Effects of Strain and Film Thickness on the Stability of the Rhombohedral Phase of HfO2

The discovery of ferroelectric polarization in ${\mathrm{Hf}\mathrm{O}}_{2}$-based ultrathin films has spawned much interest due to their potential applications in data storage. In 2018, an R3m rhombohedral phase was proposed to be responsible for the emergence of ferroelectricity in the [111]-oriented ${\mathrm{Hf}}_{0.5}{\mathrm{Zr}}_{0.5}{\mathrm{O}}_{2}$ thin films, but the fundamental mechanism of ferroelectric polarization in such films has remained poorly understood. In this paper, we employ density-functional-theory calculations to investigate structural and polarization properties of the R3m ${\mathrm{Hf}\mathrm{O}}_{2}$ phase. We find that the film thickness and in-plane compressive-strain effects play a key role in stabilizing the R3m phase, leading to robust ferroelectricity of [111]-oriented R3m ${\mathrm{Hf}\mathrm{O}}_{2}$.