Doped hafnium oxide was shown to exhibit a strong ferroelectric behavior. It was implied that doping allows the stabilization of a HfO2 non-centrosymmetric orthorhombic phase, a prerequisite for ferroelectric behavior. However, a number of reports showed comparable ferroelectric properties in undoped HfO2, although with different behaviors of the remanent polarization upon layer thickness. In this work, the ferroelectric properties and crystalline structure of doped and undoped HfO2 layers as a function of the layer thickness were studied. The results show similar properties for ultrathin layers. Indeed, both show a linear increase in the orthorhombic/tetragonal crystalline phase amount and of remanent polarization as a function of thickness up to 7 nm. For higher thicknesses, a strong increase in the monoclinic phase is observed in undoped layers alongside a strong decrease in the remanent polarization whereas, for doped layers, the remanent polarization continues to increase with thickness. The experimental results suggest that the stabilization of the undoped HfO2 orthorhombic ferroelectric phase is due to mechanical stress, which is particularly high in ultrathin layers but relaxes for thicker layers.