Probing the ionic defect landscape in halide perovskite solar cells

Point defects in metal halide perovskites play a critical role in determining their properties and optoelectronic performance; however, many open questions remain unanswered. In this work, we apply impedance spectroscopy and deep-level transient spectroscopy to characterize the ionic defect landscape in methylammonium lead triiodide (MAPbI3) perovskites in which defects were purposely introduced by fractionally changing the precursor stoichiometry. Our results highlight the profound influence of defects on the electronic landscape, exemplified by their impact on the device built-in potential, and consequently, the open-circuit voltage. Even low ion densities can have an impact on the electronic landscape when both cations and anions are considered as mobile. Moreover, we find that all measured ionic defects fulfil the Meyer–Neldel rule with a characteristic energy connected to the underlying ion hopping process. These findings support a general categorization of defects in halide perovskite compounds.


I. INTRODUCTION
Triggered by the first demonstration of a perovskite solar cell in 2009, [1] significant research efforts have been devoted to the field of perovskite photovoltaics leading to a record power conversion efficiency of 25.2 %. [2] This remarkable performance is made possible by a combination of advantageous properties of perovskite materials, among which most noteworthy are the low exciton binding energies, high absorption coefficients, high charge carrier diffusion lengths and correspondingly long lifetimes of free charge carriers. [3][4][5][6] Additionally, significant progress has been made over the last decade in the development of novel fabrication methods and device architectures as well as optimization by interfacial engineering. [7][8][9][10][11][12] Despite these advancements, several aspects of perovskite solar cells remain a challenge. For example, in many different fabrication approaches, mobile ions have proven to be a major limitation. [13][14][15][16][17] Mobile ions or ionic defects were shown to be the source of current density-voltage hysteresis and were linked to a reduced stability of devices. [13,15,[18][19][20][21] Moreover, ionic defects that form states within the bandgap which act as recombination centers, can reduce the photovoltaic performance of the device. [22,23] Despite their importance, characterization of ionic defects and their properties in perovskite materials is incomplete. According to calculations and experimental reports, the most likely native point defects in methylammonium lead triiodide (MAPbI 3 ) perovskites are charged vacancies such as V + I and V − MA and interstitials such as I − i and MA + i . [24][25][26][27][28] Experimentally, ionic defects and their migration has been observed by a range of methods. [29][30][31] a Corresponding author: deibel@physik.tu-chemnitz.de Noteworthy is the work by Futscher et al. [32], who employed transient capacitance measurements on MAPbI 3 solar cells to reveal both a fast (t < ms) and relatively slow (t ∼ s) species which varied by several orders of magnitude in both their concentration and diffusion coefficient. While in all their measurements the authors assigned the fast species to I − i and the slow species to MA + i , they also observed variations in activation energies, diffusion coefficients and ion concentrations when measuring different samples fabricated either in their laboratory or that of others. This observation is not uncommon, especially in light of the wide range of reported defect parameters presented in literature for the same perovskite material. [24,[32][33][34][35][36][37][38][39][40] One contributing factor to this observation is related to the method of evaluation of the transient iondrift measurements. Recently, we developed an extended regularization algorithm for inverse Laplace transform for deeplevel transient spectroscopy (DLTS) that reveals distributions of migration rates for ionic species instead of single migration rates. [41] This finding suggests that in part, the differences and inconsistencies reported in literature can originate from the fact that various experimental methods may probe different parts of the same ionic defect distribution.
Another significant contributing factor, is the high sensitivity of perovskite materials to their fabrication conditions. Subtle changes in the atmospheric environment [42], annealing process [43], or perovskite precursor stoichiometry [44,45] have all been shown to affect the properties of the perovskite layers. These changes will also influence the properties of the ionic defects. For example, the model reported by Meggiolaro et al. [22] describes the dependence of defect formation energies on the microstructure of the perovskite layer and is in good agreement with the experimental results of Xing et al. [46] Taken together, these observations highlight the need to investigate more deeply the ionic defect landscape in perovskite materials and identify fundamental processes that gov-ern their formation and physical properties.
