Hysteresis, Loss and Nonlinearity in Epitaxial PbZr_0.55Ti_0.45O₃ Films: A Polarization Rotation Model

Abstract

The phenomena of hysteresis, ferroelectric loss, and nonlinearity are investigated for the strain and polarization of a monoclinic, epitaxial Pb(Zr,Ti)O 3 film over the 70 Hz to 5 kHz frequency range at sub-coercive excitation fields and zero electrical bias. For the strain, a linear hysteretic behavior is found, whereas the polarization shows a strongly nonlinear hysteretic behavior. In contrast to polycrystalline structures (for instance in ceramics or chemical solution deposited thin films), the commonly referred Rayleigh model cannot explain the observed behavior. A new model is presented, based on the rotation of the polarization vector within the monoclinic or rhombohedral unit cell under an applied electric field, with the viscous interaction of domains accompanying the unit cell deformation. The model explains the amplitude and frequency scaling of the strain, polarization, and loss tangent as well as the observed higher harmonics of polarization in the measured epitaxial Pb(Zr,Ti)O 3 films. It is concluded that the nonlinear response and the hysteretic loss originate from two separate physical processes. The nonlinear response is attributed to the nonlinear angular rotation of the polarization vector, whereas the hysteresis and ferroelectric loss are due to a viscous interaction of domains while the polarization vector is rotating.

Influence of DC Bias on the Hysteresis, Loss, and Nonlinearity of Epitaxial PbZr0.55Ti0.45O3 Films

“…The validity of the linear dependence can be derived from the Landau–Devonshire model to a good approximation. [ 26 ] The observation of elliptic strain hysteresis loops in our experiments suggests that the piezoelectric loss is dominated by a viscous loss mechanism. [ 26 ] The viscous loss can be introduced as an out‐of‐phase (oop) component in the strain response which is proportional to the time derivative of the in‐phase response as , where γ S is a viscosity coefficient.…”

“…The polarization rotation model considers the rotation of the polarization vector in the (110)‐plane in a (001)‐oriented rhombohedral or monoclinic thin films under the influence of an electric field excitation. [ 26 ] The polarization, measured across the film in a parallel plate capacitor configuration, is then given by with P S the length of the spontaneous polarization vector and θ the angle between the [001]‐axis and the polarization vector. Using a grounded bottom electrode, a positive voltage on the top electrode corresponds to a downward‐oriented electric field so that in a poled film the polarization angle is measured with respect to a top‐to‐bottom oriented film normal axis.…”

“…In a fully relaxed unit cell at zero field, the polarization vector is in the body diagonal and θ equals θ 0 = 54.7°. Our films are under compressive, in‐plane stress, resulting in a rotation of the polarization vector (in zero field) toward the out‐of plane direction and, thus, in a lower polarization angle that is defined as θ 0, f [ 26 ] (the subscript f indicates that the sample is a clamped thin film). The associated polarization value is the remanent polarization P r = P S cos (θ 0, f ) of the film.…”

“…Furthermore, we assume that for the used magnitudes of the AC and DC fields the extension of the polarization vector is negligible. [ 26,31,32 ]…”

“…In an earlier publication we have shown that for epitaxial PbZr 0.55 Ti 0.45 O 3 films with a monoclinic crystal symmetry, the hysteresis, loss, and nonlinearity of functional properties can be very well described by a model that considers the rotation of the polarization vector within the unit cell and that is accompanied by a viscous interaction of the domains. [ 26 ] Moreover, with this so‐called polarization rotation model, it is possible to differentiate between the nonlinearity of the response that is caused by the nonlinear response of the angle of the polarization vector to the applied field and the loss due to viscous interaction of the domains. In addition, the polarization rotation model predicts all experimentally observed even and odd harmonics.…”