Effect of thickness and surface composition on the stability of polarization in ferroelectric Hf x Zr 1 - x O 2 thin films
Using density functional theory, we find that tailoring the surface composition provides a route to stabilize the polar phases of the promising ferroelectric material, Hf x Zr 1-x O 2 . First, we show that for pure Hf O 2 , controlling the positively polarized surface to be relatively oxygen rich adequately screens the ferroelectric surface charges and stabilizes the polar orthorhombic phase. We then demonstrate that the ferroelectric polarization, as measured by the structural polar displacements, increases with decreasing thickness, leading to the emergence of a polar rhombohedral-like phase at the ultrathin limit (1.5 unit cells). Our findings extend to the cases of Hf 0.5 Zr 0.5 O 2 and Zr O 2 , both of which have surface energy landscapes similar to that of Hf O 2 . In conclusion, these findings are consistent with and offer insights into the observed absence of a ferroelectric thickness limit in Hf x Zr 1-x O 2 -based thin films.