In this work, we purposefully tune the ionic defect landscape of MAPbI 3 perovskite samples by fractionally modifying the stoichiometry of the perovskite precursor solution. This results in a gradual change in the densities of the various types of defects as suggested by both X-ray photoemission spectroscopy [44] and photoluminescence microscopy measurements. [47] Herein, we directly probe the variations to the ionic defect landscape by impedance spectroscopy (IS) and DLTS, and reveal the interplay between this defect landscape and the electronic landscape of the device. We compared ionic migration rates with literature values, and found that the systematic variation in our study allows to categorize the results from literature, leading to a remarkably good agreement. Moreover, we show that the temperature dependent diffusion parameters of all the ionic defects fulfill the Meyer-Neldel rule, which we link to the fundamental hopping process of mobile ion transport in halide perovskite solar cells.

II. RESULTS
To controllably tune the defect landscape in MAPbI 3 perovskite solar cells, we exploited the method developed by Fassl et al. [44] to fabricate a series of samples from precursor solutions with gradually changing stoichiometry. In short, we start by intentionally preparing an understoichiometric solution, in which a slight deficiency of methylammonium iodide (MAI) is expected to result in films rich in vacancies such as V + I and V − MA . By gradually increasing the MAI content in the solution, a stoichiometric ratio is reached, followed by a transition to an overstoichimetric regime, in which access of MAI increases the densities of I − i and MA + i interstitials. To eliminate the influence of different extraction layers, all devices share a common architecture, in which poly(3,4-ethylenedioxythiophene)poly(styrenesulfonate) (PEDOT:PSS) is used for hole extraction, while [6,6]-phenyl-C 61 -butyric acid methyl ester (PC 61 BM) is used for electron extraction. A thin layer of bathocuproine (BCP) is introduced between the PC 61 BM layer and the Ag contact in order to achieve efficient holeblocking. [48,49] The current density-voltage (JV ) characteristics of the resulting photovoltaic devices are shown in Fig. S1. A very small hysteresis, often associated with the presence of mobile ions, [16,17,[50][51][52] appears when sweeping in both voltage directions. The solar cell parameters averaged over both scan directions are shown in Fig. S2 and are in agreement with the previous report by Fassl et al. [44] In short, while the fill factor (FF) and short-circuit current (J sc ) are only very slightly influenced by the changes in stoichiometry, the open-circuit voltage (V oc ) and consequently the power conversion efficiency (PCE) strongly increase for increasing stoichiometric ratios.

A. Capacitance-voltage profiling
Capacitance-voltage (CV) measurements may offer first insights into the ionic defect landscape of the devices. We performed these measurements at an ac frequency of 80 kHz using a fast sweep rate of 30 V/s in the reverse scan direction. Following the methodology of Fischer et al., [53] the devices were pre-biased for 60 s at 1 V, in order to minimize the influence of mobile ions present at the interfaces of the active layer. The results of the CV measurements ( Fig. S3) were evaluated using the Mott-Schottky approach, [54,55] where V is the applied external voltage, e is the elementary charge, ε 0 is the absolute permittivity and ε R is the relative permittivity. By applying Eqn. (1) to the range dominated by the depletion capacitance, the built-in potential (V bi ) and effective doping density (N eff ) can be extracted. In Fig. 1, these values are compared to the PCE values from Fig. S2. The results indicate that both V bi and N eff increase with increasing stoichiometry. The increase in V bi is in agreement with the findings of Fassl et al., [44] where a shift in the exponential diode characteristics revealed a similar trend in V bi . Interestingly, the increase in N eff suggests an overall higher defect density for overstoichiometric samples since ions introduce additional charges and affect the net doping concentration. [56][57][58] This is in agreement with the experimental observation of a lower photoluminescence quantum efficiency for samples with higher stoichiometry. [47]

B. Determining the defect landscape by IS and DLTS
Advanced spectroscopic techniques such as impedance spectroscopy (IS) and DLTS offer further insights into the defect landscape of the devices. In an IS experiment, the current response to an externally applied alternating voltage at a certain frequency ω is measured and considered as a capacitance signal by taking into account the imaginary part of the impedance Z, [59,60] by modeling the solar cell as a capacitor in parallel to a shunt resistance. To obtain a complete picture of the defects and to quantify their physical properties, we performed IS measurements over a wide frequency range (0.6 Hz < ω < 3.2 MHz) and at different temperatures (200 K to 350 K in 5 K increments).
