Domain Walls Stabilized by Intrinsic Phonon Modes and Engineered Defects Enable Robust Ferroelectricity in HfO2

Abstract

Ferroelectric $\mathrm{HfO}_2$ has attracted extensive research interest for its applications in AI era. The domain walls play a crucial role in phase structure stabilization and polarization switching of ferroelectric $\mathrm{HfO}_2$, however, a thorough understanding is still lacking. Here, we developed a unified framework based on phonon mode expansion to systematically study the effects of phonon modes and defects on domain wall structures. Using this approach combined with first-principle calculations, we revealed that the interface phonon modes play a key role in stability of domain walls; defects pin and stabilize ferroelectric domains, which in turn stabilizes the metastable orthorhombic phase and facilitates polarization switching. This provides an insight from the microscopic physics origin into the enhanced ferroelectricity in $\mathrm{HfO}_2$ by doping and defect engineering. Furthermore, the theoretically predicted domain structures and defect distributions were observed in La-doped $\mathrm{HfO}_2$ ferroelectric films by EELS and STEM experiments, which confirms the validity of our findings.

Figures (7)

• Figure 1: Dependence of OIII domain wall stability on interface phonon modes. (a) The domain wall model with two domains. (b) Polarization configuration, and different types of $0^\circ, 180^\circ, 90^\circ$ domain walls. (c) Dependence of OIII domain wall stability on interface phonon modes, or pseudo-chirality number at interface. The x-axis and y-axis of each stability map are the pseudo-chirality number of domain A and B in subfigure a. The figure title of each stability map shows the dipole configuration of domain A and B. The overlined axis is the compact notation for the reversed axis direction, e.g.$\overline{c}$ means $-c$.
• Figure 2: Effects of defects on DWs. (a) Dependence of the formation energy of La substitutional defect $\mathrm{La}_\mathrm{Hf}$ and oxygen vacancy $\mathrm{V}_\mathrm{O}$ pairs on their distance, exhibiting a positive correlation, with the minimum formation energy achieved at the minimum distance. (b) The structure model used to study the dependence of DW energy on the distribution of defects. We put $\mathrm{La}_\mathrm{Hf}$ and $\mathrm{V}_\mathrm{O}$ defects in one of the domains with varying distances to the DW interface. (c) Dependence of energy of the model in subfigure b on the distance from the defects to DW interface. The energy is the lowest when the defects are at the interface, which indicates that the DW interfaces are more likely to form in the area with high defect density. (d) Dependence of stability of $90^\circ$ DW with defects on interface phonon modes, or pseudo-chirality number at interface. We use different colors to distinguish the DWs that are stable with or without defects (blue) and the DWs that are unstable without defects but stable with defects (green).
• Figure 3: Ferroelectric switching mechanism based on DW motion. (a) Summary of five switching paths of OIII phase. (b) The switching path from S1 to S2, and the path from S2 to S3. The two paths correspond to the switching from inside the domain and the DW motion. The structures of S1 to S3 are shown in subfigure c. (c) Schematic of proposed switching mechanism. (d) Structures in the switching paths in subfigure b: S1, the single-domain ground state; S2, a two-cell-reversed state; S3, a three-cell-reversed state.
• Figure 4: Structural characterization and defect analysis of HLO films. (a) P-V hysteresis loop of the $\mathrm{TiN}/\mathrm{HLO}/\mathrm{TiO}_2$ stack showing a low coercive voltage of $2V_c=2.3\mathrm{V}$ and the remanent polarization of $P_r = 22 \mu \mathrm{C}/\mathrm{cm}^2$. (b) GIXRD patterns of HLO film. (c) STEM-HADDF image and corresponding fast-Fourier-transformation (FFT) patterns. (d) EELS spectra and (e) O-K edges obtained from the region marked with red line and black line in (c). (f) Atomic structures of HLO film. (g) The coexistence of O domains with DWs in a single grain. La-M edges of (h) Line1 and (i) Line2 obtained from the DW1 and DW2. Each spectrum color corresponds to similiar color position marked in (g).
• Figure S1: Structural characterization of HLO film. (a) Cross-sectional HADDF image of $\mathrm{TiN}/\mathrm{HLO}/\mathrm{TiO2}$ stack. The HADDF (b) and ABF (c) images projected along O-[011] zone axis. The green lines indicate the extraction contrast positions. (d) The contrast curve is used to identify the positions of La atoms in the HLO film. (e) The contrast curve is used to identify the positions of oxygen atoms in the HLO film.