UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 137A WINTER 2009 Instructor: Luke Theogarajan
HOMEWORK ASSIGNMENT #1 SOLUTION
3.1
φ
j
=V
T
ln N
A
N
D
n
i
2
=0.025V
( )
ln 10
19
⋅cm
−3
(
)
10
18
⋅cm
−3
(
)
10
20
⋅cm
−6
=0.979V
w
do
=2
ε
s
q
1
N
A
+1
N
D
φ
j
=2 11.7⋅8.854 x10
−14
F⋅cm
−1
( )
1.602x10
−19
C
1
10
19
cm
−3
+1
10
18
cm
−3
0.979V
( )
w
do
=3.73 x 10
−6
cm =0.0373
µ
m
x
n
=
w
do
1+N
D
N
A
=
0
.
0373
µ
m
1+10
18
cm
−3
10
19
cm
−3
=0.0339
µ
m | x
p
=
w
do
1+N
A
N
D
=
0
.
0373
µ
m
1+10
19
cm
−3
10
18
cm
−3
=3.39 x 10
-3
µ
m
E
MAX
=qN
A
x
p
ε
s
=1.60x10
−19
C
( )
10
19
cm
−3
( )
3.39x10
−7
cm
( )
11.7⋅8.854 x10
−14
F/cm =5.24 x 10
5
V
cm
3.6
w
d
=w
do
1+V
R
φ
j
| (a) w
d
= 2w
do
requires V
R
=3
φ
j
=2.55 V | w
d
=0.4
µ
m1+5
0.85 = 1.05
µ
m
3.12
j
p
=q
µ
p
pE −qD
p
dp
dx =0→E= − D
p
µ
p
1
p
dp
dx = − kT
q
1
p
dp
dx
p(x)=N
o
exp −x
L
| 1
p
dp
dx =1
L | E = −V
T
L= − 0.025V
10
−4
cm = −250 V
cm
The exponential doping results in a constant electric field.
