Suppressed Dependence of Polarization on Epitaxial Strain in Highly Polar Ferroelectrics

A combined experimental and computational investigation of coupling between polarization and epitaxial strain in highly polar ferroelectric ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ (PZT) thin films is reported. A comparison of the properties of relaxed (tetragonality $c/a\approx 1.05$) and highly strained ($c/a\approx 1.09$) epitaxial films shows that polarization, while being amongst the highest reported for PZT or ${\mathrm{PbTiO}}_3$ in either film or bulk forms $P_r\approx 82\mu \mathrm{C}/{\mathrm{cm}}^2$), is almost independent of the epitaxial strain. We attribute this behavior to a suppressed sensitivity of the $A$-site cations to epitaxial strain in these Pb-based perovskites, where the ferroelectric displacements are already large, contrary to the case of less polar perovskites, such as ${\mathrm{BaTiO}}_3$. In the latter case, the $A$-site cation (Ba) and equatorial oxygen displacements can lead to substantial polarization increases.

Figure 1

(a) XRD $\theta \mathrm{\text{−}}2\theta$ scans around the 001 reflection of 20, 50, and 100 nm-thick films, showing the increase of out-of-plane lattice constant by reducing the film thickness. Note that the reflection from ${\mathrm{SrRuO}}_3$ is not appreciable due to a rather small thickness (4 nm). (b) In-plane and out-of-plane lattice constants as a function of film thickness measured from XRD scans. Cross-sectional $Z$-contrast images of (c) 15 and (d) 116 nm-thick PZT films. The inset of (c) is a high-resolution image of the 15 nm-thick film showing a dislocation core located 6 nm above the ${\mathrm{SrRuO}}_3$ layer. The solid arrows in (c) and (d) point to the dislocation lines, indicating the reduced dislocation density in the well-strained film. STO and SRO stand for ${\mathrm{SrTiO}}_3$ and ${\mathrm{SrRuO}}_3$, respectively.

Figure 2

(a) $P(E)$ hysteresis loops at 100 Hz from 35 and 100 nm-thick PZT films. (b) Simultaneously measured pulse polarization and switching current (inset) by applying trapezoid pulses (P1 to P4), showing neither nonswitching current nor nonswitching polarization. Pulse measurements in (b) were performed at 3 V with 2.5 ms of write/read-pulse time and 1 s write-pulse delay. Tetragonality (c), remanent polarization (d), and coercive field (e) as a function of film thickness. The slope ($-0.614\pm 0.067$) in the inset of (e) is in good agreement with the classical scaling behavior ($E_c\propto d^{-2/3}$).

Figure 3

Polarization enhancement (a), tetragonality enhancement (b), and polarization inset in (a) as a function of epitaxial strain $\epsilon$ in $r\mathrm{\text{−}}{\mathrm{PbTiO}}_3$, ${\mathrm{PbTiO}}_3$, and ${\mathrm{BaTiO}}_3$. The enhancement of $u$ and $Z^{*}$ by epitaxial strain $\epsilon =-2\%$ is shown in (c) and (d), respectively. Insets in (c) and (d) (same $x$ axes as main figures) are the values of $u$ and $Z^{*}$, respectively, at zero strain. ${\mathrm{O}}_e$ and ${\mathrm{O}}_a$ refer to equatorial and apical oxygens, respectively.