High-throughput analysis of the ideality factor to evaluate the outdoor performance of perovskite solar minimodules

Halide perovskite solar cells exhibit a unique combination of properties, including ion migration, low non-radiative recombination and low performance dependence on temperature. Because of these idiosyncrasies, it is debatable whether standard procedures for assessing photovoltaic technologies are sufficient to appropriately evaluate this technology. Here, we show a low dependence of the open-circuit voltage on the temperature of a MAPbI3 minimodule that allows a high-throughput outdoor analysis based on the ideality factor (nID). Accordingly, three representative power loss tendencies obtained from I–V curves measured with standard procedures are compared with their corresponding nID patterns under outdoor conditions. Therefore, based on the linear relationship between T80 and the time to reach nID = 2 (TnID2), we demonstrate that nID analysis could offer important complementary information with important implications for outdoor development of this technology, providing physical insights into the recombination mechanism dominating performance, thus improving the understanding of degradation processes and device characterization. The investigation of perovskite solar modules under outdoor conditions could provide insights into device operation and degradation in the field. Velilla et al. report on the potential of the ideality factor to analyse outdoor device performance evolution over time, distinguish between degradation modes and estimate the lifetime.

T o evaluate the lifetime of a photovoltaic device, a parameter that refers to the time at which the device reaches 80% of its initial rated power (T 80 ) is commonly used as a figure of merit. T 80 depends on various factors, such as the materials and procedures used for device fabrication, cell interconnects, weather conditions, seasonal variations, installation conditions, shading and soiling effects and electrical mismatches between cells 1 . This parameter is commonly obtained from the relationship between maximum power and time in a long-term analysis of a device under real outdoor operating conditions. Moreover, considering that the performance over time shows seasonal behaviour and a gradual performance loss tendency, T 80 has been commonly fitted using statistical methods, such as linear regression, to estimate the degradation rate 2 . However, in the case of emerging technologies such as perovskite solar cells (PSCs), most stability studies have focused on small, laboratory-scale devices operating indoors and few statistical data have been collected under real outdoor operation 3 . Nevertheless, under high-irradiance conditions, PSCs demonstrate substantial differences from conventional Si cells, as has been shown for perovskite minimodules operating outdoors 4 and for non-encapsulated solar cells under simulated weather conditions in the laboratory 5 . These results indicate that PSCs show lower correlations of their performance and open-circuit voltage (V oc ) with temperature than other commercial technologies, such as silicon 6 , for which the deleterious effects of temperature on performance are well known 7,8 . This difference in temperature sensitivity is an important aspect of PSC technology.
PSCs are expected to have an important impact in the future if they are able to provide notable performance outdoors. Outdoor conditions are highly demanding, as they are characterized by daynight, seasonal and weather cycles that correspond to drastic variations in irradiation, temperature and moisture. While accelerated performance tests are useful for predicting the behaviour of devices, continuous outdoor tests are also required to provide information on the applicability of this technology in the real world. The outdoor exploitation of solar devices requires encapsulation to protect the electrodes and active areas of cells against the environment, avoid corrosion processes, increase the electrical insulation to eliminate leakage currents and provide thermal and mechanical support 9 . In this context, international standards such as IEC 61215 suggest various accelerated tests intended to identify potential failures in silicon photovoltaic modules (broken interconnects, cracked cells, delamination, dielectric breakdown, bypassed diodes and corrosion). Thus, based on the experience gained in recent decades through such accelerated tests and field evaluations, these failures in photovoltaic modules have been correlated with various degradation modes, such as corrosion, delamination, discoloration, glass breakage, cell cracking, potential-induced degradation, current leakage, ion migration, hot spots and soiling 10,11 . Nevertheless, because the standards do not include all possible degradation modes and, in real operation, photovoltaic devices can be affected by different degradation modes simultaneously, it is not always possible to estimate the real lifetime from these tests 12 .
