

Introduction

Lead halide perovskites have attracted extensive attention as promising photovoltaic candidates for solar cell applications during the past 10 years. The reason that makes halide perovskites suitable for photovoltaic applications is their excellent optoelectronic properties, such as tunable band gaps, high absorption coefficients, small effective masses, high carrier mobility, and long electron–hole diffusion length.[1−4] Since their first successful implementation in dye-sensitized solar cells in 2009,[5] the power conversion efficiencies (PCE) have rapidly increased from 3.8% in 2009 to 25.2% in 2019.[6] Methylammonium lead iodide (MAPbI3) and formamidinium lead iodide (FAPbI3) are the most promising photovoltaic materials.[7,8] However, in view of the nature of the organic cations, the structural stability of hybrid perovskites is usually poor,[9] which is the main factor for hindering commercial applications. An alternative approach to solve this issue is the replacement of these organic cations with an inorganic Cs cation for developing all-inorganic halide perovskites.[10] The cubic phase of CsPbI3 possesses a direct band gap of 1.73 eV,[11,12] making it a promising photovoltaic material. However, the cubic phase can only be stable at temperatures over 300 °C, and it can easily convert to an undesirable nonperovskite δ-phase at room temperature.[13]

Great efforts have been made to improve the stability of CsPbI3. Partial substitution of the iodine ion with the smaller bromine ion has been proven to be a feasible method for improving the phase stability.[14] However, the incorporation of Br can lead to an increase in the band gap of CsPbI3, which is undesirable for solar cell applications.[15] Our previous study has indicated that the band gap of CsPbI3 can be effectively tuned from 1.03 to 2.14 eV by applying strain.[16] Recently, the phase stability of the CsPbI3 perovskite can be significantly improved via organic cation doping.[17] The results suggested that dimethylammonium cation (DMA+) is a more efficient dopant in stabilizing CsPbI3 than ethylammonium (EA+) and guanidinium (GA+).[17] A moderate amount of DMA+ can substitute partial Cs+ of CsPbI3, forming the double-cation Cs1–DMAPbI3.[18] The calculated results have revealed that 12.5% of Cs doping can slightly enhance the optical absorption of MAPbI3, which makes it a possible candidate for highly efficient perovskite solar cells.[19] A three-membered cyclic organic cation-based lead halide perovskite (CH2)2NH2PbI3 was proposed to be a potential absorber material for photovoltaics due to its good stability and lower band gap.[20] The ionic radius of aziridinium ((CH2)2NH2, Az) is between those of MA and FA.[20] The previous calculated results further suggested that substitution of the Az cation at the A site can enhance the stability of the MA1–AzPbI3 perovskite and tune the band gap.[21] Therefore, it is important to investigate whether Az doping can increase the stability of CsPbI3, and the effect of Az cation on the structural stability and electronic and optical properties of the CsPbI3 perovskite needs to be further explored for evaluating the photovoltaic performance.

In this work, the effect of cation replacement with Az on the properties of CsPbI3 was investigated by applying first-principles calculations. The results show that Az doping can apparently improve the phase stability of CsPbI3. The results indicate that the structural distortion of CsPbI3 arising from Az doping is the main factor for the enhanced phase stability. At 12.5% dopant content, CsPbI3 exhibits an apparently blue-shifted band gap from 1.76 to 2.27 eV and reduced the optical absorption in the visible light region.

Results and Discussion

The CsPbI3 perovskite is a cubic structure with space group Fm3̅m at high temperatures.[13] The calculated lattice parameter of CsPbI3 is 6.26 Å, which agrees with the experimental value (6.29 Å).[13] Therefore, the optB86b-vdW functional can give an accurate lattice parameter for CsPbI3. In order to obtain 12.5% of Az doping, a 2 × 2 × 2 supercell containing eight formula units of CsPbI3 was used, and one Cs+ ion was replaced by Az+, as shown in Figure . Az has a larger ionic radius than Cs; the substitution of Cs by Az should lead to the expansion of the volume. Interestingly, the volume contraction is observed when Cs is replaced by Az, as listed in Table . Moreover, the Pb–I bonds become longer in the Az-doped CsPbI3, but the Pb–I–Pb angles are found to get smaller. A previous study[17] has showed that octahedral rotation distortion can reduce the extra space around the Cs cation, and it also explains the reason why the Cs0.875Az0.125PbI3 perovskite has a smaller cell volume with respect to the pure CsPbI3. In addition, the Coulomb interactions between the Cs cation and the inorganic framework PbI6 are increased, which is beneficial for the improved phase stability of CsPbI3.

Figure 1

Schematics for introducing 12.5% of Az doping in CsPbI3 along with optimized structures of CsPbI3 and Cs0.875Az0.125PbI3.

Table 1

Lattice Parameter and Volume of Pure and Az-Doped CsPbI3 Supercell

perovskite	a (Å)	b (Å)	c (Å)	V (Å3)	Pb–I (Å)	Pb–I–Pb (°)
CsPbI3	12.56	12.56	12.56	1981.79	3.14	180
Cs0.875Az0.125PbI3	12.49	12.31	12.35	1895.63	3.20–3.24	144.3–151.6

The structural stability of halide perovskites can be assessed by the Goldschmidt’s tolerance factor t(22)where RA is the A-site cation radius, RB is the B-site cation radius, and RX is the X-site anion radius. The perovskite structure is stable when the tolerance factor is in the range of 0.81–1.11.[23] For CsPbI3, the tolerance factor is 0.81, which approaches the lower limit of the requirement. The result also indicates that the phase stability of CsPbI3 is poor. Given that the tolerance factor of CsPbI3 is on the margin of the stable perovskite structure, increasing the tolerance factor of CsPbI3 is an effective method to improve its phase stability. The ionic radius of Az+ is 2.27 Å,[20] which is larger than that of Cs+. The tolerance factor of Cs0.875Az0.125PbI3 is 0.82, which is conducive to improve the phase stability. In addition, the octahedral factor μ (RB/RX)[24] is another important parameter to predict the structural stability of halide perovskites. The value of the octahedral factor μ is 0.54 for pure and Az-doped CsPbI3, which locates in the range of 0.44–0.90.[24]

