Understanding Contact Nonuniformities at Interfaces in Perovskite Silicon Tandem Solar Cells Using Luminescence Imaging, Lock-In Thermography, and 2D/3D Simulations

The top cell of a perovskite silicon tandem solar cell requires several material layers on each side of the perovskite absorber to efficiently extract electrons and holes, respectively. These layers must meet multiple requirements simultaneously, namely, low interface recombination, good charge carrier selectivity, low contact resistivity, and high optical transparency. Due to the complex architecture, characterization techniques are required in material and process optimization to identify loss mechanisms. Spatial resolution of the characterization is gaining importance along with the upscaling of the perovskite technology. Herein, electro‐ and photoluminescence (EL and PL) imaging is combined with illuminated lock‐in thermography (ILIT) for a comprehensive electro‐optical characterization of both subcells in perovskite silicon tandem devices with state‐of‐the‐art cell architecture. Thereby, the combination of the presented characterization methods together with numerical simulation models enables to carry out holistic investigations of device limitations. The strength of this approach is showcased by one particularly remarkable feature that is observed in the investigated tandem device, showing a low PL but high EL signal at local spots. Together with multidimensional optoelectrical device simulations, the measurements are explained and the root cause of this feature to originate from the perovskite/C60 interface is suggested.


Introduction
Perovskite silicon tandem solar cells are promising technology, enabling certified power conversion efficiencies above the intrinsic limit of silicon single-junction solar cells. [1,2]However, it is still challenging to find well-suited materials for contacts of the perovskite top cell, combining low interface recombination, low contact resistivity, high selectivity, and optical transparency.For example, recently reported high-performing perovskite silicon tandem solar cells use C 60 as electron transport layer. [3,4]However, C 60 is known to enhance nonradiative recombination losses and limit the cell performance. [5,6]o improve the tandem solar cell performance further, characterization techniques are necessary to evaluate the effect of new materials and deposition techniques on device performance parameters, such as, for example, the open-circuit voltage V oc or the implied open-circuit voltage iV oc .However, when determining V oc or iV oc to evaluate the interface quality, small local defects (e.g., at the perovskite/C 60 interface) cannot be detected in measurements that are not spatially resolved.Yet, lateral effects are crucial for understanding the loss mechanisms in a perovskite silicon tandem solar cell, as substantial process nonuniformities are expected for large-sized devices in particular.Various spatially resolved measurements based on luminescence are reported in literature.10] The combination of PL images and electroluminescence (EL) imaging on perovskite solar cells was presented to help gaining a deeper understanding of local features. [11,12]An overview of different spatially resolved quantitative analysis approaches for inhomogeneities in perovskite layers can be found in, for example, Schubert et al. [13] In this work, we combine EL and PL imaging with illuminated lock-in thermography (ILIT) measurements for a comprehensive and spatially resolved electro-optical characterization of both DOI: 10.1002/solr.202300249 The top cell of a perovskite silicon tandem solar cell requires several material layers on each side of the perovskite absorber to efficiently extract electrons and holes, respectively.These layers must meet multiple requirements simultaneously, namely, low interface recombination, good charge carrier selectivity, low contact resistivity, and high optical transparency.Due to the complex architecture, characterization techniques are required in material and process optimization to identify loss mechanisms.Spatial resolution of the characterization is gaining importance along with the upscaling of the perovskite technology.Herein, electro-and photoluminescence (EL and PL) imaging is combined with illuminated lock-in thermography (ILIT) for a comprehensive electro-optical characterization of both subcells in perovskite silicon tandem devices with stateof-the-art cell architecture.Thereby, the combination of the presented characterization methods together with numerical simulation models enables to carry out holistic investigations of device limitations.The strength of this approach is showcased by one particularly remarkable feature that is observed in the investigated tandem device, showing a low PL but high EL signal at local spots.Together with multidimensional optoelectrical device simulations, the measurements are explained and the root cause of this feature to originate from the perovskite/C 60 interface is suggested.subcells in perovskite silicon tandem solar cells.The combination of the presented characterization methods together with the numerical simulation models Quokka3 [14,15] and Sentaurus TCAD [16] enables us to carry out holistic investigations of device limitations.The benefits of the interplay of the different methods are showcased by one particularly strong local feature that we observe in the investigated tandem device, featuring a low PL but high EL signal at local spots.We present how multiple characterization methods jointly allow to distinguish different kinds of defects such as shunts and energetic barriers.

