Machine learning aided parameter analysis in Perovskite X-ray Detector

Technical Summary: Machine Learning Aided Parameter Analysis in Perovskite X-ray Detectors

Problem Statement
Perovskite X-ray detectors hold significant promise for applications in medical diagnostics, security, and non-destructive testing due to their high absorption coefficients and adjustable band gaps. However, optimizing device performance—specifically sensitivity, detection limit, and dark current—is hindered by the complex interplay of numerous intrinsic material properties. Factors such as crystal lattice parameters, carrier dynamics, trap density, and atomic composition create a non-linear system where the specific relationships governing performance remain largely unknown. Traditional trial-and-error approaches struggle to navigate this high-dimensional parameter space, particularly when aiming to achieve simultaneous high sensitivity and low dark current densities below 1 nA cm⁻².

Methodology
This study employs a machine learning (ML) framework to decode the relationships between 15 intrinsic properties of halide perovskite materials and four key device performance metrics: band gap ($E_g$), carrier mobility-lifetime product ($\mu\tau$), sensitivity, and detection limit.

1. Database Construction: A comprehensive database was compiled from 136 existing research papers and one new experimental dataset, totaling 137 samples. Each sample includes 23 features, including atomic numbers ($Z_A, Z_B, Z_X$), lattice constants ($a, b, c$), lattice angles, and various electronic properties. Missing values were estimated based on comparable literature data, with a diminished weight applied to these estimated samples during training to mitigate potential errors.
2. Model Training: Five regression algorithms were trained on the normalized dataset to predict the target performance metrics: Multivariable Linear Regression (MLR), Random Forest Regression (RFR), eXtreme Gradient Boosting (XGBoost), Support Vector Regression (SVR), and Genetic Programming Symbolic Regressor (GPSR).
3. Feature Analysis: Feature importance was ranked using permutation importance to identify which intrinsic parameters most significantly influence the target variables.
4. Experimental Validation: To verify the ML predictions in a real-world setting, a new low-dimensional lead-based perovskite, (m-F-PEA)₂PbI₄, was synthesized via temperature cooling crystallization. A single-crystal X-ray detector was fabricated and characterized to compare experimental results against model predictions.

Key Results

• Model Performance: The Random Forest Regression (RFR) model demonstrated the most robust performance, particularly for predicting the band gap ($E_g$), achieving a test $R^2$ of 0.80. However, the models showed lower predictive accuracy for $\mu\tau$, sensitivity, and detection limit (test $R^2$ values ranging from 0.02 to 0.17), suggesting that the current feature set may not fully capture the necessary predictors for these complex targets.
• Feature Importance:
  • Band Gap ($E_g$): The atomic number of the B-site metal ($Z_B$) was identified as the most critical factor influencing the band gap. This aligns with physical principles where B-site elements (e.g., Pb, Bi, or organic molecules) directly determine the electronic structure. A symbolic regression formula derived from GPSR, $E_g = \log(Z_B \times Z_X) + \sqrt{Z_B}$, further confirmed the dominance of B-site and X-site atomic numbers, while indicating the A-site has negligible direct impact on the band structure.
  • Mobility-Lifetime Product ($\mu\tau$): The lattice length parameter $b$ was found to have the greatest impact on $\mu\tau$. Variations in this lattice parameter influence band curvature, effective mass, and defect density, thereby affecting carrier transport.
• Experimental Verification: The synthesized (m-F-PEA)₂PbI₄ single crystal exhibited a band gap of 2.29 eV, closely matching the RFR prediction of 2.23 eV. The device demonstrated a sensitivity of 1033.7 µC Gy⁻¹ cm⁻² and a detection limit of 1.41 µGy s⁻¹. While there were slight deviations in the predicted values for sensitivity and detection limit, the experimental results validated the general applicability of the ML approach. The device also exhibited excellent stability, with low dark current drift and high repeatability over 1254 cycles.

Significance and Claims
The authors assert that this work provides a foundational step toward data-driven design of perovskite X-ray detectors. By constructing an open-source database and applying ML, the study successfully identified that the B-site atomic number is the primary determinant of the band gap and that lattice parameter $b$ is crucial for carrier transport properties.

The paper modestly concludes that while ML models, particularly RFR, show promise in identifying key material descriptors, the predictive accuracy for complex performance metrics like sensitivity and detection limit requires further refinement. The authors suggest that future work should focus on expanding the feature set and improving data quality to enhance model generalizability. They explicitly recommend the continued utilization of Random Forest Regression for analyzing perovskite X-ray detector applications due to its ability to handle non-linear relationships and outliers inherent in experimental data. The study does not claim to have solved the dark current challenge entirely but highlights the utility of ML in narrowing down the critical parameters for material optimization.