p – n junction
Prof.Dr.Beşire GÖNÜL
p – n junction
 The p-n junction is the basic element of all
bipolar devices. Its main electrical property
is that it rectifies (allow current to flow
easily in one
direction only).The p-n
junction is often just called a DIODE.
Applications;
>photodiode, light sensitive diode,
>LED- ligth emitting diode,
>varactor
diode-variable
capacitance
diode
The formation of p-n junction :

1)
The p-n junction can be formed by pushing
a piece of p-type silicon into close contact
with a piecce of n-type silicon. But forming
a p-n junction is not so simply. Because;
There will only be very few points of
contact and any current flow would be
restricted to these few points instead of
the whole surface area of the junction.
1) Silicon that has been exposed to the air
always has a thin oxide coating on its
surface called the “native oxide”. This
oxide is a very good insulator and will
prevent current flow.
2) Bonding arrangement is interrupted at the
surface; dangling bonds.
Surface states
To overcome these surface states
problems
p-n junction can be formed in the bulk of
the semiconductor, away from the
surface as much as possible.
p – n junction
p-type
n-type
EC
Eİ
EC
Ef
Eİ
Ef
EV
EV
EC
Eİ
p-type
n-type
EC
Ef
Eİ
Ef
EV
EV
There is a big discontinuity in the fermi level
accross the
p-n junction.
Idealized p-n junction; recombination of the carrier
and carrier diffusion
Hole
Movement
+++++
+++++
+++++
n-type +++++
+++++
+++++
+++++
+++++
----------------------------------
Metallurgic
al junction
Electron
Movement
++++
++++
++++
Fixed
positive
spacecharge
p-type
----------
Fixed
negative
spacecharge
Ohmic
end-contact
p – n junction
 Lots of electrons on the left hand side of the
junction want to diffuse to the right and lots
of holes on the right hand side of the
junction want to move to the left.
 The donors and acceptors fixed,don’t move
(unless you heat up semiconductors, so they
can diffuse) because they are elements
(such as arsenic and boron) which are
incorporated to lattice.
 However, the electrons and holes that come
from them are free to move.
Idealized p-n junction
 Holes diffuse to the left of the metalurgical junction
and combine with the electrons on that side. They
leave behind negatively charged acceptor centres.
 Similarly, electrons diffusing to the right will leave
behind positively charged donor centres. This
diffusion process can not go on forever. Because, the
increasing amount of fixed charge wants to
electrostatically attract the carriers that are trying to
diffuse away(donor centres want to keep the
electrons and acceptor centres want to keep the
holes). Equlibrium is reached.
 This fixed charges produce an electric field which
slows down the diffusion process.
 This fixed charge region is known as depletion region
or space charge region which is the region the free
carriers have left.
 Energy level diagram for the p-n junction in thermal
equilibrium
p-type
n-type
Electron Drift
EC
Electron Diffusion
Neutral p-region
EC
Ef
Ef
EV
Hole Diffussion
Neutral nregion
Hole Drift
Depletion region
EV
Thermal equilibrium; no applied field; no net current
flow
J p  J p (drift )  J p (diffusion)  0 (1)
A
J p is the hole current density ( 2 )
cm
dp
J p  qp pEx  qDp
 0 (2)
dx
where
1 dEi
Ex 
q dx
Dp 
pkT
q
Drift current is due to
electric field at
the
junction;
minority
carriers.
Diffusion current is due
the to
concentration
gradient;
majority
carriers.
(Einstein relation)
Proof
Jp
dEi
dp
 p( p
 kT
)0
dx
dx
p  ni exp(
J p  p p
Ei  E f
dE f
dx
kT
0
we conclude that
(3)
dE f
dp
p dEi
)

