Different causes for ferroelectric properties in hafnium oxide were discussed during the last decade including various dopants, stress, electrode materials, and surface energy from different grain sizes. Recently, the focus shifted to the impact of oxygen vacancies on the phase formation process. In this progress report, the recent understanding of the influence of oxygen supplied during deposition on the structural phase formation process is reviewed and supplemented with new data for mixed Hf _x Zr_1-xO _y films. Even though polar and non-polar Hf _x Zr_{1- x} O _y thin films are well characterized, little is known about the impact of oxygen exposure during the deposition process. Here, a combination of structural and electrical characterization is applied to investigate the influence of the oxygen and zirconium content on the crystallization process during ALD deposition in comparison to other deposition techniques. Different polarization properties are assessed which correlate to the determined phase of the film. Optimized oxygen pulse times can enable the crystallization of Hf _x Zr_{1- x} O _y in a polar orthorhombic phase rather than a non-polar monoclinic and tetragonal phase.