Contactless Inline IV Measurement of Solar Cells Using an Empirical Model

The current–voltage measurement is the most important measurement in solar cell quality control. As the contacting process of cells results in mechanical stress and consumes a significant amount of measurement time, this work presents an IV characterization based on contactless measurements only. An empirical model is introduced that can derive the full IV curve and IV parameters as the open‐circuit voltage, short‐circuit current density, fill factor, and efficiency. As a basis, a series of photoluminescence and contactless electroluminescence images and spectral reflectance measurements are used. An advantage of the model's convolutional neural network design lies in the semantic compression of local image structures across the input data. Within an ablation study, it is shown that the empirical model is well suited to combine these data sources, which is the optimal input configuration for contactless IV derivation. The accuracy, e.g., with an error in efficiency of 0.035 % abs and correlation of over 99%, is similar to comparing two contacting IV measurement devices. The contactless IV curves also have a close fit to their contacted counterparts. Within simulations on module level, it is demonstrated that contactless binning performs as well as contacting binning and does not result in any additional mismatch loss.

DOI: 10.1002/solr.202200599 The current-voltage measurement is the most important measurement in solar cell quality control. As the contacting process of cells results in mechanical stress and consumes a significant amount of measurement time, this work presents an IV characterization based on contactless measurements only. An empirical model is introduced that can derive the full IV curve and IV parameters as the opencircuit voltage, short-circuit current density, fill factor, and efficiency. As a basis, a series of photoluminescence and contactless electroluminescence images and spectral reflectance measurements are used. An advantage of the model's convolutional neural network design lies in the semantic compression of local image structures across the input data. Within an ablation study, it is shown that the empirical model is well suited to combine these data sources, which is the optimal input configuration for contactless IV derivation. The accuracy, e.g., with an error in efficiency of 0.035% abs and correlation of over 99%, is similar to comparing two contacting IV measurement devices. The contactless IV curves also have a close fit to their contacted counterparts. Within simulations on module level, it is demonstrated that contactless binning performs as well as contacting binning and does not result in any additional mismatch loss.
For this, we utilize a series of PL images with varying illumination intensities and integration times in order to determine the cell characteristics on multiple points of the pseudo-IV curve. Additionally, we apply contactless EL imaging using partial shading to approximate series resistances' influence. As an indication regarding short-circuit current density, we also include the spectral reflectance into the model which can be measured contactlessly inline.
As empirical model, we develop a convolutional neural network (CNN) to derive the solar cell IV characteristics and investigate its prediction quality on a big dataset of industrial heterojunction (HJT) solar cells of different quality classes. The convolutional architecture enables the model to also include local defect structure patterns into the analysis instead of mean values only because we do not expect defect areas to necessarily scale linearly with their impact on the solar cell. Moreover, the CNN model enables the assessment of superimposing defect structures across multiple measurements. We build the model in such a way that it is able to fuse information coming from different data sources (EL, PL, and RðλÞ). Here, we vary the number and combination of measurements in order to derive an optimal measurement configuration for inline applicability. We evaluate the model with regard to multiple parameters: 1) typical IV parameters as V oc , J sc , η, fill factor (FF), 2) full IV curve, and 3) contactless binning accuracy.
CNNs have shown promising results in processing spatially resolved measurement data in recent publications. Rodrigues Abreu et al. have shown an approach in which they predict ten points on the module's IV curve based on EL images using ten CNNs. [14] In comparison, we develop a single model that processes various input data from contactless measurements of solar cells to derive an IV curve with a sampling rate at 100 curve positions. In other works, it was demonstrated that IV parameters can be learned from EL, PL, or thermography images of solar cells and wafers. [15][16][17][18][19][20][21][22][23][24] Beyond that, imaging measurement methods were mostly used for defect detection.  We expect our model for contactless IV determination to compensate the drawbacks of the contacted method mentioned above. As there is no time for contacting needed, there is the potential of saving a large part of the measurement time which may allow lower cycle times and higher throughput and thus decrease equipment costs. As no mechanical stress is applied to the cells, breakage rates are reduced. Moreover, we demonstrate correlations of up to 99%, precise IV curve derivation, and a contactless binning accuracy of over 92% leading to no additional mismatch losses in the final module. Also, costs coming from contact units' wear and switching times will not be present. However, other measurement parts would be added, such as shutters to partially shade the sample, which are not necessary for the contacted measurement.
In summary, our contributions are 1) an empirical contactless model for the determination of IV parameters and the IV curve, 2) the extension of the model so that additional spectral reflectance measurements can be integrated, 3) an extensive evaluation based on an ablation study of the input data, and 4) an investigation of the impact of contactless binning at the module level.

