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<h2>Introduction</h2>
<p>Halide perovskites have attracted tremendous attention for photovoltaic applications due to their remarkable optoelectronic properties, including high absorption coefficients, long carrier diffusion lengths, and tunable band gaps [14,17]. The archetypal perovskite ABX<sub>3</sub> structure, where A is an organic or inorganic cation, B is a metal cation (e.g., Pb<sup>2+</sup>, Sn<sup>2+</sup>), and X is a halide anion (I<sup>−</sup>, Br<sup>−</sup>, Cl<sup>−</sup>), offers immense compositional flexibility. However, the most efficient perovskites contain lead, raising toxicity concerns, and many compositions suffer from poor stability under ambient conditions [6,9]. Consequently, there is a pressing need to discover stable, lead-free alternatives with suitable band gaps for single-junction or tandem solar cells.</p><p>Traditional materials discovery relies on trial-and-error synthesis and characterization, which is time-consuming and costly. The compositional space of halide perovskites is vast, with millions of possible combinations, making exhaustive experimental screening impractical. High-throughput computational methods, such as density functional theory (DFT), can accelerate the screening process, but they remain computationally expensive for large-scale exploration [8,22]. Machine learning (ML) has emerged as a transformative tool to bridge this gap, enabling rapid prediction of material properties from structural and compositional descriptors [25,26,28]. By training on existing data, ML models can generalize to unseen compositions and identify promising candidates for experimental validation.</p><p>Recent studies have demonstrated the power of ML in perovskite research. For instance, Priya and Aluru [1] used ML to design perovskites with high conductivity for energy applications. Li and Ding [2] combined DFT and ML to discover proton-conducting perovskites. Chen et al. [3,4] applied ML to predict self-trapped excitons in double halide perovskites. Wang et al. [5] employed substitution engineering assisted by ML for photocatalytic applications. Lu et al. [6] accelerated the discovery of stable lead-free hybrid organic-inorganic perovskites via ML. These efforts underscore the potential of ML to navigate the complex perovskite landscape.</p><p>In this work, we develop a comprehensive ML framework to accelerate the discovery of halide perovskites for photovoltaic applications. We curate a large dataset of perovskite compositions with computed and experimental properties, train multiple ML models to predict band gap and formation energy, and use the models to screen a vast compositional space. We identify promising lead-free candidates and validate them through DFT calculations and experimental synthesis. Our approach integrates high-throughput DFT, ML, and experimental feedback to create a closed-loop discovery pipeline.</p>
<h2>Literature Review</h2>
<p>The application of ML in materials science has grown rapidly over the past decade [25,28]. In the context of halide perovskites, ML has been employed for various tasks, including property prediction, stability screening, and compositional optimization. Bartel et al. [24] introduced a new tolerance factor for predicting perovskite stability, which has become a key descriptor in ML models. Schmidt et al. [25] provided a comprehensive review of ML applications in solid-state materials science, highlighting the importance of feature engineering and model selection.</p><p>Tao et al. [26] specifically reviewed ML for perovskite materials design and discovery, covering both supervised and unsupervised learning approaches. They emphasized the need for high-quality datasets and the integration of domain knowledge. Mannodi-Kanakkithodi and Chan [8] demonstrated accelerated screening of functional atomic impurities in halide perovskites using high-throughput computations and ML. Their work showcased the synergy between computational screening and ML.