In contrast to Chapter 6.3, where the degradation of the drain current is directly fit by (6.1), the drain current is now first converted to an approximate threshold voltage shift using the simple OTF1 relation derived in Appendix A.1
Note that
![]() | (6.4) |
In order to circumvent issues with the logarithmic fit caused by offset data due to
the uncertainty in , the parameter
is included. Besides, it is tried to fit
the data to a power-law of the form
![]() | (6.5) |
Again, the parameter is introduced to account for the offset in
.
Interestingly, it turns out that the logarithmic fit (6.4) is always possible,
while the power-law fit (6.5) produces reasonable results for high temperatures
and high only. In that high-stress regime, power-law exponents around
are obtained. For weaker stresses, the exponent
in (6.5) tends towards
zero, which corresponds to a first-order Taylor expansion of (6.5) on a
logarithmic scale. As such, in this regime the power-law fit (6.5) becomes
equivalent to the logarithmic fit (6.4).
This behavior is illustrated in Fig. 6.15 and Fig. 6.16. The data obtained
from the harshest stress conditions (,
, and
) gives a stable fit with
. For the other extreme case
(
,
, and
) the fitting algorithm gives an
exponent
of practically zero. For the case of the non-converging exponent
the logarithmic and power-law fits coincide.
Consequently, the power-law fit only makes sense for high temperatures
and/or high , as displayed in Fig. 6.17. There, the extracted
for
short-term stress is roughly one third of the often reported
of the
long-term behavior.