Contactless Measurements
As basis for contactless inline IV measurement, we use contactless EL measurements as well as up to six suns-PL measurements. In Figure 1, the contactless EL images can be seen in (a-b). They involve partial shading of the cell leading to a current flow of generated charge carriers so that series resistance effects, such as finger interruptions, become visible in the luminescence pictures, e.g., finger interruptions appear as lighter regions within the image. In Figure 1c-h, the suns-PL measurements are shown. They include different measurement settings which are chosen so that they cover reasonable sampling points on the cells pseudo, meaning R s -shifted, IV curve, starting at V oc in (c), Besides spatially resolved measurements, we also include measurements of the spectral reflection (RðλÞ) into our model, which were determined along the center trace of each sample only. The data include three reflection curves positioned next to each other on the cells' surface in the wavelength range from 360 to 1100 nm and a resolution of 2 nm in wavelength.

Empirical Model for Contactless IV Derivation
As empirical model, we develop a number of CNNs getting the measurement data mentioned as input and predicting the IV characteristics as output. CNNs consist of a series of convolutional, pooling, and nonlinear unit layers.
Step by step, they reduce the spatial dimension of the input while increasing the semantic expressiveness with regard to the target parameters. We utilize variations of the DenseNet architecture. [46] However, we expect similar modern CNN architectures to be adaptable for this task as well.
The empirical models developed are regression models predicting the scalar IV parameters but also target the problem of data fusion of EL and PL images, as well as RðλÞ measurement curves. In addition, we adapted the architecture to derive the full IV curve instead of only scalar parameters. The architectural approach chosen can be seen in Figure 2. The first row shows the processing of image-like data. They are concatenated and passed to the CNN PL producing 128 feature maps of size 7 Â 7. When only using image data, those are passed to a final network part CNN IV used to derive the respective IV parameters as output.
When it comes to fusing the RðλÞ curves into the model, it can be extended as shown in the second row in Figure 2. The data viewed as a table holding the three RðλÞ measurements M i with their reflectance values r i,j as columns at all wavelengths considered λ j , where i refers to the measurement index and j to the respective wavelength. n is the number of measurement entries per RðλÞ measurement. The matrix is passed to a small model we call CNN SR . The convolutional kernels cover all columns, i.e., they have a size of 3 Â 3, in order to value the homogeneity of all measurement lines. However, the pooling layers are applied column-wise, i.e., they have a size of 1 Â 5. The resulting RðλÞ features f have the same three-column shape with m rows. The mean of each row is calculated and upscaled to m RðλÞ feature maps of size 7 Â 7, so that the RðλÞ information is available at each pixel's position. As the image and the RðλÞ data are of same spatial size now, they can be concatenated and passed to CNN IV as additional information.
The models are either targeted to predict single scalar values or a vector representing the main IV parameters or the IV curve, respectively. As scalar output, we consider the open-circuit voltage V oc , the short-current density J sc , the FF, and the power at MPP P mpp or efficiency η. Regarding IV curve derivation, we used 100 points on the IV curve at fixed voltage positions as target vector. The points are densely sampled around V % 0 V, V % V MPP , and V % V oc to be more accurate in those most relevant regions.
In addition, a custom loss function was used for the IV curve range from 0 V to about V mpp . It has been noticed in preliminary tests that there is a slight fluctuation in the predictions in this range. By adding an approximation of the first and second derivatives into the loss function, false fluctuations of neighboring points are suppressed. The loss function is described by Equation (1).
Here, L 1 stands for the L1 loss function,î is the current vector predicted by the network, i is the current vector measured contacted, and i 1À40 andî 1À40 are the first 40 entries of i and i, respectively. The dots are referring to the difference of neighboring points as approximation of the derivations.

