Band-edge levels in semiconductors and insulators: Hybrid density functional theory versus many-body perturbation theory

We compare band-edge levels as obtained with hybrid functionals and $GW$ perturbation theory for a wide class of materials. For $sp$-bonded semiconductors, a close agreement is demonstrated. However, deviations for other materials are more significant and range up to 1 eV for the most ionic insulators. These differences stem from the degree of compensation between exchange and correlation contributions which varies among the band-edge states in $GW$ calculations. Consequently, the two schemes might deliver significantly different level alignments in defect and band-offset studies, particularly when involving wide band-gap materials.