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Environmental Gating and Galvanic Effects in Single Crystals of Organic-Inorganic Halide Perovskites Mahshid Ahmadi, Eric S. Muckley, Ilia N. Ivanov, Matthias Lorenz, Xin Li, Olga S. Ovchinnikova, Eric Lukosi, Jeremy Tisdale, Ethan Blount, Ivan I. Kravchenko, Sergei V. Kalinin, Bin Hu, and Liam Collins ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b21112 • Publication Date (Web): 02 Apr 2019 Downloaded from http://pubs.acs.org on April 2, 2019

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ACS Applied Materials & Interfaces

Environmental Gating and Galvanic Effects in Single Crystals of Organic-Inorganic Halide Perovskites

Mahshid Ahmadi1, Eric S. Muckley2, Ilia N. Ivanov2, Matthias Lorenz2, Xin Li2, Olga Ovchinnikova2, Eric D. Lukosi3, Jeremy T. Tisdale1, Ethan Blount1, Ivan I. Kravchenko2, Sergei V. Kalinin2,4*, Bin Hu1, and Liam Collins2,4

1

Joint Institute for Advanced Materials, Department of Materials Science and Engineering, University of Tennessee, Knoxville 37996, USA 2

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

3

Joint Institute for Advanced Materials, Department of Nuclear Engineering, University of Tennessee, Knoxville 37996, USA

4 Institute

for Functional Imaging of Materials, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

*Corresponding

Author Email: [email protected]

Keywords: Organometal halide perovskite, charge transport, environment, electrode, redox, relaxation time

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Abstract: Understanding the impact of environmental gaseous on the surface of organometal halide perovskites (OMHPs) couples to the electronic and ionic transport is critically important. Here, we explore the transport behavior and origins of the gas sensitivity in MAPbBr3 single crystals (SCs) devices using impedance spectroscopy and current relaxation measurements. Strong resistive response occurs when crystals are exposed to different environments. It was shown that SC response to the environment is extremely different at the surface as compare to the bulk due to disorder surface chemistry. The non-linear transport properties studied using ultra-fast Kelvin Probe Force Microscopy (G-KPFM) to unravel spatio-temporal charge dynamics at SC/electrode interface. The relaxation processes observed in pulse relaxation and G-KPFM measurements along with gas sensitivity of crystals, suggests the presence of a triple phase boundary between environment, electrode, and crystal. Results indicate that environment is a non-trivial component in the operation of OMHP devices which is reminiscent of fuel cell systems. Furthermore, the triple phase boundary can play a significant role in the transport properties of OMHPs due to the possibility of the redox processes coupled to the concentration of bulk ionic species. While instrumental for understanding the device characteristics of perovskites, our studies suggest a new opportunity of coupling the redox chemistry of the Br2-Br- pair that defines the bulk conductivity of MAPbBr3 with the redox chemistry of gaseous (or liquid) environment via a suitable electrocatalytic system to enable new class of energy storage devices and gas sensors.


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Introduction Organometallic halide perovskites (OMHP) are now at the apex of scientific interest due to their outstanding optoelectronic properties for application in advanced optoelectronic devices. Recently, there is a lot of evidence in the literature of non-trivial charge dynamics at the interfaces and environmental effects on the performance of OMHP devices1-6. Studies showed that the optoelectrical properties of OMHP SCs are highly influenced by the environmental atmosphere79.

Indeed, both unfavorable and beneficial environmental effects have been reported. For example,

on one hand, performance degradation in humidity and ambient condition has been very well established. On the other hand, several studies demonstrated benefits of environmental exposure for OMHP thin film solar cells10,

11.

It was revealed that combining light and atmospheric

treatments can drastically increase the internal luminescence quantum efficiencies of polycrystalline OMHP films with much higher carrier lifetimes and diffusion lengths, comparable with single crystalline counterpart10. The study proposed that light generates superoxide species which reduces the density of shallow surface traps. Stoeckel et al. reported that in pure O2 atmosphere the dark current in thin film OMHP devices significantly increases due to O2-mediated trap filling12. The study indicated that the iodine vacancy-filling mechanism mediated by CH3I gas and O2 is different, while CH3I forms covalent bonds which irreversibly passivate iodine vacancies, the O2 mediated trap healing mechanism is reversible12. Similarly, enhancement in photoluminescence (PL) properties of OMHPs in O2 atmosphere was attributed to decreasing the concentration of defects/defect passivation7,

8, 10, 13.

