Potential-induced degradation in perovskite/ silicon tandem photovoltaic modules

SUMMARY Despite great progress in perovskite/silicon tandem solar cells’ device performance, their susceptibility to potential-induced degradation (PID) remains unexplored. In this study, we ﬁnd that applying a voltage bias of (cid:1) 1,000 V to single-device perovskite/silicon tandem modules at 60 (cid:3) C for (cid:4) 1 day can cause a (cid:4) 50% loss in their power conversion efﬁciency, which raises concerns for tandem commercial-ization. We found no accumulation of Na + in the perovskite or silicon photon absorbers. Consequently, no obvious shunt is observed in our silicon subcells. We also ﬁnd that elements diffuse from the perovskite into the module encapsulant during PID testing. We argue that this diffusion is the main PID mechanism in our tandem modules. While applying a large positive voltage bias can partially recover this PID, introducing barriers or structures to prevent elemental diffusion out of the perovskite may be required to miti-gate this degradation phenomenon.


INTRODUCTION
To further drive down the levelized cost of energy (LCOE) 1-5 of photovoltaics (PV), strategies to enhance the reliability and durability of PV modules have gained significant research interest in recent years. Various stressors such as heat and humidity can cause catastrophic failure of PV devices. 6 For the crystalline silicon PV sector, one of the most detrimental stressors is potential-induced degradation (PID), which arises from a high system voltage, resulting from the series connection of PV modules into strings at the systems level. 7,8 For mainstream silicon solar cells with a diffused p-n junction at their front, PID may be manifested in different forms. First, the electrical potential difference between the cell and the aluminum module frame (or the ground, if frameless) may drive Na + ions from the module glass across the lamination sheet and device p-n junction into stacking faults in the silicon wafer, creating electrical shunting paths (here, PID-s), leading to fill factor (FF) losses. 9,10 Second, PID polarization as a result of the accumulation of metal ions originating from the module glass in the passivation/anti-reflection coating stack at the front of the devices has also been reported for several silicon solar cell architectures, such as p-type bifacial passivated emitter rear contact (bifacial p-PERC [11][12][13] ), n-type passivated emitter, and rear totally diffused (n-PERT), 14,15 as well as n-type, interdigitated back contact (IBC) 16 solar cells. Finally, the negative bias can lead to local delamination of the passivation layers (here, PID-c) of silicon solar cells. 17,18 For commercial thin-film technologies, including cadmium telluride (CdTe) 14,19 and copper indium gallium selenide (CIGS), PID effects have also been observed, [20][21][22] resulting in severe performance degradation.
Despite the importance of this phenomenon, PID studies on emerging perovskite PV technologies are still rare; [23][24][25] for perovskite/silicon tandem solar technologies, [26][27][28][29][30][31][32][33][34] there are no literature reports to date. For single-junction perovskite solar cells (PSCs), Carolus et al. observed a 95% drop in power conversion efficiency (PCE) after a negative-PID (n-PID) test (À1,000 V, 60 C, <60% relative humidity [RH], 18 h) and found that applying subsequently a positive-PID (p-PID) test (+1,000 V) can partially recover this loss. 23 Under the same n-PID test condition, Purohit et al. reported a $32%-$72% PCE drop for single-junction PSCs, depending on their device architecture. Based on the visual appearance and photoluminescence (PL) intensity change of the device, they attributed the degradation to decomposition and phase segregation of perovskites. 24 Brecl et al. tested voltage biases of G500 and G1000 V and found that single-junction PSCs show a high PID resistance against biases of G500 and +1,000 V, but a rapid degradation under À1,000 V, resulting from the diffusion of the detected Na + ions from glass to the perovskite bulk under such strong negative bias. 25 Notably, all of the above PID studies for single-junction PSCs are based on glass/glass mini-modules with edge-sealed encapsulation where the front side of the perovskite device is separated from the module glass by a layer of N 2 /air rather than by a lamination sheet (e.g., thermoplastic polyurethane [TPU] or ethyl vinyl acetate [EVA], which is common from most commercial PV modules). As stated, to the best of our knowledge, no investigation into PID effects in perovskite/silicon tandem devices, which recently achieved a record PCE of 31.3%, 35 has been published in the literature, despite the importance of PID robustness for commercialization. This motivates us to evaluate here the impact of a high system voltage on encapsulated perovskite/silicon tandem devices, provide insights into its root causes and formulate mitigation strategies.

