Homework 7
1.
Problem:
(a) Consider an nchannel MOSFET with uniform channel doping with
N
A
= 3
×
10
17
cm

3
and
having an oxide
10
nm thick. Calculate the subthreshold slope at
300
K.
(b) Assume now that the SiSiO
2
interface is not ideal, but there are interface traps with density
N
it
=
10
12
cm

2
/eV
. What is the subthreshold slope in this case?
Solution:
(a)
On lecture notes Part 3, the subthreshold slope is given by Eq. (280)
S
=
k
B
T
e
ln
(10)(1 +
C
D
C
ox
)
(1)
where
C
D
=
s
W
D,max
and
W
D,max
is the maximum depletion width defined by Eq. (221)
W
D,max
=
4
s
k
B
T ln
(
N
A
/N
i
)
e
2
N
A
1
/
2
= 61
.
5
nm
(2)
and
C
D
=
11
.
7
×
8
.
854
×
10

12
F/m
61
.
5
×
10

9
m
= 0
.
0017
F/m
2
,
(3)
and
C
ox
=
ox
t
ox
= 0
.
0034
F/m
2
. Inputting the above values and finally we can get the subthreshold slope
S
= 0
.
0892
.
(b)
When the SiSiO
2
interface is not ideal with an interface traps density
N
it
= 10

12
cm

2
, the subthreshold
slope is calculated using Eq. (282)
S
=
k
B
T
e
ln
(10)(1 +
C
D
+
C
it
C
ox
)
(4)
ECE344 Fall 2009
1
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where
C
it
is given by Eq. (226)
C
it
=
eN
it
= 0
.
0016
F/m
2
,
(5)
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 Spring '10
 Polizinni
 LG, Threshold voltage, subthreshold slope

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