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C: Physical Processes in Nanomaterials and Nanostructures

Role of Charge Trapping Iodine Frenkel Defects for Hysteresis in Organic-Inorganic Hybrid Perovskite From First-Principles Calculations Seong Hun Kim, and Donghwa Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01770 • Publication Date (Web): 04 Mar 2019 Downloaded from http://pubs.acs.org on March 5, 2019

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The Journal of Physical Chemistry

Role of charge trapping Iodine Frenkel defects for hysteresis in organic-inorganic hybrid Perovskite from First-Principles calculations Seong Hun Kim, and Donghwa Lee* Department of Materials Science and Engineering, and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea

Supporting Information Placeholder ABSTRACT:

First-principles density functional theory calculations are employed to provide insight into charge-trapping phenomena that leads to the I-V hysteresis in CH3NH3PbI3 (MAPbI3). Energetic studies, variation in electronic structure, and charge-density analyses show that two types of iodine Frenkel defects can be stabilized by trapping excess charge carriers in MAPbI3. As a result, these defects cause the phenomena of slow charge trapping and detrapping. Based on this insight, we propose several possible ways to eliminate charge trapping in devices based on MAPbI3.

Despite the success of hybrid organic-inorganic perovskites (OIPs)1-3, several disadvantages limit their industrial applications. First, OIPs degrade quickly in air4-6, so they must be encapsulated. They also leak toxic Pb ions7. Finally, OIPs’ current-voltage curves show hysteresis, which degrades photoconversion efficiency8-9. Since the I-V hysteresis is the variation of current depending on voltage scan rate and direction, it should be related with the change in local electronic structure under forward and reverse bias. However, the exact microscopic origin of the I-V hysteresis is under controversy. One possible source for the hysteresis is the presence of mobile ions. Since the lateral ionic transport is observed experimentally in perovskite film, many previous studies have described the origin of the I-V hysteresis using the ion migration 10-11. However, a time-dependent ion concentration in the perovskite layer suggests that variation of concentration contributes only less than 10% to the screening field 12. In addition, the migration of ions is not enough to explain the strong dependence of the hysteresis on electrode13-18. The other possible source is charge trapping/detrapping of ions. OIPs can contain trap states that impede carrier motion. Experimental study has shown that the trap density can vary between 1011 cm-3 and 1016 cm-3 depending on the film status19. Trap density can be high at interfaces and grain boundaries20-23. First-principles calculations have shown that shallow-level trap states can exist near grain boundaries24. Iodine vacancies (VI) can lead to formation of shallow trap states near the conduction band minimum25. However, fast charge trapping and detrapping of ionic defects cannot explain the scan rate dependence on the I-V hysteresis over the time range of ms to s12, 26-27. Since

Figure 1. Schematic view of (a) unit cell and (b) 2 × 2 × 2 supercell of the MAPbI3 perovskite structure. Gray: MA+; cyan: Pb2+; purple: I-. white: empty octahedral interstitial sites. Red lines: hydrogen bonding between HN and I. Sky-blue: PbI6 octahedra. both possible sources are insufficient to explain the slow modification of photocurrent, further investigation should be conducted to identify the physical origin that can slowly trap and release charges at the electrode interface. In this study, first-principles density functional theory (DFT) calculations were employed to understand the atomistic origin of charge trapping by defects in Methylammonium lead iodide (MAPbI3). This study identified that different iodine Frenkel defects (Ii+VI, IFD) can be stabilized by forming a gap state that traps electrons and holes in the presence of excess charge carriers. The variations in energetics and electronic structure under the formation of IFDs are presented. We also show that the energy barrier to formation of IFDs is high; this observation may explain the slowness of charge trapping. Finally, the effect of the formation of IFDs on the behavior of MAPbI3 is also clarified. Our findings can be used to guide development of devices based on MAPbI3.

