Machine learning the band gap properties of kesterite I$_2$-II-IV-V$_4$ quaternary compounds for photovoltaics applications

Kesterite I$_2$-II-IV-V$_4$ semiconductors are promising solar absorbers for photovoltaics applications. The band gap and it's character, either direct or indirect, are fundamental properties determining photovoltaic-device efficiency. We use a combination of accurate first-principles calculations and machine learning to predict the properties of the band gap for a large number of kesterite I$_2$-II-IV-V$_4$ semiconductors. In determining the magnitude of the fundamental gap, we compare results for a number of machine-learning models, and achieve a root mean squared error as low as 283 meV; the best results are achieved using support-vector regression with a radial-bias kernel. This error is well within the uncertainty of even the most advanced first-principles methods for calculating semiconductor band gaps. Predicting the direct--indirect property of the band gap is more challenging. After significant feature engineering, we are able to train a classifier that predicts the nature of the band gap with an accuracy of 89 \% using logistic regression. Using these trained models, the band gap properties of 1568 kesterite I$_2$-II-IV-V$_4$ compounds are predicted. We find 717 compounds with band gaps in the range 0.5 -- 2.5 eV that can potentially act as solar absorbers, and 242 materials with a band gap in the ``\emph{optimum range}" of 1.2 -- 1.8 eV. The stability of these 242 compounds is assessed by calculating the Energy Above Hull using the Materials Project database, and the band gaps are verified using hybrid functional calculations; in the end, we identify 25 compounds that are expected to be synthesizable, and have a band gap in the range 1.2 -- 1.8 eV -- most of which are previously unexplored. These results will be useful in the materials engineering of efficient photovoltaic devices.