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Note: Since the derivative of a function y = f(x) at a point y
y
the derivative of straight line y
0,
to y
. In other words, the slope of the linear fit of a straight line y= f(x) and the derivative at any of its
s
points y
are the same. Therefore for a straight line, Eqs. 9 and 10 reduce to Eqs. 4 and 8. Most
0
importantly, to the extent the drain current is weakly dependent on V
considered to be a sufficiently good approximation of Eqs. 10 and 11.
These considerations are particularly important in the field of organic electronic because, with few
notable exceptions, OFET/TFT mobilities are gate-voltage dependent. However, for weakly
dependence, Eqs. 4 and 8 and Eqs. 9 and 10 yield approximately the same numerical value for the
field effect mobility.
Transfer characteristic curves: ideal and real behaviour
For an ideal TC curves the drain current is zero for V
fact, the relation between drain current and both gate and drain voltage is more involved
sake of simplicity, we neglect the details of the functional dependence of I
and simply assume that for a well-behaved FET, the current for V
compared with I
for V
DS
GS
Notwithstanding these simplifications, depending on the value of V
two different operation regions: Subthreshold or Cutoff (for V
follows that a FET can be considered as two-state device (bit) with the state OFF (logical state 0) and
ON (logical state 1) corresponding to the two operation regions Cutoff and ON respectively.
A good transistor must therefore output a tiny (ideally zero) current while OFF and switch on very
steeply as V
approaches V
GS
Since I
is the largest current that a transistor output before entering the ON region, for
Th
characterisation purpose, it is useful to consider the threshold current to be the OFF current of the
FET. We therefore define the OFF current as
I
= I
= I
(V
).
OFF
Th
DS
Th
Eq. 11
Similarly, the ON current I
I
= I
(V
),
ON
DS
ON
Eq. 12
where V
is the typical operational gate voltage applied to the transistor to switch it ON. V
ON
therefore a not well-defined quantity, and its actual numerical value can depend on the
application/purpose of the transistor itself. For example, for inorganic FETs complying with TTL
11
Refer to references 6, 7 and 8 for more detailed analysis of the mathematical relationship between I
applied voltages and FET intrinsic material properties.
Ossila Ltd
= αx gives the same numerical value (α) for any point y
s
>> V
.
T
see Eq. 16, so to allow for fast (steep) ON/OFF transition.
Th,
is defined as
ON
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is the slope of the tangent curve of f(x) at
0
, Eqs. 4 and 8 can be
GS
<V
and increases rapidly for V
GS
T
on the driving voltages,
DS
< V
is very small when
GS
Th
, a transistor can be found in
GS
< V
) and ON (for V
GS
Th
belonging
0
>V
. In actual
GS
T
11
. For the
> V
). It
GS
Th
is
ON
,
DS
39
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