Quantitative definitions of
,
e.g., in terms of a surface potential
displacement, drain current, or gate capacitance can be found in almost any text book
relevant to the subject.
The particular problem of threshold voltage definition is that there are many
different definitions which are not consistent, even though many of
them are physically well-motivated. Worse yet, some of the definitions
are ambiguous as they demand the selection of other threshold parameters
or definitions of effective geometry parameters.
The following list gives
the
definitions relevant to this work:
The surface potential displacement
is twice the
built-in potential
,
i.e., the band structure is inverted
at the surface.
This definition applies only to long-channel devices with constant
channel doping.
cannot be measured directly.
For a fixed drain-source voltage the drain current equals some threshold
current
at
.
This definition is ambiguous because of the definition of
and
is only restrictly applicable to small devices because of the
uncertainty in
and
.
In saturation (
)
the tangent to
at the highest slope intersects the
-axis at
.
This definition applies only to long-channel devices.
A given model function
is fitted to IV data
via the set of parameters (including
).
This definition is ambiguous because it depends on the choice of the model function, parameter set, and operating points.
In linear operation (
,
usually 50mV)
the tangent to
at the highest slope intersects the
-axis at
.
This definition is unique (
)
and universal.
For a fixed drain-source voltage the drain current equals the threshold
current
at
.
For
the tangent to
at the smallest slope
intersects the
-axis at
.
This definition is unique (because of the unique definition of
),
universal, and consistent with
(for long-channel devices in
saturation).