(

)
dx
kT dx
dx
(4)
dE f
 0 which states that
dx
the Fermi Level is a CONSTANT at equilibrium.
J n  n n
dE f
dx
0
(5)
Proof
 The drift and diffusion currents are flowing
all the time. But, in thermal equilibrium, the
net current flow is zero since the currents
oppose each other.
 Under non-equilibrium condition, one of the
current flow mechanism is going to
dominate over the other, resulting a net
current flow.
 The electrons that want to diffuse from the
n-type layer to the p-layer have potential
barier.
p – n junction barrier height, Vbi
 The potential barrier height
accross a p-n
Vbi
junction is known as the built in potential and also
as the junction potential.
 The potential energy that this potential barrier
correspond is
qVbi
• Electron energy is positive upwards in the energy
level diagrams, so electron potentials are going to be
measured positive downwards.
• The hole energies and potentials are of course
positive in the opposite directions to the electrons
p – n junction barrier height
n-type
EC
qVbi
Electrıon
energy
Ei
Ef
EC
Ef
qV p
qVn
EV
Ei
EV
Depletion region
Electron potential
p-type
The p – n junction barrier height
The intrinsic Fermi Level is a very useful reference level in a
semiconductor.
q
VE

(i E
1
)
p
f)(
kT
NA
Vp 
ln
q
ni
 Ei Ef 
p ni exp

k
T


(2)
Similarly for Vn
kT
ND
Vn 
ln
q
ni
(3)
For full ionization, thebuilt involtageis asumof
kT
NAND
Vbi  Vn  Vp 
ln
q
ni2
(4)
Electrıon
energy
Hole energuy
p – n junction in thermal equilibrium
DR
Neutral
pregion
----------
+++
+++
+++
 Current Mechanisms,
Neutral
nregion
Field Direction
 Diffusion
of
carriers
cause
electric in DR.
the
an
Electron Drift
Electron Diffusion  Drift current is due
E
to the presence of
electric field in DR.
C
Ef
Hole Diffussion
 Diffusion current is
due to the majority
carriers.
EV
Hole Drift
 Drift current is due
to
the
minority
carriers.
n – p junction at equilibrium
DR
Neutral
nregion
+++
+++
+++
----------
Neutral
pregion
Electrıon
energy
Hole energuy
Field Direction
Electron Drift
Electron
Diffusion
E
C
Ef
EV
Hole Diffussion
Hole Drift
Diffusion :
 When electrons and holes are diffusing from high
concentration region to the low concentration region
they both have a potential barrier. However, in drift
case of minority carriers there is no potential barrier.
 Built in potential ;
kT N
N
A
D
V
ln
bi
2
q
n
i
A
t
f
i
x
e
d
T
,
V
i
s
d
e
t
e
r
m
i
n
e
d
b
y
t
h
e
n
u
m
b
e
r
o
f
N
a
n
d
N
a
t
o
m
s
.
b
i
A
D
p-type
-------
Potential
+++
+++
 At equilibrium, there
is no bias, i.e. no
applied voltage.
n-type
+++
+++
x
-------
 The field takes the
same sign as the
charge
areaVbi
Electric field
Charge density
Depletion Approximation, Electric Field and Potential for pn
junction
x
 Em
qVbi
x
xn
xp
Depletion
Region
 The
sign
of
the
electric
field
is
opposite to that of
the potential ;
dV
n
E
v 
dx
Depletion Approximation, Electric Field and Potential for pn
junction
 Charge density is negative on p-side and positive on
n-side.
 As seen from the previous diagram, the charge
distribution is very nice and abrupt changes occur at
the depletion region (DR) edges. Such a junction is
called as an abrupt junction since the doping abruptly
changes from p- to n-type at the
metallurgical
junction (ideal case).
x