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MAPbI3 is an OIP that has an ABX3 perovskite structure (Figure 1a) where A is a methylammonium (MA) cation, B is a Pb cation, and X is an I anion. MA cations and I anions occupy one quarter and three quarters of FCC lattice sites, respectively, and Pb cations sit at the centers of I6 octahedra. Thus, among the four octahedral interstitial sites (twelve quarters and one center) in the FCC lattice, only the central octahedral site of I6 is occupied (PbI6 cage). Consequently, the MA molecule is at the center of continuous PbI6 octahedral cages and forms hydrogen bonding with I anions at the vertices of the octahedron (Figure 1b)28. In this study, a pseudocubic structure was used to understand the atomistic origin of charge trapping by defect in MAPbI3. The pseudo-cubic structure had an octahedral tilting of a+b−b− (Glazer notation)29 with the same lattice parameter along all three directions. Our DFT calculations predicted that the energy of the pseudo-cubic structure was 0.19 eV/f.u lower than the highly-symmetric cubic structure. Hydrogen bonding between I anion and MA molecule stabilized the pseudocubic structure of MAPbI3 by tilting the PbI6 octahedron30. The tetragonal and pseudo-cubic structures showed similar energetics and electronic structures. Thus, the results discussed in this letter could also be applied to the tetragonal system. We note here that our DFT calculation is a static calculation so that dynamic effect associated with the molecular rotation of MA is not captured. Crystal structures and preferred molecular arrangements were investigated in detail (Supporting Information). We first focused on the atomistic origin of slow charge trapping/detrapping in MAPbI3. The effects of point defects are insufficient to explain slow charge variation, so we investigated various configurations in which ions moved from their lattice sites under various charge states. Our DFT calculations predicted that large MA cations or completely-enclosed Pb cations could not readily move to interstitial sites 25, 31, whereas I ions easily formed IFDs by migrating from the vertices of PbI6 octahedra to octahedral interstitial sites. The DFT calculations identified three different IFD structures, which show different energetic preferences depending on the charge state of MAPbI3. The relative energy profiles of differently charged systems were calculated as Erel [X q ] = Etot [X q ] - Etotperf + qμe + Ecorr (1) where Etot [X q ] is the total energy of the bulk or defective perf is the total energy of the perfect system X with charge q, and Etot neutral system; the electron chemical potential μe is considered to compensate for excess charge carriers in the system. Excess electrons/holes sit at the conduction band minimum (CBM)/valence band maximum (VBM), so the CBM and VBM of the perfect system were used to determine the electron chemical potential of excess charge carriers. Ecorr is the Markov–Payne correction that compensate for spurious interactions between periodically charged images using the macroscopic dielectric constant (Ɛ0 = 25.7)32-33. Further details on our calculation method are provided in supporting information The relative energy profiles of the bulk and the three IFD structures were calculated in different charge states (Figure 2a). With excess electrons (negative), one IFD structure (Figure 2b) was created preferentially. In this structure, the migration of I ions from the lattice to interstitial sites accompanied the formation of Pb-Pb bonds. The energy of IFD structure was only 0.05 eV higher than the energy of the bulk structure with two excess electrons. Further increase in the number of excess electrons increased the energetic preference for IFD. With three and four excess electrons, IFD structure became energetically 0.28 eV and 0.42 eV lower than the

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Figure 2. (a) Relative energy of bulk (black square) and three IFDs. in different charge states; reference state is the energy of bulk MAPbI3 in the neutral state. Negative charges represent excess electrons; positive charges represent excess holes. Bottom figures: schematics of (b) Pb-dimer, (c) Pb2I2, and (d) I-trimer structures. bulk structure. Thus, the accumulation of excess electrons expedited the formation of IFDs associated with Pb-Pb bonding (Pb dimers). However, this structure was unstable if the system did not have >2 excess electrons. Instead, a metastable IFD structure with an excess electron or hole (Figure 2c) was observed, in which iodine interstitial (Ii) formed Pb2I2 bonds by pushing away a nearby I ion. This structure was always energetically less stable than the bulk structure so it was a metastable configuration, regardless of the charge state of the system. When MAPbI3 gained >2 excess holes, the third IFD structure emerged (Figure 2d); in this case, the migrated I ion created additional bonds with two lattice I ions (IIi-I bond, I-trimer) and left a vacancy on the original lattice site. When >2 excess holes were present, the energetic stability of the Itrimer was 0.33 eV lower than that of the bulk structure. Similar to the case of excess electrons, the addition of excess holes further increased the stability of I-trimer structure; it was energetically 0.69 eV and 0.87 eV lower than the bulk when the number of excess holes was three and four, respectively. Although different hole trapping structure (I-dimer) has been reported,34 I-trimer is 0.29 eV more stable than simply distorted I-dimer structure under 2 excess holes (Figure S4). In summary, two distinct IFD structures were stabilized, one by the presence of >2 excess electrons, and one by the presence of >2 excess holes. Further calculation results on the energetic preference of IFDs under different carrier concentrations are provided in Table SII and Fig. S2. The formation of IFDs was accompanied by the migration of I ions from lattice to interstitial sites, so we examined the migration barrier of I ion to understand the kinetic aspects of the formation of IFD. Nudged elastic band (NEB) calculations35 (Figure S5, S6) identified that the formation of IFD was a two-step process: (1) the MA cation rotated to open space for the migration of I ion; (2) the I ion migrated from the lattice to the interstitial site. With two excess electrons (holes), the energy barrier to MA rotation was 0.17 (0.03) eV, and the energy barrier to I migration was 0.46 (0.28) eV. Therefore, the I migration step was likely the rate-limiting step during formation of IFD. We note here that the first step may not be observed at finite temperature due to the high rotational nature