Solar Cell under Investigation
For this work, a state-of-the-art perovskite silicon tandem solar cell with an active area of 4 cm 2 was analyzed.The monolithic tandem solar cell is composed of a silicon heterojunction bottom solar cell and a p-i-n perovskite top solar cell.Figure 1 shows the detailed architecture of the sample that was produced at Fraunhofer ISE according to the more detailed information in the supporting information.The sample chosen for the analysis in this publication was obtained from an early stage of the process optimization.Therefore, the sample shows defects and scratches that can be attributed to processing and handling procedures of the sample.The electrical properties of the solar cell are presented in Figure S1 and Table S1, Supporting Information.An analysis of some defective areas based on images of an optical microscope is presented in Figure S3, Supporting Information.
The solar cell had a power conversion efficiency of η ¼ 19.8% at standard testing conditions, which is a reasonably good performance considering that the silicon subcell had a planar front side, no additional passivation layer was used at the perovskite/C 60 interface, and the charge carrier extraction was hindered by damages in the busbar.Additionally, some minor shunts were detected in the perovskite top cell.The great potential of tandem solar cells with this architecture was recently demonstrated on a similar tandem solar cell produced inhouse with an active area of 0.25 cm 2 .Its stabilized maximum power efficiency was certified at Fraunhofer ISE to be η ¼ 26.1%. [17]he combination of the previously listed characteristics rendered the solar cell an ideal subject for the investigation presented in this publication.

PL and EL Imaging
A measurement setup developed at Fraunhofer ISE and built by Intego GmbH was used for PL and EL imaging measurements.The setup was the further development of the original measurement system described in Giesecke et al. [18] A blue 450 nm laser was set to a photon flux density of j ph ¼ 1.34 Â 10 17 cm À2 s À1 to excite the perovskite subcell.This corresponded to %0.85% of the 1 sun equivalent illumination intensity.The image was acquired with a silicon charge-coupled device camera.The spectral sensitivity of the camera was limited to a range between 650 and 750 nm with the help of optical filters.Only the luminescence signal of the perovskite top solar cell was detected in this spectral range.The luminescence signal of the bottom cell was thus blocked for the measurements.A power supply was used for EL measurements.The excitation current for the measurements was set to 60 mA.The same filters and camera were used for EL image acquisition as for PL imaging measurements.The detected count rate not only depends on the quasi-Fermi-level splitting (QFLS) Δμ, but also on the absorptivity αðEÞ of the sample and the spectral response SRðEÞ of the measurement setup depending on the energy E as well as a scaling factor SF describing the fraction of the photon current collected by the camera [19] In this formula C is a physical constant, k b is the Boltzmann constant, and T the temperature.It was essential to consider the dependencies mentioned before to understand the root cause of bright and dark areas in luminescence images.Using Δμ ¼ q iV oc , with q being the elementary charge, one can determine the implied open-circuit voltage from EL or PL measurements.

Illuminated Lock-In Thermography
A measurement setup from IRCAM GmbH was used for ILIT measurements to detect thermal heat dissipated due to transport and recombination losses. [20]Two light-emitting diodes with a spectral peak position at 470 nm (photon flux density set to j ph ¼ 2.4 Â 10 17 cm À2 s À1 , corresponded to %1.5 times the 1-sun equivalent illumination intensity) and 950 nm (photon flux density set to j ph ¼ 2.5 Â 10 17 cm À2 s À1 , corresponded to %2 times the 1 sun equivalent illumination intensity) were used for the excitation of the cell during ILIT measurements.With the choice of these wavelengths, the top and bottom solar cell can be independently excited, using 470 nm for the perovskite and 950 nm for the silicon subcell.The excitation signal was modulated with a frequency of 30 Hz in both measurement modes.An IR camera from IRCAM GmbH was used for image acquisition.For further details on the technique of LIIT, we refer to another study. [21]4.Electro-Optical Device Simulations

