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41
For real-world FETs, the current discontinuity at V
Th
(the step) should be replaced by a steeply
increasing, yet continuous, function. However, as far as Eq. 13 is an adequate approximation of the
FET behaviour and
is
reasonably
small, Eq. 14 indicates that the second derivative of I
DS
can still
be expected to show a peak (i.e. a maximum) as the transistor cross the threshold. Based on these
considerations, the field-effect threshold voltage can be defined as
15
Eq. 15
Eq. 15 is provides us with an alternative to the linear fit method to calculate the threshold voltage.
Since the maximum of Eq. 15 detects at which
V
GS
the
drain current changes its functional
dependence on the driving voltage, see Eq. 13, from an operational perspective, Eq. 15 is, in
principle, a mathematically more rigorous definition of the threshold voltage than the standard
definition given at the beginning of this chapter, see figure 16.
The calculation of the threshold voltage through Eq. 15 is referred in the literature as
Second
Derivative
Method
8
.
For OFET/TFT devices, especially for non-optimised R&D and/or low mobility DUTs, a larger switch
transition region
manifest itself in broad peak or even complete absence of this feature at
V
T
. To
complicate matter, a gate-voltage dependent mobility, i.e.
will also result in a broader,
less defined peak at
V
T
with the second derivative method becoming non-applicable in the worst
case scenario.
Figures of merit
The figures of merit or transistor performance parameters are those measureable features that
define the performance of a transistor. The figures of merit that are automatically calculate by
SuperFACT are mobility (
μ
); Threshold Voltage (V
Th
and
);OFF current (I
OFF
); minimum current
(I
MIN
); ON current (I
ON
); ON/OFF ratio (I
ON
/ I
OFF
) and Min/Max ratio (I
ON
/ I
MIN
).
Two additional figures of merit that are not calculated by SuperFACT are the ON/OFF frequency (
f
)
and the subthreshold swing (
S
).
render
Eq. 16
Eq. 17
15
A. Ortiz-Conde et
al A review of recent MOSFET threshold voltage extraction methods
, Microelectronics
Reliability,
2002, 42 583–596.