There are two responses in the representative IS spectra as shown in Figs. 2 and S4: a low frequency response (< 10 2 Hz) at high temperatures (> 315 K) and a step at higher frequencies (> 10 2 Hz) and lower temperatures (< 285 K) for each of the investigated samples. These responses can be assigned to two different defects. Particularly noteworthy is the increase of the low frequency section of the spectra with increasing stoichiometry, which indicates its impact on the properties of the corresponding ionic defect. From the capacitance spectra, we are able to extract the ion (defect) diffusion coefficient D based on the equation: where the k B is the Boltzmann constant, T is the temperature, D 0 is the diffusion coefficient at infinite temperature and E A is the activation energy for ion migration. This is done by extracting the ion migration rates (emission rates is the corresponding term from DLTS when applied to study electronic defects in semiconductors) [32,35,61,62] as defined by from the maxima of the derivative −ωdC/dω, shown in Fig. S5. The presence of two maxima in these spectra reveal two distinct ionic defects, β and γ. We summarized the migration rates associated with these two defects in an Arrhenius diagram (Fig. S6) and calculated the activation energies E A and the diffusion coefficients D 300K at 300 K based on Eqn. (4). Interestingly, the defects β and γ show opposing trends in terms of E A , D 300K , and N ion with varying stoichiometric ratios ( Fig. 3). For β, the activation energy decreases whereas the diffusion coefficient at 300 K increases for increasing stoichiometry, whereas γ shows the inverse behavior. This suggests that by increasing the sample stoichiometry, ion migration of defect γ is suppressed, while the defect β becomes more mobile.
The accumulation of mobile ions at the interfaces of the active layer, driven by the internal electric field of the photovoltaic devices, was reported in several studies. [16,52,63,64] The resultant inhomogeneity of the ionic distribution in the perovskite active layer leads to the formation of a Debye layer of cations at the hole transport layer and a Debye layer of anions at the electron transport layer. [65,66] As a result of the inhomogeneity, the defect density from IS measurements cannot be determined by using the approach by Walter et al. [67] for semiconductor defects. A more feasible approach can be found by taking into account the capacitance of the ionic Debye layer, [68] In this case, ∆C is proportional to the capacitance step observed in Fig. S4. Following this approach, the ionic defect concentration of β slightly decreases with increasing stoichiometry, while N ion of γ shows a notable increase as shown in Fig. 3. We conclude that defect γ dominates the behavior of overstoichiometric samples, while the more mobile defect β dominates the understoichiometric ones.
To expand the insights gained by IS, we performed DLTS measurements on the same set of solar cells. For DLTS, a voltage filling pulse (from 0 V to 1 V for a duration of 100 ms) is applied to the devices, while measuring the capacitance response at 80 kHz until the solar cell returns to equilibrium conditions. [60,69] During the filling pulse, mobile ions are pushed from both interfaces of the perovskite layer into the perovskite bulk until they reach a new steady state condition. After the filling pulse, the mobile ions move back to the interfaces caused by the internal field, which introduces a change of the solar cell capacitance. [32] The resulting transients, shown in Fig. S7, were averaged over 35 single measurements to yield a high signal-to-noise ratio, and were measured within the same temperature range as the IS measurements. For the evaluation, we performed the commonly utilized boxcar method [69] as shown in Fig. 2 and S8. The analysis of the DLTS data reveals three different temperature-dependent peaks associated with three distinct defect states. Two of these defects exhibit high migration rates at low to medium temperature range, while the third shows low migration rates at higher temperatures. Following the good agreement in the peak position shown in Fig. 2 and that of the migration rates plotted in the Arrhenius diagram (Fig. S6), we conclude that one of the two defect states with high migration rates corresponds to defect β previously identified by IS. The defect exhibiting low migration rates is attributed to γ in agreement with IS. Similarly to the IS data, defect γ dominates the boxcar spectrum for high stoichiometry samples. The remaining defect with comparably high migration rates was not observed in IS measurements and was labeled δ.
