Analytical Modeling of Short-Channel Effects in MFIS Negative-Capacitance FET Including Quantum Confinement Effects

An analytical 2-D model of double-gate metal-ferroelectric-insulator-semiconductor-negative-capacitance FET (MFIS-NCFET), using Green's function approach, in the subthreshold region, is presented in this article. The explicit solution of coupled 2-D Landau-Devonshire and Poisson equations is analytically derived. Subsequently, an analytical and explicit model of subthreshold slope is developed from potential functions. The developed model includes quantum-mechanical effects, which considers not only geometrical confinements but also electrical confinements. The analytical solution of a 2-D nonhomogeneous Poisson equation coupled with the 1-D Schrödinger equation is used to obtain the potential function in the channel. The impact of the ferroelectric thickness (t
_fe
) on quantum confinement is also studied. We find that larger tfe reduces the quantum confinement effect. Therefore, as t
_fe
increases, threshold voltage roll-off with the variation in Si-body thickness decreases.