Luminescence-Based Implied Voltage Imaging of Tandem Solar Cells Using Bandpass Filters
Abstract
A luminescence-based technique is demonstrated for selectively imaging the implied voltages of tandem solar cells. The luminescence emission is captured using a narrow bandpass filter so that the detected luminescence signal is insensitive to the optical properties of the device, thus, revealing the variations in the implied voltages. The proposed method is validated through simulation and experiments conducted on two-terminal perovskite/silicon tandem solar cells with different structures, optical properties, and compositions (e.g., different bandgaps for the perovskite cells). Implied voltage images of each sub-cell can be determined with a maximum relative error of 1%. The proposed technique can also be used to obtain local current–voltage curves. The method is expected to be a valuable tool for optimizing the performance of tandem solar cells, scaling up tandem devices, investigating local defects, and predicting the ultimate device performance.
1 Introduction
Single-junction crystalline silicon (Si) solar cells have dominated the photovoltaic (PV) market for an extensive period.[1, 2] Currently, Si cells achieve an impressive power conversion efficiency of 27.3%,[3] approaching their theoretical limit of 29.4%.[4] To surpass this boundary, tandem configurations have emerged as a promising avenue, with significant attention focused on perovskite (PVK) as the top cell.[5, 6] While this technology has made significant progress, with reported cell efficiencies as high as 34.6% on lab-scale devices (≈1 cm2),[3] further optimization is essential for their successful commercialization.[7-9] A particular challenge arises in transferring these high efficiencies to large-area, long-term stable modules.[7]
To achieve further performance enhancements, it is essential to diagnose the origin of losses. Reliable characterization techniques play a pivotal role in this regard. Spatially resolved techniques can be particularly effective in identifying local defects and material variations that currently cause substantially lower efficiencies in large-area devices. Photoluminescence (PL)[10] and electroluminescence (EL)[11] imaging have been widely used as valuable tools in PV laboratories and production lines, providing insights into the optoelectronic performance of PV devices.[12-16] These techniques have garnered significant importance in the quality assessment of precursors, solar cells, and modules owing to their rapid, non-destructive, and spatially resolved nature.[17-20] This renders them well-suited for applications such as in-line inspection in high-volume manufacturing lines.[17-20]
The open-circuit voltage (VOC) is a critical parameter for the quality evaluation of solar cells. Typically, it is determined as a single global value that does not contain any localized information about the presence of defects and their subsequent impact on the device's performance. In the case of two-terminal tandem solar cells, the assessment is limited to the overall VOC of the device, offering no insights into the individual performance of the top and bottom cells. Furthermore, direct VOC measurements via the terminals must be conducted on metalized devices, not compatible with early-stage quality assessment utilizing cell precursors. Therefore, for the effective optimization of large-area tandem solar cells and a more comprehensive understanding of the limitations of these devices, it is necessary to conduct a spatially resolved and quantitative assessment of sub-cell performance.
