Defect complexes in Ti-doped sapphire: A first principles study

摘要

First-principles calculations have been performed to study the formation of defect complexes in Ti doped α-Al_2O_3 crystals. The formation energies of isolated Ti~(3+) and Ti~(4+) defects, pairs, triples, and quadruples of Ti ions and Al vacancies are computed under different equilibrium conditions of Al-Ti-O related phases. Taking into account the charge neutrality of the whole system, we determine the equilibrium concentrations of simple and complex defects as well as the total equilibrium concentration of Ti in an α-Al_2O_3 crystal. It is shown that the equilibrium concentration of complex defects can be on the same order of or even larger than the concentrations of isolated substitutional Ti~(3+) and Ti~(4+) defects. It is found that in Ti-deficient conditions, the relative fraction of isolated defects increases and the balance is shifted towards Ti~(4+) defects. A universal relation between equilibrium concentrations of isolated and complex defects is obtained. The band structure of the system with complex defects is calculated and extra levels inside the band gap caused by such defects are found.