Motivation and Scope
I set out to accelerate the discovery of lead-free inorganic halide double perovskite materials for high-performance perovskite solar cells by combining deep learning with density functional theory (DFT). The urgency is clear: global energy demand continues to rise, fossil-fuel dependence remains a central environmental and geopolitical problem, and photovoltaic technology must become more efficient, stable, and environmentally benign. Silicon-based perovskite solar cells have achieved remarkable maturity, yet they still face limitations in cost, flexibility, and large-scale architectural integration. Halide perovskites offer a compelling alternative because of their strong optical absorption, tunable bandgaps, long carrier diffusion lengths, and solution-processable fabrication. However, the most widely studied halide perovskites often contain lead, which introduces toxicity concerns, and many suffer from instability under heat, moisture, oxygen, electric fields, and illumination. These issues motivate the search for lead-free double perovskites with suitable bandgaps for perovskite solar cells.
My central hypothesis was that a deep neural network (DNN) trained on a curated database of inorganic double perovskites could predict bandgaps with sufficient accuracy to guide DFT verification and device simulation. I further hypothesized that the synergy between data-driven screening and first-principles validation would reduce the cost and time associated with trial-and-error experimental work. The target application was perovskite solar cells, specifically n-i-p devices with a lead-free double perovskite absorber. I focused on bandgaps between 1.0 eV and 2.0 eV, because this range covers the ideal single-junction region and the medium-gap region useful for tandem perovskite solar cells.
Double Perovskite Database and Feature Engineering
I constructed a database of inorganic halide double perovskites with the general formula A₂BB′X₆. The A-site is occupied by monovalent cations, the B and B′ sites can be occupied by a monovalent/trivalent pair or two divalent metals, and the X-site is a halide anion. The initial collection contained more than 1,700 compositions. I filtered the dataset to retain materials with bandgaps between 0.5 eV and 4.0 eV. This window preserves the narrow-gap region, the ideal single-junction region, and the wide-gap region, while removing metals and insulators that are not relevant to perovskite solar cells. After cleaning, I obtained 1,181 inorganic double perovskite materials. The resulting dataset provided a balanced and physically meaningful foundation for machine learning.
| Database property | Value | Purpose for perovskite solar cells |
|---|---|---|
| Initial compositions | More than 1,700 | Broad chemical space exploration |
| Retained compositions | 1,181 | Bandgap-focused screening |
| Bandgap window | 0.5 eV to 4.0 eV | Covers single-junction and tandem regions |
| A-site elements | Li, Na, K, Rb, Cs | Structure stability and tolerance factor control |
| B/B′ elements | Mainly groups IIIB to VIA | Electronic structure and carrier transport tuning |
| X-site elements | F, Cl, Br, I | Bandgap and lattice engineering |
I used Materials Project data together with feature-engineering tools from Matminer and Pymatgen. The initial feature space contained more than 100 descriptors. To avoid multicollinearity, I calculated the Pearson correlation coefficient between features and removed redundant variables. The Pearson coefficient is defined as
$$ r_{xy} = \frac{\sum_{i=1}^{n}(x_i – \bar{x})(y_i – \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i – \bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i – \bar{y})^2}} $$
I retained features with pairwise correlation below 0.8. This reduced the descriptor set to 30 variables. The final features included atomic density, C-site Mendeleev number, B-site Mendeleev number, energy above hull, average bulk modulus, average electronegativity, valence electron count, maximum unfilled d-electron count, van der Waals radius, covalent radius, atomic number, critical temperature, and several structural and electronic descriptors. These features are physically interpretable and relevant to the bandgap formation of double perovskites for perovskite solar cells.