Spatial variations of VOC can be resolved from PL and EL data via additional calibration processes.[15, 21-26] The voltage inferred from luminescence is directly related to the quasi-Fermi level splitting (QFLS).[27, 28] As it is not directly obtained by measuring the terminal voltage of the device, it is referred to as “implied (open-circuit) voltage” (iV or iVOC). Commonly, iV can be extracted from absolute PL/EL spectra by transforming the data into a logarithmic scale and performing a linear regression fit on the high-energy tail.[21] However, this method is sensitive to the wavelength range selected for fitting.[22] iV can also be determined by the full-spectrum fitting of the absolute PL intensity spectral data using the generalized Planck radiation law.[23] Nevertheless, this approach requires accurate information regarding the sample temperature and the spectral absorptivity. Soufiani et al. introduced a new approach for extracting iV of PVK films by capturing high-energy tail PL emission using a narrow bandpass filter (BPF).[24] The absorptivity of the PVK devices with respect to this detected range is close to unity and nearly constant, thereby eliminating the need for detailed knowledge of the optical characteristics of the sample as required by the generalized Planck expression. Recently, a different BPF-based method was suggested to convert PL images of tandem solar cells into iV images.[29] In their study, a BPF with a wide transmission range was used for the PVK sub-cells. Such a wide BPF requires accurate assessments of the spectral response of the imaging system as well as the absorptivity or external quantum efficiency (EQE) of the devices. However, accurate determination of the absorptivity of sub-cells within tandem devices imposes significant challenges, while EQE measurements require a complete tandem solar cell and cannot be used in early fabrication steps. Beyond that, the extraction of the properties of individual sub-cells from EQE measurements of tandem devices is subject to a wide range of other complications.[30]
In this study, we introduce a luminescence-based technique designed to selectively resolve iV images of the two sub-cells in tandem devices using narrow BPF. This approach can be applied to both PL and EL images, enabling fast and reliable quantification of iV at various stages of device fabrication. The primary advantage of the proposed method is its insensitivity to the optical properties of the measured cells; hence, it does not require accurate data about the absorptivity or EQE of the cells. This approach can also be employed to obtain spatially resolved current-voltage measurements of each sub-cell.
2 Background
Often, spectral data for the optical response of the system and EQE are not readily available and tend to vary among different imaging systems and measured samples. Accurately acquiring such data for each system and sample has proven to be a complex task, given that the necessary measurements are both time-consuming and intricate.
3 Methodology
In this section, we introduce our proposed technique. It eliminates the necessity for spectral information about the optical response of the imaging system and EQE when extracting iV images. Simulations were first conducted based on four representative PVK/Si tandem solar cells from published studies (Cell I,[33] Cell II,[34] Cell III,[35] and Cell IV[36]). These cells feature different structures and optical properties, aiming to represent the majority of current tandem devices. Their different EQE data, sourced from the literature,[33-36] are provided in Figure 1a. Note that the EQE of solar cells is impacted by both their optical properties, such as absorptivity and reflectance and their electrical properties, such as carrier collection efficiency. By assuming the same iV for each type of sub-cells [1.15 V (top cell) and 0.7 V (bottom cells); around the VOC values], the corresponding absolute luminescence spectra were calculated from Equation (1)–see Figure 1b. A representative quantum efficiency (QE) characteristic of a Si camera (Figure 1c), was then used to calculate the detected luminescence signals () as shown in Figure 1d [linear scale] and Figure S1 (Supporting Information) [logarithmic scale]. This is referred to as the practical scenario in our simulations.
In Figure 1b, d, the simulated luminescence spectra of the four cells are diverse at long wavelengths, as expected due to their very different optical properties. Nevertheless, the luminescence spectra of these very different PVK/Si cells converge when considering the wavelength range below 730 nm for the PVK cells and below 1050 nm for the Si cells. Consequently, the detected luminescence signal in the short wavelength range is comparatively insensitive to variations in the optical properties of the device. Instead, it predominantly reflects the variations in iV. In the subsequent section, these findings form the foundational premise for the proposed technique. Experimentally, a BPF is used to narrow down the wavelength range of the detected luminescence signal to the shorter wavelength range. This eliminates the need for information regarding the OR system and EQE in Equations (3) and (4).
To evaluate the accuracy of the proposed method under extreme conditions, the extracted EQEs(λ) of the four cells (Cells I-IV) were utilized to generate a “worst-case scenario”. In this scenario, the EQEs(λ) of the PVK sub-cells were reduced by 40%, while EQEs(λ) of the Si sub-cell were set to 20% lower than those depicted in Figure 1a– refer to Figure S2(a) (Supporting Information). The 40% reduction for the PVK was determined based on EQE measurements of tandem cells after severe degradation.[37] While most Si sub-cells maintained stable performance (<10%), a 20% reduction was considered as the upper limit.[37] Hence, in this context, the worst-case scenario is defined as a situation in which a tandem solar cell operates at an exceptionally low level while remaining functional. Thus, we are considering a scenario that is plausible within the realm of practical performance, as opposed to depicting unrealistic worst-case situations. Subsequently, the detected luminescence emission in this worst-case scenario (Figure S2(b), Supporting Information) was calculated by assuming an iV of 0.8 V (0.5 V) for the PVK (Si) sub-cells, appropriate values for underperforming tandem solar cells. Again, the luminescence spectra of different cells converge for λ2 below 730 nm for the PVK cells and below 1050 nm for the Si cells.
