Subcell Operation and Long‐Term Stability Analysis of Perovskite‐Based Tandem Solar Cells Using a Bichromatic Light Emitting Diode Light Source

In monolithic tandem solar cells, current−voltage (J−V) characteristics of subcells provide invaluable information about their quality and tandem operation. However, accessing the subcell J−Vs is challenging and requires sophisticated spectral methods. Herein, a customized, bichromatic light emitting diode setup (BCLED) for in‐depth analysis of tandem solar cells, suitable for subcell operation analysis, and long‐term stability testing is presented. For this, two spectrally independent LED arrays are used to selectively bias the two subcells. The power of the developed setup is demonstrated by successfully disentangling the tandem J−V curve into subcell J−V curves. The method is based on a one‐diode model for each subcell and is validated by electrical simulations. Afterward, it is used on a fabricated 27.6% efficient perovskite/silicon tandem device, resulting in great agreement with the measured J−V curve. Therefore, the BCLED setup is a versatile tool, suitable for subcell characteristics and long‐term stability analysis of tandem solar cells.

alter the bias conditions in the subcell and significantly change the stability results.
In field operation and performance monitoring, the current mismatch effect has even greater significance due to the constantly changing solar irradiance and spectrum. Depending on the irradiance and even temperature conditions in the daily cycle, the device may exhibit different current mismatches and even switch from top cell to bottom cell limiting operation or vice versa. Increasing FF slightly compensates for the current loss due to the current mismatch, so this may not critically affect the device. [16] However, the mismatch itself could have a longterm effect on stability. Indeed, it has been shown that PVK single-junction devices are much more stable under MPP tracking than when light soaked in open-circuit conditions, [18] where no net current flows and thus charge extraction is hindered. The accumulated electric charges accelerate the degradation, even more under elevated temperatures. If a prolonged current mismatch occurs, where the PVK cell is not the limiting cell and thus the charges in the PVK layer are not all extracted, the long-term stability of the PVK-based tandems could be affected. It is critical that different mismatch conditions (top cell limiting, bottom cell limiting, current matched) are investigated to determine whether pre-existing mismatch needs to be considered in the fabrication of tandem devices for field operation instead of perfect current matching to ensure the least degrading operation. Standard solar simulators are not suitable for such long-term monitoring setups due to poor control of illumination and the durability of the light source over thousands of hours. Instead, a type of solar simulator that offers durability and spectral flexibility should be used.
In this article, we present a bichromatic light emitting diode (BCLED) light source for long-term stability measurements of tandem solar cells, specifically tailored for PVK-based tandem devices. The BCLED setup consists of two spatially interleaved LED arrays for homogeneous illumination with two wavelengths, blue (λ ¼ 470 nm) for a top cell and infrared (IR, λ ¼ 940 nm) light for bottom cell. Both subcells are thus excited independently, allowing independent control of the photocurrents in each of the subcells, which facilitates calibration of the illumination intensity and testing of different bias conditions, i.e., top cell limitation or bottom cell limitation on the same device. In addition to stability testing, BCLED can also be used for subcell selective analyses, e.g., EQE and photoluminescence biasing. Significantly, we demonstrate the procedure for extracting individual subcell JÀV curves using BCLED. Due to the series connection of the two subcells in the monolithic architecture, this is otherwise only indirectly accessible via complex methods of bias-dependent quantum efficiency, [19] photoluminescence and electroluminescence measurements, [2,20,21] and light-dependency measurements. [22,23] Compared with these works, our approach is simple and fast, does not require spectrally resolving equipment, and can provide information on true subcell JÀV curves including serial losses instead of a pseudocurve. Therefore, we use BCLED to obtain the subcell performance parameters, including open-circuit voltage (V OC ) and FF. Knowing these parameters and subcell J-V curves is important information when understanding and improving the tandem performance, or evaluating tandem solar cell degradation, as BCLED can also reveal processing damage in case of underperformance. In addition, we show results of long-term stability analysis of a monolithic PVK/silicon tandem solar cell, which shows excellent stability after 1000 h of illumination and tracking operation in air, even with improvement of PCE. The developed BCLED is therefore a powerful tool to study the stability of the tandem device and the performance of the individual subcells.

