The impact of charge compensated and uncompensated strontium defects on the stabilization of the ferroelectric phase in HfO$_2$

Abstract: Different dopants with their specific dopant concentration can be utilized to produce ferroelectric HfO$2$ thin films. In this work it is explored for the example of Sr in a comprehensive first-principles study. Density functional calculations reveal structure, formation energy and total energy of the Sr related defects in HfO$_2$. We found the charge compensated defect including an associated oxygen vacancy Sr$\text{Hf}$V$\text{O}$ to strongly favour the non-ferroelectric, tetragonal P4$\text{2}$/mnc phase energetically. In contrast, the uncompensated defect without oxygen vacancy Sr$\text{Hf}$ favours the ferroelectric, orthorhombic Pca2$\text{1}$ phase. According to the formation energy the uncompensated defect can form easily under oxygen rich conditions in the production process. Low oxygen partial pressure existing over the lifetime promotes the loss of oxygen leading to V$\text{O}$ and, thus, the destabilization of the ferroelectric, orthorhombic Pca2$\text{1}$ phase accompanied by an increase of the leakage current. This study attempts to fundamentally explain the stabilization of the ferroelectric, orthorhombic Pca2$_\text{1}$ phase by doping.