In the following sections, two one-time calibration approaches are discussed.
3.1 Calibration Approach A
First, rather than measuring the optical response of each component in the system to determine ORsystem(λ), a constant calibration factor, kcal, is employed to convert the relative luminescence signal into an absolute value. Second, EQE(λ) is replaced with a wavelength-independent calibration constant C.
To determine kcal, a light source with a known spectrum is utilized. More details are given in the Method Section. In the case of tandem solar cells, kcal must be determined individually for the spectral range of each sub-cell, owing to the use of different BPFs for the top and bottom cells. The determination of kcal is required only once for each sub-cell unless there is a change in the detection system.
Simulations were performed to quantify the errors resulting from the suggested simplification (constant kcal and C) and to illustrate the effectiveness of the narrow BPFs in determining accurate iV regardless of the optical properties of the measured cells. The simulation procedure is outlined in Figure S3 (Supporting Information). First, was calculated based on the EQE(λ) and the assumed iV for each type of sub-cells. Both the worst-case (Figure S2, Supporting Information) and the practical (Figure 1) scenarios were considered. Subsequently, was integrated across various wavelength ranges, with cut-on wavelengths (λ1) fixed at 650 nm (PVK cells) and 950 nm (Si cells), while systematically varying the cut-off wavelengths (λ2) from 660 to 800 nm for the PVK cells and from 960 to 1100 nm for the Si cells. For each distinct λ2, kcal was determined using a known spectral output [ϕlight(λ)] from the calibration light source to quantify the error introduced from the simplification of constant kcal. Then, the iV of each sub-cell was extracted, assuming a wavelength-independent C ranging from 0.38 to 0.98 [a range that reflects the EQE(λ) range of the cells].
The error in the extracted iV was calculated as the absolute difference between the calculated and input (“true”) iV. Considering the four cells (Cells I-IV), both the mean errors and the maximum errors were determined.
We first present the worst-case scenario. Across the four cells (Cells I-IV), the average and maximum iV errors for all the combinations of λ2 and C were determined and are presented in Figure 2. Note that the absolute iV error maps for the four individual cells are provided in the Supporting Information (Figure S4, Supporting Information). At shorter λ2 values, the iV error is smaller for any fixed C value, highlighting the effectiveness of our proposed method in reducing iV variations caused by the optical properties of the cell. As λ2 increases, the iV error primarily rises, reflecting the luminescence signal's increased sensitivity to the optical properties at longer wavelengths. The assumption of wavelength-independent C becomes invalid. Moreover, constant kcal becomes unacceptable at longer λ2 as the spectrum of the calibration lamp starts to have an impact. Compared to the PVK sub-cells, the lower iV errors for the Si sub-cells are attributed to the QE of the Si camera, limiting the detected luminescence signal toward the shorter wavelengths, and consequently resulting in lower iV errors for the Si sub-cells. The lowest iV error is expected when C aligns with the actual EQE range within that specific wavelength range. However, accurately quantifying the EQE of each tandem sub-cell is not always an easy task. Nevertheless, by limiting the detection range of the luminescence signal to a shorter wavelength range (for instance λ2 = 730 and 1025 nm for the PVK and Si cells, respectively), the resulting iV error can be maintained below 32 mV (4%) for the PVK and 19 mV (3.8%) for Si, even in this worst-case scenario, irrespective of the selected C.
