710
24 Transistors
Fig. 24.17 Circuit
symbols for various types
of FETs
24.4.4 Field-Dependent Mobility
So far, we have considered FETs with long channels (L a). This situation is often not the case, in
particular for high-integration or high-frequency applications. For short channels, the I –V characteristics exhibit changes. The theory needs to be modified to take into account, among other effects, the
electric-field dependence of the mobility (Fig. 8.13) that was discussed in Sect. 8.4.1.
Drift-Velocity Saturation
A material without negative differential mobility, such as Si or Ge, can be described with a drift-velocity
model
v d = μ E
1
1 + μ E/v s
.
(24.50)
In this model, μ denotes the low-field (ohmic) mobility and v s the drift-saturation velocity reached for
E v s /μ. The fraction in (24.50) describes the drift-velocity saturation.
By inserting (24.50) into (24.39), we obtain (for a n-channel)
I D = −e N D μ n E(x)
1
1 + μ E(x)/v s
[a − h(x)] Z ,
(24.51)
and after a short calculation the drain current is given by (cf. (24.42))
I D = I P
1 +
μ V G
v s L
−1
3V D
V P
− 2
(V bi + V G + V D )
3/2
− (V bi + V G )
3/2
V
3/2
P
.
(24.52)
The factor 1/(1 + z) with z = μV G /v s L reduces the channel current due to the drift saturation effect.
The effect of the parameter z is depicted in Fig. 24.18 in comparison to z = 0, i.e. without the drift
saturation effect (or v s → ∞). The forward conductance g m,sat decreases with increasing z, as shown
in Fig. 24.19.