Thermodynamic origin of instability in hybrid halide perovskites

Degradation of hybrid halide perovskites under the influence of environmental factors impairs future prospects of using these materials as absorbers in solar cells. First principle calculations can be used as a guideline in search of new materials, provided we can rely on their predictive capabilities. We show that the instability of perovskites can be captured using ab initio total energy calculations for reactants and products augmented with additional thermodynamic data to account for finite temperature effects. Calculations suggest that the instability of CH3NH3PbI3 in moist environment is linked to the aqueous solubility of the CH3NH3I salt, thus making other perovskite materials with soluble decomposition products prone to degradation. Properties of NH3OHPbI3, NH3NH2PbI3, PH4PbI3, SbH4PbI3, CsPbBr3, and a new hypothetical SF3PbI3 perovskite are studied in the search for alternative solar cell absorber materials with enhanced chemical stability.

The search for cost-effective solar cell absorber materials that can compete with the performance of crystalline silicon and thin-film (GaAs, CdTe and Cu(In, Ga)Se 2 ) solar cells remains the priority for renewable energy material research. A recently emerged class of hybrid halide perovskite materials holds a promise to lead the way towards low-cost photovoltaic devices as they combine an energy conversion efficiency of nearly 20% with a low-temperature solution processing technology [1][2][3][4] . The structure of hybrid perovskites + + − X M Z 2 3 is formed by a combination of various organic cations X + = (CH 3 NH 3 , NH 4 , CH 5 N 2 ), metallic cations M 2+ = (Pb, Sn), and halide anions Z − = (I, Cl, Br) with CH 3 NH 3 PbI 3 being a prominent example. Perovskite materials possess a unique combination of characteristics that make them useful in photovoltaic applications including a favourable band gap of about 1.5-1.6 eV, efficient optical adsorption, long lifetime of optical excitations, and high level of mobility for charge carries of both polarities [5][6][7][8] .
A major weakness of perovskite solar cells is degradation of the power conversion efficiency in moist environment 9,10 . This degradation can be observed in CH 3 NH 3 PbI 3 cells through the colour changing from black to yellow accompanied by a noted decreases in absorption and deterioration of the overall cell performance over time 11,12 . The absorbance at 410 nm has been reported to decrease by 50% after 4 hours of exposure to environment with the relative humidity of 98% 12 . The same study linearly extrapolated from the previous result concluded that the identical degradation would take approximately one year at the relative humidity of 20% 12 .
Frost et al. 13 proposed an acid-base chemistry mechanism to explain the role of water in the degradation process. In this process the decomposition is driven by protic properties of the [CH 3 NH 3 ] + ion, thus suggesting that aprotic hybrid perovskites (e.g., (CH 3 ) 4 NPbI 3 ) could potentially be more stable 13 . However, this strategy was not confirmed experimentally to the best of our knowledge.
Density functional theory (DFT) simulations of the perovskite-water interface 14,15 provided further insight to kinetics of the degradation mechanism at the atomic scale. Mosconi et al. 14 observed dissolution of iodine cage and subsequent release of methylammonium ions as well as incorporation of water molecules in the perovskite structure at the interface. The simulation results reported by Zhang and Sit 15 indicate deprotonation of methylammonium as an initial step in dissolution of the perovskite. Furthermore, first principle calculations 16 performed without taking into account solvent effects suggest that hybrid halide perovskites may be intrinsically unstable. This conclusion is based on a nearly zero enthalpy of reaction associated with decomposition of the perovskite structure, which is evaluated based on the total energy of reactant and products. Frost et al. 13  family. This result implies that the environmental factors (such as moisture, UV radiation, and elevated temperatures) may only accelerate the decomposition process. Therefore, the effectiveness of encapsulation as a strategy to prevent moisture damage may not guarantee a long-term stability of perovskite solar cells as evidenced by Han et al. 17 .
Here we utilize DFT to explore stability of perovskite structures from thermodynamic perspective. We will show that the finite temperature effects, that are omitted in former calculation of stability of CH 3 NH 3 PbI 3 18,19 , can play a decisive role when the decomposition reaction takes place in the presence of a solvent and yields a water-soluble product. We will also examine properties of several alternatives, NH 3 OHPbI 3 , NH 3 NH 2 PbI 3 , PH 4 PbI 3 , SbH 4 PbI 3 , and CsPbBr 3 , as well as a hypothetical material, SF 3 PbI 3 , in a search for perovskite compounds with an enhanced chemical stability for photovoltaic applications.