RESULTS AND DISCUSSION
Current-voltage analysis Single-device encapsulated perovskite/silicon tandem mini-modules (hereafter referred to as modules) as shown in Figure 1, with initial PCEs between 21.8% and 26.6% (after encapsulation, yet before any prolonged testing) were used in this study. These samples were then subjected to specific test procedures as listed in Table 1 to investigate possible PID effects as well as recovery methods.
The illuminated current-voltage (IV) curves of encapsulated tandems (shadow masked, defining an active area of 1 cm 2 ) following distinct device-testing steps under specific characterization conditions (1 sun, dark, 0.1 suns; Note S1) are shown in Figure S1. The testing type and time of each step are annotated in the legend in Figure S1 and can also be found in Table 1. Sample 1, which features a PCE that represents an average among the tested modules, was always stored in the N 2 cabinet and used as a control. From Figure S1 (row 1), we can see that this control device is stable, showing almost no IV curve variation over the full period during which the other samples were tested.
The trends of the main IV parameters of the other samples, including PCE, short-circuit current density (J sc ), open-circuit voltage (V oc ), and FF, measured after each test step, are normalized to the initial condition, and summarized in Figures 2 and S2. Sample 2 went through a total of 22 h of p-PID (i.e., +1,000 V bias, 60 C). From Figure 2, we can see that this sample shows changes similar to those of the samples that were merely annealed, indicating that the +1,000 V bias does not cause PID in our tandem modules. This agrees with previously reported studies about the influence of positive bias on single-junction perovskite modules 25 and most of the single-junction silicon modules. 7,19,36 Therefore, the p-PID sample is not the focus of this study and is not discussed further.
In the context of industrial PID testing, successfully passing the IEC 61215:2021 standard requires a silicon PV module to display <5% of PCE degradation at maximum system voltage (usually 1,000 V, or 1,500 V currently) for 4 full days (96 h) under damp/heat conditions (85 C/85% RH). 37 However, from Figure 2A, we find that the PCE of the perovskite/silicon tandem modules decreases drastically to $53% of their initial value already within 22 h of n-PID testing (i.e., À1,000 V bias, 60 C; samples 4, 5, and 7). In contrast, control samples (samples 3 and 6) kept at the same temperature without voltage bias degraded much slower, retaining $84% of their initial PCE. This highlights the importance of studying PID effects in perovskite/silicon tandems, including the elucidation of underlying physical mechanisms and formulation mitigation strategies.
After these first 22 h of n-PID stressing, we divided the samples into two groups to test whether PID can be recovered by subsequent test steps (e.g., by p-PID or light soaking), as reported for single-junction silicon and perovskite modules. 12,38,39 In the first group, two of the three n-PID samples (samples 4 and 5) underwent a (C) Diagram of the perovskite/silicon tandem module structure, its PID experiment setup, and the discovered element diffusion in this study. The detected diffusions of Na + , Pb + , Cs + , Br À , and I À ions (or relevant ion groups) under negative voltage bias are illustrated in the diagram. The red dashed line at the interface of C 60 and SnO 2 indicates that Na ions are not detected in the layers underneath in this study. (D) The experimental test steps of samples. The sample information and step details can be found in Table 1. subsequent p-PID test, maintaining one annealing control sample (sample 3); see also the experimental matrix in Figure 1D. We found the PCE of the control sample recovered from $84% to $92% after 11 h and then degraded to 76% after another 13 h of annealing (all PCE values here and below are relative percentages compared to the PCE before any procedures, yet after encapsulation). In contrast, p-PIDtreated samples (4 and 5) recovered faster than the control, with their PCEs increasing from $52% to values >65% in the first 11 h, but their PCEs dropped during extended p-PID, with a similar degradation rate as the annealed control sample. This finding suggests that the n-PID effect can be partially recovered by p-PID testing. However, the p-PID test in the annealing environment may simultaneously result in thermal degradation. In the second group, one n-PID-treated sample (sample 7) underwent light soaking together with one previously annealed control sample (sample 6). We find that light soaking cannot recover the n-PID effect for the studied modules. Instead, it causes further degradation. Following these experiments, all of the samples were stored in an N 2 cabinet for 72 h and then characterized further. While sample 3 (which only experienced annealing) shows almost no change during storage, all of the other samples degraded further. This suggests that the PID or light-soaking test step may introduce long-term module stability issues.
