7.6 Emission Time Constants
The degraded 
in small-area transistors with only a few defects relaxes in
discrete steps. Each step reveals a hole emission event at the emission time
of a particular defect [115, 111]. Larger devices contain
a larger number of defects, which in combination with a nearly uniform
distribution of the activation energies 
yields a log-like recovery behavior as
displayed in Fig. 7.12. As there are many different pairs of 
and 
within the device, their extraction from the experimental data is discussed
first.
By subtracting two recovery traces after stress times 
and 
, the
fraction of defects with capture time constants with 
is
determined first [116], which is shown in Fig. 7.13. By dividing the difference
trace into intervals ![[tr,i,tr,i+1 ]](diss1511x.png)
, the fraction of defects having 
and 
is obtained.
To be able to describe the frequency of occurrence of capture time constants
and emission time constants 
properly, a large set of long recovery traces
with varying 
is needed. The experiments performed cover 
from
up to 
and 
intervals between 
and 
. This
allows for an extraction of the time constants as exemplarily depicted in
Fig. 7.14.
It is now possible to explain the above mentioned effect with the varying
oxide electric field on the basis of Fig. 7.15, where the fraction of 
due to
defects with 
and 
is plotted as smoothed surface over 
and
.
For NBTI with an 
of 
the surface shows two peaks.
One peak covers 
and 
smaller than 
, while the other more
pronounced one clearly illustrates that the largest part of the degradation was
due to defects with 
larger than 
, which is highlighted by the
contour lines below the graph. When comparing the different 
for
PBTI for 
covering time constants between 
and 
, the
peak of 
mainly consists of 
, while it is widened for
towards smaller 
. This supports the hypothesis of decreased 
for higher 
after PBTI stress, which appears as faster long-term
recovery.
like
in small-area transistors 
behavior, instead. 
and 
yields the fraction of defects with capture time
constants with 
These ranges of capture time constants of
certain defects are depicted as function of 
. The contour lines below
the three graphs emphasize the amount of defects contributing to 
.
For NBTI with an 
of 
, the characteristics of 
are
not changed with increasing 
, despite some shift along the positive
-axis. The maximum 
values for all 
-ranges are obtained
for small values of 
. This implies fast relaxation. On the contrary,
PBTI (
) yields a larger degradation and additionally moves the
characteristics of 
towards increasing 
. For the largest available 
,
which covers time constants between 
and 
, the maximum of
is moved away from the minimum 
. This maximum marks the
beginning of the change of emission time constants 
depicted in Fig. 
. 
and
is depicted for three different oxide electric fields. The
contour lines below the graphs highlight the biggest changes of 
. Both
surface and contour lines are smoothed for a better visualization. It is shown
that the oxide electric field is related to the magnitude of 
. Increasing
yields a shift of the peak towards smaller 
, which corresponds to our
monitored increased recovery at larger 
. Note that only for 
a
full set of 
and 
is available and therefore the map has to be truncated
in order to be comparable with the case 
.