The dependence of the conductivity of the films of hafnium oxide HfO_2 synthesized in different modes is studied. Depending on the modes of synthesis, the conductivity of HfO_2 at a fixed electric field of 1.0 MV/cm changes by four orders of magnitude. It is found that the conductivity of HfO_2 is limited by the model of phonon-assisted tunneling between the traps. The thermal and optical energies of the traps W _t = 1.25 eV and W _opt = 2.5 eV, respectively, in HfO_2 are determined. It is found that the exponentially strong scattering of the conductivity of HfO_2 is due to the change in the trap density in a range of 4 × 10^19–2.5 × 10^22 cm^–3. In the cathodoluminescence spectra of HfO_2, a blue band with the energy of 2.7 eV is observed which is due to the oxygen vacancies. A correlation between the trap density and intensity of cathodoluminescence, as well as between the trap density and refractive index, is found. A nondestructive in situ method for the determination of the trap density of hafnium oxide with the use of the measurement of the refractive index is proposed. The optimum values of the concentrations of oxygen vacancies for emitting devices on the basis of the films of HfO_2 are found.