In the case of emerging technologies such as PSCs, no international standards have been fully established, and most published works have focused on laboratory-scale cells (that is, 1 cm 2 or smaller in size); consequently, various methods and materials have been used to evaluate the stability and degradation performance of these technologies 5,[13][14][15][16][17] . In this regard, a broadly supported consensus statement on reporting data related to stability assessment was recently published, highlighting certain particularities of PSC technology that must be taken into account 18 . For instance, in contrast to mature photovoltaic technologies such as Si and GaAs, PSCs show performance loss reversibility under day-night cycles 19,20 , a hysteresis effect in the current-voltage (I-V) curves, which could induce errors in performance determination 21 , and a lower dependence of performance and V oc on temperature 22 . Nevertheless, while these peculiarities of PSCs could be seen as drawbacks for their systematic High-throughput analysis of the ideality factor to evaluate the outdoor performance of perovskite solar minimodules Esteban Velilla 1,2 , Franklin Jaramillo 1 ✉ and Iván Mora-Seró 2 ✉ Halide perovskite solar cells exhibit a unique combination of properties, including ion migration, low non-radiative recombination and low performance dependence on temperature. Because of these idiosyncrasies, it is debatable whether standard procedures for assessing photovoltaic technologies are sufficient to appropriately evaluate this technology. Here, we show a low dependence of the open-circuit voltage on the temperature of a MAPbI 3 minimodule that allows a high-throughput outdoor analysis based on the ideality factor (n ID ). Accordingly, three representative power loss tendencies obtained from I-V curves measured with standard procedures are compared with their corresponding n ID patterns under outdoor conditions. Therefore, based on the linear relationship between T 80 and the time to reach n ID = 2 (T nID2 ), we demonstrate that n ID analysis could offer important complementary information with important implications for outdoor development of this technology, providing physical insights into the recombination mechanism dominating performance, thus improving the understanding of degradation processes and device characterization.
analysis, they also provide new opportunities for the characterization of PSCs 23 . This technology is in its infancy, and there are few statistical data available for large devices operated outdoors 3 . Therefore, insufficient data are available to fully establish or identify the degradation modes and mechanisms of PSCs and their impact on outdoor performance evolution.
Conventionally, the evolution of solar cell device performance is monitored through the systematic measurement of I-V curves considering the temperature and illumination conditions. In the laboratory, it is relatively easy to set up tests to track the performance at the maximum power point; however, such control is intrinsically unreasonable outdoors. The illumination and temperature variations induced by day-night, seasonal and weather conditions necessitate a systematic analysis of a high quantity of data, depending on the measurement sampling rate and exposure time 24 . Hence, in such power loss studies, it is common to correct for temperature and irradiance in I-V curves in accordance with standard test conditions (STC) (corresponding to an irradiance of 1,000 W m −2 and a module temperature of 25 °C). However, such conditions are difficult to reach outdoors 25 . In addition, although the conventional method of monitoring outdoor module performance based on I-V curves produces rich numerical data, it offers no direct indication of the physical processes occurring in the device and thus provides no information about the degradation process.
In this context, ideality factor, n ID , also called the quality factor or shape curve factor, has been used to define the electrical behaviour of solar devices due to its relationship with conduction, transport, recombination and behaviour at interface junctions, providing direct information on the dominating recombination processes. Therefore, in silicon, n ID has been widely studied and estimated in various ways, such as using the relationship between the open-circuit voltage (V oc ) and light intensity (equation (1)) to overcome the effects of series resistance 26 , performing numerical calculations 27 and extracting this parameter from I-V curves at different light intensities and temperatures using equivalent circuit models 28 . For PSCs, although there are relatively few reports related to this parameter, Tress and coworkers have reported a full interpretation of n ID for non-encapsulated cells, establishing the relationship between the dominating recombination process, the light intensity and V oc (ref. 29 ). In addition, n ID has been estimated through impedance/frequency-response (IFR) analysis [30][31][32] , from the I-V curve at standard test conditions using an one-diode model 33 , and from the dark I-V curve through numerical simulation considering the continuity and Poisson's equations 34 . Moreover, agreement has been shown between the n ID value estimated from the recombination resistance extracted through IFR analysis and the value calculated from V oc at different light intensities 31,32 : where e is the electron charge, m is the number of identical cells connected in series, E g is the light absorber bandgap, k B is the Boltzmann constant, T is the temperature, G is the irradiance and G 0 is a constant with the same units as G.
