Interface Effects Induced by a ${\mathrm{Zr}\mathrm{O}}_2$ Seed Layer on the Phase Stability and Orientation of ${\mathrm{Hf}\mathrm{O}}_2$ Ferroelectric Thin Films: A First-Principles Study

${\mathrm{Hf}\mathrm{O}}_2$-based films have attracted much attention due to their robust ferroelectric properties at the nanometer scale and their great potential for data storage. The interface between the substrate and the ${\mathrm{Hf}\mathrm{O}}_2$-based film has a significant effect on its ferroelectric behavior. A seed layer between the films and substrates, such as a ${\mathrm{Zr}\mathrm{O}}_2$ seed layer, is proved to be an effective way to realize the beneficial interface effect. However, the interfacial tuning mechanism for the ferroelectric properties of ${\mathrm{Hf}\mathrm{O}}_2$-based thin films brought by the substrate or seed layer remains unclear so far. By performing first-principles calculations, the phase stability and crystalline orientation of ${\mathrm{Hf}\mathrm{O}}_2$ thin films on ${\mathrm{Zr}\mathrm{O}}_2$ seed layers are systematically studied. Results indicate that the ${\mathrm{Zr}\mathrm{O}}_2$ seed layer, especially the [111]-oriented one, substantially stabilizes the orthorhombic ferroelectric phase and the high-symmetry tetragonal phase of the ${\mathrm{Hf}\mathrm{O}}_2$ thin film compared with the most stable monoclinic phase. Furthermore, the polarization magnitude of the ${\mathrm{Hf}\mathrm{O}}_2$ film on the ${\mathrm{Zr}\mathrm{O}}_2$ seed layer is in good agreement with experiment. The [100]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ seed layer also has a great effect on the stability of the orthorhombic ferroelectric phase of the ${\mathrm{Hf}\mathrm{O}}_2$ thin film. These results are meaningful for the understanding of the interfacial effects of the ferroelectricity of ${\mathrm{Hf}\mathrm{O}}_2$-based thin films and the development of ferroelectric devices.

Figure 1

The atomic structures of (a) tetragonal ${\mathrm{Zr}\mathrm{O}}_2$ (P4₂/nmc space groups) and (b) competing polymorphs of ${\mathrm{Hf}\mathrm{O}}_2$ (Pca2₁, P4₂/nmc, P2₁/c, and R3m space groups). Atomic structures are plotted using vesta software.

Figure 2

(a) Atomic structures of the ${\mathrm{Hf}\mathrm{O}}_2\text{−}$[001]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ heterostructures with $\mathrm{Hf}$- (three models on the left) or $\mathrm{O}$-terminations (three models on the right). The bottom fixed parts of the ${\mathrm{Zr}\mathrm{O}}_2$ substrates are not shown for brevity. The subscripts of each phase denote the orientations of the ${\mathrm{Hf}\mathrm{O}}_2$ thin films. For example, f₀₀₁ denotes the ferroelectric ${\mathrm{Hf}\mathrm{O}}_2$ thin film with [001]-orientation on the ${\mathrm{Zr}\mathrm{O}}_2$ substrate. The green, yellow, and red circles represent $\mathrm{Zr}$, $\mathrm{Hf},$ and $\mathrm{O}$ atoms, respectively. (b) and (c) show the relative energies (ΔE) of each phase (with different orientations) per unit cell (four $\mathrm{Hf}$ and eight $\mathrm{O}$ atoms) for the $\mathrm{Hf}$- (b) or $\mathrm{O}$-terminated (c) ${\mathrm{Hf}\mathrm{O}}_2$ thin films. N denotes the unit cell numbers (i.e., the thickness) of the ${\mathrm{Hf}\mathrm{O}}_2$ thin films. The energies of the most stable phases with different thicknesses are set to 0.

Figure 3

(a) The atomic structures of ${\mathrm{Hf}\mathrm{O}}_2\text{−}$[100]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ heterostructures with $\mathrm{Hf}$- (two models on the left) or $\mathrm{O}$-terminations (three models on the right). (b) and (c) show the relative energies (ΔE) of each phase (with different orientations) for the $\mathrm{Hf}$- (b) or $\mathrm{O}$-terminated (c) ${\mathrm{Hf}\mathrm{O}}_2$ thin films per unit cell on [100]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ substrate. The energies of the most stable phases with different thicknesses are set to 0. The heterostructures that are not stable are not shown in the energy diagram.

Figure 4

(a) The atomic structures of ${\mathrm{Hf}\mathrm{O}}_2\text{−}$[111]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ heterostructures. (b) The relative energies (ΔE) of each phase (with different orientations) for the free-standing 〈111〉-oriented ${\mathrm{Hf}\mathrm{O}}_2$ thin films per $\mathrm{Hf}\text{−}{\mathrm{O}}_2$ layer (four $\mathrm{Hf}$ and eight $\mathrm{O}$ atoms). (c) The relative energies (ΔE) of each phase (with different orientations) for the ${\mathrm{Hf}\mathrm{O}}_2$ thin films per $\mathrm{Hf}\text{−}{\mathrm{O}}_2$ layer on [111]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ substrate. N denotes the $\mathrm{Hf}\text{−}{\mathrm{O}}_2$ layer numbers (i.e., the thickness) of the 〈111〉-oriented ${\mathrm{Hf}\mathrm{O}}_2$ thin films. The energies of the most stable phases with different thicknesses are set to 0.

Figure 5

(a) The atomic structures of f₋₁₁₁ ${\mathrm{Hf}\mathrm{O}}_2$-[111]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ heterostructure along the polarization switching path marked with asterisks in (b). The arrows on the ${\mathrm{Hf}\mathrm{O}}_2$ thin film denote the directions of ferroelectric polarizations. The values under the structures represent the out-of-plane polarization magnitudes in units of µC/cm² (positive value means that the ferroelectric polarization is pointing away from the ${\mathrm{Zr}\mathrm{O}}_2$ substrate). (b) The energy profile of the polarization switching of the f₋₁₁₁ ${\mathrm{Hf}\mathrm{O}}_2$ thin films on [111]-oriented ${\mathrm{Zr}\mathrm{O}}_2$ substrate. The energy of the state with out-of-plane polarization in ${\mathrm{Hf}\mathrm{O}}_2$ thin film pointing away from the ${\mathrm{Zr}\mathrm{O}}_2$ substrate is set to 0.