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The Journal of Physical Chemistry of MA. Further increase in the number of excess electrons (holes) lowered the energy barrier to I migration, e.g., to 0.33 (0.13) eV with three excess electrons (holes). Hence, accumulation of excess electrons (holes) expedited the formation of IFDs. The reduction in the migration barrier in the presence of excess holes relative to excess electrons showed that IFD was more easily formed with excess holes than with excess electrons. Thus, IFD is expected to form faster near the anode than near the cathode. In summary, the I migration step was always the rate-limiting step to form IFD. The migration barrier was only 0.2–0.4 eV, so formation of IFDs is inevitable near both electrodes.

Figure 4. Comparison of electronic density of states (DOS) of MAPbI3 with (a) one Pb-dimer, (b) one I-trimer, (c) four Pbdimers, and (d) four I-trimers. The valence band maximum (vertical dotted line) is set to a zero eigenvalue. Black: DOS after formation of IFD by electrons or holes; red: DOS of bulk MAPbI3. In schematics: filled regions: electronically occupied states; empty regions: electronically unoccupied states. normal bond length of solid iodine (2.8 Å). Further increase in the number of excess holes increased the stability of the I-trimer. In summary, the presence of >2 excess electrons stabilized IFD structures by forming Pb-dimers, whereas >2 excess holes stabilized IFD structures by forming I-trimers.

Figure 3. Spatial locations of excess electrons (yellow) and holes (red) in bulk (a and c) and with IFDs [(b) Pb-dimer and (d) I-trimer. Red circles in (b) and (d) show VI. We focused on the variation of electronic charge density to understand the physical origin of the preferential formation of IFD with excess charge carriers. Spatial locations of the two excess electrons were different before and after the formation of IFD. Before the IFD formed, the excess electrons were distributed around Pb ions, (Figure 3a, yellow regions); this localization occurs because the conduction band (CB) is composed of p-orbitals of Pb ions33. After the IFD formed, the two excess electrons were trapped near the Pb-dimer (Pb-VI-Pb bond) (Figure 3b). The excess electrons decreased the charge states of Pb cation and VI. The charge state of VI changed from positive to negative, and the negatively-charged VI attracted two nearby Pb cations and stabilized the vacant structure by forming a Pb-dimer. The distance between the two Pb cations was initially 6.34 Å, but decreased to 3.38 Å with two excess electrons, and to 3.34 Å with three excess electrons. As a result, IFD structure became energetically stable when >2 excess electrons were present. The spatial distribution of two excess holes was also investigated before and after the formation of IFD. Before the IFD formed, excess holes were mainly distributed around the p-orbital of I anion (Figure 3c), since the valence band (VB) was composed of hybridization between the p-orbitals of I anions and s-orbitals of Pb cations33. After the IFD formed, excess holes were spatially localized on an I-trimer (Figure 3d inset: red region). Localized holes weakened the anionic character of I ions and made Ii attract two nearby I ions to form a stable I-trimer structure. The distance between I ions was reduced to 2.93 Å, which is similar to the

