  In this study, we demonstrated experimentally and theoretically that oxygen
vacancies are responsible for the charge transport in HfO$_2$. Basing on the
model of phonon-assisted tunneling between traps, and assuming that the
electron traps are oxygen vacancies, good quantitative agreement between the
experimental and theoretical data of current-voltage characteristics were
achieved. The thermal trap energy of 1.25 eV in HfO$_2$ was determined based on
the charge transport experiments.