From Figures 2C, 2E, and 2G, we can see that the effect of PID on PCE is mainly caused by FF degradation, especially for the first 11 h of the n-PID test, followed by losses in V oc and J sc during the remaining time. The trend of low light (0.1 suns) IV performance shown in Figures 2B, 2D, 2F, and 2H are similar to that at the 1-sun condition, but we can see that samples affected by n-PID suffer a higher PCE degradation at 0.1 suns than at 1 sun, especially for the first 11 h (dropping to $62% of initial PCE at 0.1 suns, while decreasing to $70% at 1 sun). Because the modules' IV performance is more sensitive to shunt resistance at low light intensity than at high light intensity, this difference suggests an n-PID induced shunt, which we discuss in greater detail below.
Because the FF variation contributes the most to the PCE change, it is necessary to analyze its main constituents such as the series resistance (R s ) and shunt resistance (R sh ) of the tandem modules. However, unlike single-junction silicon solar cells, accurate quantitative extraction of R s and R sh of each subcell in a tandem is not  The details of each test step are as follows: store-store in 22 C N 2 storage cabinet with relative humidity <35%. p-PID-positive PID test setup (shortened to p-PID); Al foil film testing setup shown in Figure 1B; +1,000 V bias (tandem cells are positively biased compared to the Al foil and glass) in 60 C dark oven with relative humidity <20%. n-PID-negative PID test setup (shortened to n-PID); Al foil film testing setup shown in Figure 1B; À1,000 V bias (tandem cells are negatively biased compared to the Al foil and glass) in 60 C dark oven with relative humidity <20%. Anneal-anneal in 60 C dark oven with relative humidity <20% without voltage bias. straightforward due to the floating nature of the recombination junction. In this study, we use the software LTspice 40 to simulate the influence of R s and R sh on tandem solar cell IV curves (detailed in Note S2), and we analyze the IV curves in Figure S1 qualitatively based on the simulation. From Figure S3, the increase in R s of either the perovskite or silicon subcell decreases the slope of the IV curve at the V oc point in the light-IV curve and flattens the dark-IV curve at a high forward bias. The decrease in R sh of either perovskite or silicon subcell increases the slope of the light-IV curve at low voltage bias and shifts up the middle part of the dark-IV curve. However, the voltage onset where the curve starts to change is obviously different and depends on the subcell from which the R sh contribution originates. This voltage onset is $0.5 and 0.9 V in the case of silicon or perovskite subcell shunting, respectively; if both subcells are shunted, the onset voltage is $0 V. Based on these findings, we review the IV curves in Figure S1, focusing on the change after each test step. We extract the reverse slopes of light IV curves at V oc , 0.5, and 0.9 V, respectively. From Figure 3A, we can see that compared to the annealing control samples, all n-PID tested samples show sharper R s -related changes in the slope of the light IV at V oc point. The changes are mitigated by subsequent p-PID testing or light soaking but are exacerbated again in the extended tests and in the following store procedure, especially for the samples that previously underwent light soaking. The perovskite degradation, shown in the subcell current limited IV and electroluminescence (EL) images (Figures 3 and 4, respectively; a detailed analysis is presented later), is believed to be the root cause of the increased R s . In terms of decreased R sh , which is one of the main reported PID effects for both single-junction perovskite and silicon modules, 14,25 we analyze its related slope in Figures 3B and 3C. We can see that although the annealing procedure will gradually reduce the reverse slopes at both 0.5 and 0.9 V points, the n-PID tested samples show a much steeper change in the R sh -related slopes. The p-PID test can partially recover the n-PID-induced slope change, but extended p-PID testing at 60 C will reduce reveres slopes again due to the thermal induced degradation. Because the light IV slope starts to change at 0.5 V, based on the LTspice simulation, the shunt is mainly from the perovskite subcell.
