textHigh dielectric constant materials are expected to replace SiO2
when the
direct tunneling currents become intolerable for circuit design considerations.
These dielectrics exhibit a trend of decreasing barrier height with increasing
dielectric constant and hence the performance trade offs of choosing various
dielectrics was performed. This work involves the numerical solution of the
Schrodinger's and Poisson's equation to obtain the direct tunneling current
through high dielectric constant materials allowing for wave function penetration
into the gate electrode. This approach has been validated for oxides as thin as 5Å.
A Franz-type complex energy band structure model with energy dependent
effective mass was used to calculate tunneling across the dielectric. In addition,
with scaling of the oxide to ultra-thin dimensions, the effects of wave function
penetration into the gate electrode on the gate capacitance become significant. It
was observed that allowing the wave function to penetrate into the gate electrode
shifts the centroid of the inversion charge closer to the interface resulting in
higher gate capacitance. This phenomenon has been comprehensively studied in
the context of gate electrodes, gate dielectrics and scaling. The characterization of
ultra-thin oxides is becoming non-trivial with transmission line effects and high
direct tunneling currents. The physical thickness characterization must now be
performed in conjunction with capacitance and tunneling current measurements.
However, most compact direct tunneling current models have a large number of
parameters that are sometimes represent incorrect physics and thus, cannot be
used as a predictive tool. Hence, there is a strong need for a first principles
compact gate capacitance and gate current model. In this work a gate capacitance
model based on the characterization of the quantized subbands is presented. This
model is fast and accurate and can be extended to evaluate tunneling currents
from each subband. The advantages and disadvantages of using simpler,
unphysical models to estimate the effective oxide thickness of capacitors are also
presented.Electrical and Computer Engineerin