Here, all of these considerations and the current state of PSC technology motivate us to explore new characterization methodologies that do not merely determine the degradation loss but also provide an understanding of the degradation modes and mechanisms involved 35 . Specifically, it is of interest to take advantage of the properties of perovskite materials and perform evaluations following the common standards and new evaluations developed, especially for PSCs, to create a better understanding of real behaviour outdoors, including the behaviour of larger devices such as minimodules or modules. In this context, despite the potential of n ID , this parameter has not been used to monitor device evolution over time to see how the relevant processes evolve, for example, in the case of degradation. Therefore, we propose to take advantage of the weak dependence of V oc on T in PSCs 4,5,22 to calculate n ID and use it as a figure of merit for monitoring and characterizing the outdoor performance of this technology. In this way, day-night cycles, including dawn and noon conditions, can naturally provide a broad range of illumination conditions allowing n ID to be determined. Moreover, we can take advantage of this interesting parameter to determine the physical processes acting on devices to link them with the degradation modes. For this purpose, we tracked outdoor MAPbI 3 minimodules and recorded the evolution of the maximum power (P max ) under power rating conditions suggested by the IEC 61853-1 standard, specifically the nominal operating cell temperature (NOCT) conditions, to compare the resulting data with the n ID evolution estimated using equation (1). We show that this new methodology identifies features similar to those found using the classical approach based on P max , enabling tracking of the physical processes occurring in the device. Finally, we show a linear relationship between the time at which the module reaches n ID = 2 (Tn ID2 ) and T 80 , indicating the complementarity of these two parameters. This complementarity has important implications for improving the characterization and understanding of degradation processes and, consequently, for the outdoor optimization of PSCs.

Evaluation of the device outdoor performance
MAPbI 3 minimodules of 8.0 cm 2 in size formed of m = 4 cells interconnected in series, with a mesoporous inverted structure (NiO x / Al 2 O 3 /MAPbI 3 /PCMB/rhodamine/Au), were fabricated on ITO substrates of 5 × 5 cm 2 in a drybox by spin coating 36 (Fig. 1a,b, Supplementary Fig. 1 and Methods). The devices were manually encapsulated with ethylene vinyl acetate (EVA). Different batches of encapsulated minimodules with different performances were exposed to natural sunlight, without a tracker, in the facilities of the Solar Cell Outdoor Performance Laboratory of the University of Antioquia (OPSUA) in Medellín, Colombia, during January to June 2019 ( Fig. 1c and Supplementary Fig. 2). Regarding full outdoor performance tests, it is worth remarking that the IEC 61853-1 international standard allows the evaluation of different solar technologies based on different power ratings, accounting for irradiance and temperature, to determine the impact of weather variables on performance 37 , while the ISOS-O-2 protocol is intended to evaluate the P max stability of devices 38 . In this sense, both protocols are compatible and complementary, and both are based on data extracted from the I-V curve. Therefore, weather variables such as irradiance and ambient temperature (T) as well as the I-V curves of the devices were registered and stored every minute during daylight hours (5:30 to 18:30) using a previously developed monitoring system 25 .
To ensure a full I-V curve, V oc was measured and recorded before any other measurement, and the curve was subsequently scanned between −0.5 V and 1.1 V oc in the forward direction. After scanning, the I-V tracer was disconnected and the device was in the open-circuit condition.
The collected high-throughput outdoor data were processed in accordance with the flowchart shown in Supplementary Fig. 3 to evaluate the performance (Supplementary Notes 1 and 2). In brief, from the I-V curves, photovoltaic parameters such as V oc , the short-circuit current (I sc ), the fill factor (FF), the photoconversion efficiency and P max were extracted. In addition, the irradiances and ambient temperatures were also recorded during I-V measurement (synchronously). Subsequently, the raw data were filtered based on the linearity determination criterion to minimize transient effects related to changes in irradiance, shadowing caused by clouds or droplets, or atypical data 4 ( Supplementary Fig. 4a). Therefore, a high-throughput set of data was obtained to estimate the outdoor performance (Fig. 2). Moreover, the power loss tendency or degradation shape was obtained by calculating the outdoor performance observed in the measurement sets, each of which contained measurements recorded over 100 h of outdoor exposure ( Fig. 3a-c). The data in each set were filtered considering a deviation of 5% from the irradiance levels corresponding to the power rating conditions indicated by IEC 61853-1 (ref. 37 ), that is, 1,000 W m −2 corresponding to STC, 800 W m −2 corresponding to NOCT conditions, 500 W m −2 corresponding to low-temperature conditions and 200 W m −2 corresponding to low-irradiance conditions. The period of time considered to estimate the average outdoor performance was slightly longer than 4 days (100 h), which is long enough to consider the data recorded in each set to be statistically valid, allowing the calculation of reliable average values for tracking the performance evolution.
