Energetics of point defects in yttrium aluminum garnet doped with Mg and Si
An influence of Mg and Si dopants on the formation energies and the concentration of point defects in yttrium aluminum garnet (YAG) is studied using the density functional approach. The formation energies of Mg and Si substitutional and interstitial defects, native point defects and defect complexes versus the oxygen chemical potential are obtained. It is shown that in YAG doped with Mg, negatively charged Mg substitutional defects are compensated by free carriers (holes) and positively charged oxygen vacancies, whereas interstitial Mg ions play a minor role. The concentration of oxygen vacancies increases under an increase in the concentration of Mg ions. In YAG doped with Si, positively charged Si substitutional defects are compensated by negatively changed isolated cation vacancies and complexes of Si ions and cation vacancies. Under an increase in the concentration of Si ions most of Al and Y vacancies bind in complexes with Si ions. As a result, the concentration of isolated cation vacancies depends nonmonotonically on the concentration of Si ions. The maximum of the concentration of isolated cation vacancies is reached at $0.02 - 0.04$ at. % of Si, depending on sintering conditions. Mg - Si complexes have very low formation energies. Due to formation of such complexes, Si and Mg increases the solubility of each other in YAG. At the same time Mg - Si complexes do not influence the concentration of anion and cation vacancies. The overall concentration of vacancies in YAG codoped with Mg and Si in equal atomic concentrations is low. At an excess concentration of Si or Mg the concentration of vacancies increases by orders of magnitude.