On the Microscopic Origin of Negative Capacitance in Ferroelectric Materials: A Toy Model

We present a simple, physical explanation of underlying microscopic mechanisms that lead to the emergence of the negative phenomena in ferroelectric materials. The material presented herein is inspired by the pedagogical treatment of ferroelectricity by Feynman and Kittel. In a toy model consisting of a linear one-dimensional chain of polarizable units (i.e., atoms or unit cells of a crystal structure), we show how simple electrostatic interactions can create a microscopic, positive feedback action that leads to negative capacitance phenomena. We point out that the unstable negative capacitance effect has its origin in the so called “polarization catastrophe” phenomenon which is essential to explain displacement type ferroelectrics. Furthermore, the fact that even in the negative capacitance state, the individual dipole always aligns along the direction of the local electrical field not opposite is made clear through the toy model. Finally, how the “$S$”-shaped polarization vs. applied electric field curve emerges out of the electrostatic interactions in an ordered set of polarizable units is shown.