Impact of Zr substitution on the electronic structure of ferroelectric hafnia

Abstract

$\mathrm{Hf}{\mathrm{O}}_2$-based dielectrics are promising for nanoscale ferroelectric applications, and the most favorable material within the family is Zr-substituted hafnia, i.e., $\mathrm{H}{\mathrm{f}}_{1-\mathrm{x}}\mathrm{Z}{\mathrm{r}}_{\mathrm{x}}{\mathrm{O}}_2$ (HZO). The extent of Zr substitution can be great, and x is commonly set to 0.5. However, the band gap of $\mathrm{Zr}{\mathrm{O}}_2$ is lower than $\mathrm{Hf}{\mathrm{O}}_2$, thus it is uncertain how the Zr content should influence the electronic band structure of HZO. A reduced band gap is detrimental to the cycling endurance as charge injection and dielectric breakdown would become easier. Another issue is regarding the comparison on the band gaps between $\mathrm{Hf}{\mathrm{O}}_2$/$\mathrm{Zr}{\mathrm{O}}_2$ superlattices and HZO solid-state solutions. In this work we systematically investigated the electronic structures of $\mathrm{Hf}{\mathrm{O}}_2$, $\mathrm{Zr}{\mathrm{O}}_2$ and HZO using self-energy corrected density functional theory. In particular, the conduction band minimum of $Pca{2}_1$-$\mathrm{Hf}{\mathrm{O}}_2$ is found to lie at an ordinary k-point on the Brillouin zone border, not related to any interlines between high-symmetry k-points. Moreover, the rule of HZO band gap variation with respect to x has been extracted. The physical mechanisms for the exponential reduction regime and linear decay regime have been revealed. The band gaps of $\mathrm{Hf}{\mathrm{O}}_2$/$\mathrm{Zr}{\mathrm{O}}_2$ ferroelectric superlattices are investigated in a systematic manner, and the reason why the superlattice could possess a band gap lower than that of $\mathrm{Zr}{\mathrm{O}}_2$ is revealed through comprehensive analysis.

23 pages, 9 figures