Figure 3 displays the average and maximum iV errors for the practical scenario (with the absolute iV error maps of the four individual cells presented in Figure S5, Supporting Information). By confining the detection range of the luminescence signal to 730 nm (for PVK) and 1025 nm (for Si), the iV errors remain below 19 mV (1.65%, for PVK) and 17 mV (2.4%, for Si), regardless of C. The relatively modest improvement observed in the case of Si, compared to the worst-case scenario, is likely attributable to the QE of the camera, which already attenuates long wavelengths. Furthermore, in the practical scenario, selecting C within the range of 0.55–0.65 for PVK limits the maximum iV error to < 9 mV (0.8%). For Si, restricting C to the range of 0.65–0.75 keeps the maximum iV error to < 6 mV (0.9%). Hence, these C ranges are recommended for common tandem devices.
When utilizing PL imaging, the developed method is fully contactless and versatile, allowing its application to both precursors and complete devices without the need for prior knowledge of their EQE, enabling the fquantification of iV with high accuracy.
3.2 Calibration Approach B
In this approach, owing to the distinct wavelength detection ranges of the top and bottom cells, two single-junction calibration cells are needed—specifically, one single-junction calibration cell for each sub-cell. Single-junction calibration cells are recommended due to the ease of accessing their terminal voltage. A high-performance PVK calibration cell is recommended to avoid issues such as band misalignment, which can lead to discrepancies between iV and terminal voltage. Importantly, with the suggested narrow BPFs, the calibration cells don't have to have identical optical properties to the cells being measured. This presents a notable advantage of the proposed method, as alternative approaches (with wide detection ranges) necessitate calibration cells with optical parameters identical to those of the measured tandem cells. The calibration cells need only be measured once unless there is a modification in the detection system.
To demonstrate the effectiveness of the narrow BPF-based technique, a similar simulation procedure as outlined in the preceding section was followed (Figure S6, Supporting Information). The impact of specific calibration cell parameters on the extraction of iV of the tandem sub-cells was evaluated using six single-junction calibration cells—comprising three PVK calibration cells and three Si calibration cells—with various optical properties and different PVK band gaps. Their EQE(λ) are provided in Figure S7 (Supporting Information), while their was set to 1 V for the PVK and 0.6 V for the Si calibration cells (approximately the low injection level terminal voltage of good single-junction cells). Again, two scenarios were considered for the tandem cells: the worst-case scenario (Figure S2, Supporting Information) and the practical scenario (Figure 1), each involving four tandem cells. The integration of was then performed for the calibration cells and tandem sub-cells within the wavelength range of λ1 = 650 nm and 660 nm ≤ λ2 ≤ 800 nm (PVK), and λ1 = 950 nm and 960 nm ≤ λ2 ≤ 1200 nm (Si) using their reported EQE(λ) and QEcamera(λ). Subsequently, iV for each sub-cell was extracted by calculating the ratio of between the sub-cell and the relevant calibration cell using Equation (7). The iV error was then quantified as the difference between the calculated and true input iV.
In the worst-case scenario, Figure 4 illustrates the distributions of the iV error across the 12 cases (four sub-cells × three calibration cells) as a function of λ2. A positive error (true input iV–calculated iV) here indicates that the EQE of the tandem sub-cell is lower than the EQE of the calibration cell within the detection range. However, experimentally, this may not be the case due to various uncertainties inherent in the experiments. For PVK cells, a shorter λ2 noticeably reduces the iV error, indicating the insensitivity of the luminescence spectra to the cell's optical properties. By restricting the detection range of the luminescence signal to a shorter wavelength (<730 nm), the absolute iV error can be maintained below 19 mV (2.3%) for these sub-cells. For Si sub-cells, the iV errors are smaller compared to the PVK sub-cells, exhibiting less variation across the 12 cases in relation to λ2. This can be attributed to a combination of factors, including the lower QE of the Si camera at longer wavelengths, which limits the detected luminescence signal from the Si sub-cells more toward the short wavelength range, as well as a less difference between the EQEs of some calibration cells and certain tandem sub-cells. Nevertheless, the absolute iV error of Si sub-cells remains below 12 mV (2.4%) for any λ2 < 1100 nm.
