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Segregation of Native Defects to the Grain Boundaries in Methylammonium Lead Iodide Perovskite Weitao Shan, and Wissam A. Saidi J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02727 • Publication Date (Web): 21 Nov 2017 Downloaded from http://pubs.acs.org on November 21, 2017

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The Journal of Physical Chemistry Letters

Segregation of Native Defects to the Grain Boundaries in Methylammonium Lead Iodide Perovskite Weitao Shan and Wissam A. Saidi* Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States * Correspondence to: [email protected]

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Abstract Native point and grain boundary (GB) defects are ubiquitous in methylammonium lead iodide (MAPbI3) sensitizers employed in solar cells that are polycrystalline in nature. Here we use density functional theory (DFT) in conjunction with a thermodynamic approach to determine the stability and electronic properties of all native point defects and their interplays with Σ5-(210) GB in MAPbI3. The transition levels of charged defects are investigated with inclusion of electrostatic charge corrections and spin-orbit coupling. We find that the GB region is a sink for most of the native point defects under different synthesis conditions. For the crystalline and bi-crystalline MAPbI3 with Σ5-(210) GB, we find respectively that the p-type antisite defects MAI and PbI, where I substitutes for MA or Pb, introduce deep levels and both are relatively stable under I-rich conditions. Hence, I-poor conditions are more preferable for synthesis of MAPbI3 to have defects with electronically benign character. TOC graphic


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The metal halide perovskites (MHPs) facilitate solar devices that combine the low processing costs of organic semiconductors with the high power conversion efficiencies (PCE) of inorganic semiconductors. Currently, the PCE of MHP based solar cells is 22.1%,1-11 which is almost commensurate with state-of-the-art copper indium gallium diselenide (CIGS) and CdTe solar cells.12-13 Based on extensive studies on methylammonium halide perovskites MAPbX3 (MA=CH3NH3; X=Cl, Br, I) and especially MAPbI3, it is largely believed that these solar sensitizers have many unique properties, such as high optical absorptions14-15, small effective mass for charged carriers16-17, long electron-hole diffusion lengths18-19, and shallow dominant point defects16, 20-21. Several theoretical studies investigated the formation energies of the native defects in MHPs under different synthesis conditions to ascertain which defect type would negatively affect the solar efficiency. For the high-temperature cubic crystalline MAPbI3 phase, it was found that defects with low formation energies only create shallow levels14, while as defects which cause deep trap levels are not thermodynamically favorable20. Similar conclusions are also found in the all-inorganic lead halide perovskites.22-23 It was also found that Schottky defects such as MAI and PbI2 vacancies have no midgap states, as well as other vacancy defects in the orthorhombic MAPbI3.21 Other studies on the room-temperature tetragonal-phase of MAPbI3 showed that incorporating Cl can passivate deleterious defects with deep levels.16, 24 MHP thin films employed in solar cells are typically polycrystalline materials25, which is unlikely to change considering that the growth of large crystalline materials is quite challenging and not cost-effective.25-26 In standard semiconductor based solar materials, intrinsic GB disorders are generally considered extremely harmful to the optical performance as these create deep levels in their bandgaps27-31 and act as recombination centers of charge carriers32-34. Unlike the case of the point defects, the effects of GBs on the conversion efficiency in MHPs is still under debate. Experimentally, there is increasing evidence that the larger grain size in the MHP sensitizers


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results in better photovoltaic performance and less hysteresis. This could be due to reducing the recombination rates that can take place in the GB region because of their high charge-trap densities.35-40 However, Yun et al. argue for the beneficial roles of GBs in separating charges and collecting carriers efficiently.41 First-principles investigations mainly focused on the impact of GBs on the electronic nature of the MHPs. Yan’s group suggest that GBs in MAPbI3 do not create deep midgap levels in the bandgap and are thus electronically benign.14, 31 Another recent study by the same group argues that the GB-induced defect state in Σ5-(310) is close to the valence band maximum (VBM), and thus acts as a shallow trap state that can hinder the hole diffusion.42 Also, in a recent study43, we investigated different low energy grain boundaries in CsPbX3 (X=Cl, Br and I) and showed that GB defects have little effect on the band structure in agreement with previous conclusions on MAPbI314, 31, 43. Long and Prezhdo argue on the other hand that GBs are not electronically benign because they accelerate the electron-hole recombination rates in MAPbI3.44 The existence of these controversies between the different studies underscores the complexity of the system. More investigations are warranted to shed more light on the influence of the GBs on the PV performance. To date, the interplay between native point defects and extended grain boundary defects in the hybrid perovskites has not been investigated. In this Letter, we employ a thermodynamic approach in conjunction with density functional theory (DFT) to determine the stability of all native defects in MAPbI3 under different experimental conditions. Our DFT methodology accounts for van der Waals (vdW) and spin-orbit coupling (SOC) corrections that we show to be appreciable, as well as for the fictitious electrostatic interactions between periodic charged defects. We focus our study on the Σ5-(210) GB that has low formation energy based on our previous study of GBs in CsPbX3 systems43. Our results demonstrate that there is a strong segregation of most point defects to the GB region under all synthesis conditions. Defects that are stable in the bulk normally have also low formation energies in the GB region; however, few