From the analysed outdoor samples, three different P max evolution patterns over time can be distinguished, named convex, linear and concave patterns because of the shapes they exhibit (Fig. 3a-c). See Supplementary Figs. 5-8 for a further analysis of each behaviour pattern. These three distinctive patterns are commonly described for degradation processes in the literature to study possible degradation paths and estimate the failure time 39 . Figure 2 shows the data collected during only the first 100 h of outdoor operation of representative devices of each pattern. The corresponding maps show the average impact of weather variables on P max , V oc and I sc over a broad set of T values and irradiances, ranging between 18 and 42 °C and up to 1,200 W m −2 , respectively. These ranges correspond to the most representative values of the weather variables and performances recorded during the time window considered ( Supplementary Fig. 2-l). Figure 2 allows us to identify some trends, such as the low-temperature dependence of V oc . In this regard, the data related to the convex pattern ( Fig. 2a,d,g) and the linear pattern (Fig. 2b,e,h) follow the expected trend, with P max , I sc and V oc increasing with increasing irradiance but showing only a low sensitivity to temperature. In contrast, the data related to the concave pattern sample do not exhibit this monotonic variation, instead showing local maxima or minima at various irradiance levels and temperatures (Fig. 2c,f,i). Moreover, when a lower total sampling time of 50 h is considered, the T 80 of this sample is estimated to be 80 h ( Supplementary Fig. 8g), indicating that during the first 100 h of exposure, fast degradation occurs, causing the non-monotonic behaviour depicted in Fig. 2c,f,i.
Although all of the minimodules were fabricated and monitored in a similar way and exposed to similar outdoor conditions ( Supplementary Fig. 2), a broad range of behaviours is observed, which appears to be mainly related to the manual encapsulation method used ( Supplementary Fig. 5). This fact allows us to check the methodology proposed here over a broad range of behaviours, as these three different P max patterns have all been previously observed for PSCs 40 , consequently showing the generality of the approach. For instance, the convex pattern has been observed for encapsulated PSCs stored at room temperature, for which the P max loss was attributed to interface deterioration inducing interfacial recombination, along with perovskite layer degradation related to the formation of deeper defect states 41 . The linear and convex patterns have both previously been observed in non-encapsulated cells under controlled relative humidity conditions, depending on the PbI 2 to MAI ratio 42 , while the concave pattern has been observed in encapsulated cells exposed to different levels of sunlight, indicating that light intensity is the main variable that accelerates the degradation process 14 . In addition, this shape has also been observed in non-encapsulated PSCs under different atmospheres and light intensities, with faster degradation under higher relative humidity 16 and in non-encapsulated devices tested under air exposure, indicating an increase in electrical traps due to ion migration from the perovskite layer to other layers as the main reason for the degradation 43 . It is worth noting that in these cases, the controlled atmospheres enabled correlation with the physical origins of the degradation, whereas under outdoor conditions, because various factors may be involved in the degradation process, determining the physical origin of the degradation is not always possible.

Evolution of the ideality factor of outdoor-exposed devices
Considering the low dependence of the performance of PSCs on T, as observed in the literature 4,5 and confirmed by the maps of our data in Figs. 2 and 3, n ID can be considered a good parameter for monitoring the outdoor evolution of this technology. While taking advantage of the different levels of illumination caused by day-night cycles to collect a large amount of data across a broad range of illumination conditions, n ID can be calculated to provide information on the physical processes occurring during the exposure. Accordingly, the average n ID values were calculated using equation (1) while considering the different measurements of V oc recorded at different irradiance levels in every 100 h of the high-throughput data ( Supplementary Fig. 9). The results are shown in Fig. 3d-f in the form of boxplots to illustrate the deviations from the average value due to temperature changes. n ID also exhibits three distinct evolution patterns or shapes, pointing to a direct relation and complementarity with P max . Specifically, a convex P max evolution pattern corresponds to a concave n ID evolution pattern (Fig. 3a,d) and vice versa (Fig. 3c,f), while for a linear P max pattern, a linear n ID pattern is observed (Fig. 3b,e). In the cases of convex P max /concave n ID patterns (Fig. 3a,d) and linear patterns (Fig. 3b,e), at times earlier than T 80 (1,442.2 and 414.2 h, respectively; Supplementary Fig. 5), n ID takes values between 1 and 2, indicating bulk Shockley-Read-Hall (SRH) recombination 29 , which is characteristic of most PSCs. After longer times, n ID exhibits values above 2, characteristic of a multiple trap distribution, originating from the formation of trap states, causing the performance degradation, as pointed out by Khadka et al. 41 . In the case of concave P max /convex n ID patterns (Fig. 3e,f), the initial values of n ID are higher than 2, indicating fast degradation in the first 100 h of exposure due to the formation of multiple trap states. After the initial increase in n ID , a progressive decrease is observed in the concave (Fig. 3d) and convex (Fig. 3f) cases, indicating an evolution from bulk recombination to interfacial recombination characterized by a low V oc . Note that this behaviour does not indicate a recovery in device performance, only a transition between two different recombination regimes in the degradation process from multiple trap recombination to a regime with higher interfacial recombination.  Fig. 3a-c. d-f, Short-circuit current. g-i, Open-circuit voltage. Parts a,d,g correspond to a device with a convex P max shape, according to Fig. 3a. Parts b,e,h correspond to a device with a linear P max shape, according to Fig. 3b. Finally, c,f,i correspond to a device with a concave P max shape, according to Fig. 3c. The colour bar indicates the variable range. At the top of each plot, the maximum recorded value used to normalize the data for each variable is shown.
