Clif Fonstad, 9/29/09
Lecture 6
- Slide 2
QNR
Flow
:
Uniform doping, non-uniform LL injection
We use the 5 QNR flow conditions* to simplify our 5 equations.
..
(assuming a p-type sample)
q
"
(
x
)
p
(
x
,
t
)
#
n
(
x
,
t
)
+
N
d
+
(
x
)
#
N
a
#
(
x
)
[ ]
=
dE
x
(
x
,
t
)
dx
J
h
(
x
,
t
)
=
q
μ
h
p
(
x
,
t
)
E
(
x
,
t
)
"
qD
h
#
p
(
x
,
t
)
x
J
e
(
x
,
t
)
=
q
μ
e
n
(
x
,
t
)
E
(
x
,
t
)
+
qD
e
n
(
x
,
t
)
x
p
(
x
,
t
)
t
+
1
q
J
h
(
x
,
t
)
x
=
n
(
x
,
t
)
t
#
1
q
J
e
(
x
,
t
)
x
$
g
L
(
x
,
t
)
#
n
(
x
,
t
)
p
(
x
,
t
)
#
n
i
2
[ ]
r
(
t
)
d
2
n
'(
x
,
t
)
dx
2
"
n
'(
x
,
t
)
D
e
e
=
"
1
D
e
g
L
(
x
,
t
)
..and end up with one equation in n':
the static diffusion equation!
"
1
q
dJ
h
(
x
,
t
)
dx
=
#
1
q
dJ
e
(
x
,
t
)
dx
$
g
L
(
x
,
t
)
#
n
'(
x
,
t
)
%
e
Quasi-static
Quasi-static
LLI
LLI
Uniform doping
Negligible minority drift
Quasi-neutrality
"
q
μ
h
p
o
(
x
)
E
(
x
,
t
)
#
qD
h
dn
'(
x
,
t
)
dx
"
J
e
(
x
,
t
)
#
qD
e
dn
'(
x
,
t
)
dx
"
q
p
'(
x
,
t
)
$
n
'(
x
,
t
)
[ ]
* Five assumptions that define flow problems AND should be validated at the end.