Thermodynamic origin of instability in hybrid halide perovskites

Abstract

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.

Introduction

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)Se₂) 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 is formed by a combination of various organic cations X⁺ = (CH₃NH₃, NH₄, CH₅N₂), metallic cations M²⁺ = (Pb, Sn), and halide anions Z⁻ = (I, Cl, Br) with CH₃NH₃PbI₃ 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 CH₃NH₃PbI₃ 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 [CH₃NH₃]⁺ ion, thus suggesting that aprotic hybrid perovskites (e.g., (CH₃)₄NPbI₃) could potentially be more stable¹³. 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 Sit¹⁵ indicate deprotonation of methylammonium as an initial step in dissolution of the perovskite. Furthermore, first principle calculations¹⁶ 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 attributed the intrinsic instability of halide perovskites to its relatively low Madelung lattice energy as compared to oxide perovskites that belong to 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 CH₃NH₃PbI₃^18,19, 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, NH₃OHPbI₃, NH₃NH₂PbI₃, PH₄PbI₃, SbH₄PbI₃, and CsPbBr₃, as well as a hypothetical material, SF₃PbI₃, in a search for perovskite compounds with an enhanced chemical stability for photovoltaic applications.

Results and Discussion

Chemical stability of CH₃NH₃PbI₃

We begin by examining the chemical stability of CH₃NH₃PbI₃ against decomposition. The structural changes in the course of degradation involve disappearance of X-ray diffraction peaks that are characteristic for CH₃NH₃PbI₃ and appearance of PbI₂ peaks²⁰, 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 is the standard reaction enthalpy change at zero temperature, and 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 CH₃NH₃PbI₃, the decomposition reaction yields two products: PbI₂ and CH₃NH₃I. The corresponding lattice parameters and total energies of the reactant and products are listed in Table 1. The values yield the dissociation reaction enthalpy of per formula unit (f.u.) for CH₃NH₃PbI₃ evaluated using Eq. (3). The result is within the range of theoretical values reported in the literature, including ²² and −0.06 eV¹⁶. The corresponding experimental value is ²³, which is far too low to explain formability of this perovskite and needs further experimental verifications. The theoretical value of 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.

Table 1 Equilibrium lattice parameters, electronic total energy E_tot per formula unit (f.u.), and change in the chemical potential that accounts for the free energy of the compounds at the finite temperature and pressure not captured in DFT total energy.

The poor chemical stability of CH₃NH₃PbI₃ is often attributed to the nearly vanishing value of ΔH^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 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 possible²⁶, 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 CH₃NH₃PbI₃ decomposition reaction

amounts to . The resultant Gibbs free energy difference in Eq. (2) is positive 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/atom²⁸.

The thermodynamic characteristics of CH₃NH₃PbI₃ 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 PbI₂ 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 solute³⁰. The mean ionic activity a_± of CH₃NH₃I 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, and γ_± ~ 1, the chemical potential of aqueous CH₃NH₃I 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 CH₃NH₃PbI₃ as previously suggested by Niu et al.²⁰. The decomposition proceeds as long as the following condition is fulfilled

Using the value of and assuming γ_± ~ 1, it is possible to estimate the saturation concentration c_s of CH₃NH₃I dissolved in water at which further decomposition of CH₃NH₃PbI₃ 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 μm³¹, 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 eV²² limits the accessible power conversion efficiency when aiming for solar cell absorber materials. Therefore, we focus on perovskite structures of the family X PbI₃ and explore several alternatives for the cation X = [NH₃OH]⁺, [NH₃NH₂]⁺, [PH₄]⁺, [SbH₄]⁺, and [SF₃]⁺. A solid solution of hydroxylammonium and hydrazinium ions were recently used in hybrid perovskite structures³². 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 mass³³. 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 [SF₃⁺] (0.053 nm³) and [CH₃NH₃]⁺ (0.051 nm³) indicate proximity in size of both ions³⁴.

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 correction³⁵. 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 SbH₄PbI₃ 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 limit³⁶.

Table 2 Dissociation reaction enthalpy of perovskite structures presented together with volume of the unit cell V₀ and the band gap energy calculated self-consistently without taking into account the spin-orbit coupling.

The chemical stability of perovskite structures in Table 2 was initially assessed by computing the decomposition reaction enthalpy . In this calculation, we shall assume that all structures decompose following the pathway similar to Eq. (1) with the exception of SF₃PbI₃. Since there are no reports in the literature for SF₃I salt, the following decomposition route is considered

This decomposition route also involves water, but in a different capacity from the degradation of CH₃NH₃PbI₃. 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 (higher values favour stability of perovskites). Among all hybrid perovskites listed in Table 2, SF₃PbI₃ 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 SbH₄PbI₃ with the promising band gap value.

