characterization, modeling, and design of esd protection circuits

132 Chapter 4. Simulation: Calibration and Results
Pt2 . Assuming a diffusivity, D, of 0.35cm2 /s, the dimension of the 3D thermal-box model
corresponding to this time constant is 4πDt2 = 4.7µm.
This dimension is too large to
be related to the gate length or junction depth, but it is only a factor of five smaller than the
device width, so the breakpoint may indicate where the failure power changes from a
1⁄ log () t dependence to a constant (refer to Fig. 2.12). However, a similar breakpoint
time was seen for wider structures, and for times less than about 40ns there is significant
uncertainty in the measurements due to circuit noise, so this conclusion is premature.
Improvement in the measurement uncertainty can probably be achieved by enhancing the
automated algorithm used to capture the second-breakdown points and by further improving
the high-frequency characteristics of the test jig. After these tasks are completed we
will take more low-end points and try to fit the resulting Pt2-t2 curve to the 3D box model.
Simulated Pt2-t2 points are also plotted in Fig. 4.52 for the 25/0.75µm structure (simulations
were actually run on 100µm-wide structures and the resulting powers were reduced
by a factor of four). In the various simulations, the pulse length is simply set to a very
large value and the pulse height is varied to yield different failure times. Each simulation
is discontinued when the maximum temperature reaches 2000K. As in the failure-power
results discussed previously, the simulated power to second breakdown is significantly
lower than the measured power for all second-breakdown times. However, the simulated
points exhibit a break in the Pt2-t2 curve at a time close to that of the experimental results.
The significance of this result must once again be questioned because of the unsatisfactory
modeling of the high-current regime. Once this modeling issue is resolved, the importance
of the simulated breakpoint (if it still exists) can be determined.
To close out this section on ESD device failure analysis using TLP, experimental Pf vs. tf and If vs. tf failure curves for structures with varying contact-to-gate spacing are plotted in
Fig. 4.53a and Fig. 4.53b, respectively. For these plots the time to failure is equal to the
TLP pulse width and 1µA leakage is used as the failure criterion. Most of these 50µmwide
structures exhibit a breakpoint between 100ns and 200ns, which again suggests a
change in the Pf-tf relationship theorized by the thermal-box model. For large failure
times, the failure points reflect the results of Fig. 4.50 and Fig. 4.51, i.e., the failure power
continually increases with CGS but the failure current reaches a sort of saturation point. In
contrast, for the smallest pulse width (50ns) increasing the contact-to-gate spacing from
3µm to 8µm does not significantly improve either Pf of If (any improvement seen is on the
order of three experimental standard deviations of any one structure). This indicates that