Results and Discussion
The BCLED setup is specifically designed for long-term measurements of PVK/silicon tandem devices, with the idea of simplifying the calibration of the light source to the tandem solar cells based on their respective EQE. Therefore, two types of spectrally independent LED arrays were chosen to separately illuminate the subcells: blue LED with a peak wavelength of 470 nm to excite the top cell and IR LED with a peak wavelength of 940 nm to excite the bottom silicon cell. This gives control over setting different photocurrent conditions for the tandem cell and eliminates unwanted current mismatch conditions due to incorrect spectral mismatch of the light source. The bichromatic light source is UV free; however, recently, it has been shown that the blue light has a very similar effect. [24,25] Therefore we expect similar processes to occur in the device under AM1.5 and our bichromatic irradiance.
The BCLED is also suitable for the analysis of PVK/CIGS, PVK/PVK tandem solar cells, or any other tandem technology with complementary bandgaps and similar absorption regions. In principle, other multijunction solar cell technologies with more subcells can also be analyzed in this way, if the LED arrays are adopted. The schematic of the BCLED is shown in cross section in Figure 1, whereas the photo of the setup is shown in Figure S1, Supporting Information. The spectra of both LEDs are shown in Figure S2, Supporting Information, along with an example of top and bottom EQE response of the PVK/silicon Figure 1. Schematic of the BCLED measurement setup. As the homogeneous illumination source, two sets of LED arrays are used. Blue LEDs with a wavelength of 470 nm (blue) are used to excite the PVK subcell. IR LEDs with a peak wavelength of 940 nm excite the silicon subcell. The sample is placed on a sample holder plate where electrical connections and photodiodes are included for controlling the intensity of the LEDs. In addition, a cooling stage allows to control the cell temperature. For MPP tracking, an in-house developed hardware was used, allowing to track several devices. www.advancedsciencenews.com www.solar-rrl.com tandem solar cell, showing that there is no overlap between the two types of LEDs and confirming the independent excitation of each subcell. To ensure uniform illumination over 7.5 Â 7.5 cm 2 , a dense LED matrix of 144 blue and 49 IR LEDs was used. The intensity of the LEDs is tracked with spectrally selective photodiodes, separately for blue and IR LEDs. BCLED currently allows simultaneous testing of four thermally connected devices. The system is equipped with a Peltier cooling system for temperature control and an in-house developed μMPP system for MPP tracking of the devices under test. [10,26] 2.1. Subcell Operation Analysis

Performance Parameter Extraction Procedure
One of the main applications with BCLED is the ability to disentangle the JÀV curve of the tandem into JÀVs of subcells and their performance parameters. The parameter extraction procedure is based on a one-diode model for each subcell. For the JÀV reconstruction of a single-junction solar cell, the following parameters must first be extracted: series resistance R S , shunt resistance R sh , saturation current density J 0 , and ideality factor n. R S and R sh can be obtained from a single JÀV curve by calculating the slope of the curve at voltages above than open-circuit voltage V OC and at short-circuit conditions, respectively. J 0 and n can be extracted by carrying out a series of I-V measurements at different light intensities and plotting the logarithm of the photocurrent density versus V OC using the following equation, where J 0 and n can be extracted from the line as the intersection with the y-axis and the slope, respectively.
In a monolithic tandem device parameter, extraction is more challenging because the two subcells are connected in series, which means that we need to extract R S , R sh , J 0 , and n for each subcell, i.e., the top and bottom cell separately. However, these parameters can be reached by biasing each subcell independently with the tunable blue and IR LEDs of the BCLED, which is not possible with conventional solar simulators with one or two lamps. Assuming that one of the devices is strongly biased, we can obtain the necessary parameters of the other, limiting subcell by tuning its light bias in different steps. The changes in performance are then associated with only one subcell, as the other is superimposed as a constant value. Once all parameters are acquired, they can be used in simulations to obtain the JÀV curve. The procedure is shown schematically in Figure 2. The tandem model schematics, where each subcell is presented with a one-diode model, is shown in Figure 3.

