Simulation of Negative Capacitance Based on the Miller Model: Beyond the Limitation of the Landau Model

Abstract

Here we demonstrate negative capacitance (NC) characteristics of a ferroelectric–dielectric (FE–DE) capacitor by means of a fully numerical, self-consistent simulation based on the Miller model (MM) and Poisson’s equation. Over the years, the Landau model (LM) has been widely used, which fits experimental data of spontaneous polarization versus electric field ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}-{E}_{\mathrm {FE}}$ </tex-math></inline-formula> ) characteristics using a so-called “S-curve”; however, it cannot capture different transitions of polarization switching and can also fail to properly represent the material properties of certain FEs. To overcome such limitations of the LM, we have used the MM to simulate an FE–DE capacitor. Even though the MM seemingly fails to show steep switching characteristics due to the absence of the negative slope in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}-{E}_{\mathrm {FE}}$ </tex-math></inline-formula> curve unlike the LM, our simulation exhibits the NC characteristics of FE–DE capacitors with significant internal voltage amplification. Notably, we explore the effect of different transitions of polarization switching by varying the coercive field of FE within the MM, and exhibit that greater NC characteristics can be achieved with a FE having a more abrupt switching transition. We have also investigated the impact of other material parameters of FE, such as saturation and remnant polarization, on the NC characteristics of FE–DE capacitors. Our results provide comprehensive insight into the mechanism of FE-DE capacitors, suggesting sophisticated engineering of material and device parameters to seek desired performance of NC devices.