Direct Observation of Surface Polarization at Hybrid Perovskite/Au Interfaces by Dark Transient Experiments

A distinctive feature of hybrid perovskite light-absorbing materials is the nonnegligible ionic conductivity influencing photovoltaic performance and stability. Moving ions or vacancies can naturally accumulate at the outer interfaces (electrode polarization) upon biasing. Contrary to that approach, a modulation of conductive or recombination properties could manifest as an alteration in the low-frequency part of the impedance response, either producing inductive or large capacitive features. Under this last view, capacitances are not the response of polarized structures or charging mechanisms, but result from the modulation of currents. This work intends to provide evidences that assist us in distinguishing between these two dissimilar mechanisms, namely, real charge polarization and delayed current effects under bias in the dark. The analysis relays upon an experimental technique based on transient charging signals using the Sawyer-Tower circuit. Instead of applying an alternating small perturbation over a steady-state voltage (differential capacitance method), transient charging measures the resulting polarization upon large bias step under suppression of dc currents. Our findings reveal that real steady-state charge is indeed induced by the applied voltage in the dark, easily interpreted by means of charged real capacitors with

values much larger than the film geometrical capacitance. The connection between that polarization and the charging of perovskite/contact interfaces is highlighted.
In just a few years, perovskite solar cells (PSCs) have gained great attention in the field of photovoltaics with an unprecedented increase in power conversion efficiency (PCE) achieved from facile solution processing routes. [1][2][3][4] Despite those technological progresses, it was identified from the very beginning that slow responses in PSCs cause annoying deviations from common photovoltaic operation. The presence of slow relaxation processes (from milliseconds to minutes) yield different hysteretic − curves depending on the bias sweep direction, scan rate, illumination and poling history. 2,[5][6][7] That phenomenon was initially connected to the observation of an excess capacitive signal in the low frequency part of the capacitance spectra, 8,9 in relation to the polarization of the outer contacts upon bias which originates the so-called dark hysteresis. Reinforcing the idea of the interfacial charging under solar cell operation, several studies identified the formation of built-in potentials in the vicinity of the interface between the perovskite absorber and extracting layers. 10 Using frequencymodulation Kelvin probe force microscopy (FM-KPFM), it has been identified that the electrical field in solar cells under working conditions mainly drops at the corresponding selective interfaces by local charge accumulation. 11 A related phenomenon is the remnant open-circuit voltage commonly exhibited in long-time photovoltage decay experiments, 12 which has been also explained in terms of the piling up of stabilized interfacial charge.
A distinctive feature of perovskite light-absorbing materials is the non-negligible ionic conductivity that is believed to influence photovoltaic operation. 13,14 Moving ions or vacancies naturally accumulate at the outer interfaces (electrode polarization) upon biasing, 15,16 originating the usually reported excess dark capacitance of order 1-10 µF cm -2 . 9 Similarly to the accumulation of ionic species, interfacial electronic pileup has been proposed in order to interpret the commonly-reported light-enhanced capacitance at low frequencies. 17 Accordingly, recent models can be found on the interplay of electronic carrier recombination and moving ion dynamics. 18,19 Previous works 20 suggested a close dependence between the ionic environment and the recombination mechanism in PSCs, in such a way that ionic vacancies move to decrease the recombination flux. It has been also argued 21 that such a coupling effect between ionic and electronic charges has an influence at low frequencies, as carrier recombination current becomes phase-delayed with respect to the voltage perturbation. Under this view, low-frequency light-enhanced capacitance is caused by out-of-phase carrier recombination instead of charge accumulation currents. Sophisticated equivalent circuits (ionically-gated transistor interface) have been proposed 22 accounting for the ionic-electronic interplay governing charge injection and recombination. Similar arguments have appeared very recently but now disregarding ionic effects and highlighting delayed electronic injection currents as the sole cause of the low-frequency capacitive phenomena even in the dark. 23 These kind of models are specially rich as introduce a modulation of conductive or recombination properties that ultimately manifests as an alteration in the low-frequency part of the impedance response. 24 Their use are well-known in Electronics. For example, the conductivity modulation of p-n junction diodes at forward bias produces inductive loops, 25 or the thermal diffusivity of thermoelectric models give rise to large low-frequency capacitances. 26 As a consequence, it is still under debate whether large capacitive effects observed at low-frequencies in PSCs are exclusively explained from charge accumulation mechanisms (interface polarization) or a dynamic interplay between ionic kinetics and electronic carrier recombination/injection current is occurring giving rise to apparent (not real) capacitors. Our work intends to provide evidences that assist us in distinguishing between real charge polarization and delayed current effects under bias stimuli in the dark. This distinction is crucial for understanding PSCs basic functioning and device operation.