Unlike IS, DLTS data allows to distinguish between positive and negative ionic defects, i.e. anions and cations. As shown in Fig. 2 and S8, defects β and δ have a positive sign and correspond therefore to anions, whereas γ corresponds to a cation. As mentioned above, the migration rates (e t = 1/τ) of these ionic defects can be extracted from the position of the peaks shown in Fig. S8 and complement the results of IS measurements when plotted in the same Arrhenius diagram (Fig. S6). We note that since the slow response of γ dominates for overstoichiometric devices, the transients for these devices at very high temperatures did not return to equilibrium within the recorded transient time length of 30 s (Fig. S7). We excluded these non-equilibrium transients from the determination of defect parameters, as they lead to overestimated migration rates for a given temperature.
The overall trend of E A and D 300K for defects β and γ, shown in Fig. 3, is comparable with the results obtained by IS. We note that while defect parameters extracted using IS and DLTS exhibit the same general trend, they do show some variance in the absolute values of the extracted defect parameters. These differences, which are visible as an offset in the defect parameters, might arise from the broad distributions of ionic defects, reported in our recent work. [41] Different parts of the same defect distribution are probed by each of the two methods. For defect δ, identified solely via DLTS, we observe a significant increase in E A for overstoichiometric samples, accompanied by a strong decrease in D 300K . The ionic defect concentration, N ion , can be extracted from DLTS measurements by using the ratio between the capacitance change ∆C caused by the ionic movement and the steady state capacitance C ∞ , given by: As shown in Fig. 3, the trend of N ion for defects β and γ with changing stoichiometry is also in agreement with the results obtained with IS. For defect δ, the ionic defect concentration is found to increase with stoichiometry, similar to the behavior of defect γ.
As part of our scenario in our recent work, [41] we assign the anion β to V − MA and δ to I − i . The cation γ is attributed to MA + i . This assignment is in good agreement with the results of Fassl et al., [44] where XPS measurements showed an increase in the I/Pb and N/Pb ratios with increasing stoichiometry. We note that the assignment of cation γ to MA + i may appear in contrast to the reports by Maier and coworkers that claim that methylammonium cations are only mobile in terms of reorientation, ruling out the migration of this species. [70,71] However, it was shown that rotational dynamics of methylammonium cations occurs with relaxation times in the ps timescale at room temperature, [72][73][74] which would be too fast to explain hysteresis. Other groups propose that methylammonium can slowly migrate, [16,33,56] since other possible cations, such as iodine vacancies, are expected to have far higher diffusion coefficient. [34,75,76] Neverthe-less, we stress that DLTS provides information solely on the charge of the ionic defects and cannot directly determine the specific ionic species.

A. Interplay between the ionic and electronic landscapes
The mixed ionic-electronic conducting nature of perovskites dictates that the ionic and electronic landscapes of these materials cannot easily be decoupled. [77,78] One aspect linking the two is related to the effect of ion accumulation at the interfaces of the perovskite layer and the extraction layers that sandwich it. [79] Such ionically charged interfacial layers influence the internal electric field and the builtin potential of the device, suggesting that the estimation of V bi from CV measurements as discussed in Sec. II A needs to be re-evaluated. [80] The validity of the Mott-Schottky relation (Eqn. (1)) is based on the assumption that the charge carrier density within the perovskite layer is homogeneously distributed, which may not be the case for perovskite solar cells. While we pre-biased the devices before measuring CV in an attempt to eliminate the accumulation of ions at the interfaces, the resultant trend in V bi is consistent with what has been observed by diode J-V characterization, for which no pre-biasing was applied. [44] This might indicate that ions still accumulate at the interfaces, resulting in a voltage drop that changes the V bi . A simple model that accounts for this voltage drop can be constructed by considering these interfacial ion densities as Debye layers. [65,68,79] The overall charge for one ionic species can be expressed by ∆Q = eN ion L D , where L D is the Debye length according to In order to account for the potential drop ∆V caused by the mobile ion density of cations N C and anions N A , we assumed a series connection of the capacitance caused by cations C A and anions C A , With Eqn. (8) the corrected V bi,corr can be obtained by correcting the determined built-in potential by CV measurements with the voltage drop caused by mobile ions at the interfaces, The capacitance responses C A and C C by anions and cations, respectively, can be estimated by the capacitance steps in the IS spectra from Fig. S4, as they correspond to the ion density N ion according to Eqn. (5). Taking into consideration the ionic interfacial layers to suppress the trend observed in V bi , a more consistent value of around 1.1 V can be obtained as shown in Fig. 1. This result is more expected, since all the devices share the same