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C: Energy Conversion and Storage; Energy and Charge Transport

Direct Observation and Quantitative Analysis of Mobile Frenkel Defects in Metal Halide Perovskites Using Scanning Kelvin Probe Microscopy Susanne T. Birkhold, Jake T. Precht, Rajiv Giridharagopal, Giles E. Eperon, Lukas Schmidt-Mende, and David S Ginger J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03255 • Publication Date (Web): 28 May 2018 Downloaded from http://pubs.acs.org on May 28, 2018

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The Journal of Physical Chemistry

Direct Observation and Quantitative Analysis of Mobile Frenkel Defects in Metal Halide Perovskites using Scanning Kelvin Probe Microscopy AUTHOR NAMES Susanne T. Birkhold, †§ Jake T. Precht, † Rajiv Giridharagopal, † Giles E. Eperon, †# Lukas Schmidt-Mende, ‡ David S. Ginger*† AUTHOR ADDRESS †

Department of Chemistry, University of Washington, Seattle, Washington 98195, United

States ‡ Department

#

of Physics, University of Konstanz, 78464 Konstanz, Germany

Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK

Corresponding Authors * Email: [email protected] * Email: [email protected]

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ABSTRACT Ion migration is seen as a primary stability concern of halide perovskite-based photovoltaic and optoelectronic devices. Here, we provide experimental studies of long-distance, reversible ion migration in methylammonium lead iodide (MAPbI3) and formamidinium lead iodide (FAPbI3) films. We use time-resolved scanning Kelvin probe microscopy on insulator-coated lateral electrodes to probe the dynamic redistribution of charged Frenkel defects over micrometer distances after application of an electric field. We combine these dynamic measurements with drift-diffusion simulations that yield self-consistent pictures of the sign, distribution, mobility, and activation energy of the associated, mobile Frenkel defects. This comprehensive approach is applied to study the impact of the organic cation on ionic mobility in metal halide perovskites, which we find to be significantly reduced in case of the FAPbI3 films compared to the MAPbI3 films.

INTRODUCTION Rapidly increasing power conversion efficiencies, currently exceeding 22%,1 combined with simple solution-based processing routes have placed metal halide perovskites in the spotlight of present photovoltaic research. This promising class of semiconductor materials forms with an ABX3 chemical formula, with methylammonium lead iodide (CH3NH3PbI3, abbreviated as MAPbI3) and formamidinium lead iodide (HC(NH2)2PbI3, abbreviated as FAPbI3) as two of the most commonly studied reference compounds. Despite their high efficiencies in photovoltaic devices, these materials can also exhibit a number of dynamic phenomena, such as slow response times and hysteresis effects,2-5 that are often explained in the context of mobile ions


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and point defects at room temperature. As a result, the mobility of ions and defects is currently of great interest for perovskite-based solar cells.2, 6 Although considerable experimental evidence suggests halide-related defects are the most mobile species in metal halide perovskites,7-8 many questions about the ionic migration mechanism remain unanswered. Varying theoretical calculations predict either vacancydominated3, 9-10 or equivalent migration11-12 of associated Frenkel defects of halide vacancies and interstitials, with a strong dependency of activation barriers on crystal direction.12-13 Furthermore, a local screening of moving ionic charge by coupled rotation of organic dipoles has been proposed to assist the migration of iodide in MAPbI3.14 The fact that calculated values for diffusion coefficients span nearly 6 orders of magnitude (10-6 – 10-12 cm2/Vs)9-10, 15 with associated activation energies that spread over 0.5 eV (0.1 – 0.6 eV),3, 9-13 highlights the need for experimental measurements of ionic mobilities. A variety of experimental, temperature-dependent techniques have been applied to evaluate the activation energy of mobile ions in metal halide perovskites, including current – or voltage responses,3-4,

9, 16-18

impedance spectroscopy,17,

19-21

conductivity,22-23 and

photoluminescence measurements.24-25 Yet, many of these methods require illumination, which has been shown to have a major impact on ion migration,22-23 or the fabrication of complete solar cell devices with different charge injecting and extracting layers.3-4,

