Hole-doping reduces the coercive field in ferroelectric hafnia

Ferroelectric hafnia ($\mathrm{Hf}{\mathrm{O}}_{2}$) holds promise for next-generation memory and logic applications because of its CMOS compatibility. However, the high coercive field required for polarization switching in $\mathrm{Hf}{\mathrm{O}}_{2}$ remains a critical challenge for efficient device operations. Using first-principles calculations and phenomenological modeling, we predict that hole-doping can reduce the coercive field from 8 MV/cm in undoped hafnia to 6 MV/cm in hafnia doped with 0.2 holes per formula unit (f.u.). In the absence of doping, the reversal of polarization of the $Pca{2}_{1}$ phase is preferred through the nonpolar, tetragonal $P{4}_{2}/nmc$ phase. This switching pathway involves the coupling of three hard distortion modes that render undoped hafnia as an improper ferroelectric. The overall energy barrier through this pathway remains unchanged ($\ensuremath{\sim}80$ meV/f.u.) upon hole-doping. However, the introduction of holes hardens the polar ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\ensuremath{-}}$ distortion mode that connects the polar $Pca{2}_{1}$ phase to the nonpolar, orthorhombic Pbcm phase, and reduces the energy barrier from 180 meV/f.u. in undoped hafnia to 80 meV/f.u. at 0.2 holes/f.u. The activation of the latter switching pathway through the Pbcm phase can lead to a reversal in the polarization direction. Overall, hole-doping makes the switching pathway through the Pbcm phase competitive, and renders hafnia as a proper ferroelectric with a lower coercive field.