Halogen Migration in Hybrid Perovskites: The Organic Cation Matters

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Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 5474−5480

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Halogen Migration in Hybrid Perovskites: The Organic Cation Matters Aleksandra Oranskaia,†,§ Jun Yin,†,§ Osman M. Bakr,† Jean-Luc Bred́ as,‡ and Omar F. Mohammed*,† †

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Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia ‡ School of Chemistry and Biochemistry, Center for Organic Photonics and Electronics (COPE), Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States S Supporting Information *

ABSTRACT: In hybrid perovskite materials, the organic cations are one of the key structural components used to tune the electronic and optical properties of this promising class of materials. Here, we studied the strong impact of organic cations, methylammonium (MA) and formamidinium (FA), on halogen vacancy and interstitial migration, as well as surface degradation in cubic-phase MAPbBr3 and FAPbBr3 crystals using density functional theory calculations. We found Br vacancies and interstitials have much lower formation energies and higher density in MAPbBr3 in comparison to FAPbBr3 crystals. Moreover, the transition energy barrier for Br migration through vacancies within the bulk phase is lower in MAPbBr3 than in FAPbBr3. We also found that FAPbBr3 has a much higher rotation barrier of the organic cation than MAPbBr3, which points to a much stronger Hbonding with Br in the former case. Our results show that incorporating organic cations with the appropriate structure, shape, and strong H-bonding capabilities in hybrid perovskite crystals is very beneficial for suppressing ion migration and thus further improving the performance of hybrid perovskite-based devices.

H

symmetric CsPbBr3 without H-bonds was not considered in our study because our focus lies on H-bonding strength effects on the ion migration properties. Therefore, we started with the structural properties of the organic cations, including the Hbonding strengths and motions within the inorganic framework. We then considered the formation energies of Br vacancies and interstitials in the bulk. Finally, we examined their migration energies within the bulk phase as well as on stable PbBr2-terminated surfaces by focusing on the role of the organic cation’s chemical interactions. We demonstrate that MAPbBr3 and FAPbBr3 have low formation energies for both Br vacancies (VBr) and interstitials (IBr), especially MAPbBr3, which has a much lower IBr formation energy than FAPbBr3. In addition, the migration barriers for VBr and IBr are found to be ∼0.30 eV for both perovskites in the bulk, while the barrier for IBr on the surface of MAPbBr3 is calculated to be remarkably low (∼0.14 eV). Finally, we highlight that this work provides new physical insights into the correlation between the structure of organic cations and the formation of the interstitial sites, halogen migration, and vacancies. This observation will help to find new ways to treat and reduce these limitations and

ybrid perovskites, one of the most promising classes of semiconductor materials, have gained a leading role in the optoelectronic materials and photovoltaics communities, which is primarily due to their high power conversion efficiency (up to ∼22.7%) in solar-cell devices. 1 This performance stems from remarkable optoelectronic properties,2 combining long charge carrier diffusion lengths,3 tunable energy band gaps, high absorption coefficients,4 and low trap densities.5−7 However, this class of hybrid materials generally suffers from anomalous J−V hysteresis in optoelectronic devices, presenting a great challenge for further improving device performance and stability.8−13 These adverse features were believed to be mainly a result of point defects,14−17 which could facilitate ion migration and lead to accumulation of charges near crystallite boundaries and on the surface of single crystals.18,19 Although there is much experimental evidence about ion migration20−26 and theoretical work on iodide-based hybrid perovskites (e.g., MAPbI3),13,27−32 neither the mechanism of ion migration in bromide-based hybrid perovskites nor the ion migration driving forces in connection with the microstructure of hybrid perovskites are fully understood. In this Letter, we investigate the effects of organic cations on bromine defect formation and migration in stable cubic perovskite crystal systems, MAPbBr3 and FAPbBr3, via density functional theory (DFT) calculations. Note that the highly © XXXX American Chemical Society

Received: August 16, 2018 Accepted: September 6, 2018 Published: September 6, 2018 5474

DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480

Letter

The Journal of Physical Chemistry Letters

Figure 1. Crystal structures of (a) cubic MAPbBr3 and (b) symm- and (c) nonsymm-FAPbBr3 with H-bonds (purple dotted lines) together with inserted H-bond lengths and strengths near symmetrically unique atoms (Pb, gray; Br, brown; N, blue; C, silver; H, white; σ and C2 represent the plane of symmetry and rotation axis). (d) Relative energies of MAPbBr3 and symm- and nonsymm-FAPbBr3 with respect to the organic cation rotation along the z-axis.