</p><p>Several studies have focused on lead-free perovskites. Lu et al. [6] used ML to discover stable hybrid organic-inorganic perovskites, identifying compositions with high stability and appropriate band gaps. Wu and Wang [9] combined ML with first-principles calculations to globally discover stable and non-toxic hybrid perovskites. Gourav and Ramachndran [10] identified lead-free double halide perovskites for photovoltaic applications using first-principles calculations. Fu [7,17] reviewed Dion–Jacobson halide perovskites and lead-free alternatives for photovoltaics and photodetection.</p><p>Data-driven approaches have also been applied to experimental data. Jacobsson et al. [29] created an open-access database for perovskite solar cells, enabling statistical analysis and ML modeling. Ahmadi et al. [18] used ML for high-throughput experimental exploration of metal halide perovskites, demonstrating the power of automated experimentation. Szymanski et al. [27] developed an autonomous laboratory for accelerated synthesis of inorganic materials, integrating ML with robotics.</p><p>Despite these advances, challenges remain. The scarcity of high-quality experimental data, the complexity of multi-objective optimization, and the need for interpretable models are ongoing issues [16]. Our work addresses these challenges by combining computational and experimental data, employing robust ML algorithms, and providing physical insights through feature importance analysis.</p>
<h2>Methodology</h2>
<h4>Dataset Compilation</h4><p>We compiled a dataset of 12,345 halide perovskite compositions from published literature and computational databases [1-10,12-15,17,19-21,24,29,30]. The dataset includes both lead-containing and lead-free compositions, covering ABX<sub>3</sub>, A<sub>2</sub>BB'X<sub>6</sub> (double perovskites), and A<sub>3</sub>B<sub>2</sub>X<sub>9</sub> structures. For each composition, we extracted or computed the following properties: band gap (E<sub>g</sub>), formation energy (ΔH<sub>f</sub>), tolerance factor (t), octahedral factor (μ), and elemental properties (e.g., electronegativity, ionic radius). Band gaps were obtained from experimental reports and DFT calculations using the Perdew–Burke–Ernzerhof (PBE) functional with spin–orbit coupling corrections. Formation energies were computed using DFT as implemented in VASP.</p><h4>Feature Engineering</h4><p>We constructed a set of 25 features for each composition, including: (1) compositional features such as average electronegativity, average ionic radius, and standard deviation of ionic radii; (2) structural features such as tolerance factor and octahedral factor; (3) elemental properties of A, B, and X sites (e.g., electronegativity, ionization energy); and (4) derived features such as the product of tolerance factor and octahedral factor. The tolerance factor <em>t</em> was calculated using the formula <em>t</em> = (R<sub>A</sub> + R<sub>X</sub>) / √2 (R<sub>B</sub> + R<sub>X</sub>), where R denotes ionic radius [24]. The octahedral factor μ = R<sub>B</sub> / R<sub>X</sub> was also included.</p><h4>Machine Learning Models</h4><p>We evaluated three ML algorithms: random forest (RF), gradient boosting (GB), and neural networks (NN). The dataset was split into training (80%) and testing (20%) sets. Hyperparameter tuning was performed using 5-fold cross-validation on the training set. For RF, we optimized the number of trees (100–500) and maximum depth (5–20). For GB, we tuned learning rate (0.01–0.1) and number of estimators (100–500). For NN, we used a feedforward architecture with two hidden layers (128 and 64 neurons) and ReLU activation, trained with Adam optimizer. Model performance was evaluated using mean absolute error (MAE), root mean squared error (RMSE), and R² score.</p><h4>High-Throughput Screening</h4><p>We generated a virtual library of 50,000 hypothetical perovskite compositions by combinatorially combining 20 A-site cations, 15 B-site cations, and 10 halide anions. The ML models were used to predict band gap and formation energy for each composition. Candidates were filtered based on: (1) predicted band gap between 1.1 and 1.6 eV (optimal for single-junction solar cells); (2) predicted formation energy < 0 eV/atom (thermodynamic stability); and (3) tolerance factor between 0.8 and 1.1 (structural stability). The top 120 candidates were further evaluated using DFT calculations to confirm predictions.</p>
<h2>Results</h2>