Furthermore, UV–O3 treatment led to an

improvement in the performance of MAPbBr3 single crystal (SC) X-ray detector by passivating the surface defects14. However, so far, the detail role of gas sensitivity and its impact on charge carrier transport remains unexplored as the most focus is efficiency and stability of thin film OMHP solar cells, which involves complex dynamic response of metastable interfaces and grain boundaries. Recently, SCs of OMHP have been established as superior candidates for optoelectronic devices including photodetectors and high energy X-ray and gamma ray sensors1417.

The devices made from OMHP SC can be expected to outperform its polycrystalline

counterparts due to higher stability, lower defect density, higher carrier mobility and longer carrier diffusion length18, 19. Moreover, in a SC device the complex effect of internal interfaces like grain boundaries can be eliminated. These considerations have stimulated this effort towards understanding the impact of environment on a simple MAPbBr3 SC device and its electronic and 3 ACS Paragon Plus Environment


ionic charge transport. Further, the interplay of the adsorbed environmental gases with surface chemistry and electrochemistry at the interface with metal electrode is explored. We first explore the environmental sensitivity using classical impedance spectroscopy (IS) to differentiate the impact of environment on the individual elements including bulk, surface and interfaces. IS in dark condition with no dc bias is performed to reconstruct the equivalent lumped circuit and establish the nature of the gas-sensitive elements. Next, voltage dependent timerelaxation measurements are used to explore the peculiarities of the transport in different environment. Finally, the observed processes are visualized using time of flight secondary ion mass spectroscopy (ToF-SIMS) revealing spatially-resolved chemical distribution and ultrafast Kelvin Probe Force Microscopy (G-KPFM) revealing spatial charge dynamics with submillisecond time resolution. Results and Discussion We explored the transport behavior in SCs of MAPbBr3 grown via inverse temperature crystallization (ITC) method20, 21 as a function of environmental gaseous. For this measurement MAPbBr3 SC is sandwiched between Au electrodes. Details of single crystal growth and electrode deposition can be found in supplementary information. We explored the device dark IV in air and in vacuum. As can be seen in Figure S1(a) on transition to vacuum the current increases more significantly for negative biases in agreement with literature.9 The observed changes in conductivity can be attributed to multiple mechanisms, including changes in surface and bulk electronic and ionic concentration coupled to the oxygen partial pressure via Br2-Br- redox pair. To further analyze the origins of observed behavior, we explored the effect of humidity on conductivity. As shown in Figure S1(b), under 5V bias the current decreases as humidity is increased to 60% relative humidity (RH). Above RH > 60%, the slight current increase may be due to opening of ionic conduction channels or formation of physisorbed water layers on the surface. Notably, when the crystal is placed back under vacuum, current goes back up to 105 nA, about 11% lower after desorption of water. We note that this process is semi-reversible, presumably due to the presence of a slow process or an electrochemical reaction under application of external field. The dynamics of this process is shown in Figure S1(c), illustrating that the resistance of the crystal generally increases as humidity is increased. Note that, upon the increase of RH, the resistivity of the MAPbBr3 sample increases slowly. The slow increase in resistivity 4 ACS Paragon Plus Environment

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could be due to continued surface passivation or bulk diffusion of water into MAPbBr3, which can result in the creation of deep traps that reduces the lifetime of charge carriers. The slow increase could also be due to ionic conduction to the electrodes, resulting in a reduction in the electric field over time. However, once the RH is set to 0%, there is a rapid decrease in the resistivity, followed by a slower decrease. This behavior suggests that within the constraints of our test conditions, in terms of apparent resistivity the water infiltration did not permanently degraded the sample upon exposure to humidity for about 7 hours which agrees with previous studies 22-24. However, the slow increase and decrease in resistivity as a function of RH, could be due to trapping or reorganization of the spatial distribution of charged species within the bulk of the crystal. Beyond the humidity effects on apparent resistivity of MAPbBr3, little is known about the surface properties and electrode-crystal interfaces under different environmental conditions. To our knowledge, thorough studies of these essential properties have not yet taken place.

