Interface effects on calculated defect levels for oxide defects

Density functional theory (DFT) has had impressive recent success predicting defect levels in insulators and semiconductors [Schultz and von Lillienfeld, 2009]. Such success requires care in accounting for long-range electrostatic effects. Recently, Komsa and Pasquarello have started to address this problem in systems with interfaces. We report a multiscale technique for calculating electrostatic energies for charged defects in oxide of the metal-oxide-silicon (MOS) system, but where account is taken of substrate doping density, oxide thickness, and gate bias. We use device modeling to calculate electric fields for a point charge a fixed distance from the interface, and used the field to numerically calculate the long-range electrostatic interactions. We find, for example, that defect levels in the oxide do depend on both the magnitude and the polarity the substrate doping density. Furthermore, below 20 {\AA}, oxide thickness also has significant effects. So, transferring results directly from bulk calculations leads to inaccuracies up to 0.5 eV-- half of the silicon band gap. We will present trends in defect levels as a function of device parameters. We show that these results explain previous experimental results, and we comment on their potential impact on models for NBTI.