Numerical modeling and investigations of 3D devices with ferroelectric layer fully embedded in a paraelectric environment

Abstract

We investigate three-dimensional devices made up of a ferroelectric layer that is fully embedded in a paraelectric environment, by modeling based on the Ginzburg-Landau formalism as well as on the Electrostatics equations, and boundary conditions that are suitable for applications. From finite element approximations and inexact Newton techniques for solving numerically the resulting nonlinear system, we develop two numerical protocols. The first protocol concerns a determination of states related to the system and incorporates a process of heating as well as of cooling of devices, in terms of the temperature, whereas the second one is devoted to the existence study of hysteresis loops. The efficiency of these protocols is particularly emphasized from numerical simulations.

Numerical Study of Switching Behavior in Finite Media Subject to 3D Ferroelectric-Paraelectric Interactions and Inspection of Calibration Effects

“…We consider the weak formulation introduced in [11,12] and associated with the model presented also therein for the analysis of three-dimensional devices made up of a ferroelectric layer that is fully embedded in a paraelectric environment. Let us represent geometrically such a device with the help of an open bounded subset Ω of R 3 , and its fully embedded layer by an open subset Ω f , Ω f ⊂ Ω, as well as its paraelectric environment by Ω p = Ω \ Ω f .…”

“…Called in the sequel, as in [12], the Electrostatic Ginzburg-Landau system and more simply (EGL), this model is related to uniaxial ferroelectric devices; namely, the ones for which the dependence of the electric polarization field, P, on the electric field, E, is nonlinear through only one of its components (which is here the third one). More precisely, we have…”

“…As introduced in [12], with more details in [11], the weak formulation associated with (EGL) consists of finding (P, ϕ) ∈ W such that for (Q, ψ) ∈ W…”

“…This method, particularly suited to an accurate description of the interplay aforementioned, has been used also in a two-dimensional context involving periodic boundary conditions [10]. Moreover, it has been applied in the frame of certain threedimensional ferroelectric devices [12,13].…”

“…Unlike in [13], where the simulations were associated with a cylindrical configuration and without an investigation of the influence of geometrical parameters, we are concerned with numerical variations of geometrical and physical parameters, moreover with the parallelepipedic configuration context. In contrast with [12], where is also presented the model related to the mentioned approach, the interest is here devoted on the one hand to considerations that are above all concrete as regards temperature applications too and on the other hand to a study of calibration effects. This interest leads us to analyze here the influence of physical and geometrical parameters, then both under concrete considerations of voltage potential and temperature applications.…”