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Problem 2:
Temperature dependence of a diode's reverse saturation current.
A1
0
2
−
cm
2
⋅
:=
N
A
10
18
cm
3
−
⋅
:=
N
D
10
16
cm
3
−
⋅
:=
L
n
5.0
µ
m
⋅
:=
L
p
5.0
µ
m
⋅
:=
From Fig. 2.8 of the text:
µ
n
250 cm
2
⋅
volt
1
−
⋅
sec
1
−
⋅
:=
µ
p
400 cm
2
⋅
volt
1
−
⋅
sec
1
−
⋅
:=
n
i
T
( )
1.08 10
31
⋅
cm
6
−
⋅
K
3
−
⋅
T
3
⋅
exp
1.12
−
eV
⋅
k
B
T
⋅
⎛
⎜
⎝
⎞
⎠
⋅
⎛
⎜
⎝
⎞
⎠
0.5
:=
V
Th
T
()
k
B
T
⋅
q
:=
I
S
T
() qA
⋅
V
Th
T
⋅
µ
n
L
n
N
A
⋅
µ
p
L
p
N
D
⋅
+
⎛
⎜
⎝
⎞
⎠
⋅
n
i
T
2
⋅
:=
(a)
V
Th
273.15 K
⋅
(
)
23.5 mV
=
n
i
273.15 K
⋅
(
)
6.953
10
8
×
cm
3
−
=
I
S
273.15 K
⋅
(
)
1.468
10
15
−
×
amp
=
(b)
V
Th
298.15 K
⋅
(
)
25.7 mV
=
n
i
298.15 K
⋅
(
)
5.825
10
9
×
cm
3
−
=
I
S
298.15 K
⋅
(
)
1.125
10
13
−
×
amp
=
(c)
V
Th
323.15 K
⋅
(
)
27.9 mV
=
n
i
323.15 K
⋅
(
)
3.547
10
10
×
cm
3
−
=
I
S
323.15 K
⋅
(
)
4.520
10
12
−
×
amp
=
The above temperatures are for 0 C, 25 C, and 50 C, after converting each to the Kelvin scale.
EE331 Devices and Circuits 1
Prof. R. B. Darling
Homework # 4 Solutions
First, define some useful units and constants:
µ
m1
0
6
−
m
⋅
:=
eV
1.602 10
19
−
⋅
joule
⋅
:=
k
B
8.62 10
5
−
⋅
eV
⋅
K
1
−
⋅
:=
q
1.602 10
19
−
⋅
coul
⋅
:=
ε
o
8.854 10
14
−
⋅
farad
⋅
cm
1
−
⋅
:=
n
i
10
10
cm
3
−
⋅
:=
V
T
0.025 volt
⋅
:=
ε
r
11.7
:=
Problem 1:
Problem 3.32 (a,b) of Jaeger and Blalock.
I
S
1.0 10
15
−
⋅
amp
⋅
:=
i
D
100
µ
A
⋅
:=
T
273.15 K
⋅
25 K
⋅
+
:=
T
298.15 K
=
V
T
k
B
T
⋅
q
:=
V
T
25.7 mV
=
(0 C = 273.15 K)
(a)
v
D
V
T
ln 1
i
D
I
S
+
⎛
⎜
⎝
⎞
⎠
⋅
:=
v
D
0.651 volt
=
(Note that the voltage has
decreased as the
temperature has increased.)
(b)
v
Dnew
v
D
1.8 mV
⋅
K
1
−
⋅
50 K
⋅
25 K
⋅
−
⋅
−
:=
v
Dnew
0.606 volt
=
EE331 HW#4 Solutions
Page 1
R. B. Darling
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d
41
0
7
−
×
farad
=
(c)
i
D
100 mA
⋅
:=
Q
d
i
D
τ
⋅
:=
Q
d
11
0
9
−
×
coul
=
C
d
Q
d
V
T
:=
C
d
0
8
−
×
farad
=
Problem 5:
Problem 3.49 of Jaeger and Blalock.
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 Winter '08
 Taicheng

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