24.5 MOSFETs
715
Fig. 24.22 a MOSFET
with inverted channel (dark
grey) of length L for small
source–drain voltage V D in
linear regime, b at the start
of saturation at pinch-off, c
in the saturation regime
with reduced channel
length L . The pinch-off
point is denoted by an
arrow in b and c. The
dashed lines denote the
extension of the depletion
region. Adapted
from [574]
(c)
(b)
(a)
S
small V D
V >V
G
T
V =V
D
D,sat
V >V
G
T
V >V
D
D,sat
V >V
G
T
p-Si
n+
n+
p-Si
n+
n+
p-Si
n+
n+
pinch-off
depletion layer
pinch-off
I D
L
L'
insulator
metal
such that, using (24.59), the inversion layer charge is
Q n (y) = Q s (y) − Q d (y)
(24.61)
= − [V G − V (y) − 2 B ] C i +
2 s e N A [2 B + V (y)] .
For the calculation of the drain current, we consider the increase of channel resistance d R(y) along a
line element dy of the channel. The integral of the conductivity over the cross section A of the channel
(width Z ) is
A
σ(x, z)dx dz = −e μ n
A
n(x, z) dx dz = Z μ n |Q n (y)| .
(24.62)
Therefore,
d R(y) = dy
1
Z μ n |Q n (y)|
.
(24.63)
Here we have assumed that the mobility is constant along the channel, i.e. not field dependent. The
change of voltage across the line element dx is