The pseudocubic structures of SF₃PbI₃ perovskite is shown in Fig. 1 alongside with the pseudocubic structure of CH₃NH₃PbI₃. 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 SF₃PbI₃ is 0.4 eV higher than that for CH₃NH₃PbI₃. It is tempting to conclude that the new compound SF₃PbI₃ 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 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 SF₃PbI₃ as being susceptible to reaction with moisture and warrants encapsulation as a protective provision against degradation.

Figure 1

Structure of pseudocubic SF₃PbI₃ (a) and CH₃NH₃PbI₃ (b).

Figure 2

Band structure of pseudocubic SF₃PbI₃ (a) and CH₃NH₃PbI₃ (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 lattice⁵³.

Finally, it will be instructive to discuss the stability of an inorganic CsPbBr₃ perovskite. Unlike CH₃NH₃PbI₃, the decomposition reaction enthalpy of CsPbBr₃ is high (Table 2). Assuming that both compounds have the same magnitude of the final temperature contribution to the free energy, one would expect the free energy of CsPbBr₃ to be approximately 0.5 eV/f.u. lower than that for decomposition products (PbBr₂ and CsBr) indicating strong chemical stability of CsPbBr₃ against spontaneous decomposition. However, it is found experimentally that the performance of CsPbBr₃-based solar cells (not encapsulated) decays over time, although slower than CH₃NH₃PbI₃-based devices³⁷. This observation reveals susceptibility of both perovskite structures to the reaction with moisture, despite of the high reaction enthalpy of CsPbBr₃ 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 CsPbBr₃ can be attributed to the greater value of , which translates into a much lower saturation concentration of CsBr c_s ~ 60 μM as compared to c_s ~ 50 mM for CH₃NH₃I (see discussion in the preceding subsection).

Conclusions

The performance of CH₃NH₃PbI₃ 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 CH₃NH₃PbI₃ structure can be stable against spontaneous decomposition, provided it is isolated from environmental factors. The situation changes drastically in the presence of water. The aqueous solubility of the CH₃NH₃I salt lowers its chemical potential relative to the solid phase, especially in a dilute limit. This property favours decomposition of CH₃NH₃PbI₃ 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(NH₂)₂I, SbH₄I, and CsBr undermines stability of the corresponding perovskite structures.

In a search for alternative perovskites, NH₃OHPbI₃, NH₃NH₂PbI₃, PH₄PbI₃, SbH₄PbI₃, CsPbBr₃, and SF₃PbI₃ compounds were investigated. NH₃OHPbI₃, NH₃NH₂PbI₃, PH₄PbI₃, and SbH₄PbI₃ were concluded unstable due to the low formation enthalpy. The CsPbBr₃ 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 SF₃PbI₃ 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 DFT³⁸. 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 package⁴⁴ based on a full potential linear augmented plane wave method.

Structure optimization

The CH₃NH₃PbI₃ 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 SF₃PbI₃, NH₃OHPbI₃, NH₃NH₂PbI₃, PH₄PbI₃, and SbH₄PbI₃. An orthorhombic (Pnma) structure was chosen to represent δ-CsPbBr₃. 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 dropped below 0.5 mHa/Bohr and components of the stress tensor were less than 1 μHa/Bohr³. 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 PbI₂ (hexagonal, space group 164 m1)), PbF₂ (cubic, space group 225 ) and PbBr₂ (orthorhombic, space group 62 (Pbnm)) were used to represent possible reactants. The structure of CH₃NH₃I undergoes several phase transitions with increasing temperature⁴⁶. A tetragonal α′-phase (space group 129 (P4/nmm)), which is stable at room temperature, resembles a rock-salt ionic structure⁴⁷. The total energy of water was derived from its natural I_h solid structure (hexagonal, space group 194 (P6₃/mmc) ref. 48). Structures of NH₃OHI, NH₃NH₂I, PH₄I, and SbH₄I 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 Ernzerhof²⁷ 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 Vanderbilt⁴⁹ GBRV (v1.5) PAW pseudopotentials were employed for all elements. VESTA 3 package was used for visualization of atomic structure⁵⁰. 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 SF₃PbI₃ and CH₃NH₃PbI₃ were calculated with the Wien2k package⁴⁴ using a full potential linear augmented plane wave method. The Brillouin zone was sampled using 6 × 6 × 6 Monkhorst and Pack⁵¹ mesh. The muffin-tin radii R_MT where set to 0.62, 1.16, 1.22, 1.38, 1.47, 2.2, 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 , which determines the accuracy of a plane wave expansion of the wave function, was set at the values of 3.5 and 6 for CH₃NH₃PbI₃ and SF₃PbI₃ compounds, respectively. The low for CH₃NH₃PbI₃ 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) potential⁵² was applied in order to overcome shortcomings of DFT semilocal exchange correlation functions in predicting band gaps of insulators.