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Modeling the Interaction of Molecular Iodine with MAPbI3: A Probe of Lead-Halide Perovskites Defect Chemistry Daniele Meggiolaro, Edoardo Mosconi, and Filippo De Angelis ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.7b01244 • Publication Date (Web): 18 Jan 2018 Downloaded from http://pubs.acs.org on January 18, 2018

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ACS Energy Letters

Modeling the Interaction of Molecular Iodine with MAPbI3: A Probe of Lead-Halide Perovskites Defect Chemistry Daniele Meggiolaro,a,b Edoardo Mosconi,a,c * Filippo De Angelis a,b,c *

a

Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, Via Elce di Sotto 8, 06123, Perugia, Italy. b

c

D3-CompuNet, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy.

Consortium for Computational Molecular and Materials Sciences (CMS)2, Via Elce di Sotto, 8, 06123 Perugia, Italy.

TOC graphics

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Abstract Understanding the defect chemistry of lead-halide perovskites is of paramount importance to further progress towards exploitation of these materials. Here we combine recent experimental observations on the behavior of MAPbI3 upon exposure to I2 vapor with first-principles calculations to extract a global picture of defect chemistry in lead-halide perovskites. By matching the reported experimental observables we disclose the origin of the p-doping observed upon exposing MAPbI3 to I2 and highlight its consequences on the charge/ion transport and trapping activity. Electron/hole traps related to positive/negative interstitial iodine dominate the defect chemistry in intrinsic conditions, while in p-doped MAPbI3 electrons are mainly trapped by positive interstitial iodine and neutral lead vacancies. I2 spontaneously dissociates on iodine vacancies, leading to vacancy passivation and to the formation of positive interstitial iodine. I2 spontaneously dissociates on nondefective MAPbI3 (001) surfaces to form pairs of negative/positive interstitial iodine. Upon trapping a hole/electron pair at negative/positive interstitial iodine, I2 release becomes thermodynamically favored possibly representing a photo-induced trap curing mechanism.


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Understanding the defect chemistry of lead-halide perovskites is of paramount importance to further progress with the practical solar cell exploitation of this outstanding class of materials. The long lifetimes and diffusion lengths of photogenerated charge carriers in MAPbI3 and related perovskites are suggestive of an apparently low density of charge traps. Clearly, a distinction should be made between defects and traps, since most of typical defects in conventional perovskites turn out to be only shallow traps in MAPbI3.1-4 This, coupled to large polarons protecting photogenerated charge carriers,5, 6 has generated the concept of the what is generically referred to as “perovskite defect tolerance”. One must recognize that defect tolerance, in the general meaning, is a fundamental ingredient of the astonishing properties of this materials class, which would otherwise probably only have a mere academic interest. Most experimental investigations provide indirect hints on defects, mainly determining the density of trap states through electrical conductivity measurements. Very low trap densities of ∼1010-1011 cm-3 have been reported for MAPbI3 single crystals,7, 8 increasing up to ∼1016 cm-3 for polycrystalline thin films.8-10 Disclosing the properties of defects in a semiconductor with atomistic resolution can be accessed through first-principles calculations, which are however limited by the scale of employed models and the intrinsic accuracy the underlying electronic structure theory. Here we sought to combine a survey of recent experimental observations on the behavior of MAPbI3 upon exposure to molecular iodine vapor with high level first-principles calculations to extract a global picture of defect chemistry in lead-halide perovskites. We thus use the effect of I2 exposure to MAPbI3 as a probe of the underlying material defect chemistry. By matching the reported experimental observables to our model defect chemistry, we disclose the origin of the observed pdoping upon I2 exposure and highlight its consequences on the charge/ion transport and trapping activity. To our knowledge, four studies have reported on the interaction between I2 vapors and MAPbI3.11-14 Here we briefly summarize the main findings of these studies which are relevant to the present work: 3 ACS Paragon Plus Environment


1) Formation of metallic lead, as revealed by XPS, related to degradation of the perovskite.11 2) 150 mV shift of the Fermi energy towards the valence band, indicative of p-doping.13 3) Irreversibility of the p-doping.11, 13 4) Quenching of the photoluminescence quantum yield.12 5) Increase of electrical conductivity due to holes. 14 6) Decrease of the ionic conductivity.14