Additionally, simulations for the practical scenario were conducted. As depicted in Figure 5, the iV error is significantly reduced compared to Figure 4, especially at shorter λ2. The maximum absolute iV error for the practical scenario is 7 mV (0.6%) for the PVK sub-cells and 5 mV (0.7%) for the Si sub-cells when λ2 is limited to 730 nm (PVK) and 1025 nm (Si). The obtained errors for the Si sub-cells align well with the iVOC errors estimated for Si single-junction solar cells,[38, 39] where the impact of different light trapping properties on the luminescence signal was investigated.
Compared to Approach A (using a calibration lamp), Approach B (using calibration cells) can allow for a relatively broader detection range (slightly larger λ2) potentially with lower iV error. Using a BPF with longer λ2 leads to a stronger luminescence signal, shorter measurement times, and an improved signal-to-noise ratio. Approach B also eliminates the need for a calibration lamp, which is required for Approach A. Nevertheless, in situations where calibration cells are unavailable, Approach A can be employed with a sufficient level of accuracy, even when only an estimated C is utilized. Using either of the calibration approaches, it has been demonstrated that narrow BPFs, with the center wavelength of the transmission band located within a sufficiently short wavelength region of the luminescence tail, allow accurate iV image quantification for tandem sub-cells with various optical properties and compositions (i.e., different bandgaps), even without any knowledge regarding the optical properties of the measured devices and optical response of the imaging system.
4 Results and discussion
4.1 Experiment Validation
The proposed method is demonstrated using two two-terminal PVK/Si tandem cells: The first cell (Tandem 1), with an active area of 1.04 cm2, was based on p-i-n structure utilizing 1.68 eV PVK processed on pyramidally textured Si heterojunction bottom cells. The second cell (Tandem 2), with an active area of 1.21 cm2, used a caesium-contained triple-cation and mixed halide (with a bandgap of ≈1.68 eV) as the top cell and a Si heterojunction as the bottom cell. The two samples were sourced from different suppliers. The measured EQEs of both cells are given in Figures S9 and S10 (Supporting Information), respectively. A detailed description of their fabrication process is provided in Sections S2.1 and S2.2 (Supporting Information).
EL images of each sub-cell under different current injections were acquired using narrow BPFs. For Approach A, a blackbody radiation source was employed to extract the calibration constant, kcal, while for Approach B, two sets of calibration cells were utilized. To demonstrate the insensitivity of the proposed method to the optical parameters of the calibration cells, two calibration sets with significantly different optical properties were employed: Set 1 includes a single junction PVK with a bandgap of ≈1.67 eV and an active area of 0.07 cm2 (PVK I)[40] and a textured interdigitated back contact (IBC) Si cell,[41] while for Set 2, a single junction PVK cell with a bandgap of ≈1.55 eV and an active area of 0.14 cm2 (PVK II)[42] and a planar passivated emitter and rear contact (PERC) Si cell[43] were used. Further details of the PVK cells (PVK I and PVK II) can be found in Sections S2.3 and S2.4 (Supporting Information).
iV images of the PVK and Si sub-cells were extracted from EL images under a current injection of 1.5 mA cm−2. Under these conditions, the impact of voltage drop due to series resistance (Rs) is negligible, thus, the iV obtained from the images should closely resemble the terminal voltage. Consequently, the proposed methods can be validated by comparing the sum of the calculated iV of the sub-cells and the measured terminal voltage.
In the following sections, we present the results obtained from Tandem 1, whereas the results from Tandem 2 are elaborated upon in Section S3.1 (Supporting Information). Both Tandem 1 and Tandem 2 are aged devices to study their iV variations. Figure 6 displays the extracted iV images of both the top [(a) and (c)] and bottom [(b) and (d)] cells using Approach A [(a) and (b)] and Approach B [(c) and (d)]. Note that for Approach A, the C values were chosen based on the above simulation results (0.65 and 0.75 for the PVK and Si sub-cells, respectively) while for Approach B, Set 1 (PVK I and a textured IBC cell) was utilized for the calibration. As anticipated, the iV of the PVK cell is noticeably higher than that of the Si cell. However, the Si cell exhibits a more uniform iV image compared to the PVK cell.