Figure 1. Impedance Spectroscopy (IS) in different environment (a) IS spectroscopy on MAPbBr3 SC device with TP electrode configuration in Ar, N2, and O2, showing magnitude of real part of impedance change as gas pressure is increased (Inset shows SC and electrode geometrics). (b) and (c) resistance and phase (model 1), (d) and (e) R1 and C1 (model 2) parameters of equivalent circuit as a function of gas pressure in different gas environment. The insets in (b) 5 ACS Paragon Plus Environment


and (d) show the lumped circuit model used. (f) Distribution of relaxation time (DRT) as a function of N2 gas pressure, where g (τ) is the distribution function of relaxation times and τ is relaxation time constant. To get insight into transport mechanism under different environments, we explored the frequency dependence transport using impedance spectroscopy (IS). Our results demonstrate that electrical response of MAPbBr3 SCs is sensitive to gas environment under dark conditions. To unfold the mechanism of electrical response of MAPbBr3 SCs to the gas environment, we employed two electrode configurations: through-plane (TP) and in-plane (IP), to study bulk versus surface properties in different environments, respectively. A full description of IS measurements can be found in the experimental method, supplementary information. The IS responses of a TP sample are provided in Figure 1(a). We note that the IS trend (Figure 1 (a)) displays a systematic change in both imaginary, Im(Z), and real, Re(Z), impedance spectra with increasing O2 and N2 pressure, while a smaller change in Ar environment. The changes are clearly happening at the low frequency regime related to the interfacial phenomena. The impedance data fitted well by the two -(R1-CPE1)-(R2-CPE2)- equivalent circuit, model 1 (Figure S2). According to the fundamental of electrochemical impedance spectroscopy, CPE or constant phase element models the behavior of a double layer, that is an imperfect capacitor25, 26. ZCPE=1/Q(ω)n where Q is the phase and n represents the deviation from an ideal capacitor. In most experimental systems, the impedance data from a real sample cannot be modelled very well by ideal resistors and capacitors. In this model, the relaxation time is τ=(RQ)1/n, when Q has dimensions of capacitance and n defines distribution of the relaxation time. In this case the relaxation times (τ) from CPE can correspond to the spatially distributed relaxation. CPE is certainly the most reasonable model given a statistical distribution of relaxation time. However, a statistical distribution of relaxation times corresponding to CPE element can be represented as an averaged relaxation time (corresponding to the maximum of the statistical distribution of relaxation time). Therefore, instead of CPE, a capacitor -based equivalent circuit model corresponding to the averaged value of relaxation times in the sample can be used. The simplified equivalent circuit model captures the essence of the physical system response, while detailed understanding of the CPE physical meaning is being investigated in our future work. Therefore, due to the large number of possible parameters to describe the dependence on environmental factors, we fitted the data using a simplified Rs-(R1C1)(R2C2) model (model 2). Clearly the analysis of circuit elements in both models (models 1 and 2) 6 ACS Paragon Plus Environment

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shows similar trend in resistance and phase/capacitance changes as a function of environmental gases as well as gas pressure (Figure 1(b) to (e)). However, in model 2 the parameters are easy to analyze. Herein, we discuss the analysis of model 2. We found that the series resistance, Rs, increases with increasing gas pressure (Figure S3 (a)). The capacitance of the first RC circuit generally increases with increasing N2 and O2 pressure, Figure 1(e). In the sample with the TP electrode configuration, the geometrical capacitance is calculated as C=

where ɛ is the static

dielectric constant of MAPbBr3, ɛ0 is the vacuum permittivity, A is the active area and d is the crystal thickness. Considering the static dielectric constant of MAPbBr3 SC (ɛ⁓58),27 the bulk capacitance should be in the range of few pico-Farad (pF), therefore here the IS fitting results for C1 is far above and cannot be attributed to MAPbBr3 bulk capacitance. Early studies have attributed a large dielectric constant for OMHPs at low frequencies to the accumulation of charges (ionic and electronic) at the electrode interface28, 29. By analyzing C1 (C⁓5 nF) as the junction capacitance, the interface depletion width was estimated to be ~177 nm in an O2 atmosphere at 120 torr. The depletion width can be on the order of the Debye screening length, LD, which is proportional to the reciprocal of the square root of the density of a single type mobile charged specie (LD

