Ab initio search for new $p$-type transparent conductors among oxide sulfides

Optimal $p$-type, i.e., hole-conducting, transparent materials must meet the design metrics of large band gap for transparency, and light hole effective masses and large hole content for good $p$-type conductivity. The oxide sulfides could potentially satisfy these design metrics better than oxides do, owing to the stronger hybridization between the S $p$ and metal orbitals that can produce a more dispersive valence band maximum (VBM) and lighter hole masses than in oxides. LaOCuS is the prototype $p$-type transparent conductor (TC) among oxide sulfides. Here, we perform a density functional study of $\sim 30$ oxide sulfides, based on transition metals and column II and III elements, to identify compounds in this set that meet the design metrics for $p$-type TCs. We screen these materials using band gaps and hole effective masses. The analysis of the VBM wavefunctions shows that these oxide sulfides can be classified into ``band-mixed,'' with a continuous distribution of the wavefunction on both anions, and ``band-segregated,'' with the VBM mostly originating from one of the anions. The correlation between the type of VBM wavefunction and the O and S arrangement in the material (anion mixed vs. anion segregated) provides a designing criterion for new mixed-anion $p$-type TCs.