Quokka3
We used Quokka3 [14] with the recently added tandem functionality [15] to perform 3D optoelectrical device simulations of the investigated tandem cells.In Quokka3, a tandem cell was modeled by including a two-diode model of the top cell in the so-called lumped skin boundary condition at the silicon bottom cell's front side.Optically, the top cell's external quantum efficiency had to be defined.By defining multiple skins in laterally different locations at the front side, it was possible to model laterally nonuniform top cell properties.Quokka3 routinely outputs 2D maps of the quasi-Fermi potential split in the bottom cell bulk as well as the junction voltage of the top cell, the latter being the series-resistance free voltage of the top cell's two-diode model.We then converted these voltage maps into equivalent luminescence intensity with arbitrary units using the proportion- , with V t being the thermal voltage.
Thereby, EL images were simulated by calculating the luminescence intensity of a dark device with an applied current density or applied voltage, whereas PL images were simulated assuming an illuminated device at open-circuit conditions.
Here, we used the top and bottom cell electro-optical properties representing typical perovskite silicon tandem cells manufactured at ISE reported in another study. [15]We then varied the top cell's series resistance and J 01 to account for varying contact resistivity and nonradiative recombination, respectively.

Sentaurus TCAD
We used a full optoelectrical simulation model elaborated in Sentaurus TCAD [16] that was capable to describe state-ofthe-art perovskite silicon tandem solar cells.It was validated by tandem solar cells developed at Fraunhofer ISE. [17,22]The bottom cell was modeled as a silicon heterojunction with rear side texturing.The planar front side featured an ITO recombination junction followed by the perovskite top cell layer stack according to Figure 1.
The optical model was elaborated and validated in previous publications [17,23] and is based on ray tracing in the crystalline silicon absorber and transfer matrix method (TMM) for the top and bottom cell thin-film layer stacks (including the perovskite).The electrical model for the silicon bottom cell was presented and used in several publications [23][24][25] and includes all electrically active layers that are shown in Figure 1.The optoelectrical model of the full perovskite-silicon tandem device was elaborated and experimentally validated in the study of Messmer et al., [26] which is capable to describe the perovskite top cell in very sophisticated detail including the drift diffusion of the mobile cations and anions within the perovskite.For the showcase presented in this article, the tandem cell was modeled in 2D as used in Fell et al. [15] with two different regions that featured different C 60 contact properties (i.e., barrier heights) to demonstrate the effect of local nonhomogeneities of the perovskite/C 60 interface on PL and EL signal.We tested the influence of typically reported ion concentration between 10 16 and 6 Â 10 16 cm À3 , seeing only minor differences in iV oc of less than 2 mV comparing high and low ion concentrations.Therefore, we considered the impact of ions in this showcase to be comparatively small.

Results and Discussion
In the following sections, we will focus on three distinguishable local features observed in the PL, EL, and ILIT measurements of the investigated sample: 1) shunts (S); 2) local contact nonhomogeneities (C); and 3) combinations of local contact nonhomogeneities and shunts (CS).Table 1 gives an overview of the different feature types and their impact on the measurement signal in EL, PL, and ILIT measurements discussed later.Figure 2 visualizes the appearance of the different feature types for all measurement methods.Optical microscope measurements of some of the observed local features are presented in Figure S3, Supporting Information.

Luminescence Imaging Measurements of Perovskite Subcell
In this section, we analyze the findings in the PL and EL images of the top cell of the perovskite silicon tandem solar cell shown in Figure 3 and 4.
Figure 3 shows the EL image of a perovskite top cell in the perovskite silicon tandem solar cell.The black frame of the image is caused by an evaporated metal frame acting as the busbar.The fingers (F) are visible as thin black lines, as indicated for example by the arrow at F in Figure 3. Spots S1 and S2 mark regions with low signal in the EL image in Figure 3. Spots C and CS mark regions with increased signal in the EL image.Note that for spot C the EL signal is increased significantly by approximately one order of magnitude compared to the surrounding area.All spots are chosen only exemplarily.
Figure 4 shows the PL image of the perovskite top cell.Similar to the EL Image, the busbar and the fingers (arrow at F) appear Table 1.Classification of observed features that are discussed in this publication.The measurement signal response to the features is distinguished between strong signal increase (þþ), signal increase (þ), no signal response (0), signal decrease (À), and strong signal decrease (ÀÀ).