),

where kB is the Boltzmann constant, T the absolute temperature, q the elementary charge and N is the dopant concentration. Considering this, the charge concentration at the junction is estimated to be approximately 1015 cm-3, significantly higher than the expected hole dopant concentration reported for MAPbBr3 SCs (109-1010 cm-3)20. Therefore, the higher capacitance can be attributed to the accumulation of charges (ionic and electronic) enhancing carrier density at the interface. The second set of RC values showed insignificant change during exposure to different gases. To avoid over-parameterization of the equivalent circuit model, we fixed the values of these R2C2 components to the average values for R and C in the circuit at 0.25 MΩ and 430 pF respectively. By analyzing C2 (⁓430 pF), depletion length was derived to be approximately 2 μm with a doping concentration around 1012 cm-3. The results suggest the formation of double space charge layers in proximity of SC/Au interface in agreement with previous report30. For subsequent analysis, we recast these observations in terms of characteristic relaxation times, τ = RC. Here, τ1 is milliseconds (ms) and become slightly faster (several tens of ms) with increasing gas pressure (Figure S4). While τ2 (R2C2) is a faster process (hundreds of µs). We note that the interfacial resistance (R1) decreases with increasing gas pressure (Figure 1 (d)) which can lead to an increase 7 ACS Paragon Plus Environment


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in interfacial recombination. Therefore, τ1 could be the relaxation from interfacial recombination due to accumulation of charges at the interface which is sensitive to the gas pressure. Several groups have used the equivalent circuit model to explain the origin of phenomena in OMHPs based on capacitive, resistive or inductive circuit elements. However, complicated systems including hybrid perovskites deviate from ideal resistor or capacitor structures and cannot be fitted well with these elements. This problem makes the interpretation of phenomena according to elements of the equivalent circuit model controversary. To completely avoid these uncertainties, we complement the results with an alternative and unambiguous way to interpret the impedance data. We use the distribution of relaxation time (DRT) method to evaluate the impedance analysis to further improve IS interpretation with either equivalent circuits or physical models. This method is a well-established method in the electrochemistry community31-33. Therefore, here we also deconvolute the distribution of relaxation time g(τ) from the IS spectra Z(f) of N2 gas via recently developed statistical model selection algorithm34:

(1) where R∞ is the high frequency cut-off resistance and Rp is the polarization resistance (here, interfacial resistance). Shown in Figure 1(f), two relaxation time constants τ1 and τ2 are observed followed by a shoulder peak at a slower time constant. The DRT clearly confirm the existence of at least two relaxation phenomena at the interface which is sensitive to the gas pressure in agreement with the two RC time constant. We note that as N2 is injected (pressure above 0 torr), the g(τ) shifts to slightly faster time constant (ms to tens of ms). The width of peak centered at τ1 shrinks as N2 pressure increases. In terms of a ZARC element, shrinkage of peak width indicates increase of diffusion-related constant, indicating transition from a constant phase element to a pure capacitance35. The estimated overall resistance Rp decreases as N2 pressure increases. These results fully agrees with the analysis via our lumped circuit elements. However, the complexity of IS and equivalent circuit model inspired us to explore environmental effects on SC surface by designing lateral electrode when electrodes deposited on the top surface of the crystal, referred to as in-plane (IP) configuration so as the crystal can be directly exposed to the gas environment.


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Figure 2. (a) Impedance spectroscopy on MAPbBr3 SC with IP electrode configuration under Ar, N2, and O2, showing magnitude of real part of impedance change as gas pressure is increased (The inset shows SC and electrode geometrics), (b) and (c) R1 and phase (model 1), (d) and (e) R1 and C1 (model 2) parameters of circuit as a function of gas pressure in different gas environment. The insets in (c) and (e) show the lumped circuit model used. The IS responses of the IP sample are provided in Figure 2(a) exhibiting a slightly depressed arc. For this configuration, the best fit was found similar by using both Rs-(R1CPE1) an Rs-(R1C1) circuit models. The corresponding parameters are shown in the Figure 2(b) to (e) and the changes in resistance and capacitance/phase with increasing gas pressure and environmental molecules are similar in both models. We note that the impedance responses similarly in Ar and O2 atmosphere while in N2 environment, the crystal impedance responses differently and decreases with increasing pressure (Figure 2 (a)). Herein, we analyze the parameters of Rs-(R1C1) circuit model. Figure S3 (b) represents the series resistance (Rs) as a function of Ar, N2 and O2 gas pressure. While Rs is slightly higher in N2 environment, it remains relatively constant with increasing gas pressures. However, the crystal charge transport resistance (R1) significantly decreases with increasing O2 pressure while it remains almost constant in Ar atmosphere, as shown in Figure 2(d). An opposite behavior is observed for N2 atmosphere, which demonstrates an increase in resistance with increasing gas pressure. Capacitance changes insignificantly (< 1%) as the gas pressure increases but shows a consistent trend with the gas species, capacitance is highest during N2 exposure and lowest during O2 exposure under the entire pressure range. We note that for the IP sample, τIP is a slower process (ms) (Figure S4), likely dominated by slower surface ionic 9 ACS Paragon Plus Environment


