Critical role of water in defect aggregation and chemical degradation of perovskite solar cells
Yun-Hyok Kye Chol-Jun Yu Un-Gi Jong Yue Chen Aron Walsh



kimuniv-m]Yun-Hyok Kye
kimuniv-m]Chol-Jun Yucor
ryongnam14@yahoo.com
kimuniv-m]Un-Gi Jong
hk]Yue Chen
icl]Aron Walsh

[cor]Corresponding author

[kimuniv-m]Department of Computational Materials Design, Faculty of Materials Science, Kim Il Sung University, 
 Ryongnam-Dong, Taesong District, Pyongyang, Democratic People's Republic of Korea
[hk]Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
[icl]Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom


The chemical stability of methylammonium lead iodide (MAPbI3) under humid conditions remains the primary challenge facing halide perovskite solar cells. We investigate defect processes in the water-intercalated iodide perovskite (MAPbI3_H2O) and monohydrated phase (MAPbI3·H2O) within a first-principles thermodynamic framework. We consider the formation energies of isolated and aggregated vacancy defects with different charge states under I-rich and I-poor conditions. It is found that a PbI2 (partial Schottky) vacancy complex can be formed readily, while the MAI vacancy complex is difficult to form in the hydrous compounds. Vacancies in the hydrous phases create deep charge transition levels, indicating the degradation of halide perovskite upon exposure to moisture. Electronic structure analysis supports a novel mechanism of water-mediated vacancy-pair formation.


Critical role of water in defect aggregation and chemical degradation of perovskite solar cells
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    Received: date / Accepted: date
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Low-cost perovskite solar cells (PSCs) based on methylammonium lead iodide (CH3NH3PbI3 or MAPbI3) are rapidly evolving, with a record power-conversion efficiency (PCE) from under 4% in 2009 <cit.> to over 22% in recent years <cit.>. However, PSCs have a critical problem of easy degradation by extrinsic as well as intrinsic factors, still preventing their outdoor installation <cit.>. In particular, the facile decomposition of MAPbI3 upon exposure to moisture has been recognized to be the major extrinsic factor of PSC degradation <cit.>. In fact, the PCE of MAPbI3 solar cells drops by nearly 90% in a few days under an ambient environment (T= 300 K, relative humidity (RH) = 30-50%) <cit.>, while MAPbI3 can be decomposed into MAI, PbI2, and HI in a few hours at high humidity conditions <cit.>.


For a chemical explanation of this phenomenon, hydrolysis of MAPbI3 was initially suggested as the main mechanism, and based on the first-principles calculations, deprotonation of MA+ by H2O was proposed as the principal cause of the hydrolysis <cit.>. Soon afterwards, however, it was demonstrated that MAPbI3 readily transformed to the monohydrate phase MAPbI3·H2O at moderate humidity (RH ≤ 60%), while to the dihydrate phase (MA)4PbI6·2H2O at high humidity  (RH ≥ 80%), at the initial stage of the MAPbI3 water-mediated decomposition process, which could be reversed by drying treatment <cit.>. This can be explained by the hydrogen bonding interaction between the lead iodide framework and the organic MA+ cations in the perovskite crystal being weakened upon its hydration <cit.>. MA+ can readily diffuse and separate from the PbI6 octahedra, resulting in a rapid decomposition of MAPbI3. The activation barrier for vacancy-mediated MA+ migration was confirmed to be reduced from 1.18 eV in MAPbI3 to 0.38 eV in water-intercalated and 1.14 eV in monohydrated phases <cit.>. Although there have been some theoretical studies of the intrinsic point defects in MAPbX3 (X = I, Br, Cl) <cit.>, those in the hydrate phases remain unexplored.


In this Letter, we investigate the origin of perovskite decomposition through point defect processes in water-intercalated MAPbI3, denoted as MAPbI3_H2O hereafter, and monohydrated phase, MAPbI3·H2O. The water-intercalated  MAPbI3_H2O is suggested as an intermediate phase during the transition to the hydrated phases due to the relatively low activation energies for water insertion into the perovskite surface (0.27 eV <cit.> or 0.31 eV <cit.>), as well as for water molecular diffusion within the bulk crystal (0.28 eV <cit.>). A density functional theory (DFT) approach combined with ab initio thermodynamics is utilized to describe defect formation and interactions. Electrostatic stabilization by water is found to play a key role in defect clustering and ultimately in the stability of perovskites in humid environments. 


