Insights into the operational stability of wide-bandgap perovskite and tandem solar cells under rapid thermal cycling

Domain: physics
Published: 2026-01-14
Editorial outcome: minor_revision

Abstract
Temperature variations can induce phase transformations and strain in perovskite solar cells (PSCs), undermining their structural stability and device performance. Despite growing interest, the operational stability of triple-cation wide-bandgap (WBG) PSCs and tandem solar cells (TSCs) under rapid solar-thermal cycling remains poorly understood. Here, we investigate the operational stability of WBG PSCs (~1.68 eV) with a champion power conversion efficiency (PCE) of 24.31% and extend the study to TSCs. We find that degradation during device operation under rapid solar-thermal cycling (temperature change rate of 10 °C/min) is independent of passivation and occurs in two distinct regimes: an initial burn-in phase, which accounts for a rapid 60% relative loss in performance, followed by a steady degradation characterized by temperature-dependent fluctuations in photovoltaic parameters. By operando grazing-incidence wide-angle X-ray scattering and photoluminescence measurements, we reveal that temperature-induced strain, phase transition, and the increased non-radiative recombination collectively contribute to the degradation of PSCs. This work advances the understanding of the degradation mechanisms of WBG PSCs and TSCs, providing insights toward improving their operational thermal stability for real-world applications.

Introduction
Single-junction perovskite solar cells (PSCs) have achieved remarkable progress in recent years, with the certified power conversion efficiency (PCE) reaching 27.3%1. To further overcome the Shockley-Queisser limit, tandem perovskite solar cells (TSCs), by integrating wide-bandgap perovskite solar cells (1.63 eV−1.80 eV) with other solar cells, e.g., crystalline silicon, CIGS, and narrow-bandgap PSCs are utilized2–9, and their certified PCE is now reaching 34.85%10. In terms of the wide-bandgap PSCs for tandem application, a higher bromide content is required to realize the desired bandgap11,12. Nevertheless, a higher bromide content in perovskites normally leads to a rapid crystallization process, which in turn results in higher defect densities accompanied by structure and composition inhomogeneity and a high density of grain boundaries13–15. In addition, compared with their mid-bandgap counterparts (1.5 eV–1.63 eV), wide-bandgap PSCs suffer from phase separation under light illumination and non-radiative recombination at perovskite/charge transporting layers (CTLs)6,16,17, leading to a large open-circuit voltage (VOC) deficit (defined as Eg/q − VOC, where Eg and q refer to bandgap and elementary charge, respectively). Universal methods, such as forming a 2D capping layer with bulky organic cations, e.g., phenylethylammonium (PEA+) and butylammonium (BA+)18–20, using Lewis bases (e.g., short-chain diammonium ligands)10,18,21–24, adding an ultrathin LiF or MgFx interlayer10,25,26, and additive engineering2,27, have been proven effective in reducing the VOC losses and inhibit phase segregation in wide-bandgap PSCs.

In addition, to understand the behavior of the perovskite-based solar cells for terrestrial and extraterrestrial applications28–30, their thermal cycling performance needs to be evaluated. Previous work demonstrated that perovskite and its respective CTLs endure alternating tension and compression under thermal cycling, which could result in ion migration, phase transition, crystal disorder, delamination, and device failure31–34. However, these pioneering studies have primarily focused on the mid-bandgap PSCs (around 1.5 eV) under thermal cycling32,34,35, leaving the thermal and operational stability of WBG PSCs and perovskite/Si TSCs, especially under thermal cycling, largely unexplored. In particular, the cycling duration is not specified in the International Summit on Organic Photovoltaic Stability (ISOS) protocols for thermal cycling (ISOS-T) and solar-thermal cycling (ISOS-LT). These protocols define only parameters such as temperature range, environmental atmosphere, and light source29. In this regard, cycling durations have varied significantly in thermal cycling stability tests reported in the literature34,36. In addition, the International Electrotechnical Commission (ICE) standard test procedure specifies a cycle duration of 3 to 6 h, with a maximum temperature change rate of 100 °C/h37,38. However, such a low rate is not suitable for operando studies or rapid prototyping of perovskite composition, passivation, and device structures. Therefore, we define a full thermal cycle with a temperature change rate of ~10 °C/min as rapid thermal cycling.

In this work, a champion PCE of 24.31% is achieved in 0.05-cm2 WBG PSCs (1.68 eV) with dual passivation using 3-fluorophenethylamine iodide (3-F-PEAI) and ethylenediamine diiodide (EDAI2). We first determine the temperature coefficients of single-junction WBG PSCs with and without dual passivation and perovskite/Si TSCs at different temperature ranges. We note that the thermal coefficients of single-junction PSCs and TSCs extracted from J–V measurements at constant temperatures do not reflect device performance under thermal cycling conditions. We further investigate the solar cell behavior of WBG PSCs under rapid solar-thermal cycling conditions, while concurrently analyzing their structural evolution by GIWAXS. We find that the degradation of WBG PSCs universally follows two characteristic regimes, an initial burn-in phase followed by steady degradation, regardless of their initial performance or passivation strategy. The degradation behavior is driven by the accumulation of non-radiative recombination centers, temperature-induced phase transitions, and strain, collectively leading to pronounced losses in fill factor (FF) and VOC. When integrated with Si bottom cells, TSCs demonstrate an improved temperature resilience at low temperatures and retain 94% of their original PCE after over 200 min of thermal cycling.

Results
Photovoltaic performance
First, we investigate the effects of single and dual passivation on the properties of perovskite films. Hereafter, the samples without passivation, with EDAI2 passivation, and with 3-F-PEAI and EDAI2 dual passivation are referred to as control, EDAI2 and DP, respectively. The photoluminescence (PL) spectra (Supplementary Fig. 1a) show that the passivation does not alter the bandgap of the perovskite. As demonstrated in previous work, EDAI2 shifts the Fermi level closer to the conduction band minimum, leading to stronger n-type doping and effective field-effect passivation after treatment10,21,22,24, whereas F-PEAI is shown to form a 2D capping layer (Supplementary Fig. 2) and suppress the defective centers of the perovskite surface6,39, contributing to a better device performance. Together, these passivation strategies enhance film quality without altering optical absorption, as confirmed by the unchanged absorbance spectra (Supplementary Fig. 1b), highlighting their promise for defect suppression and interface optimization.

To further characterize the chemical composition of the respective perovskite thin film, Fourier transform infrared (FTIR) spectra are performed (Supplementary Fig. 1c), where the molecular vibration features of C–N and C–F asymmetric stretching signals vas(C–N) and vas(C–F) locate at 1715 cm−1 and 1120 cm−1, respectively, indicating the successful incorporation of 3-F-PEAI into perovskite thin film. The root-mean-square (RMS) roughness of perovskite thin film after passivation slightly decreases in the order of EDAI2 (13.27 nm) and DP (14.53 nm) thin films compared to that of control (16.25 nm) film, as evidenced by atomic force spectroscopy (AFM) measurements (Supplementary Fig. 3). In addition, in situ PL is utilized to assess the phase stability in response to light-induced stress (Supplementary Fig. 4). We find a slight redshift in the control thin film over time, while EDAI2 and DP thin films demonstrate better stability under light illumination (with no visible change in peak positions), showing the passivation effect for suppressing photo-induced phase segregation and potentially improving device operational stability.

Next, we fabricate solar cells with the configuration of ITO/NiOx/self-assembled monolayers (SAMs, Me-4PACz)/WBG PSCs (750 nm, Cs0.05MA0.1FA0.85PbI0.77Br0.23)/passivation layer/C60/BCP/Ag (Fig. 1a, detailed fabrication process can be found in the Experimental section). The champion device performance for all three types of PSCs is shown in Fig. 1b, Supplementary Fig. 5, where the control device demonstrates a champion PCE of 20.38%, an FF of 76.83%, a short-circuit current (JSC) of 22.29 mA/cm2, and a VOC of 1.19 V. In comparison, the device with dual passivation displays superior performance, achieving a PCE of 24.31%, a JSC of 22.34 mA/cm2, a VOC of 1.29 V, and an FF of 84.36%. In addition, the statistical photovoltaic parameters for all three PSCs types are compared (Supplementary Fig. 6), in which the DP devices demonstrate the highest VOC (average of 1.279 V) and FF (average of 79.68%), suggesting reduced non-radiative recombination and better energy alignment after passivation, ultimately contributing to the highest PCE among all the devices. Furthermore, the integrated JSC extracted from the external quantum efficiency (EQE, Fig. 1c, Supplementary Fig. 7) measurements is 21.2, 21.0, 21.2 mA/cm2, showing less than a 5% mismatch compared to those obtained from the J–V measurements. (Fig. 1b). The corresponding bandgap extracted from the EQE spectra are approximately 1.69 eV (Supplementary Fig. 8). Moreover, the quasi-steady-state measurement (steady state PCEs) of control, EDAI2, and DP devices are 17.74, 21.50, and 21.96%, respectively (Fig. 1d, Supplementary Fig. 9).

Despite standard testing conditions (STC) specifying a temperature of 25 °C for measuring the device performance, the actual device temperature can reach 65 °C under operational conditions40. Furthermore, for further deployment of perovskite/silicon tandem solar modules in an outdoor environment, understanding device performance across a range of temperatures is essential for predicting solar cell and panel performance. The temperature coefficient (γ), which is equal to the change in PCE relative to PCE at room temperature divided by the change in temperature during device operation at varying temperature40,41, can be calculated as:

γ = (PCE_T − PCE_RT) / (|T − T_RT| × PCE_RT) (1)

where PCE_T and PCE_RT correspond to PCE at varied temperature T and room temperature, T_RT, respectively. As such, to calculate γ, the device performance is measured at different temperatures ranging from 5 to 85 °C in 5 °C intervals (Fig. 1e). The experimental setup for temperature-dependent J–V measurements is described in detail in the Experimental section and shown in Supplementary Fig. 10. We determine the temperature coefficients by extracting the slope from the linear fits of PCE as a function of temperature and normalizing it to the PCE at room temperature (25 °C). Notably, the temperature coefficients in the 5–25 °C range (γ_LT) and the 25–80 °C (γ_HT) are largely different. At higher temperatures (above room temperature), however, DP devices suffer from a faster degradation, likely due to dimensionality collapse, penetration of bulky organic cation into the 3D perovskite layer within 2D/3D heterostructure, which hinders charge transfer42–44. The calculated γ_HT values of control and DP devices are −0.28% K−1 and −0.88% K−1 respectively, comparable to −0.29% K−1 of SunPower’s silicon modules, -0.39% K−1 of a standard monocrystalline module, and the thermal coefficients reported in the literature (Supplementary Table 1), while slightly lower than −0.17% K−1 of a triple-cation PSC (Cs0.05(FA0.83MA0.17)0.95Pb(I0.83Br0.17)3)40,41. This difference in temperature coefficient might arise from many factors or a combination of them, e.g., perovskite composition, device configuration, measurement conditions, and light-soaking effects. However, identifying the exact cause of this difference is not the main scope of this work, since device behavior differs significantly under static temperature-dependent J–V measurement and rapid thermal cycling conditions. In addition, the γ_LT values are −0.26% K−1 and −0.13% K−1 for the control and DP device, respectively, showcasing better stability at low temperatures with dual passivation. Overall, the metastability of high-efficiency WBG PSCs under non-standard temperature conditions suggests that current passivation strategies may not be suitable for operation under extreme conditions or may not necessarily contribute to enhanced stability, highlighting the need to develop dedicated strategies specifically aimed at improving stability.

Operational stability under rapid thermal cycling
To concurrently track the structural evolution and changes in device performance of WBG PSCs under rapid thermal cycling conditions, operando GIWAXS measurements are performed during device operation, as mapped out in Fig. 2a. As the degradation behavior is quite similar in all types of PSCs, only the evolution of photovoltaic parameters for devices with dual passivation is shown in Fig. 2b–e, Supplementary Fig. 11. Overall, the average PCE of DP devices decreases to 42% of its original PCE after 1 h of solar-thermal cycling, originating from the combined degradation of JSC (9%), VOC (22%), and FF (41%). Similarly, the control devices (Supplementary Fig. 12) follow a comparable trend, with their average PCE decreasing to 51% of the original value, accompanied by reductions in JSC (12%), VOC (15%), and FF (32%) values. The FF fluctuations (characterized by the series resistance in the limit of infinitely large shunting resistance, Supplementary Fig. 13) can be correlated with the high defect densities and the asymmetric strain experienced during rapid solar-thermal cycling, which will be discussed in the following sections. The timescale of light illumination and electrical bias, together with the temperature change rate, likely contribute collectively to the different degradation rates observed in devices under rapid solar thermal cycling compared with those under static temperature conditions. By simulating the PCE using the extracted coefficients and comparing it with the measured PCE over time and temperature (Supplementary Fig. 14), we decouple degradation mechanisms from temperature-induced performance changes under rapid solar thermal cycling. We classify the degradation process into two regimes by their degradation rates: the initial burn-in regime (approximately up to the first PCE recovery, Supplementary Fig. 14), which contributes to more than 60% of the total degradation in all three types of PSCs, and the steady degradation regime, where photovoltaic parameters partially recover, stabilize, and align well with temperature evolution. In addition, VOC and FF are the most affected parameters during solar-thermal cycling. Breaking down the degradation of respective photovoltaic parameters, we find that VOC follows an opposite trend with respect to temperature evolution, reaching its maximum at the lowest temperature. In principle, a higher temperature leads to an enhanced intrinsic charge carrier concentration, resulting in an increase in the dark saturation current (J0) and, therefore, a decrease in VOC (Eq. (2)).

VOC = (nkBT/q) ln(JSC/J0 + 1) (2)

Where q, n, and kB refer to the elementary charge, the ideality factor, and Boltzmann’s constant, respectively. JSC exhibits a similar trend following the temperature profile, which can be attributed to temperature-induced bandgap broadening or narrowing. However, at elevated temperatures, increased non-radiative charge carrier recombination and structural degradation may counteract this effect, leading to non-monotonic and even decreasing JSC behavior.

The hysteresis index (HI), defined as HI = (PCE_reverse − PCE_forward) / PCE_reverse, behaves quite differently across different types of WBG PSCs (Supplementary Fig. 15). Moreover, the HI of all types of PSCs gradually decreases over time, with the HI evolution of the DP device closely following the temperature profile (Supplementary Fig. 11). However, it remains challenging to disentangle whether ion accumulation or interfacial recombination at the perovskite/charge transport layer (CTL) interface plays the dominant role or whether both contribute jointly, to the hysteresis33,45,46. In addition, the hysteresis index tends to increase further at elevated temperatures, likely due to the reduced activation barrier for ion migration and the formation of trap states at the CTL interfaces47. To evaluate the long-time stability of these WBG PSCs under solar-thermal cycling conditions, we extend the measurement duration to 300 min (Supplementary Figs. 16–18), with selected time-resolved J–V curves shown in Supplementary Fig. 19. The average PCE of control devices declines to 34% of its initial PCE, originating from the combined degradation of VOC (20%), JSC (30%), and FF (42%). In contrast, the DP devices demonstrate improved stability over prolonged solar-thermal cycling, resulting in a 46% PCE retention, attributed to a 12% degradation in VOC, 18% in JSC, and 37% in FF. Compared to the solar thermal cycling in the first hour, where the PCE drops significantly, further solar thermal cycling leads to only a minimal loss in both control and DP devices. Further enhancing device stability under rapid thermal cycling conditions requires holistic approaches, such as replacing commonly-used carbazole containing phosphonic acid SAMs, which are susceptible to thermal disordering, with alternative anchoring groups (e.g., trimethoxysilane)23, using co absorbents, bifunctional ligands48, or superwetting overlayers to establish more rigid contact between the perovskite and the charge transport layer49, and developing SAM bilayers or multilayer molecular contacts that harness covalent interlayer connections9, as well as incorporating metallofullerene materials and ordered dipolar materials34,50–52. In addition, the respective hysteresis index is calculated and plotted against temperature and time, as shown in Supplementary Figs. 20–22, where they all follow the temperature evolution, that is, the hysteresis index reaches its maximum within one thermal cycle when operated at the highest temperature. In addition, the HI of DP devices tends to stabilize at 11.3% after an initial rapid decrease, which likely correlates with reduced ion migration and/or interfacial non-radiative recombination with dual passivation. This behavior is in stark contrast to the continuous HI evolution observed in the control devices.

Phase and structural evolution under rapid thermal cycling
Prior to showing the structural change of WBG PSCs, we utilize in situ PL (Fig. 3a, b, Supplementary Fig. 23) to monitor the phase stability of the respective perovskite thin film under the identical conditions, particularly to simulate the initial burn-in regime (first thermal cycle). To better analyze the phase stability, the peak positions are extracted, as shown in Fig. 3c, displaying the minor changes in the peak positions before and after degradation. In other words, there is no obvious phase separation after rapid thermal cycling and light illumination and likely minimal ion migration. In addition, to quantify the impact of mobile ions on device performance at different timescales (i.e., 0 min, 15 min or 1 thermal cycle, and 60 min or 4 thermal cycles) during the aging process46,53, we perform fast hysteresis J–V measurements on the DP device over a large scan speed range (0.1–800 V s−1; details in “Methods”). As shown in Supplementary Fig. 24, the contribution of ionic loss remains nearly constant (~10%) before and after rapid solar-thermal cycling conditions. This also explains that in the initial burn-in regime, the rapid degradation is not attributed mainly to ion migration, but rather likely to interface loss and an increase in non-radiative recombination centers, which are related to the decrease of FF and VOC. A similar study also demonstrated that defect density increases significantly at the perovskite/CTL interface, with this effect being more pronounced under day/night cycling conditions than under continuous illumination54. Furthermore, the evolution of the peak position indicates no significant bandgap shift before and after thermal cycling. Instead, a bandgap shift of 8 meV is observed within one thermal cycle for the control thin film, and 6 meV for the DP thin film. We further calculate the defect density (Nd) according to:

ΔE = (kBT/q) ln(Nc/Nd) (3)

where Nc refers to the effective density of states in the conductive band. Figure 3d displays the corresponding defect density of control and DP perovskite thin films at a given temperature and time frame. It should be noted that the DP perovskite thin film demonstrates lower defect density. In addition, both perovskite thin films at 80 °C give rise to the highest defect density (2.47 × 1017 cm−3 for control and 2.35 × 1017 cm−3 for DP), in accordance with the VOC trend in Fig. 2c. Interestingly, we notice that the DP thin film exhibits a lower defect density at 5 °C in comparison to the control thin film, corroborating its phase stability at a lower temperature. Extended in situ PL measurements further demonstrate the intrinsic stability of both control and DP thin films over two thermal cycles (Supplementary Fig. 25).

We try to understand the origin of the degradation of WBG PSCs under rapid solar-thermal cycling by correlating the device performance with their structural change (Fig. 4, Supplementary Fig. 26). To this end, we use operando GIWAXS, which enables concurrent tracking of structural evolution during device operation and thus provides a direct link between structural information and device behavior. It is observed that no PbI2 peak is formed, and the perovskite peaks exhibit periodic oscillation following the temperature evolution (Fig. 4a, Supplementary Fig. 26) in all types of PSCs during device operation, that is, peaks shift towards lower q at elevated temperature and higher q at reduced temperature, demonstrating lattice distortion over temperatures. In addition, they also undergo reversible phase transition from cubic phases at low temperature, e.g., q ≈ 1 Å−1 and 2.0 Å−1, to tetragonal phase (β phases, q ≈ 1.65 Å−1 and 1.70 Å−1, highlighted by the red dotted line, Fig. 4b–d, Supplementary Figs. 27–29)34,55. However, it should be pointed out that these tetragonal phases in the DP device are slightly suppressed, as indicated by the peak intensities in comparison to the control device, which also accounts for the relatively stable JSC against thermal cycling. To quantitatively analyze strain of PSCs operated under solar-thermal conditions, which originates from the thermal expansion coefficient mismatch between perovskite (typically 6.1 × 10−5 K−1) and other charge transport layers, as well as glass substrates (3.7 × 10−6 K−1)56,57, we calculate the strain as the ratio of the relative q shift and its original q position (Fig. 4e). The strain is oscillated expectantly with temperature evolution in the range of −0.18% (tensile strain) and 0.19% (compressive strain) in the case of the DP device, which results in the enhanced non-radiative recombination and the degradation of FF and VOC58, whereas the control device experiences strain in the range of −0.27% to 0.25%. The asymmetric strain of the control device might explain its large variation of FF during solar-thermal cycling conditions. It was also reported that lattice shrinkage in perovskite continuously induces deep-level defects that cannot be self-healed under day/night conditions, and this effect is expected to be more severe under accelerated thermal cycling conditions54. In summary, the temperature-induced strain together with the phase transition are the main driving factors that lead to the overall device failure under rapid solar-thermal cycling conditions, as illustrated in Fig. 4f. We acknowledge that further research is needed to directly measure and quantify non-radiative recombination and interfacial losses in perovskite solar cells during device operation under solar-thermal cycling conditions. Additionally, disentangling the effects of ion migration, structural changes, and charge extraction would significantly advance the understanding of the underlying physics in PSCs.