| Feature category | Representative descriptors | Physical relevance |
|---|---|---|
| Density and packing | Atomic density, atomic volume, packing fraction | Controls bond lengths and orbital overlap |
| Periodic-table position | B-site Mendeleev number, C-site Mendeleev number, group number | Controls electronegativity and orbital energies |
| Thermodynamic stability | Energy above hull, formation energy | Indicates metastability and defect behavior |
| Mechanical properties | Average bulk modulus, shear modulus | Correlates with lattice rigidity and octahedral tilting |
| Electronic descriptors | Valence electrons, unfilled d states, electronegativity | Controls band-edge character and spin-orbit coupling |
| Geometric descriptors | Ionic radius, covalent radius, van der Waals radius | Governs tolerance factor and octahedral factor |
Machine Learning Models and Training Protocol
I trained and compared five machine learning models for bandgap prediction: random forest regression (RFR), gradient boosting regression (GBR), support vector regression (SVR), extreme gradient boosting regression (XGBR), and a deep neural network (DNN). The dataset was split into 60% training, 20% validation, and 20% testing. The training set contained 709 materials, the validation set contained 237 materials, and the test set contained 237 materials. I used normalization, dropout, dynamic learning-rate scheduling, grid search, and ten-fold cross-validation to optimize all models. The DNN was chosen as the primary model because of its capacity for nonlinear mapping and automatic high-dimensional feature extraction.
| Model | Key hyperparameters |
|---|---|
| RFR | bootstrap=True, max_depth=8, max_features=’sqrt’, min_samples_leaf=2, min_samples_split=2, n_estimators=300 |
| GBR | learning_rate=0.05, max_depth=3, max_features=’sqrt’, min_samples_leaf=5, min_samples_split=10, n_estimators=150, subsample=0.8 |
| SVR | kernel=’rbf’, gamma=0.1, epsilon=0.2, C=15 |
| XGBR | colsample_bytree=0.2, gamma=0.1, learning_rate=0.1, max_depth=3, min_child_weight=2, n_estimators=150, subsample=0.4, reg_alpha=0.1, reg_lambda=1 |
| DNN component | Setting |
|---|---|
| Input dimension | 30 features |
| Hidden layer 1 | 768 neurons |
| Hidden layer 2 | 384 neurons |
| Activation | Swish in hidden layers, linear in output layer |
| Output | Single continuous value for bandgap |
| Optimizer learning rate | 0.001 |
| Epochs | 1500 |
| Callbacks | EarlyStopping, ReduceLROnPlateau |
| Regularization | Dropout and normalization |
The performance metrics were the coefficient of determination, mean absolute error, and mean squared error. These are defined as
$$ R^2 = 1 – \frac{\sum_{i=1}^{n}(Y_i – y_i)^2}{\sum_{i=1}^{n}(Y_i – \bar{Y})^2} $$
$$ \text{MAE} = \frac{1}{n}\sum_{i=1}^{n}|Y_i – y_i| $$
$$ \text{MSE} = \frac{1}{n}\sum_{i=1}^{n}(Y_i – y_i)^2 $$
Here, Y_i is the DFT-calculated bandgap, y_i is the machine-learning-predicted bandgap, and \bar{Y} is the mean DFT bandgap. A high R² and low MAE/MSE indicate a model suitable for screening perovskite solar cells.
DFT Methodology
I used the Vienna Ab initio Simulation Package (VASP) with the projector augmented-wave (PAW) method and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. The plane-wave cutoff was 400 eV. Structural optimization used a 3×3×3 k-point mesh, and electronic property calculations used a 5×5×5 k-point mesh. The self-consistent electronic convergence criterion was 1×10⁻³ eV. Ionic relaxation continued until forces were below 0.02 eV/Å, and the final force threshold was 0.01 eV/Å. The high-symmetry path for band structures was Gamma–X–R–M–Gamma–R. I visualized crystal structures with VESTA. These calculations provided the ground-truth bandgaps and stability indicators for the deep-learning screening workflow.
