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Kesterite I$_2$-II-IV-V$_4$ semiconductors are promising solar absorbers forphotovoltaics applications. The band gap and it's character, either direct orindirect, are fundamental properties determining photovoltaic-deviceefficiency. We use a combination of accurate first-principles calculations andmachine learning to predict the properties of the band gap for a large numberof kesterite I$_2$-II-IV-V$_4$ semiconductors. In determining the magnitude ofthe fundamental gap, we compare results for a number of machine-learningmodels, and achieve a root mean squared error as low as 283 meV; the bestresults are achieved using support-vector regression with a radial-bias kernel.This error is well within the uncertainty of even the most advancedfirst-principles methods for calculating semiconductor band gaps. Predictingthe direct--indirect property of the band gap is more challenging. Aftersignificant feature engineering, we are able to train a classifier thatpredicts the nature of the band gap with an accuracy of 89 \% using logisticregression. Using these trained models, the band gap properties of 1568kesterite I$_2$-II-IV-V$_4$ compounds are predicted. We find 717 compounds withband gaps in the range 0.5 -- 2.5 eV that can potentially act as solarabsorbers, and 242 materials with a band gap in the ``\emph{optimum range}" of1.2 -- 1.8 eV. The stability of these 242 compounds is assessed by calculatingthe Energy Above Hull using the Materials Project database, and the band gapsare verified using hybrid functional calculations; in the end, we identify 25compounds that are expected to be synthesizable, and have a band gap in therange 1.2 -- 1.8 eV -- most of which are previously unexplored. These resultswill be useful in the materials engineering of efficient photovoltaic devices.

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