Table 1 summarises the global harmonic mean iV calculated from the iV image of each of the sub-cells and the entire tandem cell. The calculated iV within each sub-cell, estimated by the two approaches differ by ≈5 mV (<0.7%). When compared to the terminal voltage, Approach B demonstrates a smaller iV discrepancy (0.06%) than Approach A (0.5%). Nevertheless, both methods estimate the voltage within 1% relative to the terminal voltage (a small discrepancy below 7.1 mV), highlighting the accuracy of the proposed methods in determining the iV of tandem cells.
| Current density injection of 1.5 mA cm−2 | Average iV [mV]:Approach A | Average iV [mV]:Approach B | Measured terminal voltage [mV] |
|---|---|---|---|
|
PVK top cell Si bottom cell Entire device |
1108.8 ± 4.6 | 1104.3 ± 4.6 | – |
| 527.3 ± 2.4 | 523.7 ± 2.4 | – | |
| 1636.1 ± 5.4 | 1628.1 ± 5.4 | 1629 ± 2 |
As discussed previously, Approach A does not require accurate information regarding the EQE of each of the sub-cells and only utilizes a constant C. To investigate (again) the impact of constant C, the iV errors were calculated for Tandem 1, assuming a constant C ranging between 0.38 and 0.98 (for each sub-cell), as depicted in Figure 7. The lower limits of C, as suggested by the above simulation (Figure 3), are indicated by dash-dotted lines. Consistent with the simulation results, the recommended C range leads to a maximum error of 15 mV. The error decreases to 7 mV (indicated by the star) if C of 0.65 (0.75) for PVK (Si) sub-cell is used and further to 5 mV (square) when the mean EQEs for each sub-cell within the detected wavelength range are utilized. Given that the proposed method aims to estimate the iV of any tandem cells within an acceptable range of error, the recommended C values can be generally applied. Additional knowledge regarding the EQE of the measured cell can further reduce the associated error.
To validate the insensitivity of Approach B to the selection of the calibration cells, the two calibration sets, with different optical properties, were utilized. Table 2 summarises the global harmonic mean iV obtained by each of these sets. Consistent with the simulation, the determined iV of the sub-cells by each of the calibration sets is nearly identical (within 3 mV). Both sets estimate the iV of the entire tandem device within 0.2% (<3.5 mV) of the measured terminal voltage. This is a clear demonstration of the usefulness of using narrow BPFs for minimizing the impact of the optical properties of the measured devices and calibration cells.
| Current density injection of 1.5 mA cm−2 | Average iV [mV]:Set 1 (PVK I and textured IBC cells) | Average iV [mV]:Set 2 (PVK II and planar PERC cells) | Measured terminal voltage [mV] |
|---|---|---|---|
|
PVK top cell Si bottom cell Entire device |
1104.3 ± 4.6 | 1105.8 ± 4.6 | – |
| 523.7 ± 2.4 | 526.5 ± 2.4 | – | |
| 1628.1 ± 5.4 | 1632.3 ± 5.4 | 1629 ± 2 |
Additional validation measurements using Tandem 2 as well as single junction PVK and Si cells are provided in the Supporting Information (Sections S3.1,S3.2, Supporting Information). Again, a great agreement between the extracted iV and the measured terminal voltage was achieved for those cells (with a maximum relative deviation of 0.9%).
