ECE 340
Homework X
Fall 2003
Due: Monday, October 20, 2003
(30 points total)
1.
An abrupt Si p-n junction has the following properties at 300 K:
p-side
n-side
A = 10
-3
cm
2
N
a
= 2x10
17
/cm
3
N
d
= 4x10
15
/cm
3
τ
n
=
0.1 μs
τ
p
= 10 μs
μ
p
= 190 cm
2
/V-s
μ
n
= 1200 cm
2
/V-s
μ
n
= 600 cm
2
/V-s
μ
p
= 420 cm
2
/V-s
(a)
Draw the band diagram qualitatively under forward and reverse bias showing the quasi-Fermi levels.
(b)
Calculate the reverse saturation current due to holes, due to electrons and the total reverse saturation
current.
(c)
Calculate the total injected minority carrier current for V = V
o
/3 and V
o
/2.
(d)
Assuming μ’s and
τ
’s do not change with temperature, repeat part (c) for a temperature of T = 400 K at
which the intrinsic carrier concentration n
i
= 6x10
12
/cm
3
.
Solutions:
(a):
(b), Reverse saturation current due to the holes:
,
,
p n
side
p
n
p n
side
D
I
qA
p
L
−
−
=
Einstein relation:
2
0.0259
420
10.88
/
p
p
kT
D
cm
s
q
µ
=
=
×
=
0.01043
p
p
p
L
D
cm
τ
=
=
,
2
4
3
5.625
10
i
n
n
n
p
cm
n
−
=
=
×
,
19
3
4
15
,
10.88
1.6
10
10
5.625
10
9.387
10
0.01043
p n
side
p
n
p n
side
D
I
qA
p
A
L
−
−
−
−
−
=
=
×
×
×
×
×
=
×
Reverse saturation current due to the electrons:
,
,
n p
side
n
p
n p
side
D
I
qA
n
L
−
−
=
Einstein relation:
2
0.0259
600
15.54
/
n
n
kT
D
cm
s
q
µ
=
=
×
=

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