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

Abstract

First-principles calculations have been performed to study the formation of defect complexes in Ti doped α-Al2O3 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 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-Al2O3 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.

Control of charge state of dopants in insulating crystals: Case study of Ti-doped sapphire

“…In this paper we present a thorough investigation of the problem of control of the charge state of titanium in Ti:sapphire. Our investigation compliments the study [14,15] and our recent study [1].…”

“…They differ from ones calculated in Refs. [1,15], where this correction was not taken into account. The concentration of electrically neutral defects depends only on its own formation energy:ñ…”

“…In this paper we consider the problem of control of the charge state of dopants with reference to Ti-doped sapphire crystals. Some elements of our approach were already presented in our previous paper [1], where the results of DFT study of defect complexes of Ti-doped sapphire were reported.…”

“…Energetics of defect complexes in Ti-doped sapphire was studied in detail in Ref. [1]. The formation energies and the binding energy of pairs, triples and quadruples formed by Ti 3+ , Ti 4+ and V 3− Al were calculated.…”

Atomic structures of Ti‐doped α‐Al2O3 Σ13 grain boundary with a small amount of Si impurity

“…We again confirmed that Ti segregated at both the type‐I and type‐II grain boundary cores. By referring the Ti‐ L 2,3 edges of Ti 2 O 3 (Ti 3+ ) and TiO 2 (rutile, Ti 4+ ), 39 the valence state of Ti in the type‐I grain boundary core is determined to be 3+, although it has been proposed that the valence state of the Ti doped in α‐Al 2 O 3 single crystal is basically 4+ when the sample is annealed in air 40,41 . Since the valence state of Al is considered to be 3+, the present Ti 3+ substitutes Al site at the type‐I grain boundary core without any Al or O vacancies.…”