Non-uniform doping/excitation:
Summary
What we have so far:
Five things we care about (i.e. want to know):
Hole and electron concentrations:
Hole and electron currents:
Electric field:
p
(
x
,
t
)
and
n
(
x
,
t
)
J
hx
(
x
,
t
)
and
J
ex
(
x
,
t
)
E
x
(
x
,
t
)
And, amazingly, we already have five equations relating them:
Hole continuity:
Electron continuity:
Hole current density:
Electron current density:
Charge conservation:
"
p
(
x
,
t
)
"
t
+
1
q
"
J
h
(
x
,
t
)
"
x
=
G
#
R
$
G
ext
(
x
,
t
)
#
n
(
x
,
t
)
p
(
x
,
t
)
#
n
i
2
[
]
r
(
t
)
"
n
(
x
,
t
)
"
t
#
1
q
"
J
e
(
x
,
t
)
"
x
=
G
#
R
$
G
ext
(
x
,
t
)
#
n
(
x
,
t
)
p
(
x
,
t
)
#
n
i
2
[
]
r
(
t
)
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
%
(
x
,
t
)
=
" &
(
x
)
E
x
(
x
,
t
)
[
]
"
x
$
q p
(
x
,
t
)
#
n
(
x
,
t
)
+
N
d
(
x
)
#
N
a
(
x
)
[
]
So...we're all set, right? No, and yes
.....
Clif Fonstad, 9/17/09
Lecture 3 - Slide 2
We'll see today that it isn't easy to get a general solution, but we can prevail.