Environmental Engineering Reference
In-Depth Information
1.3.9.2
Channel length modulation
The channel length modulation was discussed in previous sections and
was modeled by the channel length modulation factor, in (1.34). In this
model, the pinch-off point was assumed to be close to the drain end.
A more effective modeling would take into consideration the fact that, in
practice, the pinch-off point moves towards the source as increases due
to the variation in the drain depletion region. As a consequence, the effective
channel length, is further reduced as shown in Fig. 1.14. Defining
as the distance between the drain end and the pinch-off point we get
The value of is a function of and the doping
concentration of the channel. Substituting, for example, (1.67) in (1.33) we
observe that, due to a shorter channel, the drain current increases with
Obviously, this effect is particularly evident in short-channel devices [8].
1.3.9.3
Mobility reduction due to vertical electric field
As known, the mobility,
relates the electrical field,
E,
to the drift
velocity of carriers,
v
d
,
as [1]-[2]
In our previous model we assumed the mobility to be a constant. Actually
the value of this parameter depends on several physical factors, the most
important of which is related to the carrier-scattering mechanisms.
The carrier scattering in the channel is greatly influenced by the vertical
electric field induced by the gate voltage. Consequently mobility changes
with A semi-empirical equation used to model the mobility reduction
due to vertical fields is [6]
where is now the new mobility (or better the new surface mobility), is
the mobility in the case of low fields and is the mobility degradation factor
whose value can be related to oxide thickness as
It can be shown that this effect can be modeled as a series resistance,
in the source of the MOS where
