Work Functions of Sc$_{2}$O$_{3}$ surfaces containing Ba/BaO for thermionic electron emitters using Density Functional Theory

The work functions of (001), (011) and (111) bixbyite Sc$_{2}$O$_{3}$ surfaces with adsorbed Ba atoms, Ba-O dimers, and rocksalt BaO films have been calculated using Density Functional Theory (DFT) to investigate the role Ba plays in producing the low experimental scandate cathode work functions of $\sim $1.1-1.4 eV. Our lowest calculated work function was 1.48 eV for a single rocksalt film layer of BaO (011) on Sc$_{2}$O$_{3}$ (011). Work functions for Ba atom and Ba-O dimer adsorption on Sc$_{2}$O$_{3}$ (011) and (111) surfaces ranged between 2.1 to 3.7 eV, and depended on the Sc$_{2}$O$_{3}$ surface termination, coverage density, and adsorption geometry employed. We found the total work function change of a surface with adsorbed species can be decomposed into two parts: the dipole component and Fermi level shift component. The dipole component is described by the Helmholtz equation, and takes into account charge transfer into valence band states and surface charge rearrangement. The Fermi level shift is a result of either mobile charge transfer into conduction band states, or a restructuring of the valence band, which can also modify the work function.