Simulations
The validation of the procedure is first investigated using the simulation software SPICE. The corresponding input parameters for each subcell used for the electrical simulation can be found in Figure 3b, for values of R S , R sh , J 0, and n. As in typical PVK/ silicon tandem solar cells the PVK subcell is more prone to lower (worse) shunt resistance compared with the wafer-based silicon subcell, we chose three different values (500, 1000, and 5000 Ω cm 2 ) for PVK R sh and conducted the simulations for all three. With the chosen values shown in Figure 3, the silicon single-junction PCE under standard test conditions (STCs) is %23% and that of PVK around 19% (for R sh ¼ 5000 Ω cm 2 ), which corresponds to the state-of-the-art PCEs of the tandem subcells. The simulated JÀV curves for PVK with R sh ¼ 1000 Ω cm 2 are shown in Figure 4. In Figure 4a, the PVK subcell is the limiting device and the blue LED intensity (current source J L ) is changed in 4 mA cm À2 steps. In Figure 4b, the silicon subcell is the limiting device and therefore the IR LED intensity is changed. In both cases, J SC of the nonlimiting subcell is fixed at 25 mA cm À2 .
A quick glance at graphs in Figure 4a,b already shows that the lower PVK R sh of the PVK subcell has an impact on the tandem device only in the case where the PVK limits the photocurrent of the tandem device ( Figure 4a). Moreover, the tandem R sh is guided by the R sh of the limiting cell, whereas the R S of the tandem is a sum of the R S_pero and R S_Si . The extracted value of the tandem R S of 5.5 Ω cm 2 is higher than the value set in the initial parameters (1 Ω cm 2 þ 3 Ω cm 2 < 5.5 Ω cm 2 ), but a more accurate value can be extracted at (much) higher voltages. Nevertheless, the obtained R S cannot be separated into the individual R S of the subcells due to  www.advancedsciencenews.com www.solar-rrl.com their series connection. Thus, from the JÀVs we can easily obtain the R sh of the subcells, whereas for the R S we can assume that the series resistance of silicon is lower than that of PVKs. Now that we have extracted all four parameters for both subcells, we can reconstruct the tandem JÀV and also access the JÀVs of both subcells.
The results are shown in Figure 4e, where we focused on PVK as the limiting subcell due to its lower R sh , which was set to 1000 Ω cm 2 . Black lines show simulations of the tandem device (left) and PVK (middle) and silicon (right) single-junction (subcell) devices with the initial parameters from Figure 3. Red lines show The initial parameters are stated in Figure 3b. The extracted parameters used to simulate single-junction cells were also extracted from the tandem device and are shown in Figure 4. PVK shunt resistance R sh,top ¼ 1000 Ω cm 2 .
www.advancedsciencenews.com www.solar-rrl.com simulations with the extracted parameters, based on the procedure explained earlier and shown in Figure 4. The graphs are arranged so that the tandem JÀV curve (first column) is shown as the sum of the PVK (second column) and silicon JÀVs (third column), as the top and bottom cell are connected in series. We obtain an excellent agreement, validating our procedure. Even for lower PVK R sh (500 Ω cm 2 in Figure S5, Supporting Information), the agreement is very good. However, there is a slight discrepancy around the MPP point, which extends toward V OC and can also be seen in the deviation of the JÀVs of both subcells. Therefore, the method can be applied with good accuracy even for cells with poor R sh (<1000 Ω cm 2 ). For higher R sh the procedure gives excellent agreement.