We begin by re-investigating native defects in MAPbI3 by state of the art first-principles calculations in 2x2x1 tetragonal supercells using hybrid DFT, including dispersion corrections and spin-orbit coupling (SOC). We use the modified HSE06 exchange-correlation functional including 43% exact exchange proposed in Ref. 15, which provides band edge energetics comparable to highlevel GW-SOC calculations.16 Hybrid functionals are important to characterize defects with unpaired electrons,17, 18 such as the neutral Ii0 and VI0 defects. The central quantity to our discussion is the Defect Formation Energy (DFE), see Supplementary Information. Knowledge of the DFE of relevant defects in different charge states allows one to calculate: i) the thermodynamic ionization levels, correspond to oxidation and reduction potentials of the defective system, whose energy with respect to the band edges determine the defect trapping activity; ii) the defect density; and iii) the native Fermi level of the system.19 The DFE diagram of MAPbI3 grown in iodine medium (corresponding to 1:1 ratio of the PbI2 and MAI precursors) and excess I2 vapors are reported in Figure 1a and 1b, respectively; the associated thermodynamic ionization levels are reported in Figure 1c.


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ACS Energy Letters

Figure 1. DFEs diagrams calculated by SOC-HSE06 in iodine medium conditions (a) and under a

simulated I2 pressure of 10-4 atm (b); c) Thermodynamic transition levels, which are independent of the growth conditions. In iodine-medium conditions the most stable defects are MA interstitials (MAi+), negative interstitial iodine (Ii-) and lead vacancies (VPb2-), which pin the Fermi level at mid-gap (0.71 eV above VBM over a 1.58 eV calculated band gap), Figure 1a. Positive interstitial iodine (Ii+) and iodine vacancy (VI+) have a ∼0.2 eV higher DFE, while interstitial lead (Pbi2+) lies at much higher DFE. The close to mid-gap native Fermi level is consistent with the intrinsic (or mildly p-doped) nature of MAPbI3,13, 20 while thin films show n-doping related to a Pb-rich surface environment.21 To properly account for defect activity, the defect activation energy to migration should be taken into account, since the presence of defects with high activation energy could be kinetically limited. Defects related to I and MA ions are the major migrating species,22-24 with I faster than MA, faster than Pb migration.25 Recent X-ray and neutron diffraction measurements on MAPbI3 revealed significant structural disorder associated to interstitial iodine in MAPbI3 films.26



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Table 1. DFEs and defect densities calculated in iodine-medium and at I2 partial pressure of 10-4

atm. P(I2) = 10-4 atm

iodine-medium Defect

DFE (eV)

Density (cm-3)

DFE (eV)

Density (cm-3)

VPb2-

0.66

∼ 1010

0.44

∼ 1014

VPb0

1.10

∼ 103

0.71

∼ 1010

MAi+

0.57

∼ 1012

0.69

∼ 1010

Ii+

0.72

∼ 1010

0.44

∼ 1014

Ii-

0.60

∼ 1012

0.49

∼ 1014

VI +

0.87

∼ 107

0.98

∼ 106

Pbi2+

1.16

∼ 102

1.38

∼0

Interstitial iodine is an amphoteric defect that can trap both electrons and holes with +/0 and 0/- ionization levels placed at 0.57 and 0.30 eV below and above the CB and VB edges, Figure 1c. Notice that the neutral state of interstitial iodine is unstable, 15 similar to the typical iodine chemistry whereby I2- (or a neutral I atom) is unstable with respect to I- and I3-.27 The metastable nature of Ii0 implies that Ii- should trap two holes to convert to Ii+, with the (-/+) transition placed at mid-gap; the two-electron nature of the process, however, imparts it a vanishingly small cross section since the probability of two consecutive trapping events at the same defect site is vanishingly small. VI+ has a transition level resonant with the CB, thus although showing a low activation energy to migration,28 it can at most represent a shallow trapping site in bulk crystals. VPb is stable in the 2- charge state in 6 ACS Paragon Plus Environment