Feature type
Abbreviation Perovskite signal Silicon signal black as they shade the solar cell.While spots C and CS appear bright in the EL image in Figure 3, all spots marked as C, CS, S1, and S2 appear dark in the PL image in Figure 4.
Comparing the appearance of the highlighted spots C, CS, S1, and S2 in Figure 3 and 4, it is obvious that the different spots have to be attributed to different effects.Optical effects of light in-and out-coupling can be ruled out to cause these effects since EL measurements do not depend on light incoupling, and the light outcoupling mechanism is the same for PL as for EL measurements.

ILIT Measurement of the Perovskite and Silicon Subcell
ILIT measurements are sensitive to power dissipation in a solar cell, for example, due to shunts or regions with increased nonradiative recombination rates.To check the occurrence of such defects in the tandem solar cell under investigation, subcellselective ILIT measurements were performed.
ILIT measurements of the perovskite subcell are presented in Figure 5. Bright spots are detected at spots S1 and S2, suggesting that a shunt or a region with highly increased nonradiative recombination is present.At spot CS, the signal is also increased though hardly noticeable.This indicates that a small shunt or a region with high nonradiative recombination is present.These findings agree with EL measurements on the silicon bottom cell presented in Figure S2, Supporting Information.No increased signal is found at spot C that can be distinguished from the local noise in the measurement signal.We assume that the nonradiative recombination rate at spot C is not increased.However, we cannot fully rule out nonradiative recombination below our detection limit.
Since shunts in the silicon subcell will influence the EL image of the perovskite subcell for two terminal tandem devices, ILIT   measurements of the silicon subcell are performed to evaluate the quality of the silicon subcell.Figure 6 shows the amplitude image of the ILIT measurement on the silicon subcell.Several regions show an increased signal.However, for none of the spots C, CS, S1, or S2, a shunt or a region with increased nonradiative recombination rates is indicated since the measurement signal is not increased.Hence, a shunt in the silicon subcell can be ruled out to cause the high EL signal in the perovskite subcell in Figure 3.

Defects with Similar Appearance in EL and PL Images
If the recombination rate is increased locally, for example, due to defects in the perovskite absorber, the QFLS will be lower in these regions compared to other parts of the cell, as long as charge carriers are homogeneously injected.The QFLS also drops in regions where a shunt short circuits the cell.
According to (1), the detected signal is lower for these regions in the EL image as well as in the PL image.This can be observed in spots S1 and S2 in Figure 3 and 4 and is summarized in Table 1.Additionally, the ILIT image of the perovskite top cell shows an increased power dissipation at these two spots.Consequently, spots S1 and S2 can be attributed to increased nonradiative recombination or shunts in the perovskite subcell consistently for all measurements.
The appearance of the spots C and CS is contrary in the EL and PL images in Figure 3 and 4. In the following, we discuss two effects that can explain these local features.We refer to these effects as the "J 0 R c Hypothesis" and the "Φ b Hypothesis".The plausibility of the explanations is validated against numerical device simulations.