We studied the density of states (DOS) to understand the effect of IFD on the electronic structure of MAPbI3. The formation of IFDs led to a gap state within the bandgap. The Pb-dimer that formed in the presence of two excess electrons generated a filled gap state at 0.28 eV below the CBM (Figure 4a). Similarly, the Itrimer that formed in the presence of two excess holes created an empty gap state at 0.64 eV below the CBM (Figure 4b). Thus, both IFDs generated gap states, in which excess charge carriers were present. Bonding characteristics of the two gap states were examined in detail (Figure S7). We further investigated the creation of multiple IFDs to realize the formation of IFD clusters with excessive charge carriers near electrodes. DFT study predicted that the increase in excess charge carriers expedited the formation of multiple IFDs (Table SIV). Thus, spontaneous formation of multiple IFDs is expected when significant excess charge carriers accumulate near electrodes. Electronic DOS of MAPbI3 were calculated when four IFDs were formed with eight excess electrons and holes. Although strong structural distortion modified the shape of the DOS and led to defective states, the general DOS profile was still preserved. The formation of four Pb-dimers caused their DOS to overlap, and broadened the gap state (Figure 4c); the broadened gap state was completely occupied by eight excess electrons. Similarly, four Itrimers produced the broadened gap state, which was occupied by eight excess holes (Figure 4d). Therefore, the formation of two IFD clusters at the electrodes is inevitable: Pb-dimer clusters would form near cathode, and I-trimer clusters would form near the anode. These defect clusters trap/detrap excess charge carriers, so formation of IFD clusters may be the atomistic origin of slow charge trapping /detrapping that leads to hysteresis or other local charge modification in MAPbI3. To summarize, we propose that two different types of IFDs form near electrodes and can lead to hysteresis or slow charge modification in MAPbI3. The I-V hysteresis is known to increase with faster voltage scan rate.13 Since the faster scan rate represents



the increased applied voltage per unit time, it can enhance the accumulation of local charge at electrode interface. Our DFT calculations show that excess charge carriers can stabilize the IFD structures (Pb-dimer; I-trimer). Thus, the faster scan rate can increase the probability of the formation of IFD structures and enhance the I-V hysteresis. Formation of IFDs requires migration of I ions from lattice to interstitial sites, so the formation is much slower than charge-trapping of general point defects. Thus, MAPbI3-based devices can exhibit the I-V hysteresis that varies with the voltage scan rate over a time range of ms to s. Finally, we briefly discuss a way to improve the photovoltaic efficiency of devices using OIPs. The method involves preventing the formation of IFDs. Formation of IFDs is mainly a result of migration of I ions from the lattice to interstitial sites, so interstitial defects can suppress this formation by reducing the number of available sites35. In addition, the formation requires excess electrons or holes, so suppressing charge accumulation can also reduce the formation of IFDs. Especially, the formation of I-trimer by the accumulation of holes near anode is energetically easier than the formation of Pb-dimer by the accumulation of electrons near cathode, so use of a hole-extraction layer on the anode may significantly reduce the hysteresis.

ASSOCIATED CONTENT Supporting Information Computational methodology, relative energetic stability of I Frenkel defect, crystal structure of MAPbI3, Migration barrier of I Frenkel defect formation, bond character of I Frenkel defects are included in the supporting information. The Supporting Information is available free of charge on the ACS Publications website. Computational details (PDF)

AUTHOR INFORMATION Corresponding Author Corresponding author: [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning No. NRF-2015M1A2A2053003 and NRF2015R1C1A1A01054315 and NRF-2016M3D1A1027665 and NRF-2017R1A4A1015811 and NRF-2018M3D1A1058997. Computational resources were supported by the National Institute of Supercomputing and Network/Korea Institute of Science and Technology Information with supercomputing resources including technical support No. KSC-2016-C3-056 and KSC-2016-C3-0048.

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Figure 1. Schematic view of (a) unit cell and (b) 2 × 2 × 2 supercell of the MAPbI3 perovskite structure. Gray: MA+; cyan: Pb2+; purple: I-. white: empty octahedral interstitial sites. Red lines: hydrogen bonding between HN and I. Sky-blue: PbI6 octahedra 223x154mm (300 x 300 DPI)


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Figure 2. (a) Relative energy of bulk (black square) and three IFDs. in different charge states; reference state is the energy of bulk MAPbI3 in the neutral state. Negative charges represent ex-cess electrons; positive charges represent excess holes. Bottom figures: schematics of (b) Pb-dimer, (c) Pb2I2, and (d) Itrimer structures. 183x163mm (300 x 300 DPI)



Figure 3. Spatial locations of excess electrons (yellow) and holes (red) in bulk (a and c) and with IFDs [(b) Pb-dimer and (d) I-trimer. Red circles in (b) and (d) show VI 193x174mm (300 x 300 DPI)


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Figure 4. Comparison of electronic density of states (DOS) of MAPbI3 with (a) one Pb-dimer, (b) one Itrimer, (c) four Pb-dimers, and (d) four I-trimers. The valence band maximum (verti-cal dotted line) is set to a zero eigenvalue. Black: DOS after for-mation of IFD by electrons or holes; red: DOS of bulk MAPbI3. In schematics: filled regions: electronically occupied states; empty regions: electronically unoccupied states. 252x147mm (300 x 300 DPI)


Role of Charge Trapping Iodine Frenkel Defects for ... - ACS Publications

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