characterization, modeling, and design of esd protection circuits

3.6. Extraction of MOSFET Pf vs. tf Curve 85
It is clear, however, that by applying boundary conditions with large thermal resistances
around the 2D simulation structure the peak temperature is increased for a given input
power, which means the simulated power to failure is reduced. This method will be used
in the next chapter to calibrate simulated Pf vs. tf curves to experimental curves, but it is
apparent that caution should be taken against using thermal resistances which are higher
than physically justifiable, a definite risk considering the inherent overestimation of the
power to failure in the 2D model.
This section has focused on the use of monitoring the peak lattice temperature in
predicting thermal failure of ESD protection devices. Presumably, when the peak
temperature reaches a critical value, second breakdown occurs and device damage follows
instantaneously due to gross melting. If the object of simulation were to correlate
simulations with this analytical thermal-model definition of failure, then it would only be
necessary to monitor the peak temperature in the simulations. But although device failure,
which is really defined by an increase in leakage current above a specified threshold level,
correlates well with the occurrence of second breakdown for stress times greater than
about 100ns, as mentioned in Chapter 2 for very short pulses device leakage can be
increased above the failure level without the device exhibiting second breakdown because
the damage site is too localized to reduce the resistance of the entire device. Since there is
no unique series of events which leads to thermal failure, various phenomena should be
monitored both experimentally and in simulations. During a transmission-line pulse test of
a real structure, it is not possible to monitor the transient temperature profile, so thermally
induced damage must be inferred by observing second breakdown on an oscilloscope
during a pulse and/or confirmed by measuring an increased amount of leakage after the
pulse. In contrast, simulations can be used to study not only the voltage drop due to second
breakdown but also to study the 2D profiles of the lattice temperature, electric field, heat
generation ( J ⋅
E),
and intrinsic carrier concentration (ni ). Considering the difference
between the 2D and 3D thermal models, it may even be beneficial to compare
experimental and simulated current to failure rather than power to failure, as suggested by
Diaz [24]. Thus, while much effort was devoted to analyzing the thermal model’s ability
to predict Pf vs. tf behavior, the larger goal of electrothermal simulation is to be able to
predict thermal failure in actual devices using any physical characteristics accessible in a
calibrated simulation.