The energy levels of atomically localized defects, calculated using a semi-local and hybrid density-functional scheme were compared for materials with various band-gaps. Since the second scheme partially relieved the band-gap problem, the study described how the calculated defect levels shifted when the band-gap approached the experimental value. When suitably aligned, the defect levels obtained from total-energy differences corresponded closely: exhibiting average shifts of at most 0.2eV, regardless of the band-gap. Systematic deviations from the ideal alignment increased with the extent of the defect wave function.

Defect Energy Levels in Density Functional Calculations - Alignment and Band Gap Problem. A.Alkauskas, P.Broqvist, A.Pasquarello: Physical Review Letters, 2008, 101[4], 046405