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.