Table 1. Crystal Structure and Electronic Properties of Cubic MAPbBr3 and symm- and nonsymm-FAPbBr3, Together with the Valence Band Maximum (VBM) and Conduction Band Minimum (CBM) Energies Obtained at the Symmetric K-Point (0.5, 0.5, 0.5) crystal structural properties

electronic properties 3

compound

a (Å)

b (Å)

c (Å)

volume (Å )

band gap (eV)

VBM (eV)

CBM (eV)

rel. energy (eV)

MAPbBr3 symm-FAPbBr3 nonsymm-FAPbBr3

6.068 6.227 6.205

6.199 6.083 6.206

6.137 6.311 6.211

230.80 239.05 239.17

2.24 1.93 2.18

− 1.28 1.07

− 3.21 3.25

− 0.136 0

After incorporating MA and FA inside the inorganic framework to form the cubic-phase perovskites, we further optimized the crystal structures by fixing the lattice angles at 90° for MAPbBr3, symm-FAPbBr3, and nonsymm-FAPbBr3 (see Figure 1a−c) at the GGA/vdW-DF2 level of theory (for details, see Computational Methods). The calculated average lattice constants of the pseudocubic crystal cells are 6.134 and 6.207 Å for MAPbBr3 and FAPbBr3, respectively (see Table 1); these values are slightly overestimated compared to the experimental values33 of 5.923 and 5.992 Å but agree well with previous calculations at the same level.34,35 As shown in Figure 1d, FAPbBr3 has two energetically stable minimums, i.e., symm-FAPbBr3 and nonsymm-FAPbBr3, with different alignments of the FA cations but nearly the same cell volumes. It should be noted that the crystal structure of nonsymmFAPbBr3 is closer to a perfect cubic system, while symmFAPbBr3 has a slightly distorted cell with an enlarged c lattice constant due to the vertically aligned FA. Although FA is 23% larger in volume than MA, the cell volume of FAPbBr3 is only 4% larger than that of MAPbBr3. Importantly, this indicates that MA leaves more space for ion migration inside the

subsequently improve the optoelectronic performance of these organic perovskites. As a first step toward evaluating the H-bonding interactions between organic cations and the inorganic framework as well as their impact on halogen migration, we compared the two free organic cations, methylammonium (MA) and formamidinium (FA), in terms of their H-bond donating abilities by considering their shape, volume, polarity, and spatial-structural orientation. These features of the organic cations indeed affect their capability to fit into the perovskite framework and their bonding strength with Br. We found that (i) MA has C3vsymmetry, has a bulky structure, and is more extended in three dimensions, with a volume of 55.0 Å3/molecule; FA has C2h symmetry and is a flat π-conjugated system extended essentially in two dimensions with a larger volume of 67.7 Å3/molecule. (ii) MA has three polar N−H bonds at the NH3+-terminus, while FA has two spatially separated pairs of more polar N−H bonds. (iii) the positive charge in MA is located on the ammonium end of the molecule, while in (isolated) FA, it is equally distributed between the two NH2 end groups. 5475

DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480

Letter

The Journal of Physical Chemistry Letters

The ion migrations in hybrid perovskites strongly depend on the point defects with the lowest formation energy and the lowest migration barrier of the elemental migration step. Here, we studied the most abundant defects, which are bromide vacancies (VBr) and bromide interstitials (IBr) (the optimized supercell structures of MAPbBr3 and FAPbBr3 with these defects are given in Figure S2 of the Supporting Information). To compare the densities of these defects in MAPbBr3 and FAPbBr3, we calculated the defect formation energies under three representative growth conditions: Br-poor (Pb-rich), moderate, and Br-rich (Pb-poor).42−44 As shown in Table 3 and Figure S3, under all growth conditions, the formation energies for both VBr and IBr in MAPbBr3 are smaller than those in FAPbBr3. Although the MA cation has a weaker Hbonding capability than FA within their perovskite crystals, Br interstitial formation is more energetically favorable in MAPbBr3 because of the lower rotation barrier of the cation. Thus, the easier reorientation of the MA cation can help stabilize Br interstitials (see the interstitial structures in Figure S4). We used the NEB method, which has been widely applied in APbI3 (A = MA or FA) system,27,29,30 to calculate the migration barriers of Br point defects by considering all possible pathways in supercells (see Figures 2a,c and S5−S8; note that Figures 2 and S8 show only the minimum energy profiles). As shown in Figure 2b,d, the minimum energy migration barriers for VBr are 0.27 and 0.33 eV for MAPbBr3 and FAPbBr3, respectively, confirming the stronger H-bonding stabilization in FAPbBr3 than MAPbBr3. This agrees well with the previous study on APbI3 system showing that iodine vacancy of MAPbI3 has a much smaller migration barrier than that of FAPbI3 using the same DFT methods.30 Note that in both systems, Br vacancy migration is not accompanied by significant relaxations of the crystal structures, while transitions between the initial and final structures are stabilized by slight rotations of the nearest organic cations (see Figure S9). The minimum energy barrier for the through-cell Br vacancy migration pathway in MAPbBr3 is 0.46 eV, which is much smaller than that in FAPbBr3, 0.85 eV (see Figure S5, 1−1x and 1−1y for MAPbBr3 and FAPbBr3). The calculated migration barriers can be compared with the experimental activation energy for ionic conductivity by using the reported value for I-based hybrid perovskites (0.43 eV) as their lower limit.45 If we take into account the stronger Hbonding capability of Br atoms, which are more electronegative than I atoms (H-bonding energies for symm- and nonsymmFAPbBr3 are 481 and 339 meV versus 346 and 256 meV for symm- and nonsymm-FAPbI3, as calculated from QTAIM in the same manner as described above), the activation energy for ionic conductivity in Br-based perovskites should be somewhat higher than 0.43 eV. Thus, we can assume that the direct through-cell pathway will contribute to the ionic motion in MAPbBr3, making it even more important in Br migration through VBr than FAPbBr3. Interestingly, in both cases, the

perovskite lattice than FA. The calculated band gaps are 2.24 eV for MAPbBr3 and 1.93/2.18 eV for symm/nonsymmFAPbBr3, respectively; these values are slightly underestimated compared to the experimental values obtained from optical band gap measurements at room temperature (MAPbBr3, 2.34 eV; FAPbBr3, 2.26 eV).33 To understand the role of MA and FA on Br migrations, we first compare the H-bonding strength by using a topological analysis of the electron density distribution in the context of the quantum theory of atoms in molecules (QTAIM).36 Here, following earlier work, the bond critical points (BCPs) for the H-bonds were set in the range of 2.47−3.86 Å, and the corresponding bond strength was estimated as EHB = 0.429 ∇2ρi(rBCP), where ∇2ρi(rBCP) is the Lagrangian kinetic energy density term.37,38 As indicated in Figure 1a−c and Table 2, Table 2. Electronic Topological Properties of Cubic MAPbBr3 and symm- and nonsymm-FAPbBr3: Electron Density (ρi) and Its Lagrangian (∇2ρi) at the Bond Critical Points Corresponding to the H-Bonds of Length Li Together with Their H-Bonding Energy (Ei)a compound MAPbBr3

symmFAPbBr3

nonsymmFAPbBr3

Li (Å)

ρi (e/bohr2)

∇2ρi (e/bohr5)

Ei (meV)

ΣEi (meV)

2.55 (×2) 2.72 3.45 (×2) 2.68 (×2)

0.0157 0.0119 0.00329 0.0121

0.0381 0.0346 0.00902 0.0314

107 87.9 20.0 82.6

342

2.78 (×2) 3.86 (×4) 2.47 (×2)

0.00969 0.00177 0.0182

0.0292 0.00350 0.0462

71.6 7.67 132

2.69 (×2) 3.06 (×2)

0.00908 0.00590

0.0305 0.0152

72.6 36.0

339

481

An exponential fit of the H-bonding strength versus length, Ei = f(Li), is given in Figure S1 in the Supporting Information.