4.2 Spatial Resolved Pseudo-Dark Current Density-Implied Voltage Measurements
Given that the injected current density in EL measurements is equivalent to the total recombination current density, plotting the injected current density as a function of the derived iV results in a pseudo-dark current density-implied voltage (J-iV) curve for each of the sub-cells. For a proof-of-concept demonstration, the iV image of each sub-cell was determined at different injected current densities, ranging from 1.5 to 28 mA cm−2. By computing the mean iV across these iV images, the global pseudo-dark J-iV curves of the top and bottom sub-cells were generated. Figure 8a presents the calculated pseudo-dark J-iV and the measured dark J-V of Tandem 1. The pseudo-dark J-iV acquired by both approaches are nearly identical, with a variation of less than 5 mV. Importantly, the difference between the estimated pseudo-dark J-iV and the measured dark J-V of the tandem cell is within 1% at a low current injection level (where the effects of the Rs are negligible). At high current injections, a discrepancy is observed, probably due to the effect of Rs.[44] This also opens up opportunities for quantifying the injection-dependent Rs. Here, Rs of 3.1 ± 0.2 Ω cm2 were extracted at a current density injecting of 24 mA cm−2.
The developed method can be employed to derive local pseudo-dark J-iV curves of individual sub-cells within tandem solar cells. The inset of Figure 8b illustrates the iV images of the PVK and Si sub-cells at a current density injection of 24 mA cm−2 obtained using Approach B. Three regions of interest (ROI) were selected in the inset of Figure 8b, where the mean variation in iV of PVK is ≈65 mV. The local pseudo-dark J-iV of these ROIs in the PVK and Si sub-cells are compared in Figure 8b. As expected, the three local pseudo-dark J-iV curves of the Si cell are mostly identical. However, there is a significant difference in the local pseudo-dark J-iV measurements across the PVK cell. Notably, ROI-3 exhibits a noticeably lower performance compared to the other ROIs, which could be attributed to high recombination losses and/or high Rs in this particular region. This type of information can be crucial for assessing the origin of various losses in each sub-cell, thereby aiding in the development of large-area high-efficiency PVK/Si tandem cells. It is important to note that the results presented here assume a uniform current distribution across the device. However, this assumption may be invalid at high current injection, as the Rs could induce variations in the iV and current at different regions of the cell. Alternatively, the proposed method could leverage PL measurements to extract the iV images, thus removing the impact of Rs. By comparing PL- and EL-based iV images, Rs and recombination features can be distinguished. It is worth mentioning that for samples with high diffusion lengths, any spatially confined defect of high recombination activity tends to deplete neighboring regions of excess charge carriers, resulting in excess charge carrier gradients and smearing of the PL image.[19] This affects the accuracy of the extracted local pseudo-dark J-iV, especially at low injection levels. However, as PVKs have a relatively low diffusion length,[45] the impact of lateral carrier flow on the extracted local pseudo-dark J-iV is expected to be minor.
The capability to spatially resolve pseudo-dark J-iV offers the ability to estimate the losses associated with different defects. By eliminating the defective regions in the iV images, the pseudo-dark J-iV curve of defect-free tandem sub-cells can be extracted. The inset of Figure 8a presents the pseudo-dark J-iV curve of the defect-free tandem cell. This curve was obtained by replacing defective and low-performing regions in the PVK sub-cell (defined here as regions with iV values below 70% of the iV-value range at each current injection) with the median iV of the remaining portions of the image. A ≈15 mV improvement is noticeable at a current density of 24 mA cm−2, representing the expected performance of a uniformly good tandem cell. This can assist in identifying performance-limiting local defects and evaluating their impacts on the overall device performance.
5 Conclusions
A luminescence-based technique to directly image the iV of tandem sub-cells with reduced sensitivity to the optical properties of each cell was demonstrated. By employing narrow BPF, the detected luminescence signal becomes almost insensitive to the optical properties of the sub-cells, thus, directly correlating with iV variations. Through two proposed calibration approaches, we have validated our technique using simulations and experiments conducted on tandem solar cells with very different optical properties and compositions. The relative errors associated with our method are within ±1%. Furthermore, we have adapted this technique to spatially resolve the pseudo-dark J-iV characteristics of each sub-cell.