9, 16-17, 19

These

approaches, while powerful, can be complicated by extrinsic factors, and do not always allow the direct examination of mobile ions. Considering the dynamics of mobile ions, significantly fewer experimental reports are available. Besides photoluminescence quenching experiments based on significant laser illumination,26 experimental determination of the ionic diffusion coefficient has primarily been obtained by impedance spectroscopy,19, 21 which evaluates the small scale displacement of mobile ions, as well as by dark current decays of perovskite solar cells.18 3 ACS Paragon Plus Environment


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Here, we present a complementary method to directly observe ion migration in metal halide perovskites across the micrometer scale. Using a simple device geometry of insulated lateral electrodes and time-resolved scanning Kelvin probe microscopy (SKPM),27 we study the spatial redistribution of mobile defects after exposure to an electric field. Combining these dynamic SKPM measurements with drift-diffusion simulations, we describe a self-consistent picture of the sign, diffusion coefficient and activation energy of the mobile ions. We further study the difference in ionic motion in films with different cation concentrations, and we find that ionic migration is significantly retarded in FAPbI3 as compared to MAPbI3.

MATERIALS AND METHODS Materials. Unless otherwise noted, all materials were purchased from Sigma-Aldrich or Alfa Aesar and were used as received. Methylammonium iodide (MAI) and formamidinium iodide (FAI) were purchased from Dyesol Ltd. Film formation and device fabrication. Devices were fabricated in the architecture of glass/perovskite/PMMA/SiO2/Au. Glass substrates were cleaned by sonicating in dilute detergent, acetone and 2-propanol for 10 min each, followed by oxygen plasma treatment for 10 min. Afterwards, substrates were transferred into a nitrogen-filled glovebox. The stoichiometric MAPbI3 precursor solution consists of 1 M PbI2 and 1 M MAI dissolved in a mixed solvent of 35 % DMSO and 65 % DMF and was filtered before use. The precursor was spin-coated on the glass substrate and directly transferred into an anisole bath. After 20 s the films were removed from the bath and blow-dried with a nitrogen gun. Films were then heated at 60 °C for 3 min and 100 °C for 5 min. FAPbI3 films were prepared similarly, using a FAPbI3 precursor solution of 1 M PbI2 and 1 M FAI mixed in 35 % DMSO and 65 % DMF and using annealing steps of 70 °C for 5 min and 170 °C for 10 min. The thickness of MAPbI3 and FAPbI3 films was determined to be ~250 nm by profilometer measurements. For the insulating top 4 ACS Paragon Plus Environment

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layer, 5 wt% of poly(methyl methacrylate) (PMMA, Mw 120k) was dissolved in toluene and spin-coated on top of the perovskite layer at 8000 rpm for 1 min. Then, a 50 nm thick SiO2 layer was deposited by E-beam evaporation. Gold contacts had an electrode distance of around 10 µm and were thermally evaporated with a 0.0005” round tungsten wire held taut across the evaporation mask to create the lateral junction. Kelvin Probe measurements. The device was mounted in a Cypher ES Environmental AFM (Asylum Research) and was operated in a nitrogen atmosphere. We used Pt-coated MikroMasch tips (HQ:NSC15/Pt, ~ 325 kHz and 40 N/m). The cantilever was oriented parallel to the long axis of the gap to minimize artifacts and scanning was performed in the direction perpendicular to the long axis.28 Scanning Kelvin probe microscopy (SKPM) measurements were conducted in amplitude modulation mode with a lift height of 30 nm. The displayed potential equals the bias applied to the tip to nullify the contact potential difference (CPD), with Vtip = - VCPD. For measurements after electrical bias, the device was biased with + 8 V at the left electrode for 30 min and SKPM measurements were started directly after the bias had been turned off and both electrodes were grounded. The SKPM signal was measured by repeatedly scanning the same line across the electrode gap, each line scan taking 6.6 s. After one measurement, the temperature of the chamber was changed by 10 degrees and allowed to equilibrate for 15 minutes. Then, the device was biased at + 8 V at the left electrode for 30 minutes again before conducting the next SKPM measurement. Drift-diffusion simulations. A one-dimensional drift-diffusion model was implemented to simulate the experimental SKPM results using MATLAB’s built-in partial differential equation solver for parabolic and elliptic equations (pdepe). The code solves the continuity and Poisson’s equation for negative and positive charged mobile ions and the electrostatic potential as a function of space and time. The boundary conditions were set to be completely reflective for ionic charge. The initial conditions of the ionic distribution and potential profile were chosen 5 ACS Paragon Plus Environment


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to fit the measured data that was acquired immediately after application of the electric field. The simulated data was fitted to the measured data by optimizing the simulated to the measured potential using a simulated annealing algorithm within MATLAB’s optimization toolbox. The fit parameters were the ionic mobilities µn and µp.