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unstable defects in the bulk, such as MAi and Pbi, become stabilized in the GB region. Under Irich synthesis conditions, two detrimental defects MAI and PbI have low formation energies respectively in the bulk and Σ5-(210) GB regions. MAI is also a metastable defect in the bulk under moderate synthesis conditions. Both of these defects have a deep transition level and thus can act as Shockley-Read-Hall nonradiative recombination centers that can harm the PCE. Other deep-level defects in both crystalline and polycrystalline MAPbI3 are confirmed not to be energetically favorable. Thus, we conclude that I-poor synthesis conditions are more preferable for electronically defect-benign polycrystalline MAPbI3. In our DFT45-49 calculations, the Perdew-Burke-Ernzerhof (PBE)50 generalized gradient approximation (GGA)51 were employed as implemented in FHI-aims52-55. Further, we used van der Waals corrections based on Tkatchenko-Scheffler (TS) dispersion56-57 which has been shown to be important for the hybrid perovskites.58 We computed spin-orbit coupling (SOC) corrections to the electronic band structure non-self-consistently using FHI-aims,59 and to the energies with self-consistency using Vienna ab-initio simulation package (VASP)60-63. The room-temperature tetragonal phase of MAPbI3 is adopted in our calculations. SOC was found to have a significant effect on the bandgap and optical absorption results of MAPbI3 perovskites, which is due to strong relativistic effects in heavy metals such as Pb and dominant 6p character of the conduction band.64 Importantly, we demonstrate that SOC corrections are significant not only for the band structure, which is widely acknowledged,65 but also for the computed energies. For example, we show that SOC can lower the formation energy on average by 0.3 eV, and up to 0.7 eV for some antisite defects. Also, we found that SOC corrections stabilize the tetragonal phase by 0.26 eV, as we discuss in the SI. The Σ5-(210) GB was generated by rotating the crystal lattice around the by θ = 53.13° (Figure S1), as the interface between two grains is located on the (012) plane (Figure 1). The Σ value is used for describing the coincident level of the GB, which is the


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ratio between the volume of CSL primitive cell and the volume of crystalline primitive cell. More details about the computational approach and validations are presented in the SI. The formation energy of a defect with charge q is calculated using:

= − ± ( + ) + ( + + ∆) + .

Here and are the energies of the defective structure with charge and pristine structure, µi is the chemical potential change of the ni component with respect to its ground state energy Ei (more details are in SI), is the energy level of VBM of the pristine structure and is the Fermi level measured with respect to . In the formation energy, the potential

alignment term ∆ and the charge correction term account a posteriori for the fictitious long-range electrostatic defect-defect interactions based on Freysoldt et al66 as implemented in Ref. 67. The defect formation energies are computed using 1×1×1 and 2×2×2 tetragonal supercells to assess finite size effects (see SI). We will use rather than to indicate the formation energy of a neutral defect for simplicity. The transition level !(⁄ " ) is defined as the Fermi energy under which the formation energies of two defects states with charges and " are equal, i.e., !(⁄ " ) =

"

1 ) (,&'( − ,&'( ) −

This indicates that under this condition, it is energetically favorable for the defect to gain or loss electrons and change its charge state between and " . Considering only the native defects of the tetragonal bulk phase, there are three vacancies (Iv, Pbv, MAv), three interstitials (Ii, MAi, Pbi) and six antisite defects (IMA, MAI, PbI, IPb, PbMA, MAPb), where AB indicates that A is substituted by B. We categorize the defect sites according to either


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belonging to MAI or PbI2 layers viewed along , as schematically shown in Figure 1b. The investigations of the equilibrium defect structures in the GB region are more complicated than the bulk case because the GB region has less symmetry and thus more potential defect sites. Fortunately, for the tilt Σ5-(210) GB, the existence of the mirror symmetry with respect to the GB plane perpendicular to the c-axis direction (see Figure 1c) significantly reduces the number of potential sites. In our study, we considered all non-equivalent potential sites totaling 8 for vacancy, 16 for antisite and 18 for interstitial defects. To explore the impact of the synthesis condition on the formation energies of the defects, we discuss the most stable defects under three different chemical growth conditions: I-rich, moderate and I-poor, which are schematically shown as A, B and C points in Figure S2 and explicitly defined in the SI. Vacancy. Pbv and MAv have the lowest under I-rich conditions for bulk and GB vacancy defects, which are lower than the most stable vacancy Iv under I-poor conditions (Figure 2). The formation energies of the bulk vacancy defects are slightly lower than previously reported

