Fabrication of Pn
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Transcript of Fabrication of Pn
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Tutorial -7
ELEC4510-fall/2011
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PN junction and fabrication-I Grown, alloyed, diffusion, and implantation junction.
Implantation vs. Diffusion
Performed at low temperature, thus immunity to impurity
Abrupt
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PN junction and fabrication-II
Fabrication of PN junction and Al electrode deposition Mask used to defined the junction region: SiO2, photoresist
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Types of junction
Abrupt Graded
Two proles encountered most often in real devices Easy to analyze from device physics point of view
Good approximation for shallow, high concentration junctions (xj < 1m) and epitaxially grown junctions
Good approximation for deep junctions (xj > 3 m)
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The PN Junction Diode
Quick view of PN junction properties: Rectify Increase exponentially at forward bias Saturate at reverse bias
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As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.
Efn Efp
n
p
E-field
Built-in potential
PN junction-physics process
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d
c
i
acbi
N
N
n
NN
q
kTVV lnln12
2
d
ckTVq
cdN
N
q
kTVeNNn ln11 N-region
2ln
i
adbi
n
NN
q
kT
2
2
2
ln2i
ackTVq
c
a
i
n
NN
q
kTVeN
N
nn P-region
PN junction-Built-in potential
Recall previous tutorial: built-in potential in non-uniformly doped semiconductor
Built-in potential
(Unit: Volts)
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PN junction- Poissons Equation Gausss Law:
s: permittivity (~12o for Si) : charge density (C/cm3)
D x
E ( x ) E ( x + D x )
x
Poissons equation
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In the depletion region on the N side:
bxqN
E
qN
dx
dE
si
D
si
D
si
(x)
x -qNA
qND
In the depletion region on the P side:
xaqN
E
qN
dx
dE
si
A
si
A
si
DA bNaN
a
-b
PN junction- E-field in depletion
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PN junction- depletion width
W x xno po
x N x Npo a no d
xnoqNa
Esi
dai
da
NNn
NN
q
kTW
11ln
222
Know the E, Vbi,
Try to derive this expression for W
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EXAMPLE: A P+N junction has Na=1020 cm-3 and Nd
=1017cm-3. What is a) its built in potential, b)Wdep , c)xN , and d) xP ?
Solution: a) b) c) d)
V 1cm10
cm1010lnV026.0ln
620
61720
2
i
adbi
n
NN
q
kT
m 12.010106.1
11085.812222/1
1719
14
d
bisdep
qNW
m 12.0 depN Wx
0 2.1m102.1 4 adNP NNxx
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kTEEkTEE
c
kTEE
cfpfnfpcfnc eeNeNxn
/)(/)(/)(
P )(
kTqV
P
kTEE
P enenfpfn /
0
/)(
0
The minority carrier densities are raised
by eqV/kT
Ec
Efp
Ev
Efn
0N 0P
x
Ec
Efn
Efp
Ev
x
Efn
xN xP
PN junction- Minority Carrier Injection
1)( kT
qV
pppp
a
ennxnn
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The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.
The minority-carrier concentrations at the edges of the depletion region are changed by the factor
60 mV rule
np(x)
np0
A
ip
N
nn
2
0 Equilbrium concentration
of electrons on the P side:
edge of depletion region
x'
PN junction- Minority Carrier Injection
kTqVDe/
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EXAMPLE: Carrier Injection
A PN junction has Na=1019cm-3 and Nd=10
16cm-3. The applied voltage is 0.6 V. Question: What are the minority carrier concentrations at the depletion-region edges? Solution:
Question: What are the excess minority carrier concentrations? Solution:
-311026.06.0
0 cm 1010)( eenxnkTVq
PP
-314026.06.04
0 cm 1010)( eepxpkTVq
NN
-31111
0 cm 101010)()( PPP nxnxn-314414
0 cm 101010)()( NNN pxpxp
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PN junction- Minority Carrier Injection
p
p
p
L
xx
npppL
xpqD
L
expqD
dx
xpdqDxJ
p
n
)(= )(=
)()(
)()(=)()( npnnpppn XJxJxJxJJ
The current flowing across the junction is comprised of hole diffusion and electron diffusion components:
Negligible drift current
n
n
n
L
xx
pnnnL
xnqD
L
exnqD
dx
xndqDxJ
n
p
)(= )(=
)()(
1= 1=
2 kT
qV
pd
p
na
ni
kT
qV
p
np
n
pnaa
eLN
D
LN
DqAne
L
pD
L
nDqAAJI
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PN junction- Injected minority carrier distribution
Ideal diode equation:
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Questions
As the mid-term approaches, I received lots of emails asking question in notes and HW
In order to give you more detailed explanation, please bring your questions and discuss with me after tutorial