In light of the relatively large ionic radius of Az, it is necessary to assess whether the organic cation Az can be incorporated into the lattice of CsPbI3 in terms of stability. The formation energies of pure and Az-doped CsPbI3 can be defined as followswhere x is the replacement ratio of Cs by Az. E(Cs1–AzPbI3), E(CsI), E(AzI), and E(PbI2) are the total energies of Cs1–AzPbI3, CsI, AzI, and PbI2, respectively. The calculated formation energy of CsPbI3 is 0.17 eV/f.u. The results show that the calculated formation energy of Cs0.875Az0.125PbI3 is −0.01 eV/f.u., which indicates that the phase stability is apparently enhanced. However, the formation energy is only about −10 meV, which is not low enough to guarantee the phase stability at high temperatures. In the words, the short-term stability of Cs0.875Az0.125PbI3 can be improved, but it still suffers long-term instability. Recently, the calculated results revealed that the phase stability of CsPbI3 can be significantly improved by large organic cation doping.[17]

The band gap of the absorber material is very crucial as it is related to photovoltaic performance of the device and also determines the optical absorption in the visible light region. The band gap of CsPbI3 is 1.31 eV by Perdew–Burke–Ernzerhof (PBE) calculation, which is lower than its experimental value.[11,12] Our calculated data is well consistent with the reported results.[25,26] In order to gain more accurate band gap, HSE06 calculations were further employed. The band structure of CsPbI3 is shown in Figure a. It can be seen that CsPbI3 is a direct band gap semiconductor with a value of 1.76 eV, which is in good agreement with the experimental value (1.73 eV).[11,12] Importantly, the value of the band gap of CsPbI3 rapidly increases from 1.76 to 2.27 eV after Az doping. The electronic structures of halide perovskites were affected by structural distortion, and the key factor is the Pb–I–Pb angles.[27] Our results have showed that the enlargement of the band gap can be ascribed to the larger structural distortion for Az-doped CsPbI3. It can be observed from here that there is no benefit of Az doping in CsPbI3 as the band gap increases beyond the ideal value for photovoltaics. However, Cs0.875Az0.125PbI3 may be an ideal material for tandem solar cells due to its larger band gap.

Figure 2

Band structures of (a) CsPbI3 and (b) Cs0.875Az0.125PbI3 at the HSE06 level.

The density of states (DOS) and partial DOS of pure and Az-doped CsPbI3 are shown in Figure . It can be seen that Cs/Az cations do not contribute to the band edge states. The valence band maximum of pure and Az-doped CsPbI3 is mainly dominated by the I-5p orbital, while the conduction band minimum is contributed by the Pb-6p orbital.

Figure 3

Calculated density of states (DOS) and partial DOS (PDOS) of (a) CsPbI3 and (b) Cs0.875Az0.125PbI3 at the optB86b-vdW level.

We also compared the optical absorption of Az-doped CsPbI3 at a doping content of 12.5% with that of the pure CsPbI3. We used an optB86b-vdW functional along with the scissors correction to obtain an accurate band gap as that of the HSE06 functional. The band gap is usually underestimated in PBE calculations and overestimated for the dielectric properties. Based on the scissors correction, we compared the optical absorption of Az-doped CsPbI3 with that of the pure structure CsPbI3, as shown in Figure . Due to the larger band gap, Cs0.875Az0.125PbI3 exhibits a blue-shifted onset with respect to the pure CsPbI3. Although the optical absorption coefficient is apparently decreased in the visible spectrum, a slight absorption advantage for ultraviolet light can be observed. The reduced optical absorption can be ascribed to the wider band gap. In general, considering the improved phase stability, the photovoltaic performance of Cs0.875Az0.125PbI3 is expected to be further improved.

Figure 4

Calculated absorption coefficients for pure and Az-doped CsPbI3.

Conclusions

In conclusion, our calculated results indicate that the structural stability of CsPbI3 can be improved by Az doping. However, the Az-doped CsPbI3 shows blue-shifted band gap and reduced optical absorption in the visible spectrum. Further analyses reveal that the structural distortion of a perovskite material is the main reason for the improved phase stability and decreased optical properties. Our work can provide theoretical insight to further explore better phase stability of the CsPbI3 perovskite.

Computational Methods

Our calculations were carried out by employing density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).[28] The Perdew–Burke–Ernzerhof (PBE) version of the generalized gradient approximation[29] (GGA)-based DFT methods using the projector augmented plane wave (PAW) was adopted.[30] The energy cutoff of the plane wave basis was set to 500 eV. The optB86b-vdW functional was used to account for dispersion interactions in the halide perovskites.[31,32] The criterion of 1 × 10–5 eV for the total energy convergence was required. The atomic coordinates were fully optimized until the residual forces were smaller than 0.01 eV/Å. For CsPbI3, a 6 × 6 × 6 k-point mesh was used for structural optimization. A 3 × 3 × 3 k-point mesh was used for the CsPbI3 supercell. It is well known that the GGA-PBE functional usually underestimates the band gaps of halide perovskites. In order to obtain the band gap more accurately, Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional was applied.[33,34] In the HSE06 method, the screened parameter was set to 0.2 A–1, and 20% of the screened Hartree–Fock (HF) exchange was used with the PBE functional.