Slater model applied to polarization graded ferroelectrics

Abstract

Ferroelectric thin films of BaxSr1−xTiO3 with compositional gradients normal to the growth surface have been formed by the successive deposition and annealing of films having step-variable Ba to Sr ratios. By suitably tailoring the magnitude and sense of the gradient in Ba to Sr ratio, directional potentials can be built into the structures yielding a new, but controllable, hysteresis phenomenon. Slater’s empirical model for ferroelectric materials has been extended to also describe thin films with polarization gradients normal to the growth surface, i.e., graded ferroelectric devices. This model accounts for several aspects of these structures, including: the broadness of the permittivity plots with temperature, the formation of a spontaneous potential upon oscillatory field excitation, offsets in the hysteresis graphs along the displacement axis with directions which are gradient dependent, and the electric field dependence of that offset.

Explicit expressions for the dynamic polarization behavior in ferroelectrics with symmetric/asymmetric electrical conductivity

“…However, the drift magnitude might be surprisingly large and was reported to be an order larger than the spontaneous polarization. [33][34][35] Although our model assumes a single ferroelectric sample, our analysis is thought to be roughly valid for a graded ferroelectric, which is a multilayered composite. A composite possesses effective dielectric and ferroelectric properties, and we imagine this ''effective'' sample is placed in the Sawyer-Tower circuit.…”

A General Conductivity Expression for Space-Charge-Limited Conduction in Ferroelectrics and Other Solid Dielectrics

“…Such a phenomenon of polarization offsets in compositionally graded ferroelectric films is characterized by three key experimental observations: (i) The shift magnitude exhibits a strong dependence on electric field and temperature (Schubring et al, 1992). In particular, it typically exhibits a power 3 to 5 dependence on the magnitude of the applied electric field (Bao et al, 2000a(Bao et al, , 2000b(Bao et al, , 2000c(Bao et al, , 2001bBouregba et al, 2003;Brazier et al, 1998;Mantese et al, 1997); (ii) The vertical hysteresis shift changes from upward to downward, or vice versa, when the compositional gradient is inverted (Bouregba et al, 2003;Brazier et al, 1998;Mantese et al, 1997). (iii) A vertical polarization offset typically develops like the charging up of a capacitor, where the "time constant" is of the order of magnitude as the product of the capacitance and input impedance of the reference capacitor in the Sawyer-Tower circuit.…”

“…polarization offsets, when driven by an alternating applied electric field and placed inside a Sawyer-Tower circuit (Chan et al, 2004;Sawyer & Tower, 1930) for typical D-E measurements of ferroelectric materials. This intriguing phenomenon, believed to have potential device applications in infrared detection, actuation and energy storage (Mantese & Alpay, 2005), has triggered much subsequent research in the ferroelectrics community into a theoretical understanding of its origin (Alpay et al, 2003;Bouregba et al, 2003;Brazier et al, 1999;Chan et al, 2004;Fellberg et al, 2001;Mantese & Alpay, 2005;Mantese et al, 1997;Okatan et al, 2010;Poullain et al, 2002). Such a phenomenon of polarization offsets in compositionally graded ferroelectric films is characterized by three key experimental observations: (i) The shift magnitude exhibits a strong dependence on electric field and temperature (Schubring et al, 1992).…”

“…In the past two decades, various theoretical ideas and models have been proposed to account for the origin of this phenomenon: Originally, the vertical hysteresis shift, or "polarization offset", was thought of as a static polarization developed across the graded ferroelectric film (Mantese et al, 1997), upon excitation by an alternating applied electric field. However, the experimental values of those "offsets" are at least an order of magnitude larger than the typical spontaneous polarization of the ferroelectric material, and therefore such a large static polarization component is deemed unlikely, if not impossible (Brazier et al, 1999).…”

“…Our theoretical investigation of SCLC began with a study of the well-known phenomenon of polarization offsets in compositionally graded ferroelectric films (Bao et al 2000a(Bao et al , 2000b(Bao et al , 2000c(Bao et al , 2001a(Bao et al , 2001bBouregba et al, 2003;Brazier et al, 1998;Chen et al, 1999;Mantese et al, 1997;Matsuzaki & Funakubo, 1999;Schubring et al, 1992). Ferroelectric materials are materials that generally exhibit nonlinear, hysteretic D-E or P-E relations, where D is the electric displacement, P is the polarization and E is the electric field.…”