Oxygen vacancies in amorphous-Ta$_{2}$O$_{5}$ from first-principles calculations

Oxygen vacancies are thought to play a crucial role in the electrical and optical properties of tantalum pentoxide (Ta$_{2}$O$_{5}$) devices. Even though numerous experimental studies on oxygen vacancies in Ta$_{2}$O$_{5}$ exist, experimentally detected defects are ambiguously identified due to the absence of an accurate and conclusive theoretical analysis. We investigate oxygen vacancies in amorphous Ta$_{2}$O$_{5}$ with first-principles calculations based on hybrid density functional theory. The calculated thermodynamic and optical transition levels of stable oxygen vacancies are in good agreement with measured values from a variety of experimental methods, providing conclusive clues for the identification of the defect states observed in experiments. We determine the concentration of oxygen vacancies and their dominant oxidation state as a function of growth conditions. We analyze the characteristics of extra electrons introduced by donor-like oxygen vacancies, which include the formation of polarons. Our results provide insight into the fundamental properties of oxygen vacancies in Ta$_{2}$O$_{5}$, which is essential to controlling the properties of films and optimize the performance of devices.