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© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
Slide 21
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 22
© 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
–
Builtin potential in terms of hole or electron concentrations
•
Current in PN Junction
–
Forward Bias junction
–
Reverse Bias junction
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© 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 nonuniform 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 24
© 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
0
0
2
1
2
1
2
1
2
1
Expand this in a
Taylor series
keeping only the
first two terms
Slide 25
© 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)
dx
dn
l
v
th
n
−
=
ϕ
dx
dn
l
qv
q
J
n
th
n
n
=
−
=
)
(
dx
dp
l
qv
q
J
p
th
p
p
−
=
=
This is the
diffusion
current
of
electrons
Slide 26
© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
() ( ) ( ) ( ) ( )
() () () () ()
x
E
x
qp
x
v
x
p
q
x
J
x
E
x
qn
x
v
x
n
q
x
J
p
p
p
n
n
n
µ
=
⋅
⋅
=
=
⋅
⋅
=
Diffusion and Drift
If we combine the equations above for Drift
current with the equations
for Diffusion
current we get the following expressions for electron and
hole current density:
Note: In these expressions
E
(
x
)
is the electric field.
Electrons in a solid drift
under the influence of an electric field. They move
at a velocity proportional to field, the proportionality constant is called the
mobility,
μ
n
for electrons and
μ
p
for holes
() ()()
( )
()
() () ()
x
J
x
J
x
J
dx
x
dp
qD
x
E
x
p
q
x
J
dx
x
dn
qD
x
E
x
n
q
x
J
p
n
p
p
p
n
n
n
+
=
−
=
+
=
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© 2006 Marko Sokolich
All Rights Reserved
EE 121B – Chi On Chui
Directions of Current Flow and Particle Flow
n
(
x
)
p
(
x
)
E
(
x
)
Consider a
semiconductor with the
gradients shown and
electric field pointing to
the right
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This note was uploaded on 11/11/2010 for the course EE 121b taught by Professor Bjtgamma during the Winter '08 term at UCLA.
 Winter '08
 BJTGamma
 Electrical Engineering

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