RESULTS AND DISCUSSION Kelvin probe measurements on lateral electrodes have proven to be a valuable method to study field-induced ion migration, e.g. in polyelectrolytes, electrochemical cells and metal halide perovskites.22, 27, 29-35 Previous Kelvin probe studies on ion migration in metal halide perovskites applied lateral electrodes with direct, charge injecting contacts between the electrodes and the perovskite. However, the field-induced spatial separation of ionic charge across the electrode gap is complicated in case of a direct metal/semiconductor interface, as opposite electronic charge carriers are injected from the source into the perovskite to enable charge neutrality in the film. As a consequence of this screening effect, the ionic distribution cannot be directly observed after biasing, but instead p- or n-doping is detected at the regions where increased ionic concentrations are expected.22, 33-34

Here, we use lateral electrodes with an insulating layer between the electrodes and the perovskite film to allow a direct observation of the ionic charge redistribution by preventing screening by electronic charge carriers. To ensure good electronic insulation, a double layer of the polymer poly(methyl methacrylate) (PMMA) and SiO2 has been employed. Fig. S1 presents the compact film morphology of the probed MAPbI3 films, with grain sizes of 100 – 200 nm. Figure 1 displays the applied device architecture and the potential profile measured across the electrode gap before and after application of an electric field. Application of the Poisson equation: 6 ACS Paragon Plus Environment

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∇2 𝑉 (𝑥, 𝑡) =

𝑞 Ɛ0 Ɛ𝑟

𝜌(𝑥, 𝑡)

Equation (1)

with q as elementary charge, Ɛ0 as the permittivity of free space and Ɛr as the relative static dielectric constant (we take the static Ɛr = 25 for the perovskite),36 allows the charge density ρ to be extracted from the potential V. The initial potential profile displays no significant features on the applied scale due to the small work function differences between MAPbI3 and gold of around 100 meV (Figure 1). After the left electrode was biased with +8 V for 30 min, both electrodes were grounded and the altered potential profile was immediately measured (Figure 1). Now, two significant potential peaks of opposite sign and similar strength of around 2 V are detected within the electrode gap. Application of Equation 1 indicates these potential peaks arise from a residual charge density of around ± 2 · 1015 cm-3 close to the electrode edges, with an accumulation of negative charge close to the previously positively biased electrode, and vice versa. We note that a charge density of ~ 1015 cm-3 is in the order of typical defect densities reported in many samples of MAPbI3.5, 37-38 This initial charge distribution has its maximum close to the electrode edges and decays exponentially towards the gap center with a decay length of around 800 nm (see Fig. S2). The deviation of the spatial extent of the measured charge distribution from the expected Debye length of a localized charge density of similar magnitude

Figure 1. SKPM measurements across the lateral electrode of the device glass/MAPbI3/PMMA/SiO2/Au. Potential and charge profile before (left) and directly after (right) an electric field of 0.8 V/µm has been applied for 30 min and then set back to zero (electrodes shorted). Schematic illustrations above and within graphs display device architecture. 7 ACS Paragon Plus Environment


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(~ 100 nm) might be based on a spatially broad, rather than highly localized distribution of charge, a deviation between surface and bulk charge densities, the choice of dielectric constant, or a potential shielding effect by the insulating layer.39

Next, we consider the time evolution of this charge distribution within the electrode gap in more detail. Figure 2 displays the dynamic relaxation of the charge distribution in time after the bias is removed. This real-time observation is achieved by repeatedly scanning the same line between the two grounded electrodes, starting directly after the electric bias has been turned off. For MAPbI3, the potential and charge density peaks are observed to decay within ~200 s (Figure 2a-c). Based on these slow timescales, we conclude that the origin and the dynamics of the charge distribution are governed by the accumulation of mobile ions across the 10 µm wide