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a wide range of Fermi energies, thus this defect can trap holes by the (-/2-) transition level whose energy falls 0.15 eV above the VBM, suggesting a shallow trapping activity. The (0/2-) transition implies the trapping of two holes on the same defect site, and as such it has a vanishingly small capture cross section. The deep (0/-) transition falling at mid-gap is not active in iodine-medium conditions due to the low density of VPb0, see Table 1. Notably, VPb0 decomposes into VPb2- + Ii+ + VI+ on the same site, which is more stable than the simple neutral Pb vacancy by 0.40 eV. The (0/-) ionization level of VPb is thus the analogous of the (+/0) transition of Ii, falling approximately in the same energy range. As previously mentioned, lead vacancies have a large (∼1 eV) migration barrier,28 thus their formation could be kinetically limited. In iodine-medium conditions the main deep electron and hole traps among native defects are thus related to interstitial iodine. The match between the calculated Ii+/- density (~1010-1012 cm-3, see Table 1) and the measured trap density points at Ii+ and Ii- as the experimentally observed electron and hole traps in MAPbI3 single crystals.7 By increasing the iodine partial pressure, mimicking experiments in which the perovskite is exposed to I2 vapors, we are shifting the equilibrium towards iodine-rich conditions. To quantify the chemical potential shift due to exposure of MAPbI3 to I2 pressures of the order of ∼10-4 atm employed in experiments,13,

14

we calculated the variation of I2 chemical potential induced by

pressure referred to iodine rich conditions as: ∆µ= -RT ln(P/P0) -T∆St

(2)

where P is the actual pressure referred to the standard P0=1 atm, T is the absolute temperature (300 K here), and ∆St is the variation of translation entropy of I2 gas with pressure estimated assuming an ideal gas behavior, see Table S1, Supporting Information. We verified that other terms in the Gibbs free energy (e.g. thermal contributions to enthalpy due to vibrations, and rotational-vibrational contributions to entropy) remain roughly constant in the explored pressure variation range. Notice 7 ACS Paragon Plus Environment


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that variation of the chemical potential of a gaseous species in a sizable range (0.2 eV or more) is easily achieved by varying its partial pressure, while tuning the chemical potential of a species in solution by a factor ∼2.3 RT (∼0.06 eV) implies variation of its activity (concentration) by 1 order of magnitude, a situation which can be hardly realized in standard perovskite synthetic conditions. Upon exposing MAPbI3 to I2 the most notable effect is the stabilization of positive interstitial iodine and lead vacancies, Figure 1b, with a consequent p-doping of the material. Accordingly, the calculated Fermi level shifts by 80 meV, from 0.71 to 0.63 eV above the VBM, consistent with the 150 mV work function increase measured by Zohar et al.13. The increase in electric conductivity associated to hole transport observed by Senocrate et al.14 is also readily explained since holes are the dominant free carriers under p-doped conditions and their concentration is predicted to increase by ~3 orders of magnitudes a consequence of the observed pdoping. Our results are also consistent with the formation of metallic lead observed by Wang et al. upon exposure of MAPbI3 to I2,11 related to the stabilization of lead vacancies, i.e. the expulsion of lead from its bulk crystal site. Under p-doped conditions the main charge trap is now Ii+ (and to a lesser extent VPb0) whose density increases by several orders of magnitude compared to intrinsic conditions, see Table 1. Both defects can effectively trap electrons, thereby explaining the photoluminescence quenching observed by Li et al. after MAPbI3 interaction with I2.12 Our model has so far allowed us to rationalize most of the experimental observations related to I2 exposure, with the exception of the decreased ionic conductivity measured by Senocrate et al.14 These authors ascribed such behavior to the saturation of iodine vacancies, implying a mechanism of iodine incorporation mediated by vacancies. This seems a perfectly reasonable explanation, since iodine vacancy sites would “attract” mobile iodine atoms

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from I2 to restore a perfect crystal

lattice. Ion conductivity is a function of both the density of ionic migrating species and their migration energy barrier. A decrease in ionic conductivity can be either caused by a reduction of the density of migrating defects (e.g. iodine vacancies) or by an increase of the migration energy 8 ACS Paragon Plus Environment

