Compact modeling of direct tunneling gate current considering quantum mechanical corrections in nano-scale mosfets

Abstract

A physically based, accurate model for the direct tunneling (DT) gate current of nano-scale MOS devices considering quantum mechanical (QM) effects is developed. Effect of wave function penetration into the gate-dielectric is also taken into account. When electrons tunnel from the MOS inversion layer to the gate, the system becomes quantized with finite lifetimes of the inversion carriers. In such a system, the Eigen energies are complex quantities. The imaginary part of these complex Eigen energies, r is required to estimate the lifetimes of these states. r follows an exponential relationship with the thickness of the gate-dielectric layer even in the sub-l-nm-thickness regime. In this work, an empirical equation of r is developed as a function of surface potential, rp., from a developed .self-consistent numerical simulator (Schrodinger-Poisson solver) considering open boundary condition. Inversion layer electron concentration is determined using Eigen energy, calculated by modified Airy function approximation that considers wave function penetration effect. Good agreement of the developed compact model with self-consistent numerical simulator and experimental data for a wide range of substrate doping densities and oxide thicknesses states the accuracy and robustness of the developed modeL Though the developed model holds good for only Si02 used as gate oxide, following the same methodology compact model of DT gate current for MOS devices with high-k gate dielectric can also , '.be developed.