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Chapter 5-2 Quantitative electrostatic relationships
We make the analysis in 1 dimension, even though actual diode
as shown may not be a one-dimensional system. This makes the
analysis simple. The metallurgical junction is located at x= 0.
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Quantitative Electrostatic Relationships in Microelectronics | ECSE 2210, Study notes of Electrical and Electronics Engineering
Material Type: Notes; Professor: Schubert; Class: MICROELECTRONICS TECHNOLOGY; Subject: Electrical & Comp. Sys. Engr.; University: Rensselaer Polytechnic Institute; Term: Spring 2005;
Typology: Study notes
Pre 2010
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Chapter 5-2 Quantitative electrostatic relationships
We make the analysis in 1 dimension, even though actual diodeas shown may not be a one-dimensional system. This makes theanalysis simple. The metallurgical junction is located at
x^
Quantitative analysis: Electric field
E
p
n
n
D
p
A
0 s
where
d d
x x
x x
x x
N
q
x x
N
q
K
x
ε
< < − ε − = ε =ε
ρ ε
E
p^
n
N A
N D
− x
p^
x n
W^ E
max
=^
−^
q N
x A
/εp
=^
−^
q N
x D /εn
( )
n
p
n
n D
p
p A 0
x x ; x x
x x
x x
qN
o x x
x x
qN
x
≤ ≤ − ε − =
≤ ≤ − + ε − = E
Built-in voltage:
V
bi
dx x
V
dV dx
x x
or
n p
bi^
E
E^
∫^ −
= V bi^
=^
−^
{area under
E
versus
x^
curve}
=^
−^
W
q N
x D
/n ε) }
q^
ε)
N
x D
W n
D
A
A
n
D
A
D A^
since
2
N
N
N W x W N N
N
N
q
ε
2 1 bi
D A
D
A
2
/ V
N N
N
N
q
W
⎛^ ⎜⎜ ⎝
ε
=
Quantitative analysis: Electrostatic potential
n
n D
bi
p
p A
n p
n D
p
p A
zero to set
at
potential
reference the with
d d
x x
x x
qN
V
x x
x x
qN x V
x x
x x
x x
qN
x x
)x
x(
qN V x
)
≤ ≤ − ε − =
≤ ≤ − + ε =
ε
≤ ≤ − + ε =
V
x V bi
Effects of forward and reverse bias
PN-junction energy-band diagrams
Example 2
Consider the diode of Example 1. Calculate the depletion layerwidth and the maximum electric field if a reverse voltage of 10 Vis applied across the diode. Calculate the depletion layer width inthe n-side and p-side under this biased condition.What will be
W
if
V
= 0.5 V?A
What happens if we apply
V
A^
>^
V bi