Simulation and Machine Learning Prediction of the Dielectric Properties of Pure ZnO: Real ε₁(E,T) and Imaginary ε₂(E,T) Parts Using the Tauc–Lorentz–Kramers–Kronig Formalism

Aims: This study presents the theoretical modelling and machine-learning-based prediction of the dielectric properties of pure zinc oxide (ZnO) as a function of photon energy and temperature. Study Design: Theoretical modelling and machine-learning-based prediction. Place and Duration of Study: Solar Energy Materials and Systems Laboratory (LASES), Faculty of Science and Technology, Université Cheikh Anta Diop – Dakar, Senegal. Methodology: The complex dielectric function is described using the Tauc–Lorentz model, in which the real part, ε₁(E,T), is obtained through the Kramers–Kronig transformation, while the temperature dependence of the optical band gap is incorporated using the empirical Varshni law. The simulated data constitute a reference dataset of 4,500 samples (inputs: photon energy E and temperature T; outputs: ε₁ and ε₂), randomly split into a training set (80%, 3,600 samples) and an independent test set (20%, 900 samples). This dataset is used to train and evaluate two machine learning models: Random Forest (RF) and Multi-Layer Perceptron (MLP). Model validation is based on the coefficient of determination (R²), the root mean square error (RMSE), residual analysis, parity plots, and energy-dependent spectral comparison at T = 300 K. Results: Over the temperature range of 0–400 K, the band-gap energy decreases from 3.441 to 3.373 eV, corresponding to a redshift of 68 meV. The maximum of ε₁ increases from 6.931 to 7.666 (+10.6%), while the maximum of ε₂ increases from 2.939 to 3.805 (+29.5%) and shifts from 3.961 to 3.905 eV. For ε₁, the MLP model gives the best performance (R² = 0.999330, RMSE = 0.016569), compared with the RF model (R² = 0.998770, RMSE = 0.022444). For ε₂, the trend is reversed: the RF model outperforms the MLP model (R² = 0.999526, RMSE = 0.016334 versus R² = 0.999347, RMSE = 0.019173). Conclusion: Both models reproduce the TL+KK+Varshni reference model with very high accuracy and provide a fast surrogate for numerical Kramers–Kronig calculations. This agreement is a validation against the theoretical reference model, not an experimental validation. The main limitation is the assumption of a temperature-independent broadening parameter C, which will be addressed in future work by introducing a Bose–Einstein-type temperature-dependent function C(T) and by comparison with experimental ellipsometric data.