Hydrogen Impurity in Yttria: \textit{Ab-Initio} Study by Semi-Local and Hybrid Functionals

A study based on density functional theory calculations was performed for the three charge states of interstitial hydrogen in Yttria. The present calculations were carried out by employing the GGA-PBE and the HSE06 exchange-correlation functional. It is observed that the ground state H$^0$ and H$^-$ configurations are similar in behaviour; these prefer to relax in the O vacant site, with limited structural relaxation. For the neutral and the negative charged systems more two different geometrical configurations occur with higher energies, which evidence the existence of metastable sites of H in the Yttria lattice. The H$^+$ equilibrium state is found only when a strong bond between the impurity ion and an anion, O-H bond of $\sim$1 \AA, is formed. The formation energy of the interstitial impurity is studied, for which amphoteric behaviour is found for this defect and for the ground state structures. These results evidence that hydrogen counteracts the prevailing conductivity of the host lattice, thus passivating any existing electrical levels originated from other doping sources. To compare results with non-equilibrium and short time-scale $\mu$SR measurements, the formation energy of the higher energy configurations were also evaluated. For the Bond O geometrical site, H evidences a donor-dopant behaviour, hence enabling the coexistence of donor behaviour with the ground-state amphoteric behaviour. From the density of states results, and for the H$^0$ and H$^-$ charge states, a defect level was observed in the band gap. For the ground state Vacant O configuration and the metastable Interstitial structure the defect level was found to be slightly above the valence band maximum, hence indicating no dopant-donor character for the Yttria material. But, for the Bond O, local-minimum, configuration, the defect level is located above the middle of the band gap, closer the conduction band.