The total energy in DFT can be written schematically as
$$ E_{\text{total}} = T_s[n] + E_{\text{ext}}[n] + E_{\text{Hartree}}[n] + E_{\text{xc}}[n] + E_{\text{ion-ion}} $$
For thermodynamic stability, I evaluated the formation energy and energy above hull. The formation energy is
$$ \Delta H_f = E_{\text{total}}(\text{compound}) – \sum_i n_i \mu_i $$
where n_i is the number of atoms of species i and \mu_i is the corresponding chemical potential. Negative formation energy indicates that the compound is thermodynamically favorable relative to its constituents. For structural stability, I calculated the tolerance factor and octahedral factor:
$$ t_f = \frac{R_A + R_X}{\sqrt{2}\left(\frac{R_B + R_{B’}}{2} + R_X\right)} $$
$$ \mu_f = \frac{\frac{R_B + R_{B’}}{2}}{R_X} $$
I required t_f to lie between 0.75 and 1.08 and \mu_f to lie between 0.4 and 1.0. These criteria are widely used to identify structurally stable double perovskites for perovskite solar cells.
Model Performance, Cross-Validation, and Feature Importance
The DNN outperformed the four baseline models. Its test-set MAE was 0.264 eV, its MSE was 0.175 eV², and its R² was 0.925. Ten-fold cross-validation gave an average R² of 0.926, confirming that the model generalized well across the 1,181-material database. The traditional models achieved reasonable accuracy but were consistently less precise, especially for materials near bandgap boundaries and for compositions with strong spin-orbit coupling or octahedral tilting.
| Model | R² | MAE (eV) | MSE (eV²) | Rank |
|---|---|---|---|---|
| DNN | 0.925 | 0.264 | 0.175 | 1 |
| XGBR | 0.901 | 0.312 | 0.231 | 2 |
| GBR | 0.889 | 0.334 | 0.258 | 3 |
| RFR | 0.874 | 0.361 | 0.294 | 4 |
| SVR | 0.852 | 0.392 | 0.345 | 5 |
| Cross-validation fold | R² |
|---|---|
| Fold 1 | 0.921 |
| Fold 2 | 0.928 |
| Fold 3 | 0.924 |
| Fold 4 | 0.930 |
| Fold 5 | 0.919 |
| Fold 6 | 0.927 |
| Fold 7 | 0.925 |
| Fold 8 | 0.932 |
| Fold 9 | 0.923 |
| Fold 10 | 0.931 |
| Average | 0.926 |
Feature-importance analysis revealed that atomic density was the most influential descriptor. High atomic density shortens B–X bond lengths, increases orbital overlap, broadens the valence band, and tends to widen the bandgap. The C-site Mendeleev number, which encodes halide identity, was the second most important feature. Heavier halides such as iodide raise the p-orbital energy, reduce electronegativity, and narrow the bandgap. Energy above hull ranked third, reflecting the role of metastability, lattice distortion, and defect states. The B-site Mendeleev number and average bulk modulus ranked fourth and fifth. Together, these features connect the deep-learning predictions to known physical mechanisms in perovskite solar cells.
| Rank | Feature | Physical interpretation |
|---|---|---|
| 1 | Atomic density | Controls bond lengths and orbital overlap |
| 2 | C-site Mendeleev number | Encodes halide electronegativity and p-orbital energy |
| 3 | Energy above hull | Indicates metastability and lattice distortion |
| 4 | B-site Mendeleev number | Controls metal orbital energies and spin-orbit coupling |
| 5 | Average bulk modulus | Correlates with lattice rigidity and octahedral tilting |
| 6 | Average electronegativity | Controls charge transfer and band-edge positions |
| 7 | Valence electron count | Determines bonding and band filling |
| 8 | Maximum unfilled d electrons | Influences transition-metal states |
| 9 | Van der Waals radius | Affects packing and steric effects |
| 10 | Critical temperature | Correlates with bonding strength and stability |
Screening Criteria and Candidate Selection
After training the DNN, I used it to predict the bandgaps of 55 lead-free double perovskite candidates. I selected these candidates from elemental substitution strategies and from promising entries in public databases. I completely excluded lead-containing compositions. I then applied a multi-stage screening protocol. First, I required a direct bandgap between 1.0 eV and 2.0 eV. Direct-gap perovskites generally have stronger optical absorption, more efficient carrier generation, and shorter absorption lengths than indirect-gap materials. Second, I required negative formation energy. Third, I required t_f between 0.75 and 1.08 and \mu_f between 0.4 and 1.0. These criteria are essential for stable and efficient perovskite solar cells.