Performance of perovskite/silicon tandem solar cells under rapid thermal cycling
Knowing the degradation behavior of single-junction WBG PSCs under rapid thermal cycling, we further extend the study on perovskite/Si tandem solar cells (detailed fabrication can be found in the Experimental Section) based on the DP device. A PCE of 28.64%, with a VOC of 1.908 V, JSC of 19.8 mA/cm2, and an FF of 75.82% for the tandem solar cell at room temperature is achieved. To extract the temperature coefficients, the PCEs of TSCs are measured by statically varying the temperature between 5 and 85 °C (Fig. 5a). The device performance drops substantially at higher temperature ranges, mainly related to the degradation of FF and VOC, which is consistent with single-junction PSCs. The calculated temperature coefficients, i.e., γ_LT and γ_HT, are −0.60% K−1 and −0.08% K−1, respectively (Fig. 5b), demonstrating enhanced stability at lower temperatures when integrating into tandem solar cells. The long-term operational stability of tandem solar cells is also examined under solar-thermal cycling conditions (Fig. 5c). Over 220 min of aging, the tandem solar cell retains 94% of its initial performance, mainly due to a reduced initial burn-in compared to single-junction PSCs. We infer that the high thermal conductivity of the silicon bottom cell facilitates efficient heat dissipation, while the tandem configuration mitigates charge carrier thermalization losses59, collectively reducing heat accumulation and enhancing device stability under such conditions compared with single-junction PSCs. However, we also acknowledge that the differences in the layer stack, minor variations in perovskite thin film morphology arising from stoichiometry and crystallization differences on the Si bottom cells, as well as a current mismatch between the bottom and top cells, may also contribute to mitigating the initial burn-in degradation. That being said, disentangling the effects of perovskite bandgap, the phase homogeneity of perovskite, local solar spectrum, operating temperature range, and the limiting subcell in perovskite/Si tandem solar cells under constant temperature conditions remains complex60,61, and addressing this challenge under dynamic rapid thermal cycling requires more holistic approaches combined with appropriate in situ and operando characterizations.

Methods
Materials
Cesium iodide (CsI, 99.9%), formamidinium iodide (FAI, 99%), methylammonium iodide (MAI, 99%), lead iodide (PbI2, 99%), lead bromide (PbBr2, 99.999%), bathocuproine (BCP, 96%), chlorobenzene (anhydrous, 99.8%), dimethylformamide (DMF, anhydrous, 99.8%), dimethyl sulfoxide (DMSO, anhydrous 99.9%), isopropanol (IPA, anhydrous, 99.5%), chlorobenzene (CB, anhydrous, 99.8%), and fullerene (C60, 99.5%) were purchased from Sigma-Aldrich. [4-(3,6-Dimethyl-9H-carbazol-9-yl)butyl]phosphonic Acid (Me-4PACz, anhydrous, 98%) was purchased from Tokyo Chemical Industry. All materials were used directly without further processing if otherwise stated elsewhere.

Single-junction WBG perovskite device fabrication
Single-junction PSCs: The ITO substrates (X07-20AC, Shangyang Tech) were ultrasonically cleaned in the sequence of detergent, DI water, ethanol, acetone, and isopropanol for 15 min each. After drying with N2, the substrates were treated with O2 plasma for 10 min before using. The NiOx solution (5 mg/ml) was spin-coated on ITO substrates at 3000 rpm for 30 s. The Me-4PACz solution (1 mg/mL in ethanol) was spin-coated at NiO/ITO substrates at 3000 rpm for 30 s, followed by annealing at 100 °C for 10 min. Subsequently, a 1.8 M perovskite solution (Cs0.05MA0.1FA0.85PbI0.77Br0.23 in 1 mL mixed solvent, V_DMF:V_DMSO = 4:1) was spin-coated on top of ITO/Me-4PACz substrates at 4000 rpm for 50 s with an acceleration of 2000 rpm/s. The anti-solvent (CB) was slowly dropped on top of the perovskite at 15 s prior to ending, followed by annealing at 100 °C for 30 min. The passivation layer was prepared by either dissolving EDAI2 (1 mg) or EDAI2 and F-PEAI in mixed solvent (1 mg F-PEAI and 1 mg EDAI2 in 1 mL IPA, stirred overnight at 60 °C) and was spin-coated on top of the perovskite layer at 4000 rpm for 25 s. Then the substrates underwent 100 °C annealing for 5 min. At last, 15 nm C60, 7 nm BCP, and 100 nm Ag were sequentially thermal evaporated on top of the perovskite layer at a pressure of 10−7 bar. Finally, an anti-reflection foil (Mitsubishi Chemical Group) was glued from the light illumination side.

Perovskite/Si tandem device fabrication
The silicon bottom cells were subjected to UV-ozone treatment for 5 min before NiOx modification. A NiOx film was then spin-coated as described in the single-junction fabrication process. Subsequently, the same SAM, 1.5 M perovskite, passivation layer, and C60 deposition steps described above were applied to the Si/NiOx substrate. A 20 nm SnO2 layer was deposited by atomic layer deposition (ALD) as a buffer layer. The substrate temperature was maintained at 90 °C during ALD deposition, which was carried out using Tetrakis(dimethylamino)tin(IV) (TDMASn) as the precursor at 70 °C and H₂O at room temperature. The pulse and purge times for TDMASn were 1 and 10.0 s with 90 sccm N₂, and for H₂O, 0.2 and 15.0 s with 90 sccm N₂. A total of 200 cycles were performed. Subsequently, a 45 nm IZO layer was sputtered from an IZO target through a shadow mask using 190 W power, with pure Ar and O2 at 1 mTorr. An Ag finger with a thickness of 600 nm was thermally evaporated using a high-precision shadow mask. The finger width is approximately 75 μm. A 100 nm MgF2 layer was thermally evaporated on top of the Ag as an anti-reflection coating.

Device characterization
J–V measurements were recorded with a Keithley 2400 source meter under 1-sun AM 1.5G illumination (calibrated by a Si reference cell). All single-junction devices were masked with metal aperture masks (0.05 cm2) and measured under a sweep mode of reverse scan (from 1.3 V to −0.3 V) and forward scan (from −0.3 V to 1.3 V). For operando measurements under thermal cycling and for device characterization at varied temperatures, measurements were performed using both reverse (1.3 V to −0.3 V) and forward (−0.3 V to 1.3 V) voltage scans. The protocol was initiated at 25 °C and subsequently conducted at each target temperature. External quantum efficiency measurements were carried out with a Bentham PVE300-IVT system, where the LED light intensity was calibrated by the silicon and germanium diodes. The QSS J–V measurements were performed by a Keithley 2400 source meter under AM 1.5G light illumination (calibrated by a NREL-calibrated silicon reference cell). The QSS J–V measurements were 10-point measurements, where the QSS points density is set to be 99, and each point was stabilized for 45 s. For perovskite/silicon tandem solar cells, J–V measurements were carried out in the air under an LED-based solar simulator (WaveLabs Sinus 70) at room temperature. The solar simulator irradiation intensity was calibrated with a certified silicon solar cell (Fraunhofer ISE CalLab). The active area was defined by a black metal mask featuring an aperture with a precisely measured area of 1.0 cm2. The devices underwent test through both reverse scans (2.1 V to −0.1 V, incrementing in 20 mV steps) and forward scans (−0.1 V to 2.1 V, with the same incremental step), conducted at a scan rate of 10 mV s−1 and a delay time of 10 ms. For MPP tracking of TSCs, the unencapsulated devices were operated under 1-sun LED illumination (PURI materials). Fast hysteresis measurements were performed using a triangular voltage pulse from VOC to 0 V and back to VOC at different scan speeds (0.1, 1, 10, and 800 V s−1), with the holding time at VOC set to five times the total scan duration46,53.