a

MAPbBr3 has a total H-bonding energy of 342 meV by summing up five H-bonds, and symm-FAPbBr3 has 339 meV for eight H-bonds. Interestingly, the largest H-bonding energy (481 meV) is found in nonsymm-FAPbBr3, which has the shortest average H−Br bonds. To further understand the impact of the H-bonding strength in these systems, we used the nudged elastic band (NEB) methodology39−41 to obtain the rotation profiles of the organic cations along the z-axis, as shown in Figure 1d. The transition barriers between 0° and 90° are found to be related to the H-bonding strengths and correspond to 48.4, 3.10, and 95.0 meV for MAPbBr3 and symm- and nonsymm-FAPbBr3, respectively (we recall that the thermal energy at room temperature is ∼25 meV). Because symm-FAPbBr3 is less energetically and far less kinetically stable than nonsymm-FAPbBr3, symm-FAPbBr3 is excluded from the following discussions about ion migration.

Table 3. Formation Energies (in eV) of Neutral Defects for MAPbBr3 and FAPbBr3 at A (Br-Poor, Pb-Rich), B (Moderate), and C (Br-Rich, Pb-Poor) Growth Conditions VBr0

IBr0

V(MA/FA)0

I(MA/FA)0

defect

A

B

C

A

B

C

A

B

C

A

B

C

MAPbBr3 FAPbBr3

1.25 1.28

2.01 2.04

2.77 2.80

1.64 1.82

0.88 1.06

0.12 0.30

2.45 2.41

1.74 1.67

1.04 0.93

2.03 1.35

2.73 2.09

3.43 2.84

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DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480

Letter

The Journal of Physical Chemistry Letters

Figure 2. (a and c) Bromide vacancy (VBr) and interstitial (IBr) migration pathways and (b and d) their energy profiles along the migration paths in MAPbBr3 and FAPbBr3. Note that relative energy refers to the minimum energy of optimized crystal structure before ion migration.

Figure 3. (a) Illustration of Frenkel VBr−IBr pair migrations and (b) their migration energy profiles in MAPbBr3 and FAPbBr3.

minimum energy pathways for VBr (including the MAPbBr3 minimum energy through-cell pathway) lie in the direction of the minimum electrostatic potential of the cation dipole, and in both systems, the most energetically favorable pathways lie near N-termini. Moreover, as compared to nonsymmetric FAPbBr3, MAPbBr3 have much larger lattice distortions (i.e., a smaller average Br−Pb−Br angle; see Figure S10) induced by strong electrostatic interactions between the vacancy and the dipole moment of the organic cation, which agrees well with previous study on the APbI3 system.46 The minimum energy Br interstitials are formed through the stabilization of Br atoms on the unit crystal face accompanied by a pronounced cation rotation to maximize H-bonding with IBr. The minimum energy barriers for IBr are 0.34 and 0.24 eV for MAPbBr3 and FAPbBr3, respectively, consistent with the lower rotation barrier in MA than FA. This leads to easier reorientation to stabilize IBr (see Figure S11). Similar to VBr, IBr minimum energy pathways lie in the direction of the minimum electrostatic potential of the cation dipole. Notably, the shortest Br−Br distances for the minimum energy and transition IBr structures are 3.19 and 3.29 Å for MAPbBr3 and 3.13 and 3.14 Å for FAPbBr3, which are similar to the 3.3 Å value reported as the minimum distance between Br2 molecules in bromine crystal phases.47,48 This distance corresponds to the maximum of Br−Br noncovalent interactions that strengthen IBr bonding with the crystal Br and ease the corresponding migration in hybrid perovskites. IBr