We select here perovskite films of methylammonium lead iodide (MAPbI3) as active layer, symmetrically contacted by interdigitated gold electrodes (see below for experimental conditions). This experimental setup allows avoiding the formation of a photovoltage under light irradiation, expected when asymmetrical (different work function) materials are used as selective contacting layers. One can observe in Fig. 1 the impedance and capacitance responses registered at zero-bias in the dark and ambient conditions, exhibiting two main features: at high-and intermediate-frequencies ( 100 Hz) the geometrical capacitance 2.7 pF and sample resistance dominate; and at low-frequencies the commonly reported excess capacitance increment ≫ is observed. The same electrical response is observed for 1 V-bias ( Fig. S1) and corresponds to the equivalent circuit of Fig. S2. An estimation of the effective polarization area of the interdigitated electrodes is included as Supplemental Information, which results in values of the geometrical capacitance per unit area of 0.1 nF cm -2 .

FIG. 1 a) Example of impedance plot and b) capacitance spectrum response of a 320 nm-thick
MAPbI3 film, measured at zero bias in the dark, exhibiting the low-frequency capacitive features. In both graphs, red lines represent a fitting with the corresponding equivalent circuit (Fig. S2).
Because small-amplitude capacitive analysis by itself is not able to unambiguously discern if the low-frequency capacitance is effectively caused by charge polarization, we propose here to relay upon a different experimental technique based on transient charging signals. Instead of applying an alternating small perturbation over a steadystate voltage (differential capacitance method), transient charging measures the resulting polarization upon large bias step under suppression of dc currents. The experimental setup is based on the Sawyer-Tower circuit (ST) 27 which is the classical set-up used to explore hysteretic loops of ferroelectric materials. The configuration of the circuit is shown in Fig. 2(a). A step voltage signal ( app ) is applied to the sample across a reference linear capacitor , with both capacitors in series connection. The condition ≫ must be accomplish to assure that the applied voltage principally drops within the perovskite sample. Under this condition the charge storage in (as in ) is = , being the voltage at the reference capacitor ([see Fig. 2(b], which is recorded with an ultrahigh input resistance (1 TΩ) potentiostat to avoid loading effects from the recording instrument. The total transfer function of the measuring set-up is given in SI.
As observed in Fig. 2b, the voltage at follows the bias perturbation steps in such a way that only a small portion drops at it, i.e. ≪ app . Note that this fact discards the observation of the reference capacitor charging through the perovskite sample shunt resistance, which would yield = app in the long time (see more discussion below). To verify the effective perovskite film effect on the reported polarization, the set-up response comprising only gold electrodes on glass substrates were checked (see Fig.  S3). Since the reference capacitor suppresses any dc current, a registered steady-state voltage after long-enough poling should correspond to the effect of a true charging mechanism. Otherwise the reference capacitor cannot withstand a constant polarization. A delayed or modulated injection current is not able to yield a permanent voltage on the reference capacitor plate. On the contrary, a measured potential at should indicate a kind of locally imbalance charges at the perovskite sample.
All materials were used in our experiments as received: CH3NH3I (DYESOL), PbI2 (TCI, 99.99%), N, N-dimethylformamide anhydrous (Sigma Aldrich, 99.8 %), dimethylsulfoxide anhydrous (Sigma Aldrich, ≥ 99.9 %), and chlorobenzene anhydrous (Sigma Aldrich, 99.8 %). The perovskite precursor solution is obtained from reacting dimethylformamide (DMF) solutions (50 wt. %) containing MAI and PbI2 (1:1 mol %) and MAI, PbI2, and DMSO (1:1:1 mol %). Perovskite layers were deposited on the top of 25×25 mm 2 glass by spin-coating at 4000 rpm (4000 ac) for 50 s. Chlorobenzene was used as anti-solvent and added just before the white solid begins to crystallize in the substrate. A mask with an interdigitated (ID) pattern (9 digits, 0.2 mm between digits, 0.2 mm width, and 7.8 mm length) was used. Gold was thermally evaporated (100 nm) at a base pressure of 6×10 -6 mbar. The films were characterized by UV-Vis absorption spectra in a Cary 500 Scan VARIAN spectrophotometer (250-900 nm), obtaining the distinctive spectra with the corresponding absorption edge at 780 nm for MAPbI3 with a bandgap of 1.60 eV (see Fig. S4). A mechanic Dektak 6M profilometer (Veeco) was used for film thickness measurement and the values were optimized by changing the spinning speed (see Fig. S5). Also, XRD patterns of MAPbI3-films are included in Fig.  S8. SEM analysis also shows the polycrystalline nature of the perovskite [ Fig. 2(c)], and the ID geometric configuration [ Fig. 2(d)] of the contacts. The examination of different thickness allows obtaining the optimum values (see Fig. S5). Direct impedance measurements of Fig. 1 and Fig. S1 were carried out by using a PGSTAT-30 Autolab potentiostat equipped with impedance module. Also ST transients, as in Fig. 2(b), were recorded with the same potentiostat. All electrical experiments were performed at room temperature in the air.   Fig. 2(a), occurring in a MAPbI3 perovskite film of 320 nm-thick with an ID contact configuration. Here reference capacitors within the range of = 10 − 100 µF are employed, which are previously checked using impedance analysis (see Fig. S6), and show a plateau at the frequencies of interest ( < 1 kHz). By examining Fig. 3(a), one can observe charging signals upon application of a step bias of height app = 1 V in dark conditions. A necessary test to check experiment consistency consists of verifying that ≪ app . As observed in Fig. 3, inversely scales with the reference capacitor with values (in the mV range) much lower than the bias (1 V), in good accordance with the assumption = (see transfer function calculation in SI). This fact precludes the possibility of seeing the charging of the reference capacitor through the perovskite sample shunt resistance with time constant = 10 − 10 s, which would yield a saturation of the registered voltage as at long time polarization. Contrary to this response, a rather steady-state voltage (charge) is attained (accumulated) for ~50 s-poling. This is particularly visible for = 10 µF.
