PN Junction Dr. Abdallah Hammad Assistant professor Faculty of Engineering at Shoubra Benha University ECE 111
PN Junction
Dr. Abdallah Hammad Assistant professor
Faculty of Engineering at Shoubra Benha University
ECE 111
Objective
• band diagram • pn-junction • depletion region • depletion width • built-in potential • biased junction
Selected areas covered in this lecture:
Dr. Abdallah Hammad (2012-2013)
Charter member of the family of all the solid state devices. Basic theory of operation of p-n junctions is essential to the understanding of all the other devices. Many of these devices also contain parasitic p-n junctions. It is essential to understand how these parasitic junctions affect the performance of the main device. What are p-n junctions? In part I of this course we focused on semiconductors which are either n-type or p-type. Now we will study the behavior of samples that are doped with different type of impurities in different parts of the sample.
P-N Junctions - Introduction
Dr. Abdallah Hammad (2012-2013)
P-N Junction formation technology
There are three main methods of formation of p-n junctions: Diffusion
Start with an n-type wafer. Diffuse a p-type impurity at a high temperature. Or start with a p-type wafer and diffuse an n-type impurity. In both cases a p-n junction is formed near the surface of the wafer. Typical junction depths are a few microns.
Ion implantation Start with an n-type wafer and shoot ions of a p-type impurity. Ion energies typically 50 - 200 KeV. Alternatively, implant ions of an n-type impurity into a p-type substrate.
Epitaxy Start with an n-type wafer. Deposit a thin layer of p-type Si epitaxially (single crystal Si).
The first two techniques are extensively used in Si technology. Epitaxial junctions are more common in GaAs technology.
Dr. Abdallah Hammad (2012-2013)
Step junction versus linearly graded junction
Step junction: If the conductivity type changes abruptly at some plane, then the junction is called a step junction or abrupt junction. Epitaxial method results in abrupt junctions. The plane x= xj at which the conductivity type changes is called the junction-plane or the metallurgical junction.
X<Xj, NA > ND (usually ND on the p-side is very small) X> Xj, ND >NA (usually NA n-side is very small)
Dr. Abdallah Hammad (2012-2013)
Linearly graded junctions: Diffused junctions are generally linearly graded junctions. The plane X=Xj at which ND = NA is called the junction plane.
» For x < Xj, NA > ND (p-type) » For x > Xj, ND > NA (n-type) » At X=Xj, n= p= ni. Hole concentration (p= NA-ND)
increases linearly to the left of Xj. Electron (n= ND-NA) concentration increases linearly to the right of Xj
Dr. Abdallah Hammad (2012-2013)
abrupt junction
p-type
NA
n-type
ND
Dr. Abdallah Hammad (2012-2013)
pn-junction in thermal equilibrium
EFno
EC
EV
Ei
p-type
EFpo
n-type
EC
EV
Ei
Eg
EFno
EC
EV
Ei
p-type
EFpo
n-type
EC
EV
Ei
before connection
connection
Dr. Abdallah Hammad (2012-2013)
0=dx
dEFfor thermal equilibrium consequence: the Fermi levels in the p- and n-type semiconductors must be equal
requirement of thermal equilibrium
EFn
EC
EV
Ei
ener
gy
EFp
EC
EV
Ei
biqV built-in potential (diffusion potential)
After connection
Dr. Abdallah Hammad (2012-2013)
depletion region
EF
EC
EV
Ei
ener
gy
EF
EC
EV
Ei
char
ge d
