156
Compact Models for Integrated Circuit Design
becomes zero. At the pinch-off point, E x  = E y , and when E y  > E x , the mobile
carriers are pushed off the surface near the drain region creating drain
depletion or pinch-off region as shown in Figure 4.11c. Then from Equation
4.78, the pinch-off voltage, commonly referred to as the saturation drain
voltage, V dsat is given by
V
V V
dsat
gs
th
=
–
(4.80)
Equation 4.80 shows that the pinch-off voltage V dsat equals the effective gate
voltage V gst that increases with increasing V gs as shown in Figure 4.10 by the
V s
V s
V s
L
Gate
X j
Depletion
layer
(a)
(b)
(c)
Inversion
layer
Oxide
n+ Drain
V gs ≥ V th
V gs ≥ V th
V gs ≥ V th
P
V gs < V dsat
V ds = V dsat
V ds > V dsat
l d
n+
n+
n+
n+ Source
n+
FIGURE 4.11
Schematic diagram of an nMOSFET device at strong inversion showing channel pinch-off as
V ds is increased; (a) an inversion layer connects the source and drain, V ds  < V dsat and (b) at the
onset of saturation, the channel pinches off at the drain end, V ds  = V dsat , and (c) the pinch-off
point P moves toward the source.