Results and Discussion
Chemical stability of CH 3 NH 3 PbI 3 . We begin by examining the chemical stability of CH 3 NH 3 PbI 3 against decomposition. The structural changes in the course of degradation involve disappearance of X-ray diffraction peaks that are characteristic for CH 3 NH 3 PbI 3 and appearance of PbI 2 peaks 20 , which suggests the following reaction (phases) The standard approach for predicting the direction of a chemical reaction involves evaluation of the change in the Gibbs free energy between reactants and products (see ref. 21, Chap. 7), which can be split into two terms for convenience Here ∆H 0K o is the standard reaction enthalpy change at zero temperature, and µ ∆ T o captures finite temperature effects on the chemical potentials of species involved.
The enthalpy change at zero temperature can be readily evaluated based on the DFT total energy calculations where n and E tot are the number and the total energy of the chemical species involved in the reaction. It should be noted that the bare DFT total energies in Eq. (3) do not fully capture the standard enthalpy changes at zero temperature as they do not include a zero-point vibrational energy and, less importantly, the standard pressure effects on E tot . Therefore, the relation (3) is approximate. In the case of CH 3 NH 3 PbI 3 , the decomposition reaction yields two products: PbI 2 and CH 3 NH 3 I. The corresponding lattice parameters and total energies of the reactant and products are listed in  23 , which is far too low to explain formability of this perovskite and needs further experimental verifications. The theoretical value of ∆H 0K o contrasts sharply with the formation enthalpy of major solar cell compound materials, such as GaAs and CdTe, which is of the order of 0.8-1 eV/f.u. 24,25 .
The poor chemical stability of CH 3 NH 3 PbI 3 is often attributed to the nearly vanishing value of Δ H 16,18 . In fact this only implies that the decomposition does not involve a heat exchange with environment. It is the finite temperature contribution to the chemical potential difference between reactants and products ∑ ∑ that remains overlooked in previous stability analysis 18,19,23 . Here µ  T o represents the final temperature correction to the chemical potential of spieces which is not captured in a bare DFT total energy. Although the extension of DFT calculations to finite temperatures is possible 26 , it is computationally intensive. Therefore, NIST-JANAF thermochemical tables as well as other experimental resources were used to evaluate the final temperature correction using Eq. (5) (see Table 1 and references therein). The final temperature correction to the Gibbs free energy of CH 3 NH 3 PbI 3 decomposition reaction indicating that the final temperature effects tend to stabilize the perovskite structure against spontaneous decomposition under standard conditions for temperature and pressure. However, the result should be taken with caution, since the uncertainty in reaction energies obtained with Perdew, Burke, and Ernzerhof (PBE) 27 exchange-correlation functional is of the order of ± 0.03 eV/atom 28 .
The thermodynamic characteristics of CH 3 NH 3 PbI 3 perovskites indicate that its chemical stability is fragile, and the balance can be easily shifted if the environment changes. A possible scenario that will be discussed here involves presence of a solvent. Unlike PbI 2 that has a limited solubility in water, the methylammonium iodide is highly soluble in water, which should be taken into account when calculating its chemical potential (see ref. 29,Chap. 8).
The actual chemical potential of an electrolyte can be significantly different from its value in the standard state depending on the activity coefficient a ± of the solute 30 . The mean ionic activity a ± of CH 3 NH 3 I solution is determined by its molar concentration c relative to the concentration in standard state c o = 1 M and the mean ionic activity coefficient γ ± , which account for non-ideality of the solution. In a dilute solution limit,  c 1M and γ ± ~ 1, the chemical potential of aqueous CH 3 NH 3 I drops much below its value in the solid phase which shifts the balance in Eq. (1) to the right. Accordingly, the aqueous solubility of methylammonium iodide drives the dissociation of CH 3 NH 3 PbI 3 as previously suggested by Niu et al. 20 . The decomposition proceeds as long as the following condition is fulfilled Using the value of ∆ = . G 0 16eV 300 K o and assuming γ ± ~ 1, it is possible to estimate the saturation concentration c s of CH 3 NH 3 I dissolved in water at which further decomposition of CH 3 NH 3 PbI 3 is suppressed. Equation (10) yields c s ~ 50 mM (or ~8 g/L). Given the fact that the thickness of the absorbing material in perovskite solar cells is only 0.5 μm 31 , even a droplet of water is sufficient to destroy a device with the area of a several square centimeters.
