A Computational Framework for Gradually Switching Ferroelectric-Based Negative Capacitance Field-Effect Transistors

Abstract

While the Landau approach is widely used to model polarization switching of ferroelectric (FE) materials, it cannot accurately describe gradual transition of polarization switching for a stand-alone FE in steady states. To overcome such limitations, the Miller model (MM) was used previously to replicate the switching behavior of FE within an FE–dielectric (FE-DE) capacitor. In this study, we demonstrate a new computational framework for gradually switching FE-based negative capacitance (NC) field-effect transistors (FETs) in steady states. In particular, we solve three modules iteratively: 1) non-equilibrium Green’s function (NEGF) for carrier transport; 2) Poisson’s equation for electrostatics; and 3) the MM for spontaneous polarization ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}$ </tex-math></inline-formula> ) versus applied 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">${E}_{\text{FE}}$ </tex-math></inline-formula> ). Unlike the FE-DE capacitor, polarization varies along the device position due to the applied field across the device, and hence, polarization interactions are considered. Our simulation result exhibits hysteresis-free, steep-switching characteristics of the NCFET even with the “positive 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">${P}-{E}_{\text{FE}}$ </tex-math></inline-formula> curve originating from the MM. We have also explicated the physical origin of the experimentally demonstrated critical FE thickness, at which minimum subthreshold swing can be achieved, using two competing mechanisms. Finally, we vary FE parameters (i.e., saturation polarization, remnant polarization, and coercive field) within the MM to investigate their effects on the characteristics of the NCFET. This work not only suggests a novel computational framework for the simulation of the NCFET based particularly on gradually switching FE but also provides irreplaceable physical insight into the optimization of the NCFET by tuning material and device parameters.