"J 0 R c Hypothesis": Explaining Opposite EL/PL Contrast by High Recombination Rates and Low Contact Resistance
Besides the recombination properties, for PL imaging, the local injection of charge carriers mainly depends on the incoming photon current density or optical properties like reflectivity, parasitic absorption, as well as the absorptivity of the perovskite layer.On the contrary, for EL imaging, the local injection of charge carriers is strongly influenced by the present series and contact resistance.Hence, a locally decreased contact resistance at any interlayer increases the local QFLS (and therewith the detected signal) in EL images only.Possibly, an overall significant contact resistance is present in the device, which is locally decreased at spots C and CS.This explains the locally increased signal in the EL image in Figure 3.A possible origin is a nonuniform contact resistance at the perovskite/C 60 interlayer.Considering the mechanism of recombination at the perovskite/C 60 interface according to, for example, Warby et al., [5] it is likely that a decreased contact resistance correlates with an increased nonradiative surface recombination rate, leading to a decreased PL signal in spot C and CS in Figure 4.In the case of the EL image, the enhanced recombination rate is overcompensated by the increased charge carrier injection in the local regions, which can explain the opposite contrast observed in the PL and EL images.Contrary to spot C, spot CS shows a slightly increased heat dissipation in the ILIT image of the perovskite subcell (Figure 5).This suggests that for spot CS, the phenomenon present at spot C is combined with an additional defect as, for example, a small shunt.
The plausibility of the "J 0 R c Hypothesis" is tested against Quokka3 simulations.In particular, we test whether 1) the contrast between background and local feature can be reproduced both in the PL and EL cases; 2) lateral carrier transport has a sufficiently small impact to allow the experimentally observed image sharpness; and 3) the cell properties required to reproduce the image contrast are compatible with a still reasonable cell performance (for electrical parameters, see Figure S1 and Table S1, Supporting Information).
We created a 3D tandem cell domain that consists of a of 6 mm Â 6 mm large area A and a spot C with a size of 0.5 mm Â 0.5 mm in Quokka 3. It is presented in Figure 7.This approximately represents the feature size and area fraction observed in  the EL and PL images in Quokka3.We start with a nominal value of J 01 ¼ 4 Â 10 À21 A cm À2 to represent nonradiative surface recombination and a negligible series resistance of R s = 0.05 Ω cm 2 to represent contact resistivity all over the cell domain.We then increased the value of J 01 at spot C and increased the series resistance at area A until we matched the signal intensity difference (approx.one order of magnitude) at spot C compared to area A in the EL and PL images.This results in J 01 = 4 Â 10 À20 A cm À2 for spot C and a series resistance of R s = 10 Ω cm 2 for area A. The properties are also presented in Figure 7.The resulting luminescence signal intensity for the EL and PL simulation is presented in Figure 8 and 9, respectively.Notably, the contours in both images appear very sharp, meaning that lateral conduction effects do not have a detrimental impact, which is in line with the experimentally observed sharpness.This sharpness is due to the poor lateral conductivity of the perovskite absorber and the poor lateral conductivity of the layers between the subcells.
In a next step we simulate the device efficiency for different assumptions on J 01 and R s .For an ideal and uniform device, we uniformly set J 01 ¼ 4 Â 10 À21 A cm À2 (as for area A in Figure 7) and a uniform negligible series resistance R s = 0.05 Ω cm 2 (as for spot C in Figure 7) on the whole area.We find that the domain in Figure 7 corresponding to the experimental cell shows a moderate efficiency loss of %2.5% abs compared to the ideal and uniform device.This is consistent with the experimentally measured reasonable J-V performance (compare Figure S1 and Table S1, Supporting Information).We further find that the loss is largely dominated by the poor contact resistance of area A, while the increased recombination in spot C has negligible impact on efficiency.A hypothetical cell with uniform and low series resistance R s ¼ 0.05 Ω cm 2 but a high J 01 of 4 Â 10 À20 A cm À2 results in a negligible efficiency loss of 0.05% abs according to Quokka 3 simulations.

