Exercise Problems
3.1
Consider a MOS system with the following parameters:
18
-3
A
10
2
1.6nm
1.04V
N
=2.8 10
cm
4 10
C/cm
ox
GC
OX
t
Q
q
a.
Determine the threshold voltage V
T0
under zero bias at room temperature (T = 300 K).
Note that
0
3.97
ox
and
0
11.7
si
.
SOLUTION :
First, calculate the Fermi potentials for the p-type substrate and for the n-type polysilicon gate:
10
18
1.45 10
(
)
ln
0.026V ln
0.49V
2.8
10
i
F
A
n
kT
substrate
q
N
The depletion region charge density at
V
SB
= 0 is found as follows:
0
19
18
14
7
2
2
2
(
)
2 1.6 10
(2.8
10 ) 11.7 8.85 10
2 0.49
9.53 10
C/cm
B
A
Si
F
Q
q N
substrate
The oxide-interface charge is:
19
10
-2
9
2
1.6
10
C
4 10
cm
6.4 10
C/cm
ox
ox
Q
q N
The gate oxide capacitance per unit area is calculated using the dielectric constant of silicon dioxide and
the oxide thickness
t
ox
.
14
6
2
7
3.97 8.85 10
F/cm
2.2 10
F/cm
1.6 10
cm
ox
ox
ox
C
t
Now, we can combine all components and calculate the threshold voltage.
0
0
2
(
)
1.04
( 0.98)
( 0.53)
(0.03)
0.44V
B
ox
T
GC
F
ox
ox
Q
Q
V
substrate
C
C
b.
Determine the type (p-type or n-type) and amount of channel implant (N
I
/cm
2
) required to change the
threshold voltage to 0.6V

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