Local deformation gradients in epitaxial Pb(Zr_0.2Ti_0.8)O₃ layers investigated by transmission electron microscopy

Lead zirconate titanate samples are used for their piezoelectric and ferroelectric properties in various types of micro-devices. Epitaxial layers of tetragonal perovskites have a tendency to relax by forming [Formula: see text] ferroelastic domains. The accommodation of the a/c/a/c polydomain structure on a flat substrate leads to nanoscale deformation gradients which locally influence the polarization by flexoelectric effect. Here, we investigated the deformation fields in epitaxial layers of Pb(Zr_0.2Ti_0.8)O₃ grown on SrTiO₃ substrates using transmission electron microscopy (TEM). We found that the deformation gradients depend on the domain walls inclination ([Formula: see text] or [Formula: see text] to the substrate interface) of the successive [Formula: see text] domains and we describe three different a/c/a domain configurations: one configuration with parallel a-domains and two configurations with perpendicular a-domains (V-shaped and hat-[Formula: see text]-shaped). In the parallel configuration, the c-domains contain horizontal and vertical gradients of out-of-plane deformation. In the V-shaped and hat-[Formula: see text]-shaped configurations, the c-domains exhibit a bending deformation field with vertical gradients of in-plane deformation. Each of these configurations is expected to have a different influence on the polarization and so the local properties of the film. The deformation gradients were measured using dark-field electron holography, a TEM technique, which offers a good sensitivity (0.1%) and a large field-of-view (hundreds of nanometers). The measurements are compared with finite element simulations.