"Φ b Hypothesis": Explaining Opposite EL/PL Contrast by Energetic Barrier Lowering
The above presented "J 0 R c Hypothesis" explains the lower PL signal in spot C in the PL image in Figure 4 by increased recombination.However, spot C shows no detectable heat dissipation increase compared to the surrounding background signal in the ILIT measurement of the perovskite subcell (Figure 5).Therefore, an alternative explanation is elaborated in this section that can explain the behavior of spot C by an energetic barrier lowering effect only, that is, without assuming a laterally varying surface recombination velocity and contact resistivity.We refer to this approach as the "Φ b Hypothesis", with Φ b being the conduction band offset for electrons at the perovskite/C 60 interface.Note that this approach is not essentially contradicting the "J 0 R c Hypothesis", since J 0 , R c, and Φ b can all be different for different parts of the solar cell.To assess the validity of the "Φ b For the poor contact area A, we set J 01 ¼ 4 Â 10 À21 A cm À2 and R s ¼ 10 Ω cm 2 .For the small spot C with good contact properties, we set J 01 ¼ 4 Â 10 À20 A cm À2 and R s ¼ 0.05 Ω cm 2 .For the Sentaurus TCAD simulation on a 2D cross section only the conduction band offset at the ETL/perovskite interface is varied.It is set to ΔE ETL C,spot = 0 eV for the small spot C while it is set to ΔE ETL C,spot = 0.5 eV for the surrounding area.Spot C is 0.2 mm wide and area A is 3.8 mm wide in the Sentaurus TCAD domain.Hypothesis", we performed 2D simulations in Sentaurus TCAD. [16]The 2D simulation domain is shown in Figure 7.
For the "Φ b Hypothesis", a difference in selectivity due to different energetic barriers at the respective perovskite/C 60 interfaces is assumed between spot C and area A in Figure 7. Thereby, a conduction band offset at the perovskite/C 60 interface ΔE ETL C,area > 0 is assumed in area A according to literature, [27] whereas a barrier lowering effect is assumed for spot C, reducing the barrier to ΔE ETL C,spot = 0 eV.Thus, the selectivity at spot C is very high, extracting the electrons without any significant voltage loss, whereas in the surrounding area A, the selectivity of the perovskite/C 60 interface is significantly reduced.Notably, the assumed parameter range for the energetic barrier to reproduce the experimental contrasts is quantitatively consistent with values reported in literature. [27]We want to stress that regions (spot C and surrounding area A) feature otherwise identical properties, including the perovskite, C 60 , and interface properties.In particular, the same recombination parameters were assumed in both regions.The recombination is modeled by a "recombination rate" for holes within the perovskite close to the C 60 /perovskite interface to recombine with electrons within the C 60 (which is the dominating recombination mechanism as suggested by Warby et al. [5] ).The only difference between spot C (shown in orange in Figure 10) and area A (shown in blue) is the laterally varied conduction band offset at the perovskite/C 60 interface.In the following, this simulation domain is investigated for three different cases.
In the first case, we assume spot C and area A in Figure 7 to be under illumination, however, without any lateral electrical contact between spot C and the surrounding area A. Therefore, in this case, spot C and the surrounding area A are regarded as independent of each other.Figure 10a depicts the band diagrams of spot C in orange and its surrounding area A in blue at opencircuit conditions.The reference point for the energy axis is set to the back contact and the open-circuit voltage of the Si bottom cell is labeled with V Si oc .The lower energetic barrier provides a higher selectivity for spot C compared to area A, which assures that the external voltage in spot C matches the internal voltage V oc,spot % iV oc,spot .This is reflected in a constant quasi-Fermi level of the electrons, represented by the dotted orange line in Figure 10.On the other hand, in area A, the assumed conduction band offset at the perovskite/C 60 interface of ΔE ETL C,area = 0.5 eV (shown in gray) reduces the selectivity which leads to an external voltage which is about 90 mV less than the internal voltage V oc,area < iV oc,area .This is reflected in a drop in the electron quasi-Fermi level toward the interface that is labeled by ΔV Pero oc,area and represented by the dotted blue line in Figure 10.In this laterally independent case of Figure 10a, the PL signal of spot C and area A is equally high, which is reflected in iV oc, spot ¼ iV oc,area .In contrast, the external voltage of area A is about 90 mV lower than for spot C due to the selectivity losses in area A, that is, V oc,area < V oc,spot .
In the next case we showcase spot C and the surrounding area A in Figure 7 when they are laterally contacted by a highly conductive ITO and under illumination to simulate the PL measurements, see Figure 10b.Due to the lateral contact, the external voltages of spot C and area A are leveled out at the same open-circuit voltage, V oc, spot = V oc,area .In this 2D simulation, V oc,spot of spot C is forced to the lower V oc,area of area A because of the different sizes of the two domains.Due to the low energetic barrier, also iV oc,spot is forced to the lower V oc,spot .Since the PL signal corresponds to the internal quasi-Fermi-level splitting, we consequently observe a lower PL signal in spot C with respect to area A, despite spot C inhibiting superior electrical properties.At room temperature, this voltage loss of about 90 mV corresponds to a PL signal that is reduced by a factor of around 30, which is in line with the experimentally observed reduction in PL.
Finally, we assume spot C and area A in Figure 7 to be in electrical contact in the dark with an externally applied bias voltage to simulate the EL measurement.Figure 10c shows the band diagrams of spot C (orange) and area A (blue) for the EL case of the same 2D symmetry element.The band diagrams were extracted at no illumination for an injected current density that approximately corresponds to the j sc for the illuminated case of Figure 10b, that is, at 20 mA cm À2 .One can see that the external voltage of both regions is equal due to lateral contact via the ITO.However, the internal voltage of area A is about 75 mV lower due to the low electron conductivity originating from the energetic barrier ΔE ETL C,area causing lower selectivity.In consequence, also the EL signal corresponding to the internal voltage is lower.On the other hand, at spot C, the electrons are injected without notable voltage loss, leading to an EL signal that is about 20 times higher at spot C than for area A.
Conclusively, Figure 10 showcases that a single laterally inhomogeneous energetic property, namely the energetic barrier, can consistently explain the observed PL and EL measurements.