In the first stage, we performed structural optimizations of pristine MAPbI3,  water-intercalated MAPbI3_H2O, and monohydrated MAPbI3·H2O. The lattice constant and bandgap of MAPbI3 were calculated to be 6.33 Å and 1.53 eV, which are in good agreement with the experimental values of 6.32-6.33 Å <cit.> and 1.50 eV <cit.>. For the case of MAPbI3_H2O, the unit cell containing a water molecule in the large interstitial space formed by a huge PbI6 framework became triclinic after optimization. The initial structure of MAPbI3·H2O with a monoclinic crystalline lattice and experimentally identified atomic positions <cit.> was also optimized, giving the lattice constants of a=10.46 Å, b=4.63 Å, c=11.10 Å and β=101.50^∘ agreed well with the experimental values <cit.>. The bandgaps were calculated to be 1.86 eV in MAPbI3_H2O, and 2.47 eV in MAPbI3·H2O, being comparable with the previous DFT value of 2.52 eV for the monohydrated phase <cit.> and experimental value <cit.>.


In the second stage, using the optimized unit cells, we built (3×3×3) supercells for MAPbI3 (324 atoms) and MAPbI3_H2O (405 atoms), while the (2×3×2) supercell for MAPbI3·H2O (360 atoms), with and without vacancy defects, and performed atomic relaxations with the fixed lattice constants (see Figures S1-S3). Isolated vacancy point (V_I, V_MA, V_Pb) and pair defects (V_MAI, V_PbI2) were created. 

For each vacancy defect, various charge states were considered to identify the thermodynamic charge transition levels. Figure <ref> presents the defect formation energy diagrams at I-poor (Pb-rich and MA-rich) and I-rich (Pb-poor and MA-poor) conditions. These conditions correspond to an iodine precursor in orthorhombic solid form and a lead precursor in fcc solid form, respectively.





Amongst the vacancy point defects, lead vacancies with a charge state of -2 (V^-2_Pb) in these three compounds, and additionally -1 charge state (V^-1_Pb) and neutral state (V^0_Pb) in the case of hydrous compounds, have the lowest formation energies in the whole range of Fermi level (E_F) at I-rich conditions. For I-poor growth, meanwhile, the iodine vacancies with a charge state of +1 (V^+1_I) have the lowest formation energies in the lower part of E_F, whereas the V^-2_Pb in the higher range of E_F. Note that for the case of MAPbI3 our results are consistent with the previous DFT results <cit.>, with some minor numerical differences due to the inclusion of dispersion corrections in this work.

Under I-poor conditions, MA vacancies with a neutral state (V^0_MA) and a charge state of -1 (V^-1_MA) have typically higher formation energies than V_Pb and V_I in MAPbI3 and MAPbI3_H2O, but in-between values are found in the case of MAPbI3·H2O. 





For vacancy pair defects, which can be viewed as compensated partial Schottky-type aggregates, we considered various charge states.  We calculated the binding energy defined as E_b=H_f[A]+H_f[B]-H_f[AB] <cit.>. 
Table <ref> summarizes the formation and binding energies of the neutral  pairs of V^0_MAI and V^0_PbI2 (for E_b of charged pairs, see Table S1). For the case of MAPbI3, the formation energy of V^0_MAI is 0.23 eV, which is much lower than 1.80 eV reported by Kim et al. <cit.>. If we use the MAI molecule instead of MAI solid as they did, it becomes 1.98 eV in better agreement. V^0_PbI2 has the formation energy of -0.03 eV, being slightly lower than 0.03 eV reported by Kim et al. <cit.>, possibly due to a different crystal lattice. In general, the formation energies of these complex defects in the hydrous compounds are higher than those in the pristine MAPbI3.

The formation of V^0_PbI2 in all the compounds is more favorable than the formation of the individual vacancy point defects V^+1_I and V^-2_Pb due to their positive binding energies (Table <ref>). Therefore, it is expected that V^+1_I and V^-2_Pb are formed first (they are dominant defects), and then the interaction between them leads to the formation of V^0_PbI2 independently of whether the hydrous compound or not. Water adsorption into the perovskite crystal reduces the activation barrier for vacancy-mediated I- ion migration <cit.>, resulting in an enhancement of V^0_PbI2 formation. As shown in Figure <ref>, the formation energy of V^+1_I (V^-2_Pb) at the I-rich condition is higher (lower) than at the I-poor condition (their concentrations have a reverse feature), and thus the reaction speed of V^0_PbI2 formation can be lower at the I-rich condition (Pb2+ ion migration is quite difficult). Experimentally, the I-rich condition can be realized by directly adding I_3^- in solution <cit.>. In indirect ways, increasing PbI2 concentration relative to MAI concentration as in many other experimental works <cit.> can effectively inhibit the formation of V^0_PbI2 from the decomposition of MAPbI3 from the viewpoint of chemical equilibrium of reaction, and furthermore, formation of a passivating MAPbI3/PbI2 interface <cit.> also provide PbI2 excess environment to prevent the forward reaction for V^0_PbI2 formation. Surprisingly, the binding energies of V^0_MAI in the hydrous compounds are negative, although it is positive in the pristine perovskite. This indicates that in the hydrous compounds other products such as HI, CH3NH2 and I2 rather than MAI can be formed during chemical decomposition.





