Hf_xZr_1-xO₂ and lanthanum-doped Hf_xZr_1-xO₂:La thin films are candidates for applications in ferroelectric random-access memory. Here, we explore the atomic and electronic structure of Hf_0.5Zr_0.5O₂ and Hf_0.5Zr_0.5O₂:La thin films grown by atomic layer deposition. Using X-ray photoelectron spectroscopy, it was found that the oxides under study have an almost identical electronic structure and a bandgap of about 5.4 eV. The Hf_0.5Zr_0.5O₂:La film was shown to consist of the mixture of Hf_0.5Zr_0.5O₂ and La₂O₃ phases. The bombardment with argon ions of the studied films leads to oxygen vacancy generation in the near-surface layer. The oxygen vacancy concentrations in the bombarded films were evaluated from the comparison of experimental valence band photoelectron spectra with the theoretical ones calculated using the density functional theory.