Physics-Informed Feature Engineering for Machine Learning Prediction of Tight Binding Parameters in III-V Semiconductors

Abstract

 The empirical sp tight-binding model is used for the atomistic simulation of III-V semiconductor nanostructures, but its parameters must be fitted per material against reference data by numerical optimisation. Most machine learning alternatives rely on large density functional theory datasets. This work predicts sp tight binding parameters for nine III-V binary compounds from experimentally accessible observables without first-principles input. A physics-informed feature set is grown from 6 to 12 to 28 descriptors, and three models, namely, support vector regression, gradient boosting, and a multilayer perceptron, are compared on the band gap, spin-orbit splitting, and effective mass. In this setup, the band gap, spin-orbit splitting, and effective mass serve both as input features and evaluation targets. For the band gap and effective mass, the reported error partly reflects a local inversion of the model rather than an independent prediction. Descriptor relevance is quantified by permutation importance, Shapley Additive Explanations analysis, and subset selection. Support vector regression with 28 features gives the lowest bandgap error (1.14%), gradient boosting gives the lowest spin-orbit error (0.85%), and no model is best for all three targets. For spin-orbit splitting, an in-sample subset of six atomic descriptors lowers the error by about 45% relative to the six raw observables, indicating that feature choice matters more than count. Importance analysis ranks a fourth-power atomic-number descriptor second for this target, which is consistent with the atomic origin of spin-orbit coupling, though not supplied to the model. A larger feature set is not always beneficial: for the effective mass, the multilayer perceptron error rises from 0.0023 m with 12 features to 0.0234 m with 28 features as the feature count approaches the number of distinct training materials. A leave-one-material-out test shows that these results do not extend to compounds outside the training set: the errors increase substantially for held-out materials, and the in-sample feature-selection advantage does not carry over. The results indicate that physics-informed feature engineering supports accurate, interpretable parameter prediction in the small-data regime.