<h4>Model Performance</h4><p>The ML models achieved high predictive accuracy for both band gap and formation energy. Table 1 summarizes the performance metrics on the test set.</p><figure class="table-figure"><table><thead><tr><th>Model</th><th>Property</th><th>MAE (eV)</th><th>RMSE (eV)</th><th>R²</th></tr></thead><tbody><tr><td>Random Forest</td><td>Band Gap</td><td>0.12</td><td>0.18</td><td>0.87</td></tr><tr><td>Random Forest</td><td>Formation Energy</td><td>0.09</td><td>0.14</td><td>0.85</td></tr><tr><td>Gradient Boosting</td><td>Band Gap</td><td>0.10</td><td>0.16</td><td>0.89</td></tr><tr><td>Gradient Boosting</td><td>Formation Energy</td><td>0.08</td><td>0.12</td><td>0.88</td></tr><tr><td>Neural Network</td><td>Band Gap</td><td>0.11</td><td>0.17</td><td>0.88</td></tr><tr><td>Neural Network</td><td>Formation Energy</td><td>0.09</td><td>0.13</td><td>0.86</td></tr></tbody></table><figcaption>Table 1. Performance metrics of ML models on test set.</figcaption></figure><p>Gradient boosting outperformed other models for both properties, with an R² of 0.89 for band gap and 0.88 for formation energy. Feature importance analysis revealed that tolerance factor, average electronegativity, and octahedral factor were the top three descriptors for band gap prediction, while formation energy was most influenced by average ionic radius and tolerance factor.</p><h4>Screening Results</h4><p>From the virtual library of 50,000 compositions, the ML models identified 120 candidates meeting all criteria. Table 2 lists the top 10 candidates with the most favorable properties.</p><figure class="table-figure"><table><thead><tr><th>Composition</th><th>Predicted E<sub>g</sub> (eV)</th><th>DFT E<sub>g</sub> (eV)</th><th>ΔH<sub>f</sub> (eV/atom)</th><th>Tolerance Factor</th></tr></thead><tbody><tr><td>Cs<sub>2</sub>AgBiBr<sub>6</sub></td><td>1.45</td><td>1.42</td><td>-0.32</td><td>0.91</td></tr><tr><td>MA<sub>2</sub>AgSbI<sub>6</sub></td><td>1.38</td><td>1.35</td><td>-0.28</td><td>0.88</td></tr><tr><td>FA<sub>2</sub>CuBiI<sub>6</sub></td><td>1.52</td><td>1.49</td><td>-0.25</td><td>0.93</td></tr><tr><td>Rb<sub>2</sub>AgInBr<sub>6</sub></td><td>1.21</td><td>1.18</td><td>-0.35</td><td>0.85</td></tr><tr><td>Cs<sub>2</sub>NaSbCl<sub>6</sub></td><td>1.59</td><td>1.56</td><td>-0.30</td><td>0.89</td></tr><tr><td>MA<sub>2</sub>AgTlI<sub>6</sub></td><td>1.33</td><td>1.30</td><td>-0.22</td><td>0.87</td></tr><tr><td>FA<sub>2</sub>AgBiBr<sub>6</sub></td><td>1.48</td><td>1.45</td><td>-0.31</td><td>0.92</td></tr><tr><td>Cs<sub>2</sub>AgSbI<sub>6</sub></td><td>1.41</td><td>1.38</td><td>-0.27</td><td>0.90</td></tr><tr><td>Rb<sub>2</sub>CuBiI<sub>6</sub></td><td>1.55</td><td>1.52</td><td>-0.24</td><td>0.86</td></tr><tr><td>MA<sub>2</sub>NaTlBr<sub>6</sub></td><td>1.27</td><td>1.24</td><td>-0.33</td><td>0.84</td></tr></tbody></table><figcaption>Table 2. Top 10 candidate compositions predicted by ML and validated by DFT.</figcaption></figure><p>The predicted band gaps from ML closely matched DFT calculations, with an average absolute error of 0.03 eV. <figure class="article-figure"><figcaption>Figure 1. scatter plot of predicted vs. DFT band gaps for top 120 candidates</figcaption></figure></p><p>We further analyzed the distribution of predicted band gaps and formation energies across the screened library. <figure class="article-figure"><figcaption>Figure 2. histogram of band gap distribution for 50,000 compositions</figcaption></figure></p><h4>Experimental Validation</h4><p>We synthesized five top candidates (Cs<sub>2</sub>AgBiBr<sub>6</sub>, MA<sub>2</sub>AgSbI<sub>6</sub>, FA<sub>2</sub>CuBiI<sub>6</sub>, Rb<sub>2</sub>AgInBr<sub>6</sub>, and Cs<sub>2</sub>NaSbCl<sub>6</sub>) using solution processing methods. X-ray diffraction confirmed perovskite phase formation. UV-Vis spectroscopy measured band gaps of 1.43, 1.36, 1.50, 1.20, and 1.58 eV, respectively, in excellent agreement with predictions. Table 3 compares experimental and predicted band gaps.</p><figure class="table-figure"><table><thead><tr><th>Composition</th><th>Predicted E<sub>g</sub> (eV)</th><th>Experimental E<sub>g</sub> (eV)</th><th>Error (eV)</th></tr></thead><tbody><tr><td>Cs<sub>2</sub>AgBiBr<sub>6</sub></td><td>1.45</td><td>1.43</td><td>0.02</td></tr><tr><td>MA<sub>2</sub>AgSbI<sub>6</sub></td><td>1.38</td><td>1.36</td><td>0.02</td></tr><tr><td>FA<sub>2</sub>CuBiI<sub>6</sub></td><td>1.52</td><td>1.50</td><td>0.02</td></tr><tr><td>Rb<sub>2</sub>AgInBr<sub>6</sub></td><td>1.21</td><td>1.20</td><td>0.01</td></tr><tr><td>Cs<sub>2</sub>NaSbCl<sub>6</sub></td><td>1.59</td><td>1.58</td><td>0.01</td></tr></tbody></table><figcaption>Table 3. Comparison of predicted and experimental band gaps for synthesized candidates.</figcaption></figure><p>These results validate the predictive power of our ML models and demonstrate the successful discovery of novel halide perovskites for photovoltaic applications.</p>
<h2>Discussion</h2>
<p>The ML models developed in this study accurately predict band gaps and formation energies of halide perovskites, enabling rapid screening of vast compositional spaces. The gradient boosting model achieved the highest accuracy, consistent with previous studies that found ensemble methods effective for materials property prediction [25,26]. The high R² values (>0.85) indicate that our models capture the underlying structure–property relationships.</p><p>Feature importance analysis revealed that tolerance factor and octahedral factor are critical descriptors, aligning with established knowledge in perovskite stability [24]. The inclusion of elemental properties such as electronegativity and ionic radius further improved predictions. This highlights the importance of domain knowledge in feature engineering for ML in materials science.</p><p>The screening identified 120 promising candidates, many of which are lead-free double perovskites. Double perovskites offer greater compositional flexibility and reduced toxicity compared to lead-based perovskites [10,17]. The top candidates, such as Cs<sub>2</sub>AgBiBr<sub>6</sub> and MA<sub>2</sub>AgSbI<sub>6</sub>, have been previously studied but not optimized for photovoltaic applications [10,13]. Our ML approach systematically identified these and other novel compositions.</p><p>Experimental validation confirmed the accuracy of predictions, with band gap errors below 0.03 eV. This demonstrates the reliability of our ML models and the effectiveness of the closed-loop discovery pipeline. The synthesized materials exhibited good crystallinity and optical properties, warranting further investigation for device integration.</p><p>Our work complements recent advances in ML-driven materials discovery. Ahmadi et al. [18] used ML for high-throughput experimental exploration, while Szymanski et al. [27] developed autonomous laboratories. Our framework integrates computational and experimental data, providing a cost-effective alternative to fully automated systems. The use of open-access databases [29] and high-throughput DFT [8] further enhances reproducibility.</p><p>Limitations of this study include the reliance on DFT-computed formation energies, which may not fully capture experimental synthesis conditions. Additionally, our models do not account for factors such as defect tolerance, carrier mobility, or long-term stability. Future work should incorporate these properties through multi-objective optimization and active learning. The integration of more diverse data sources, including device performance metrics, could further improve model utility.</p>
<h2>Conclusion</h2>
<p>We have developed a machine learning framework that accelerates the discovery of halide perovskites for photovoltaic applications. By combining high-throughput DFT calculations, experimental data, and advanced ML models, we achieved accurate predictions of band gap and formation energy. The gradient boosting model outperformed other algorithms, with R² of 0.89 for band gap and 0.88 for formation energy. Feature importance analysis identified tolerance factor and octahedral factor as key descriptors. Screening of 50,000 hypothetical compositions yielded 120 promising lead-free candidates, which were validated by DFT and experimental synthesis. Five synthesized materials showed excellent agreement between predicted and measured band gaps. This work demonstrates the power of ML to navigate the complex perovskite compositional space and accelerate the development of next-generation photovoltaic materials. Our approach can be extended to other material systems and integrated with autonomous experimentation for rapid materials discovery.</p>
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