Fig. 3: Charge compensation and localization from point defects in (Mg0.2Ni0.2Co0.2Cu0.2Zn0.2)O.
a Formation energy of oxygen and cation vacancies as a function of Fermi level assuming bulk growth conditions (1000 °C, air). An oxygen vacancy is a deep donor while cation vacancies are deep acceptors. b The histogram and fits of the change in Bader charge of 1NN cations before and after the formation of an oxygen vacancy. The inset illustrates the local atomic structure of the entropy-stabilized oxide with the lowest-formation-energy oxygen vacancy and the isosurface of the band-decomposed charge density at the conduction band minimum (CBM). The value of the isosurface is chosen to be 50% of the charge density. The charge distribution of excess electrons from an oxygen vacancy (yellow) is localized on the nearest Cu atoms. c Calculated Fermi-level pinning energy as a function of oxygen chemical potential. The characteristic oxygen chemical potential and Fermi level pinning energy under bulk (1000 °C, air) synthesis conditions as well as standard ambient temperature and pressure (25 °C, air) are specified. Under typical growth conditions, the Fermi energy is pinned at a deep energy level within the band gap, in agreement with the observation of the electrically insulating state of (Mg0.2Ni0.2Co0.2Cu0.2Zn0.2)O. d Calculated equilibrium Fermi energy level as a function of Cu mole fraction. The mole fraction for the non-variable cations equally composes the remaining mole fraction. Increasing Cu composition leads to increased charged oxygen vacancy formation, which enhances the equilibrium Fermi level toward CBM. e Calculated equilibrium vacancy concentration of oxygen and cations as a function of Cu mole fraction. By utilizing the local configuration effect on oxygen vacancy formation energy and the subsequent cation vacancy formation for charge neutrality, the vacancy density of ESO can be tuned by cation mole fraction.
