Effect of a Single Dislocation in a Heterostructure Layer on the Local Polarization of a Ferroelectric Layer

We study, on an atomic scale, the influence of a single dislocation in a ${\mathrm{SrTiO}}_3$ sublayer on the local ferroelectric polarization of the neighboring ferroelectric ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ (PZT) sublayer in an epitaxial ${\mathrm{SrTiO}}_3/{\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3/{\mathrm{SrTiO}}_3$ three-layer heterostructure. The strain field of the dislocation in the ${\mathrm{SrTiO}}_3$ layer propagates across the interface into the PZT layer and leads to a strong variation of the $c$-lattice parameter of the PZT layer. Accompanying a strong reduction of the $c$-lattice parameter, the off-center displacements of the $\mathrm{Zr}/\mathrm{Ti}$ atoms away from the center of the oxygen octahedra are also strongly decreased, resulting in a decrease of the local spontaneous polarization by up to 48%.

Figure 1

(a) Atomic-resolution $[110]$ image of part of a STO/PZT/STO heterostructure including a dislocation denoted by “$\perp$”, recorded under NCSI conditions. The interface between the bottom STO and PZT layers is marked by a dotted line. The curved arrow shows the strong upward bending of the (001) planes. The numbered symbols mark the (001) $(\mathrm{Zr}/\mathrm{Ti}){\mathrm{O}}_2$ planes for quantitative analysis. (b) A magnification of an area directly above the interface in (a). The columns of PbO, $\mathrm{Zr}/\mathrm{Ti}$ and O are denoted. The relative displacements between positively charged cations (Pb, $\mathrm{Zr}/\mathrm{Ti}$) and negatively charged anion (O) result in an electric dipole in the unit cell and define the spontaneous polarization vector as show by an arrow. Two lines trace the lattice bending from left to the right of the image, which amounts to about one degree.

Figure 2

Lattice plane bending in the PZT layer as a function of the distance from the left edge of the image in Fig. 1a. The bending is represented by the vertical shifts $\Delta$ of the $\mathrm{Zr}/\mathrm{Ti}$ columns in a given (001) $(\mathrm{Zr}/\mathrm{Ti}){\mathrm{O}}_2$ plane ($j=1–9$) with respect to the $\mathrm{Zr}/\mathrm{Ti}$ columns in the perfect area at the position of the symbol group in Fig. 1a.

Figure 3

$c$-lattice parameter (a), vertical spacing ${\delta }_{\mathrm{O}\mathrm{\text{−}}\mathrm{Zr}/\mathrm{Ti}}$ between O and $\mathrm{Zr}/\mathrm{Ti}$ columns (b) and spontaneous polarization (c) of the PZT layer as a function of the distance from the left edge of the image in Fig. 1a. In (c) circles display the result calculated from relation (1) and diamonds from (3). The error bars represent the mean error with a confidence level of 95%.