Contactless Binning and Influence on Module Level
We also perform a contactless binning of the cells and investigate the influence on module level regarding mismatch losses, i.e., the power loss due to nonidentical cells built into the module. For this, we define binning classes and sort the cells Figure 2. Schematic architecture of the empirical model for contactless IV determination. To fuse different type of data, the first line shows the processing of image-like data, while the second one shows the processing of curve data as spectral reflectance measurements.
www.advancedsciencenews.com www.solar-rrl.com according to their power at MPP P mpp . We do this with regard to both contacted and contactless measurements to compare. Besides the evaluation of the binning accuracy, we simulate the modules to compute their mismatch losses for each bin class which we would expect from binning in a common 60 cells module with cells contacted in series with bypass diodes. We calculate the mismatch loss P ml as defined in Equation (2).
Here, P sim holds the simulated module power and P sum is the sum of all powers of the respective 60 cells at MPP (see Equation (3)) with P mpp,i being the power of the ith cell at MPP.

Experiments
As dataset, we use 4500 industrially manufactured HJT solar cells of size 158 Â 158 mm 2 . The cells come from four different quality classes. In addition, we include about 150 cells sorted out during production to increase the heterogeneity of the dataset. All cells were measured with PL, partially shaded PL, and contacted IV. For some of them, additional spectral reflectance measurements have been carried out. The measurement settings for the PL and partially shaded PL measurements are shown in Table 1. For all PL images, homogeneous illumination was used. PL1 is at V oc and PL4 roughly at MPP as described in the approach. PL2 is on the pseudo-IV curve between V oc and MPP. PL3-6 are located at or around the MPP. For the contactless EL measurement, two partially shaded measurements were conducted using the measurement settings shown in the last row of Table 1. Both PL and contactless EL were performed with a measurement system from ISRA Vision and finally scaled to a size of 224 Â 224 px 2 . For 800 of the cells, additional spectral reflectance measurements were done with a Zeiss OFR104. As a reference, contacted IV measurements were carried out with a measuring system from halm GmbH.
As model, we use a variation of the DenseNet [46] implemented in PyTorch. [47] For optimization, we use the Adam optimizer [48] and vary within a grid search the learning rate and decay. The models were optimized on a Nvidia GeForce RTX 2080 Ti with a batch size of 30 samples. Furthermore, the full dataset was randomly subdivided into three datasets: the training dataset with 70% of the samples and the validation and test dataset with 15% of the data each. The models were trained on the training dataset. The best model was selected with the validation dataset and all results calculated on the test dataset to make sure the models generalize well.

Experiment 1: Contactless IV Parameter
We trained empirical models to derive the main IV parameters from contactlessly measured data. We focus on V oc , J sc , FF, and P mpp . By a variation of the inputs, we want to find a good input configuration. All variations tested are shown, e.g., in Table 2.
The second and third column show whether and which EL and PL measurements were used in each of the 12 different configurations. Variation 1 uses only the partially shaded EL images. Gradually, more measurement images are added starting with the PL4 (at MPP) and PL1 (at V oc ) until in variation 9 all measurement images are used. In variations 10-12, no partially shaded PL images are included. In addition, each of these variations is performed once with and once without RðλÞ, as indicated in the second row. The models are evaluated based on the mean absolute error (MAE) and the Pearson correlation coefficient ρ.

Experiment 2: Contactless IV Curve
Within this experiment, we investigate the quality of the empirical contactless models with respect to the prediction of the complete IV curve. We consider three input variations: 1) only partially shaded PL images, 2) partially shaded PL images and all six homogeneous PL images, and 3) all mentioned images plus RðλÞ measurement as input data. We compare the empirical models with respect to their MAE and correlation coefficient at each point of the IV curve with the contacted IV curve as reference.
Additionally, for the best model based on MAE, we perform a qualitative analysis of exemplary IV curves and the corresponding cells. For this purpose we use a medium quality cell, as well as cells with particularly low V oc and J sc , respectively, and investigate the cell having the highest error to assess the quality and stability of the model in such edge cases.

Experiment 3: Contactless Binning
In Experiment 3, we investigate the contactless binning in comparison to the contacted binning and examine what influence these two variants would have on the module level. For this purpose, the cells are sorted into four binning classes based on the contacted and contactless power measurements from experiment 1. The classes start at 5300 mW and proceed in 50 mW steps up to 5500 mW. In terms of efficiency, this corresponds approximately to 0.2% large bin classes from 21.5% to 22.3%.
The quality of the contactless binning is evaluated on the one hand using the consistency with the contacted binning as