Alternative absorber materials. The stability of hybrid lead halide perovskites can be improved by substituting iodine with more electronegative elements (bromine or chlorine) 23 . However, the associated increase of the band gap that exceeds 2 eV 22 limits the accessible power conversion efficiency when aiming for solar cell absorber materials. Therefore, we focus on perovskite structures of the family X PbI 3 and explore several alternatives for the cation X = [NH 3 32 . Phosphonium and particularly stibonium ions were theoretically predicted to produce more efficient photovoltaic materials when substituted for methylammonium in lead iodide-based perovskites due to the reduced band gap and improved effective mass 33 . Sulphur trifluoride represents an aprotic cation that can be beneficial in the context of resistance to degradation according to the mechanism discussed by Frost et al. 13 . Similar ionic volumes of [SF 3 + ] (0.053 nm 3 ) and [CH 3 NH 3 ] + (0.051 nm 3 ) indicate proximity in size of both ions 34 .
Unit cell volumes and band gaps of the corresponding perovskite structures are listed in Table 2. The band gaps were calculated without taking into account relativistic effects. This approach allows to minimize the error by taking advantage of an error cancelation between the band gap reduction due to spin-orbit coupling and its opening introduced by a port-DFT correction 35 . As a result, values of the band gap are only slightly overestimated (approximately 0.1 eV). The results indicate that small changes in the volume (less than 5%) lead to a sizeable change in the band gap. In contrast to group IV, III-V and II-VI semiconductors, the band gap in perovskite structures increases when the unit cell expands as Dittrich et al. 8 noticed. Out data clearly follow this trend with Scientific RepoRts | 6:37654 | DOI: 10.1038/srep37654 SbH 4 PbI 3 being a favourite candidate for single-junction solar cells due to proximity of its band gap to the ideal value of 1.4 eV, which corresponds to the maximum efficiency in the Shockley-Queisser limit 36 .
The chemical stability of perovskite structures in Table 2 was initially assessed by computing the decomposition reaction enthalpy ∆H 0K o . In this calculation, we shall assume that all structures decompose following the pathway similar to Eq. (1) with the exception of SF 3 PbI 3 . Since there are no reports in the literature for SF 3 I salt, the following decomposition route is considered This decomposition route also involves water, but in a different capacity from the degradation of CH 3 NH 3 PbI 3 .
Here water directly reacts with the perovskite. Results for the decomposition reaction enthalpy calculated using Eq. (3) are given in Table 2, where the compounds are sorted in the order of increasing ∆H 0K o (higher values favour stability of perovskites). Among all hybrid perovskites listed in Table 2, SF 3 PbI 3 shows the highest decomposition reaction enthalpy indicating that the reaction (11) is strongly endothermic. All other hybrid perovskites with the negative reaction enthalpy can be rendered as unstable, including SbH 4 PbI 3 with the promising band gap value.
The pseudocubic structures of SF 3 PbI 3 perovskite is shown in Fig. 1 alongside with the pseudocubic structure of CH 3 NH 3 PbI 3 . The band structure of both materials calculated taking into account spin-orbit coupling and a meta-GGA band gap correction are presented in Fig. 2. Both structures share qualitative similarities of the band dispersion. The band gap of SF 3 PbI 3 is 0.4 eV higher than that for CH 3 NH 3 PbI 3 . It is tempting to conclude that the new compound SF 3 PbI 3 is stable due to the positive value of the enthalpy. It should be emphasized, however, that calculations of stability based on the formation enthalpy alone can lead to spurious results. If we take into account the final temperature correction µ  300 K o for the reactants and products in Table 1, we obtain the Gibbs free energy difference of ∆ =− .
The negative value suggests that the reaction (11) can proceed spontaneously. This renders SF 3 PbI 3 as being susceptible to reaction with moisture and warrants encapsulation as a protective provision against degradation.