To unambiguously conclude whether the silicon subcell is also shunted by the n-PID test, at the end of the experiment, we applied a subcell current-limited IV analysis by controlling the illumination spectra. 41 LTspice simulations to demonstrate the mechanism of this subcell's current limited IV analysis of tandem can be found in Note S3 and Figure S4. In short, if the current is limited by the perovskite subcell, then the light IV curve will be only sensitive to R sh of the perovskite subcell but not to that of the silicon subcell, and vice versa for the silicon subcell limited case. Using this method, we can independently determine from which subcell the shunt originates.
Using the stored control sample in Figure 3D as a reference, from Figure 3E, we can see that after the anneal/anneal/store procedure, the silicon subcell in sample 3 shows no noticeable shunt, but the perovskite subcell is shunted, although much

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less than the n-PID or light-soaked samples discussed below. This suggests that the silicon subcell is stable during storage and moderate temperature annealing, while the stability of the studied perovskite subcell is not ideal. In addition, R s of the silicon subcell slightly increases when compared to the stored control sample in Figure 3D because of the shunted perovskite subcell, which can be regarded as an additional R s of the silicon subcell. From Figure 3F, expectedly, the silicon subcell is found to be stable under light soaking, whereas the perovskite subcell shows more degradation under light than under heat in Figure 3E. From Figure 3G, we can see that n-PID followed by light soaking will cause shunts in both subcells. This is the only sample in Note that even if reverse slopes are with a unit of U , cm 2 , the absolute value of them does not accurately correspond to R s and R sh . Since the IV is sensitive to absolute changes in R s and R sh , we do not normalize them here. Because the 0.1 sun IV curves show strong noise, making the slope extraction unreliable, we only analyze the 1-sun light IV curves here. Also note that the y axes of (B) and (C) are in log scale. Also, similar to R sh analysis in singlejunction modules, only when R sh has orders of magnitude change and only when R sh is lower than a certain threshold, does R sh have an impact on the IV.
Here, we use the lowest initial reverse slope at 0 time point as this threshold, and only consider the value below it as effective points. Any variation above this threshold is assumed to be noise. which we see a noticeable shunt in the silicon subcell, matching the strong local shunt of the silicon subcell observed in the EL images of sample 7 after light soaking in Figure 4. In contrast, if n-PID is followed by p-PID recovery, the shunt is noticeable only in the perovskite subcell. In addition to the previous samples, we added a 138-h n-PID-treated sample (initial PCE of 24.8%) here, which is also used for later elemental analysis. Its subcell limited IV characteristic as shown in Figure 3I indicates that long-term n-PID will cause extreme shunting in the perovskite subcell (increasing obviously the effective R s of the silicon subcell). However, the silicon subcell does not become noticeably shunted in such tandems by n-PID.

EL and PL
We measured the EL and PL images of samples after each test step (more details in Note S5) and the results are shown in Figure 4. We found the initial EL signals of the perovskite of samples 4, 5, and 7 (i.e., those with higher initial PCE), are 1-2 orders of magnitude higher than after PID testing and higher than the EL signals of silicon subcells. This finding matches the fact that perovskites have a much higher band edge absorption/emission coefficient than that of silicon, 42 and also suggests that PID can cause strong non-radiative recombination to reduce the EL of perovskite.