migration barriers are remarkably low in spite of the fact that the excess Br has a relatively large atomic radius that has been inserted into the close-packed cubic perovskite framework. This result agrees with the most recent findings on halogen interstitial migration in hybrid perovskites.22 The minimum energy barriers for organic cation vacancies and interstitials are 0.70 and 0.39 eV for MAPbBr3 and FAPbBr3, respectively, which is consistent with FA having two terminal H-bonding groups that participate in stabilizing and lowering its transition state. The minimum energy barrier for IMA in MAPbBr3 is very low, 0.22 eV, in comparison to the 0.34 eV barrier in FAPbBr3; this result indicates that the dipole− dipole interactions between MA cations in the intermediate structure are more favorable to cation migration than the π−π interactions between FA cations in the intermediate structure (see Figures S12−S14). To further compare defect densities created not only during crystal growth but also as a result of Frenkel pair formation, we used the NEB method to calculate the VBr−IBr pair migration barriers in MAPbBr3 and FAPbBr3. As shown in Figures 3 and S15, both the Frenkel VBr−IBr and VMA/FA−IMA/FA pair migration barriers (>0.8 eV) of MAPbBr3 and FAPbBr3 are much higher than the barrier for Br vacancies and interstitials (the supercell structures used for calculating migration barriers are given in Figures S16 and S17). We also compared Br defect migration in the bulk and on the crystal surface, in which case we used slab models with 5477

DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480

Letter

The Journal of Physical Chemistry Letters

Figure 4. (a and c) Illustration of VBr and IBr migration pathways and (b and d) their corresponding energy profiles in MAPbBr3 and FAPbBr3 PbBr2-rich slabs.

Table 4. Migration Barriers (in eV) for Vacancy, Interstitial, and Frenkel Pair Defects in MAPbBr3 and FAPbBr3 Bulk/Slab defect

VBr

IBr

VBr−IBr

Vcation

Ication

Vcation−Ication

MAPbBr3 FAPbBr3

0.27/0.27 0.33/0.18

0.34/0.14 0.24/0.30

0.82 1.22

0.70/0.64 0.39/0.86

0.22/0.00 0.34/0.22

1.03 1.15

ion migrations can be largely suppressed by using strong Hbonding hybrid perovskite materials. In summary, we have compared at the DFT level the influence of the MA and FA cations on Br defect formation and migration in the cubic MAPbBr3 and FAPbBr3 perovskites. We find a strong correlation between the H-bonding strengths of the organic cations and the stabilization of Br vacancies and interstitials. Our results underline that, under all growth conditions, the rotation barriers of the organic cations and the formation energies for both VBr and IBr in MAPbBr3 are smaller than those in FAPbBr3 systems. Consequently, ion migration barriers in MAPbBr3 are lower than in FAPbBr3. Our results imply that incorporating organic cations with stronger Hbonding capacity and more restricted motion inside the inorganic framework is beneficial for suppressing ion migration and thus improving the performance of hybrid perovskitebased optoelectronic devices.

(MA/FA)Br-rich and PbBr2-rich surfaces for both MAPbBr3 and FAPbBr3 and aligned their z-direction (normal to the surface) with the minimum surface dipole (see the slab structures in Figure S18, and the possible pathways in Figure 4a,c). The PbBr2-rich surface energies (13.0 and 7.8 meV/Å2) for MAPbBr3 and FAPbBr3 are calculated to be much smaller surface energies than their MABr- and FABr-counterparts (43.2 and 32.5 meV/Å2), underlying the higher stability of the PbBr2-rich surface in both cases; as a result, the highly energetically strained bare (MA/FA) surfaces are not considered for calculating the defect migration barriers. As shown in Figure 4b,d and Table 4, the minimum energy barriers for VBr migration on the PbBr2-rich surfaces are 0.27 and 0.18 eV in MAPbBr3 and FAPbBr3, respectively; both are energetically favorable processes with a 0.3 eV lowering with respect to the bulk. The minimum energy barriers for IBr migration on the surface are 0.14 and 0.39 eV for MAPbBr3 and FAPbBr3. Interestingly, in FAPbBr3, the shortest Br−Br distance in the presurface IBr minimum energy structure is only 3.09 Å, which strongly stabilizes the interstitial and prevents its migration out of the FAPbBr3 bulk (see Figures S19 and S20). Similar to what happens in the bulk phase, the minimum energy barriers for VMA/FA migration on the surface are relatively high at 0.64 and 0.39 eV, while the minimum energy barriers for IMA/FA migration on the surface are very low: 0.00 and 0.22 eV in MAPbBr3 and FAPbBr3, respectively. Moreover, both IMA and IFA migrations on the surface are energetically favorable with 0.7 and 0.4 eV lowerings for MAPbBr3 and FAPbBr3 (see Figures S21−S23). The migration barriers for the defects in MAPbBr3 and FAPbBr3 are summarized in Table 4. Our results indicate that the MAPbBr3 surface tends to degrade, which is consistent with our recent experimental observation that the ion migration from the MAPbBr3 bulk to the surface promotes its surface degradation.20 Overall, we provide the detailed atomistic understanding of H-bonding strength effects on the ion migrations and suggest that the hysteresis of J−V curves in the optoelectronic devices due to