Summary and Conclusion
We investigated local features in perovskite silicon tandem solar cells by subcell-selective EL, PL and ILIT imaging techniques.Additionally, multidimensional device modeling software is used to attribute electrical cell properties to observed optical effects.In the case of a simple ohmic shunt, we show that it is easy to attribute the defect to an individual subcell with the help of subcellselective ILIT measurements.To showcase the strength of combining characterization methods and simulation, we focus on a particular point-shaped feature in the perovskite top cell featuring an increased EL signal and at the same time decreased PL signal without an observable difference in the ILIT signal compared to the surrounding area.
Quokka3 simulations show that the "J 0 R c Hypothesis", assuming a combination of locally decreased contact resistance and increased nonradiative recombination rate, can explain the observed pattern in the EL and PL images.Further, the Quokka3 simulations suggest that the apparent spatial variation of these parameters does not contradict power conversion efficiencies of more than 20%.The simulation shows that it is beneficial for the performance of the cell under investigation to lower the contact resistance of the surrounding area at the expense of an increased nonradiative recombination rate.
We elaborated on a second "Φ b Hypothesis" with the help of 2D Sentaurus simulations, for which a laterally inhomogeneous energetic barrier lowering at the perovskite/C 60 interface is assumed.The simulations show that also a laterally inhomogeneous, locally lowered energetic barrier can explain the decrease in PL signal and increase in EL signal.The expected losses would occur in the area according to this explanation (with no increased thermal radiation signal in the spots) and can therefore explain that no locally increased heat dissipation was observed by ILIT measurements in the spots.Furthermore, the second hypothesis could explain all experimental observations by a lateral variation of a single physical property only.
Both, the "J 0 R c Hypothesis" and the "Φ b Hypothesis", can explain the observations from the comparison of EL and PL measurements.The "J 0 R c Hypothesis" would implicate an increased local thermal heat dissipation in spot C, whereas the "Φ b Hypothesis" would expect the major losses to occur homogeneously distributed across the much bigger area A. Since the ILIT measurements do not show any increased local heat dissipation in spot C, the "Φ b Hypothesis" seems to be more consistent with regard to the complete set of measurement results.However, it is possible that the thermal heat dissipation due to the change in the nonradiative recombination in spot C is lower than the detection limit of the measurement system.Notably, both hypotheses are not fundamentally contradicting each other, for example, it is plausible to expect that if Φ b changes locally, also J 0 changes, which can be reproduced in simulations by assuming different surface recombination properties.It is likely that in reality the effective contact resistivity, recombination, and selectivity are all changing between spot C and area A. In a future work, additional measurement techniques could be used to further analyze the observed features.For example, PL images could be analyzed at a bias voltage V = 0 V.This would allow to analyze the charge-extraction coefficient using the method of potentiostatic PL imaging, suggested by Wagner et al. [8] As a final remark, we note that spots of type C appearing dark in the PL image should not be mistaken to be a defect in contrast to a shunt.Spots of type C inhibit superior electrical properties regarding achievable device efficiencies.This demonstrates that the images from a single-measurement method can easily be misinterpreted.It highlights the strength of the combination of various characterization methods together with simulation to perform holistic investigations of recent device limitations, as demonstrated in this article.