t
h
e
w
i
d
t
h
o
f
t
h
e
D
R
o
n
n
s
i
d
e
n
x

t
h
e
w
i
d
t
h
o
f
t
h
e
D
R
o
n
p
s
i
d
e
p
Depletion Approximation, Electric Field and Potential for pn
junction
 In reality, the charge distribution tails-off
into the neutral regions, i.e. the charge
distrubition is not abrupt if one goes from
depletion region into the neutral region.
This region is called as a transition region
and since the transition region is very thin,
one can ignore the tail-off region and
consider the change being abrupt. So this
approximation is called as DEPLETION
APPROXIMATION.
Depletion Approximation, Electric Field and Potential for pn
junction
Electric Field Diagram
:
 The electric field is zero at the edge of the DR and
increases in negative direction. At junction charge
changes its sign so do electric field and the
magnitude of the field decreases (it increases
positively).
Potential Diagram :
 Since the electric field is negative through the whole
depletion region ,DR, the potential will be positive
through the DR. The potential increases slowly at left
hand side but it increases rapidly on the right hand
side. So the rate of increase of the potential is
different an both sides of the metallurgical junction.
This is due to the change of sign of charge at the
junction.
Depletion Approximation, Electric Field and Potential for np
junction
Potential
density
Electric field
Charge
n-type
+++
+++
-------
+++
+++
p-type
x
-------
 Em
Field direction is positive x direc
areaVbi
x
x
Depletion
Region
Field direction
Abrupt junction
Charge
density
p-type
-------
+++
+++
n-type
+++
+++
x
-------
xp
Depletion
Region
w
• The amount of uncovered
negative charge on the left
hand side of the junction
must be equal to the amount
of positive charge on the
right hand side of the
metalurgical junction. Overall
space-charge
neutrality
condition;
N
x
N
x
Ap
D
n
xn
The higher doped side of the junction has
the narrower depletion width
when
N

N

x

x
A
D
n
p
Abrupt junction
 xn and xp is the width of the depletion layer on the nside and p-side of the junction, respectively.
W
h
e
n
N


N
(
u
n
e
q
u
a
l
i
m
p
u
r
i
t
y
c
o
n
c
e
n
t
r
a
t
i
o
n
s
)
D
A
a
n
d
x


x
,
W
x
p
n
p
 Unequal impurity concentration results an unequal
depletion layer widths by means of the charge
neutrality condition;
NA.xp N
.xn
D
W = total depletion
region
Abrupt junction
W
h
e
n
N


N

x


x

W

x
A
Dnp
n
• Depletion layer widths for n-side and p-side
1
xn 
ND
2SiVbiNAND
q(NA  ND)
1
xp 
NA
2SiVbiNAND
q(NA  ND)
Abrupt junction
For equal doping densities W  xn  x p
Total depletion layer width , W
1
1
W (

)
NA
ND
W 
2 SiVbi N A N D
q( N A  N D )
2 SiVbi ( N A  N D )
qN A N D
Abrupt junction
Si 
or
-1
2
op
e
rm
ittiv
ityo
fv
a
c
u
u
m8
.8
5
x
1
0
F
/m
r relativ
ep
e
rm
ittiv
ityo
fS
ilic
o
n
1
1
.9
x
,x
n
dW
d
e
p
e
n
d
so
nNN
, Da
n
dV
n
pa
A
b
i
k
T N
N
A
D
V

l
n
b
i
2
q n
i
One-Sided abrupt p-n junction
heavily doped p-type
p-type -
+++
+++
+++
+++
-------
+++
+++
n-type
NA ND
x
-
Depletion
Region
Abrupt p-n junction
xp
xn
x
be
negl
pcan
One-Sided abrupt p-n junction
SiV
N
SiV
N
1 2
1 2
b
iN
A
D
b
iN
A
D
Wx
n

N
q
N
 AN
 N
D qN
D
D
A
neglegted
since NA>>ND
2
SiV
b
i
W

q
N
D
o
b
ta
inas
im
ila
re
q
u
a
tio
nfo
rW
x
p
inth
ec
a
s
eo
fN
N
D
A
One-sided abrupt junction
p-type
-
+++
+++
-x direction
n-type
Electric field
+++
+++
x
-
Electric field
Charge density
One-Sided abrupt p-n junction
areaVbi
x
Potential
 Em
qVbi
x
xn
xp
Appliying bias to p-n junction
+
-
p
n
forward bias
-
+
p
n
reverse bias
 How current flows through the p-n
junction when a bias (voltage) is
applied.
 The current flows all the time
whenever a voltage source is
connected to the diode. But the
current flows rapidly in forward
bias,
however
a
very
small
constant current flows in reverse
bias case.
Appliying bias to p-n junction
I(current)
Reverse Bias
Vb
I0
Forward Bias
V(voltage)
Vb ; Breakdown voltage
I0 ; Reverse saturation current
 There is no turn-on voltage because current flows in
any case. However , the turn-on voltage can be
defined as the forward bias required to produce a
given amount of forward current.
 If 1 m A is required for the circuit to work, 0.7 volt
can be called as turn-on voltage.
Appliying bias to p-n junction
Zero Bias
p
Forward Bias
+
-
-- ++ n
-- ++
p
Ec
Ec
Ev
n
qVbi VF 
Potential
Energy
Ev
qVbi
- +
- +
Vbi
Reverse Bias
+
p
---
++
++
n
Ec
Ev
qV
 bi V
r
Vbi  VR
Vbi  VF
Appliying bias to p-n junction
V
forward
voltage
F
V

