Ab initio thermodynamic characteristics of the formation of oxygen vacancies, and boron, carbon, and nitrogen impurity centers in anatase

Using the ab initio projector augmented wave (PAW) method, calculations are performed for the electronic energy-band structure of titanium dioxide having the structure of anatase doped with boron, nitrogen, and carbon. Thermodynamic characteristics are determined for the formation of impurity centers, such as the preference energy for the interstitial position, the energy of impurity oxidation, and the energy of oxygen vacancy formation. It is shown that under the conditions of thermodynamic equilibrium the interstitial position of boron atoms is stable, whereas carbon atoms, depending on the oxygen pressure, can occupy both interstitial positions and substitutional positions of oxygen atoms, and nitrogen atoms replace oxygen atoms. It is shown that the presence of oxygen vacancies promotes the thermodynamic stability of carbon and nitrogen atoms. The obtained densities of electronic states correspond to ESR spectroscopy data, which indicates the presence of spin-polarized electrons in the states of the oxygen vacancy.