Figure 1 .
Figure 1.Architecture of the analyzed perovskite silicon tandem solar cell with an active area of 2 Â 2 cm 2 .

Figure 2 .
Figure 2. Closeup of three different features that are analyzed in this work.The features are shown in this work to be 1) shunts (S), 2) local contact nonhomogeneities (C), and 3) combinations of local contact nonhomogeneities and shunts (CS).

Figure 3 .
Figure 3. EL image of perovskite top cell of perovskite silicon tandem solar cell.The sample was forward biased to inject a current of 60 mA.Optical filters are applied to selectively detect the EL signal of the top cell only.F, C, CS, S1, and S2 mark spots that are referred to in the text.

Figure 4 .
Figure 4. PL image of perovskite top cell of perovskite silicon tandem solar cell.The image was acquired with an integration time of 0.5 s under a photon flux density of 1.34 Â 10 17 cm À2 s À1 with a 450 nm laser.F, C, CS, S1, and S2 mark spots that are referred to in the text.

Figure 5 .
Figure 5. ILIT image of perovskite subcell using blue light for charge carrier excitation.The image displays the amplitude of the measurement signal.F, C, CS, S1, and S2 mark spots that are referred to in the text.Bright interruptions of the busbar on the right-hand side are due to a locally peeled off silver busbar.

Figure 6 .
Figure 6.ILIT image of silicon subcell using infrared light for charge carrier excitation.The image displays the amplitude of the measurement signal.F, C, CS, S1, and S2 mark spots that are referred to in the text.

Figure 7 .
Figure 7. Sketch of the 2D/3D simulation domain for simulating the analyzed device with Sentaurus TCAD and Quokka 3.For Quokka 3 the 3D domain represents a 6 mm Â 6 mm area A of the tandem solar cell with a 0.5 mm Â 0.5 mm local spot C with different top cell properties.For the poor contact area A, we set J 01 ¼ 4 Â 10 À21 A cm À2 and R s ¼ 10 Ω cm 2 .For the small spot C with good contact properties, we set J 01 ¼ 4 Â 10 À20 A cm À2 and R s ¼ 0.05 Ω cm 2 .For the Sentaurus TCAD simulation on a 2D cross section only the conduction band offset at the ETL/perovskite interface is varied.It is set to ΔE ETL C,spot = 0 eV for the small spot C while it is set to ΔE ETL C,spot = 0.5 eV for the surrounding area.Spot C is 0.2 mm wide and area A is 3.8 mm wide in the Sentaurus TCAD domain.

Figure 8 .
Figure 8. Simulated EL image of perovskite subcell normalized to peak intensity (similar as measured EL image in Figure3).

Figure 9 .
Figure 9. Simulated PL image of perovskite subcell scaled to approximately match background signal of measured PL image in Figure4).

Figure 10 .
Figure 10.Simulated band diagrams for a simulation domain shown in Figure7with a spot C (shown in orange, corresponds to spot C in EL and PL measurements in Figure3 and 4) with high selectivity and its surrounding area A (shown in blue) featuring lower selectivity due to the higher Pero/C 60 conduction band offset ΔE ETL C,area .a) Simulated band diagram for spot C and area A when they are illuminated and in no lateral electric contact (quasi 1D) with iV oc indicating a homogeneous PL signal intensity.The lower selectivity in area A leads to a voltage drop ΔV Pero oc,area and therefore V oc,area < V oc,spot b) Simulated band diagram for an illuminated domain with laterally contacted spot C and area A. The lateral contact leads to a lower PL signal at spot C due to iV oc,spot < iV oc,area .c) Simulated band diagram for an electrically biased domain in the dark.For this case we find iV oc,spot > iV oc,area , due to the lower selectivity in area A indicating a higher EL signal in spot C compared to area A.