ECE 440
Homework XIV
Spring 2006
1.
Redraw Figure 612 of band diagrams for the ideal MOS structure in an ntype silicon at (a)
thermal equilibrium (b) electron accumulation (c) electron depletion and (d) strong inversion.
Also, in the drawing show a simple circuit illustrating how the biasing is applied in each
case.
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2.
For an ideal MOS structure, the SiO
2
thickness is 300 Å, and the substrate is doped with
2x10
16
/cm
3
acceptors. Determine the threshold voltage, V
T
, required to achieve strong
inversion and find the electric field in the oxide when the applied bias V=V
T
. Repeat
for a
different MOS where the SiO
2
thickness is 40 Å but the substrate doping is the same.
For an ideal MOS, the equation to determine threshold voltage is (633)
F
i
d
s
i
d
T
C
Q
C
Q
V
φ
φ
2
+
−
=
+
−
=
So we need to calculate the three unknown quantities.
0.365V
ln
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
=
i
A
F
i
F
n
N
q
kT
E
E
φ
2
7
8
14
10
15
.
1
10
300
10
85
.
8
9
.
3
cm
F
d
C
i
i
−
−
−
×
=
⋅
⋅
×
=
=
ε
2
8
10
98
.
6
2
2
cm
C
qN
qN
qN
qN
W
qN
Q
A
F
s
A
A
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 Spring '11
 Leburton
 Electric Potential, Qd, Extrinsic semiconductor, Threshold voltage, 10 cm, ideal MOS structure

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