First principles calculations of intrinsic defects and extrinsic impurities in rutile titanium dioxide

Titanium dioxide has been intensively studied as a wide band-gap transition metal oxide due to its n-type semiconducting property. In this dissertation, first the defect formation enthalpies of Frenkel and Schottky defects in rutile TiO2 are calculated. The results predict that Frenkel defects are more energetically favorable than Schottky defects and both of them prefer to cluster together in TiO2. The possible diffusion routes for interstitial Ti atoms are also investigated.;Secondly, the dependence of defect formation energies on supercell size is investigated. The results indicate that the electrostatic Makov-Payne correction improves the convergence of defect formation energies as a function of supercell size for charged titanium interstitials and vacancies. However this correction gives the wrong sign for defect formation energy correction for charged oxygen vacancies. This is attributed to the shallow nature of the transition levels for oxygen vacancies in TiO2.;Next, a new computational approach that integrates ab initio electronic-structure and thermodynamic calculations is given and applied to determine point defect stability in rutile TiO2 over a range of temperatures, oxygen partial pressures, and stoichiometries. The favored point defects are shown to be controlled by the relative ion size of the defects at low temperatures, and by charge effects at high temperatures. The ordering of the most stable point defects is predicted and found to be almost the same as temperature increases and oxygen partial pressure decreases: titanium vacancy → oxygen vacancy → titanium interstitial. Also it is found that the formation energies of Schottky, Frenkel, and anti-Frenkel defect complexes do not change with the Fermi level. At high temperatures the formation of these complexes will restrict the further formation of single point defects, such as oxygen vacancies. In the study of ambipolar doping behavior of aluminum in TiO2, the concept of pseudo-state is proposed to describe thermodynamic equilibrium procedure between impurities and host ions. It is predicted that at high temperatures aluminum substitutional defects become the predominant dopant in TiO2 while n-type doping of aluminum interstitials is limited by high concentrations of titanium interstitials and oxygen vacancies.;Finally, the origin of shallow level n-type conductivity in rutile TiO2 is discussed. The calculated densities of states for defective structures with fully charged titanium interstitials show a broader lower conduction band, which may enhance short-range cation-cation orbital overlap and thus lead to the formation of shallow donor levels.