We describe and compare defect calculations based on density functional theory within the local density approximation (LDA), the orbital-dependent LDA + U, and using hybrid functionals. Limitations of the LDA in describing defect formation energies and transition levels are discussed, followed by corrections based on the LDA + U, and the use of the hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE). The band-gap error in LDA leads to large uncertainties not only in defect transition levels but also in formation energies.
LDA + U provides a partial correction to the band gap and, when combined with LDA, provides an accurate method for predicting transition levels. Formation energies obtained from the LDA + U/LDA approach depend on the ability of LDA + U to correctly describe the position of the band edges on an absolute energy scale. Although computationally demanding, HSE is demonstrated to be a reliable method for predicting structure and electronic properties of semiconductors, including transition levels and formation energies of defects.