Theoretical Prediction of Intrinsic Self-Trapping of Electrons and Holes in Monoclinic ${\mathrm{HfO}}_2$

We predict, by means of ab initio calculations, stable electron and hole polaron states in perfect monoclinic ${\mathrm{HfO}}_2$. Hole polarons are localized on oxygen atoms in the two oxygen sublattices. An electron polaron is localized on hafnium atoms. Small barriers for polaron hopping suggest relatively high mobility of trapped charges. The one-electron energy levels in the gap, optical transition energies and ESR $g$-tensor components are calculated.

Figure 1

Scheme of the lattice relaxation and spin localization in the three polaronic states. Left part shows the lattice relaxation and right part shows an isosurface ($\mathrm{\text{value}}=0.007$) of the spin distribution in the area of the polaron. (a) corresponds to a self-trapped electron, (b) to a self-trapped hole in 3C oxygen, and (c) to a self-trapped hole in 4C oxygen. Bright balls represent Hf atoms and dark balls represent O atoms.

Figure 2

(a) Density of states of $m\mathrm{\text{−}}{\mathrm{HfO}}_2$ with the polaron states in the gap region marked by arrows. (b) Schematic of the optical transitions involving hole and electron polarons. Resonant states are indicated by dotted lines.