Experiment 1-Results: Contactless IV Parameters
The contactless method works well for all investigated IV parameters on the test dataset.   have the best results, although these are only slightly better than models with less inputs. Also for η, models with many measurement data achieved the best results, again with very small differences compared to models with fewer inputs. The results of the best models per parameter are shown in more detail in Figure 3. The x-axis shows the contacted measurand and the y-axis the contactless measurand. In case of complete correspondence, all values would lie on the diagonal. It can be seen that especially the contactless P mpp in (a) and the contactless V oc in (c) can be derived accurately. The contactless J sc in (d) shows a slightly higher spread but good correlation as well. The contactless FF in (d) can be derived with similar precision as P mpp and V oc .
Both the inclusion of the partially shaded PL images and the RðλÞ measurements improve the accuracy of the contactless models. With respect to the partially shaded images, this becomes clear, for example, when comparing variant 9 to variant 12 for P mpp and FF. There, the error increases by about 17% and almost 24%, respectively. Also the RðλÞ measurement improves the contactless models in most cases. Comparing the MAEs with respect to the V oc of all variations without and with RðλÞ, the errors become on average about 34% lower. However, this behavior is not apparent with the same clarity for the J sc prediction. Here, especially PL5 and PL6, the PL measurements closest to the J sc , seem to be helpful in combination with the RðλÞ.

Experiment 2-Results: Contactless IV Curve
The contactless IV curves can be derived with low error, and each additional contactless measurement improves the prediction. Figure 4 shows, on the one hand, the MAE (continuous curves, left y-axis) and, on the other hand, the correlation coefficient (dashed curves, right y-axis) for the considered input variations 1) EL only in green; 2) EL and PL in orange; and 3) EL, PL, and RðλÞ in blue. It can be seen that the model receiving only the partially shaded EL images performs the worst. Slightly improved results are obtained with the addition of the PL measurements. The prediction accuracy is significantly improved when the reflectance RðλÞ is also added as input. This is particularly apparent in the area V < V mpp , where the absolute error is reduced by about 34% and the correlation factor increases by 10% abs . In the range of V > V mpp the absolute error increases, which is due to the fast change of the IV curve; however, still the model receiving all measurements performs best. In all models, the correlation coefficients increase over 98% in that region, indicating the correct shape of the curve.
The contactless IV curve of the best model receiving all measurements visually follows well the IV curve measured contacted. Figure 5 shows the contactless and contacted IV curves as continuous and dashed curves, respectively, for four example cells. Their EL images are shown in Figure 5e-h for visualization purposes only; they have not been used for training. The cell in (e) is a moderate cell with no obvious defects (related to the blue IV curves), while the cell in (f ) (related to the red IV curves) is suspected to have slight material inclusions as the black dots indicate and correspondingly a lower V oc . In (g) (related to the green IV curves), on the cell's surface scratches can be seen, which result in a reduced J sc . The EL image in (h) shows the cell with the highest error between contacted and contactless IV curves. In Figure 5b-d, the areas of the IV curve around J sc , MPP, and V oc , respectively, can be viewed in detail. As can be observed, in the area of J sc in (b), the quality of the cell with low J sc is slightly overestimated by about 25 mA, while the curves for the other two cells are in good agreement. Regarding MPP in (c), the curves line up well in all cases. Also for V oc , the curves fit quite well. For the average cell, it matches perfectly. The other two run parallel with an offset of less than 1 mV. In (a-d), the IV curves of the cell with the highest error are shown in red. It can be seen that in the range of J sc it overestimates the current

Experiment 3-Results: Contactless Binning
By binning solar cells based on the contactless IV models, high correspondence with the contacted binning can be achieved. In Table 4, the contactless binning accuracy is shown for all input variations with the contacted binning as reference in column 4 and 7. It can be seen that high accuracy can be achieved of up to over 92%. Furthermore, it can be observed that the additional input of RðλÞ measurement improves the binning quality significantly, on average by almost 6% abs . Contactless binning is equally well suited for sorting solar cells as contacted binning on module level because the best models achieve the same mismatch loss as the contacted one. In Table 4, the resulting mean mismatch losses of the contactless binning P ml for the variations are shown in columns 5 and 8 for a module with 60 cells. Columns 6 and 9 show the mean mismatch loss difference ΔP ml ¼ P ml À P ml;ref between contactless and contacted binning. The mismatch loss of the contacted binning of the dataset without RðλÞ is P ml;ref ,1 ¼ 3.24 mW and of the dataset with RðλÞ P ml;ref ;2 ¼ 3.10 mW. Without RðλÞ, the power loss is low, ranging from 60 mW to a few 100 mW. With RðλÞ, no mismatch loss is apparent in many cases. In some input variations, e.g., in 4, 5 and 7, the mismatch loss of the contactless binning is even lower than that of the contacted one.

