198
Compact Models for Integrated Circuit Design
As a result, the relation v d   =  μE does not hold at high electric field. Since
average electric field for short channel devices  >  10 4   V cm −1 , small geometry MOSFET devices will operate at v d  = v sat  ≅ 1 × 10 7  cm sec −1 , that is, the
saturation velocity of electrons.
We discussed earlier that the mobility is not a constant at high electric
field; therefore, we must account for the high lateral electric field effects in
1.E+02
1.E+05
1.E+06
1.E+07
Carrier velocity (cm/sec)
1.E+08
T = 300°K
1.E+03
H
o l e s
E l e c t r o n s
1.E+04
E c
Electric field (V/cm)
1.E+05
1.E+06
v sat
FIGURE 5.11
Drift velocity versus electric field showing carrier velocity saturation in silicon at an electric
field near 1 × 10 4  V cm −1 .
V gs
V ds
C d
A
Body
p-Substrate
n+ Source
n+ Drain
C ox
C dsc
FIGURE 5.10
MOSFET device showing gate capacitance C ox , bulk capacitance C d , and source drain to channel coupling capacitances C dsc ; all the capacitances have an effect on the channel potential and
subthreshold conduction.