V
6.012 Electronic Devices and Circuits
Formula Sheet for Hour Exam 2, Fall 2003
Parameter Values:
Periodic Table:
q
=
1.6
x
10
19
Coul
III
IV
=
8.854
x
10
14
F
/
cm
,
r,Si
=
11.7,
=
3.9
o
r,SiO
2
B
C
N
10
12
F
/
cm
,
SiO
2
3.5
x
10
13
F
/
cm
Al
Si
P
Si
n
i
[
Si
@
R
.
T
]
10
10
cm
3
Ga
Ge
As
kT
/
q
0.025
V
;
(
kT
/
q
)
ln10
0.06
V
In
Sn
Sb
1
m
=
1
x
10
4
cm
Drift/Diffusion:
Electrostatics:
Drift velocity :
s
= ±
E
dE
(
x
)
1
x
m
x
=
(
x
)
E
(
x
)
=
(
x
)
dx
Conductivity :
=
q
(
n
+
h
p
)
d
dx
(
x
)
e
(
x
)
=
E
(
x
)
dx
Diffusion flux :
F
=
D
∂
C
m
dx
=
E
(
x
)
m
m
D
kT
∂
x
d
2
(
x
)
=
(
x
)
(
x
)
=
1
(
x
)
dxdx
m
Einstein relation :
=
dx
2
q
m
The Five Basic Equations:
∂
n x
,
t
e
(
2
Electron concentration :
(
)
1
∂
J
x
,
t
)
=
g
L
(
x
,
t
)
[
n
(
x
,
t
)
(
x
,
t
)
n
i
]
r
(
T
)
∂
t
q
∂
x
⋅
p
∂
p
(
x
,
t
)
+
1
∂
J
h
(
x
,
t
)
=
g
L
(
x
,
t
)
2
Hole concentraton :
q
∂
x
[
n
(
x
,
t
)
⋅
p
(
x
,
t
)
n
i
]
r
(
T
)
∂
t
∂
n
(
x
,
t
)
Electron current density :
J
(
x
,
t
)
=
q
n
(
x
,
t
)
E
(
x
,
t
)
+
qD
e
e
e
∂
x
∂
p
(
x
,
t
)
Hole current density :
J
h
(
x
,
t
)
=
q
h
p
(
x
,
t
)
E
(
x
,
t
)
qD
h
∂
x
∂
E
(
x
,
t
)
=
q
[
p
(
x
,
t
)
n
(
x
,
t
)
+
N
d
+
(
x
)
Poisson's equation :
N
(
x
)
]
a
∂
x
Uniform doping, full ionization, TE
n - type, N
d
>> N
a
kT
N
D
2
n
N
d
N
≡
N
D
,
p
o
=
n
i
n
o
,
=
ln
o
a
n
q
n
i
p - type, N
a
>> N
d
kT
N
A
p
o
N
N
d
≡
N
A
,
n
o
=
n
i
2
p
o
,
p
=
ln
a
q
n
i
Uniform optical excitation, uniform doping
dn
'
n
=
n
+
n
'
p
=
p
o
+
p
'
n
'
=
p
'
=
g
l
(
t
)
(
p
o
+
n
+
n
'
)
n
'
r
o
dt
o
Low level injection, n',p' << p
o
+ n :
dn
'
+
n
'
=
g
l
(
t
)