Accurate gap levels and their role in the reliability of other calculated defect properties

The functionality of semiconductors and insulators depends mainly on defects which modify the electronic, optical, and magnetic spectra through their gap levels. Accurate calculation of the latter is not only important for the experimental identification of the defect, but influences also the accuracy of other calculated defect properties, and is the most difficult challenge for defect theory. The electron self-interaction error in the standard implementations of ab initio density functional theory causes a severe underestimation of the band gap, leading to a corresponding uncertainty in the defect level positions in it. This is a widely known problem which is usually dealt with by a posteriori corrections. A wide range of corrections schemes are used, ranging from ad hoc scaling or shifting, through procedures of limited validity (like the scissor operator or various alignment schemes), to more rigorous quasiparticle corrections based on many-body perturbation theory. We will demonstrate in this paper that consequences of the gap error must to be taken into account in the total energy, and simply correcting the band energy with the gap level shifts is of limited applicability. Therefore, the self-consistent determination of the total energy, free of the gap-error, is preferred. We will show that semi-empirical screened hybrid functionals can successfully be used for this purpose. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim