Koopmans' tuning of HSE hybrid density functional for calculations of defects in semiconductors: A case study of carbon acceptor in GaN

Hybrid density functional theory has become a standard method for calculations of defects in semiconductors. The majority of work in this field is done using hybrid functionals tuned to reproduce the experimental bandgap of the host material. This approach usually yields results in reasonable agreement with the experiment. Alternatively, hybrid functional can be tuned to fulfill the generalized Koopmans' condition for defect orbitals, which cancels self-interaction energy and restores the linear behavior of energy with respect to electron occupation. Here, we investigate the methods of hybrid functional tuning, which both satisfy the generalized Koopmans' condition and reproduce the experimental bandgap, using one of the most well-studied defects in GaN, carbon acceptor. We test different charged defect correction schemes, the influence of Ga3d-electrons, and compare the results with accurate photoluminescence measurements. We find that using different charged defect correction methods can lead to substantially different hybrid functional parametrizations. However, the calculated optical properties of the carbon acceptor are found to be weakly dependent on specific parameters.