Figure 2. Time-resolved SKPM measurements after bias for a) – c) glass/MAPbI3/PMMA/SiO2/Au and d) – f) glass/FAPbI3/PMMA/SiO2/Au devices, measured at 20 °C. a), b), d) e) show the potential decay and c), f) the charge density decay. Each line represents a line scan across the electrode gap with a time resolution of 6.6 s. 8 ACS Paragon Plus Environment

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electrode gap during electric biasing. We note that a partial screening of ionic charge by intrinsic charge carriers due to unintentional doping of the film cannot be excluded.40-41 Therefore, the measured charge density in Figure 2c,f is assumed to provide a lower limit of ionic density. After bias, the slow decay of the potential and charge density peaks displays a symmetric, reversed migration of oppositely charged mobile ions due to electronic drift and diffusion that are caused by the concentration gradient of the charged defects. Based on the nearly identical peak heights and dynamics of positive and negative charge density peaks, we propose that we are observing the motion of interstitials and vacancies of the same ionic defect (Frenkel defects), rather than of two oppositely charged vacancies of different cation and anion species (Schottky defects). These defects may have formed either during the initial crystallization process, and migrate under the applied field, or may be caused by the electric field. The common crystallographic origin of the Frenkel defects will result in coupled dynamics, as an encounter of matching vacancies and interstitials is expected to cause the annihilation of both defects. Interestingly, we observe that the timescales for this ion motion are different between MAPbI3 and FAPbI3 films. Figure 2d-f shows the decay of both charged defects after biasing a FAPbI3 film, which comprises the larger and less polar cation formamidinium (FA). While the general behavior is similar to that observed for MAPbI3, and shows two opposite potential peaks and an associated charge separation across the electrode gap, Figure 2 shows that the relaxation dynamics are significantly slower for FAPbI3. These slower dynamics would be consistent with a reduced ionic mobility for FAPbI3. This observation agrees with calculations by Haruyama et al., who predicted higher activation energies for ionic conduction in FAPbI3 than in MAPbI3 based on density functional theory.13

In the recent literature, the organic A-site cation, halide X-site anion, and even the lead B-site cation have all been proposed or even demonstrated to be mobile in MAPbI3 films.2, 8, 13, 22, 429 ACS Paragon Plus Environment


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We note that SKPM probes charge only, and since migration of a positive ion leaves a

negative compensating charge behind (and vice versa) we cannot identify the mobile ions (e.g. I- or MA+ or Pbx+) directly from our measurements. It is possible to make an assignment indirectly based on relative timescales, and indeed we rule out Pb2+ as the primary mobile species observed in our experiments, based on timescale and activation energy.9, 43 However, the large variation in reported mobilities and activation energies of both iodide and methylammonium (MA) related mobile defects makes it difficult to distinguish between these species without additional data. If we assume that the organic cation is responsible for ion migration at these timescales, the faster ionic mobility in MAPbI3 films could be due to the smaller geometric size of the organic cation. In the case that iodide is the mobile ion observed in Figure 2, coupled dynamics of cation rotation and iodide migration might provide a local screening of ionic charge by the larger, more mobile dipole moment of MA cations, thus facilitating the hopping mechanism of iodide ions in MAPbI3.14

We also performed temperature-dependent transport measurements to probe the energetics of ion migration. Figure 3a-d shows the potential decay for MAPbI3 films for different temperatures, while Figure 3e displays the decay of the total positive charge ptotal(t) and negative charge ntotal(t) within the electrode gap, with 𝑛𝑡𝑜𝑡𝑎𝑙 (𝑡) = ∫ 𝑛(𝑥, 𝑡) 𝑑𝑥 and 𝑝𝑡𝑜𝑡𝑎𝑙 (𝑡) = ∫ 𝑝(𝑥, 𝑡) 𝑑𝑥 and n(x,t) and p(x,t) as positive and negative charge densities of the measured net charge, respectively. The faster decay dynamics of the potential peaks and the more rapid decrease in total charge with increasing temperature is consistent with a thermally activated process, as one might expect for mobile ionic defects. Furthermore, Figure 3e displays slightly faster decay dynamics for the negatively charged species at all temperatures. This slight discrepancy between decay dynamics of oppositely charged defects might originate from


