Phase-field simulation and design of a ferroelectric nano-generator

We study the behavior of ferroelectric material (BaTiO3) for the design of a nano-generator to convert mechanical into electrical energy. The investigations consider an electro-mechanical phase-field model with polarization as state variable. This widely accepted model has its origins in the work of(1-3) and is fully developed by Landis and coworkers.(4, 5) We use a finite element model to simulate tetragonal regions of ferroelectric material sputtered on substrate. Different geometries as well as various mechanical and electrical boundary conditions are considered. The model parameters are normalized to achieve better computational conditions within the stiffness matrix. The major objective of this contribution is the fundamental understanding of domain switching caused by a cyclic electrical field. The corresponding hysteresis loops of the overall polarization cannot be achieved by using a two-dimensional model because the domain topologies evolve in three dimensions. The three-dimensional nature of the domain structure evolution is even true for flat regions or thin films.(6) We show some examples of three-dimensional domain topologies, which are able to break energetically unfavorable symmetries. Finally, the computational model of a tetragonal nano-generator with dimensions 10 x 60 x 10 nm is presented. The specific ratio of height to width and the mounting on substrate is essential for its performance and principle of energy harvesting. We discuss the challenges and scopes of such a system.