Finally, it will be instructive to discuss the stability of an inorganic CsPbBr 3 perovskite. Unlike CH 3 NH 3 PbI 3 , the decomposition reaction enthalpy of CsPbBr 3 is high ( Table 2). Assuming that both compounds have the same magnitude of the final temperature contribution µ ∆ 300 K o to the free energy, one would expect the free energy of CsPbBr 3 to be approximately 0.5 eV/f.u. lower than that for decomposition products (PbBr 2 and CsBr) indicating strong chemical stability of CsPbBr 3 against spontaneous decomposition. However, it is found experimentally that the performance of CsPbBr 3 -based solar cells (not encapsulated) decays over time, although slower than CH 3 NH 3 PbI 3 -based devices 37 . This observation reveals susceptibility of both perovskite structures to the reaction with moisture, despite of the high reaction enthalpy of CsPbBr 3 and lack of proton-donating groups. We believe that the aqueous solubility of CsBr has some significance for explaining this effect. The slow degradation rate of CsPbBr 3 can be attributed to the greater value of ∆G 300 K o , which translates into a much lower saturation concentration of CsBr c s ~ 60 μM as compared to c s ~ 50 mM for CH 3 NH 3 I (see discussion in the preceding subsection).

Conclusions
The performance of CH 3 NH 3 PbI 3 perovskites solar cells deteriorates when exposed to environmental factors, such as moisture and sunlight. This remains the main barrier on the way to their commercialization. The ability to assess stability of solar cell absorber materials using first principle calculations is an important attribute for design of new materials. We showed that the instability of perovskites can be captured using DFT total energy calculations for reactants and products augmented with additional thermodynamic data to account for finite temperature effects. The finite temperature effects play a minor role stabilizing the perovskite structure when products of the decomposition reaction are solids. However, the finite temperature contribution to the Gibbs free energy of the degradation reaction becomes crucially important in the case of when products of the decomposition are aqueous solutions or gases.
Our calculations suggest that the CH 3 NH 3 PbI 3 structure can be stable against spontaneous decomposition, provided it is isolated from environmental factors. The situation changes drastically in the presence of water. The  Table 2. Dissociation reaction enthalpy ∆H 0K o of perovskite structures presented together with volume of the unit cell V 0 and the band gap energy − E g DFT GGA calculated self-consistently without taking into account the spin-orbit coupling. The generalized reaction for chemical decomposition is given by Eq. (1), except for SF 3 PbI 3 that decomposes following the pathway in Eq. (11). a The positive value favours formation of the perovskite structure. b 0.21 eV/f.u. is an alternative DFT result reported by Zhang et al. 16 .
aqueous solubility of the CH 3 NH 3 I salt lowers its chemical potential relative to the solid phase, especially in a dilute limit. This property favours decomposition of CH 3 NH 3 PbI 3 in the moist environment. Therefore, a limited solubility of the decomposition reaction products is anticipated to improve structural stability. Generalizing this result to other perovskites, the aqueous solubility of HC(NH 2 ) 2 I, SbH 4 I, and CsBr undermines stability of the corresponding perovskite structures.
In a search for alternative perovskites, NH 3 OHPbI 3 , NH 3 NH 2 PbI 3 , PH 4 PbI 3 , SbH 4 PbI 3 , CsPbBr 3 , and SF 3 PbI 3 compounds were investigated. NH 3 OHPbI 3 , NH 3 NH 2 PbI 3 , PH 4 PbI 3 , and SbH 4 PbI 3 were concluded unstable due to the low formation enthalpy. The CsPbBr 3 structure is prone to degradation in moist conditions, in spite of the favourable formation enthalpy, due to solubility of CsBr. Straightforward comparison of DFT total energies of reactants and products provides an argument in favour of the chemical stability for the SF 3 PbI 3 structure. The predicted value for the energy band gap of this new compound is approximately 2 eV. However, more detailed analysis that incorporates finite temperature effects renders the material unstable to decomposition in a moist environment thus signifying the importance of those effects for future analysis.
Computational details. The first-principles electronic structure calculations were carried out using DFT 38 .
Two implementations were employed. A projector augmented wave (PAW) method 39,40 implemented in the ABINIT package [41][42][43] was utilized for the structural optimization and calculations of the chemical stability. The band structure calculations were performed in the Wien2k package 44 based on a full potential linear augmented plane wave method.
