LDA + U and hybrid functional calculations for defects in ZnO, SnO2, and TiO2

Abstract 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.