Understanding order in compositionally graded ferroelectrics: Flexoelectricity, gradient, and depolarization field effects

Abstract

A nonlinear thermodynamic formalism based on Ginzburg-Landau-Devonshire theory is developed to describe the total free energy density in (001)-oriented, compositionally graded, and monodomain ferroelectric films including the relative contributions and importance of flexoelectric, gradient, and depolarization energy terms. The effects of these energies on the evolution of the spontaneous polarization, dielectric permittivity, and the pyroelectric coefficient as a function of position throughout the film thickness, temperature, and epitaxial strain state are explored. In general, the presence of a compositional gradient and the three energy terms tend to stabilize a polar, ferroelectric state even in compositions that should be paraelectric in the bulk. Flexoelectric effects produce large built-in fields which diminish the temperature dependence of the polarization and susceptibilities. Gradient energy terms, here used to describe short-scale correlation between dipoles, have minimal impact on the polarization and susceptibilities. Finally, depolarization energy significantly impacts the temperature and strain dependence, as well as the magnitude, of the susceptibilities. This approach provides guidance on how to more accurately model compositionally graded films and presents experimental approaches that could enable differentiation and determination of the constitutive coefficients of interest.

Thin-film ferroelectric materials and their applications

“…The focus is now on routes to achieve even larger pyro electric and electrocaloric effects. These efforts are aided by advanced modelling approaches, which have explored, for example, the role of domain walls and domain structure 59,60 , film thickness and strain state [132][133][134] , thermalmismatch strains 135,136 , chemical and other gradients 137 , and multilayer structures 138,139 . One study clarified the relative importance of different contributions to the pyroelectric response 62 , including intrinsic (arising from the response of the polarization within the domains), extrinsic (arising from the temperature-driven change in the domain structure) and secondary (arising from a temperature-driven, piezoelectric-induced change in the polarization) pyroelectric effects in PbZr 1 − x Ti x O 3 (FIG.…”

Electrical Properties of Epitaxial Ferroelectric Heterostructures

“…Different lattice relaxation processes could generate strain gradients in the films, which could imply a flexoelectric field. The effects of these supplementary fields lead to different behaviours in polarization switching, shift of the hysteresis loop along Epitaxyvoltage axis, modification of remnant polarization and occurrence of diode-like current characteristics with dependence on polarization direction [20][21][22].…”

Formation of polarization needle-like domain and its unusual switching in compositionally graded ferroelectric thin films: an improved phase field model

“…25,26 Recent development in theoretical approach based on principles of non-linear thermodynamics can shed light on the polarization stabilities, phase transformation characteristics and dielectric properties of cgFEs. [27][28][29] These theoretical studies provide an explanation as to why cgFEs should have lower dielectric losses and lower leakage currents compared to homogeneous ferroelectrics. In addition, role of the exoelectric effect in the enhancement and stabilization of polarization components in cgFEs has also been demonstrated by using an extended thermodynamic theory.…”

“…In addition, role of the exoelectric effect in the enhancement and stabilization of polarization components in cgFEs has also been demonstrated by using an extended thermodynamic theory. 27,28,30 Although the use of theoretical approaches can explain some experimental observations, there still lacks a consideration of domain structures and their response to the mechanical and electric excitations, despite of their crucial roles in determination of macroscopic properties. This thus limits the use of theoretical methods for cgFEs, particularly with complex domain structures.…”