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barrier, or both. In this respect, one should notice that iodine vacancies are stable in their positive charge state in all conditions, meaning that to preserve electroneutrality I2 dissociation in a vacancy should also imply formation of a positive interstitial iodine, as: VI+ + I2→perf + Ii+

(3)

where perf means the perfect crystal. We first calculated the thermodynamics for reaction (3) in a tetragonal 2x2x2 bulk MAPbI3 supercell, finding it favorable by 0.39 (0.72) eV with no corrections (including dispersion and entropic corrections, see Computational Details). Thus vacancy filling by I2 is in all cases a thermodynamically favored reaction which produces Ii+. The question is now whether positive interstitial iodine has a higher migration energy barrier than a positive iodine vacancy. To check this point we searched for the minimum energy pathway to Ii+ migration, by scanning the potential energy surface along a displacement coordinate, followed by short ab initio molecular dynamics simulations to properly allow for local atomic rearrangement.22 This procedure is expected to deliver lower activation energies than standard calculations by virtue of the effective relaxation around the migration pathway. In Table 2 we report migration energy barriers for relevant defects calculated at the SR-PBE level used for geometry optimizations and refined by SOC-HSE06. Table 2. Migration energy barriers (eV) calculated by SR-PBE and SOC-HSE06 levels of theory on

the SR-PBE optimized geometries. SR-PBE

SOC-HSE06

VI +

0.09

0.11

Ii+

0.19

0.24

Ii-

0.08

0.06



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As it can be noticed, SR-PBE and SOC-HSE06 levels of theory provide similar activation energies. Notably, while VI+ and Ii- have roughly the same energy barrier, we predict a factor 2 increase in the migration energy barrier for Ii+ compared to VI+, from ∼0.1 to ∼0.2 eV, consistent with the decrease of ionic conductivity experimentally measured in Ref.

14

. This points at saturation of iodine

vacancies by I2 leaving behind an Ii+ defect, further contributing to p-doping and photoluminescence quenching. Besides the vacancy saturation pathway, I2 could possibly interact with both the intact perovskite bulk and surfaces. A recent computational study reported the favorable interaction of I2 with MAPbI3 surfaces, leading to split iodine interstitials.30 To investigate the energetics and structural features of this processes in the bulk and on surfaces, we explicitly added one I2 molecule to a bulk 2x2x2 MAPbI3 tetragonal supercell and to MAI-terminated 2x2x3 slabs exposing (001) and (110) facets, see Figure 2 and Supporting Information. In these cases the MA cations were initially aligned antiparallel to quench the molecular dipole. Most notably, I2 is not stable in its molecular form and spontaneously dissociates into a positive and a negative interstitial iodine (Ii+ and Ii-), similarly to what found by Zhang et al. 30, being stabilized by the bond with I and Pb atoms, respectively, see Figure 2.

Figure 2. a) Starting bulk MAPbI3 structure with added I2 (yellow atoms) and b) final relaxed

structures. Notice in b) the formation of the typical Ii+ trimer and Ii- dimer. c) Optimized structure of I2 added at the MAI-terminated MAPbI3 surface (001) facet, delivering the same Ii+/ Ii- pair. I-I distances (Å) are also reported. 10 ACS Paragon Plus Environment

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I2 incorporation into bulk MAPbI3 is unfavorable (favorable) by 0.40 (0.02) eV with no corrections (including dispersion and entropic corrections), so we expect the vacancy-mediated I2 incorporation mechanism to dominate the bulk chemistry. The Ii+ / Ii- intimate defect couple is more stable than the non-interacting Ii+ and Ii- defects by ~0.15 eV. This means that formation of interacting Ii+ and Ii- defects, which is possible due to their low barriers to migration, could increase their density in bulk MAPbI3. I2 dissociation becomes thermodynamically favorable by 0.73 (0.16) eV on MAPbI3 (001) facets with no corrections (with corrections) forming the same Ii+ / Ii- interacting defect couple, see Figure 2c.30 Notably, I2 dissociation is unfavorable by 0.10 eV on the (110) facet, see Supporting Information, suggesting a different reactivity of the various MAPbI3 surfaces. I2 dissociation at surfaces could thus still represent a pathway of VI+ saturation. The calculated thermodynamics is consistent with the irreversibility of the p-doping observed in Ref.

