p – n junction

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 :

 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;

1) 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.
2) 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.
3) 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 EC
Ef
Eİ Eİ
Ef
EV EV

p-type n-type
EC EC
Ef
Eİ 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 +++++ ----- p-type
+++++ -----
+++++ -----
+++++ -----
+++++ -----

Electron Metallurgical
Movement junction

++++ - ---
++++ Fixed positive - --- Fixed negative Ohmic
++++ space-charge - --- space-charge 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.

 It is called as depletion region since it is depleted of free

carriers.
 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 n-region

EV

Hole Drift
Depletion region
Thermal equilibrium; no applied field; no net current flow

J p  J p (drift )  J p (diffusion)  0 (1)

Drift current is due to
electric field at the
A
J p is the hole current density ( 2 ) junction; minority
cm carriers.

Diffusion current is
dp due the to
J p  q p pE x  qD p  0 (2) concentration
dx gradient; majority
where carriers.

1 dEi  p kT
Ex  Dp  ( Einstein relation)
q dx q
Proof
dEi dp
Jp  p( p  kT )0 (3)
dx dx

Ei  E f dp p dEi dE f
p  ni exp( )  (  )
kT dx kT dx dx

dE f
J p  p p 0 (4)
dx

dE f
we conclude that  0 which states that
dx
the Fermi Level is a CONSTANT at equilibrium.
dE f
J n  nn  0 (5)
dx
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 Vbi accross a p-n 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

p-type n-type

EC
qVbi

Electron potential
Ei
EC
Electrıon energy

Ef
qV p Ef
EV
qVn
Ei

EV

Depletion region
The p – n junction barrier height

The intrinsic Fermi Level is a very useful reference level in a

semiconductor.
 Ei  E f 
qV p  ( Ei  E f ) (1) p  ni exp  
 kT 
kT NA
Vp  ln (2)
q ni
Similarly for Vn
kT ND
Vn  ln (3)
q ni
For full ionization, the built  in voltage is a sum of
kT N AND
Vbi  Vn  V p  ln 2
(4)
q ni
p – n junction in thermal equilibrium
DR
 Current Mechanisms,
---- +++
Neutral Neutral
---- +++  Diffusion of the carriers
p-region n-region
cause an electric in DR.
---- +++
Field Direction
Electron Drift  Drift current is due to
the presence of electric
Electrıon energy

Electron Diffusion field in DR.

Hole energuy

EC
 Diffusion current is due
Ef to the majority carriers.
Hole Diffussion
 Drift current is due to
EV the minority carriers.

Hole Drift
n – p junction at equilibrium
DR

Neutral +++ ----

Neutral
n-region +++ ----
p-region
+++ ----
Field Direction
Electrıon energy

Electron Drift
EC
Hole energuy

Electron Diffusion

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 AND
Vbi  ln 2
q ni

At fixed T , Vbi is determined by the number of N A and N D atoms.

 Depletion Approximation, Electric Field and Potential for pn
junction

---- +++
 At equilibrium, there is
p-type n-type no bias, i.e. no applied
---- +++ voltage.

+++
 The field takes the
Charge density

+++ x same sign as the

----
charge
---- area  Vbi
 The sign of the electric
x field is opposite to that
Electric field

of the potential ;

 Em

qVbi dVn
Ev  
dx
Potential

x
xn xp

Depletion
 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).

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

+++ ----
n-type p-type
+++ ----

Charge density +++

+++ x
----

 Em ----
Field direction is positive x direction
area  Vbi Field direction
Electric field

x
Potential

Depletion
Abrupt junction

• The amount of uncovered

---- +++ negative charge on the left hand
p-type n-type
side of the junction must be
---- +++
equal to the amount of positive
charge on the right hand side of
Charge density

the metalurgical junction.

