  Recent experimental observations indicate that bulk $Sc_2O_3$ (~200 nm
thick), an insulator at room temperature and pressure, must act as a good
electronic conductor during thermionic cathode operation, leading to the
observed high emitted current densities and overall superior emission
properties over conventional thermionic emitters which do not contain
$Sc_2O_3$. Here, we employ ab initio methods using both semilocal and hybrid
functionals to calculate the intrinsic defect energetics of Sc and O vacancies
and interstitials and their effects on the electronic properties of $Sc_2O_3$
in an effort to explain the good conduction of $Sc_2O_3$ observed in
experiment. The defect energetics were used in an equilibrium defect model to
calculate the concentrations of defects and their compensating electron and
hole concentrations at equilibrium. Overall, our results indicate that the
conductivity of $Sc_2O_3$ solely due to the presence of intrinsic defects in
the cathode operating environment is unlikely to be high enough to maintain the
magnitude of emitted current densities obtained from experiment, and that
presence of impurities are necessary to raise the conductivity of $Sc_2O_3$ to
a high enough value to explain the current densities observed in experiment.
The necessary minimum impurity concentration to impart sufficient electronic
conduction is very small (approximately $7.5x10^{-3}$ ppm) and is probably
present in all experiments.