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,

which we verified to be due to the inclusion of SOC and vdW corrections in our study. Interstitial. We chose the largest hollow sites on MAI and PbI2 layers as potential interstitial + + +

positions. As shown in Figure 1b, these are located between two MA molecules at *, , , , ,- in the bulk unit cell for MAI layer, and in the middle of the unit cell edge for the PbI2 layer, which makes them respectively similar to the tetragonal and octahedral interstitial sites in FCC crystals. In crystalline MAPbI3, Ii located on the MAI layer has the lowest formation energy, which is stabilized by a newly formed Pb-I bond with the neighboring Pb atom. We find that the split I interstitial defect (two I atoms occupy one I site) that was reported before16 not to be stable, which could be due to finite size effects as we employ a larger supercell than used in Ref. 16. In contrast to the low formation energy of Ii, MA (stable on MAI layer) and Pb (stable on PbI2 layer)


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interstitials are found to have higher formation energies (seen in Figure 2) owing to the significant structural deformations they induce in the inorganic framework mainly due to their large size. In the GB, the interstitial defects are still stable on the same layer as in the bulk, but the excess volume associated with GBs results in lower formation energy for interstitial defects even for MAi and Pbi. Antisite. The lowest-energy antisite defects in bulk are MAI and PbMA under I-rich conditions, and MAPb under I-poor conditions. These defects have also very low in the GB region (Figure 2). Additionally, PbI is the lowest energy defect under I-rich conditions for the GB case, although it has a relatively high in bulk. The negative formation energies for the GB defects such as PbI and PbMA under I-rich conditions could be due to the chosen reference states of the different species, or could indicate that these defects can occur spontaneously. This is not uncommon and has been reported before for GB defects in other materials.68-70 The low of MAI or PbI is due to the formation of an I trimer from the substituting I and two neighboring I atoms (see Figure S3). In contrast, the formation of the Pb trimer (Figure S4) in the bulk is not favorable as this will break atomic bonds and leave dangling bonds as in IPb. This is also the case in the GB except that IPb results in the formation of a new Pb-I framework in GB, which eliminates the dangling bonds and results in lower defect formation energy. The extra stability of the I3 complex in contrast to Pb3 complex can be understood due to charge rearrangements, as discussed in the SI. Figure 3 shows the transition levels associated with the most stable point defects in both crystalline and polycrystalline MAPbI3. Here, the range of changes of the Fermi energy is limited to the bandgap of the system, which is 0.76 eV for crystalline system and 0.86 eV for Σ5-(210) GB. Though the PBE-SOC bandgap underestimates the experimental value, a previous study showed that this functional still yields good description of transition levels comparable to those obtained using HSE-SOC71. Also, previously we found that PBE-SOC yields a good description of energy level renormalization with temperature that is comparable to that obtained using HSE-


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SOC.72 Typically, mono-charge defects introduce shallow states near the conduction band for donor defects or valence bands for acceptor defects, while as defects with larger charge introduce deep-level states in the bandgap (or trap states).73 We can see that the transition levels largely abide by these rules. Here, we consider defects to be shallow if their transition levels are located in the bandgap within 6/ 0 ≈ 0.155 4 from valence band maximum (VBM) or conduction band minimum (CBM), where / is the Boltzmann constant and 0 is room temperature. Defects with deep level in the bandgap indicates difficulty of being ionized at room temperature, which can result in the capture of both electrons and holes as recombination centers. The crystalline transition levels in Figure 3a are in agreement with previous results

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except for

the I interstitial, which is due to the differences in the atomic structure as discussed before. Only two antisite defects, IPb and MAI, are found to have deep-level defect in the bandgap. Both of these two defects possess a negative-U behavior, which is usually associated with strong structural relaxations that can strongly trap an electron at a defect site (polaron state). For instance, the (+3/+2) level of IPb is higher than the (+2/+1) level, which indicates that +2 charge state is a metastable state, and thermodynamically the charge can transition directly from +3 to +1. For the GB case, PbI and Pbi are two deep-level defects but do not form negative-U centers. We also investigated the band structures of pristine and defective structures of both crystalline and bicrystalline MAPbI3 perovskites, which can be found in our SI. Most defects have lower formation energy in the GB region than in the grain interior, as can be seen in Figure 2. For example, for the vacancy defects, GB Iv and MAv have ~0.3 eV lower than the corresponding bulk values under both I-poor and I-rich conditions. Also, all interstitials in the GB have lower than the corresponding bulk values, which is not surprising considering the excess volume introduced by the GB configuration.74 We also show that most antisite defects in the GB have lower than the corresponding bulk values, except for IMA, MAI and MAPb, which have very similar energies as in bulk. Using the Boltzmann distribution


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