Next, we derived thermodynamic transition levels ε(q_1/q_2) between defects in different charge states q_1 and q_2. Figure <ref> shows the possible transition levels together with the relative band alignment of MAPbI3_H2O and MAPbI3·H2O with respect to MAPbI3. Water molecules inserted through the film surface extract electrons, resulting in the shift of the valence band maximum (VBM) towards lower values and the conduction band minimum (CBM) towards higher values, and thus the bandgap change from the pristine to the water-intercalated and to the monohydrated phase. It is apparent that in the case of MAPbI3 all of the vacancy defects have shallow transition levels, whereas in the case of hydrous compounds the vacancies exhibit deep trap behavior that can facilitate the recombination of charge carriers, resulting in the degradation of solar cell performance. Specifically, in the case of MAPbI3, V_I and V_MA are shallow donors and acceptors due to their transition levels ε(1+/0) and ε(0/1-) near the CBM and VBM, respectively. In the case of hydrous compounds, transition levels are located deep in bandgap region, although V_MA transition levels are not far away from the valence band. In particular, V_Pb has no transition level (ε(0/2-) inside the valence band) in MAPbI3, but two deep transition levels ε(0/1-) and ε(1-/2-) are possible in the hydrous compounds. Similar features are found for V_MAI (two transition levels) and for V_PbI2, which has two/four transition levels in the pristine/hydrous MAPbI3.





The electronic density of states (DOS) in the pristine and vacancy-containing structures are shown in Figure <ref>. Only the neutral states are considered. To make clear the role of each species, the atom-projected DOS (PDOS) are presented in Figure S4-S6. In all the compounds, the lower conduction band is from Pb 6p, while the upper valence band is from mostly I 5p states and minor part of Pb 6s  <cit.>. In the case of MAPbI3,  V_I formation causes a donor level near the conduction band and the positive potential results results in a downshift of the local valence band, while V_Pb and V_MA form acceptor states and their negative potential result in a local upshift of the valence band. The DOS characteristics of V_PbI2 and V_MAI can be explained by combining the effects of individual point defects. Similar features are observed in the hydrous compounds. One distinction is that the n-type donor level created by V_I  is deeper in the band gap due to the presence of the water molecule. The electronic states of the water molecule overlap with I 5p at about -2 (-3) eV and with the MA states at about -4 (-5) eV in MAPbI3_H2O (MAPbI3·H2O), through the hydrogen bonding interaction between water and I atoms of PbI6 as well as MA moiety. When the vacancy defect V_I or V_Pb is formed, similar interactions are observed.


To study charge transfer during the formation of a vacancy defect, we plot the electron density difference Δρ=ρ_V_D-ρ_perf+ρ_D in Figure <ref>. In the case of MAPbI3,  charge is depleted around the V^+_I defect, while charge is accumulated around V^-_MA and V^-2_Pb, as expected. 
When the hydrous phases are formed, the extent of charge exchange is reduced because the water molecule can donate (for positive point defect) or accept (for negative ones) some electrons, indicating a stabilization by water  of the Schottky-type defects. 
In the absence of water, V_I, V_MA and V_Pb with the charge states of +1, -1 and -2 are the most stable over a large range of Fermi energy. In the case of hydrous compounds, however, these defects exchange the electrostatic stabilization by water opens up alternative charge states, leading to the creation of deep levels, which can enhance non-radiative processes and ultimately lead to the degradation of perovskite solar cells.





In summary, we have investigated defect processes in MAPbI3 and its hydrous phases MAPbI3_H2O and MAPbI3·H2O in order to reveal the effect of water on the performance and stability of iodide perovskites. The formation energies of V_I, V_MA, V_Pb, V_MAI and V_PbI2 with various charge states, the binding energies of the complex defects (V_MAI and V_PbI2), the density of states, and electronic charge density differences were presented to draw the following conclusions. 
The formation of V_PbI2 from its individual vacancy point defects is spontaneous, and due to the greatly reduced kinetic barrier for I- ion migration when hydrated, the concentration of V_I should be reduced to prevent this formation, which can be realized by imposing  I-rich conditions. 
In the hydrous compounds, the formation of individual point defects V_I and V_MA is more favorable than the formation of V_MAI, and thus I2 or CH3NH2 or HI can be formed rather than MAI during the decomposition. Unlike in  bulk  MAPbI3, all the vacancy defects create deep transition levels in the hydrous compounds arising from electrostatic interactions with water molecules. 
To overcome the negative effects of water on the performance and stability of halide perovskites, controlling the processing conditions such as 
the halide chemical potential during growth and annealing will be important, in additional to the physical encapsulation of devices.