All of the analysed minimodules ( Supplementary Fig. 5a) exhibit behaviour that can be statistically associated with one of these three patterns ( Supplementary Fig. 5b). Moreover, the samples analysed here show different degradation rates ( Supplementary Fig. 5c), with a relatively low degradation rate of the initial P max of 0.29% per day for the convex data, a moderate degradation rate of 1.39% per day for the linear data and a faster degradation rate of 7.68% per day for the concave data. The faster power loss observed for samples with concave P max /convex n ID patterns can be associated with failures of the encapsulation that allowed moisture ingress, bleaching the perovskite to a yellow-white colour 16 ; see Supplementary Figs. 2d-i and 10 for outdoor and indoor examples, respectively. Similarly, a rapid power drop, within less than 5 d, has also been observed in encapsulated perovskite minimodules under outdoor conditions due to a breach of the edge sealant that allowed water ingress, along with the associated colour change 44 . For devices exhibiting convex P max /concave n ID data or linear data, there was no evidence of colour change even after more than 900 h of exposure; nevertheless, they also degraded, indicating another kind of degradation mechanism ( Supplementary Fig. 2a,b). Note that encapsulation protects against not only moisture ingress but also degradation originating from the release of organic components of MAPbI 3 into the atmosphere. Different MAPbI 3 degradation reactions result in the formation of a PbI 2 solid and NH 2 CH 3 , HI, NH 3 , CH 3 I 45,46 or I 2 gases 47 . Correspondingly, samples exhibiting convex P max /concave n ID or linear patterns show different degradation rates that can be associated with differences in the quality of the encapsulation process. During the first stage (when n ID < 2), the samples undergo SRH recombination dominated by lead vacancies and interstitial halogen 47 . However, the formation of different types of gas leads to the appearance of multiple trap states, causing n ID to become higher than two. These gases can be released into the atmosphere through small pores formed during the preparation of the encapsulant or produced by its degradation. Convex P max /concave n ID patterns could be indicative of the latter case, where the rate of degradation increases after a certain time (Supplementary Fig. 5c).   , Ideality factor analysis of the same samples: n ID exhibits a concave pattern for samples exhibiting a convex P max pattern (d), n ID exhibits a linear pattern for samples exhibiting a linear P max pattern (e) and n ID exhibits a convex pattern for samples exhibiting a concave P max pattern (f). The average n ID was calculated using all data points recorded during each 100 h period ( Supplementary Figs. 3 and 9). The boxplots were estimated by calculating n ID , filtering the data by T between 25 and 37 °C in steps of 2 °C with a deviation of ±1 °C, and obtaining the maximum and minimum n ID to define the upper and lower bars, respectively. The thick black line on each box represents the average performance in the corresponding time window. The boxplots were obtained by calculating the variables observed in the measurement sets, each of which contained measurements recorded over 100 hours of outdoor exposure. Moreover, in all cases, a red line is included for the NOCT P max data and the n ID data as a visual guide to illustrate the shapes related to the convex, linear and concave patterns.