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Figure 3. Time-resolved SKPM measurements after bias for glass/MAPbI3/PMMA/SiO2/Au devices at temperatures of a) 0 °C, b) 10°C, c) 20°C, d) 30°C. e) Decay of the total negative (dotted line) and positive charge (solid line) integrated within the lateral electrode at different temperatures. unintentional p-doping in our films, that causes a screening of negative ions by positive electronic charge carriers.41 Unfortunately, insufficient stability of FAPbI3 films did not allow Measurements are done a) before and b) after application44-45 of an electric field of 1V/um for reliable temperature-dependent measurements for FAPbI . 3 30min. Blue line shows the charge density after bias. Schematic illustrations above graphs display device architecture. A precise determination of the diffusion coefficient as a function of temperature would allow for the extraction of the activation energy of the observed ion migration. For a quantitative analysis of the dynamics of ionic motion at the different temperatures we consider both drift and diffusion as driving forces that act on the ionic distribution. We assume a uniform distribution of ionic charge parallel to the electrode front, and apply two one-dimensional driftdiffusion equations to model the evolution of ionic charge densities nion(x,t) and pion(x,t) of



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negative and positive ionic species. In this model, the ionic current densities of positive and negative ions, Jn and Jp, are described by: 𝐽𝑛 (𝑥, 𝑡) = 𝑞 ∙ µ𝑛 ∙ 𝐸(𝑥, 𝑡) ∙ 𝑛𝑖𝑜𝑛 (𝑥, 𝑡) + 𝑞 ∙ 𝐷𝑛 ∙ ∇ 𝑛𝑖𝑜𝑛 (𝑥, 𝑡)

Equation (2)

𝐽𝑝 (𝑥, 𝑡) = 𝑞 ∙ µ𝑝 ∙ 𝐸(𝑥, 𝑡) ∙ 𝑝𝑖𝑜𝑛 (𝑥, 𝑡) − 𝑞 ∙ 𝐷𝑝 ∙ ∇ 𝑝𝑖𝑜𝑛 (𝑥, 𝑡)

Equation (3)

Here, µn and µp are the mobilities and Dn and Dp the diffusion coefficients of negative and positive ions, respectively. The first term in Equation 2 and 3 describes the drift under the electric field 𝐸(𝑥, 𝑡) = ∇ 𝑉(𝑥, 𝑡) that is caused by the displacement of positively and negatively charged defects along the one-dimensional system. The second term describes the diffusion caused by the concentration gradient of the ionic species. We assume that the Einstein relation 𝑘𝐵 𝑇

with 𝐷 =

𝑞

∗ µ is valid and that the mobilities µn and µp are constant over time. Additionally,

the Poisson equation, that relates the potential V with the charge density 𝜌(𝑥, 𝑡) in the film, was applied: 𝑞

∇2 𝑉 (𝑥, 𝑡) =

Ɛ0 Ɛ𝑟

𝜌(𝑥, 𝑡) =

𝑞 Ɛ0 Ɛ𝑟

(𝑝𝑖𝑜𝑛 (𝑥, 𝑡) − 𝑛𝑖𝑜𝑛 (𝑥, 𝑡))

(Equation 4)

Combining Equation 2 - 4 into the continuity equation allows to calculate the temporal evolution of the ionic distribution: 𝑑𝑛𝑖𝑜𝑛 (𝑥,𝑡) 𝑑𝑡

𝑑𝑝𝑖𝑜𝑛 (𝑥,𝑡) 𝑑𝑡

1

=

𝑞

= −

∇ 𝐽𝑛 (𝑥, 𝑡) − 𝑘𝑟𝑒𝑐 ∙ 𝑛𝑖𝑜𝑛 (𝑥, 𝑡) ∙ 𝑝𝑖𝑜𝑛 (𝑥, 𝑡) 1 𝑞

∇ 𝐽𝑝 (𝑥, 𝑡) − 𝑘𝑟𝑒𝑐 ∙ 𝑛𝑖𝑜𝑛 (𝑥, 𝑡) ∙ 𝑝𝑖𝑜𝑛 (𝑥, 𝑡)

