Residual Stress and Ferroelastic Domain Reorientation in Declamped {001 Pb(Zr_0.3Ti_0.7)O₃Films

Ferroelectric films are often constrained by their substrates and subject to scaling effects, including suppressed dielectric permittivity. In this work, the thickness dependence of intrinsic and extrinsic contributions to the dielectric properties was elucidated. A novel approach to quantitatively deconstruct the relative permittivity into three contributions (intrinsic, reversible extrinsic, and irreversible extrinsic) was developed using a combination of X-ray diffraction (XRD) and Rayleigh analysis. In situ synchrotron XRD was used to understand the influence of residual stress and substrate clamping on the domain state, ferroelastic domain reorientation, and electric field-induced strain. For tetragonal {001 textured Pb0.99(Zr0.3Ti0.7)0.98Nb0.02O3 thin films clamped to an Si substrate, a thickness-dependent in-plane tensile stress developed during processing, which dictates the domain distribution over a thickness range of 0.27- 1.11~\mu \text{m}. However, after the films were partially declamped from the substrate and annealed, the residual stress was alleviated. As a result, the thickness dependence of the volume fraction of {c} -domains largely disappeared, and the out-of-plane lattice spacings ( {d} ) for both {a} - and {c} -domains increased. The volume fraction of {c} -domains was used to calculate the intrinsic relative permittivity. The reversible Rayleigh coefficient was then used to separate the intrinsic and reversible extrinsic contributions. The reversible extrinsic response accounted for 50% of the overall relative permittivity (measured at 50 Hz and alternating current (ac) field of 0.5\cdot {E}_{c} ) and was thickness dependent even after poling and upon release.