The method used for n ID determination has been verified through indoor measurements. In indoor tests, excellent agreement between the n ID values estimated from V oc -light intensity data and the results of IFR analysis has been observed 31,32 . Thus, the methodology applied to obtain n ID can be validated by comparing the values obtained from the analysis of V oc versus G using equation (1) with the results of an independent additional calculation of n ID . Figure 4a shows the n ID values calculated by fitting the V oc data collected at different light intensities using equation (1). n ID takes values close to 1.6 for a fresh device and higher than 3 for a device after a long period of outdoor testing. Impedance spectra were independently measured under different light intensities to calculate the recombination resistance 30,32,48 , R rec , considering negligible transport and charge transfer resistances in both the bulk and the contact layers and at interfaces 49 . In this case, n ID can be calculated from the slope of the logarithmic plot of R rec versus V oc (refs. 30,32,48 ). The IFR data at different intensities ( Fig. 4b and Supplementary Fig. 12) were fitted to the equivalent circuit shown in Supplementary Fig. 13 to obtain R rec : where R 00 is an independent parameter expressed in units of resistance. The n ID values calculated using equation (2) (Fig. 4c) show excellent agreement with the n ID values calculated using equation (1), validating the calculation of n ID from V oc versus G data collected outdoors (Supplementary Fig. 9). Moreover, this comparative analysis also highlights the relationship between n ID and R rec related to recombination processes. To this end, Supplementary Fig. 15 shows the results of simultaneously monitoring P max , n ID and R rec , from which it can be observed that P max exhibits monotonic behaviour, while n ID and R rec show similar and richer patterns that allow the changes in the recombination mechanism to be tracked more directly than can be achieved with P max . These observations illustrate the valuable complementarity that the determination of n ID can provide for the study and understanding of outdoor PSC tests. This approach can be used as a diagnostic tool to detect initial failures or validate the status of devices.

relationship between n ID and T 80
T 80 is an extensively used parameter in the photovoltaic industry 1,2 . This parameter can be calculated from the power loss tendency depicted by the boxplots for the different PRCs cases considered in Fig. 3a-c. Because the NOCT conditions are considered the most representative power rating conditions for outdoor operation 25 and NOCT performance is included on the datasheets for commercial solar modules, we normalized the average P max under NOCT conditions with respect to the average value obtained for each sample during the first 100 h of outdoor exposure to determine T 80 (Fig. 5a). Using the samples characterized in Figs. 2 and 3 as representative examples, it is observed that the sample with the concave shape degrades faster (T 80 = 80 h) than the sample with the linear pattern (T 80 = 414.2 h), while the one with the convex pattern shows the slowest degradation rate (T 80 = 1,442.2 h). The degradation in P max can be mainly attributed to the decreases in V oc and I sc for the convex and linear patterns, respectively, while for the concave pattern, both of these parameters are considerably degraded ( Supplementary  Figs. 6-8). T 80 can be obtained directly from the normalized power loss tendency (Fig. 5a).
A complementary analysis to the P max methodology can be performed by considering the average n ID values over time (Fig. 3c-e) and defining Tn ID2 as the time in which the value of n ID first reaches 2. In this way, it is possible to observe that for times longer than T 80 (Fig. 5a), n ID exhibits values higher than 2 (Fig. 5b). Accordingly, Fig. 5c analyses the relation between Tn ID2 and T 80 , showing a strong linear relationship. This linear relationship indicates that these parameters are correlated and complementary probes of the degradation processes occurring in the devices. T 80 provides valuable commercial information and a clear idea of a fundamental property of a photovoltaic module, namely, its lifetime, which is a key concern for the customer. On the other hand, Tn ID2 has a physical meaning related to the transition point from bulk SRH recombination through a single level to recombination through multiple levels as a result of device degradation 29 . The linear relationship between these parameters indicates that the degradation processes causing the reduction in device performance, as monitored by T 80 , manifest as a change in the recombination mechanism, as tracked by T nID2 .  (1). These data indicate that n ID = 1.6 for the fresh device and 3.5 for the outdoor-exposed device. b, Nyquist diagrams of impedance at different light intensities (experimental data, plotted as dots) and their corresponding fits (plotted as solid lines) for a fresh device (upper plot) and an outdoor-exposed device (lower plot). The fits correspond to the best solutions obtained by using a genetic algorithm combined with the simplex method to minimize the error between the experimental data and the circuit model ( Supplementary Fig. 13), according to equation (3). The calculated parameters from the IFr fitting analysis are shown in Supplementary Table 4 for the fresh device and in Supplementary  Table 5 for the outdoor-exposed device. c, Calculation of n ID from the relationship between R rec and V oc using equation (2). The linear regression fits indicate that n ID = 1.5 for the fresh device and 3.4 for an outdoor-exposed device. The measurements were carried out at room temperature (25 °C).
