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P-N Junction
BHAVIN KAKANI
IT-NU
Diodes – Basic Diode Concepts
10.1 Basic Diode Concepts
10.1.1 Intrinsic Semiconductors
* Energy Diagrams – Insulator, Semiconductor, and Conductor
the energy diagram for the three types of solids
2
Diodes – Basic Diode Concepts
1.1.1 Intrinsic Semiconductors
* Intrinsic (pure) Si Semiconductor:
Thermal Excitation, Electron-Hole Pair, Recombination,
and Equilibrium
When equilibriu m between
excitation and recombination
is reached :
electron density  hole density
ni  pi  1.5  10 10 cm -3
for intrinsic Si crystal at 300 K
( Note : Si crystal atom density
is ~ 5  10 22 cm -3 )
3
Diodes – Basic Diode Concepts
1.1.1 Intrinsic Semiconductors
*Apply a voltage across
a piece of Si:
electron current
and hole current
4
Diodes – Basic Diode Concepts
1.1.2 N- and P- Type Semiconductors
* Doping: adding of impurities (i.e., dopants) to the intrinsic semiconductor material.
* N-type: adding Group V dopant (or donor) such as As, P, Sb,…
n  p  constant for a semiconductor
For Si at 300K

n  p  ni2  pi2  1.5  10 10

2
In n - type material
n  N d the donor conceration
n  N d  ni , p  pi
We call
electron the major charge carrier
hole the minor cahage carrier
5
Diodes – Basic Diode Concepts
1.1.2 N- and P- Type Semiconductors
* Doping: adding of impurities (i.e., dopants) to the intrinsic semiconductor material.
* P-type: adding Group III dopant (or acceptor) such as Al, B, Ga,…
n  p  constant for a semiconductor
For Si at 300K

n  p  n  p  1.5  10
2
i
2
i

10 2
In p - type material
p  N a the acceptor conceration
p  N a  pi , n  ni
We call
hole the major charge carrier
electron the minor cahage carrier
6
Diodes – Basic Diode Concepts
1.1.3 The PN-Junction
* The interface in-between p-type and n-type material is called a
pn-junction.
The barrier potential VB  0.6  0.7V for Si and 0.3V for Ge
at 300K : as T ,VB  .
7
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 A N D
Vbi 
ln
2
q
ni
HOW sir?????
At fixed T , Vbi is determined by the number of N A and N D atoms.
How much is the Built-in Voltage?
qVbi  (Ei  EF )Left  (EF  Ei )Right
N side
P side
p  Na
N a  ni e
n  Nd
( Ei  EF )
(Ei  EF )Left
kT
 Na 
 kT ln 
 ni 
N d  ni e
( EF  Ei )
(EF  Ei )Right
kT
 Nd 
 kT ln 
 ni 
ECE 663
How much is the Built-in Voltage?
Vbi
kT  Na  kT  Nd 

ln
ln


q
q
 ni 
 ni 
 Vbi
kT  Na Nd

ln
 n2
q

i




Na acceptor level on the p side
Nd donor level on the n side
ECE 663
Depletion Approximation, Electric Field and Potential for pn
junction
-------
Potential
+++
+++
-------
 At equilibrium, there is
no bias, i.e. no applied
voltage.
n-type
+++
+++
Electric field
Charge density
p-type
x
area  Vbi
x
 The field takes
same
sign
as
charge
 The sign of the electric
field is opposite to that
of the potential ;
 Em
qVbi
x
xn
xp
Depletion
Region
the
the
dVn
Ev  
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 ntype at the metallurgical junction (ideal case).
xn  the width of the DR on n-side
x p  the width of the DR on p-side
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
+++
+++
-------
+++
+++
p-type
x
-------
 Em
Electric field
Charge density
n-type
Field direction is positive x direction
area  Vbi
x
Potential
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 A x p  N D xn
xn
The higher doped side of the junction
has the narrower depletion width
when N A  N D  xn  x p
Abrupt junction
 xn and xp is the width of the depletion layer on the n-side
and p-side of the junction, respectively.
When N D  N A (unequal impurity concentrations)
and
x p  xn , W  x p
Unequal impurity concentration results an unequal depletion
layer widths by means of the charge neutrality condition;
N A . x p  N D . xn
W = total depletion
region
Abrupt junction
When N A  N D  xn  x p
 W  xn
• Depletion layer widths for n-side and p-side
1
xn 
ND
2 SiVbi N A N D
q( N A  N D )
1
xp 
NA
2 SiVbi N A N D
q( N A  N D )
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   o r
 o  permittivity of vacuum  8.85 x10-12 F/m
 r  relative permittivity of Silicon  11.9
xn , x p and W depends on N A , N D and Vbi
kT N A N D
ln
Vbi 
2
ni
q
One-Sided abrupt p-n junction
heavily doped p-type
p-type
-
+++
+++
+++
+++
-------
+++
+++
n-type
N A  N D
x
-
Depletion
Region
Abrupt p-n junction
xp
xn
x p can be neglected
One-Sided abrupt p-n junction
1
W  xn 
ND
2 SiVbi N A N D
1

