Large built-in electric fields due to flexoelectricity in compositionally graded ferroelectric thin films

Abstract

TitleLarge built-in electric fields due to flexoelectricity in compositionally graded ferroelectric thin films We investigate the origin of large built-in electric fields that have been reported in compositionally graded ferroelectric thin films using PbZr 1−x Ti x O 3 (0.2 < x < 0.8) as a model system. We show that the built-in electric fields that cause a voltage offset in the hysteresis loops are dependent on strain relaxation (through misfit dislocation formation) and the accompanying polarization distribution within the material. Using a GinzburgLandau-Devonshire phenomenological formalism that includes the effects of compositional gradients, mechanical strain relaxation, and flexoelectricity, we demonstrate that the flexoelectric coupling between the out-of-plane polarization and the gradient of the epitaxial strain throughout the thickness of the film, not other inhomogeneities (i.e., composition or polarization), is directly responsible for the observed voltage offsets. This work demonstrates the importance of flexoelectricity in influencing the properties of ferroelectric thin films and provides a powerful mechanism to control their properties.

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

“…Again, it is assumed that the thermodynamic, elastic, and electromechanical coefficients of the compositionally graded Ba 1−x Sr x TiO 3 films are a linear function of z determined from a weighted average of the coefficients for BaTiO 3 and SrTiO 3 given in Sec. II A consistent with prior work [59].…”

“…In contrast to their homogeneous counterparts, compositionally graded ferroelectrics exhibit self-poling [1], built-in potentials [2], asymmetric or shifted hysteresis loop [3], and the potential for geometric frustration [4]. Their distinctive electric-field, thermal, and stress susceptibilities make such systems potentially important for a range of devices [2].…”

“…Their distinctive electric-field, thermal, and stress susceptibilities make such systems potentially important for a range of devices [2]. Compositionally graded ferroelectrics have been probed both experimentally [3,[5][6][7][8] and theoretically using Slater models [9], phenomenological Landau theory [10][11][12][13], transverse Ising models [14,15], and first-principles calculations [4] in an attempt to understand their internal crystal and polarization structure and the mechanisms underlying the manifestation of exotic properties. In this work, we focus on phenomenological approaches and thus narrow our discussion in this capacity.…”

“…This also includes the ability to produce deterministically controlled gradients of phys-* lwmartin@berkeley.edu ical quantities such as strain and composition in ferroelectric films [1,6,8,[26][27][28]. In order to account for the resulting spatial asymmetries that form in these graded films, researchers have suggested the possible inclusion of a number of additional energy terms to adapt such phenomenological models, including (1) flexoelectric, (2) gradient, and (3) depolarization energies [3,10,29,30]. The relative importance, and necessity, of each of these three energies has not, however, been fully considered.…”

Piezoelectricity above the Curie temperature? Combining flexoelectricity and functional grading to enable high-temperature electromechanical coupling

“…The work in Ref. 15 showed that flexoelectricity plays an important role in increasing the pyroelectric property of graded ferroelectric materials and 16 investigated the large built-in electric fields in graded ferroelectric thin films due to flexoelectric coupling. In our previous work, 5 we have computationally demonstrated the possibility of designing such composites through suitable topologies, material property differences, and the selection of optimum feature sizes.…”