Validation of a Predictive MLLR Model for IV Parameters in Perovskite Solar Cells
The advancement of perovskite solar cell (PSC) technology is a dynamic field, drawing significant attention due to its potential for high efficiency and low production costs. A key aspect of this research involves leveraging machine learning, particularly via the Multiple Linear Regression (MLLR) model, to predict current-voltage (IV) parameters based on electroluminescence (EL) spectroscopy data. This article explores the validation of a predictive MLLR model and its implications for understanding and optimizing solar cell performance.
Overview of the MLLR Model
The trained MLLR model is primarily validated using test datasets derived from EL spectroscopy results. Four different devices, labeled P1, P2, P3, and P4, are evaluated independently as well as collectively, providing various scenarios for model testing. The focus is on comparing predicted IV parameters—particularly open-circuit voltage (Voc), short-circuit current (Jsc), fill factor (FF), and photovoltaic efficiency (PV-Eff)—against actual measured values. The proposed FWHM-based predictive MLLR model serves as the foundation for these assessments.
Analyzing the Results from the FWHM-based Model
Figure 4 illustrates the predicted versus actual values of IV parameters for Days 1 through 8, providing a visual representation of model performance over time. Additionally, Table S15 showcases the prediction accuracy percentages for individual devices, underscoring variations in predictive capability dependent on device specifics. Each device’s unique properties might contribute to these differences, potentially affecting the model’s predictive reliability.
Detailed Accuracy Metrics
Secondarily, the model’s accuracy is quantified, further emphasizing its predictive prowess. Figure S5.1 displays the average accuracy of the FWHM-based predictive MLLR model when integrating all test datasets. Using a 25% tolerance level, notable distinctions arise: the model achieves an impressive accuracy of 100% for Voc, 96% for Jsc and FF, and 73% for PV-Eff. The variability in these outcomes is explicable, as Voc tends to be less influenced by external factors compared to Jsc and FF, which are subject to complex interactions according to environmental conditions and material properties.
Evaluation of Model Performance and Predictive Capabilities
The average prediction accuracy merely emphasizes the strengths of the MLLR model. Achieving an average accuracy of 91.5% for all devices illustrates the model’s competence in navigating the complexities inherent in predicting IV parameters derived from EL measurements. Table 1 further highlights that devices P1 and P4 significantly surpass P2 and P3 in prediction accuracy, likely due to higher non-linearities affecting the latter.
The performance metrics indicate clear distinctions in the effectiveness of the proposed model. Figure S5.2 elaborates upon the model’s mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE) for their respective parameters. The MAPE value, particularly, shows that the model accurately predicts within 4%, 11%, 12%, and 18% for Voc, Jsc, FF, and PV-Eff, respectively, which reaffirms its reliability for practical applications.
Insights into Model Variability and Future Improvements
Despite the promising results, the variability observed in prediction accuracy emphasizes the need for further refinement of the model. A thorough analysis of how tolerance levels impact prediction accuracy, as outlined in Table S19, presents opportunities for improvement. Addressing these variances can accelerate the development of new PSC materials and enhance device efficiency.
The last columns of Table 1 reveal an interesting perspective on predicted PV-Eff versus calculated values, showing minimal deviation. This consistency reinforces the predictive capabilities of both the MLLR model and more traditional equations used in efficiency calculations, making a compelling case for the validity of the proposed model.
Comparison with CCT-based MLLR Model
The FWHM-based model provides a distinctive method for estimating IV parameters but is not the only approach available. A complementary CCT-based MLLR model also assesses the same parameters, revealing further nuances. Through these comparative analyses, it’s observed that while both models show noteworthy accuracy, FWHM-based estimates for Jsc and FF slightly outperform those generated by the CCT-based method.
Figure S9 delineates the comprehensive evaluation for both models across individual devices, illustrating the nuanced performance characteristics and emphasizing that Voc estimation is particularly robust within the CCT framework.
Analysis of Discontinuous Datasets
To further substantiate the MLLR model’s applicability, researchers conducted analyses using discontinuous datasets from additional fresh devices, which illuminates the model’s flexibility in accommodating varying experimental conditions. The results, depicted in Tables S16, S17, and subsequent figures, indicate that the FWHM-based model outperforms the CCT-based model when navigating gaps in data collection.
Aspects such as defect density and its impact on PV-Eff reveal an inverse correlation between FWHM values and efficiency over time, reiterating the practicality of these models in understanding device behavior longitudinally.
Exploring Voc and Loss Analysis with Thermodynamic Approaches
In probing the complexities of Voc and its associated losses, thermodynamic perspectives frame the conversation of PSC efficiency. Researchers point to a theoretical Voc limit that remains unfulfilled in practical applications. Studies affirm that encapsulating these dynamics through both EL analysis and predictive modeling can deepen understanding and optimization of PSCs.
By evaluating the contributions of non-radiative losses, and applying rigorous models to predict efficiency enhancements stemming from optimized EL performance, this line of inquiry broadens the landscape for future innovations. As analysis persists, alternative modeling approaches, like FWHM and CCT, stand out for their effectiveness in predicting Voc against conventional thermodynamic frameworks.
Through this detailed examination and the continuous refinement of predictive models, the potential for developing highly efficient solar cells grows exponentially. The intersection of machine learning and traditional physics not only reveals the capabilities of existing models but sets the groundwork for explorative avenues aiming at surpassing current efficiency benchmarks in photovoltaic technology. The journey continues, with each dataset and analysis illuminating deeper insights into the magic of perovskite solar cells.