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COMPUTATIONAL METHODS Density functional theory calculations on the isolated organic cations (methylammonium and formamidinium) were performed with the B3LYP hybrid functional and 6-311G* basis set using Gaussian 09 (version: D.01). The volumes of the organic cations were calculated from 10−3 e/Bohr3 envelopes on the basis of electron density analysis. The DFT calculations on the periodic crystal structures of MAPbBr3 and FAPbBr3 were carried out at the generalized gradient approximation (GGA)/Perdew−Burke−Ernzerhof (PBE) level of theory using Quantum Espresso code (version 6.0).49 The nonrelativistic ultrasoft pseudopotentials were used to describe the electron−ion interactions.50 The cutoffs of the planewave basis sets were set to 60 and 300 Ry for the smooth part of the wave functions and the augmented charge, respectively. The unit cells of MAPbBr3 and FAPbBr3 were optimized using the Broyden−Fletcher−Goldfarb−Shanno (BFGS) relaxation algorithm with the constraint α = β = γ = 90° until the forces and stresses were less than 10−6 Ry/Bohr 5478

DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480

The Journal of Physical Chemistry Letters and 0.02 kbar. For the nondefective supercells, the lattice dimensions were fixed, and only forces were minimized until reaching 10−4 Ry/Bohr at the gamma point. The van der Waals functional (vdW-DF2)51 was included for the structural optimizations in order to take properly into account the noncovalent interactions. A 20 Å vacuum space was used between the slab images to prevent the interslab interactions. While the middle layers in the slab geometry were fixed, the surface layers were relaxed. Monkhorst−Pack-type K-meshes of 6 × 6 × 6 were used for the bulk and of 6 × 6 × 1 for the slabs. Note that the thickness was reduced to 7 atomic layers for the NEB calculations. The optimizations of the defective supercells were performed by relaxing the atomic positions near the defects (less than 10−2 Ry/Bohr) and then relaxing all the atomic positions (less than 10−3 Ry/Bohr). The nudged elastic band method was used to study ion migration by describing discrete paths of 7−13 images. The forces on each image were less than 10−4 Ry/Bohr, and the norm of the force orthogonal to the path was less than 0.03 eV/Å for rotation and 0.05 eV/Å for migration profiles. Here, the climbing image modification of NEB was used, where the highest-energy image was driven up to the saddle point without feeling the spring forces along the band.52 The first and the last images were optimized to confirm that the corresponding minimums indeed belong to the minimum energy path under consideration. Note that we performed spinunpolarized calculations because the difference in energy barriers between spin-unpolarized and polarized NEB calculations was less than 0.01 eV. The defect formation energies were calculated at three representative growth conditionsBr-poor (Pb-rich), moderate, and Br-rich (Pb-poor)using the methodology described in ref 17. The topological analysis of the electronic density was performed by exploiting the AIM-UC program.53 The VESTA code was used to visualize all the crystal structures.54

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the King Abdullah University of Science and Technology (KAUST), the Georgia Research Alliance, and the Vasser-Woolley Foundation. We acknowledge the IT Research Computing Team and Shaheen II KAUST Supercomputer for their computational and storage resources, as well as their gracious assistance.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b02522. Crystal structure of defective supercells; defect formation energies; Br and MA/FA vacancy, interstitial, and Frenkel pair defect migration pathways and

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Letter

corresponding energy profiles (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jun Yin: 0000-0002-1749-1120 Osman M. Bakr: 0000-0002-3428-1002 Jean-Luc Brédas: 0000-0001-7278-4471 Omar F. Mohammed: 0000-0001-8500-1130 Author Contributions §

A.O. and J.Y. contributed equally to this work.

Notes

The authors declare no competing financial interest. 5479

DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480

Letter

The Journal of Physical Chemistry Letters

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DOI: 10.1021/acs.jpclett.8b02522 J. Phys. Chem. Lett. 2018, 9, 5474−5480