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40
Logic
12
, V
ON
can be any value between 2.2 and 5 V. For OFET/TFT, unless the operation voltage at
which the DUT is expected to operate as component of some OFET/TFT-based device, V
ON
is usually
assumed to be the maximum gate voltage at which the FET is swept in linear or saturation regime.
The ratio between the I
ON
and I
OFF
currents is referred to as the
ON/OFF ratio
. It is important
transistor figure of merit, especially if the transistor is to be used as digital component.
Threshold voltage: second derivative method
From the definition of FET operation regions above, we saw that the transistor is entering the ON
region for V
GS
> V
T
. The transition however is not step-like, and an extra ΔV voltage is required on top
of V
Th
to drive the transition to its
operative
ON state. For inorganic FETs, as the gate voltage crosses
the threshold, the current increase is so steep that we can safely assume the FET to be
fully
ON
for
V
GS
> V
Th
+ΔV, with ΔV/V
ON
<<1, with ΔV extra voltage required to ‘move’ the DUT from the
OFF
to the
fully
ON
region. Inorganic standard FETs are therefore characterised by a very narrow
ON-OFF
transition region.
For OFET/TFT, the current increase for V
GS
> V
T
can far more gradually (low mobility) with a wider
ON-OFF transition region. Nevertheless, it is still reasonable to approximate I
DS
as
Eq. 13
where
is given by Eq. 1 or Eq. 6, while
is the current for
.
For an ideal FET with
= 0 and
0 (steep ON/OFF transition), the derivative of
with
respect to the gate voltage would then be a step function i.e.
Eq. 14
with
slope of the TC curve
13
. If Eq 3 is differentiated again, and if
is constant, the resulting
function will be zero everywhere with the exception of the threshold voltage
V
Th
where the
derivative is infinite
14
.
12
TTL (Transistor-Transistor Logic) is a protocol whereby a signal/state is assumed to be
Low
(0) if the voltage
is between 0 and 2 V, and high (1) if the voltage is between 2.2 and 5V. SuperFACT multiplexer is complying
with TTL logic.
13
Without loss of generality, we have assumed that the slope
α
is gate voltage independent.
14
For an ideal FET with constant slope over the ON region, the second derivative of the transfer characteristic
with respect to the gate voltage is a Delta of Dirac.