Experimental Section
We tested the subcell parameter extraction procedure in an experiment on a high-efficiency monolithic PVK/silicon tandem solar cell with a device architecture as published recently. [2] In Figure 5, the PVK subcell analysis with measured I-Vs at different blue LED intensities and fixed IR LED intensity is shown. In Figure S6a, Supporting Information, the case for silicon subcell analysis is shown. The left panel of Figure 5c shows the measured IÀV of the fabricated tandem solar cell under equivalent 1 sun irradiance of BCLED, converting 27.6% of the incident light power into electrical power. To exclude any possible degradation, we conducted a downward and upward intensity test for both subcells: starting from 1.4 sun equivalent blue/IR light intensity and reducing the intensity to 0 and then increasing it back to almost 1.4 suns equivalent. The comparison in Figure S7, Supporting Information, shows no degradation during the test. Interestingly, the R sh of PVK was not constant throughout the test and ranged from 4.3 kΩ cm 2 for lowest intensities to 1000 Ω cm 2 for highest. Nevertheless, all the values were higher than 1000 Ω cm 2 , which we previously set as a limit for successful extraction and reconstruction. The tandem cell R S was only 3.7 Ω cm 2 assuring high-conversion efficiency under STC conditions. The extracted ideality factors were around 1.2 for both of the subcells (Figure 5b). The extracted value for PVK might seem low; however, we recently extracted a similar value for a PVK single-junction device with a very similar architecture. [10] For J 0 determination, we also need V OC values of the subcells. www.advancedsciencenews.com www.solar-rrl.com V OC of the silicon is easily obtainable, by only turning on the IR LEDs. Interestingly, for PVK, this does not work as by turning only the blue LEDs on, we also see a minor contribution of the silicon subcell, i.e., the measured V OC under such conditions of %1.4 V is higher than the expected %1.15 V. We postulated that the photoluminescence of PVK gives a small rise to the V OC in silicon, thus influencing our measurement. [27] According to Equation (1), assuming a 0.02% photoluminescence quantum yield of the top cell [2] and half of the emitted light absorbed by the silicon bottom cell, the so-induced V OC in the considered silicon cell would be 450 mV. There is also a possibility that a minor overlap between silicon EQE and the lowenergy tail of the blue LED exists, which, however, was not detected by our measurement setups. Nevertheless, this effect is strong only when the bias intensity of the cell in question is very low or zero. For other measurements, this effect plays no role. The PVK subcell V OC can then be obtained by subtracting the silicon subcell V OC from the tandem cell V OC .
With the extracted parameters, the JÀVs shown in Figure 5c were simulated. In the left graph, the comparison between the measurement and simulation with extracted parameters is shown, whereas middle and right graphs show the corresponding PVK and silicon subcell JÀV s . The agreement between the experimental and simulated JÀV was very good, except around MPP. Such a discrepancy in PVK/silicon tandem devices has been observed before. [16] Here, we attributed it to a nonconstant, voltage-dependent J 0 and n of both subcells in the fabricated device, which can originate i) from the voltage-dependent selectivity at the recombination contact [28] in the fabricated solar cell, as in the simulations, we assumed perfect ohmic connection between the two subcells and/or ii) due to voltage-dependent photocurrent that has also been observed, e.g., in CdTe solar cells. [29] The parameters for the above comparison were extracted around 1 sun V OC voltages for both subcells ("V OC " case), whereas the main discrepancy in the JÀV curve was around MPP. Therefore, we also extracted J 0 and n parameters from a voltage range that was closer to the MPP value at 1 sun condition, as shown in Figure 5b ("V MPP " case). With these parameters, the matching between experimentally obtained JÀV and simulated one was much better around MPP but worse around and above V OC . Note that the V MPP s estimated from the "V OC " case were 0.99 and 0.60 V for PVK and silicon subcell, respectively.
By applying our procedure, we could access the JÀV curves of both subcells. In the middle panel of Figure 5c, the PVK JÀV is shown, whereas the right one shows JÀV of the silicon subcell. Both cases are shown, using parameters extracted near V OC (colored lines) and V MPP (gray lines). From the curves, we calculated the subcell performance parameters, which are shown in Table 1. The extracted V OC s of the silicon and PVK subcells are 0.715 and 1.151 V, respectively, as obtained from the "V OC " case, matching with the experimentally measured tandem V OC ¼ 1.866 V. For FF values, it is more reasonable to consider the "V MPP " extraction case due to a better matching near MPP. Therefore, the FF was 75.8% for both of the subcells and almost the same as measured for the tandem cell (75.3%). Both FF and V OC values were high, proving that both subcells were excellent solar cells, as could have also been deduced from the high PCE of the fabricated tandem device. The earlier results confirm that with our procedure, subcell parameters and their JÀVs are reliably extracted; therefore, the BCLED setup is capable of analyzing instantaneous performance of tandem subcells.

