Local field inhomogeneity and ferroelectric switching dynamics in ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films

We report on the inhomogeneity of the internal bias according to the Zr alloy concentration confirmed by the ferroelectric switching dynamics of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films. The analytic model for the internal bias was considered in terms of the dipole-dipole interaction accompanied by Zr concentration variation. The ferroelectricity and switching dynamics of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films were investigated using conventional electrical measurements and local piezoresponse microscopy. Analysis of static and dynamic polarization reversal revealed a correlation between the activation field for polarization switching and Zr concentrations through the variation in local ferroelectric coercivity and the characteristic ferroelectric switching time. The spatially inhomogeneous local built-in electric field was attributed to the defect interaction in the ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films.

Figure 1

Structural analysis of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films using x-ray diffraction. (a) Rietveld refinement of the grazing incident x-ray diffraction plot of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films with $x$ values from 0.34 to 0.70 with measured data (black dots) and simulated curves (red line). (b) The orthorhombic phase fraction of the ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films estimated by Rietveld analysis.

Figure 2

(a) Hysteresis of the relative permittivity ε_r of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films with $x$ values from 0.34 to 0.70. The inset shows the dielectric constant of the nonswitched part at the end of the curve (empty black squares). (b) Polarization-voltage hysteresis of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films with $x$ values from 0.34 to 0.70. The inset shows the extracted coercive field (solid blue squares) and polarization (solid red squares) values.

Figure 3

Ferroelectric switching dynamics of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films. (a) Time dependence of the polarization flip Δ$P$($t$) of ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films under various external voltages $V_{\mathrm{ext}}$. (b) The distribution functions $F(\log t_0$) of the logarithmic characteristic switching time $t_0$.

Figure 4

The external electric field ($E_{\mathrm{ext}}$)–dependent (a) characteristic switching time and (b) full width at half maximum value of the distribution with various Zr contents. (c) The ratio of activation field α and half width Γ at half maximum of local field distributions with a Zr concentration change.

Figure 5

Local piezoresponse and coercive voltage distribution of the ${\mathrm{Hf}}_{1-x}{\mathrm{Zr}}_x{\mathrm{O}}_2$ thin films. The piezoresponse hysteresis amplitude (solid black squares) and phase (solid red squares) for (a) ${\mathrm{Hf}}_{0.66}{\mathrm{Zr}}_{0.34}{\mathrm{O}}_2$, (b) ${\mathrm{Hf}}_{0.48}{\mathrm{Zr}}_{0.52}{\mathrm{O}}_2$, and (c) ${\mathrm{Hf}}_{0.30}{\mathrm{Zr}}_{0.70}{\mathrm{O}}_2$. The hysteresis loops were collected in arrays of 10 × 10 points covering an area of $0.5\times 0.5\mu {\mathrm{m}}^2$, with regular spacing of 50 nm between the adjacent nodes of the grid. Coercive voltage distributions of (d) ${\mathrm{Hf}}_{0.66}{\mathrm{Zr}}_{0.34}{\mathrm{O}}_2$, (e) ${\mathrm{Hf}}_{0.48}{\mathrm{Zr}}_{0.52}{\mathrm{O}}_2$, and (f) ${\mathrm{Hf}}_{0.30}{\mathrm{Zr}}_{0.70}{\mathrm{O}}_2$, respectively.

Figure 6

Schematic diagrams of normalized local field distributions with (a) inhomogeneous local fields and (b) uniform local fields.