From Figure 4A, the PL images at both injection levels (1 and 0.1 suns) of sample 3 (anneal/anneal/store), we can see that carrier recombination associated with the silicon subcell is quite stable during the annealing and store procedures, which suggests that the V oc variations noted in Figures 2E and 2F are mainly related to the perovskite subcell. Comparing the EL of the silicon subcell at different injection levels, we can see that the low injection EL images demonstrate no noticeable change, while those related to high injection level vary slightly with a trend similar to that of tandem IV parameters in Figure 2 and EL images of the corresponding perovskite. This again suggests that degradation of the perovskite subcell acts as added series resistance to the bottom silicon subcell, matching the observation in Figure 3. The high injection EL images of the perovskite match quite well to the 1-sun IV parameters trend of Figure 2, indicating again that the thermal stability of the used perovskite is not ideal and it is the main reason for the IV performance variation of the complete tandem under the annealing procedure. Also, comparing the high-and low-injection EL responses of perovskite, we can see that the uniformity is better under low injection conditions, suggesting that either the different locations of perovskite have different injection level-dependent recombination or there is R s issue for this perovskite subcell, and this R s effect is enhanced by heating.
From Figure 4C, the PL images at both injection levels of sample 6 (anneal/light soaking/store), the light soaking after annealing slightly improves the PL signal from the silicon subcell, possibly due to the light-enhanced surface passivation effect as reported for single-junction silicon heterojunction solar cells. 43 The PL improvement of the silicon subcell suggests that the V oc variations noted in Figures 2E and 2F are mainly related to the perovskite subcell. The EL of the silicon subcell at low injection levels is roughly the same over the testing history for most samples. The high-injection EL of the silicon subcell is roughly stable before light High-injection (HI) and low-injection (LI) for EL means that 17 and 1.7 mA currents are applied, respectively. HI and LI for PL means that 1 sun and 0.1 sun light intensity are applied, respectively. PL of perovskite (PVK) is not available due to equipment limitation. Because the signal is noticeably different between samples and between different EL/PL conditions, different color scales are used (listed at the left of each image row). Because the EL of PKV changes orders of magnitude after processing, 2 color scales are used for EL of PVK: 1 for the first image on the left of the row and 1 for the rest on the right side. A dashed line after the first image is used to delineate the different color scales.
soaking; after light soaking the EL image distribution changes, and it is very likely because of the perovskite-induced R s , considering those patterns are not seen in the PL and low-injection EL.
From Figure 4B, for sample 5 (n-PID/p-PID/store), which is different from the previous two samples without any PID test, after n-PID, the PL and EL signals of silicon subcell drop. This indicates either increased recombination or shunt, or that the above-layer optical properties changed. Because no obvious shunt in the silicon subcell is observed in Figure 3I, recombination or optical property changes may be the main reason (discussed further when examining Figure 5). The subsequent p-PID can almost fully recover the silicon subcell and make it even better than the initial condition. This matches the observation in Figures 3H and 3I. About the perovskite subcell, the high injection EL images show good agreement with Figure 2. The low-injection EL also corresponds well to the FF trend in Figure 2H, considering that shunting has more influence on low-injection EL than on high injection.
Moving to the n-PID/light soaking/store sample (sample 7) in Figure 4D, the EL and PL images of the silicon subcell are similar to sample 5 above, but without p-PID testing, the degradation after n-PID testing, especially for the low-injection cases, cannot be recovered. What makes it worse is that the light soaking introduces local shunting as shown in the low-injection EL. This matches the observation in Figure 3G. The reason why light soaking can introduce local shunting in the silicon subcell is yet unknown and under investigation. The EL images of the perovskite subcell match well with the IV trend in Figure 2, suggesting the degradation of the tandem is mainly from the top subcell.

