Optimal Structure of Lanthanum-Doped Hafnium Oxide: First-Principle Modeling

The atomic and electronic structure of lanthanum-doped hafnium oxide ($\left.\mathrm{HfO}_{2}: \mathrm{La}\right)$ is studied within the density functional theory simulation. $\mathrm{HfO}_{2}: \mathrm{La}$ is a promising material for resistive and ferroelectric random-access memory elements. By considering all possible spatial configurations of the oxygen vacancy and two lanthanum atoms in the hafnium substitution position in 95-atom supercell of five crystalline phases of HfO
2
, the energetically optimal structures of $\mathrm{HfO}_{2}: \mathrm{La}$ were found. For these structures of crystalline HfO
2
with the 2.1 at. % La content the La atoms are located at a distance of about 5.8 Å from each other, and at least one of the lanthanum atoms is distanced from the oxygen vacancy. These structures are characterized by a bandgap free from defect levels, and the bandgap value is almost the same as that of perfect crystals. It is shown that the presence of La and hydrostatic pressure facilitates the stabilization of the ferroelectric and tetragonal phases of HfO
2
, but these phases remain energetically unfavorable as a bulk crystal.