The proposed technique offers several advantages: it is fast, non-destructive, and applicable at various fabrication stages, ranging from precursors to complete devices. It is well-suited for in-line monitoring of process homogeneity and troubleshooting the production line, as well as facilitating direct performance comparisons between different sub-cells and tandem devices. Additionally, the capability to extract local pseudo-dark J-iV information enables the investigation of local defects and their impact on overall performance. We expect that the proposed technique will be beneficial for device optimization and predicting ultimate device performance.
6 Experimental Section
EL images of each sub-cell under different current injections using a scientific complementary metal oxide semiconductor (sCMOS) camera (FLI, KL400 BI) equipped with two BPFs that were selected based on the above simulation results. A BPF centered at 720 nm with an 18 nm bandwidth was used for the top cell,[46] while a BPF with a transmission range between 975 and 1025 nm was used for the bottom cell, refer to Figure S8 (Supporting Information). A source measure unit (SMU, Keithley 2461) was used to inject different currents while simultaneously recording their corresponding terminal voltages. For both the single junction and tandem cells, the terminal voltage stabilized within 50 s. Once the terminal voltage stabilized, three EL images were captured while the corresponding terminal voltages were recorded. The reported EL image and terminal voltage are the averaged values. All EL images were taken at a temperature of 23 ± 0.5 °C.
For Approach A, kcal was determined by using a blackbody radiation source (Omega, model BB705) with a stable and well-known spectrum. The blackbody radiation source is coupled with optical fiber (1500 µm/0.5 NA) into an integrating sphere, where the absolute spectral photon flux at the integrating sphere's output port can be determined. The integrating sphere was positioned at the same height as the measured cells. Once the blackbody radiation source is stabilized at a temperature of 1027 °C, the emitted signal is captured by the imaging setup with the BPF. kcal can be derived by comparing the acquired luminescence image from the integrating sphere's output with the known spectral photon flux of the blackbody. The emitted luminescence from the blackbody was directly measured using a spectrometer before as well as after connecting the fiber and integrating sphere to assess losses within the optical fiber and integrating sphere.
For Approach B, the two calibration sets were utilized. For Set 1, a uniform textured IBC cell (thickness of 147±4 µm) and a triple cation PVK solar cell with a bandgap of ≈1.67 eV were utilized as calibration cells.[41] The EL images of the calibration cells were captured at a low current injection level and were adjusted to obtain a terminal voltage of 0.590 V for the IBC and 1.019 V for the PVK cells. For Set 2, a uniform planar cell with a thickness of 468±4 µm and a triple cation PVK solar cell with a bandgap of ≈1.55 eV were used as calibration cells.[42, 43] The EL images of Set 2 were captured at a low current injection level and were adjusted to obtain a terminal voltage of 0.590 V for the PERC and 0.980 V for the PVK cells. The terminal voltages were chosen to minimize voltage drops due to Rs, ensuring that iV closely approximates the terminal voltage. The median EL count across the calibration cells and the associated terminal voltage were used to determine the iV of the measured tandem sub-cells.
Note that some single-junction PVK solar cells may have band energy misalignment,[46-48] resulting in a discrepancy between the iV and the terminal voltage. In this case, an LED whose spectrum is similar to the luminescence spectrum of PVK cells can also be used for calibration Approach B.
Acknowledgements
S.Z. and S.N. contributed equally to this work. This work was supported by the Australian Government through the Australian Renewable Energy Agency (ARENA) under Grant TRAC 2022/001 and the Australian Centre for Advanced Photovoltaics. A.H.-B. acknowledged the support of the Australian Research Council via the Future Fellowship FT210100210. G.W. acknowledged the support of the University of Sydney International Stipend Scholarship (USydIS). The views expressed herein were not necessarily the views of the Australian Government, and the Australian Government does not accept responsibility for any information or advice contained herein.
Open access publishing facilitated by University of New South Wales, as part of the Wiley - University of New South Wales agreement via the Council of Australian University Librarians.
Conflict of Interest
The authors declare no conflict of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