Investigation of the PID mechanism based on elemental analysis
The diffusion of Na + ions from the glass into solar cells is one of the main PID mechanisms reported for single-junction silicon and perovskite modules. 9,10,18,25 To investigate whether this phenomenon also occurs in perovskite/silicon tandems, we prepared a 138-h n-PID-treated perovskite/silicon tandem module, to be compared with one control sample without an n-PID test. These two modules were then intentionally deconstructed for further analyses. The TPU layer can be easily separated from the tandem cells due to the poor adhesion between the C 60 layer and the SnO 2 layer in the electron-collecting front contact of the tandem. 44 This implies that all of the layers overlaying the C 60 layer are separated from the tandem cell together with the TPU. We applied secondary-ion mass spectrometry (SIMS) on the side of the separated TPU, facing the tandem cells (check details in Note S6). The SIMS results of the separated TPU of both n-PID and control samples are shown in Figures 5A-5D. By comparing the SIMS positive-ion profiles of the two samples in Figures 5A and 5B, first, we can see that the n-PID-treated sample has an order of magnitude higher Na + ion signal than the control sample, indicating Na + ions diffuse from glass to the tandem cells due to the strong electrical field used during n-PID testing. This confirms results reported in the literature, 9,10,18,25 even though we also found that Na is mostly confined above the C 60 layer. Second, we (E) TEM EDX of the tandem cell below C 60 layer after opening the encapsulation of a n-PID processed tandem module. The TEM EELS shows similar information as TEM EDX and can be found in Note S7.

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Cell Reports Physical Science 3, 101026, September 21, 2022 found that the Cs and Pb concentrations are more than one order of magnitude higher in the n-PID-treated sample, suggesting that elements of the perovskite also diffuse to the TPU during the n-PID testing. However, considering the electrical field direction, it is not straightforward to understand why Cs and Pb can diffuse along this direction. To investigate this, we also measured with SIMS the negative ions profiles of the two samples, as shown in Figures 5C and 5D. We can see that the Br and I signals are more than one order of magnitude higher in the n-PID sample than in the control sample, confirming the diffusion of the perovskite elements to TPU under n-PID testing. This implies that n-PID can introduce structural changes in the perovskite, resulting in optical and electrical degradation of the perovskite subcell, explaining the perovskite subcell degradation observed from the IV and EL results. To the best of the authors' knowledge, this is the first time such a PID mechanism has been reported in perovskite/silicon tandem modules (summarized in Figure 1C). In terms of the mechanism of this perovskite element diffusion, for Br and I, it is likely that, as negative ions, the n-PID electrical field can drive them into the TPU. For Cs and Pb, we suspect that they are initially in the form of negative ion groups, such as CsI, CsBr, PbI, and PbBr, so they can diffuse along the electric field to TPU and then be detected by SIMS.
In addition, we applied transmission electron microscopy energy-dispersive X-ray analysis (TEM EDX) and electron energy loss spectroscopy (EELS) on the n-PIDtreated tandem after opening its encapsulation to check whether the Na ions diffused into the perovskite or silicon subcells (details in Note S7). TEM EDX is the method used in the literature to detect the Na + ions in single-junction silicon modules. 9,10,18 However, as shown in Figure 5E, the Na + ion signal is very low and hardly distinguishable from the background noise in both TEM EDX and EELS. From the two-dimensional (2D) and 3D SIMS in Brecl et al., 25 materials or interfaces can confine Na + ions, which may explain the reason why Na + ions are detected in their samples but not in ours, considering the many more materials and interfaces present in our tandem modules. Even if some Na + ions penetrate down to the perovskite, the concentration is too low to be detected by TEM EDX and EELS. The absence or insufficiency of Na + ions diffusing to silicon also explains the reason why we do not see the shunt in the silicon subcell of our tandem, which is otherwise widely observed in the PID of single-junction silicon devices. 9,10,18 Discussion on potential mitigating strategy Based on the underlying PID mechanism in perovskite/silicon tandem solar modules, one promising strategy is the use of encapsulant-free module structures, such as the new industrial cell encapsulation (NICE) technology. 45 In such an encapsulant-free module structure, the cell is surrounded by an inert atmosphere and has no direct contact with the glass, so the potential bias almost fully drops on the interface between glass and inert atmosphere. Most important, ion migration, causing the module degradation under PID testing, is prevented by the inert atmosphere. However, the encapsulant between glass and cell in standard modules can provide mechanical support, optical coupling, electrical isolation, and protection against environmental exposure. [46][47][48][49] Compared to silicon modules, the choice of encapsulant is expected to be more important for perovskite/silicon tandem modules, especially when the backsheet is used, 46 as the perovskite is much more sensitive to moisture than silicon. [50][51][52][53] Therefore, while using an encapsulant-free module structure is a promising method to prevent PID effects in tandem modules, it is also important to study the PID effect in the module structure with an encapsulant. For modules with an encapsulant, a potential future research direction is to introduce a barrier material that ll OPEN ACCESS does not influence the cell performance but can prevent the diffusion of the element out of the perovskite in the presence of a strong electrical field.