extraction layers and contacts. As shown in a recent study, [78] a shift in V bi can also be caused by electronic charge carrier accumulation at the hole transport layer interface. While our calculation correct the influence of ions on V bi , we cannot rule out an additional electronic influence. However, the result of our correction suggests that, here, the consideration of ions is sufficient. One interesting, and seemingly contradicting, observation is related to the observed increase in V oc , which coincides with an increase in the overall ionic defect density with increasing stoichiometry. Recent studies suggest that mobile ions may act as non-radiative recombination centers, [22,23,81] evidenced, for example, by a decrease in the photoluminescence quantum efficiency (PLQE). Indeed, overstoichiometric samples exhibit a markedly lower PLQE than understoichiometric ones. [47] Based on these results, one might expect for overstoichiometric devices lower open-circuit voltages than for understoichiometric ones, [82] in contrast to the experimental observation shown in Fig. S2. However, this apparent discrepancy can be reconciled when taking into account the substantial increase in V bi with higher stoichiometric ratio. Consequently, while a high ionic defect concentration has a negative effect on V oc due to increase of non-radiative recombination, this effect is weaker than the considerable increase introduced by changes to the energetic alignment between MAPbI 3 and the transport layers and the resultant change in V bi . [44] Moreover, the impact of ions on the energy landscape is in agreement with a recent study by the group of Maier, [83] where the authors report an increase of band bending in MAPbI 3 toward the electron transport layer originating from an ionically dominated space charge. The interplay of ions and the space charge potential enable device improvements by interfacial engineering.
The intricacy of the interplay between the ionic and elec-tronic landscapes is exemplified by plotting the E A versus the V bi,CV as shown in Fig. 4. The E A of defects β and γ are of similar magnitude and show a broadly linear dependence on the built-in potential, albeit with slopes of opposing signs. Straight dashed lines with slopes of ±1 were added to Fig. 4 as a guide to the eye. These similar, but opposing trends in slope supports our earlier assignment of these defects to be related to the same type of MA ion. We can associate defect β with an MA vacancy with negative charge, and γ with a positively charged MA interstitial. Our interpretation of defect δ cannot be confirmed in this manner, since we do not observe the corresponding defect species with an opposing charge. The dependence of E A on V bi might be a consequence of the band bending introduced by the interfacial ion accumulation. As the ion concentration increases, stronger band bending at the interfaces leads to higher fields that impedes the ionic hopping process at the interfaces lowering their overall mobility. This explanation is supported by plotting E A and D 300K versus N ion (see Fig. S9). Although the trends are less clear, we generally observe an increase of E A and a decrease in D 300K for higher defect concentrations. The dependence is in agreement with our finding that mobile ions are pushed stronger towards the interfaces caused by the relation between the internal electric field and the ion density. As a result, the diffusion coefficient decreases with higher ion density. This interaction between the ionic and electronic landscapes highlights the need to construct a clearer picture of the underlying defect physics in perovskite devices.

B. Unraveling the defect landscape across the literature
To evaluate our results in a broader context, we compared the migration rates measured herein, with data available from literature. We chose several studies with similar measurement methods such as DLTS and IS, but with a selection of different perovskite materials and transport layers (as summarized in Tab. 1 in SI). Included in Fig. 5 are the results of Samiee et al. [38] who observed two different defects in a mixed halide perovskite using IS, and three defects (attributed to cations) probed by Yang et al. [36] using DLTS on FAPbI 3 . Additionally, included are the emission rates of two defects measured using current DLTS by Rosenberg et al. [37] in MAPbBr 3 single crystals and those probed by Xu et al. [40] on FAPbI 3 lightemitting diodes. Finally, the results of Futscher et al. [32] using transient ion-drift measurements (which is DLTS under a different name) were added, which exhibit two ionic species assigned as I − i and MA + i interstitials in MAPbI 3 solar cells. This comparison reveals a remarkable agreement between reports despite the use of different perovskite compositions and device structures. The reported emission rates broadly fall into two categories: those with low emission rates at high temperatures or those with high emission rates at high or medium temperatures. This assessment indicates that there are most likely two dominant underlying ionic defects which can be universally observed in all perovskite materials investigated thus far.  [32,[36][37][38]40] (often called emission rates in the papers) plotted in an Arrhenius diagram for comparison to our findings (species β, γ, δ). All reported emission rates can be associated with two regimes at low emission rates and high temperatures and at high emission rates at high and middle temperatures.