Materials characterization
GIWAXS: The thermal cycling GIWAXS data were recorded by a LAMBDA 9M detector (X-Spectrum) with a beam energy of 11.87 keV at beamline P03 at PETRA III synchrotron (DESY, Hamburg)62. The data were collected with a sample-to-detector distance (SDD) of 243 mm, an exposure time of 1 s per frame, and an incidence angle of 0.6°. The SDD was calibrated with LaB6 and CeO2 powders with the DPDAK package and further calibrated with the ITO peak (2.132 Å−1)63. Before each operando measurement, an irradiation damage test was performed to determine the maximum allowable exposure time per experiment, and the subsequent operando measurements were conducted within this time limit. The data reduction, including transformation to q-space, detector absorption, solid angle, and line cuts, was processed by the Python tool INSIGHT64. The setup was connected with a cooling-water system (Julabo) to exclude external heat-induced degradation, as in the previous study65,66. In particular, a home-built sample holder with a Peltier element is integrated in the sample holder, enabling rapid heating and cooling with each thermal cycling duration of 15 min. Considering the high temperature change rate, technical constraints, and heat dissipation, the temperature range was set to 5–85 °C. The absorption data were recorded by an ultraviolet/visible (UV/Vis) spectrometer (Perkin Elmer 35). The photoluminescence data were acquired with a fluorescence spectrometer (Perkin Elmer LS55) with an excitation wavelength of 450 nm and a slit width of 10 nm. The in situ PL was conducted with a self-constructed and mobile photoluminescence setup, which consists of a continuous laser source (Thor Labs CPS450, 450 nm) and a spectrometer (Instrument Systems CAS 140CT). The in situ measurements are conducted under thermal cycling conditions achieved by the pocket solar setup, as described above, with a laser as the light source and a time resolution of 1 s. The FTIR spectra were collected by a Broker Equinox FTIR instrument with a spectral resolution of 2 cm−1. The atomic force microscopy measurements were carried out with an AFM instrument (Nanosurf).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors investigated the rapid thermal cycling decay mechanisms of perovskite single-junction solar cells and tandem cells, by in-situ photoluminescence spectroscopy and in-situ GIWAXS. The conclusion drawn is that the degradation under rapid thermal cycling can be attributed to two regimes, namely initial burn-in and steady degradation. In the initial burn-in regime, the device degradation is caused by temperature-induced strain, phase transformation, and enhanced non-radiative recombination at the perovskite/CTL interface. Overall, this study is important to the community. However, more work needs to be done before the acceptance of this manuscript in Nature Communications.\nQ1) In Supplementary Fig. 1a, the passivation layer changes the PL emission peak. Does this imply a change in the band gap? If so, why is this not reflected in the absorption spectrum of Supplementary Fig. 1b?\nQ2) I noticed that the in-situ PL peak positions in Supplementary Fig. 3 are different from those in Supplementary Fig. 1a.\nQ3) Please confirm that the parameters in Figure 1b are obviously inconsistent with the IV curve.\nQ4) In Fig. 1e, more temperature conditions should be tested to verify the repeatability and accuracy of the temperature coefficients. Addition, in the acquisition of temperature coefficients and the rapid thermal cycling experiment, the authors only used three samples as statistical data, which is insufficient to support the conclusion.\nQ5) The temperature coefficient of DP provided in the manuscript is -0.42%/K. However, during the first cyclic heating stage (from 25℃ to 80℃), the PCE decreased by approximately 40% (corresponding to a temperature coefficient of about -0.72%/K). What causes the difference in the measured temperature coefficients of devices with the same structure?\nQ6) In Fig.4, in-situ GIWAXS measurements allow for a direct observation of the strain in the perovskite lattice during rapid thermal cycling. However, I have not seen additional evidence demonstrating the correlation between lattice strain/distortion and the degradation of device efficiency, and the authors should provide more supporting evidence.\nQ7) In Fig.3, is the temperature measurement taken from the substrate or the perovskite film? If it is from the substrate, the actual temperature of the perovskite film requires further detection. If the temperature measurement is from the perovskite film, why is it that the temperature has been almost constant at around 80°C between 100 and 250 seconds, yet the PL peak is still undergoing a blue shift according to the data results in Figure 3c?\nQ8) The discussion on the perovskite/silicon tandem solar cell section is insufficient. A more in-depth study can be conducted from aspects such as the temperature coefficient of silicon solar cells, the spectral matching of tandem cells under temperature variation, and the stress at the perovskite/silicon interface.", "reviewer_2": "In this work, Sun et al. report an impressive power conversion efficiency of 24.6% for single-junction wide-bandgap (1.68 eV) perovskite solar cells, representing one of the highest device performances reported to date and providing strong stimulus for further unlocking the device performance potential for perovskite/Si tandem solar cells . In addition, the authors investigate the operational stability of 1.68 eV wide bandgap perovskite solar cells under rapid solar thermal cycling conditions, a long-standing technical challenge in the field that has remained insufficiently understood, and further extend this analysis to perovskite/Si tandem devices. Given the combination of excellent device performance, valuable insights into the operational stability of both wide bandgap perovskites and perovskite/Si tandems, and the potential to broaden our understanding for extraterrestrial applications, I strongly recommend this work for publication in Nature Communications after minor revision.\nSpecific comments:\n1. Could the authors summarize the thermal coefficients of perovskite solar cells with different bandgaps from previous publications, as this would also provide new insight of non-motoic temperature co-efficents?\n2. The authors mentioned that “whereas F-PEAI is shown to form a 2D capping layer and improve the homogeneity of the perovskite/C60 layer.” Is there any evidence from, e.g., GIWAXS or PL? Also, how can one ascertain whether the molecule used for passivation can form a 2D capping layer? Can this be generalized?\n3. The authors used a device configuration of ITO/NiOx/self-assembled monolayers (SAMs, Me-4PACz)/WBG PSCs (750 nm, Cs0.05MA0.1FA0.85PbI0.77Br0.23)/passivation layer/C60/BCP/Ag in the manuscript. How about the device performance without passivation layer under rapid solar-thermal cycling conditions? What is the effect of passivation layer?\n4. Technical details regarding the operando GIWAXS measurement are missing, e.g., incidence angle. How do the authors exclude the possibility of beam-induced degradation? Since the authors calculate strain based on their q shift—which, in my opinion, is highly dependent on the sample-to-detector distance (SDD)—how can they ascertain that there was no change in SDD?\n5. The authors investigated the degradation mechanism of WBG PSCs under solar thermal cycling conditions; however, including a broader discussion on potential strategies (e.g., appliation of metallofullerene materials and ordered dipolar materails)to enhance the stability of WBG PSCs under such conditions would significantly strengthen the manuscript.", "reviewer_3": "In this manuscript, the authors investigated the degradation behavior of triple-cation wide-bandgap (WBG) perovskite solar cells (PSCs) and tandem solar cells (TSCs) under rapid solar-thermal cycling. Device degradation during operation occurs in two distinct regimes: initial burn-in and steady-state degradation. This work offers valuable insights for enhancing the operational stability of WBG PSCs and TSCs, thereby facilitating their real-world applications. However, several issues remain to be addressed. Detailed comments on these aspects are provided as follows:\n1. According to IEC61215:2016 protocols, the temperature range for the thermal cycling test is between -40 ± 2 °C and 85 ± 2 °C. Given this standard requirement, why do authors choose 5-85 °C instead of -40-85 °C for solar-thermal cycling tests?\n2. In this manuscript, it mentioned that “We note that the thermal coefficients of single-junction PSCs and TSCs extracted from J-V measurements at constant temperatures do not reflect device performance under thermal cycling conditions.” What is the rationale for introducing the thermal coefficients, and how do they support the core conclusions of this work?\n3. In comparison, the device with dual passivation using F-PEAI and EDAI2 exhibits enhanced photovoltaic performance and thermal stability. What synergistic mechanism exists between these two molecules to contribute to such improvements?\n4. In Figure 1e, how are the devices subjected to sequential testing under different temperature conditions? Additionally, within the temperature range of 5–25 °C, why does the device efficiency exhibit an increase with increasing temperature?\n5. Compared with the control group, why does the optimized device with dual passivation exhibit a faster degradation rate within the 25-80 ℃ range?\n6. After dual passivation, the device exhibits significantly reduced temperature-dependent fluctuation in FF. The authors are recommended to provide an explanation to gain deep insights into the enhanced thermal stability.\n7. “As the degradation behavior is quite similar in all types of PSCs, only the evolution of photovoltaic parameters for devices with dual passivation is shown in Fig. 2b-f.” However, there is no 2f in Figure 2. The authors should supplement Figure 2f with corresponding explanations.\n8. What is the temperature change rate shown in the Fig. 2b-e? It should be consistent with the change rate mentioned in the main text.\n9. It mentioned that “in the initial burn-in regime, the rapid degradation is not attributed mainly to ion migration, but rather likely to interface loss and an increase in non-radiative recombination centers”. Please provide related experimental characterization and in-depth analysis to verify this claim. In comparison, what are the main reasons for the performance degradation in the steady degradation regime?\n10. Fig. 3d displays the corresponding defect density of control and DP perovskite thin films at a given temperature and time frame. Why is the testing time inconsistent?\n11. In Supplementary Fig. 20-22, it should indicate the conditions corresponding to a and b.\n12. “In single-junction PSCs, heat accumulation and hotspot formation in the absorber layers may deteriorate thermal stability and exacerbate performance loss; hence, these devices are less stable compared to tandem cells.” The authors are suggested to monitor the heat accumulation within single-junction and tandem cells during thermal cycling. What is the impact of passivation layer on heat accumulation?"}, "author_response": "Response to Reviewers\nReviewer #1 (Remarks to the Author):\nIn this manuscript, the authors investigated the rapid thermal cycling decay mechanisms of\nperovskite single-junction solar cells and tandem cells, by in-situ photoluminescence\nspectroscopy and in-situ GIWAXS. The conclusion drawn is that the degradation under rapid\nthermal cycling can be attributed to two regimes, namely initial burn-in and steady degradation.