New energy gap-refractive index relationship: A nonlinear regression analysis using python

The refractive index is a fundamental optical property that controls light propagation in different types of materials and plays a major role in optoelectronics, photonics and semiconductor device applications. Since determining the refractive index experimentally often requires complex setups, developing theoretical and empirical models are good alternatives. Most existing models, including those by Moss, Reddy and Herve, relate the refractive index (n) to the bandgap ( E g ), but their accuracy depends on empirical constants. In order to understand the exact functional dependency of the correlation equation, I performed a comprehensive nonlinear regression analysis in python by systematically investigating and crosschecking logarithmic, polynomial, exponential, hyperbolic, square root, rational and non-rational functions. In this work, I present a novel empirical model for predicting the refractive index over a wide bandgap range of 0–10 eV. The model combines a logarithmic dependency on the bandgap, a linear bandgap term, and constant fitting parameters, which together capture the refractive index variation with improved accuracy compared to existing approaches. Statistical methods (MSE, R 2 , MAPE) validate the accuracy of the new model, while box plots, residual analysis, and t-tests confirm its reliability. Furthermore, boxplots, parity plots, residual error analysis and paired t-test all confirmed its reliability. The findings demonstrate that the new model shows better performance than a number of conventional models, especially in the case of minimizing errors over a wide range of bandgaps. For researches in condensed matter physics, semiconductor industry and materials science, the proposed model offers a reliable alternative for refractive index estimation. • Best model confirmed by comparison with all available models. • Tested multiple mathematical functions to find the optimal equation. • Developed using 100 + experimental data points for high accuracy. • Achieved the best error metrics, including R² and MSE. • Explained the physical significance of the proposed model.