| Screening stage | Criterion | Reason |
|---|---|---|
| Composition | No Pb | Environmental and health safety |
| Bandgap nature | Direct gap | Strong absorption for perovskite solar cells |
| Bandgap value | 1.0 eV to 2.0 eV | Single-junction and tandem relevance |
| Thermodynamic stability | Negative formation energy | Suppresses decomposition |
| Tolerance factor | 0.75 to 1.08 | Perovskite framework stability |
| Octahedral factor | 0.4 to 1.0 | B-site octahedral coordination stability |
| Device compatibility | Favorable band alignment | Efficient carrier extraction |
From the initial 55 materials, I obtained 14 candidates after DFT verification and preliminary filtering. I then narrowed the list to four final candidates: Cs₂GaAgCl₆, Cs₂AgIrF₆, Cs₂InAgCl₆, and Cs₂AlAgBr₆. Their predicted and DFT bandgaps, bandgap nature, formation energies, and stability factors are summarized below.
| Compound | ML bandgap (eV) | DFT bandgap (eV) | Bandgap status | \Delta H_f | t_f | \mu_f |
|---|---|---|---|---|---|---|
| Cs₂GaAgBr₆ | 0.509 | 0.062 | Direct | -1.48 | 0.98 | 0.49 |
| Cs₂AgAuCl₆ | 0.690 | 0.704 | Indirect | -1.45 | 0.95 | 0.55 |
| Cs₂AgMoBr₆ | 0.709 | Metallic | Metallic | -1.38 | 0.97 | 0.49 |
| Cs₂AgBiI₆ | 0.850 | 0.852 | Indirect | -1.12 | 0.92 | 0.49 |
| Cs₂CeAgI₆ | 0.907 | Metallic | Metallic | -1.49 | 0.92 | 0.49 |
| Cs₂AgMoCl₆ | 1.090 | Metallic | Metallic | -1.46 | 0.98 | 0.54 |
| Cs₂AgBiBr₆ | 1.306 | 1.358 | Indirect | -1.51 | 0.94 | 0.56 |
| Cs₂AgIrF₆ | 1.338 | 1.364 | Direct | -2.09 | 0.84 | 0.75 |
| Cs₂GaAgCl₆ | 1.389 | 1.015 | Direct | -1.70 | 0.99 | 0.53 |
| Cs₂AlAgBr₆ | 1.448 | 1.202 | Direct | -1.60 | 0.98 | 0.47 |
| Cs₂InAgCl₆ | 1.535 | 1.081 | Direct | -1.74 | 0.94 | 0.54 |
| Cs₂KAgF₆ | 1.558 | Metallic | Metallic | -2.09 | 0.76 | 0.98 |
| Cs₂AgBiCl₆ | 1.838 | 1.803 | Indirect | -1.71 | 0.96 | 0.60 |
| Cs₂CoAgF₆ | 1.943 | 0.943 | Direct | -2.32 | 0.99 | 0.76 |
| Final candidate | DFT bandgap (eV) | Bandgap nature | \Delta H_f | t_f | \mu_f |
|---|---|---|---|---|---|
| Cs₂GaAgCl₆ | 1.015 | Direct | -1.70 | 0.99 | 0.53 |
| Cs₂AgIrF₆ | 1.364 | Direct | -2.09 | 0.84 | 0.75 |
| Cs₂InAgCl₆ | 1.081 | Direct | -1.74 | 0.94 | 0.54 |
| Cs₂AlAgBr₆ | 1.202 | Direct | -1.60 | 0.98 | 0.47 |
DFT Band Structures and Stability of the Final Candidates
The four final candidates all have direct bandgaps in the desired range. Cs₂GaAgCl₆ has a DFT bandgap of 1.015 eV, Cs₂InAgCl₆ has 1.081 eV, Cs₂AlAgBr₆ has 1.202 eV, and Cs₂AgIrF₆ has 1.364 eV. The direct-gap character is important for perovskite solar cells because it enables strong optical absorption and efficient photon-to-carrier conversion. The negative formation energies indicate thermodynamic stability. The tolerance factors and octahedral factors fall within the acceptable ranges, suggesting that the double perovskite framework can be retained without collapse. Importantly, none of these materials contain lead, so they avoid the toxicity problem that limits many high-efficiency perovskite solar cells.