The total amount of charge, calculated by using one exponential fitting, attains values within the range of max 10 − 30 nC [inset of Fig. 3b]. Remarkably, all curves collapse in the initial (~10 s) part of the transient, thus reinforcing our claim that charges as a consequence of the perovskite interface polarization and not through the shunt resistance. The reported dispersion in total accumulated charge can be understood in terms of the ionic and, presumably, reactive character of the polarization mechanism occurring at the interfaces (see below).
It is remarkable that the amount of charge does not match that expected from the polarization of perovskite bulk. As inferred from Fig. 1(b), the dielectric properties of the films give rise to a geometrical capacitance 2.7 pF, corresponding to the highfrequency plateau of the capacitance spectra. A value that would entail polarization charges of the order of pC (given 1 V-bias) as app . Such a small value is in contradiction to those actually encountered within the order of 10 nC [ Fig. 3(b)]. Instead, that amount of charge correlates with the values attained by the low-frequency capacitance in Fig. 1(b): 2 nF at = 0.1 Hz, and even higher capacitances are expected at lower frequencies.
By comparing capacitive and transient charging experiments, we can infer that the same mechanism in behind both responses. That mechanism manifests either as a lowfrequency excess capacitance or as a steady-state charge induced by the applied voltage. The important difference between these two measuring techniques is that while impedance gives the differential, alternating-current small-amplitude response, transient charging is a large-amplitude procedure yielding in our experiments a permanent charge only explainable if a true polarization occurs. Therefore, a modulated or delayed injection current cannot be claimed as originating that observed steady-state response, simply because dc current is suppressed in the used setup. If the low-frequency excess capacitance was an apparent response, one would have expected polarization charges only caused by dielectric properties app , in opposition to that observed here. The occurrence of polarized interfaces in PSCs were proposed some years ago. 9 In the dark, the corresponding excess capacitance has been connected to the formation of double layer-like structures in the vicinity of the perovskite/contact interface in which mobile ions are piled up (Fig. 4) and shield part of the applied voltage. 16,28 Excess dark capacitance of order 1-10 µF cm -2 can be readily explained by this way. We can even roughly estimate the concentration of mobile ions contributing to the surface polarization at the outer electrodes. The perovskite total volume of our samples can be calculated (see Fig. S7) as ~10 $% cm 3 , which gives rise to mobile ionic densities of order & 10 '( cm -3 , which only corresponds to the density portion effectively contributing to the interface polarization. That value results in agreement with recent and previous estimations. 29 Apart from purely electrostatic views accounting for the interface polarization, it has been also recognized that chemical interactions between mobile ions, photogenerated electronic carriers and contacting materials might give rise to the formation of dipole-like structures. 30,31 A survey about the chemical reactivity of the perovskite/contact materials can be found elsewhere. 28 It is emphasized by Bisquert and co-workers in that review paper that the kinetics of charging is hardly understood exclusively in terms of diffusion and double-layer formation. Moreover, interface reactivity forming local chemical bounds largely influence the resulting electronic and ionic overall dynamics. The complexity and lack of complete reproducibility inferred from the dispersion in the total accumulated charge of Fig. 3(b) should be related to the known chemical interaction between MAPbI3 and gold electrodes, as recently highlighted. 30  FIG. 4 The process of interfacial polarization is schematized. Ionic mobile charges are driven by the applied electric field (dashed line) towards the contacts, causing a real polarization/accumulation of charge at the interface between Au contacts and MAPbI3 film.
We remark that our findings corroborate the occurrence of a real polarization (charge imbalance) taking place in perovskite absorbers upon bias in the dark. On the contrary, several papers have recently proposed 21-23 that the commonly reported lowfrequency capacitance features relate to the modulation of operating currents, either recombining or injecting currents, that evolve during the measurement. This effect creates out-of-phase signals not originated by charge polarization and wrongly interpreted in terms of the response of true capacitors. Following this view, it has been even claimed that measured capacitances are just apparent 23 and not connected to any carrier pileup or space charge formation, even under dark conditions. 23 Obviously, that explanation should be confronted with additional experiments, not only impedance responses. Here we have demonstrated the appearance of steady-state polarization voltages in the dark, easily interpreted by means of charged capacitors with values much larger than the film geometrical capacitance. We connect that polarization to the charging of perovskite/contact interfaces by mobile ions.
See the supplementary material for additional information on sample preparation and set-up checking and transfer function calculation.
Data available on request from the authors.