Stability Measurements
Finally, we used BCLED to test the stability of the fabricated monolithic PVK/silicon tandem solar cell. In this case, a device with a PVK bandgap of 1.62 eV and an initial PCE of 23.1% (as measured under LED class AAA solar simulator) was tested. The stability measurement was carried out in air with an unencapsulated device at 25 C. The intensities of the blue and IR LEDs were set to reach the equivalent STC photogenerated conditions in both subcells as determined by the EQE measurement ( Figure S2, Supporting Information). Results are shown in Figure 6, showing a 1000 h MPP track of the monolithic PVK/silicon tandem solar cell, together with V MPP and J MPP . Initial PCE MPP under BCLED was 23.2% and fit well with the Table 1. Performance parameters of the measured tandem device and reconstructed PVK and silicon subcells using BCLED extraction procedure. For reconstruction, two sets of parameters were used. First set was obtained around V OC and is labeled as "V OC. " Second set was extracted around MPP and is labeled as "V MPP. " The expected V OC and FF of the subcell are stated in bold. For V OC , the "V OC " case was considered and for FF, the "V MPP " due to a better fit at the corresponding points in JÀV.  Figure 6. Continuous long-term stability testing using the BCLED setup for more than 1000 h of an unencapsulated monolithic PVK/silicon tandem solar under constant MPP conditions in air. The black curve shows the P MPP , the blue curve shows the J MPP (left y-axis) and the V MPP is shown as red curve (right y-axis).
www.advancedsciencenews.com www.solar-rrl.com PCE JV ¼ 23.1% from IÀV measurement under a standard LED sun simulator (see Figure S8, Supporting Information, for JÀV curves before and after stability measurement  [30,31] This might have occurred for this sample here as well. Comparing AM1.5G, IÀV measurements also reveal that the tandem PCE can be slightly higher in MPP than that extracted from JÀV scans, also in the certification laboratory. [2] 3. Conclusion We have presented a BCLED setup based on two spatially interleaved arrays of blue LEDs with a wavelength of 470 nm and IR LEDs with a wavelength of 940 nm to enable advanced long-term stability testing of tandem solar cells. The independently controlled light intensities make BCLED a powerful tool for a variety of analyses on monolithic tandem solar cells. We have described a procedure to extract the JÀV curves of individual subcells in a monolithic tandem device by varying the intensity of the LEDs with a selected wavelength. With this method, the parameters R sh , R S , J 0, and n of a one-diode model can be extracted for each subcell and used to analyze the tandem device. In this way, invaluable properties about the quality and operation of the subcells are obtained. The method was validated using simulations for three different shunt resistances of the PVK subcell. Excellent agreement was obtained between the simulations with the initial and extracted parameters for R sh > 1000 Ω cm 2 . This procedure was then applied on a high-efficiency fabricated PVK/silicon tandem solar cell. We get a very good agreement between measured and simulated JÀV with extracted parameters. The slight discrepancy around the point of maximum power is attributed to the voltage-dependent parameters J 0 and n. With the extracted one-diode parameters, we can also obtain JÀV of both subcells and their performance parameters, which provide reliable in-depth information on the operation of the tandem solar cell and the possible location of damage caused by processing.
In addition, the BCLED setup has been used for long-term stability measurements of tandem devices, as demonstrated by conducting a 1000 h stability test. The longer operating times of the LEDs and the ease of calibration are two of the main advantages of the system. Due to the ease of changing the subcell bias, the setup can be used to test different tandem conditions, such as stability under blue-rich or blue-deficient irradiance. We believe that the presented advantages of the bichromatic light source will promote new interesting results on PVK-based and also other tandem technologies.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.