I also examined the electronic structure trends. The chloride-based candidates have wider gaps than the bromide-based candidate, consistent with the higher electronegativity of Cl and its lower p-orbital energy. The iridium-containing Cs₂AgIrF₆ has a more complex electronic structure because of Ir d states, yet it still maintains a direct gap and a favorable band alignment. The indium-containing Cs₂InAgCl₆ has a relatively small gap and strong absorption in the visible range. These properties make the four candidates attractive for perovskite solar cells, especially when paired with suitable electron and hole transport layers.
Device Simulation with SCAPS-1D
I evaluated the photovoltaic performance of the four candidates using SCAPS-1D, a one-dimensional solar-cell capacitance simulator. The device architecture was n-i-p FTO/TiO₂/Cs₂BB′X₆/Cu₂O/Au. FTO served as the transparent front contact, TiO₂ as the electron transport layer, the double perovskite as the absorber, Cu₂O as the hole transport layer, and Au as the back contact. I aligned the band edges to promote electron extraction toward TiO₂ and hole extraction toward Cu₂O. The simulation solved the Poisson equation, the drift-diffusion transport equations, the continuity equations, and the diffusion-length relations.
The Poisson equation is
$$ \frac{\partial^2 \phi}{\partial x^2} = -\frac{q}{\epsilon}\left[p(x) – n(x) + N_D^+(x) – N_A^-(x) + p_t(x) – N_t(x)\right] $$
where \phi is the electrostatic potential, q is the elementary charge, \epsilon is the dielectric constant, n and p are electron and hole densities, N_D^+ and N_A^- are donor and acceptor concentrations, and p_t and N_t are trapped hole and electron densities. The transport equations are
$$ J_n = n q \mu_n E + q D_n \frac{\partial n}{\partial x} $$
$$ J_p = p q \mu_p E – q D_p \frac{\partial p}{\partial x} $$
The diffusion length and diffusion coefficient are
$$ L_{n,p} = \sqrt{D_{n,p}\tau_{n,p}} $$
$$ D_{n,p} = \frac{k_B T}{q}\mu_{n,p} $$
where L_{n,p} is the carrier diffusion length, D_{n,p} is the diffusion coefficient, \tau_{n,p} is the carrier lifetime, \mu_{n,p} is the mobility, k_B is the Boltzmann constant, and T is temperature. The continuity equations are
$$ \frac{\partial n}{\partial t} = \frac{1}{q}\frac{\partial J_n}{\partial x} + G_n – R_n $$
$$ \frac{\partial p}{\partial t} = -\frac{1}{q}\frac{\partial J_p}{\partial x} + G_p – R_p $$
I used AM1.5G illumination with an incident power density of 100 mW/cm². The transport-layer parameters are listed below.