§ COMPUTATIONAL METHODS

The formation enthalpy of a point defect with a charge state q is calculated using the grand canonical expression <cit.>,


    Δ H_f[D^q]≅{E[D^q]+E_corr[D^q]}-E_perf-n_iμ_i+qE_F


where E[D^q] and E_perf are the total energies of the supercell including a defect D and the perfect crystal supercell, and n_i and μ_i are the number of removed (minus sign) or added (plus sign) i-type species and its chemical potential. E_corr[D^q] is a correction to the error in the total energy of charged supercell that can be calculated by E_corr=α q^2/ε L in the monopole approximation, where α is the Madelung constant, ε the static dielectric constant, and L the lattice constant, respectively <cit.>. Using the density functional perturbation theory, we computed the isotropic static dielectric constants as 23.55, 25.88, and 16.30 for MAPbI3, MAPbI3_H2O, and MAPbI3·H2O. E_F is the Fermi energy expressed as referenced to the valence band: E_F=ϵ_VBM+Δϵ_F+Δ V, where ϵ_VBM is the energy level of the VBM, Δϵ_F is the Fermi level with respect to the VBM and Δ V is the potential alignment. We ignored the band-filling correction for shallow defects due to its negligible value with large supercell size in this work. Self-interaction and spin-orbit coupling were not included, which are not expected to affect the comparison between the defect physics of pristine and hydrated MAPbI3 compounds and thereby draw the conclusion about the decomposition mechanism upon hydration, but they will be important for quantitative defect spectroscopy <cit.>.

The chemical potentials depend on the growth conditions, which can fall between  I-rich or I-poor conditions. The I-rich condition corresponds to the iodine precursor in orthorhombic solid form (space group Cmca), and thus the upper limit of the iodine chemical potential is that μ_I^rich=E_I(orth). The synthesis equations constrain the chemical potentials as follows,


    μ_MAI+μ_PbI2=μ_MAPbI3
    μ_Pb+2μ_I=μ_PbI2
    μ_MA+μ_I=μ_MAI


Eqs. (<ref>) and (<ref>) correspond to the real synthetic reactions, but Eq. (<ref>) acts only as a theoretical reference. 
From Eq. (<ref>), we identified the iodine poor conditions, μ_I^poor≈1/2(E_PbI2-μ_Pb^rich), where μ_Pb^rich=E_Pb(fcc) 
referred to the bulk Pb in fcc phase and E_PbI2 is referred to the bulk PbI2 in rhombohedral phase (space group P3̄m1) <cit.>, and Pb-poor condition, μ_Pb^poor≈ E_PbI2-2μ_I^rich. 
Then, using Eqs. (<ref>) and (<ref>), the MA-poor and -rich conditions are established like μ_MA^poor≈ E_MAPbI3-E_PbI2-μ_I^rich and μ_MA^rich≈ E_MAPbI3-E_PbI2-μ_I^poor. 
For the vacancy pair defects, the chemical potentials were not affected by the iodine chemical potential; μ_MAI≈ E_MAPbI3-E_PbI2 and μ_PbI2≈ E_PbI2.

Pseudo-cubic unit cells were adopted for MAPbI3, and (3×3×3) and (2×3×2) supercells were used for vacancy-containing MAPbI3, MAPbI3_H2O and MAPbI3·H2O, respectively. The DFT total energies were calculated using the Quantum ESPRESSO code <cit.> with the ultrasoft pseudopotentials provided in the code and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional <cit.> added by the van der Waals (vdW) energy in the flavor of vdW-DF-OB86 <cit.>. Scalar-relativistic effects are included.
A plane-wave cutoff energy of 40 Ry and a Γ point for structural relaxation of vacancy-containing supercells, while 2×2×2 special k-points for DOS calculations, were used for all the configurations. All the atomic positions of each configuration were relaxed until the forces on atoms converge to 5× 10^-5 Ry/Bohr. 



§ APPENDIX A. SUPPLEMENTARY DATA

Supplementary data related to this article can be found at URL.



§ NOTES

The authors declare no competing financial interest.

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