12

. This is at variance with

MAPbI3 interaction with O2, which is characterized by a much smaller interaction energy, accounting for the reversibility of the reaction.31 Finally, it is interesting to notice that the energetics of I2 dissociation and incorporation at surfaces can be reverted when introducing an electron/hole pair into the system. By simulating the lowest triplet state of the MAPbI3 (001) surface with the Ii+ / Ii- interacting defect couple, we find that destabilization of neutral interstitial iodine by electron/hole trapping at Ii+ / Ii-, respectively, leads to spontaneous I2 release from the surface, which is now favorable by 0.19 (0.74) eV with no corrections (with corrections). This I2 formation pathway following electron/hole capture may constitute a source of light-induced trap annihilation, analogously to the previously proposed Frenkel (vacancy/interstitial) mediated pathway.28 The main difference between the two mechanisms is that since I2 would remain close to the perovskite surface, unless it is evacuated as a gas, it may reversibly re-dissociate to reform the electron/hole Ii+ / Ii- trapping defects. In a typical experiment in which MAPbI3 is exposed to inert atmosphere (by e.g. N2) while irradiating the 11 ACS Paragon Plus Environment


sample, we thus predict that increasing (decreasing) the pressure of N2 will lead to a decrease (increase) of the effectiveness of light-induced trap annihilation, by disfavoring (favoring) the exit of gaseous I2. At the same time, removing the formed I2 by e.g. fluxing N2 could lead to more effective and partly irreversible decrease in the material trap density. In summary, we have constructed a global picture of defect chemistry in lead-iodide perovskites. Under intrinsic conditions, i.e. when the Fermi level is close to mid-gap, positive and negative interstitial iodine constitute the main source of electron and hole traps, respectively. Upon exposing the material to I2 a Fermi level down shift is calculated, which closely matches the experimental work function variation. I2 dissociates on iodine vacancies restoring the pristine crystal but leaving behind positive interstitial iodine. The higher migration energy barrier of positive interstitial iodine compared to iodine vacancy accounts for the decreased ionic transport, while the associated p-doping increases the hole electrical conductivity. Notably, I2 dissociates both in the bulk and on surfaces to produce a pair of positive/negative interstitial iodine defects, with the reaction being strongly favored on (001) surfaces. Upon light irradiation, a hole and an electron can be trapped at the positive/negative interstitial iodine defect pair, leading to destabilization of the defect pair and I2 exit from the perovskite. This may represent an additional pathway of lightinduced defect annihilation. Supporting Information Available: Computational Details, (110) structures, I2 chemical

potentials. References:

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(5) Miyata, K.; Meggiolaro, D.; Trinh, M. T.; Joshi, P. P.; Mosconi, E.; Jones, S. C.; De Angelis, F.; Zhu, X. Y. Large polarons in lead halide perovskites. Sci. Adv. 2017, 3. (6) Zhu, X. Y.; Podzorov, V. Charge Carriers in Hybrid Organic–Inorganic Lead Halide Perovskites Might Be Protected as Large Polarons. J. Phys. Chem. Lett. 2015, 6, 4758-4761. (7) Adinolfi, V.; Yuan, M.; Comin, R.; Thibau, E. S.; Shi, D.; Saidaminov, M. I.; Kanjanaboos, P.; Kopilovic, D.; Hoogland, S.; Lu, Z.-H.; Bakr, O. M.; Sargent, E. H. The In-Gap Electronic State Spectrum of Methylammonium Lead Iodide Single-Crystal Perovskites. Adv. Mater. 2016, 28, 3406-3410. (8) Chen, Y.; Yi, H. T.; Wu, X.; Haroldson, R.; Gartstein, Y. N.; Rodionov, Y. I.; Tikhonov, K. S.; Zakhidov, A.; Zhu, X. Y.; Podzorov, V. Extended carrier lifetimes and diffusion in hybrid perovskites revealed by Hall effect and photoconductivity measurements. Nat. Commun. 2016, 7, 12253. (9) Leijtens, T.; Eperon, G. E.; Barker, A. J.; Grancini, G.; Zhang, W.; Ball, J. M.; Kandada, A. R. S.; Snaith, H. J.; Petrozza, A. Carrier trapping and recombination: the role of defect physics in enhancing the open circuit voltage of metal halide perovskite solar cells. Energy Environ. Sci. 2016, 9, 3472-3481. (10) deQuilettes, D. W.; Vorpahl, S. M.; Stranks, S. D.; Nagaoka, H.; Eperon, G. E.; Ziffer, M. E.; Snaith, H. J.; Ginger, D. S. Impact of microstructure on local carrier lifetime in perovskite solar cells. Science 2015, 348, 683-686. (11) Wang, S.; Jiang, Y.; Juarez-Perez, Emilio J.; Ono, Luis K.; Qi, Y. Accelerated degradation of methylammonium lead iodide perovskites induced by exposure to iodine vapour. Nat. Energy 2016, 2, 16195. (12) Li, C.; Guerrero, A.; Zhong, Y.; Gräser, A.; Luna, C. A. M.; Köhler, J.; Bisquert, J.; Hildner, R.; Huettner, S. Real-Time Observation of Iodide Ion Migration in Methylammonium Lead Halide Perovskites. Small 2017, 13, 1701711-n/a. (13) Zohar, A.; Levine, I.; Gupta, S.; Davidson, O.; Azulay, D.; Millo, O.; Balberg, I.; Hodes, G.; Cahen, D. What Is the Mechanism of MAPbI3 p-Doping by I2? Insights from Optoelectronic Properties. ACS Energy Lett. 2017, 2, 2408-2414. (14) Senocrate, A.; Moudrakovski, I.; Kim, G. Y.; Yang, T.-Y.; Gregori, G.; Grätzel, M.; Maier, J. The Nature of Ion Conduction in Methylammonium Lead Iodide: A Multimethod Approach. Angew. Chem. Int. Ed. 2017, 56, 7755-7759. (15) Du, M.-H. Density Functional Calculations of Native Defects in CH3NH3PbI3: Effects of Spin– Orbit Coupling and Self-Interaction Error. J. Phys. Chem. Lett. 2015, 6, 1461-1466. (16) Umari, P.; Mosconi, E.; De Angelis, F. Relativistic GW calculations on CH3NH3PbI3 and CH3NH3SnI3 Perovskites for Solar Cell Applications. Sci. Rep. 2014, 4, 4467. (17) Alkauskas, A.; Pasquarello, A. Band-edge problem in the theoretical determination of defect energy levels: The O vacancy in ZnO as a benchmark case. Phys. Rev. B 2011, 84, 125206. (18) Iwata, J.-I. S., Keisuke; Oshiyama, Atsushi A precaution for the hybrid density functional calculation of open-shell systems. 2016, arXiv:1605.00338. (19) Van de Walle, C. G.; Neugebauer, J. First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys. 2004, 95, 3851-3879. (20) Shi, D.; Adinolfi, V.; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland, S.; Rothenberger, A.; Katsiev, K.; Losovyj, Y.; Zhang, X.; Dowben, P. A.; Mohammed, O. F.; Sargent, E. H.; Bakr, O. M. Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals. Science 2015, 347, 519-522. (21) Sadoughi, G.; Starr, D. E.; Handick, E.; Stranks, S. D.; Gorgoi, M.; Wilks, R. G.; Bär, M.; Snaith, H. J. Observation and Mediation of the Presence of Metallic Lead in Organic–Inorganic Perovskite Films. ACS Appl. Mater. Interfaces 2015, 7, 13440-13444. (22) Azpiroz, J. M.; Mosconi, E.; Bisquert, J.; De Angelis, F. Defect migration in methylammonium lead iodide and its role in perovskite solar cell operation. Energy Environ. Sci. 2015, 8, 2118-2127. 13 ACS Paragon Plus Environment


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