\nIn the initial burn-in regime, the device degradation is caused by temperature-induced strain,\nphase transformation, and enhanced non-radiative recombination at the perovskite/CTL interface.\nOverall, this study is important to the community. However, more work needs to be done before\nthe acceptance of this manuscript in Nature Communications.\nResponse: We thank the reviewer for the positive feedback and recommendation for publication.\nWe are also grateful for the constructive comments, which have significantly helped improve our\nmanuscript. In preparing our response letter, we carefully considered all suggested changes. A\ndetailed, point-by-point response to each comment is provided below.\nQ1) In Supplementary Fig. 1a, the passivation layer changes the PL emission peak. Does this\nimply a change in the band gap? If so, why is this not reflected in the absorption spectrum of\nSupplementary Fig. 1b?\nResponse: We thank the reviewer for pointing out this difference. We have repeated the PL\nmeasurements (Fig. R1), which show that the PL peak positions remain unchanged after\npassivation, indicating that the bandgap is not affected.\nFig. R1 (Supplementary Fig. 1a). Normalized photoluminescence spectra of respective perovskite\nthin film deposited on glass substrates.\nQ2) I noticed that the in-situ PL peak positions in Supplementary Fig. 3 are different from those\nin Supplementary Fig. 1a.\nResponse: We thank the reviewer for raising this point in support of our manuscript. As noted in\nresponse to Q1, we repeated the PL measurements, confirming that passivation does not alter the\nperovskite bandgap, as the peak positions are consistent with those observed in the in situ PL\nresults.\nFig. R2 a) Normalized PL spectra of the respective perovskite thin films. b) Normalized PL\nspectra extracted from the in situ PL measurements at room temperature.\nQ3) Please confirm that the parameters in Figure 1b are obviously inconsistent with the IV curve.\nResponse: We thank the reviewer for pointing this out. We have corrected the typos in Figure 1b\nand updated the corresponding values on Page 8, Lines 1-4, in the revised manuscript. The\nupdated version is provided here for reference.\nFig. R4 (Fig. 1b). J-V curves of the respective champion device under AM 1.5G illumination\nequivalent to 100 mW cm-2, retrieved from the reverse scan.\nQ4) In Fig. 1e, more temperature conditions should be tested to verify the repeatability and\naccuracy of the temperature coefficients. Addition, in the acquisition of temperature coefficients\nand the rapid thermal cycling experiment, the authors only used three samples as statistical data,\nwhich is insufficient to support the conclusion.\nResponse: We thank the reviewer for this constructive comment. As you suggested, additional\ntemperature conditions with 5 °C intervals and a total 8 solar cells in the acquisition of\ntemperature coefficients and the rapid thermal cycling experiments have been included in Figure\n1e and Figure 2 in the revised manuscript, which we paste here for reference. Notably, we found\nthat the extracted thermal coefficient depends on the temperature step size. We note that DP\ndevices exhibit a lower temperature coefficient at higher temperatures when measured with\nincreased precision (i.e., smaller temperature steps).\nFor the rapid thermal cycling experiment, we repeated the measurements once more, resulting in\na total of five samples to verify repeatability and accuracy. The corresponding photovoltaic\nparameters have also been updated; while they remain overall similar, some slight differences are\nobserved.\n.\nFig. R5 (Fig. 1e). PCE as a function of temperature, where the error bar indicates the standard\ndeviation extracted from 8 pixels.\nFig. R6 (Fig. 2): Evolution of the device performance under solar-thermal cycling\nconditions. a Schematic illustration of operando GIWAXS measurements during device\noperation under rapid solar-thermal cycling conditions. Normalized photovoltaic parameters as a\nfunction of time and temperature (indicated by the grey curve, showing the thermal cycling\nbetween 5 and 80 °C with each individual cycle of 15 min and a temperature change rate of\n~15 ℃/min). The J-V measurements were performed at 1 min intervals, and the shaded areas\nrefer to error bars derived from the standard deviation of respective photovoltaic parameters of\nfive samples subjected to rapid solar-thermal cycling. b Normalized PCE and temperature versus\ntime, c normalized V and temperature versus time, d normalized J and temperature versus\nOC SC\ntime, e normalized FF and temperature versus time.\nQ5) The temperature coefficient of DP provided in the manuscript is -0.42%/K. However, during\nthe first cyclic heating stage (from 25℃ to 80℃), the PCE decreased by approximately 40%\n(corresponding to a temperature coefficient of about -0.72%/K). What causes the difference in the\nmeasured temperature coefficients of devices with the same structure?\nResponse: We are grateful for the reviewer’s comment. In response to Q4, we have added\nadditional statistics for extracting the thermal coefficients, yielding an extracted value of\n−0.88%/K, which is close to the one obtained from thermal cycling. The slight differences arise\nfrom the distinct measurement conditions, namely static temperature change versus continuous\ntemperature variation. Specifically, (1) in the static case, the devices were held at the set\ntemperature for 30 s before measuring device performance and extracting the thermal\ncoefficients. In contrast, under thermal cycling (with a temperature change rate of 15 ℃/min), the\ntemperature varied continuously, and the devices experienced periodic strain due to the mismatch\nin thermal expansion coefficients between the perovskite, CTL, and ITO substrates.\n(2) The time scales of electrical bias and light illumination also differed between the two\nconditions: under thermal cycling, electrical bias (1 min intervals) and light illumination were\ncontinuously applied, whereas under static conditions, the duration of applied bias and\nillumination was comparatively negligible (≤ 1 min per measurement). These differences are\nlikely responsible for the different degradation rates of perovskite solar cells under thermal\ncycling compared with constant temperature conditions. We also acknowledge that electrical bias\nand light illumination may further contribute to device degradation.4, 5, 6, 7 The following\nstatements have been added to the revised manuscript on Page 10, Lines 13-16:\nThe timescale of light illumination and electrical bias, together with the temperature change rate,\nlikely collectively contribute to the different degradation rates observed in devices under rapid\nsolar thermal cycling compared with those under static temperature conditions.\nQ6) In Fig.4, in-situ GIWAXS measurements allow for a direct observation of the strain in the\nperovskite lattice during rapid thermal cycling. However, I have not seen additional evidence\ndemonstrating the correlation between lattice strain/distortion and the degradation of device\nefficiency, and the authors should provide more supporting evidence.\nResponse: We thank the reviewer for the valuable comment. We carried out operando GIWAXS\nmeasurements designed to probe the structural evolution and device performance under actual\noperating conditions, rather than a perovskite film or perovskite/charge transport layer stack.\nMoreover, device degradation mainly originates from the loss of V and FF, with FF loss can be\nOC\nattributed to the temperature-induced strain. We have further elaborated on this in the revised\nmanuscript and have updated Figure 2a, and it reads on Page 15, Lines 12-14:\nTo this end, we use operando GIWAXS, which enables concurrent tracking of structural evolution\nduring device operation and thus provides a direct link between structural information and\ndevice behavior.\nFig. R7 (Fig. 2a): Schematic illustration of operando GIWAXS measurements during device\noperation under rapid solar-thermal cycling conditions.\nQ7) In Fig.3, is the temperature measurement taken from the substrate or the perovskite film? If it\nis from the substrate, the actual temperature of the perovskite film requires further detection. If\nthe temperature measurement is from the perovskite film, why is it that the temperature has been\nalmost constant at around 80℃ between 100 and 250 seconds, yet the PL peak is still undergoing a blue shift according to the data results in Figure 3c?\nResponse: We appreciate the reviewer’s constructive comment. The temperature measurement\nwas taken directly from the perovskite film, measured by a thermal couple. The PL signal is\nhighly localized, and heat transfer from the perovskite surface (on the order of square\ncentimeters) to the excitation spot (on the order of square millimeters) may introduce a time\ndelay. In addition, like the annealing process, which typically requires some time for phase\ntransition (e.g., in FAPbI₃), there is also a certain delay in temperature-induced peak shifts, as a\nsufficient amount of heat accumulation is necessary before these changes occur. This behavior\nexplains why the PL emission peak continues to exhibit a slight blueshift over time.\nQ8) The discussion on the perovskite/silicon tandem solar cell section is insufficient. A more in-\ndepth study can be conducted from aspects such as the temperature coefficient of silicon solar\ncells, the spectral matching of tandem cells under temperature variation, and the stress at the\nperovskite/silicon interface.\nResponse: We thank the reviewer for raising this point. We fully agree that a more in-depth study\nof perovskite/silicon tandem solar cells under both constant temperature and thermal cycling\nconditions is necessary, and that identifying the primary causes of degradation under these\nconditions is of great importance to the community. However, the focus of this work is to\nunderstand the evolution of WBG PSCs under rapid solar-thermal cycling conditions. In addition,\ndisentangling the effects of silicon bottom-cell temperature coefficients, spectrum matching of\ntandem devices under temperature variation, and interfacial stress at the perovskite/silicon\njunction is highly complex. In general, the temperature coefficients of silicon solar cells are\npositive because their bandgap narrows as temperature increases.8 When integrated into tandem\ndevices, however, the effective temperature coefficients can be positive, negative, or a\ncombination of both across the operating temperature range,9 depending on factors such as the\ninitial current mismatch,9 the perovskite bandgap,10 the local spectrum,9 the limiting subcell,9 and\nthe operating temperature,10 as the reviewer suggested. In addition, when perovskite/silicon\ntandem solar cells are subjected to rapid solar thermal cycling, these parameters may jointly\ncontribute to device degradation. Given the limitations of operando techniques, along with the\noverall complexity, identifying the dominant degradation mechanism remains particularly\nchallenging. We recently discovered that the different composition and phase homogeneity of\nperovskites could also influence their thermal stability. Given the overall complexity of the study,\nit is essential to conduct a separate investigation specifically dedicated to elucidating the thermal\nstability of perovskite/silicon solar cells and addressing the reviewer’s concerns, as this topic is\nalso of significant importance to the field. Nevertheless, we have incorporated a discussion on\nthis aspect into the revised manuscript, and it reads on Pages 18, Lines 19-24:\nDisentangling the effects of perovskite bandgap, the phase homogeneity of perovskite, local solar\nspectrum, operating temperature range, and the limiting subcell in perovskite/Si tandem solar\ncells under constant temperature conditions remains complex,9, 10 and addressing this challenge\nunder dynamic rapid thermal cycling requires more holistic approaches combined with\nappropriate in situ and operando characterizations.