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An influence of Mg and Si dopants on the formation energies and theconcentration of point defects in yttrium aluminum garnet (YAG) is studiedusing the density functional approach. The formation energies of Mg and Sisubstitutional and interstitial defects, native point defects and defectcomplexes versus the oxygen chemical potential are obtained. It is shown thatin YAG doped with Mg, negatively charged Mg substitutional defects arecompensated by free carriers (holes) and positively charged oxygen vacancies,whereas interstitial Mg ions play a minor role. The concentration of oxygenvacancies increases under an increase in the concentration of Mg ions. In YAGdoped with Si, positively charged Si substitutional defects are compensated bynegatively changed isolated cation vacancies and complexes of Si ions andcation vacancies. Under an increase in the concentration of Si ions most of Aland Y vacancies bind in complexes with Si ions. As a result, the concentrationof isolated cation vacancies depends nonmonotonically on the concentration ofSi ions. The maximum of the concentration of isolated cation vacancies isreached at $0.02 - 0.04$ at. % of Si, depending on sintering conditions. Mg -Si complexes have very low formation energies. Due to formation of suchcomplexes, Si and Mg increases the solubility of each other in YAG. At the sametime Mg - Si complexes do not influence the concentration of anion and cationvacancies. The overall concentration of vacancies in YAG codoped with Mg and Siin equal atomic concentrations is low. At an excess concentration of Si or Mgthe concentration of vacancies increases by orders of magnitude.

Energetics of point defects in yttrium aluminum garnet doped with Mg and Si