ECE 440
Homework IV
Fall 2009
Due: Friday, September 25, 2009
Print your name and netid legibly. Show all work leading to your answer clearly
and neatly. Staple multiple pages.
1.
A Si bar is 0.2 cm long and 200 µm
2
in crosssectional area. Find the current at 300 K
with 10 V applied to (a) the Si bar is doped with 1x10
17
/cm
3
gallium and (b) the Si bar is
doped with 1x10
17
/cm
3
gallium and 2x10
17
/cm
3
arsenic. Refer to Fig. 323 or the mobility
chart posted online.) (c) The silicon sample is grounded at x=0 and biased at +10 V at
x=0.2 cm. Draw the corresponding energy band diagram for case (a).
Solution:
To find the current, use Ohm’s law.
(1)
IR
V
=
(2)
R
V
I
/
=
We know bias so we need to find resistance.
(3)
σ
ρ
1
⋅
=
=
A
L
A
L
R
(4)
A
p
n
q
L
p
n
)
(
⋅
+
⋅
=
μ
μ
Substituting (13) into (11):
(5)
A
L
V
p
n
q
I
p
n
⋅
⋅
⋅
+
⋅
=
)
(
μ
μ
This expression is only valid if the drift velocity of the carriers is below the saturation
velocity. For silicon, the saturation velocity is
s
cm
/
10
7
≈
.
(6)
=
⋅
⋅
s
cm
v
cm
V
E
s
V
cm
2
μ
For Si bar is doped with 1x10
17
/cm
3
gallium.
(a)
3
17
10

=
=
cm
N
p
A
s
cm
s
cm
cm
V
s
V
cm
7
4
2
10
10
5
.
1
2
.
0
10
300
<
×
=
⋅
⋅
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A
L
V
p
q
I
p
⋅
⋅
⋅
≈
μ
.
mA
m
cm
V
s
V
cm
C
I
48
.
0
200
2
.
0
10
)
10
1
300
(
10
6
.
1
2
1
17
19
=
⋅
⋅
⋅
×
⋅
×
≈


μ
(b)
3
17
10

=

≈
cm
N
N
n
A
D
3
3
17
20
10
25
.
2
10
10
25
.
2

×
=
×
=
cm
p
Using Figure (323) in S&B we can see that
s
V
cm
n
⋅
≈
2
400
μ
in this case.
Check for saturation:
s
cm
s
cm
cm
V
s
V
cm
7
4
2
10
10
2
2
.
0
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 Fall '09
 Lie
 Condensed matter physics, Drift velocity, Electron mobility

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