reverse
voltage
R
 When a voltage is applied to a diode , bands
move and the behaviour of the bands with
applied forward and reverse fields are shown
in previous diagram.
Forward Bias
 Junction potential reduced
 Enhanced hole diffusion from p-side to n-side
compared with the equilibrium case.
 Enhanced electron diffusion from n-side to p-side
compared with the equilibrium case.
 Drift current flow is similar to the equilibrium case.
 Overall, a large diffusion current is able to flow.
 Mnemonic. Connect positive terminal to p-side for
forward bias.
 Drift current is very similar to that of the equilibrium
case. This current is due to the minority carriers on
each side of the junction and the movement minority
carriers is due to the built in field accross the
depletion region.
Reverse Bias
 Junction potential increased
 Reduced hole diffusion from p-side to n-side
compared with the equilibrium case.
 Reduced electron diffusion from n-side to p-side
compared with the equilibrium case
 Drift current flow is similar to the equilibrium case.
 Overall a very small reverse saturation current flows.
 Mnemonic. Connect positive terminal to n-side for
reverse bias.
Qualitative explanation of forward bias
+
Carrier Density
p
- +
- +
n
pn
np
pno
npo
p-n junction in forward bias
 Junction
potential
is
reduced from Vbi to Vbi-VF.
 By forward biasing a large
number of electrons are
injected from n-side to pside accross the depletion
region and these electrons
become minority carriers on
p-side, and the minority
recombine with majority
holes so that the number of
injected minority electrons
decreases
(decays)
exponentially with distance
into the p-side.
Qualitative explanation of forward bias
 Similarly, by forward biasing a large number
of holes are injected from p-side to n-side
across the DR. These holes become minority
carriers at the depletion region edge at the
n-side so that their number (number of
injected excess holes) decreases with
distance into the neutral n-side.
 In summary, by forward biasing in fact one
injects minority carriers to the opposite
sides. These injected minorites recombine
with majorities.
Qualitative explanation of forward bias
 How does
current flow occur if all the
injected
minorities
recombine
with
majorities ?
 If there is no carrier; no current flow occurs.
 Consider the role of ohmic contacts at both
ends of p-n junction.
 The lost majority carriers are replaced by
the majority carriers coming in from ohmic
contacts to maintain the charge neutrality.
 The sum of the hole and electron currents
flowing through the ohmic contacts makes
up the total current flowing through the
external circuit.
Ideal diode equation
 “o” subscript denotes the equilibrium carrier
concentration.
n

equilibriu
m
electron
concentra
ion
in
n
type
mat
no
n

equilibriu
m
electron
concentra
ion
in
p
type
mat
po
p

equilibriu
m
hole
concentrat
ion
in
p
type
mate
po
p

equilibriu
m
hole
concentrat
ion
in
n
type
mate
no
n. p  n
2
i
Ideal diode equation
n
.pn
2
i
 At equilibrium case ( no bias )
nno
.pnon 
ntype
material
(1
)
2
i
npo
.ppon 
ptype
material
(2)
2
i
Ideal diode equation
kT NAND
Vbi  ln 2
assuming full ionization
q
ni
NA  ppo ; ND  nno majority carriers
kT ppo.nno
Vbi  ln
q
ni2
nno. pno  ni2 for n-type
kT ppo
 qVbi 
Vbi  ln
 ppo  pno exp
 (3)
q
pno
 kT 
Ideal diode equation
Similarly, fromequation(2)
kT ppo.nno
Vbi  ln 2
q
ni
npo.ppo n
2
i
kT nno
qVbi 
Vbi  ln nno npoexp
 (4)
q npo
 kT 
This equation gives us the equilibrium majority carrier concent
Ideal diode equation
What happens when a voltage appears across the p-n
junction ?

