Electronic and optical properties of native point defects in CuInS$_2$ and CuGaS$_2$

We present a detailed study of common intrinsic defects in CuInS$_2$ and CuGaS$_2$ using the Heyd, Scuseria and Ernzerhof (HSE) hybrid functional scheme. The impact of the two HSE parameters, $\alpha$ and $\omega$ on the band gap and compliance with the generalized Koopmans' theorem is investigated. Using the formation energy formalism and calculated thermodynamic charge-transition levels, we assess the electronic properties of the defects and explore the connection of charge-transition levels with optical-transition levels. Calculated Franck-Condon shifts for emission highlight the importance of lattice relaxation for the attribution of defects to luminescence peaks. Our results show that once these effects are included, predictions become closer to photoluminescence measurements available in literature.