species. Our observations are in agreement with recent studies suggesting that the disorder surface chemistry of MAPbBr3 SC can lead to extremely different environmental sensitivity at the surface in compare to the bulk6. Overall, impedance changes measured at low frequency regime (Figure 1(a) and 2(a)) indicate impedance dependence on gas environment and pressure. In addition, the effect of gas is not fully reversible and the impedance in vacuum is slightly different in each panel. At high frequency (1 MHz), negligible impedance change is observed under changing gas environments which suggests that change in impedance is not strictly related to changes in bulk properties due to gas adsorption. The percent change of the real impedance (∆Re(Z)) under different gas conditions (Ar, N2, O2) for IP and TP samples is provided in Figure 3(a). As expected, the IP sample exhibits significantly higher gas response than the TP sample due to higher surface area in contact with gas environment. The observed change of ∆Re(Z) with the logarithm of pressure suggests that the responses are linear with the electrochemical potential of the volatile component (Figure 3(a)) where the expected weakest dependence is seen with Ar. In N2 atmosphere the response changes the sign between the two-electrode configuration (Figure 3(b)). Although surprising, previous studies have also noticed different behavior of OMHP thin films under inert gases, N2 and Ar36. It was shown that N2 interaction with OMHPs effects on the absorption coefficient at energies sensitive to surface phenomena. While N2 is not a reactive gas, the reactivity can be related to the presence of impurities which suggest that the redox state of the surface plays a significant role on the electronic surface properties. It has been also suggested that N2 molecules has a strong diffusivity in OMHP grain boundaries/free surfaces which blocks the desorption of volatile species.36 In a systematic analysis Wang et al. has shown that O2 and N2 can both p-dope MAPbBr3 SC by moving the Fermi level through physical absorption.37 This can change the conductivity of p-type MAPbBr3 in agreement with the results observed in the TP sample (Figure 3 (a) and (b)). However, as the rate of absorption increases for example with increasing gas pressure and longer exposure, O2 can bond with C from MA+ without direct evidence of reaction between O2 and MAPbBr3. Therefore, increasing pressure and exposure time of O2 can change the concentration of charges in agreement with recent studies38. This can explain the changes observed in Figure 1(e) when capacitance increases with increasing O2 pressure up to 120 torr, then slightly decreases from 120 to 200 torr due to lower concentration of charges at the interface.


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The reversibility of the environmental test is shown in Figure 3(b) by placing the sample back under vacuum. Although we can still expect the edge effect acting as non-homogenous centers, sample with TP electrode configuration shows high reversibility compared to IP. This is expected as in the IP sample the surface of SC is directly in contact with the environment. In this condition gas molecules can be easily adsorbed by the surface, whereas in the TP sample gas molecules cannot fully diffuse to the bulk. Recently the irreversibility of OMHPs properties in the presence of gas environment was attributed to a desorption process as the pressure of inert atmosphere lead to different degradation rate and kinetics36. In addition, due to solution growth, the surface of these SCs possess higher concentration of defects due to a large number of dangling bonds, undercoordinated atoms (e.g. Pb+2, etc), surface dislocations and chemical impurities in the form of hydrocarbons, amines or diamines39-41. Therefore, in the IP sample gas molecules adsorbed by the surface changes the electrical transport properties, i.e. increasing resistance with increasing gas pressure in N2 and reducing resistance in O2 atmosphere (Figure 2(d)). The O2 behavior is consistent in both IP and TP samples. For O2, its oxidizing nature leads to a reduction in surface electron concentration, so the increase in device conductivity must be due to an increase in surface hole carrier transport or concentration. The interaction of O2 can be through chemical bonding or O2 molecules forming interstitial defects or passivating/filling halide vacancies12, 42. Note that alternative mechanism can include other chemical interaction between O2 and the surface, including oxidation of Br-, formation of superoxide species at Br vacancies10,