+++
Overall space-charge neutrality
+++ x condition;
----

---- N A x p  N D xn
xp xn
Depletion

Region The higher doped side of the junction

has the narrower depletion width
w

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 2 SiVbi N A N D
xn 
ND q( N A  N D )

1 2 SiVbi N A N D
xp 
NA q( N A  N D )
Abrupt junction

For equal doping densities W  xn  x p

Total depletion layer width , W

1 1 2 SiVbi N A N D
W (  )
NA ND q( N A  N D )

2 SiVbi ( N A  N D )
W 
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
Vbi  ln 2
q ni
One-Sided abrupt p-n junction

heavily doped p-type - +++ N A  N D

p-type n-type
- +++

+++ +++

+++ +++ x
---- -

---- -

Depletion

Region

Abrupt p-n junction

xp xn

x p can be neglected
One-Sided abrupt p-n junction

1 2 SiVbi N A N D 1 2 SiVbi N A N D
W  xn  
ND q  N A  ND  ND qN A
neglegted
since NA>>ND

2 SiVbi
W obtain a similar equation for W  x p
qN D
in the case of N D  N A

One-sided abrupt junction

One-Sided abrupt p-n junction
-x direction
- +++
p-type n-type
- +++ Electric field
Charge density

+++

+++ x
-

- area  Vbi
Electric field

 Em

qVbi
Potential

xn xp
Appliying bias to p-n junction

+ -

 How current flows through the p-n

p n
junction when a bias (voltage) is
forward bias 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
p n a very small constant current flows in
reverse bias case.
reverse bias
Appliying bias to p-n junction
I(current)
Reverse Bias Forward Bias

Vb I0
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 Forward Bias Reverse Bias
+ - - +

p -- ++ n p - + n p -- ++
-- ++ - + -- ++
n

Ec Ec Ec
q Vbi  VF 
qVbi
Ev Ev Ev q Vbi  Vr 
Potential Energy

Vbi  VR
Vbi
Vbi  VF
Appliying bias to p-n junction

VF  forward voltage
VR  reverse voltage

 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

 Junction potential is reduced

+ -
from Vbi to Vbi-VF.
 By forward biasing a large
p - + n number of electrons are
- + injected from n-side to p-side
pn accross the depletion region
Carrier Density

and these electrons become

np
minority carriers on p-side, and
pno the minority recombine with
npo majority holes so that the
number of injected minority
electrons decreases (decays)
exponentially with distance into
the p-side.
p-n junction in forward bias
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.

nno  equilibriu m electron concentrat ion in n - type material.

n po  equilibriu m electron concentrat ion in p - type material.
p po  equilibriu m hole concentrat ion in p - type material.
pno  equilibriu m hole concentrat ion in n - type material.

2
n. p  n i
Ideal diode equation
2
n. p  n
i

 At equilibrium case ( no bias )

2
nno . pno  n  n  type material
i (1)
2
n po . p po  n  p  type material
i (2)
Ideal diode equation

kT N A N D
Vbi  ln assuming full ionization
q ni2

N A  p po ; N D  nno majority carriers

kT p po .nno
Vbi  ln nno . pno  ni2 for n-type
q ni2

kT p po  qVbi 
Vbi  ln  p po  pno exp   (3)
q pno  kT 
Ideal diode equation

Similarly, from equation (2)

kT p po .nno 2
Vbi  ln n po . p po  n
i
q ni2

kT nno  qVbi 
Vbi  ln  nno  n po exp   (4)
q n po  kT 

This equation gives us the equilibrium majority carrier concentration.

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. Vbi – VF if a forward bias is applied.

ii. 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  n p 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
p p  p po
• Non equilibrium electron concentration in n-type when a
forward bias is applied ,

 q (Vbi  VF ) 
nn  n p exp   non-equilibrium.
 kT 
Ideal diode equation

 q (Vbi  VF ) 
nn  nno nno  n p   (5)
 kT 
 qVbi 
nno  n po exp   (6)
 kT 
combining (5) and (6)

 q (Vbi  VF )   qVbi 
n p exp    n po exp  
 kT   kT 
Ideal diode equation
 Solving for non-equilibrium electron concentration in p-type
material, i.e. np

 qVF 
n p  n po exp   and subtracting n po from both sides
 kT 

  qV  
n p  n po  n po  exp    1   n
  kT  

 n  the excess concentration of minority electrons

over the equilibrium concentration at the edge of the DR
Ideal diode equation

Similarly ,

  qV  
pn  pno  pno exp    1   p the non-equilibrium
  kT  

 p  the excess concentration of minority holes

over the equilibrium concentration at the edge of the DR
Forward-bias diode; injection of minority carriers across DR

