We combine experiments and simulations to investigate leakage current and breakdown (BD) in stoichiometric and sub-stoichiometric hafnium oxides. Using charge-transport simulations based on phonon-assisted carrier tunneling between trap sites, we demonstrate that higher currents generally observed in HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> are due to a higher density of the as-grown oxygen vacancy defects assisting the charge transport. Reduction of the dielectric BD field ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BD</sub> ) in HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> is explained by the lower zero-field activation energy ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A,G</sub> ) of the defect generation process, as extracted from time-dependent dielectric BD experiments.