43,

and even

formation of PbO as MAPbBr3 SC surface is rich in Pb component44. To further explore the mechanism behind this gas sensitivity the resistance changes of IP and TP samples under pulsed N2 exposure was measured (Figure 3(c)). The results indicate that the TP sample (ΔRTP) is more reversible than the IP. Most charge transport in the TP sample occurs through the bulk of crystal, and therefore it is not strongly affected by N2 adsorption at the surface. For IP sample (ΔRIP), resistance increases with N2 exposure and shows poor reversibility even after N2 is removed. This suggests that N2 interaction with the crystal surface results in some chemical adsorption and/or irreversible charge transfer with the surface, resulting in formation of a surface depletion region which strongly decreases charge mobility across the crystal surface. In the IP sample, charge transport occurs across the crystal surface, so depletion of the holes from surface region strongly decreases charge mobility. We further explored the time constant related to ΔR kinetics of N2 adsorption/desorption shown in Figure 3(d). The ΔRTP response in Figure 11 ACS Paragon Plus Environment


3(c) was fit to a single exponential model (ΔR = R0 exp(-t/τ), where t = time and τ = time constant) for N2 adsorption and desorption during the last 3 N2 pulses. The value of τ was extracted from each exponential fit and plotted in Figure 3(d). The time constant generally increases with N2 pressure, which is expected since the full adsorption/desorption process takes longer to complete when the concentration of adsorbate molecules is higher. The value of τ is ~20% higher for adsorption compared to desorption. This suggests that N2 undergoes relatively slow (τ ≈ 23-30 min) adsorption, and exposure to vacuum results in slightly faster (τ ≈ 19-25 min) desorption, indicating relatively weak physical interaction of N2 with the crystal surface. Time constants for ΔRIP were not extracted due to low signal-to-noise ratio and low reversibility of the ΔRIP response to N2. Note that detailed analysis of observed phenomena is complicated by the fact that Ar and N2 are not expected to be reactive gases, whereas O2 can be kinetically limited by diffusion. Further, earlier studies revealed that the reactivity of O2 with OMHP thin films can be dependent on the morphology, grain size and concentration of halide vacancy43. Murali et al. reported that the morphology and trap states at MAPbBr3 SC surface is different from bulk and the disorder surface chemistry of these SCs can transform them to more polycrystalline surfaces.6 Analysis of available data indicate that gas response of MAPbBr3 SC is complex and likely related to volatilization phenomena which can change the defect mechanisms and it is highly localized on the surfaces and interfaces which require further studies to unravel the mechanism behind this. Hence, observed behaviors suggest that defect chemistry at the surface or in other words redox state of the surface plays significant role in the transport phenomena but does not offer readily controlled redox environment.


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Figure 3. Summary of impedance experiments for in-plane (IP) and through-plane (TP) electrode configurations (a) showing magnitude of real part of impedance change as gas pressure is increased, (b) reversibility and change in IP and TP sample in different gas environment. (c) Resistance change of MAPbBr3 SC with in-plane (ΔRIP, red) and through-plane electrode configuration (ΔRTP, black), during exposure to pulses of N2. Pressure of N2 is shown by blue pulses (right axis). (d) Exponential time constant related to ΔRTP kinetics of N2 adsorption/desorption shown in (c). We further proceeded to explore the non-linear surface transport properties of MAPbBr3 SC device in different environment. Note that IS measurements generally provide only information on the linear elements of equivalent circuit. Similarly, static IV measurements do not contain temporal information. Bias-induced transport in semiconducting devices can typically be understood by separating different relaxation processes by their associated time scales. In light of this, we carried out pulse dependent relaxation measurements on an IP sample. In these



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measurements, 3 ms voltage pulses were applied across the crystal and the potential drop was detected as a function of time.

Figure 4. (a) Potential drop across crystal during pulsed charging/discharging at 100 mV, 500 mV, 1 V, 2 V, 3 V, and 4 V bias in in-plane configuration measured in air. Signals were averaged using 100 oscilloscope traces, (b) and (c) time constants extracted from double exponential fits vs applied biases in air during bias-on and -off, respectively and, (d) Potential drop across crystal measured in air, O2, and N2 when 4 V bias is applied. The data suggests the presence of three primary processes. Immediately upon the application of the bias, there is an instant potential jump related to capacitance, followed by one (low bias) or two (high bias) relaxation processes. To describe this behavior quantitatively, we fitted the relaxation processes shown in Figure 4 to a double exponential model (2): ∆V(t) =

+

(2)

Details of fitting can be found in Figure S5. When switching the bias on, different processes develop, i) the electronic and ionic charges redistribute creating surface and interface space charge layers, and also ii) environmental molecules can inject or transfer charges, creating additional ionic 14 ACS Paragon Plus Environment

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carriers of both polarities. Notably, the sign of the two relaxation processes is opposite, suggesting both processes have fundamentally different origins. For low biases (

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