Electronic structure of oxygen vacancies in the orthorhombic noncentrosymmetric phase Hf$_{0.5}$Zr$_{0.5}$O$_2$

The electronic structure of stoichiometric and oxygen-depleted Hf$_{0.5}$Zr$_{0.5}$O$_2$ in the orthorhombic noncentrosymmetric phase has been studied by X-ray photoelectron spectroscopy and quantum-chemical simulation based on the density functional theory. It has been established that the ion-etching-induced peak in the photoelectron emission spectrum with the energy above the top of the o-Hf$_{0.5}$Zr$_{0.5}$O$_2$ valence band is due to oxygen vacancies. A method of estimating the density of oxygen vacancies from the comparison of the experimental and theoretical photoelectron spectra of the valence band has been proposed. It has been established that oxygen polyvacancies in o-Hf$_{0.5}$Zr$_{0.5}$O$_2$ are not formed: the energetically favorable spatial arrangement of oxygen vacancies in a crystal corresponds to noninteracting oxygen vacancies distant from each other.