Physical Cause and Impact of Negative Capacitance Effect in Ferroelectric P(VDF-TrFE) Gate Stack and Its Application to Landau Transistor

Abstract

A novel approach to overcome Boltzmann’s tyranny is to exploit the negative capacitance (NC) effect found naturally in many ferroelectric (FE) materials. We apply a set of coupled equations based on electrostatics, Kirchoff’s law, and a well-calibrated Ginzburg-Landau-Khalatnikov technology computer-aided design (TCAD) model to simulate an organic FE poly(vinylidene fluoride- co -trifluoroethylene) [P(VDF-TrFE)]-based resistor metal-FE-metal ( $R$ -MFM) series circuit and a Landau transistor (LT) exhibiting sub-60 mV/decade subthreshold swing (SS). TCAD simulation parameters for P(VDF-TrFE) are derived from the reported experimental polarization versus voltage characteristics using Landau theory. Unlike oxide FEs, the P(VDF-TrFE)-based $R$ -MFM series circuit can exploit the NC effect at a lower supply voltage ( $V_{G}$ ) of ±0.5 V with little energy dissipation of ~2.7 fJ through $R$ . Our simulation results show an 84.89% reduction in the P(VDF-TrFE)’s coercivity concerning the oxide FE. We show that the underlying mechanism of the NC effect is directly related to FE polarization (FE- $P$ ) switching. The NC effect occurs only when the FE- $P$ is in the negative curvature of the P(VDF-TrFE)’s free energy landscape. The NC effect is explored in terms of $V_{G}$ , FE thickness, domain variations, $R$ , and dipole switching resistivity. The influence of $R$ variation on the NC time ( $\delta t$ ) is investigated at 100 kHz. We can observe that $\delta t$ and $R$ have a linear relationship. As $R$ approaches zero, we determined that the inherent FE- $P$ switching speed exclusively restricts the NC effect. Finally, a 32 nm P(VDF-TrFE) LT provides a minimal SS of 23.39 mV/decade, 74.92% less than its CMOS counterpart. Therefore, the proposed organic MFM stack could open the path for developing beyond CMOS transistor technology operating in sub-60 mV/decade.