  The oxygen vacancy is a crucial intrinsic defect in metal-ultrathin oxide
semiconductor heterostructures, and its formation at an interface is of great
importance in determining the device performance and degradation. This paper
presents an ab initio thermodynamic study of oxygen vacancies at metal/oxide
interfaces. Electronic energies and entropies are calculated for defective
interface systems, as a function of interface-vacancy distance. The study
indicates that oxygen vacancies near the interface modify its bonding
structure, and significantly change the thermodynamic properties of the system
(i.e., electronic energy and entropy) compared to bulk-like oxygen vacancies.
We illustrate that different factors, including the vacancy location dependence
on the energy and entropy, the temperature dependence on the entropy, and the
temperature and partial pressure dependence on the oxygen chemical potential,
are all important in determining the Gibbs free energy of formation of oxygen
vacancy.