| Material property | FTO | TiO₂ | Cu₂O |
|---|---|---|---|
| Thickness (nm) | 300 | 50 | 300 |
| Bandgap (eV) | 3.5 | 3.2 | 2.17 |
| Electron affinity (eV) | 4.0 | 4.0 | 3.2 |
| Relative dielectric constant | 9 | 9 | 6.6 |
| Effective conduction-band density (cm⁻³) | 2.200×10¹⁹ | 1.000×10¹⁸ | 2.500×10²⁰ |
| Effective valence-band density (cm⁻³) | 1.800×10¹⁹ | 1.000×10¹⁹ | 10²⁰ |
| Electron thermal velocity (cm/s) | 10⁷ | 10⁷ | 10⁷ |
| Hole thermal velocity (cm/s) | 10⁷ | 10⁷ | 10⁷ |
| Electron mobility (cm²/V·s) | 20 | 2 | 3.4 |
| Hole mobility (cm²/V·s) | 10 | 1 | 3.4 |
| Absorber property | Cs₂AgIrF₆ | Cs₂AlAgBr₆ | Cs₂GaAgCl₆ | Cs₂InAgCl₆ |
|---|---|---|---|---|
| Thickness (nm) | 600 | 600 | 600 | 600 |
| Bandgap (eV) | 1.36 | 1.20 | 1.02 | 1.08 |
| Electron affinity (eV) | 4.10 | 4.15 | 4.30 | 4.00 |
| Relative dielectric constant | 10 | 8 | 12 | 10 |
| Effective conduction-band density (cm⁻³) | 1.720×10¹⁹ | 2.000×10¹⁹ | 2.000×10¹⁹ | 2.000×10¹⁹ |
| Effective valence-band density (cm⁻³) | 10¹⁹ | 2.000×10¹⁹ | 2.000×10¹⁹ | 2.000×10¹⁹ |
| Electron thermal velocity (cm/s) | 10⁷ | 10⁷ | 10⁷ | 10⁷ |
| Hole thermal velocity (cm/s) | 10⁷ | 10⁷ | 10⁷ | 10⁷ |
| Electron mobility (cm²/V·s) | 12 | 10 | 11.8 | 5 |
| Hole mobility (cm²/V·s) | 5 | 5 | 2 | 3 |
The simulated photovoltaic metrics are summarized below. Cs₂AgIrF₆ and Cs₂AlAgBr₆ delivered the best performance. Cs₂AgIrF₆ reached a power conversion efficiency of 23.71%, with an open-circuit voltage of 0.94 V, a short-circuit current density of 31.19 mA/cm², and a fill factor of 80.81%. Cs₂AlAgBr₆ reached 22.37%, with Voc = 0.78 V, Jsc = 36.73 mA/cm², and FF = 77.66%. Cs₂InAgCl₆ reached 21.29%, and Cs₂GaAgCl₆ reached 19.85%. The high open-circuit voltages and fill factors of the best two materials indicate efficient carrier separation and reduced non-radiative recombination in perovskite solar cells.
| Absorber | V_OC (V) | J_SC (mA/cm²) | FF (%) | PCE (%) |
|---|---|---|---|---|
| Cs₂AgIrF₆ | 0.94 | 31.19 | 80.81 | 23.71 |
| Cs₂AlAgBr₆ | 0.78 | 36.73 | 77.66 | 22.37 |
| Cs₂GaAgCl₆ | 0.61 | 44.55 | 73.36 | 19.85 |
| Cs₂InAgCl₆ | 0.68 | 41.85 | 75.32 | 21.29 |
The J–V characteristics and quantum efficiency trends agree with the bandgap and band-alignment analysis. Cs₂GaAgCl₆ produced the highest short-circuit current but the lowest open-circuit voltage and fill factor. This suggests significant non-radiative recombination and incomplete carrier collection. Cs₂AgIrF₆ had a lower current but a much higher voltage and fill factor, leading to the highest efficiency. Cs₂AlAgBr₆ balanced current and voltage, giving the second-best efficiency. These results highlight the importance of both bandgap and interface quality in perovskite solar cells.
Discussion
I found that the deep learning and DFT synergy was effective for screening lead-free double perovskites for perovskite solar cells. The DNN reduced the computational burden by rapidly predicting bandgaps for 1,181 materials and then for 55 candidate compositions. DFT provided the necessary validation and stability metrics. The feature-importance analysis connected data-driven predictions to physical mechanisms. Atomic density, halide identity, energy above hull, metal identity, and bulk modulus emerged as the most important descriptors. These descriptors are not merely statistical artifacts; they reflect bond lengths, orbital overlap, electronegativity, lattice distortion, and thermodynamic stability.
