Sensing of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 60

uniform along the channel at small V D values. Under such conditions, the channel
with width W and length L G is equivalent to a resistor and, according to Ohm's law,
the drain current I D is given by

I D D n C ox W.V G V th /V D =L G ; (2.7)

where n is the mobility of electrons in the channel. From ( 2.7 ), it can be seen that
I D depends linearly on V D and can be tuned via V G . This situation corresponds to
the linear region of the transistor, in which an input signal is amplified.
When V D is further increased, it induces a nonuniform electron distribution in
the channel. In the particular case of a linear distribution of electrons in the channel
for V G V th >V D , such that the density of electrons is maximum at the source
and minimum at the drain, we get the second region of the MOSFET, called triode
region, in which

I D D n C ox WŒ.V G V th /V D mV D =2=L G :

(2.8)

The coefficient m is given by m D 1 C .1=C ox /=." s qN s =4 j F j / 1=2 and is termed
body effect coefficient; its typical values range between 1.1 and 1.4. The triode
region is a nonlinear region.
Increasing further V D , we arrive at a regime with no charges near the drain, in
which the channel is pinched off, and thus, the drain current does not depend on V D .
This is the saturation regime of the MOSFET, which starts at V D D .V G V th /=m D
V DSat and is characterized by a saturation current

I D D n C ox W.V G V th / 2 =2mL G : (2.9)

In the saturation region, the transistor works digitally, switching between the off
state, when there is no current flow and V D D 0, and the on state corresponding
to the saturation region, for which V D V DSat . The three working regimes of the
MOSFET are visualized in Fig. 2.3 .
Other essential parameters for any FET are the gain or transconductance,
defined as

I D

saturation regime

triode regime

Fig. 2.3 The working
regimes of a MOSFET at a
certain value of the gate
voltage

linear regime

V D