C. Meyer-Neldel Rule
To gain an understanding of the underlying mechanism for ion transport, we examine the relationship between the diffusion coefficient D 0 (at infinite temperature) and the activation energy E A according to Eqn. (3) and Fig 3. Fig. 6a reveals a clear linear dependence between these two values for each of the ionic defects. Such a linear relation is known as the Meyer-Neldel rule, which is often used to describe thermally activated processes. [84] According to the Arrhenius Eqn. (3), the Meyer-Neldel rule states that the pre-factor D 0 itself depends on the activation energy E A via: where D 00 refers to the critical diffusion coefficient, E MN is the characteristic energy and T MN is the corresponding characteristic temperature. Eqn. (10) yields very similar values for E MN : 28 meV, 30 meV and 35 meV for β, δ and γ, respectively. The critical diffusion coefficient D 00 of β with 3 · 10 −7 cm 2 /s is one order of magnitude higher than for δ (1 · 10 −8 cm 2 /s). γ has the lowest D 00 which is equal to 4 · 10 −10 cm 2 /s. As a consequence of the Meyer-Neldel rule, the migration rates shown in Fig. S6 and the diffusion coefficients (presented in Fig. 6b) that are associated with the same defect, intersect at 1000/T MN . At this intersection point, which is different for each defect species, the migration rates become independent of stoichiometry. In other words, the ionic defect landscape is no longer affected by stoichiometry at T MN . As guide to the eye, we added dashed lines to Fig. 6b, which were extracted from the values of the fits presented in We propose two possible origins for the Meyer-Neldel behavior. The first is based on disordered organic semiconductors, where the legitimacy of the Meyer-Neldel rule was linked to a Gaussian distribution of defect levels or hopping energies. [85] Despite being crystalline materials, it is well established that halide perovskites contain a significant amount of disorder due to spatial and temporal variations of octahedral tilts and molecular rotations. [86] A range of defect environments and transition pathways are therefore expected. Indeed, in our recent work, we demonstrated a distribution of migration rates for each of the reported defects. [41] This is also supported by a combined experimental-theoretical work where modeling of ion migration induced PL quenching was only possible by applying a Gaussian distribution of ion migration rates. [87] A second explanation arises if a multi-excitation entropy model is considered. A single hopping event is usually the result of a multi-phonon excitation, since the activation energy for ion migration is large compared to the phonon energy (e.g. 16.5 meV for optical phonons). [88,89] Consequently, a large number of activation pathways are available for each hopping event. A higher activation energy results in a larger number of distinct pathways expressed by the entropy, which is proportional to the exponential pre-factor D 0 . [90,91] Based on this model, the Meyer-Neldel rule originates from the absorption of N A phonons with N A · E ph = E A , which transfers the ion first to an activated state, and then-accompanied by the emission of multiple phonons-to the target site of the perovskite lattice. [92] To probe the atomistic nature of a typical diffusion process, we performed first-principles calculations of charged vacancy migration in the room temperature phase of MAPbI 3 using the technical setup reported elsewhere. [33] We consider a low en-ergy transition in the (001) plane as illustrated in Fig 7. The associated migration barrier of 0.55 eV and it follows a curved diffusion pathway. Even in a single plane, due to the presence of MA, the initial and final states differ in energy by 60 meV, which supports the first disorder explanation. We further determine the vibrational frequency at T = 300 K around using CarrierCapture. [93] Effective frequencies of 0.4-0.7 THz represent the curvature of the potential energy surface along the directions of ion diffusion. These are unusually soft owing to a combination of the heavy elements and the flexible perovskite structure.
A simple estimation of N A suggests that hundreds of phonon modes are involved in a single hopping process, which supports the second explanation.