Structure optimization. The CH 3 NH 3 PbI 3 perovskite is known to exist in three different polymorphs 5,45 : orthorhombic, tetragonal, and cubic. A tetragonal β-phase is stable at room temperature and was used in these calculations. A pseudocubic structure was used to represent SF 3 PbI 3 , NH 3 OHPbI 3 , NH 3 NH 2 PbI 3 , PH 4 PbI 3 , and SbH 4 PbI 3 . An orthorhombic (Pnma) structure was chosen to represent δ-CsPbBr 3 . Optimization of lattice parameters was carried out in conjunction with relaxation of internal degrees of freedom for all structures studied here. The structure was considered optimized when the magnitude of Hellmann-Feynman forces acting on atoms Scientific RepoRts | 6:37654 | DOI: 10.1038/srep37654 dropped below 0.5 mHa/Bohr and components of the stress tensor were less than 1 μHa/Bohr 3 . The Brillouin zone was sampled using an unshifted mesh with the density one k-point per every 0.01 Bohr −1 length of each reciprocal lattice vector. The cutoff energy for a plane wave expansion was set at 15 Ha.
Standard structures of solid PbI 2 (hexagonal, space group 164 (P3m1)m1)), PbF 2 (cubic, space group 225 (Fm3m)) and PbBr 2 (orthorhombic, space group 62 (Pbnm)) were used to represent possible reactants. The structure of CH 3 NH 3 I undergoes several phase transitions with increasing temperature 46 . A tetragonal α′ -phase (space group 129 (P4/nmm)), which is stable at room temperature, resembles a rock-salt ionic structure 47 . The total energy of water was derived from its natural I h solid structure (hexagonal, space group 194 (P6 3 /mmc) ref. 48). Structures of NH 3 OHI, NH 3 NH 2 I, PH 4 I, and SbH 4 I were derived using CsCl structure as a prototype. All structures were fully optimized as describe in the preceding paragraph (without constrains to the geometry).
Gaseous phases were modelled as an individual molecule surrounded by 30 Bohrs of vacuum. The internal degrees of freedom were relaxed. Only Γ -point was used in the Brillouin zone.
Perdew, Burke, and Ernzerhof 27 version of the generalized gradient approximation was chosen for the exchange correlation functional due to its superior accuracy in predicting cohesive properties of solids and molecules.
Garrity, Bennett, Rabe, and Vanderbilt 49 GBRV (v1.5) PAW pseudopotentials were employed for all elements. VESTA 3 package was used for visualization of atomic structure 50 . Structure files of all perovskite compounds and non-trivial salts are included in the supplementary information in a cif-format.
Band structure. The band structure of pseudocubic SF 3 PbI 3 and CH 3 NH 3 PbI 3 were calculated with the Wien2k package 44 using a full potential linear augmented plane wave method. The Brillouin zone was sampled using 6 × 6 × 6 Monkhorst and Pack 51 mesh. The muffin-tin radii R MT where set to 0.62, 1.16, 1.22, 1.38, 1.47, 2.2, Figure 2. Band structure of pseudocubic SF 3 PbI 3 (a) and CH 3 NH 3 PbI 3 (b) calculated along the path between high-symmetry points in the Brillouin zone (c) taking into account spin-orbit coupling and non-local exchange correction. The origin of the energy scale is set at the Fermi energy E F . Labels of the high-symmetry point in the Brillouin zone correspond to an orthorhombic lattice 53 . and 2.2 Bohr for H, N, C, S, F, I, and Pb respectively. The cutoff energy of − 6 Ry was used to separates valence and core electrons. The product R K min MT max , which determines the accuracy of a plane wave expansion of the wave function, was set at the values of 3.5 and 6 for CH 3 NH 3 PbI 3 and SF 3 PbI 3 compounds, respectively. The low R K min MT max for CH 3 NH 3 PbI 3 is due to a small size of the muffin-tin sphere around hydrogen atoms. Optimized lattice parameters and atomic positions from ABINIT calculations were used. The Tran-Blaha modified Becke-Johnson (TBmBJ) potential 52 was applied in order to overcome shortcomings of DFT semilocal exchange correlation functions in predicting band gaps of insulators.