ensi
ty
DqN
AqN−
Dr. Abdallah Hammad (2012-2013)
depletion region ch
arge
den
sity
DqN
AqN−
depletion region
neutral region neutral region
metallurgical junction
Dr. Abdallah Hammad (2012-2013)
depletion region po
tent
ial
char
ge d
ensi
ty
DqN
AqN−
E-fie
ld
biV
Dr. Abdallah Hammad (2012-2013)
At equilibrium condition the drift current due to the electric field must exactly cancel the diffusion current due to the concentration gradient
0p p pdpJ qμ p qDdx
= − =E
0=+=dxdnqDnqμJ nnn E
Thermal equilibrium condition
1D Poisson’s equation:
[ ])()()()(
)()()(2
2
xnxpxNxNεq
εxρ
dxxd
dxxψd
AD
s
−+−−=
=−=−=E ψ - electrostatical potential
ρ
εs - space charge density
- semiconductor permittivity
Dr. Abdallah Hammad (2012-2013)
εqN
dxxd
dxxψd A−=−=
)()(2
2 E for 0<≤− xxp
for nxx ≤<0ε
qNdx
xddx
xψd D=−=)()(
2
2 E
Poisson’s equation for abrupt junction
junction potential
DqN
AqN−
biV
nxpx−
x
x
x
ψ
ρ
E
0)(=
dxxdE
Dr. Abdallah Hammad (2012-2013)
electric field distribution
DqN
AqN−
biV
nxpx−
x
x
x
εAqN
dxxd −
=)(E
1)( EE +−= xqNx A
ε
pA xqN
ε−=1E
( )pA xxqNx +−=
ε)(E
ψ
ρ
E
Dr. Abdallah Hammad (2012-2013)
electric field distribution
DqN
AqN−
biV
nxpx−
x
x
x
εDqN
dxxd
=)(E
2)( EE += xqNx D
ε
nD xqN
ε−=2E
( )nD xxqNx −=
ε)(E
ψ
ρ
E
Dr. Abdallah Hammad (2012-2013)
maximum electric field
nD
pA xqNxqN
εε−=−== )0(max EE
pDpA xNxN =consequence:
nx xpx−
potential distribution
dxsdx )()( ψ
−=E
∫−= dxxs )()( Eψ
Dr. Abdallah Hammad (2012-2013)
potential distribution
DqN
AqN−
biV
nxpx−
x
x
x
( )dxxxqNx pA∫ +=
εψ )(
1
2
2ψ
ε+
+= xxxqN
pA
2
2
1pA xqN
εψ =
0)( =− pxψwith
( )22
)( xxqNx pA +=ε
ψ
ψ
ρ
E
0px x− < <
Dr. Abdallah Hammad (2012-2013)
potential distribution
DqN
AqN−
biV
nxpx−
x
x
x
( )dxxxqNx nD∫ +=
εψ )(
2
2
2ψ
ε+
−=
xxxqNn
D
2
2
2nD
bixqNV
εψ −=
bin Vx =)(ψwith
( )22
)( xxqNVx nD
bi −−=ε
ψ
ψ
ρ
E
0 nx x< <
Dr. Abdallah Hammad (2012-2013)
built-in potential
( )22
)( xxqNx pA +=ε
ψ( )22
)( xxqNVx nD
bi −−=ε
ψ
for 0=x both expressions
must give the same value:
22
22)0( p
An
Dbi xqNxqNV
εεψ =−=
( )22
2 pAnDbi xNxNqV +=ε
Dr. Abdallah Hammad (2012-2013)
depletion width
( )22
2 pAnDbi xNxNqV +=ε nDpA xNxN =
+=
+=
A
DDn
A
nDAnDbi N
NNqxN
xNNxNqV2
22
2
22 εε
biDAD
An V
NNNN
qx 2
2+
=ε
pnd xxx +≡
biAAD
Dp V
NNNN
qx 2
2+
=ε
+=
+
= A
D
ApnA
D
pADbi N
NNqxxN
NxN
NqV2
222
22 εε
Dr. Abdallah Hammad (2012-2013)
depletion width
biDAD
An V
NNNN
qx 2
2+
=ε
biAAD
Dp V
NNNN
qx 2
2+
=ε
( )
( )( )
biAD
DA
ADDA
DADAbi
biADA
Dbi
DAD
A
biADA
Dbi
DAD
Apnd
VNNNN
qNNNNNNNNV
q
VNNN
Nq
VNNN
Nq
VNNN
Nq
VNNN
Nq
xxx
+=
+++
=+
⋅+
⋅+
++
+=+=
εε
εε
εε
222
222
22
22
22
2222
( )bi
AD
DAd V
NNNN
qx +
=ε2
Dr. Abdallah Hammad (2012-2013)
one-side abrupt junction
if
D
bind qN
εVxx 2=≅
( )bi
AD
DAd V
NNNN
qx +
=ε2
np xx <<
Dr. Abdallah Hammad (2012-2013)
potential vs. carrier concentration
=−= 2ln
i
ADpnbi n
NNq
kTψψV
The derivation will be done in the lecture:
Dr. Abdallah Hammad (2012-2013)
E [eV]
x
qVbi EFn EFp
EC
EV
EFi pqψ−
nqψ
n-type p-type
P N
unbiased junction
EFp EFn
x
q(Vbi-VF) E [eV]
EC EFi
n-type
p-type
P N + - IF
-qVF forward-biased junction
Dr. Abdallah Hammad (2012-2013)
p n + - IR EV q(Vbi+VR)
E [eV]
EFp
EC
EFn qVR
reverse-biased junction
generalized depletion layer width
( )B
bid qN
VVεx −=
2
NB – lightly doped bulk concentration V - positive for FB, negative for RB
Dr. Abdallah Hammad (2012-2013)