Some of these definitions are not practically useful because they are not applicable to deep-sub-micron devices (1,3). The threshold-current definition 2 is attractive because of its simplicity and is being widely used by different groups inside companies. The numbers obtained are comparable only for a limited range of technology parameters. The same applies to the model-fit definition 4. One severe drawback of both methods 2,4 is that the numbers obtained by different organizations are almost for sure not comparable.E.1
The linear threshold voltage definition 5 does not suffers from any of the
aforementioned drawbacks:
depends on no other definitions and
it applies to a wide range of devices. The only restriction of
is
the assumption of a small drain-source voltage, which precludes the investigation
of DIBL phenomena.E.2
The definition of the drain-source voltage
6 was developed
in this work and can be used to characterize the
dependence of
the threshold voltage.
Note, that this definition relies entirely on the unique definition of
,
which in turn relies on that of
.
This makes the definition
of
as unique and universal as that of
.
The value
is usually in the range of several 
for
and can vary considerably with other device parameters.
For a long-channel device in saturation
and
are identical
(this follows directly from the definition of
).
The necessary difference between
and
is that
is
independent of
and is valid also for
where
would be
infinite, whereas
reflects the drain voltage dependence well for
.
For this work, parameter extraction algorithms for
and
(definitions 5 and 6) were developed
using polynomial regression analysis of the IV
data.
For both
and
(i.e., for
)
the IV data are analyzed
pointwise to find an appropriate range using heuristic algorithms.
From these data subsets third-order polynomials are determined,
from which
and
can be computed.
-method.