Equations (3) and (4) still valid but you should drop
(0) subscript and change Vbi with
i.
ii.
Vbi – VF if a forward bias is applied.
Vbi + VR if a reverse bias is applied.
VF : forward voltage
VR : reverse voltage
With these biases, the carrier densities change from
equilibrium carrier densities to non- equilibrium
carrier densities.
Ideal diode equation
 Non-equilibrium majority carrier concentration in
forward bias;
 q(Vbi  VF ) 
pp  pn exp 

kT


For example; nn for reverse bias
 q(Vbi  VR ) 
nn  np exp 

kT


• When a voltage is applied; the equilibrium nno
changes to the non equilibrium nn.
Assumption; low level injection
• For low level injection; the number of injected
minorities is much less than the number of the
majorities. That is the injected minority carriers do
not upset the majority carrier equilibrium densities.
nn  nno
pp  ppo
• Non equilibrium electron concentration in n-type
when a forward bias is applied ,
q
(
V

V
)


b
i
F
n

n
e
x
p
n
o
n
e
q
u
i
l
i
b
r
i
u
m
.
n
p


T
k

Ideal diode equation
(
V
V
)
q
b
i
F
n
n
n
n
5
)
n
n
o
n
o
p

(
T 
 k
V
q
b
i
n
n
x
p
6
)
n
o
p
oe

(
T
k
c
o
m
b
in
in
g
(
5
)a
n
d
(
6
)
(
V
V
)
V
q
q
b
i
F
b
i
n
x
p

n
x
p
pe
p
oe
 
 k

T 
T

k
Ideal diode equation
 Solving for non-equilibrium electron concentration in ptype material, i.e. np
qV
F
np npoexp
 andsubtractingnpo frombothsides
 kT 
 qV 
np nponpoexp 1n
 kT 
n theexcessconcentrationofm
inorityelectrons
overtheequilibriumconcentrationattheedgeoftheD
R
Ideal diode equation
S
i
m
i
l
a
r
l
y
,
 
q
V

pp


p
e
x
p

1

h
e
n
o
n
e
q
u
i
l
i
b
r
i
u
m
n
n
o
n
o
pt
 


k
T

 



t
h
e
e
x
c
e
s
s
c
o
n
c
e
n
t
r
a
t
i
o
n
o
f
m
i
n
o
r
i
t
y
h
o
l
e
s
p
o
v
e
r
t
h
e
e
q
u
i
l
i
b
r
i
u
m
c
o
n
c
e
n
t
r
a
t
i
o
n
a
t
t
h
e
e
d
g
e
o
f
t
h
e
D
R
Forward-bias diode; injection of minority carriers across DR
+
p
o
in
tA

n
n
p
p
o
-
p
o
in
tB

p
p
n
n
o
- +
- +
p
n
•
l
i
s
t
h
e
d
i
s
t
a
n
c
e
f
r
o
m
D
R
e
d
g
e
i
n
t
o
p
s
i
d
e
p
•
l
i
s
t
h
e
d
i
s
t
a
n
c
e
f
r
o
m
D
R
e
d
g
e
i
n
t
o
n
s
i
d
e
n
ppo
nno
B
A
pno
npo
lp
ln
When a forward bias is applied; majority
carriers are injected across DR and appear as
a minority carrier at the edge of DR on
opposite side. These minorities will diffuse in
field free opposite-region towards ohmic
contact. Since ohmic contact is a long way
away, minority carriers decay exponentially
with distance in this region until it reaches to
its equilibrium value.
Exponential decay of injected minority carriers on
opposite sides
 The excess injected minorities decay exponentially as
 lp 
 p(l p )   n(0) exp  