Accordingly, the complementarity shown in Fig. 5c between these two parameters allows us to correlate the commercial parameter with a parameter that has physical meaning. This fact has important implications for the commercial development of perovskite photovoltaics for outdoor applications. Therefore, although it is not possible to extract direct conclusions from T 80 regarding the degradation mechanisms and how the recombination pathways evolve during the degradation process, it is possible to obtain complementary information from Tn ID2 to correlate changes in n ID with recombination mechanisms or degradation processes occurring in a device. Establishing this correlation will provide critical complementary insight regarding the fundamental recombination within PSCs, which can be linked to T 80 . This relationship can then be used to improve the characterization and understanding of the outdoor degradation processes affecting PSC technologies, aid in evaluating other cell configurations and/or encapsulants and potentially assist in linking outdoor data to indoor tests.

Conclusions
This work presents a complementary methodology based on the evaluation of the ideality factor for monitoring the outdoor performance of halide PSCs, which can improve device characterization under outdoor testing conditions. This methodology takes advantage of the properties of this new class of photovoltaic technology and the direct relationship between n ID and the recombination pathway to provide insight to enable improved data interpretation and understanding of the device degradation processes under outdoor conditions that are relevant to the commercial application of PSCs. By applying this methodology, a high-throughput outdoor performance analysis of MAPbI 3 minimodules was carried out following the international standard IEC 61853-1 to evaluate the impact of weather variables on performance. The collected data were processed in measurement sets based on measurements recorded over 100 h of exposure. In each set, n ID was calculated while taking advantage of the different illumination conditions encountered during day-night cycles, and the outdoor performance was calculated based on the NOCT power rating conditions identified in the IEC 61853-1 standard.
Taking advantage of the low dependence of PSCs on temperature, we proposed and then demonstrated an analysis of outdoor performance using n ID . The main advantage of this approach is that it provides direct physical insight related to recombination processes. To this end, we defined Tn ID2 as the time at which n ID first reaches a value of 2, with a physical meaning related to the transition point between bulk SRH recombination through a single level to recombination through multiple levels as a result of device degradation 29 . We showed that the three different degradation patterns identified for P max can also be identified by monitoring n ID . In addition, based on the linear relationship between T 80 and Tn ID2 , these two indexes are correlated. Consequently, it is possible to take advantage of their complementarity for the future development of PSCs. While T 80 provides direct commercial information, namely, the module lifetime, Tn ID2 provides direct information on recombination behaviour and physical insight into the device state. Therefore, the proposed method provides a deeper understanding of the evolution of recombination processes originating from different degradation mechanisms, revealing not just the degradation profile but also how it is produced in terms of recombination pathways. This complementarity is especially interesting for photovoltaic devices whose outdoor behaviour is under study, development and optimization, as is currently the case for PSCs.
Finally, it should be noted that each technology has its own peculiarities, which often necessitate the revision of characterization methods, and PSCs are no exception. Proof of this is provided by the very recent consensus 16 related to the stability measurement of PSCs. Here, we contribute to this discussion by providing a high-throughput analysis that takes advantage of the peculiarities of perovskite technology for the determination of the outdoor performance of PSCs. Regarding future systematic studies of PSCs operating outdoors, we recommend reporting data collected under the NOCT power rating conditions suggested by IEC 61853-1, which are commonly addressed in datasheets for commercial technologies and are possible to achieve under outdoor test conditions. The complementary analysis and determination of n ID can provide critical information for device characterization and the understanding of degradation processes to accelerate the optimization of this    Table 3). b, Ideality factor over time for the samples analysed in a. The red dashed line corresponds to n ID = 2 and is used to calculate Tn ID2 . The coloured markers represent the average n ID values extracted from the experimental data ( Fig. 3d-f), and the solid line of each colour corresponds to the fit to the data with the corresponding pattern (Supplementary Table 3). c, relation between the time to reach a 20% power loss (T 80 ) and time to reach an n ID value higher than 2 (Tn ID2 ). The blue line corresponds to the fit to the data, T 80 = 1.2Tn ID2 + 60.1. In all cases, solid lines correspond to fits, while coloured symbols correspond to the estimated data.
technology or other technologies with similar properties that could be under development.

Methods
Monitoring system. The monitoring system used in this study includes electronic analysers for measuring I-V curves and a data management system for storing, synchronizing and processing electrical and weather records 25 . The irradiance levels were measured using a Spektron 210 sensor (TRITEC International). Moreover, we considered the NOCT conditions defined in the IEC 61853-1 standard, corresponding to ambient temperature and an irradiance of 800 W m −2 , and the ambient temperature was recorded using PT-1000 sensors (TRITEC International).
