Polarization switching pathways of ferroelectric Zr-doped HfO₂ based on the first-principles calculation

Based on the first principles calculation, the mechanisms of polarization switching behavior in ferroelectric Zr-doped HfO2 are investigated. Seven switching pathways, divided into two categories by the identified orientation of polarization switching and value, are analyzed based on atomic migration and energy barrier. The effects of Zr dopant on switching energy barrier (Eb) and spontaneous polarization (Ps) are analyzed as well. In one of the categories, two pathways with tetragonal-like transition states show low energy barriers and can be further minimized with higher Zr dopant proportion, which originates from the stabilizing effect of Zr dopant on the tetragonal phase (T, P42/nmc). Especially, in the two tetragonal-like pathways, a distorted tetragonal-like transient state (T' , Pbcn) resulting from distinct atomic displacement is transformed to a highly symmetric T-phase along with the incorporation of Zr, elucidating this pathway as energy favorable as the regular T-pathway. This work provides an atomic insight for ferroelectric switching behavior and predicts the probable ferroelectric switching pathway in Zr-doped HfO2 films.