(Equation 5)

(Equation 6)

To describe the annihilation of Frenkel defects upon encounter of oppositely charged, mobile defects, a recombination term is included in Equation 5 and 6, with a recombination constant 𝑘𝑟𝑒𝑐 = Ɛ

𝑞 0 Ɛ𝑟

∙

(𝜇𝑝 +𝜇𝑛 ) 2

. If recombination of oppositely charged ions is excluded from the model,

the overall calculated number of ionic carriers is conserved, while it decays continuously if the recombination term is included, as displayed in Fig. S3 and Fig. S4. The simulated and 12 ACS Paragon Plus Environment

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experimentally measured charge decay are in good qualitative agreement if recombination of opposite defects is included in the model (Fig. S4), supporting our assumption that the measured decay of potential peaks is caused by the motion and annihilation of related Frenkel defects. We note that the small deviations between simulated and experimentally measured results might be expected to arise from several effects. First, our model assumes completely reflective boundary conditions that prevent migration of ionic charge out of the modeled system. However, it can be assumed that in experimental measurements a small diffusion current of ions out of the electrode gap is present in the perovskite film. For the sake of simplicity, we further exclude several other possible influences, such as a time dependence of ionic mobility or a presence of intrinsic electronic charge carriers, which might affect the amount and dynamics of the experimentally measured net charge distribution within the electrode gap. To extract the ionic mobilities from the measured SKPM data, we use µp and µn as fit parameters and solve the set of coupled partial differential equations (Equation 2 - 6) to minimize the difference between simulated and measured potential. Despite the assumptions discussed above, the quality of the fit is very good, as displayed in Figure 4a,b and Fig. S5 for MAPbI3 at 30 °C and for all other temperatures, as well as for FAPbI3 at 20 °C, in Fig. S6. The resulting fit parameters µp and µn are given in Table 1.

MAPbI3: 0°C MAPbI3: 10°C MAPbI3: 20°C MAPbI3: 30°C FAPbI3: 20°C

Mobility: Anion [cm2/Vs]

Mobility: Cation [cm2/Vs]

4.6 x 10-10 5.2 x 10-10 8.3 x 10-10 1.2 x 10-9 1.0 x 10-10

4.3 x 10-10 5.5 x 10-10 9.5 x 10-10 1.2 x 10-9 1.2 x 10-10

Table 1. Mobilities for positive and negative ions acquired by fitting the simulated to the measured potential.

Measurements are done a) before and b) after application of an electric field of 1V/um for 30min. Blue line shows the charge density after bias. Schematic illustrations above graphs display device architecture. 13 ACS Paragon Plus Environment


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Figure 4. Measured and simulated potential of MAPbI3 at 30 °C displayed as a) line plot of every second line scan for the first 125 s or b) as surface plot. c) Calculated diffusion coefficients of positive (cations) and negative ions (anions) for MAPbI3 at different temperatures, displayed in an Arrhenius plot to extract the activation energy Ea of ionic motion. We find that the studied positive and negative ionic defects in MAPbI3 films are equally mobile, with mobilities in the order of 9 x 10-10 cm2/Vs at room temperature. It is interesting to note Measurements are done a) before and b) after application of an electric field of 1V/um for that this mobility of long-range ionic motion, measured across multiple grains in a lateral device 30min. Blue line shows the charge density after bias. Schematic illustrations above graphs display device architecture. configuration, is comparable to the ionic mobility determined by current density decays or short-range impedance spectroscopy measurements, techniques which target mobile ions within grains (~10-10 cm2/Vs).9,

18-19

This implies that cross-grain boundary transport may not

significantly impact the ionic mobility. Here, we have to add that the existence of a significantly faster ionic conduction mechanism, with a reported mobility in the range of 10-6 – 10-7 cm2/Vs,10, 21 cannot be evaluated due to the limited time resolution of our current approach; future approaches will focus on methods that can measure sub-millisecond potential 14 ACS Paragon Plus Environment

