Ferroelectric structural transition in hafnium oxide induced by charged oxygen vacancies

The discovery of ferroelectric ${\mathrm{HfO}}_2$ in thin films and more recently in bulk is an important breakthrough because of its silicon compatibility and unexpectedly persistent polarization at low dimensions, but the origin of its ferroelectricity is still under debate. The stabilization of the metastable polar orthorhombic phase was often considered as the cumulative result of various extrinsic factors such as stress, grain boundary, and oxygen vacancies as well as phase transition kinetics during the annealing process. We propose a mechanism to stabilize the polar orthorhombic phase over the nonpolar monoclinic phase that is the bulk ground state. Our first-principles calculations demonstrate that the doubly positively charged oxygen vacancy, an overlooked defect but commonly presenting in binary oxides, is critical for the stabilization of the ferroelectric phase. The charge state of the oxygen vacancy serves as a degree of freedom to control the thermodynamic stability of competing phases of wide band gap oxides.

Figure 1

(a) Defect-free atomic structure of M-phase ${\mathrm{HfO}}_2$ and the local atomic relaxations around the ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_{\mathrm{O}}^{2+}$; yellow surface represents the charge density isosurface of the doubly occupied defect state due to ${\mathrm{V}}_{\mathrm{O}}$; the strong outward and inward displacements of neighboring Hf and O atoms around ${\mathrm{V}}_{\mathrm{O}}^{2+}$ are indicated by blue and green arrows. (b) Density of states of different phases of ${\mathrm{HfO}}_2$ with ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_{\mathrm{O}}^{2+}$; blue shaded areas represent occupied states. The values of doubly occupied defect levels are shown by red dashed lines. The energy difference of defect levels ($\mathrm{\Delta }{\varepsilon }_D$) is 0.49 eV.

Figure 2

(a) Energies of the PO phase of ${\mathrm{HfO}}_2$ with different vacancy charge states and relaxation conditions relative to the M phase ($\mathrm{\Delta }E$) as a function of vacancy concentration obtained with $2\times 3\times 2$ supercells. (b) Vacancy concentration dependence of local polarization for PO and M phases with oxygen vacancy at different charge states.

Figure 3

The energy differences of defect levels multiplied by the effective charge ($q\mathrm{\Delta }{\varepsilon }_D$) versus relative phase stability [$\mathrm{\Delta }{E}_P$ in Eq. (4)] in various wide band gap oxides.

Figure 4

(a) The energy variation of the ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_{\mathrm{O}}^{2+}$ during their migrations along the pathways shown in the inset and yellow surface represents the charge density isosurface of the defect state; (b) the corresponding density of states of initial/final and intermediate states with ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_{\mathrm{O}}^{2+}$ of M-phase ${\mathrm{HfO}}_2$.