\nReviewer #2 (Remarks to the Author):\nIn this work, Sun et al. report an impressive power conversion efficiency of 24.6% for single-\njunction wide-bandgap (1.68 eV) perovskite solar cells, representing one of the highest device\nperformances reported to date and providing strong stimulus for further unlocking the device\nperformance potential for perovskite/Si tandem solar cells. In addition, the authors investigate the\noperational stability of 1.68 eV wide bandgap perovskite solar cells under rapid solar thermal\ncycling conditions, a long-standing technical challenge in the field that has remained\ninsufficiently understood, and further extend this analysis to perovskite/Si tandem devices. Given\nthe combination of excellent device performance, valuable insights into the operational stability\nof both wide bandgap perovskites and perovskite/Si tandems, and the potential to broaden our\nunderstanding for extraterrestrial applications, I strongly recommend this work for publication in\nNature Communications after minor revision.\nResponse: We thank the reviewer for the positive feedback and recommendation for publication.\nWe sincerely thank the reviewer for the constructive comments that have greatly contributed to\nimproving our manuscript. In our response letter, we carefully considered the reviewer’s\nsuggested changes. A detailed, point-by-point response to each of the reviewers’ comments is\nprovided below.\nSpecific comments:\n1. Could the authors summarize the thermal coefficients of perovskite solar cells with different\nbandgaps from previous publications, as this would also provide new insight of non-motoic\ntemperature co-efficents?\nResponse: We thank the reviewer for the suggestion. We have added a table summarizing the\nthermal coefficients of perovskite solar cells with different bandgaps in Supplementary Table.1\nand pasted it here for your reference.\nSupplementary Table S1. State-of-the-art perovskite solar cells with their thermal coefficients\nextracted from the literature.\nPerovskite Perovskite Type Temperature PCE at Thermal Re\ncomposition configuration range 25℃ coefficie f\n(℃) (%) nts\n0.05 0.83 0.1\n)Pb (I Br ) 2PACz/perovsk % K-1\n7 1.1 0.83 0.17 3 rel\nite/C /SnO /C\n60 2\nu\n0.79 0.16 0.05\nPb(I Br ) ovskite/LiF/C ~17% rel %/°C\n0.83 0.17 3 60\n/BCP/Ag\n0.75 0.22 0.03\nPb(I Br Cl ) ovskite/LiF/C ~17% rel %/°C\n0.82 0.15 0.03 60\n/BCP/Ag\n3\non tandem % K−1\n3\novskite/C /BC %/°C\nelectrode\n0.10 0.90 0.83 2\nBr ) vskite/Spiro- non-\n0.17 3\nOMeTAD/Au monotono\nus\n2. The authors mentioned that “whereas F-PEAI is shown to form a 2D capping layer and\nimprove the homogeneity of the perovskite/C60 layer.” Is there any evidence from, e.g.,\nGIWAXS or PL? Also, how can one ascertain whether the molecule used for passivation can\nform a 2D capping layer? Can this be generalized?\nResponse: We thank the reviewer for this helpful comment. We have added the GIWAXS data\nfor both the control and DP samples in the revised Supplementary Information and pasted it here\nfor reference, showing that the addition of F-PEAI leads to the formation of 2D layers (q 0.72,\n0.82 Å-1, Supplementary Fig. 2).15, 16\n≈\nFig. R8 (Supplementary Fig. 2). Pseudo-XRD data of control and DP devices, with arrows\nmarking the 2D phase formed after F-PEAI passivation.\n3. The authors used a device configuration of ITO/NiOx/self-assembled monolayers (SAMs, Me-\n4PACz)/WBG PSCs (750 nm, Cs0.05MA0.1FA0.85PbI0.77Br0.23)/passivation\nlayer/C60/BCP/Ag in the manuscript. How about the device performance without passivation\nlayer under rapid solar-thermal cycling conditions? What is the effect of passivation layer?\nResponse: The device performance without passivation (i.e., the control) behaves quite similarly\nunder rapid solar thermal cycling conditions, also exhibiting an initial rapid degradation period\nfollowed by a steady degradation phase. However, a slight difference is observed between the\ncontrol and DP devices: the control shows a 12% decrease in J compared with 9% for the DP\nSC\ndevice. The passivation layer reduces defects and induces the formation of a low-dimensional\nperovskite, which can also act as a protective layer. This is supported by the calculated defect\ndensity extracted from the in situ PL results (Fig. 3). Nevertheless, the overall effect of\npassivation under rapid solar thermal cycling remains limited, as reflected in the JV results (Fig.\n2 and Supplementary Fig. 12).\n4. Technical details regarding the operando GIWAXS measurement are missing, e.g., incidence\nangle. How do the authors exclude the possibility of beam-induced degradation? Since the\nauthors calculate strain based on their q shift—which, in my opinion, is highly dependent on the\nsample-to-detector distance (SDD)—how can they ascertain that there was no change in SDD?\nResponse: We thank the reviewer for pointing this out. We have added the technical details in the\nMethods section in the revised manuscript, and it reads on Page 22, Lines 24-25:\nThe data were collected with a sample-to-detector distance (SDD) of 243 mm, an exposure time\nof 1 s per frame, and an incidence angle of 0.6°.\nBefore each operando measurement, an irradiation damage test was performed to determine the\nmaximum allowable exposure time per experiment, and the subsequent operando measurements\nwere conducted within this time limit. To minimize X-ray beam–induced degradation, the sample\nwas shifted in micrometer steps using the high-precision Hexapod at the P03 beamline, given the\nmicrometer-sized X-ray beam. For SDD calibration, an initial calibration with CeO and LaB\n2 6\nwas carried out, followed by an additional calibration using the characteristic ITO peak at\n2.132Å-1. We therefore have included the following statements in the revised manuscript on Page\n23, Lines 1-3:\nBefore each operando measurement, an irradiation damage test was performed to determine the\nmaximum allowable exposure time per experiment, and the subsequent operando measurements\nwere conducted within this time limit.\n5. The authors investigated the degradation mechanism of WBG PSCs under solar thermal\ncycling conditions; however, including a broader discussion on potential strategies (e.g.,\napplication of metallofullerene materials and ordered dipolar materials) to enhance the stability of\nWBG PSCs under such conditions would significantly strengthen the manuscript.\nResponse: We thank the reviewer for this helpful comment. We have included a broader\ndiscussion on potential strategies for further enhancing the stability of wide-bandgap perovskite\nsolar cells under solar-thermal cycling conditions in the revised manuscript on Page 12, Lines 3-\n10.\nFurther enhancing device stability under rapid thermal cycling conditions requires holistic\napproaches, such as replacing commonly-used carbazole containing phosphonic acid SAMs,\nwhich are susceptible to thermal disordering, with alternative anchoring groups (e.g.,\ntrimethoxysilane),17 using co absorbents, bifunctional ligands, or superwetting overlayers to\nestablish more rigid contact between the perovskite and the charge transport layer,18, 19 and\ndeveloping SAM bilayers or multilayer molecular contacts that harness covalent interlayer\nconnections,20 as well as incorporating metallofullerene materials and ordered dipolar\nmaterials.21, 22, 23, 24\nReviewer #3 (Remarks to the Author):\nIn this manuscript, the authors investigated the degradation behavior of triple-cation wide-\nbandgap (WBG) perovskite solar cells (PSCs) and tandem solar cells (TSCs) under rapid solar-\nthermal cycling. Device degradation during operation occurs in two distinct regimes: initial burn-\nin and steady-state degradation. This work offers valuable insights for enhancing the operational\nstability of WBG PSCs and TSCs, thereby facilitating their real-world applications. However,\nseveral issues remain to be addressed. Detailed comments on these aspects are provided as\nfollows:\nResponse: We would like to thank the reviewer for the constructive comments and suggestions to\nfurther improve the quality of our manuscript. In preparing our response letter, we carefully\nconsidered all suggested changes. A detailed, point-by-point response to each comment is\nprovided below.\n1. According to IEC61215:2016 protocols, the temperature range for the thermal cycling test is\nbetween -40 2 ℃ and 85 2℃. Given this standard requirement, why do authors choose 5-\n85 ℃ instead of -40-85 ℃ for solar-thermal cycling tests?\n± ±\nResponse: We thank the reviewer for this valuable comment. We acknowledge that the IEC61215\nprotocol specifies that the thermal cycling test should be performed between -40 ℃ to 85 ℃ with\na temperature change rate of 100 ℃/h. In our work, we aimed to accelerate the solar-thermal\ncycling test by applying a much faster temperature change rate of 15 °C/min (900 ℃/h). From a\ntechnical perspective, given this high temperature change rate, the achievable temperature range\nwas necessarily narrowed due to the integration of our operando setup into the synchrotron\nfacility, where both space and power were limited. These constraints impose restrictions on both\nthe maximum attainable temperature and the temperature ramping speed. In addition, heat\ndissipation at such rapid temperature change rates further contributes to the temperature\nlimitations. We have added the following statements in the revised manuscript on Page 23, Lines\n9-10:\nConsidering the high temperature change rate, technical constraints, and heat dissipation, the\ntemperature range was set to 5-85 ℃.\n2. In this manuscript, it mentioned that “We note that the thermal coefficients of single-junction\nPSCs and TSCs extracted from J-V measurements at constant temperatures do not reflect device\nperformance under thermal cycling conditions.” What is the rationale for introducing the thermal\ncoefficients, and how do they support the core conclusions of this work?\nResponse: We thank the reviewer for this helpful comment. By introducing thermal coefficients,\nwe highlight their nonmonotonic behavior in SJ PSCs across different temperature regions and\nthe contrast between SJ PSCs and TSCs. By simulating the PCE using the extracted coefficients\nand comparing it with the measured PCE over time and temperature (Fig. R9), we decouple\ndegradation mechanisms from temperature-induced performance changes under rapid solar\nthermal cycling. Hence, the whole degradation process can be divided into two phases: the initial\nburn-in phase (30% PCE loss, approximately up to the first PCE recovery) and the steady\ndegradation phase (20% PCE loss, as extracted from the two points indicated by the arrows,\nrepresenting the unrecovered portion of the PCE). We have added the following statements in the\nmanuscript, and it reads on Page 10, Lines 16-19.