characterization, modeling, and design of esd protection circuits

102 Chapter 4. Simulation: Calibration and Results
for all model coefficients revealed that the spacing between Id-Vgs curves for different Vbs (the subscripts d, s, g, and b stand for drain, source, gate, and substrate, respectively), i.e.,
the body effect, did not match the experimental data. Since the body-effect parameter [61],
2εsqNa γ =
--------------------- , (4.39)
C ox
where εs is the permittivity of silicon, q is the electron charge, Na is the effective channel
doping, and Cox is the gate oxide capacitance, is not dependent on mobility but is dependent
on the channel doping profile, the doping profile was modified in the 0.5µm and
3.0µm structures until the spacing between simulated Id-Vgs curves matched experiments.
This is justified because the change was relatively minor (the peak of the threshold-adjust
implant was reduced by a factor of two) and the initial channel profile was not extracted
experimentally but rather assumed from the SUPREM-IV simulation and thus was subject
to modification. In addition to the channel-doping modification, a fixed-charge density
was introduced at the gate oxide-silicon interface to align the simulated and experimental
grounded-substrate (Vbs = 0) curves, i.e., to align the threshold voltage, VT . The chargedensity
value used is reasonable in comparison to extracted values from real devices.
In the Id-Vgs simulations Vds is only 0.1V while Vgs is swept up to 3.3V (VCC ), so the
electric field perpendicular to carrier flow, E⊥ , is much larger than the parallel field, E || ,
and only the perpendicular-field mobility parameters in Eq. (3.21) and Eq. (3.22) need to
be adjusted to fit the Id-Vgs curves; the bulk term, µ b (Eq. (3.23)), is left constant.
Performing a simple sensitivity analysis by running separate simulations with BN, CN,
and DN set to twice the respective default value, and noting the resulting change in the Id- Vgs characteristic, it was found that BN has no discernible effect on the curves while CN
and DN each has a significant effect. Therefore, CN and DN were chosen as the
coefficients to vary and BN was left at its default value. Also, even though the curves are
sensitive to the doping exponent EN in Eq. (3.22), EN was left at its default value because
the structures’ doping profiles remained fixed after the channel profile adjustment. CN and
DN were varied in a full-factorial manner over a simulation design space covering
approximately one order of magnitude above and below their default values, and from
these simulations a set of values was found which yields an excellent fit for both the
0.5µm and 3.0µm curves. The chosen values are both within a factor of three of their
respective default values.