characterization, modeling, and design of esd protection circuits

4.1. Calibration Procedure 103
After determining the perpendicular-field mobility coefficients by calibrating the gate
characteristic, calibration of the drain characteristic was used to set the remaining mobility
coefficients in the bulk mobility term and high-field Caughey-Thomas expression (Eq.
(3.24)). Here the advantage of doing the gate calibration before the drain calibration
becomes obvious: in the Id-Vds curves the drain voltage is swept to VCC and the gate
voltage is stepped to VCC , so E || and E⊥ are both high, but since the E⊥ coefficients have
already been determined by the Id-Vgs fit, the optimization space is reduced to variation of
the E || coefficients. (Actually, a few iterations may need to be performed between gate and
drain calibrations because the bulk mobility and saturation velocity do affect the Id-Vgs curves.) As was the case for the gate-characteristic calibration, hole current is not solved
for in the drain simulations because its contribution is negligible. In initial Id-Vds simulations the saturation current, Idsat , as well as the separation between curves at
different Vgs values (i.e., the transconductance, gm ), were too high for the 0.5µm and
3.0µm structures. To reduce Idsat , the saturation velocity can be effectively lowered by
reducing βn in the Caughey-Thomas expression. The default value for βn in MEDICI is
2.0, but in this case the default value is too high because it is taken from an old publication
[48]. In a more recent publication, Jacoboni et al. report a βn of 1.11 based on a best fit of
several reported curves of drift velocity vs. electric field [62], so the need to reduce βn was
actually expected.
Instead of taking a full-factorial approach to the Id-Vds calibration, βn was first individually
optimized in an attempt to create a “quick fix” for Idsat . Using one value for βn , a good
fit could be made for the 0.5µm-gate Idsat and gm , but this resulted in too low an Idsat for
the 3.0µm-gate structure. Likewise, a larger value of βn resulted in a good fit at 3.0µm, but
Idsat and gm are then too high for 0.5µm. Adjusting the bulk mobility does change Idsat and
gm , but it affects the current of both structures proportionately, so µ b could not be used to
remedy the problem. The solution was to adjust βn to calibrate the 3.0µm-gate structure
(the final value of βn is nearly equal to the value of 1.11 reported by Jacoboni) and then
introduce a series source/drain resistance in the structures which effectively reduces Idsat and gm by dropping part of the drain voltage external to the device. This resistance, added
by defining lumped resistors at the source and drain electrodes in the simulations, has a
much larger effect on the 0.5µm structure than the 3.0µm structure because the current
level is much higher for the shorter gate. Using this method, good fits for both drain curves
were attained using a resistance of 12.5Ω on the source and on the drain. The lumped