\nBy simulating the PCE using the extracted coefficients and comparing it with the measured PCE\nover time and temperature (Supplementary Fig.14), we decouple degradation mechanisms from\ntemperature-induced performance changes under rapid solar thermal cycling.\nFig. R9 (Supplementary Fig. 14). Normalized PCE and simulated PCE obtained using the\nnonmonotonic thermal coefficients as a function of temperature and time, where the overall\ndegradation process can be divided into two phases: an initial burn-in phase (44% PCE loss) and\na steady degradation phase (6% PCE loss, extracted from the two points indicated by the arrows).\nFurthermore, as suggested, we have removed the detailed discussion of the thermal coefficients\nfrom the abstract in the revised manuscript.\n3. In comparison, the device with dual passivation using F-PEAI and EDAI2 exhibits enhanced\nphotovoltaic performance and thermal stability. What synergistic mechanism exists between\nthese two molecules to contribute to such improvements?\nResponse: We thank the reviewer for this helpful comment. Recent studies have shown that a\nsingle molecule may fail to simultaneously address both surface and interfacial recombination.25\nTherefore, a dual passivation strategy that mitigates both processes has been increasingly utilized.\nAs previously reported, the combination of F-PEAI and EDAI induces the formation of an n-\n2\ntype low-dimensional structure that facilitates interfacial charge transfer while concurrently\nsuppressing nonradiative interfacial recombination.25, 26 In particular, EDAI shifts the Fermi\n2\nlevel closer to the conduction band minimum, leading to stronger n-type doping and effective\nfield-effect passivation after treatment.26 In addition, F-PEAI forms a 2D perovskite capping\nlayer that reduces defects.27 We have therefore included the following statements in the revised\nmanuscript on Page 5, Lines 22-26, which we paste here for reference:\nAs demonstrated in previous work, EDAI shifts the Fermi level closer to the conduction band\n2\nminimum, leading to stronger n-type doping and effective field-effect passivation after\ntreatment,26, 28, 29 whereas F-PEAI is shown to form a 2D capping layer (Supplementary Fig.2)\nand suppress the defective centers of the perovskite surface;27, 30 contributing to a better device\nperformance.\n4. In Figure 1e, how are the devices subjected to sequential testing under different temperature\nconditions? Additionally, within the temperature range of 5–25 ℃, why does the device\nefficiency exhibit an increase with increasing temperature?\nResponse: We thank the reviewer for bringing this up. The devices were subjected to temperature\nsoaking at each temperature for 30 s prior to JV measurements. Furthermore, this is precisely the\npoint we aim to convey to the broader community. The metastability of perovskite-based devices,\nparticularly current high-efficiency WBG PSCs and their TSCs under non-standard temperature\nconditions, suggests that the state-of-the-art passivation strategies may not be suitable for\noperation under extreme conditions or may not necessarily contribute to enhanced stability. This\ncan be attributed to interfacial defect activation at low or elevated temperatures, ion migration,\nphase transformation, and other related dynamic processes. Therefore, developing dedicated\npassivation strategies to address these challenges is essential. The following statement has been\nadded to the revised manuscript, and it reads on Page 9, Lines 23-26:\nOverall, the metastability of high-efficiency WBG PSCs under non-standard temperature\nconditions suggests that current passivation strategies may not be suitable for operation under\nextreme conditions or may not necessarily contribute to enhanced stability, highlighting the need\nto develop dedicated strategies specifically aimed at improving stability.\n5. Compared with the control group, why does the optimized device with dual passivation exhibit\na faster degradation rate within the 25-80℃ range?\nResponse: We thank the reviewer for raising this point. Indeed, dual passivation can largely\nenhance device efficiency, and the stability of thin film and device under rapid solar-thermal\ncycling conditions, particularly with low temperature range, which attributes to the less defect\ndensities and strain (see Question 6). However, previous studies have shown that the\ndimensionality of 2D perovskites formed at the 3D/2D heterojunction can collapse and reform\ndepending on the aging conditions and their bulky organic spacers,31, 32, 33 which can trigger\nredox reactions that reduce charge transport mobility. This collapse is typically more pronounced\nunder photo-thermal aging at higher temperatures (e.g., 85 °C). Therefore, we infer that 2D/3D\npassivation is more effective at lower temperatures than at higher temperatures. We have\nincluded the following statement in the revised manuscript on Page 9, Lines 7-11:\nNotably, the temperature coefficients in the 5-25 °C range (γ_ ) and the 25-80°C (γ_ ) are\nLT HT\nlargely different, where PSCs with dual passivation demonstrate better stability at lower\ntemperatures. At higher temperatures (above room temperature), however, DP devices suffer\nfrom a faster degradation, likely due to dimensionality collapse, penetration of bulky organic\ncation into the 3D perovskite layer within 2D/3D heterostructure, which hinders charge\ntransfer.31, 32, 33\n6. After dual passivation, the device exhibits significantly reduced temperature-dependent\nfluctuation in FF. The authors are recommended to provide an explanation to gain deep insights\ninto the enhanced thermal stability.\nResponse: We thank the reviewer for this helpful comment. As suggested, we have included the\nstrain analysis in Figure 4e and extracted the evolution of the series resistance, demonstrating that\nthe control sample experiences larger strain and higher series resistance under solar thermal\ncycling conditions.\nThe fill factor can be expressed as:\n𝑣𝑣𝑂𝑂𝑂𝑂 −ln(𝑣𝑣𝑂𝑂𝑂𝑂 +0.72) 𝐽𝐽𝑆𝑆𝑂𝑂\n𝐹𝐹𝐹𝐹 = (1−𝑅𝑅𝑆𝑆 )\nin the limit of infinitely large shunting res𝑣𝑣is 𝑂𝑂 t 𝑂𝑂 an+ce1, where R refers𝑉𝑉 t 𝑂𝑂 o 𝑂𝑂 the series resistance.34, 35, 36\nS\nFirst, in situ PL results (Fig. 3) show that DP devices exhibit lower defect densities compared\nwith the control devices under rapid solar thermal cycling. Second, GIWAXS strain analysis (Fig.\n4e) reveals that the DP devices exhibit smaller strain fluctuations (approximately from −0.18% to\n0.19%) compared to the control devices (approximately from −0.25% to 0.27%). The control\ndevices also exhibit a gradual increase in tensile strain (indicated by the arrow in the figure),\nwhich may contribute to the large FF fluctuations observed. To further corroborate these findings,\nwe have plotted the series resistance as a function of time (Supplementary Fig. 13) and included\nit in the revised SI, showing that the control devices display significantly larger fluctuations\ncompared with the DP devices. In addition, shunt resistance may also contribute to FF losses, and\nvariations in device behavior (as reflected by their standard deviations) likely explain the larger\nFF variations observed in the control devices.\nFig. R10 (Fig. 4e). Strain evolution extracted from the evolution of control and DP devices at q≈\n2.0 Å-1. The strain is calculated according to the relative q shift divided by its original q value at\n25℃.\nFig. R11 (Supplementary. Fig.13). Normalized series resistance of control and DP device as a\nfunction of time.\nHence, the following statement has been added in the revised manuscript on Page 10, Lines 10-\n13:\nThe FF fluctuations in control devices (characterized by the series resistance in the limit of\ninfinitely large shunting resistance, Supplementary Fig.13) can be correlated with the high defect\ndensities and the asymmetric strain experienced during rapid solar-thermal cycling, which will\nbe discussed in the following sections.\n7. “As the degradation behavior is quite similar in all types of PSCs, only the evolution of\nphotovoltaic parameters for devices with dual passivation is shown in Fig. 2b-f.” However,\nthere is no 2f in Figure 2. The authors should supplement Figure 2f with corresponding\nexplanations.\nResponse: We appreciate the reviewer for pointing this out. We have corrected this in the revised\nmanuscript, where the evolution of the hysteresis index is now shown in Supplementary Figure\n11, and it now reads on Page 10, Lines 3-5:\nAs the degradation behavior is quite similar in all types of PSCs, only the evolution of\nphotovoltaic parameters for devices with dual passivation is shown in Fig. 2b-e and\nSupplementary Fig.11.\nFig. R12 (Supplementary Fig. 11). Normalized hysteresis index of DP device and temperature\nversus time.\n8. What is the temperature change rate shown in the Fig. 2b-e? It should be consistent with the\nchange rate mentioned in the main text.\nResponse: We thank the reviewer for raising this question. We have now added the temperature\nchange rate (15 ℃/min) in the Figure caption, which is consistent with the change rate mentioned\nin the main text.\n9. It mentioned that “in the initial burn-in regime, the rapid degradation is not attributed mainly\nto ion migration, but rather likely to interface loss and an increase in non-radiative recombination\ncenters”. Please provide related experimental characterization and in-depth analysis to verify\nthis claim. In comparison, what are the main reasons for the performance degradation in the\nsteady degradation regime?\nResponse: We thank the reviewer for raising this question. As suggested, we conducted fast\nhysteresis measurements, in which the device was scanned over a wide range of scan speed (10-3-\nions.37, 38\nThe experimental details are as follows:\nFast hysteresis measurements were conducted before and after solar-thermal cycling at different\ntime intervals (i.e., 0 min, 15 min or 1 thermal cycle, and 60 min or 4 thermal cycles) to\ninvestigate the effect of ion migration on device performance. As shown in the figure, the ionic\nloss before and after rapid-solar thermal cycling (1h) remains relatively constant (~10%),\ndemonstrating that ionic loss is not the main driving factor of degradation. Instead, interfacial\nloss and non-radiative recombination centers (as indicated by the defect densities in the in situ PL\ndata) are more likely responsible for the degradation, as further evidenced by the significant loss\nof FF and V . We have now added the corresponding figure in the revised SI and pasted it here\nOC\nfor reference. Accordingly, we have revised the statements in the manuscript, and it reads on\nPage 14, Lines 1-8:\nIn addition, to quantify the impact of mobile ions on device performance at different time scales\n(i.e., 0 min, 15 min, or 1 thermal cycle, and 60 min or 4 thermal cycles) during the aging process,\nwe perform fast hysteresis JV measurements on DP device over a large scan speed range (0.1-\nremains nearly constant (~10%) before and after rapid solar-thermal cycling conditions. This\nalso explains that in the initial burn-in regime, the rapid degradation is not attributed mainly to\nion migration, but rather likely to interface loss and an increase in non-radiative recombination\ncenters, which are related to the decrease of FF and V .\nOC\nFig. R13 (Supplementary Fig. 24). a) The absolute PCE at fast and slow scan speeds versus aging\ntime under rapid solar-thermal cycling conditions. b) V at fast and slow scan speeds versus\nOC\naging time. c) J at fast and slow scan speeds versus aging time. d) FF at fast and slow scan\nSC\nspeeds versus aging time, and e) Exemplary JV curves measured at fast and slow scan speeds at\ndifferent aging times.