q  N A  ND  ND
2 SiVbi N A N D
qN A
neglegted
since NA>>ND
W
2 SiVbi
qN D
obtain a similar equation for W  x p
in the case of N D  N A
One-sided abrupt junction
p-type
-
+++
+++
-x direction
n-type
Electric field
+++
+++
-
Electric field
Charge density
One-Sided abrupt p-n junction
x
area  Vbi
x
 Em
Potential
qVbi
x
xn
xp
Diodes – Basic Diode Concepts
1.1.4 Biasing the PN-Junction
* There is no movement of charge
through a pn-junction at
equilibrium.
* The pn-junction form a diode which
allows current in only one direction
and prevent the current in the
other direction as determined by
the bias.
24
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.
Diodes – Basic Diode Concepts
1.1.4 Biasing the PN-Junction
*Forward Bias: dc voltage positive terminal connected to the p region and
negative to the n region. It is the condition that permits current
through the pn-junction of a diode.
26
1.1.4 Biasing the PN-Junction
*Forward Bias: dc voltage positive terminal connected to the p region and
negative to the n region. It is the condition that permits current
through the pn-junction of a diode.
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.
27
10. Diodes – Basic Diode Concepts
10.1.4 Biasing the PN-Junction
*Forward Bias:
28
Diodes – Basic Diode Concepts
*Reverse Bias: dc voltage negative terminal connected to the p region
and positive to the n region. Depletion region widens until its potential
difference equals the bias voltage, majority-carrier current ceases.
29
Diodes – Basic Diode Concepts
*Reverse Bias:
majority-carrier current ceases.
* However, there is still a very
small current produced by
minority carriers.
30
Diodes – Basic Diode Concepts
1.1.4 Biasing the PN-Junction
* Reverse Breakdown: As reverse voltage reach certain value,
avalanche occurs and generates large current.
31
Diodes – Basic Diode Concepts
1.1.5 The Diode Characteristic I-V Curve
32
Appliying bias to p-n junction
Zero Bias
p
Forward Bias
+
-
-- ++ n
-- ++
p
Ec
Ec
Ev
p --
n
qVbi  VF 
Potential Energy
Ev
qVbi
- +
- +
Reverse Bias
+
--
++
++
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 diagram.
n
Ec
Ev
q Vbi  Vr 
VF  forward volta
VR  reverse voltag
Vbi
Vbi  VR
Vbi  VF
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.
Diodes – Ideal-Diode Model
1.4 Ideal-Diode Model
* Graphical load-line analysis is too cumbersome for complex circuits,
* We may apply “Ideal-Diode Model” to simplify the analysis:
(1) in forward direction: short-circuit assumption, zero voltage drop;
(2) in reverse direction: open-circuit assumption.
* The ideal-diode model can be used when the forward voltage drop and reverse
currents are negligible.
36
Diodes – Ideal-Diode Model
Example 1.5 – Analysis by Assumed Diode States
Analysis the circuit by assuming D1is off and D2 on
(1) assume
D1 off, D2 on 

(2) assume
D1 on, D2 off
i D2

 0.5mA OK!
v D1  7V
not OK!
 i D1  1 mA OK!
v D2  -3 V
OK!
37
Diodes – Basic Diode Concepts
1.1.6 Shockley Equation
* The Shockley equation is a theoretical result
under certain simplification:
  vD  
  1
i D  I s exp
  n VT  
where I s  10 -14 A at 300K is the (reverse) saturation
current, n  1 to 2 is the emission coefficient,
VT 
kT
 0.026V at 300K is the thermal voltage
q
k is the Boltzman' s constant, q  1.60  10 -19 C
 v 
when v D  0.1V, i D  I s exp D 
 n VT 
This equation is not applicable when v D  0
38
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.
2)
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 p-side 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
Charge stored in
coloumbs
Capacitance
in farads
Q
C
V
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
Capacitance per unit area of a diode ;
CDEP 
 Si F
W cm 2
For one-sided abrupt junction; e.g.
N A  N D  xn  W  xn
N A x p  N D xn
CDEP 
 Si
W

 Si
xn
 xn 
2 SiVbi
qN D
for N A  N D
The application of reverse bias ;
CDEP 
 Si
2 Si (Vbi  VR )
qN D

q Si N D
2(Vbi  VR )
Depletion Capacitance
If one makes C - V measurements and draw 1/C 2
against the voltage VR ; obtain built-in voltage and
doping density of low-doped side of the diode from
the intercept and slope.
2(Vbi  VR )
1

2
C
q Si N D
2
slope 
q Si N D
kT
N AND
Vbi 
ln(
)
2
q
ni
Diffusion Capacitance
• Self Study…!!!
Special Purpose Diodes
BHAVIN V KAKANI
Electronics & Communication Engineering Department
IT-NU