To simplify the methodology, the ambient temperature was used in the various calculations, as it presents a trend similar to that of the module temperature, this approach introduces a relative error lower than 5% (Supplementary Fig. 17). Further discussion on the relation between the ambient temperature and the temperature of a perovskite device can be found elsewhere 4 . Moreover, the devices were evaluated at the University of Antioquia (6° 15′ 38′′ N, 75° 34′ 05′′ W), facing south at a fixed angle of 10°. Weather data (irradiance and ambient temperature) and electrical data (I-V curves) were recorded every minute during daylight hours (5:30-18:30). The methods and equipment used have been discussed and explained in previous work 4,25,36 . A brief description of the methods used to process the data is provided in Supplementary Fig. 3. The electrical and weather data were synchronized at the remote server using the timestamp of each record, creating a database including date, time, irradiance, temperatures and data extracted from the I-V curves, such as V oc , I sc , FF, P max and efficiency. Then, to minimize the influence of atypical data or data related to unclear days, shadowing, dirt or droplets on the surface, a linearity determination criterion was applied based on the linear behaviour observed between P max and the irradiance and validated by a high coefficient of determination (r value) close to 1 ( Supplementary Fig. 4a).
In this way, the best-fit data with a deviation of ±5% were selected as the filtered data, which were taken to represent the average conditions during the exposure time. The outdoor performance, power rating conditions and n ID results were calculated using these filtered data in accordance with the flowchart described in Supplementary Notes 1 and 2.
Indoor measurements. To obtain the n ID value indoors, we used an LED lamp. The light intensities were controlled using an optical filter from Thorlabs. To measure the impedance frequency and V oc at each intensity, an Autolab procedure was developed (Supplementary Note 3). In this procedure, V oc was recorded for 1 min, and the average value was taken as the V oc value corresponding to that light intensity. Subsequently, the bias of a potentiostat was set to V oc , and we conducted IFR analysis in the range of 100 to 1 MHz, using an AC signal of 10 mV in amplitude and scanning first from high to low frequency (down) and then from low to high frequency (up) to ensure the reliability of the measurement while avoiding parasitic effects ( Supplementary Fig. 12). Finally, the I-V curve of the device at 1 Sun was recorded. All experiments were performed at room temperature (approximately 25 °C). On the other hand, the IFR data were fitted considering the equivalent circuit, as reported elsewhere 49 and shown in Supplementary Fig. 13, to estimate the parameters involved in the circuit such as R s , L s , R b , C b , C g and R rec . For impedance fitting, a global optimization process involving a genetic algorithm and the simplex method was used, as reported in a previous work 33 , to minimize the square error between the measured impedance (Z) and the impedance calculated using the equivalent circuit (Z model ) at the frequencies considered (f), considering all samples recorded (NS) (equation (3)). The main parameters of the genetic algorithm used to perform the optimization process were a randomly initialized population with a size of 200, tournament selection, a two-point crossover function, uniform mutation and 600 generations as the stopping criterion. After that, the genetic algorithm finds the solution, which is used as the initial condition in the Simplex method to improve the error: Device fabrication. Minimodules were fabricated with an inverted structure of ITO/NiO x /Al 2 O 3 /MAPbI 3 /PCMB/rhodamine/Au, which has been demonstrated to be feasible for the fabrication of large-area devices up to 100 cm (refs. 24,36 ). However, in this work, we used an ITO substrate of 5 × 5 cm 2 with four cells interconnected in series, each with an of active area of approximately 2 cm 2 (Fig. 1, Supplementary Fig. 1 and Supplementary Table 1), to produce more samples for evaluation. In this structure, the incorporation of the NiO x and the mesoporous layer (Al 2 O 3 ) improves the reproducibility for fabrication over large areas and reduces hysteresis 50,51 , while the incorporation of rhodamine improves the electronic effects 52 . Moreover, the perovskite MAPbI 3 was obtained by dissolving the precursor in acetonitrile/methylamine. The full characterization of the MAPbI 3 layer, which included a solvent treatment with methyl ammonium chloride and the creation of scribe lines (P1, P2 and P3), has been reported in previous work 36 . Finally, the devices were manually encapsulated with ethylene vinyl acetate, and the borders were covered with epoxy resin to minimize the direct exposure of the EVA.
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
All data generated or analysed during this study are included in the published article and its Supplementary Information. All experimental data collected in the outdoor test and used in this work have been gathered in an open data repository at the University of Antioquia and are available at the following web site http:// elektra.udea.edu.co/solarudea/. To reproduce the results of this work, weather data and data extracted from the I-V curves were processed in accordance with the flowchart shown in Supplementary Fig. 3. Guidelines on how to use these data are reported in Supplementary Notes 1 and 2.