L
n 

 ln
 n(ln )   p(0) exp  
 Lp




Ln and Lp are diffusion lengths
for electrons and holes
Number of Injected Minority Holes Across The Depletion
Region
• By means of forward-biasing a p-n junction
diode, the holes diffuse from left to right
accross the DR and they become minority
carriers.
• These holes recombine with majority
electrons when they are moving towards
ohmic constants.
• So, the number of minority holes on the nregion decreases exponentially towards the
ohmic contact. The number ofDistance
injected
into then region
minority holes;excess holes;
from the Depletion


l
n
p
()
l

p
(
0
)
e
x
p
(

)
n
L
p
Region
Diffusion Length
for holes
Number of Injected Minority Holes Across The Depletion
Region
p o in t A  n p  n p o
 n (l p )   n (0 ) e x p ( 
lp
Ln
)
qV


 n ( 0 )  n po  e x p (
)  1
kT



 qV  
 p ( 0 )  p no  e x p 
  1
 kT  

Ideal diode equation
• Similarly by means of
forward biasing a p-n
junction, the majority
electrons are injected
from right to left across
the Depletion Region.
These
injected
electrons
become
minorities
at
the
Depletion Region edge
on the p-side, and they
recombine
with
the
majority holes. When
they move into the
neutral
p-side,
the
number
of
injected
excess
electrons
decreases
exponentially.
lp
n(lp)n(0)exp(
 )
L
n
lp
qV 

n(lp)npoexp()1exp(
 )
kT 
L

n
Ideal diode equation
D
if
f
u
s
io
n
c
u
r
r
e
n
td
e
n
s
ity
f
o
re
l
e
c
tr
o
n
s;
D
n
d
n
d
q
V
   lp
np
o 
J
q
D

q
D
n
()
lp 

q
e
x
p

1
e
x
p


n
n
n 
 


d
x
d
x
L
k
T
  L
n  
n

q
D
n
q
V
 
np
o 
Jl
(

0
)

e
x
p

1
M
in
u
ss
ig
n
s
h
o
w
sth
a
te
l
e
c
tr
o
n
c
u
r
r
e
n
t
n p
 


L
k
T
 
n  
d
e
n
s
ity
isin
o
p
p
o
s
ite
d
ir
e
c
tio
n
to
in
c
r
e
a
s
in
g
lp.T
h
a
tisin
th
e
p
o
s
itiv
e
x
d
ir
e
c
tio
n
.
S
im
il
a
r
l
y
f
o
rh
o
l
e
s
;
D
p
d
p q
V
q
 
p
n
o
J
(
ln
0
)

q
D

e
x
p
1
p
p
 


d
x
L
k
T




p
T
h
e
to
ta
lc
u
r
r
e
n
td
e
n
s
ity
;
D

n
p
V
q
 
n
p
o D
p
n
o 
J
J
J
q

e
x
p
1


T
o
ta
l
n
p
 

L
L
k
T





p 
 n

Ideal diode equation
D

n
 q
V 
V 
q
n
p
o D
pp
n
o 
J
q

x
p
1
Joe
x
p
1
e
T
o
ta
l
 
 


L
L
k
T
k
T








p 
 n

m
u
ltip
ly
in
gb
ya
re
a;
 q
V 
IIoe
x
p
1
 

k
T
   
Ideal diode equation
This equation is valid for both forward and reverse biases; just change
the sign of V.
Ideal diode equation
• Change V with –V for reverse bias. When qV>a few kT;
exponential term goes to zero as
 

