
46-6 Optical
and the solutions are
ψ
ψ ψ
ε
ψ
= − ⋅ + − < <
=
− ⋅ ⋅ −
< <
=
⋅ ⋅
V E x d d x
q N x x
x t
q N x
G ox
D n
s
A
( )
( )
( )
(
max
0
2
0
2
−− −
< < +
t x
t x t x
p
s
p
)
( )
2
2
ε
(4
6
.6)
w
here
E
ox
is the electric eld in the oxide layer
V
G
is the gate bias voltage
x
n
is the position of the potential maximum
Figure
46.1 sh
ows
a ty
pical
po
tential
pr
ole
ac
ross
th
e
MO
S
ca
pacitor
in a bu
ried-channel
CC
D
. No
te
th
e
p
resence
o
f
a p
otential
m
aximum,
ψ
max
, where the electrons will reside. It is given by
ψ ψ
max
= ⋅ +
J
A
D
1
N
N
(46.7)
where
J A p S
/
q N x
2( )
.
Si
nce
x
p
increases linearly with N
D
, the potential maximum ψ
max
and hence the charge storage capa-
bility
al
so
in
crease