point A  n p  n po
+ -
point B  pn  pno
p - + n
- + •l p is the distance from DR edge into p-side
ppo •ln is the distance from DR edge into n-side

nno When a forward bias is applied; majority

B carriers are injected across DR and
A appear as a minority carrier at the edge
of DR on opposite side. These minorities
pno will diffuse in field free opposite-region
npo towards ohmic contact. Since ohmic
contact is a long way away, minority
carriers decay exponentially with
distance in this region until it reaches to
lp ln 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   
 Ln 

 ln 
 n(ln )   p (0) exp   
 Lp 
 

Ln and L p 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 n-region
decreases exponentially towards the ohmic
contact. The number of injected minority
holes;excess holes;
Distance into then region
from the Depletion Region
ln
 p (ln )   p (0) exp(  )
Lp
Diffusion Length for
holes
Number of Injected Minority Holes Across The Depletion Region

point A  n p  n po

lp
 n(l p )   n(0)exp(  )
Ln

 qV 
 n(0)  n po exp( )  1
 kT 

  qV  
 p (0)  pno exp    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 lp
the Depletion Region.  n (l p )   n (0) exp( )
Ln
These injected electrons
become minorities at the
Depletion Region edge on
the p-side, and they  qV  lp
recombine with the
 n (l p )  n po exp( )  1  exp( )
 kT  Ln
majority holes. When they
move into the neutral p-
side, the number of
injected excess electrons
decreases exponentially.
Ideal diode equation
Diffusion current density for electrons ;
dn d Dn n po   qV    l p 
J n  qDn  qDn  n(l p )  q  exp    1 exp   
dx dx Ln   kT    Ln 
qDn n po   qV  
J n ( l p  0)   exp    1 Minus sign shows that electron current
Ln   kT  
density is in opposite direction to increasing l p .That is in the positive x direction.
Similarly for holes;
dp qD p pno   qV  
J p (ln  0)  qD p  exp  kT   1
dx Lp    
The total current density;
 Dn n po D p pno    qV  
J Total  Jn  J p  q     exp    1
 Ln L p    kT  
Ideal diode equation

 Dn n po D p pno    qV     qV  
J Total  q   exp    1  J o  exp    1
 Ln Lp    kT     kT  

multiplying by area ;

  qV  
I  I o exp    1 Ideal diode equation
  kT  

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

   qV  
I  I o exp    1 I   Io Reverse saturation current
  kT  

Current

Forward Bias

VB I0
Voltage

VB ; Breakdown voltage
I0 ; Reverse saturation current
Reverse Bias
Forward bias current densities

+ -

p n  Jtotal is constant through the

whole diode.
Ohmic contact

J total  J n  J p  Minority current densities

decreases exponentially into
Current density

the the neutral sides whereas

the current densities due to
the majorities increase into the
neutral sides.
Jn Jp

lp=0 ln=0
p-n junction in reverse bias
- +

• Depletion region gets bigger with

p n increasing reverse bias.
• Reverse bias prevents large
Carrier density

diffusion current to flow through

the diode.
• However; reverse bias doesn’t
npo pno prevent the small current flow
pn due to the minority carrier. The
presence of large electric field
np across the DR extracts almost all
the minority holes from the n-
Current density

region and minority electrons

J total  J n  J p from the p-region.
• This flow of minority carriers
Jn across the junction constitudes I0,
Jp the reverse saturation current.
lp=0 ln=0
• 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.

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
Q
C
Capacitance
in farads
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 ;
 Si F
CDEP 
W cm 2
For one-sided abrupt junction; e.g. N A  N D  xn  W  xn
N A x p  N D xn

 Si  Si 2 SiVbi
C DEP    xn  for N A  N D
W xn qN D
The application of reverse bias ;
 Si q Si N D
C DEP  
2 Si (Vbi  VR ) 2(Vbi  VR )
qN D
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.

1 2(Vbi  VR )
2

C q Si N D

2 kT N AND
slope  Vbi  ln( 2
)
q Si N D q ni
Depletion Capacitance