© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
Slide 2-1
EE 121B
Principles of Semiconductor Device Design
Review of PN Junctions
Professor Chi On Chui
Electrical Engineering Department
University of California, Los Angeles
Email: [email protected]
Slide 2-2
© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
Outline
•
Review of Currents in Semiconductors
–
Diffusion current
–
Drift current
–
Electric Field in a Semiconductor
–
Einstein Relation
•
PN Junction in Equilibrium
–
Band Diagram
–
Built-in potential in terms of hole or electron concentrations
•
Current in PN Junction
–
Forward Bias junction
–
Reverse Bias junction

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Slide 2-3
© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
Diffusion Processes
Consider the one dimensional diffusion problem.
We would like to know the nature of a particle flux (the number
of particles per second per area) crossing a boundary in a
semiconductor with a non-uniform concentration,
n
(
x
)
.
Assume that particles can only
move left or right.
In this example, we would
expect more particles to
cross from left to right than
from right to left because
there are more on the left to
begin with.
Slide 2-4
© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
Diffusion Processes
One dimensional diffusion problem.
n
(
x
)
x
0
n
(
-l
)
l
-l
n
(
l
)
n
(0)
Half the particles at
n
(
-l
)
moving at the thermal
velocity will reach the
x=
0
boundary in each
collision time provided that
l
is the mean free
path.
(The other half are going the other way).
The flux of particles from the left is:
(
)
( )
(
)
( )
(
)
( )
( )
dx
dn
l
v
dx
dn
l
n
dx
dn
l
n
v
l
n
l
n
v
l
n
v
l
n
v
th
th
net
th
net
th
th
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎥
⎦
⎤
⎢
⎣
⎡
+
−
⎥
⎦
⎤
⎢
⎣
⎡
−
=
−
−
=
←=
−
→=
ϕ
ϕ
ϕ
ϕ
ϕ
0
0
2
1
2
1
2
1
2
1
Expand this in a
Taylor series
keeping only the
first two terms