The final four candidates are promising for perovskite solar cells because they combine direct bandgaps, negative formation energies, acceptable tolerance factors, and no lead content. Cs₂AgIrF₆ and Cs₂AlAgBr₆ are especially attractive. Their simulated efficiencies exceed 22%, and their open-circuit voltages and fill factors are high enough to suggest low non-radiative recombination. Cs₂InAgCl₆ and Cs₂GaAgCl₆ also have useful bandgaps, but their device performance is limited by lower voltages and fill factors. Future work should optimize absorber thickness, defect densities, interface passivation, and transport-layer doping to improve these perovskite solar cells further.
| Material | Main strength | Main limitation | Suggested optimization for perovskite solar cells |
|---|---|---|---|
| Cs₂AgIrF₆ | High V_OC and FF, best PCE | Moderate J_SC | Thickness and interface tuning |
| Cs₂AlAgBr₆ | High J_SC and good PCE | Lower V_OC than Cs₂AgIrF₆ | Defect passivation and band alignment |
| Cs₂InAgCl₆ | Good visible absorption | Low fill factor | Transport-layer optimization |
| Cs₂GaAgCl₆ | Highest J_SC | Low V_OC and FF | Recombination suppression |
Conclusion
I demonstrated a synergistic deep learning and DFT framework for discovering lead-free double perovskites for perovskite solar cells. I built a database of 1,181 inorganic double perovskites, engineered 30 physically meaningful features, and trained a DNN that achieved a test-set R² of 0.925, MAE of 0.264 eV, and MSE of 0.175 eV². The DNN outperformed random forest, gradient boosting, support vector regression, and extreme gradient boosting. Ten-fold cross-validation gave an average R² of 0.926, confirming strong generalization. Feature-importance analysis identified atomic density, C-site Mendeleev number, energy above hull, B-site Mendeleev number, and average bulk modulus as the dominant descriptors for bandgap prediction in perovskite solar cells.
Using the trained DNN and DFT verification, I screened 55 candidates and selected four lead-free double perovskites: Cs₂GaAgCl₆, Cs₂AgIrF₆, Cs₂InAgCl₆, and Cs₂AlAgBr₆. All four have direct bandgaps between 1.0 eV and 1.4 eV, negative formation energies, and acceptable tolerance and octahedral factors. SCAPS-1D device simulations of n-i-p FTO/TiO₂/Cs₂BB′X₆/Cu₂O/Au architectures showed that Cs₂AgIrF₆ and Cs₂AlAgBr₆ achieved power conversion efficiencies of 23.71% and 22.37%, respectively. Their high open-circuit voltages and fill factors indicate efficient carrier separation and low non-radiative recombination. These results support the use of deep learning and DFT synergy as a practical route for accelerating the rational design of high-performance, stable, and environmentally friendly perovskite solar cells.
| Key outcome | Value or finding |
|---|---|
| Database size | 1,181 inorganic double perovskites |
| Feature set | 30 descriptors after correlation filtering |
| Best model | Deep neural network |
| Test R² | 0.925 |
| Test MAE | 0.264 eV |
| Test MSE | 0.175 eV² |
| Cross-validation R² | 0.926 |
| Top feature | Atomic density |
| Final candidates | Cs₂GaAgCl₆, Cs₂AgIrF₆, Cs₂InAgCl₆, Cs₂AlAgBr₆ |
| Best PCE | 23.71% for Cs₂AgIrF₆ |
| Second-best PCE | 22.37% for Cs₂AlAgBr₆ |
| Environmental benefit | Lead-free perovskite solar cells |
Overall, my results show that data-driven bandgap prediction can be tightly integrated with first-principles validation and device modeling. This workflow reduces the search space for perovskite solar cells, prioritizes stable and non-toxic compositions, and provides clear targets for experimental synthesis. The combination of deep learning and DFT is therefore a powerful strategy for advancing lead-free perovskite solar cells toward higher efficiency, better stability, and environmental compatibility.