While we cannot yet assign the validity of the Meyer-Neldel rule to a single origin, it offers interesting insights into the physical mechanisms of ion migration in halide perovskites.

IV. SUMMARY
In summary, we investigated the ionic defect landscape of MAPbI 3 samples with gradually varying defect densities, introduced by fractionally varying the stoichiometry of the perovskite precursor solution (MAI:PbAc 2 ). By combining the results of IS and DLTS measurements, we identify three ionic defect, which we attribute to V − MA , I − i and MA + i . We explore the tight link between the ionic defect and electronic landscapes in perovskite devices and reveal that the accumulation of defects at the interfaces of the perovskite layer results in an increase of the built-in potential for increasing stoichiometry, which we show to be the dominant factor influencing the open-circuit voltage of the devices. The presence of ionic in- terfacial layers is also shown to affect the E A of the various defects, by impeding their transport due to high electric fields they introduce. We compared the temperature dependent ion migration rates to the literature, and were able to categorize defect parameters of different perovskite materials and device architectures. Importantly, we find that the ionic defects we observed fulfill the Meyer-Neldel rule. We propose that the origin of the Meyer-Neldel rule lies either in the distribution of migration pathways or the multi-phonon emission process that characterizes the hopping of ions. Our results offer significant insights into the defect physics of perovskite materials and progress the current understanding of the underlying processes that govern the properties of this phenomenal class of materials.
Modified poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (m-PEDOT:PSS) was spin cast on the clean substrates at 4000 rpm for 30 s and annealed at 150 • C for 15 min to act as hole transport layer. [94] The MAPbI 3 active layer was formed using the lead acetate trihydrate route following previous works. [44,49] In short, the perovskite solution (at different stoichiometry of 2.96:1 to 3.06:1 in 0.02 steps PbAc 2 :MAI) was spin cast at 2000 rpm for 60 s in a dry air filled glovebox (relative humidity < 0.5 %). After blowing 25 s and drying 5 min, the as-spun films were annealed at 100 • C for 5 min forming a uniform perovskite layer. The prepared samples were transferred to a nitrogen filled glove box, where an electron transport layer [6,6]-phenyl-C61-butyric acid methylester (PC 61 BM), 20 mg/ml dissolved in chlorobenzene, was dynamically spin cast at 2000 rpm for 30 s on the perovskite layer followed by a 10 min annealing at 100 • C. Sequentially, a bathocuproine (BCP), 0.5 mg/ml dissolved in isopropanol, hole blocking layer was spin cast on top of the PC 60 BM. The device was completed with a thermally evaporated 80 nm thick silver layer.
jV characterization: The current density-voltage (jV) characteristics were measured by a computer controlled Keithley 2450 Source Measure Unit under simulated AM 1.5 sunlight with 100 mW/cm 2 irradiation (Abet Sun 3000 Class AAA solar simulator). The light intensity was calibrated with a Si reference cell (NIST traceable, VLSI) and corrected by measuring the spectral mismatch between the solar spectrum, the spectral response of the perovskite solar cell and the reference cell.
Defect spectroscopy measurements: All defects were measured using a setup consisting of a Zurich Instruments MFLI lock-in amplifier with MF-IA and MF-MD options, a Keysight Technologies 33600A function generator and a cryo probe station Janis ST500 with a Lakeshore 336 temperature controller. We performed the defect spectroscopy in the temperature range of 200 K to 350 K in 5 K steps, controlled accurately within 0.01 K, using liquid nitrogen for cooling. DLTS, IS and CV measurements were done applying an AC frequency of 80 kHz with amplitude of V ac = 20 mV. For DLTS, the perovskite solar cells were biased from 0 V to 1 V for 100 ms. The transients were measured over 30 s and averaged over 35 single measurements. For CV profiling, the solar cells were pre-biased at 1 V for 60 s and rapidly swept with 30 V/s in reverse direction. 6 - Capacitance-voltage measurement on the perovskite solar cells with variation of precursor stoichiometry at room temperature an with an ac frequency of 80 kHz. The data were evaluated according to the Mott-Schottky approach by plotting 1/C 2 and fitting the linear part at around 0.8V which correspond to the depletion capacitance.