\n10. Fig. 3d displays the corresponding defect density of control and DP perovskite thin films at a\ngiven temperature and time frame. Why is the testing time inconsistent?\nResponse: We thank the reviewer for this helpful comment. Since the majority of degradation\noccurs during the initial rapid degradation stage, within the first 15 minutes or during the first\nthermal cycle, we aimed to simulate this period using an identical timescale. In addition, Figure\n3d presents representative data points at the specified times and temperatures. We have added the\nfollowing statement in the revised manuscript on Page 13, Lines 13-16:\nPrior to showing the structural change of WBG PSCs, we utilize in situ PL (Fig. 3a,b, and\nSupplementary Fig.23) to monitor the phase stability of the respective perovskite thin film,\nparticularly to simulate the initial burn-in regime under the conditions of rapid thermal cycling\nand continuous light illumination.\nAs suggested, we also extended the measurement duration to up to two thermal cycles and have\nadded it here and in Supplementary Fig.25:\nFig. R14 (Supplementary Fig. 25): In situ photoluminescence evolution as a function of time over\ntwo thermal cycles, excited with a 450 nm laser for a control perovskite thin film and b DP\nperovskite thin film.\n11. In Supplementary Fig. 20-22, it should indicate the conditions corresponding to a and b.\nResponse: We thank the reviewer for raising this point. We have added the conditions\ncorresponding to panels a and b in the captions of Supplementary Figs. 27–29. The updated\nversion is also pasted here for reference.\nFig. R15 (Supplementary Fig. 27). Selected reshaped 2D GIWAXS data of the control perovskite\nsolar cells at a) 25 ℃ and b) at 5 ℃ within one thermal cycle, where the red arrows indicate the\nphase transition.\nFig. R16 (Supplementary Fig. 28). Selected reshaped 2D GIWAXS data of the EDAI perovskite\n2\nsolar cells at a) 25 ℃ and b) at 5 ℃ within one thermal cycle, where the red arrows indicate the\nphase transition.\nFig. R17 (Supplementary Fig. 29). Selected reshaped 2D GIWAXS data of data DP perovskite\nsolar cells at a) 25 ℃ and b) at 5 ℃ within one thermal cycle, where the red arrows indicate the\nphase transition.\n12. “In single-junction PSCs, heat accumulation and hotspot formation in the absorber\nlayers may deteriorate thermal stability and exacerbate performance loss; hence, these devices are\nless stable compared to tandem cells.” The authors are suggested to monitor the heat\naccumulation within single-junction and tandem cells during thermal cycling. What is the impact\nof passivation layer on heat accumulation?\nResponse: We thank the reviewer for raising this point. We agree that the claim “heat\naccumulation and hotspot formation in the absorber …” may be misleading and have therefore\nremoved it. In our case, the rapid heating and cooling rates indicate active thermal dissipation and\nefficient heat exchange, suggesting that the effect of heat accumulation should be minimal. For\nthis reason, we have removed the statement from the manuscript. In addition, since the\npassivation layer is only a few tens of nanometers thick, much thinner than the perovskite active\nlayer (several hundred nanometers) and the TCO layer (millimeter scale), its contribution to heat\naccumulation is expected to be minimal. However, as discussed in Q5, the dual passivation\nresults in faster degradation, likely due to dimensionality collapse and the penetration of bulky\norganic cations into the 3D perovskite layer within the 2D/3D heterostructure, which hinders\ncharge transfer.31, 32, 33 Also, our results demonstrate that suitable passivation strategies should be\nexplored to enhance the stability of PSCs under extreme conditions, instead of targeting PCE\nimprovement alone. Moreover, the tandem configuration enables more efficient utilization of the\nsolar spectrum than single-junction PSCs, as high-energy photons are absorbed by the wide-\nbandgap top cell, thereby generating a higher voltage and reducing thermalization losses.\nConsequently, thermal accumulation within the absorber is alleviated relative to single-junction\ndevices.\nWe have included the discussion in the revised manuscript, and it reads on Page 18, Lines 12-15:\nWe infer that the high thermal conductivity of the silicon bottom cell facilitates efficient heat\ndissipation, while the tandem configuration mitigates carrier thermalization losses,39 collectively\nreducing heat accumulation and enhancing device stability under such conditions compared with\nsingle-junction PSCs."}, {"round": 2, "reviewer_comments": {"reviewer_1": "All comments have been properly addressed, and I recommend to accept this manuscript.", "reviewer_2": "The authors have adequately addressed all reviewer comments, and the manuscript is now suitable for acceptance.", "reviewer_3": "The authors have revised the work and included new data. However, the authors are suggested to provide the following suggestions for revisions to further enhance the clarity and readability of the paper. More specifically:\n1. In the revised manuscript, it mentioned that \" By simulating the PCE using the extracted coefficients\". The authors should provide the detailed simulation process in the text. What does the red vertical line in Supplementary Fig. 14 represent? How are the two stages of the degradation process divided in figures (such as Supplementary Fig. 11 and 14)?\n2. \"The devices were subjected to temperature soaking at each temperature for 30 s prior to JV measurements.\" Can the devices and the environment reach thermal equilibrium in such a short period of time?\n3. In Fig. 2, it mentioned that \"showing the thermal cycling between 5 °C and 80 °C with each individual cycle of 15 min.\" A complete thermal cycling process (5 °C → 80 °C → 5 °C) takes 15 min. Based on this, the temperature change rate is ~10 ℃/min, which is inconsistent with the change rate mentioned in the main text."}, "author_response": "Response letter to referees\nReviewer #1 (Remarks to the Author):\nAll comments have been properly addressed, and I recommend to accept this manuscript.\nResponse: We thank the reviewer for the constructive suggestions for the first round and\nrecommendation for publication. We are pleased that our revisions and clarifications have\naddressed your concerns.\nReviewer #2 (Remarks to the Author):\nThe authors have adequately addressed all reviewer comments, and the manuscript is now\nsuitable for acceptance.\nResponse: We thank the reviewer for your endorsement for our work and recommendation for\npublication.\nReviewer #3 (Remarks to the Author):\nThe authors have revised the work and included new data. However, the authors are suggested to\nprovide the following suggestions for revisions to further enhance the clarity and readability of\nthe paper. More specifically:\nWe are also grateful for the constructive comments, which have significantly helped improve our\nmanuscript. In preparing our response letter, we carefully considered all suggested changes. A\ndetailed, point-by-point response to each comment is provided below.\n1. In the revised manuscript, it mentioned that \" By simulating the PCE using the extracted\ncoefficients\". The authors should provide the detailed simulation process in the text. What does\nthe red vertical line in Supplementary Fig. 14 represent? How are the two stages of the\ndegradation process divided in figures (such as Supplementary Fig. 11 and 14)?\nResponse: We would like to thank the reviewer for the constructive comments and suggestions to\nfurther improve the quality of our manuscript.\nThe simulation was based on the initial room-temperature PCE and the measured temperature\ncoefficients for 5–25 °C and 25–85 °C. These coefficients were applied to the experimental\ntemperature profile, assuming no additional performance losses. We have added the following\nstatements in the figure caption of Supplementary Fig.14 and it reads on Page 15:\nThe simulation is carried out to model the expected behavior under the experimental temperature\nprofile, assuming no concurrent performance loss (i.e., degradation unrelated to reversible\nthermal effects). The model is built using the initial PCE recorded at room temperature and the\nextracted temperature coefficients for the specified ranges (5−25°C and 25−85 °C), which are\nthen applied across the measured temperature profile.\nIn addition, the red vertical line is intended to separate the two degradation regimes. Different\nstages are defined by the point in time where the solar cell's measured behavior first aligned with\nboth the temperature profile and the simulated J-V curve. This transition point is then consistently\napplied to all photovoltaic parameters. We have therefore revised the dash lines in Supplementary\nFig.11 as well as in Fig. 2b-d to improve the readability of our manuscript.\nFig. 2: Evolution of the device performance under solar-thermal cycling conditions. a\nSchematic illustration of operando GIWAXS measurements during device operation under rapid\nsolar-thermal cycling conditions. Normalized photovoltaic parameters as a function of time and\ntemperature (indicated by the grey curve, showing the thermal cycling between 5 and 80 ℃ with\neach individual cycle of 15 min and a temperature change rate of ~10 ℃/min). The J-V\nmeasurements were performed at 1 min intervals, and the shaded areas refer to error bars derived\nfrom the standard deviation of respective photovoltaic parameters of five pixels subjected to rapid\nsolar-thermal cycling. b Normalized PCE and temperature versus time, c normalized V and\nOC\ntemperature versus time, d normalized J and temperature versus time, e. normalized FF and\nSC\ntemperature versus time.\n2. \"The devices were subjected to temperature soaking at each temperature for 30 s prior to JV\nmeasurements.\" Can the devices and the environment reach thermal equilibrium in such a short\nperiod of time?\nResponse: We thank the reviewer for this insightful question. In a typical perovskite device, the\ntime to reach a thermal equilibrium is governed by the thermal time constant ( ). Given that the\nsubstrate (TCO/glass) thickness (0.7 mm) far exceeds the active layer thickness (less than 1 µm),\n𝜏𝜏\nwe neglect the thin films and focus on the substrate.\nThe time constant can be calculated as:\n2\n𝐿𝐿\n𝜏𝜏 =\nwhere is the thickness (0.7 mm), and is the the𝛼𝛼rmal diffusivity, defined as .\nUsing t\n𝐿𝐿\nhe values of =1.0 W/ (m·K),\n𝛼𝛼\n= 2500 kg/m3), = 840 J/(kg·K), the\n𝛼𝛼\nca\n=\nlc u\n𝑘𝑘\nla\n/\nt\n(\ne\n𝜌𝜌\nd\n𝐶𝐶\nt𝑝𝑝im\n)\ne\nconstant is approxim\n𝑘𝑘\nately 1 s, leading\n𝜌𝜌\nto a time to reach\n𝐶𝐶\no𝑝𝑝f equilibrium (assuming a temperature\nchange from 25 ℃ to 85 ℃) of roughly 3 s. Hence, the established 30 s soaking period is more\nthan sufficient to ensure the device has reached thermal equilibrium prior to J-V measurements.\n3. In Fig. 2, it mentioned that \"showing the thermal cycling between 5 °C and 80 °C with each\nindividual cycle of 15 min.\" A complete thermal cycling process (5 °C → 80 °C → 5 °C) takes\n15 min. Based on this, the temperature change rate is ~10 ℃/min, which is inconsistent with the\nchange rate mentioned in the main text.\nResponse: We thank the reviewer for pointing out this oversight. The temperature change rate has\nbeen corrected to 10 ℃/min in both the main text and the corresponding figure caption.\n∼"}]

Decision letter