In this work, we systematically studied PID in perovskite/silicon tandem solar modules via different characterization methods. In contrast to the IEC 61215:2021 standard, which requires the silicon module to display <5% PCE degradation at maximum system voltage (usually 1,000 V, or 1,500 V currently) for 4 full days (96 h) under 85 C/85% RH conditions, 37 we found that À1,000 V bias at 60 C for $1 day can already degrade the PCE of the perovskite/silicon modules by $50%, which raises concerns for tandem commercialization. More specifically, the negative PID affects the FF most by both the increased R s and reduced R sh due to the degradation of the perovskite subcell. Via SIMS, we found that certain perovskite elements, including Br, I, Pb, and Cs, diffuse into the TPU after the n-PID test. This elemental diffusion out of the perovskite is expected to cause structural damage, resulting in optical and electrical degradation of the perovskite, as detected in IV, EL, and PL. To the best of the authors' knowledge, this is the first time such a PID mechanism has been reported. Although via SIMS, Na + diffusion from module glass via the TPU is detected, we found no accumulation of Na + in the perovskite or silicon of our tandem cells via both TEM EDX and TEM EELS ( Figure S7). We suspect the Na + ions are confined within the materials or interfaces above C 60 . As a consequence, no obvious shunt is noticed in the silicon subcell, which is otherwise widely observed in the PID of single-junction silicon devices. 9,10, 18 We find that +1,000 V bias at 60 C does not introduce PID. Instead, it can partially recover the negative PID. This matches reports in the literature for single-junction perovskite and silicon modules. 7,23 In conclusion, the PID in perovskite/silicon tandems mainly affects the top perovskite subcell. While the positive voltage bias can partially recover the negative PID, introducing materials or structures to prevent the elemental diffusion out of the perovskite in the presence of a strong electric field may be a promising research direction for mitigating PID in perovskite/silicon tandem modules.

EXPERIMENTAL PROCEDURES
Resource availability Lead contact Further information should be directed to the lead contact, Lujia Xu (lujia.xu@kaust. edu.sa).

Materials availability
This study did not generate new unique materials.

Data and code availability
The published article and its supplemental information include all data generated or analyzed during this study.

Samples, experimental design, and PID conditions
Single-device encapsulated perovskite/silicon tandem modules, as shown in Figure 1, with initial PCEs between 21.8% and 26.6% (after encapsulation, yet before any prolonged testing), were used in this study. These tandems are in the so-called p-i-n architecture, implying that electrons are collected at their sunward side; the front contact stack of the perovskite subcell has as structure perovskite/LiF/C 60 /SnO 2 /IZO/MgF 2 . 54 The tandem cells are laminated between two glass sheets using TPU as encapsulant on both sides; the module edge is sealed with butyl rubber to improve its resilience to humidity. 50 These samples then were subjected to specific test procedures as listed  Table 1 to investigate possible PID effects and as well as recovery methods. A G1,000-V voltage bias is chosen to simulate the widely used maximum system voltage expected from a PV system consisting of a string of multiple modules; 60 C is used as the annealing temperature for the PID test as it is a realistic temperature for module operation outdoors. 5 The Al foil method 7 is used to apply voltage to the front glass in the n-PID and p-PID procedures listed in Table 1, as shown in Figures 1B and 1C. More characterization-related details are provided in the supplemental information.

DECLARATION OF INTERESTS
W.L. is currently with Huawei Digital Power.