q
V
 
I
I
e
x
p

1
o
 


k
T
   
I   Io
Reverse saturation current
Current
Forward Bias
VB
I0
Voltage
VB ; Breakdown voltage
Reverse Bias
I0 ; Reverse saturation
current
Forward bias current densities
+
-
p
n
 Jtotal is constant through
the whole diode.
Current density
Ohmic contact
Jtotal
Jn Jp
Jp
Jn
lp=0
ln=0
 Minority current densities
decreases
exponentially
into the the neutral sides
whereas
the
current
densities
due
to
the
majorities increase into the
neutral sides.
p-n junction in reverse bias
-
+
Carrier
p
n
npo
pno
pn
Current density
density
np
Jtotal
Jn Jp
Jn
Jp
lp=0
ln=0
• Depletion region gets bigger
with increasing reverse bias.
• Reverse bias prevents large
diffusion
current
to
flow
through the diode.
• However; reverse bias doesn’t
prevent the small current flow
due to the minority carrier.
The presence of large electric
field across the DR extracts
almost all the minority holes
from
the
n-region
and
minority electrons from the pregion.
• This flow of minority carriers
across
the
junction
constitudes I0, the reverse
saturation current.
• These
minorities
are
generated thermally.
p-n junction in reverse bias
• The flow of these minorities produces the reverse
saturation current and this current increases
exponentially
with
temperature
but
it
is
independent of applied reverse voltage.
I(current)
Forward Bias
Vb
I0
V(voltage)
VB ; Breakdown voltage
I0 ; Reverse saturation current
Reverse Bias
Drift current
Junction breakdown or reverse breakdown
• An applied reverse bias (voltage) will result in a
small current to flow through the device.
• At a particular high voltage value, which is called as
breakdown voltage VB, large currents start to flow.
If there is no current limiting resistor which is
connected in series to the diode, the diode will be
destroyed. There are two physical effects which
cause this breakdown.
1) Zener breakdown is observed in highly doped p-n
junctions and occurs for voltages of about 5 V or
less.
1)
Avalanche breakdown is observed in less highly
doped p-n junctions.
Zener breakdown
• Zener breakdown occurs at highly doped p-n
junctions with a tunneling mechanism.
• In a highly doped p-n junction the
conduction and valance bands on opposite
side of the junction become so close during
the reverse-bias that the electrons on the pside can tunnel from directly VB into the CB
on the n-side.
Avalanche Breakdown
• Avalanche breakdown mechanism occurs
when electrons and holes moving through
the DR and acquire sufficient energy from
the electric field to break a bond i.e. create
electron-hole pairs by colliding with atomic
electrons within the depletion region.
• The newly created electrons and holes
move in opposite directions due to the
electric field and thereby add to the
existing reverse bias current. This is the
most important breakdown mechanism in
p-n junction.
Depletion Capacitance
• When a reverse bias is applied to p-n junction diode,
the depletion region width, W, increases. This cause
an increase in the number of the uncovered space
charge in depletion region.
• Whereas when a forward bias is applied depletion
region width of the p-n junction diode decreases so
the amount of the uncovered space charge decreases
as well.
• So the p-n junction diode behaves as a device in
which the amount of charge in depletion region
depends on the voltage across the device. So it looks
like a capacitor with a capacitance.
Depletion Capacitance
Capacitance
in farads
Q
C
V
Charge stored
in coloumbs
Voltage
across
the capacitor in
volts
 Capacitance of a diode varies with W (Depletion Region
width)
 W (DR width varies width applied voltage V )
Depletion Capacitance
C
a
p
a
c
i
t
a
n
c
e
p
e
r
u
n
i
t
a
r
e
a
o
f
a
d
i
o
d
e
;

S
i F
C

D
E
P
2
W
c
m
F
o
r
o
n
e
s
i
d
e
d
a
b
r
u
p
t
j
u
n
c
t
i
o
n
;
e
.
g
.N


N

x


W

x
A
D
n
n
N
x

N
x
A
p
D
n


2

S
i
S
i
S
iV
b
i
  
x
C
D
E
P
W x
n
n
q
N
D
fo
rN
N
A
D
T
h
ea
p
p
lic
a
tio
no
fre
v
e
rs
eb
ia
s;
C
D
E
P
Si
2
Si(V
V
)
b
i
R
q
N
D

q
SiN
D
2
(
V
V
)
b
i
R
Depletion Capacitance
If one makes C-V measurements and draw1/C2
against the voltage VR;obtain built-in voltage and
doping densityof low-doped side of the diode from
the intercept and slope.
1 2(Vbi VR)

2
C
qSi ND
2
slope 
qSi ND
kT NAND
Vbi 
ln( 2 )
q
ni
Depletion Capacitance