Discussion
We have developed models for contactless IV derivation based purely on inline capable measurement technology that can show high correspondence with the current state-of-the-art contacted measurement. In particular, η, V oc , and FF have as low errors as one would expect when comparing two contacting measurement devices. Even the J sc can be measured with a mean error of just 0.056 mA cm À2 . Surprisingly, it could also be well approximated based on PL images only, which we attribute to a high correlation between V oc and J sc in our dataset. For this, we used  There are other parameters which have not yet been integrated into the model. For instance, the shunt resistance R sh , which is of interest for characterization, has not been built into the model so far. Within our approach, the IV region relevant for R sh was not as important because there were no R sh problems in the dataset, so the PL measurement sequence was not optimized for the region around I sc . Regarding empirical models, this point needs to be addressed in the future; however, it has already been shown that this parameter may be derived from contactless measurements. [6] The IV curve can be derived with decent accuracy from contactless measurements. It becomes clear, however, that there is a large improvement in the results when all and not only a part of the input data is used. While the addition of PL images to the contactless EL images gives only a slight improvement to the contactless model, with additional RðλÞ measurements as input there is a significant improvement. This behavior is especially evident for the range V < V mpp and at I sc , which is understandable because the reflection affects the luminescence current and correspondingly the short-circuit current. The current is approximately constant up to MPP and can accordingly be better approximated in this range. However, there exists still potential in exactly this range. In the example cell with low J sc , the IV curve was slightly overestimated in this region. For the evaluated moderate and low V oc cell, the contactless and contacted IV curves match almost precisely.
The binning of the solar cells based on the contactless efficiency η works well. A binning accuracy of significantly more than 90% could be achieved with the contacted measurement as reference. Due to measurement uncertainty, however, inaccuracy is to be expected here as well. Within the module simulations, we are pleased to see that no additional mismatch loss due to contactless binning is to be expected compared to contacted binning, if the RðλÞ measurement is taken as input.
The contactless IV measurement reduces the measurement time and leads to cost saving. If we assume that the Move-In and Move-Out of the cell takes about 500 ms and add to the measurement times from Table 1 with some buffer, the measurement time for one cell could be about 600-700 ms. This is less than the standard of about 1-1.25 s. [1] In addition, the cell is not exposed to mechanical damage and there are fewer measurement components that can wear out, which could also save material and maintenance costs.
Nevertheless, contactless IV measurement still has some limitations. One main drawback is that so far no reverse characteristic of the solar cell can be derived without contacting it. Therefore, a suitable contactless measurement technique has to be identified. Also, it is thinkable to perform a classification into reverse-defect and no-reverse-defect, e.g., based on the PL images, as, e.g., indicated by Demant et al. for microcracks in silicon wafers. [49] In addition, it is likely that the models will need to be retrained if they should be used with a different cell line or cell type. This point could be particularly relevant, e.g., for research lines because here a lot of very different solar cells are to be expected, to which the models would have to be adjusted.

Conclusion
We introduced an empirical approach to contactless IV measurement as an alternative to the contacted measured IV characteristics. For this, we used a number of inline applicable contactless measurements such as partially shaded as well as homogeneously illuminated PL and spectral reflectance measurements. These were combined within a convolutional neural network to calculate IV parameters such as V oc , J sc , FF, and η on the one hand and the full IV curve on the other. We evaluated our approach on a comprehensive set of heterojunction solar cells and performed an ablation study to find the best input measurement configuration.
The contactless models have shown good results in deriving the IV parameters and the full IV curve and we found in module simulation that a contactless binning performs well. Mean deviations of 0.035% abs for η, 0.375 mV for V oc , 0.056 mA cm À2 for J sc , and 0.076% abs for FF between contactless and contacted measurements were obtained. We found the full contactless IV curves to fit the contacted ones almost precisely. Furthermore, module simulations have shown that contactless binning can replace contacted binning.
We expect that contactless IV measurement can be cheaper than contacting one due to shorter measurement times. This may bring it into interest for future high throughput manufacturing. However, a solution still needs to be found for contactless reverse characteristic measurement and a method for efficient transfer to new cell lines and concepts.