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variations.46 Furthermore, if higher electronic charge densities would be present in the film, e.g. due to simultaneous charge injection at the electrodes, the dynamics of ionic motion might be decelerated if electronic carriers accompany oppositely charged mobile ions and reduce their electronic drift. By replacing the organic cation, the ionic mobility is reduced to 1x10-10 cm2/Vs in FAPbI3 films at 20°C. This decrease in ionic mobility by almost one order of magnitude agrees with the qualitative data shown in Figure 2d-e, as well as with impedance spectroscopy measurements by Bag et al.19 Moreover, our results show that previous impedance spectroscopy measurements on perovskite pellets, that reported an increased ionic mobility in FAPbI3,21 do not reflect the mobility of ions in perovskite films. We evaluate the activation energy, Ea, of the thermally activated ionic motion from the temperature-dependent diffusion coefficient 𝐷(𝑇) =

𝐷(𝑇) = 𝐷0 𝑒

−

𝑘𝐵 𝑇 𝑞

∗ µ(T) and the relation:47

𝐸𝑎 𝑘𝐵 𝑇

(Equation 7)

Figure 4c displays the Arrhenius plot of Equation 7, that gives an activation energy of around 0.28 eV for both negative and positive ions. Although our method probes only charge density, the results provide indirect evidence which allows us to speculate as to the nature of the defects that we measure under poling. Specifically, we observe (1) symmetric densities and mobilities of positive and negative species; (2) activation energies of 0.28 eV; and (3), mobilities of ~1 x 10-9 cm2/Vs at room temperature. Based on these observations we propose that we are measuring the motion of Frenkel defects comprising iodide vacancies and interstitials: this mechanism should give rise to paired positive and negative defect densities, and the measured activation energy for iodide migration is more consistent with the range that has been predicted for iodide migration (0.08 – 0.59 eV)3, 9-13 as opposed to organic cation migration (0.46 – 1.12 eV).3,

9, 11-13

Furthermore, our observation of similar activation energies and mobilities of 15 ACS Paragon Plus Environment


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mobile cations and anions support theoretical calculations that predict equal migration mechanisms of iodide vacancies and interstitials in MAPbI3.11-12

CONCLUSION In summary, we have presented an approach to directly observe a reversible, long-range motion of Frenkel defects in metal halide perovskites. While previous studies on lateral electrodes have focused on increased p- or n-doping after electric biasing, which may likely involve redox processes as well as ion motion,48-51 we apply insulator-coated lateral electrodes to prevent screening of the ionic charge distribution, as well as dynamic SKPM measurements to observe the motion of ions with spatial and temporal resolution. By analyzing the ionic redistribution with drift-diffusion simulations we provide a reliable and comprehensive tool to quantify both activation energy and diffusion coefficients of related Frenkel defects. Besides that, our results of a reduced ionic mobility in FAPbI3 compared to MAPbI3 provide a fundamental basis for further strategies to control ion migration by the polarity or size of organic cations in metal halide perovskites. While these measurements have focused on ion motion in the dark, the reports of photoinduced ion migration in the literature suggest that future experiments examining ion transport in the light could be fruitful.23-24 These measurements will likely require combinations of fast and slow dynamics, employing methods like time-resolved electrostatic force microscopy,52-53 G-Mode SKPM,46, 54 or heterodyne SKPM.55-56 ASSOCIATED CONTENT Film topography, analysis of initial charge distribution, details on drift-diffusion simulation.

AUTHOR INFORMATION Corresponding Authors 16 ACS Paragon Plus Environment

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Email: [email protected] Email: [email protected] Present Addresses §

Department of Physics, University of Konstanz, 78464 Konstanz, Germany

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This manuscript is based primarily on work supported by the DOE (DE-SC0013957). S.T.B. acknowledges financial support from the Fulbright Commission and the Carl Zeiss Foundation. G.E.E. is supported by the European Union’s Framework Programme for Research and Innovation Horizon 2020 (2014-2020) under the Marie Skłodowska-Curie Grant Agreement No. 699935. J.T.P. is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1256082. We acknowledge additional support from the Alvin L. and Verla R. Kwiram Endowment from the Department of Chemistry at the University of Washington.

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